City-Level Effectiveness of the National Clean Air Programme (NCAP) in India

1 Introduction

1.1 Economic Growth and the Escalating Air Pollution Crisis

India’s economic trajectory since the liberalisation reforms of 1991 has been marked by rapid industrialisation, urban expansion, and sustained improvements in living standards. Yet this progress has come with profound environmental costs. Among these, air pollution has emerged as one of the most severe public health challenges. India is home to 17 of the 30 most polluted cities in the world (Clean Air Fund, 2025), and exposure to fine particulate matter (PM_2.5) contributed to more than two million premature deaths in 2023 alone (Health Effects Institute, 2025). According to recent estimates, the average Indian loses over 3.5 years of life expectancy due to sustained exposure to elevated PM_2.5 concentrations (Greenstone et al., 2025).

To place this aggregate burden into a spatial perspective, Figure 1.1 maps annual mean PM_2.5 concentrations for 2023 at the sub-district level and highlights the locations of the 130 non-attainment cities analysed in this thesis. The map illustrates the striking concentration of extreme pollution in the IGP and northern states, while also showing that elevated PM_2.5 levels extend across large swathes of central and western India. The spatial clustering of high-exposure areas underscores that India’s air quality crisis is not confined to a handful of megacities but is instead a regionally embedded phenomenon affecting entire airsheds.

PM_2.5 is particularly harmful because of its ability to penetrate deep into the respiratory system and enter the bloodstream, exacerbating cardiovascular and respiratory diseases (Health Effects Institute, 2025). It is also the pollutant most commonly used by epidemiologists and environmental economists to quantify the health and welfare burden of air pollution. Understanding the drivers of PM_2.5 concentrations and the effectiveness of policies designed to reduce them is therefore crucial for public health and economic development.

Until recently, India’s policy response to air pollution was fragmented, often reactive, and largely driven by judicial directives or city-specific interventions. Recognising the need for a coordinated national strategy, the Government of India launched the NCAP in 2019. The programme identified 131 “non-attainment” cities — those that failed to meet national air-quality standards — and set ambitious targets of achieving up to a 40% reduction in particulate pollution by 2026. The NCAP represented a significant shift from ad hoc mitigation efforts toward a structured, target-oriented national framework.

However, launching a policy does not guarantee its effectiveness. The NCAP operates in a complex institutional environment characterised by non-binding targets, limited regulatory capacity, and significant inter-state heterogeneity. This raises a central question for both policymakers and researchers: Has the NCAP produced measurable improvements in fine particulate pollution across India’s cities?

1.2 The Empirical Challenge

Evaluating the NCAP’s causal impact is methodologically complex. Pollution dynamics in India are shaped not only by local emissions but also by basin-wide meteorology, agricultural burning, industrial clustering, and long-range transport (S. K. Guttikunda et al., 2014). Cities in the IGP, for example, experience winter inversions and severe seasonal spikes that differ fundamentally from the pollution regimes of coastal or southern cities. Simple before–and–after comparisons are therefore insufficient, as they conflate underlying structural trends with policy effects.

The existing literature evaluating the NCAP remains limited. Most studies rely on descriptive comparisons or sparse ground-monitoring data, which in India are subject to substantial spatial and temporal biases. The recent work by Bala et al. (2025) offers an important step towards causal identification but adopts a framework that treats policy effects as relatively homogeneous across cities. Given India’s deep geographic, meteorological, and economic heterogeneity, this assumption risks masking region-specific successes or failures.

Moreover, the standard econometric tool commonly used in policy evaluation — DiD — relies on a strong “parallel trends” assumption. It requires that, in the absence of the policy, pollution in treated cities would have followed the same trajectory as in untreated cities. This assumption is unlikely to hold in India, where non-attainment cities were selected precisely because they were among the most polluted and often structurally distinct from the average untreated city. If left unaddressed, such divergence leads to biased DiD estimates.

1.3 Methodological Approach and Research Objectives

This thesis addresses the empirical challenges inherent in evaluating India’s air quality policies by combining high-resolution satellite-based PM_2.5 data with recent advances in causal inference. Central to this approach is the use of the SDiD estimator, which constructs a synthetic counterfactual by optimally weighting untreated units to match the pre-treatment trends of treated cities. Unlike traditional DiD methods, SDiD relaxes the parallel trends assumption and allows for heterogeneous trends in the pre-policy period, making it particularly well-suited to the Indian context where non-attainment cities often exhibit distinct historical pollution trajectories.

The study makes three primary contributions to the existing literature. First, it improves data quality by employing a harmonised dataset of satellite-derived PM_2.5 concentrations spanning the period from 1998 to 2023. This ensures uniform spatial and temporal coverage across all treated and untreated cities, effectively circumventing the limitations associated with India’s sparse and uneven ground-monitoring network. Second, the analysis enhances methodological rigour by moving beyond standard DiD to the SDiD framework. This explicitly addresses pre-treatment trend divergence and provides more credible estimates of the causal effect of the NCAP, which are further validated through event studies and placebo tests. Third, the research offers a granular and mechanism-oriented analysis by disaggregating policy effects at national, regional, and city levels. This approach recognises the heterogeneity of pollution drivers and policy implementation across the subcontinent, while a dedicated mechanism analysis investigates whether financial resources, measured through fund utilisation ratios, explain observed variations in treatment effects. Together, these contributions allow for a more nuanced and empirically robust evaluation of the programme’s effectiveness.

Guided by this methodological framework, the analysis pursues five primary research objectives. The primary objective is to determine whether the NCAP reduced PM_2.5 concentrations among the treated non-attainment cities at the national level. Beyond the aggregate effect, the study examines how policy outcomes vary across India’s major airshed regions, such as the IGP, the West, the North East & East, the Central and the South. To capture local heterogeneity, the analysis further identifies which specific cities exhibit meaningful reductions in pollution relative to their synthetic counterfactuals. Additionally, the research investigates the funding mechanism to assess whether higher fund utilisation is associated with greater pollution reduction. Finally, the robustness of these findings is tested against alternative identification strategies, placebo tests, and varying control group definitions to ensure the validity of the conclusions.

1.4 Structure of the Thesis

The remainder of this thesis is organised as follows. Chapter 2 reviews the evolution of environmental regulation in India, frames air pollution as an economic problem, examines the institutional design of the NCAP and reviews the existing literature on the NCAP. Chapter 3 describes the data sources and econometric framework, including the justification for adopting the SDiD estimator. Chapter 4 begins with the descriptive analysis and proceeds to present empirical results, from national averages to regional and city-level heterogeneity, and examines potential mechanisms. Finally, Chapter 5 concludes with a discussion of policy implications and avenues for future research.

2 Policy Background & Literature Review

2.1 Foundations of the NCAP: History & Policy Context

2.1.1 Historical Evolution of Environmental Policies in India

India has navigated a complex trajectory from colonial subjugation to developmental ambition since its independence from British rule in 1947. In the aftermath of independence, the country adopted a state-led development model inspired by socialist ideals. The government implemented centrally planned Five-Year Plans aimed at rapid industrialisation, focusing on the creation of heavy industries and state-owned enterprises. Private enterprise was heavily regulated under the so-called “Licence Raj”, while agriculture was largely neglected, leading to recurring food crises and dependence on imports during the 1960s. These policies produced modest industrial growth but also inefficiencies, corruption, and fiscal strain, as political considerations often overrode economic rationality. The ensuing economic stagnation prompted gradual policy changes. The Green Revolution of the late 1960s improved food security, and limited liberalisation measures began in the 1980s. However, the decisive turning point came with the 1991 economic reforms, which dismantled the Licence Raj, reduced import barriers, and encouraged foreign investment, resulting in sustained growth and a reduction in poverty (Adhia, 2015).

These developmental policies came at a devastating environmental cost, which was largely ignored by successive governments until the 1970s. A major shift in attitude occurred following India’s participation in the 1972 Stockholm Conference, which led to constitutional amendments and the establishment of key environmental laws such as the Wildlife (Protection) Act 1972, the Water (Prevention and Control of Pollution) Act 1974, and the Air (Prevention and Control of Pollution) Act 1981, along with the creation of institutions such as the Central and State Pollution Control Boards to implement these Acts (Sarkar, 2014). The Environment (Protection) Act 1986, enacted after the Bhopal Gas Tragedy, consolidated various regulatory mechanisms under a single framework (Ballal et al., 2021).

During the 1990s, the policy focus shifted towards participatory and rights-based approaches. Initiatives such as the Joint Forest Management Programme, initiated under the National Forest Policy of 1988, and the Forest Rights Act 2006 empowered local communities. The National Environmental Policy 2006 sought to mainstream environmental concerns into development planning and focused on attaining WHO air-quality standards, treating urban wastewater, increasing energy efficiency, and expanding forest cover. However, India’s policy implementation remained weak due to a lack of institutional coordination and the persistence of pollution subsidies rather than deterrent environmental taxation. To address these deficiencies, the National Green Tribunal was established in 2010, imbued with legal authority (Sarkar, 2014). Later, India’s alignment with international frameworks such as the Paris Agreement (2015) and the Convention on Biological Diversity (1992) encouraged greater emphasis on climate adaptation, renewable energy, and biodiversity protection, leading to national missions under the NAPCC (2008) (Singh, 2024).

India’s environmental governance in the post-2010 period entered a new phase characterised by data-driven and outcome-oriented policy design building upon the earlier frameworks. The growing urgency of urban air pollution, waste management, and climate resilience prompted the introduction of several new initiatives, including the National Electric Mobility Mission Plan (2013), the National Smart Cities Mission (2015), and the National Adaptation Fund on Climate Change (2015). The launch of the NCAP in 2019 represented a strategic shift towards target-based and decentralised pollution abatement, setting quantifiable reduction goals for PM concentrations across Indian cities. This policy direction was further strengthened through initiatives such as the National Green Hydrogen Mission (2022), aligning India’s environmental agenda with its global sustainability commitments under the Paris Agreement. These developments in policy and regulatory sphere signify a gradual transformation from reactive and centralised regulation to proactive, locally adaptive, and performance-driven environmental governance ((Singh, 2024); MoEFCC, (2019a)).

2.1.2 The National Clean Air Programme (NCAP)

The NCAP was launched in January 2019 by the MoEFCC as a comprehensive initiative in partnership with various ministries and states to improve air quality at the city level. The initial goal was to reduce PM concentrations by 20–30% by 2024, later revised to a 40% reduction by 2026 relative to 2017 base levels. Initially, 94 cities were identified as exceeding the NAAQS values continuously for PM₁₀ during 2011–2015 and were classified as non-attainment cities by the CPCB. Eight more cities were added to this list based on the WHO Ambient Air Quality Database’s fourth revision, which considered PM_2.5 levels, and a further 29 cities were later added based on newly available pollution data and population levels (cities with populations exceeding one million), bringing the number of non-attainment cities to 131 (Bala et al., 2025). A steering committee meeting held in 2024 merged the city Patancheru with Hyderabad reducing the total number of NCAP cities from 131 to 130 (Centre for Research on Energy and Clean Air (CREA), 2025). The list of these cities can be found in Appendix A.

The NCAP is structured around a set of well-defined objectives, implementation strategies, and institutional frameworks aimed at ensuring sustained improvement of ambient air quality across Indian cities. Its core objectives include the stringent implementation of mitigation measures for the prevention, control, and abatement of air pollution; the establishment of a comprehensive and reliable air quality monitoring network; and the promotion of public awareness, capacity-building, and inclusive participation through data dissemination and outreach initiatives. The programme was initially designed as a five-year mid-term action plan with 2019 as the base year. However, recognising that meaningful reductions in air pollution require a longer time horizon, the NCAP framework envisions an extension of up to 20–25 years following a mid-term evaluation of its outcomes.

In terms of its approach and implementation, the NCAP emphasises collaborative, multi-level, and cross-sectoral coordination between central ministries, state governments, and local bodies. It seeks to integrate existing national policies such as the NAPCC and related sectoral initiatives, with particular focus on missions like the National Solar Mission, National Mission for Enhanced Energy Efficiency, National Mission on Sustainable Habitat, National Mission for a Green India, and the National Mission for Sustainable Agriculture. The CPCB serves as the nodal agency responsible for executing the nationwide programme under the provisions of the Air (Prevention and Control of Pollution) Act, 1981. The implementation process is supported by inter-sectoral groups involving ministries such as Power, Petroleum and Natural Gas, Housing and Urban Affairs, Agriculture, and Road Transport, along with NITI Aayog, academia, and civil society. The NCAP also leverages the Smart Cities framework to prioritise 43 non-attainment cities that overlap with Smart City initiatives, ensuring integrated and resource-efficient interventions (MoEFCC, (2019b)).

Funding under the NCAP is designed as a supplemental and performance-linked grant aimed at supporting city-level action plans. This funding is provided alongside the XV-FC grants, which support air quality improvement in million-plus population cities (MoEFCC, (2022)). Up to 2025, a total of INR 134.15 billion (USD 1.6 billion¹) was allocated to non-attainment cities (Central Pollution Control Board, 2025), of which INR 99.77 billion² (USD 1.2 billion) was utilised, reflecting a utilisation ratio of approximately 74.4%.

Given the scale of funding and resources invested, the NCAP has the potential to significantly improve India’s air quality if implemented effectively. Bala et al. (2025) estimate that the combined population of the 131 cities is around 350 million and that, if the NCAP achieves its 40% reduction target, about 118,000 deaths could be avoided annually. However, the realisation of these benefits depends on various factors such as proper implementation of the policy, political will, lobbying pressures, and corruption, which remain prevalent in India’s socio-political landscape.

2.2 Theoretical & Institutional Foundations

2.2.1 Market Failure & Environmental Goods

Air pollution is not only a technical issue. It reflects a deeper economic problem where private decisions create social costs that are not priced in the market. Clean air does not have a clear owner, and its benefits are shared by everyone. Because of this, individuals and firms often pollute more than what would be socially desirable (Baumol & Oates, 1988).

A central reason for this outcome is the presence of negative externalities. Producers and consumers account for their own private marginal costs, such as labour or capital, but they do not compensate society for the health losses and ecological damage that their emissions create (Pigou, 1920). The true social cost of production therefore exceeds the private cost. When firms react only to private costs, they produce more than the socially efficient level and generate welfare losses for society (Kolstad, 2011). Pigou proposed that such behaviour can be corrected when governments impose taxes equal to the marginal external damage.

Clean air also has the features of a public good. It is non-rival, since one person breathing clean air does not reduce the amount available to others, and it is difficult to exclude anyone from enjoying it (Samuelson, 1954). These features make voluntary provision ineffective. Individuals have an incentive to free ride and hope that others will invest in cleaner air, which leads to chronic under-provision of environmental quality (Stiglitz, 2000).

Governments can respond in two broad ways. The first is through command and control. Regulators set emission limits, prescribe technologies, or impose standards that all firms must follow (Heyer, 2011). These tools create clarity but not efficiency, since they treat all firms the same even when their abatement costs differ widely (Stavins, 1998). The second option uses market-based instruments. Pollution taxes and tradable permit systems encourage abatement at the lowest possible cost by allowing firms to choose how much they reduce emissions (Tietenberg, 2006). These instruments rely on strong monitoring systems and credible enforcement, which are often difficult to maintain in developing countries (Greenstone et al., 2015).

In the context of these theoretical frameworks, the NCAP emerges as a hybrid instrument that does not fit neatly into the traditional dichotomy of command-and-control versus market-based regulation. Structurally, it functions as a non-statutory command-and-control framework layered with performance-based fiscal incentives. To understand why such a hybrid structure might fail to correct the market failures described above, it is necessary to examine the specific institutional mechanisms through which the policy is deployed.

2.2.2 Institutional Mechanisms and Design Critiques

Regulatory theory shows that environmental policies succeed only when institutions possess clear authority, binding rules, and the capacity to enforce them (May, 2005; Delmas & Toffel, 2008; Kagan et al., 2003). The design of the NCAP does not fully meet these conditions. Technically functioning as a non-statutory “central sector scheme” rather than a binding policy, the NCAP operates through a soft-law framework of cooperative federalism. The weakness of the NCAP stems from this particular aspect. Kumari (2021) argues that this voluntary nature allows state governments and municipal bodies to delay or adjust measures without consequence, thereby diluting the incentives required to drive substantive behavioural change.

The structural weakness of the NCAP becomes clearer when compared with the governance model of Chinese Clean Air Programmes. P. Wang et al. (2023) argue that China’s success in reducing PM_2.5 was driven by a vertical accountability system, where local officials’ promotions were directly tied to meeting binding environmental targets. In contrast, India relies on a fragmented federal approach where the CPCB sets standards, but implementation falls to State Boards that lack political incentives. Along with political incentives, Peng et al. (2021) finds political feasibility as a deciding factor in the success of any environmental policies. NCAP could also be categorised as a high-feasibility policy, where most of the suggested methods and action plans follow paths that are easy to implement rather than acknowledging the real culprits in the pollution generation like coal power plants since policies or actions related to coal phase-out are politically difficult (Peng et al., 2021).

The absence of binding legal constraints is evident in the quality of implementation and the allocation of resources. Early analyses reveal that institutions often prioritise procedural requirements over targeted design, resulting in City Action Plans based on generic templates rather than local evidence. For instance, Ganguly et al. (2020) report that several states submitted plans without conducting essential source apportionment studies; in Uttar Pradesh, this led to 14 out of 15 non-attainment cities submitting identical action points despite significant differences in their urban form. This incoherence extends to financial management, where substantial funds are distributed without strict expenditure mandates. As noted by Kumari (2021), the absence of clear prioritisation guidelines increases the risk of allocative inefficiency, weakening the connection between public investment and measurable environmental outcomes.

Independent reviews by the CREA support these observations. The 2022 progress report finds that most cities remained in the preparatory stage and had not implemented tangible control measures (Centre for Research on Energy and Clean Air (CREA), 2022). Funds were often underutilised and city-level monitoring networks exhibited inconsistencies in coverage and data quality. The 2025 report notes some improvement, especially in the expansion of continuous monitoring stations, but progress remained uneven and many action plans continued to lack measurable performance indicators (Centre for Research on Energy and Clean Air (CREA), 2025).

2.3 Empirical Evidence of NCAP Effectiveness & Comparative Lessons

Quantitative analyses by S. K. Guttikunda et al. (2025) and Gopikrishnan and Kuttippurath (2025) reveal that PM concentrations have decreased modestly in some treated cities, while increases were observed in the Indo-Gangetic Plain and major metropolitan centres such as Delhi and Mumbai. S. K. Guttikunda et al. (2025) use the annual average PM_2.5 and PM₁₀ levels to identify the most polluted cities for each year and evaluate the percentage reduction (or increase) in pollution levels from 2019 to 2023 to assess the performance of NCAP interventions. Gopikrishnan and Kuttippurath (2025) considered 28 locations in his paper analysing the PM₁₀ concentrations and estimated that the NCAP reduced mortality by approximately 62,219 in 20 target-attained cities. Using a random forest model, PM_2.5, NO₂, and O₃ were identified as key precursors of PM₁₀, with the IGP and Central India emerging as high-pollution regions, in contrast to generally lower pollution levels in peninsular areas (e.g. Hubballi) (Gopikrishnan & Kuttippurath, 2025).

Research conducted during the NCAP period offers a broad descriptive picture of how India’s air quality has evolved in recent years. The findings point to clear progress in expanding the monitoring network and modest overall declines in AQI levels, though outcomes vary widely across states. Notably, few studies employ causal inference designs to isolate the policy’s specific effects. Addressing this gap, Bala et al. (2025) provide the first causal evaluation of the NCAP using a large city-level panel dataset of satellite-derived PM_2.5 concentrations. Employing several DiD strategies, they find a precisely estimated zero impact of the NCAP on air pollution, with the lower bound of the 95% confidence interval suggesting at most a 1.6% decline that is far from the policy’s stated target of a 40% reduction by 2025–26. Their identification relies on a national pool of untreated cities and standard TWFE DiD. Complementing the quantitative analysis, the authors conduct a nationwide survey experiment revealing that information about the NCAP increased public approval of government policies even when respondents were informed of the programme’s ineffectiveness. This highlights a profound lack of government accountability, where performative governance effectively insulates the state from the political costs of implementation failure.

While the evidence from the Indian context so far fails to demonstrate any tangible benefits of the policy, findings from international experiences underscore the critical role of regulatory design and enforcement in achieving measurable improvements in air quality. Chay and Greenstone (2005) and Isen et al. (2017) demonstrated that the Clean Air Act of 1970 in the United States generated substantial welfare gains and that exposure to cleaner environments during early life enhanced long-term human capital formation and earnings. Although some argued that reductions in pollution might stem from technological progress or productivity growth, Shapiro and Walker (2018) found that regulatory interventions were the primary drivers of emission reductions. Similarly, China’s Air Pollution Prevention and Control Action Plan, implemented in 2013, led to significant improvements, with an estimated 23% reduction in sulphur dioxide intensity among pilot cities compared to non-pilot ones (Niu et al., 2023). Collectively, these studies demonstrate that when designed effectively and implemented with institutional commitment, environmental regulations can produce substantial and lasting improvements in air quality, even in highly polluted and industrialised contexts.

The literature establishes that the NCAP’s institutional design prioritises formal compliance over substantive pollution reduction, lacking the binding enforcement and accountability mechanisms required for effective environmental regulation. While administrative strides in monitoring are evident, they stand in sharp contrast to the limited evidence of causal impact, confirming the theoretical expectation that policy performance is inseparable from the quality of implementing institutions. This disconnect underscores the pivotal role of enforcement capacity and defines the primary objective of this thesis: to rigorously evaluate whether the NCAP has translated administrative intent into measurable and sustained air quality improvements across diverse Indian cities.

2.4 Methodological Imperatives

2.4.1 Ground Data vs. Satellite Data

Most existing studies rely on ground-level measurements from CAAQMS and manual monitoring stations, which typically capture pollution within only a small local radius. In India, where many non-attainment cities operate just one monitoring station, these data often provide a limited and sometimes unrepresentative picture of urban air quality (S. K. Guttikunda et al., 2025; Brauer et al., 2016). Site-selection biases, instrumentation differences, and irregular sampling further contribute to inconsistencies between reported city-level trends and broader regional pollution patterns.

Satellite-derived PM_2.5 estimates offer a more spatially comprehensive alternative. By providing consistent coverage across entire urban airsheds along with areas without ground monitors, satellite data help reveal population exposure levels that ground networks alone may miss (Ma et al., 2014). Although these estimates are not free from retrieval uncertainty, they supply long, continuous time series that are especially valuable in countries where monitoring networks expanded only recently (Kumar et al., 2007).

For evaluating the NCAP, this distinction is critical. Since policy targets and action plans apply at the city level, outcome measures must reflect city-wide air quality rather than conditions at a single site. Satellite-based PM_2.5 therefore provides a more appropriate metric for assessing the programme’s effectiveness, while ground observations serve mainly for validation and local interpretation.

2.4.2 Evolution of Identification Strategies

Credible causal identification in policy evaluation rests on assumptions that are often difficult to justify. Studies on the NCAP have therefore relied on cross-sectional comparisons or simple pre-post designs, yet these approaches cannot adjust for city-specific temporal dynamics or unobserved structural heterogeneity. Among quasi-experimental tools, DiD has become foundational. As Cunningham (2021) explains, the modern formulation of DiD emerged during the “first wave” of DiD research, beginning with the 1984 NBER working paper by Orley Ashenfelter and David Card that first introduced the term, even though earlier empirical traditions by scholars such as John Snow and Ignaz Semmelweis employed similar comparative logic. The use of DiD expanded substantially after 2011 as applied researchers began to emphasise the parallel trends assumption and adopted event study designs more routinely in empirical work (Cunningham, 2021). Studies such as Niu et al. (2023) and Godard-Sebillotte et al. (2019) illustrate this broader methodological uptake, each relying on the premise that treated and control units would have followed comparable trajectories in the absence of the intervention.

Even though this is a widely used method, the credibility of this assumption is especially fragile in the Indian context. Cities differ substantially in industrial composition, meteorological conditions, background emissions, institutional capacity, and historical pollution profiles. These differences produce heterogeneous pre-treatment trends that cannot be fully captured by additive fixed effects. Since NCAP treatment assignment is correlated with persistent high pollution levels, the likelihood that treated and control cities shared a common counterfactual trajectory is low, which introduces bias into standard DiD estimators.

SCMs were developed to address such limitations by constructing a weighted combination of control units that reproduces the pre-treatment trajectory of the treated unit (Abadie et al., 2010). This matching-based strategy is especially valuable where no single untreated city resembles a treated city but a composite of several can approximate its historical pollution path. Building on this framework, Arkhangelsky et al. (2021) introduced SDiD, which integrates the pre-treatment balancing of synthetic controls with the stability of fixed-effects estimation, and this is particularly suitable for NCAP because many treated megacities lack close untreated analogues and display distinctive long-run pollution patterns that simple DiD cannot accommodate.

A related contribution by Doudchenko and Imbens (2016) clarifies the relationship between these approaches. DiD assigns uniform weights to all control units, while SCMs optimise weights but impose constraints that restrict flexibility when treated units lie outside the convex hull of the donor pool. Their estimator introduces an intercept to adjust for persistent level differences and uses regularisation to select appropriate weights, thereby combining the strengths of both methods and motivating the class of hybrid estimators to which SDiD belongs. Further methodological detail is presented in Section 3.3.

2.5 Summary & Implications for the Empirical Strategy

This chapter situated the NCAP within India’s broader environmental and institutional landscape and reviewed the theoretical and empirical literature relevant to air-quality regulation. The evidence highlights two central themes: persistent institutional constraints that weaken policy implementation, and limited causal work capable of isolating the NCAP’s impact from underlying pollution trends. These gaps motivate the empirical strategy of this thesis. Since Indian cities exhibit heterogeneous pre-treatment dynamics and vary in monitoring quality, the subsequent chapter employs high-resolution satellite data along with DiD and SDiD frameworks to construct credible counterfactuals and evaluate the policy’s effectiveness.

3 Data & Methodology

This chapter details the empirical framework employed to rigorously evaluate the causal impact of the NCAP. It begins by describing the construction of a comprehensive panel dataset that overcomes the spatial and temporal limitations of India’s ground monitoring network by leveraging high-resolution satellite-derived PM_2.5 estimates. The discussion then turns to the identification strategy, outlining the definition of valid control groups based on demographic and meteorological criteria, and motivating the shift from a standard DiD design to the more robust SDiD estimator to address heterogeneous pollution dynamics. Finally, the chapter presents the mechanism analysis, specifying the meta-regression approach used to disentangle the relationship between financial utilisation and policy effectiveness.

3.1 Data

3.1.1 Satellite-Derived PM_2.5 Data

The analysis primarily uses the Global Annual and Monthly PM_2.5 Concentration Dataset (V6.GL.02.04) developed by van Donkelaar et al. (2021) and Shen et al. (2024). This dataset combines Aerosol Optical Depth (AOD) retrievals from satellite-based NASA instruments, including MODIS (Terra and Aqua), MISR (Terra), SeaWiFS (SeaStar), and VIIRS (SNPP and NOAA-20), with simulations from the GEOS-Chem chemical transport model. The resulting estimates are subsequently calibrated against global ground-based observations using a residual Convolutional Neural Network (CNN). The version used in this study integrates a modified padding strategy and stronger geophysical constraints, addressing limitations identified in previous versions, such as abnormally low values observed under certain rare conditions (Shen et al., 2024; Hammer et al., 2023).

The satellite data provide globally consistent estimates of ground-level PM_2.5 concentrations at high spatial (0.01° × 0.01°) and temporal (monthly and annual) resolution for the period 1998–2023 (Atmospheric Composition Analysis Group, 2024). It offers near-complete coverage³ across India and serves as the primary dataset for evaluating air-quality trends under the NCAP. The long temporal span and high spatial resolution make this dataset well-suited for studying both national and regional variations in pollution levels over time.

3.1.2 Ground-Based Air Quality Monitoring Data

Jha (2023) published the dataset titled “Time Series Air Quality Data of India (2010–2023)”, which was used to verify the credibility of the satellite-derived data through a correlation analysis. This dataset was compiled directly from the CPCB online portal⁴, where station-level air quality monitoring data are publicly available. It contains information on air quality conditions in 241 Indian cities equipped with 453 real-time monitoring stations distributed across the country.

The ground-based data are used in this study only as a broad validity check rather than as the main analytical input primarily due to the presence of extensive missing observations, particularly before 2015; the limited availability of PM_2.5-specific data resulting from the small number of stations capable of monitoring fine particulate matter; and growing concerns over data integrity and potential manipulation of air-quality readings. A recent newspaper report by Kapoor (2025) highlighted allegations of deliberate interference with monitoring stations in Delhi, raising concerns about the transparency and reliability of ground-based pollution data in India.

3.1.3 Other Data

Along with the air-quality datasets, demographic and institutional variables are necessary for the analysis. The demographic data for the cities were obtained from the 2011 Census of India (Ministry of Rural Development, 2011), which are also available within the SHRUG Database (Asher et al., 2021) under the dataset titled “Location Population and Area.” These data were accessible at multiple administrative levels, including district and sub-district granularity. The variables relevant to this study were the population and area of the respective administrative regions, as these form the basis for classifying a boundary as a village, town, city, or urban agglomeration.

Funding information for all treated cities was collected using a web-scraping procedure implemented through the Selenium library in Python. The data were extracted directly from the PRANA portal⁵, which reports city-level allocations and expenditures under the NCAP. Selenium enabled automated navigation and retrieval of multiple linked pages, ensuring consistency in the extraction process and allowing the scraper to handle dynamic website elements that prevent simple static downloads. However, the amount of funds released for the cities of Jammu and Srinagar in Jammu and Kashmir, and Thane in Maharashtra, were not available in the dataset and therefore these cities were excluded from the analysis related to fund utilisation. These funding data are subsequently used to examine the relationship between fund utilisation ratios and the presence (or absence) of statistically significant treatment effects.

3.2 Data Construction & Sample Design

After assembling the above datasets, several steps were taken to process, clean, harmonise, and spatially align the data for empirical analysis. The satellite data were processed using the R programming language and merged with the Indian administrative boundaries using the SHRUG open polygons and spatial statistical data created by Asher et al. (2021) and provided by the Development Data Lab⁶. SHRUG offers multiple layers of spatial granularity, ranging from village/town “shrid” level boundaries to higher administrative units, such as sub-districts (tehsils/taluks) and districts. While Bala et al. (2025) employed the shrid-level maps representing individual towns and villages as defined in the 2011 Population Census, this study utilises the sub-district level shapefile. The finer shrid-level data was not used since the composition of NCAP cities as smaller towns was not available due to the government data portal being inaccessible during the data collection period.

Sub-district and district levels of aggregation are widely used in environmental and epidemiological analyses in India, where district and sub-district units offer a practical compromise between spatial detail and data reliability. This approach is supported by the fact that long-term satellite-derived PM$_{2.5}$ datasets and reanalysis products, although available at fine spatial resolutions (e.g., 1 km), are often aggregated to district-level units in national-scale assessments. This is because chemical transport models do not reliably capture intra-urban spatial variation and therefore offer no accuracy gains at finer administrative levels (S. Guttikunda & Nishadh, 2022). Moreover, air pollution in India exhibits strong regional dispersion patterns, with exposure shaped by basin-wide meteorological conditions, long-range transport, and rural-urban emission linkages (Sahu et al., 2023). Hence, sub-district and district boundaries provide a more realistic spatial representation of populations’ exposure to air pollution than village or town level polygons.

3.2.1 Treatment Group

After finalising the spatial units of analysis, the first step in the data-processing workflow was to link the satellite-derived PM_2.5 estimates to India’s administrative boundaries. This was accomplished by merging the satellite dataset with the SHRUG sub-district shapefile, which provides a nationally consistent set of administrative units. The result was a complete sub-district–level pollution dataset for the period 1998–2023, forming the main dataset on which the rest of the analysis was built.

The next challenge was to map the NCAP city list to these administrative units. Since NCAP cities do not correspond neatly to Census-defined boundaries, and because official city names often differ from their Census 2011 equivalents, a direct one-to-one match was not possible. Many cities appeared under alternative spellings or administrative labels (e.g., Delhi as a state, Gulbarga as Kalaburagi, Balasore as Baleshwar), while several NCAP cities consisted of multiple Census units. To address this, a hierarchical matching procedure was developed. Each NCAP city was first searched within the satellite dataset at the sub-district level. When a sub-district match was unavailable, the search was expanded to the district level, and, if necessary, to the state level (Delhi was the only city matched at state level). This approach ensured that each city was matched at the highest spatial resolution feasible, while still providing a fallback mechanism for cities whose names did not appear in the sub-district records.

This matching procedure generated a comprehensive mapping file that linked every NCAP city to its corresponding administrative unit in the satellite dataset. For cities spanning multiple sub-districts, such as Hubli–Dharwad, Greater Mumbai, Navi Mumbai, or Vasai–Virar, all constituent sub-districts were identified and treated collectively. Their monthly PM_2.5 values were averaged to derive a single pollution measure that represents the full geographical extent of the city. Similar steps were taken for cities with non-standard names, where manual verification was used to identify the correct administrative region. Although the NCAP designates Navi Mumbai and Thane as separate non-attainment cities, both belong to the Thane district. To avoid double-counting the same underlying administrative area, they were merged into a single analytical unit. Following this aggregation process, 99 cities were represented at the sub-district level, 34 at the district level, and one at the state level (Delhi), yielding a final count of 129 treated cities.

Using the finalised mapping file, the PM_2.5 values for each NCAP city were extracted from the sub-district-level pollution dataset and compiled into a unified city-level panel spanning 1998–2023. The panel contains monthly pollution observations, with each city linked to the administrative unit(s) from which its values were derived. Finally, a treatment indicator was created to flag the 129 NCAP cities, while the remaining sub-districts in the pollution dataset formed the pool of potential control units for the empirical analysis.

Building on this structure, the next stage involved enriching the pollution dataset with demographic characteristics to allow meaningful comparisons between treated and potential control units. Population and land-area information from the 2011 Census, as provided in the SHRUG database, were merged with the monthly PM_2.5 time series at the sub-district level. Before merging, the demographic dataset was cleaned to remove invalid or duplicated administrative codes, ensuring that each sub-district was uniquely identified and correctly aligned with its pollution record. Using the SHRUG state, district, and sub-district identifiers, a hierarchical ID was then constructed that encodes the spatial aggregation level (state, district, or sub-district). This ID served as the key for merging population and area data into the pollution dataset and later for aggregating observations to the appropriate analytical unit for each NCAP city. Because all subsequent aggregation of land area and population was performed with respect to this harmonised ID, the resulting demographic measures are internally consistent with the spatial structure of the treatment definition. This made it possible to calculate population density and incorporate variations in demographic scale and settlement patterns, which is essential when contrasting NCAP cities with untreated cities or sub-districts and for choosing a comparable control group.

With the demographic information integrated, the final step in preparing the analytical dataset was to introduce temporal structure for policy evaluation. A post-treatment indicator was constructed to distinguish observations occurring after the introduction of the NCAP in January 2019⁷ from those in the pre-policy period. Together with the treatment indicator assigned earlier, this yielded a balanced panel suitable for DiD estimation. Although the satellite dataset is originally available at a monthly frequency from 1998 to 2023, the analysis aggregates PM_2.5 to the annual level to match the temporal structure employed in Bala et al. (2025) and to reduce short-term meteorological noise that may obscure longer-run pollution dynamics relevant for policy evaluation. The resulting analytical panel comprises 129 treated units and 5,450 untreated units, and provides, for each sub-district and each year, information on mean annual PM_2.5 concentrations, population, land area, a treatment indicator, and a post-policy indicator.

3.2.2 Control Group

Constructing an appropriate control group is a central component of the empirical strategy, as the credibility of the counterfactual determines the validity of the estimated treatment effects. Since the NCAP was implemented only in selected urban centres, untreated units must be chosen carefully to reflect the underlying demographic, spatial, and pollution characteristics of the treated areas. This section outlines a set of progressively refined control groups, motivated by economic reasoning, urban classification principles, and the assumptions required for credible difference-in-differences estimation.

The first step in defining the control group involves clarifying what constitutes an urban administrative unit in the Indian context. According to the Rural-Urban Classification Circular for Census 2021 (Office of the Registrar General, India, 2018), an administrative unit is classified as a statutory “city” if it is legally designated as a Municipal Corporation, Municipality, Cantonment Board, or Nagar Palika and has a minimum population of 100,000 persons. Units that are not legally urban may still be classified as “census towns” provided they satisfy all three of the following criteria:

• a minimum population of 5,000 persons;

• at least 75% of the male working population engaged in non-agricultural activities;

• a population density of at least 400 persons per square kilometre.

These definitions form the conceptual basis for designing control groups that increasingly resemble NCAP cities in terms of settlement type and demographic scale. Although the satellite data are available from 1998 onwards, the DiD analysis uses the period 2010–2023. The reasoning behind this choice, and the contrast with the SDiD pre-treatment window, is discussed in Section 3.3.2.2.

Control Group 1: Demographically Comparable Urban Units

Given the urban focus of NCAP, the first control group is constructed by retaining only those untreated sub-districts that meet key demographic thresholds. “Control 1” includes units with (i) a population exceeding 100,000 and (ii) a population density above 400 persons per square kilometre. These thresholds follow the statutory and census definitions of urban areas and exclude sparsely populated or primarily agrarian regions whose pollution dynamics differ substantially from those of treated cities. By limiting the control group to large and densely settled urban spaces, this approach aims to reduce observable differences in settlement structure, economic activity, and emission sources, thereby improving the plausibility of the parallel trends assumption for the baseline difference-in-differences design.

Control Group 2: Density-Matched Urban Controls

A second control group is defined using a data-driven approach. The mean population density of treated units is calculated, and a grid search is performed over a wide range of candidate density thresholds. For each threshold, all untreated units with population densities above the cutoff are retained and the resulting average density of the control group is computed. The threshold that minimises the absolute difference between the treated and untreated mean densities is selected as the defining boundary for Control Group 2. This produces a subset of untreated cities whose population density closely resemble those of the NCAP cities.

Control Strategy 3: Regionally Stratified Urban Controls (Airsheds)

While Control Groups 1 and 2 account for demographic and density differences, they construct the counterfactual using untreated units from across the entire country. This approach implicitly assumes that an untreated city in the tropical Southern Peninsula can serve as a valid counterfactual for a treated city in the landlocked IGP. From a meteorological perspective, this assumption is strong and unlikely to hold since the seasonality of pollution, the role of winter inversions, and the background dust load differ fundamentally across regions.

To address this, a third control strategy relying on exact matching within common airsheds is constructed. Motivated by recent atmospheric literature (World Bank, 2023; S. K. Guttikunda & Gurjar, 2012), it is posited that pollution dynamics are governed by regional topography and meteorology rather than administrative state boundaries. Consequently, valid counterfactuals must share the same underlying atmospheric physics.

The transboundary airshed definitions proposed by the World Bank (World Bank, 2023) are adapted to classify all administrative units into five distinct climatic zones (see Table 3.1). Specifically, the ‘West/Central’ and ‘Central/Eastern’ IGP regions are merged into a single contiguous IGP cluster to capture basin-wide winter inversion dynamics. Additionally, the Arid West, influenced by crustal dust (Kulkarni et al., 2022), is distinguished from the Central transition zone.

Under Control Strategy 3, a treated unit is compared exclusively to untreated units that:

1. Are located within the same airshed region (IGP, Arid West, Central, South, or NEE);

2. Satisfy the urban criteria of Control Group 1 (Population $> 100,000$ and Density $> 400$ persons/km$^2$).

By restricting the donor pool to the same climatic zone, this strategy ensures that the treated and control units share the same underlying atmospheric physics, thereby increasing the plausibility of the parallel trends assumption required for difference-in-differences estimation.

3.2.3 Validity Check for Satellite Data

A crucial preliminary step before using satellite-derived PM_2.5 concentrations for econometric analysis is to assess the extent to which these remotely sensed estimates replicate patterns observed in ground-based monitoring data. Although India’s monitoring network suffers from uneven coverage, missing values, and concerns regarding data integrity, these observations nevertheless provide a useful benchmark for evaluating the broad validity of the satellite-based series. Ground-monitoring data were cleaned by removing missing observations and harmonising city names to match the satellite records, after which both datasets were merged for the overlapping period 2010–2023.

Figure 3.1 shows the correlation between satellite and ground measurements using monthly observations and annual averages along with an OLS regression fit. The resulting Pearson coefficients of 0.83 (monthly) and 0.69 (annual) fall within the ranges typically interpreted as “strong” and “moderate” correlations respectively, according to the classification proposed by Schober et al. (2018). The OLS fit (red line) similarly indicates a pronounced linear association with a slope parameter close to unity, suggesting that the satellite product captures ground-measured variation reasonably well across a broad spectrum of pollution levels.

To examine seasonal stability, Figure 3.2 reports separate correlations for winter, summer, monsoon, and post-monsoon months. These values range from 0.51 to 0.87, corresponding to “moderate” to “very strong” correlations under standard interpretive guidelines (Schober et al., 2018). This pattern of seasonal differences aligns with international evidence. For example, Zou et al. (2017) report seasonal cross-validated $R^2$ values between 0.78 and 0.92 for satellite-based PM_2.5 modelling in the Beijing–Tianjin–Hebei region of China, with weaker correspondence during wet seasons due to precipitation-driven aerosol washout. The seasonal behaviour observed in the Indian data mirrors this dynamic where correlation peaks during the post-monsoon and winter months when atmospheric stability enhances consistency across measurement platforms, and declines during the monsoon when rainfall introduces substantial short-run noise. These correlation results provide strong evidence that the satellite-derived PM_2.5 dataset used in this study is sufficiently reliable for the subsequent econometric analysis.

3.3 Methodology

3.3.1 Difference-in-Differences

The first econometric method employed in this study is the DiD design, a quasi-experimental strategy for estimating causal effects in the presence of a policy intervention or other exogenous⁸ shock. A quasi-experiment, or natural experiment, arises when an external event such as a policy reform alters the environment in which individuals, households, firms, or geographical units operate. Such settings typically allow for the construction of a treatment group, which is directly affected by the policy, and a control group, which remains unaffected. When treatment and control status differ across groups such as across cities, districts, or regions, the DiD estimator provides a widely used approach for evaluating policy effectiveness, provided the underlying identifying assumptions can be credibly defended (Angrist & Pischke, 2009; Wooldridge, 2020).

DiD Framework

The canonical two-period, two-group DiD model takes the form $$Y_{it} = \alpha + \delta \,\text{Post}_{t} + \gamma \,\text{Treat}_{i} + \beta \,(\text{Treat}_{i} \times \text{Post}_{t}) + \varepsilon_{it},$$(3.1) where $Y_{it}$ denotes the outcome for unit $i$ at time $t$, $\text{Treat}_{i}$ indicates whether unit $i$ belongs to the treatment group, and $\text{Post}_{t}$ indicates whether unit $i$ belongs to the post-treatment or pre-treatment time periods. The interaction term $(\text{Treat}_{i} \times \text{Post}_{t})$ isolates the change experienced by the treated group after the intervention and therefore serves as the source of identification in the DiD design. The parameter $\beta$, which is the coefficient of this interaction, measures how much the treated group’s outcome changed after the intervention relative to how the control group’s outcome changed over the same period. In doing so, it eliminates any differences between the groups that are constant over time as well as any shocks that affect all units in the same period.

The validity of Equation (3.1) relies critically on the parallel trends assumption, which states that, in the absence of treatment, treated and untreated units would have followed the same trajectory over time. This assumption cannot be tested directly, because the counterfactual outcomes for treated units post-intervention are unobserved. Nevertheless, its plausibility can be assessed indirectly by examining pre-treatment trends, conducting placebo tests, and employing event-study designs that include leads of the treatment indicator. Additional identifying requirements include the absence of contemporaneous shocks disproportionately affecting the treated group and the stability of group composition over time (Cunningham, 2021). Another important, but less commonly discussed in empirical applications, is the SUTVA. The SUTVA assumption implies that potential outcomes for a treated unit are unrelated to other units (Delgado & Florax, 2015) and that there are no spillover effects (Gerber & Green, 2012). When these conditions hold, the DiD estimator yields an unbiased causal estimate.

For empirical implementation, the analysis follows the multi-period DiD framework of Bala et al. (2025) using a balanced annual panel spanning 2010–2023. The principal specification employs a TWFE estimator, where the effect of the NCAP is identified from the interaction between an indicator for NCAP cities and a post-2019 policy period. The estimating equation is

$$pm25_{ct} = \beta \,(\text{Post}_{t} \times \text{NCAP}_{c}) + \delta_c + \tau_t + \varepsilon_{ct},$$(3.2)

where $$\text{NCAP}_{c} = \begin{cases} 1 & \forall\, c \in \mathcal{T},\\[4pt] 0 & \forall\, c \notin \mathcal{T}, \end{cases} \qquad \text{Post}_{t} = \begin{cases} 1 & \forall\, t \geq 2019,\\[4pt] 0 & \forall\, t < 2019. \end{cases}$$

In this specification, $\mathcal{T}$ denotes the subset of treated units and $pm25_{ct}$ denotes the annual mean PM$_{2.5}$ concentration in sub-district $c$ at year $t$. The coefficient of interest, $\beta$, measures the average causal effect of NCAP implementation on ambient PM$_{2.5}$ levels. Sub-district fixed effects $\delta_c$ absorb all time-invariant geographical, infrastructural, and socio-economic characteristics, while time fixed effects $\tau_t$ capture nationwide shocks affecting all locations simultaneously, including seasonal pollution cycles, meteorological patterns, macroeconomic conditions, and major disruptions such as the Covid-19 lockdown. Identification therefore derives from within-unit changes over time rather than cross-sectional variation.

In this multi-period setting, the main effects of $\text{NCAP}_{c}$ and $\text{Post}_{t}$ become perfectly collinear with the unit and time fixed effects and are therefore subsumed by them, leaving the interaction term $\text{Post}_{t} \times \text{NCAP}_{c}$ as the sole identifying source of variation. Under the parallel trends assumption, the coefficient $\beta$ identifies the ATT as the DiD estimator captures the change in PM$_{2.5}$ concentrations in NCAP treated sub-districts relative to untreated areas after accounting for the fixed effects. Standard errors are clustered at the sub-district level to allow for arbitrary serial correlation within units over time, following the recommendations of Bertrand et al. (2004).

Event-Study Framework

To evaluate the credibility of the identifying assumptions and to analyse the temporal dynamics of treatment effects, an event-study specification is also estimated. The event-study approach has become a central diagnostic tool in modern DiD applications because it provides a transparent assessment of whether treated and untreated units behaved similarly prior to treatment and reveals how the treatment effect evolves over time (Cunningham, 2021). By including leads of the treatment indicator, the event-study specification compares treated and control units in the years preceding the introduction of the NCAP, thereby allowing an assessment of whether pre-treatment trends are statistically indistinguishable. The inclusion of lags traces the dynamic response of PM$_{2.5}$ concentrations following the programme’s implementation, showing whether the effects of the NCAP emerge immediately, build up gradually, or attenuate in later years.

Following Bala et al. (2025), the event-study model used in this study is specified as $$pm25_{ct} = \sum_{y=2010}^{2017} \gamma_y \left( NCAP_{c} \times {1}[t = y] \right) + \sum_{y=2019}^{2023} \beta_y \left( NCAP_{c} \times {1}[t = y] \right) + \delta_c + \tau_t + \varepsilon_{ct},$$(3.3) where the coefficients $\gamma_y$ capture pre-treatment differences relative to the omitted base year 2018 and hence inform the plausibility of the parallel trends assumption. If parallel trends hold, then $\gamma_y$ should be statistically indistinguishable from zero for the period from 2010–2017. The coefficients $\beta_y$ represent dynamic post-treatment effects, describing how the impact of the NCAP evolves from 2019 onwards.

Limitations

However, despite their widespread use, a conventional TWFE DiD and its associated event-study formulation may not fully capture the true effectiveness of the NCAP since the policy was implemented heterogeneously across India. As documented by Bala et al. (2025) (Ganguly et al., 2020; Centre for Research on Energy and Clean Air (CREA), 2025), cities in different states adopted distinct mitigation measures, varied in enforcement capacity, and faced differing institutional constraints along with differences in pollution sources and meteorological factors. Such heterogeneity in both policy implementation and underlying pollution dynamics can generate differential treatment effects that a standard DiD framework may average out or misattribute, thereby obscuring important variation in the programme’s impact.

A further concern relates to the credibility of the identifying assumptions. NCAP eligibility was partly determined by historical pollution levels and administrative classifications (Ministry of Environment, Forest and Climate Change, 2019b), raising the possibility that treated cities were on systematically different trajectories even prior to the programme. Furthermore, the potential presence of control units geographically adjacent to treated cities may violate the SUTVA. This concern is partially mitigated by the size of the control group; since there are thousands of untreated sub-districts, the majority are not in close proximity to the treated cities, which may dilute any spillover effects of the treatment. In any case, a partial violation of SUTVA via positive spillovers would likely lead to an underestimation of the treatment effect (a conservative estimate). These probable violations of causal identifying assumptions necessitate the use of a more robust identification methodology. Therefore, the TWFE DiD framework should be interpreted as providing a baseline estimate rather than a comprehensive measure of policy effectiveness.

3.3.2 Synthetic Difference-in-Differences

A central challenge in evaluating the NCAP is the construction of a credible counterfactual for the regulated cities. Standard DiD relies on the parallel trends assumption, which requires that selection into treatment is driven only by additive unit and time effects. This implies that unobserved confounders enter the outcome equation through the structure $\alpha_i + \beta_t$. Such an assumption is restrictive in contexts where treated and untreated units display pronounced differences in their pre-intervention trajectories. This is particularly relevant in India, where the largest non-attainment cities have long-run pollution patterns that differ substantially from those of smaller sub-districts and cities. SCMs relax the parallel trends requirement by reweighting untreated units to replicate the pre-treatment path of the treated units, although they do not share the formal inferential properties of regression-based estimators.

To address these limitations, the analysis employs the SDiD estimator proposed by Arkhangelsky et al. (2021). The estimator combines the strengths of the two approaches. It constructs weights to reproduce pre-exposure trends in the spirit of SCM, and it incorporates fixed effects to absorb additive unit-specific and time-specific shocks in the spirit of DiD. This hybrid structure improves robustness when untreated units do not form a credible unweighted counterfactual for the treated units.

Theoretical Framework

The SDiD framework begins with a latent factor model that decomposes the outcome $Y_{it}$, which represents PM_2.5 levels in unit $i$ at time $t$, into a systematic component, a treatment effect, and an idiosyncratic error term: $$Y_{it} = L_{it} + \tau W_{it} + E_{it}.$$(3.4) Here, $W_{it}$ denotes treatment status. It takes the value of 1 for NCAP cities in the post-2019 period and 0 otherwise. The parameter $\tau$ measures the average treatment effect on the treated during the post-treatment period. The error term $E_{it}$ captures transitory shocks to pollution that are unrelated to treatment assignment.

The systematic component $L_{it}$ is represented as a low-rank matrix. This structure implies that the high-dimensional $N \times T$ outcome matrix can be approximated by a smaller number of latent forces. Arkhangelsky et al. (2021) model this systematic component using interactive fixed effects: $$L_{it} = \gamma_i \nu_t^{\top},$$(3.5) where $\gamma_i$ is a vector of latent unit-specific factors, and $\nu_t$ is a vector of latent time-specific factors. In the NCAP context, these latent forces reflect persistent determinants of air pollution, such as regional meteorological cycles, seasonal agricultural practices, industrial activity, and long-run economic trends. Different units load onto these common factors with varying intensity, which accounts for the heterogeneous pre-treatment trajectories observed across Indian cities.

Unlike the SCM estimator, which constructs only unit weights, SDiD employs two sets of weights designed to balance the latent factors across treated and untreated units:

1. Unit weights $\hat{\omega}^{sdid}$ align the pre-treatment outcome paths of untreated units with those of the treated units. They balance differences in the latent factors $\gamma_i$ that shape long-run pollution behaviour.

2. Time weights $\hat{\lambda}^{sdid}$ align the distribution of pre-treatment periods with that of the post-treatment period for the treated units. They balance the latent time factors $\nu_t$ by emphasising pre-treatment periods that bear closer resemblance to the post-treatment environment.

The estimator is obtained by solving a weighted two-way fixed effects regression: $$(\hat{\tau}^{sdid}, \hat{\mu}, \hat{\alpha}, \hat{\beta}) = \operatorname*{argmin}_{\tau, \mu, \alpha, \beta} \sum_{i=1}^{N} \sum_{t=1}^{T} \left( Y_{it} - \mu - \alpha_i - \beta_t - \tau W_{it} \right)^2 \hat{\omega}^{sdid}_i \hat{\lambda}^{sdid}_t,$$(3.6) where $\alpha_i$ and $\beta_t$ denote unit and time fixed effects. The weighting scheme allows the estimator to reproduce the treated units’ counterfactual trends more accurately than an unweighted DiD. Detailed explanation of the SDiD estimator is provided in Appendix B.2.

Identifying Assumptions and Data Requirements

The consistency and asymptotic normality of the SDiD estimator depend on four formal assumptions presented in Arkhangelsky et al. (2021).

Assumption 1 (Properties of Errors). The rows of the idiosyncratic error matrix $E$ are independent and identically distributed Gaussian vectors, and the eigenvalues of their covariance matrix are bounded and bounded away from zero. While serial correlation within units is permitted, cross-sectional independence of the error terms is required for the theoretical argument. In the context of air pollution, this assumption implies that all spatial dependence such as intra-annual (since we are using annual data) patterns must be fully captured by the systematic latent factor structure ($L$). Any remaining spatial correlation in the idiosyncratic errors (e.g., local spillovers between adjacent cities) would technically violate this condition.

Assumption 2 (Sample Sizes). The estimator requires a large panel structure in which both the number of control units and the number of pre-treatment periods grow sufficiently large. A long pre-treatment window is central because the estimator must observe enough historical variation to recover the latent factor structure. This is important for the NCAP context, where cities have distinct long-run pollution paths.

Assumption 3 (Structure of $L$). The matrix $L$ must exhibit low rank, which means that its singular values decay at an adequate rate. This condition ensures that the systematic component of air pollution is governed by a small number of common forces that influence all units.

Assumption 4 (Properties of Weights). There must exist feasible weights that balance the latent unit and time factors while avoiding concentration on a small set of units or periods. In practice, this requires a sufficiently heterogeneous group of control units and enough variation across time.

These assumptions guide the data choices adopted in this study. The SDiD estimator is applied using the satellite-derived PM_2.5 series, which extends from 1998 to 2023. The pre-treatment period for the SDiD analysis is defined as 1998–2018, while the DiD specifications use the period from 2010 onwards. This provides 21 years of historical data for SDiD, which is sufficient for recovering the latent factor structure in a setting with heterogeneous long-run trends.

This divergence in pre-treatment period selection is motivated by the distinct econometric properties of the DiD and SDiD estimators. Standard DiD implicitly assigns uniform weight to all pre-treatment periods (Arkhangelsky et al., 2021), meaning that including distant historical data (for example from the late 1990s) could introduce bias if structural breaks occurred that violate the parallel trends assumption. The SDiD estimator, on the other hand, employs data-driven time weights ($\hat{\lambda}_t$) to identify and prioritise only those pre-treatment periods that best predict post-treatment dynamics (Arkhangelsky et al., 2021). Consequently, the extended 1998–2018 pre-treatment window benefits the SDiD estimator by providing a richer information set from which to learn the latent factor structure.

Inference

Inference is conducted using a tiered approach tailored to the level of aggregation. For the primary national and regional specifications, the jackknife variance estimator proposed by Arkhangelsky et al. (2021) is employed. This method is computationally efficient and robust to serial correlation, making it the standard approach for SDiD when the treatment group comprises multiple units.

However, for the granular city-level analysis where the treatment group consists of a single city, a cluster-bootstrap procedure with $B=100$ replications is implemented. In this procedure, donor units from the same airshed are resampled with replacement to construct a distribution of placebo treatment effects. Standard errors are derived from the standard deviation of these bootstrap estimates, and 95% confidence intervals are calculated using the normal approximation ($\hat{\tau} \pm 1.96 \cdot \widehat{SE}$). This approach allows for the assessment of the precision of the estimated effect for each individual city, while accounting for the specific composition of its regional donor pool. Refer to Appendix B.2.3 for detailed explanation of the Bootstrap method and SE calculation.

3.4 Mechanism Analysis: Meta-Regression of Fund Utilisation

To investigate the mechanisms determining policy effectiveness and to distinguish between potential implementation bottlenecks versus policy design limitations, the relationship between financial implementation and pollution outcomes is examined. While the SDiD estimator identifies whether air quality changed among different cities, it does not identify the mechanism behind it. A plausible hypothesis is that variation in effectiveness, if any, may be driven by the speed and extent of fund utilisation. If supported, this would suggest that implementation bottlenecks, rather than policy design, are the primary culprits in cities where no pollution reductions were observed.

This hypothesis is tested using a cross-sectional meta-regression framework. A utilisation ratio ($R_i$) for each city $i$ was calculated using the funds data mentioned in Section 3.1: $$R_i = \frac{\text{Total Funds Utilised}_i}{\text{Total Funds Released}_i}$$(3.7) This financial data were linked to the estimated SDiD treatment effects ($\hat{\tau}_i$) derived in Section 3.3.2 using the unique identification codes to ensure matching accuracy.

Since the dependent variable ($\hat{\tau}_i$) is an estimated parameter rather than a direct observation, the error term in the second-stage regression is inherently heteroskedastic. The variance of this error depends on the precision of the synthetic control fit for each specific city, meaning that some data points are far more reliable than others. Consequently, a standard OLS estimator would be inefficient.

To address this, a WLS specification is employed: $$\hat{\tau}_i = \alpha + \beta R_i + \varepsilon_i$$(3.8) The observations are weighted by the inverse of their variance ($w_i = 1 / \text{SE}(\hat{\tau}_i)^2$). This weighting scheme ensures that the regression estimates are driven by the cities with the most precise treatment effects, effectively down-weighting noisy or unreliable data points to maximise efficiency. A detailed derivation of this estimator provided in Appendix B.4.

A negative and statistically significant coefficient for $\beta$ would provide evidence that higher fund utilisation is associated with larger reductions in PM$_{2.5}$, supporting the implementation failure hypothesis. Conversely, a null coefficient would suggest that financial liquidity is not the binding constraint and policy ineffectiveness could be due to design failure.

3.5 Implementation Strategy and Roadmap

The empirical analysis proceeds in a hierarchical sequence designed to test the robustness of the findings across increasingly granular levels of aggregation. A national baseline is first established by estimating the aggregate effect of the NCAP using the standard Two-Way Fixed Effects (TWFE) DiD estimator applied to demographically matched Control Groups 1 and 2. Following this, the meteorological variation discussed in Section 3.2.2.3 is accounted for by estimating the SDiD model separately for each of the five defined airsheds — IGP, Arid West, Central, South, and NEE — ensuring that synthetic counterfactuals are constructed from donor units sharing the same atmospheric dynamics.

The analysis then advances to a granular city-specific estimation, where the SDiD estimator is applied individually to each of the 129 treated cities, restricting donor pools strictly to untreated urban units within the same airshed to generate a distribution of unique treatment effects ($\hat{\tau_i}$). Finally, these city-specific estimates serve as the dependent variable in the meta-regression framework described in Section 3.4, formally testing the link between financial utilisation and policy efficacy. The results of these four estimation phases are presented in detail in the following chapter.

4 Results & Discussion

This chapter presents the empirical findings of the study based on the methodologies discussed in the previous chapter, beginning with a descriptive analysis of pollution trends and demographic characteristics to contextualise the treatment group. It then proceeds to evaluate the causal impact of the NCAP through a tiered econometric strategy, starting with baseline DiD models before advancing to the more robust SDiD estimator at the national, regional, and city levels to correct for pre-treatment trend divergence. Finally, the chapter investigates potential mechanisms behind the observed results by examining the relationship between policy effectiveness and fund utilisation rates, concluding with a discussion that synthesises these findings to assess the overall efficacy of India’s clean air framework.

4.1 Descriptive Analysis

Understanding the structure and distributional characteristics of the data is a critical prerequisite for any causal analysis. This section provides a detailed descriptive overview of the dataset and outlines the empirical context in which the NCAP was implemented. It highlights key patterns in pollution levels, demographic differences, and the spatial variation that characterises India’s sub-districts prior to the econometric analysis.

Figure 4.1 presents the average PM_2.5 concentration for the years 1998, 2010, 2019, and 2023 across all sub-districts in India, with the 129 treated units covered under the NCAP highlighted. The figure illustrates the substantial rise in pollution, particularly across the northern IGP and regions situated along the Himalayan foothills, which have historically experienced some of the highest particulate matter concentrations in the world. This heightened pollution burden is closely linked to the region’s unique geographical and atmospheric conditions, where restricted wind flow, frequent winter inversions, and sinking air currents prevent pollution from rising, trapping it close to the surface for prolonged periods (Mishra et al., 2025).

4.1.1 Summary Statistics

Table 4.1 reports the summary statistics for the treated, untreated, and combined samples. Consistent differences emerge between treated and untreated sub-districts, both in terms of pollution exposure and demographic characteristics⁹. Treated units are substantially larger and more densely populated, reflecting their predominantly urban and metropolitan nature. In contrast, untreated units exhibit markedly lower values for population, land area, and population density. This difference follows naturally from the fact that the untreated group comprises a large number of rural and semi-urban sub-districts, which reduces their average scale of settlement. The standard deviations for all the factors are also high, showing the heterogeneous nature of the Indian subcontinent.

These descriptive differences underscore the need for a careful construction of the counterfactual group and appropriate adjustment for observable heterogeneity in the empirical analysis that follows.

Note: Each panel divides cities into ten deciles (1 = lowest, 10 = highest) for the corresponding variable. The black boxes represent the interquartile range of PM_2.5, with the median shown as a horizontal line. Vertical whiskers show values outside the IQR, and grey points represent all observations. The value of ρ in each panel is the Pearson correlation coefficient between PM_2.5 and the respective variable.

To further examine how basic demographic and spatial characteristics relate to particulate pollution, Figure 4.2 combines decile-based distributions with the corresponding Pearson correlation coefficients. All three covariates — population, area, and population density — exhibit only weak linear associations with PM_2.5 levels, with correlation coefficients of 0.12, –0.01, and 0.13 respectively. These small coefficients indicate that simple linear relationships are insufficient to explain cross-sectional variation in pollution. Nevertheless, the decile plots reveal some non-linear patterns. PM_2.5 tends to rise modestly across population and density deciles, particularly in the upper tails, suggesting that highly urbanised and densely settled units experience somewhat elevated pollution levels compared to sparsely populated areas. In contrast, area-based deciles show virtually no systematic pattern, consistent with the near-zero correlation. These results imply that demographic scale and density have only limited explanatory power in isolation and that more complex structural and geographic factors likely drive the substantial heterogeneity observed in PM_2.5 concentrations.

4.1.2 Temporal Evolution of PM_2.5 (1998–2023)

Figure 4.3 depicts the evolution of annual mean PM_2.5 concentrations from 1998 to 2023 and shows a clear rising trend in ambient particulate pollution across India over the past two decades. Although PM_2.5 levels steadily increase until the late 2010s, a noticeable break in this upward trend occurs around 2019, the year the NCAP was launched. However, this reduction cannot be causally attributed to NCAP, as both treated and untreated areas experience similar declines during the same period, suggesting that broader macroeconomic and meteorological factors might have played a more dominant role.

The short-lived downturn observed in 2019–2020 is further accentuated by the nationwide COVID-19 lockdown, which sharply curtailed industrial activity and vehicular movement and produced an exceptional but temporary improvement in air quality across India (Kumari et al., 2020). In Delhi, the effect was particularly striking, with mean PM_2.5 concentrations falling by 53% from 80.51 µg/m³ during 2–21 March 2020 (pre-lockdown) to 37.75 µg/m³ during 25 March–14 April 2020 (lockdown), representing one of the most substantial short-term reductions in particulate pollution ever recorded in the city (Mahato et al., 2020).

Another particularly striking pattern is the persistent disparity between treated and untreated units. Throughout the sample period, treated units have consistently experienced higher levels of particulate pollution compared to untreated units. This divergence predates the policy by nearly two decades and reflects the deeper structural characteristics of these cities such as larger populations, more intensive industrial activity, and denser economic agglomerations. The widening of this gap during the 2000s aligns with India’s post-liberalisation growth phase, when rapid urban expansion and industrialisation contributed disproportionately to pollution in major metropolitan areas.

Table 4.2 summarises the key PM_2.5 statistics for treated, untreated, and combined units across the pre- and post-policy implementation periods. In both periods, the treated group exhibits consistently higher mean, median, and standard deviation values compared to the untreated and combined groups, reflecting their more polluted and heterogeneous urban environments. Interestingly, the highest maximum PM_2.5 concentration before 2019 is observed in an untreated unit, suggesting that the extreme pollution levels were not exclusive to treated cities and hint towards the presence of areas with higher pollution not being in the policy-affected areas. This pattern shifts in the post-2019 period, where treated areas register the upper bound.

Figure 4.4 shows the seasonality of PM_2.5 concentrations across treated and untreated areas for selected years between 1998 and 2023. The heatmap highlights a strikingly consistent annual cycle, with pollution levels increasing sharply during the winter months, particularly from November to January, and falling during the summer and monsoon seasons. These seasonal swings are strongly shaped by meteorological conditions. Changes in temperature, wind speed, relative humidity, and boundary layer height¹⁰ influence pollutant dispersion and accumulation (Vaishali et al., 2023; Begum et al., 2025). As a result, winter months exhibit the most severe pollution, while months with stronger winds and deeper mixing layers show substantially lower PM_2.5 levels (S. K. Guttikunda & Gurjar, 2012).

Seasonal meteorological dynamics have been repeatedly shown to amplify winter pollution events across northern India. S. K. Guttikunda and Gurjar (2012) report that, even when emissions remain relatively stable throughout the year, pollution concentrations in Delhi are 40%-80% higher during winter (November-January) and 10%-60% lower during the summer months (May-July). This pattern emerges because winter conditions lead to atmospheric stagnation due to weak horizontal winds, suppressed vertical mixing, and low boundary layer heights, which trap pollutants close to the surface (Gao et al., 2016; Zheng et al., 2015; Paulot et al., 2022; Chen et al., 2018). These stagnation events, which often coincide with cooler temperatures and higher relative humidity, substantially reduce the atmosphere’s natural cleansing capacity and thereby intensify PM_2.5 build-up (Schnell & Prather, 2017; X. Wang et al., 2018; Garrido-Perez et al., 2018).

4.1.3 Spatial Evaluation of PM_2.5

To evaluate whether fine particulate concentrations exhibit systematic spatial structuring across India, spatial autocorrelation was assessed using the Global Moran’s I statistic. This metric quantifies the degree to which pollution levels in one sub-district resemble those in neighbouring areas. The analysis considers the long-term average PM$_{2.5}$ concentration for each sub-district over the 1998–2023 period to capture persistent spatial patterns.

The analysis yields a Global Moran’s I coefficient of 0.956 ($p < 0.001$). This near-perfect spatial dependence implies that pollution levels in any given sub-district are overwhelmingly determined by regional atmospheric conditions rather than local administrative boundaries. This pattern aligns with established atmospheric mechanisms such as regional advection, stagnation events, and the spatial concentration of urbanisation (Q. Li et al., 2021). Further technical details regarding the construction of the spatial weight matrix are provided in Appendix B.1, while the full statistical results are reported in Table C.1.

While global statistics reveal broad regional dependence, they do not formally identify where these statistically significant clusters are located. To rigorously test the hypothesis that pollution in India acts as a transboundary ‘airshed’ phenomenon rather than a series of isolated urban events, spatial autocorrelation techniques are employed. Following the approach of Anselin (1995) and recent applications (Tang et al., 2020; Y. Li et al., 2023; Song et al., 2020), we utilise Local Indicators of Spatial Association (LISA) to decompose global spatial patterns into local clusters. This allows for the precise identification of ‘hotspots’ (High-High) and ‘coldspots’ (Low-Low) where pollution levels are spatially correlated with their neighbours. The resulting cluster map in Figure 4.5 identifies pronounced High-High pollution clusters across the Indo-Gangetic Plain, highlighting the spatial coherence of pollution hotspots. In contrast, Low-Low clusters dominate peninsular and northeastern India, confirming that pollution in India is a regionally continuous phenomenon rather than a localized city-specific issue.

4.2 Econometric Analysis

4.2.1 Difference-in-Differences Results

This section presents the main econometric results from the DiD specifications introduced in Section 3.3.1. The baseline estimates are obtained from the TWFE model in Equation (3.2), using alternative definitions of the control group to assess the robustness of the findings. Table 4.3 provides descriptive diagnostics for the treated units and each control group, documenting key differences in settlement characteristics prior to the implementation of the NCAP and a summary of the estimated ATTs for analysis using Control 1 and 2 are reported in Table 4.4. The event-study figures in each control group result subsection complement the regression results by illustrating the dynamic evolution of treatment effects relative to the 2018 baseline and by offering a visual assessment of the plausibility of the parallel trends assumption.

Control Group 1: Large Urban Untreated Units

Control Group 1 restricts the set of untreated observations to sub-districts with a population exceeding 100,000 inhabitants and a population density above 400 persons per square kilometre. This choice aims to construct a control group that more closely resembles NCAP cities in terms of demographic scale and urban character, thereby reducing observable differences in settlement structure and emission sources.

The TWFE estimate for this specification is reported in column (1) of Table 4.4. The coefficient on the interaction term between the post-2019 indicator and the treatment dummy is equal to 1.79 and is statistically significant at the 1% level (standard error 0.44). Taken at face value, this implies that, after controlling for time-invariant sub-district characteristics and common time shocks, PM_2.5 concentrations in NCAP cities were on average about 1.8 $\mu g/m^3$ higher in the post-policy period than in comparable untreated urban areas. Given the level of pollution faced by treated cities (mean annual concentrations around 45–50 $\mu g/m^3$), the magnitude of this effect is modest in absolute terms but clearly inconsistent with the programme having generated substantial short-run improvements in air quality.

However, this estimate cannot be interpreted as a credible causal effect of the NCAP. The event-study plot in Figure 4.6 reveals that several pre-treatment coefficients deviate from zero, with at least one pre-2019 year showing a statistically significant difference between treated and control units. This pattern indicates a violation of the parallel trends assumption central to the TWFE estimator. Furthermore, TWFE estimates are sensitive to treatment-effect heterogeneity and staggered implementation, which can induce non-trivial bias even when average pre-trends appear similar (Goodman-Bacon, 2021; Sun & Abraham, 2021; de Chaisemartin & d’Haultfoeuille, 2020). Consequently, the results for Control Group 1 should be viewed as descriptive evidence that pollution in NCAP cities did not improve relative to comparable urban areas, rather than as a definitive measure of the programme’s causal impact.

Control Group 2: Density-Matched Urban Controls

As reported in Table 4.4, the two-way fixed effects estimates for Control Group 2 indicate that NCAP cities experienced an average post-2019 increase of approximately $3.06 \,\mu\text{g}/\text{m}^{3}$ in annual PM_2.5 concentrations relative to untreated cities of comparable population density. Although highly statistically significant, this coefficient likely reflects differences in underlying pollution trajectories rather than a policy-induced impact. Notably, while untreated density-matched units exhibit higher absolute PM_2.5 levels, difference-in-differences relies on similarity in trends. The positive interaction term therefore arises because NCAP cities were already on a steeper upward trajectory compared to equally dense untreated cities, despite their lower baseline pollution.

The event-study results in Figure 4.7 reinforce this interpretation. The pre-treatment coefficients do not cluster around zero but instead display a clear upward trend relative to the 2018 baseline, indicating that treated and control units were diverging prior to the NCAP’s introduction. This violation of parallel trends precludes a causal interpretation. Following 2019, the coefficients continue to rise, reflecting a persistence of this pre-existing divergence rather than a discrete policy shift. Taken together, the TWFE estimate of $3.06\,\mu\text{g}/\text{m}^{3}$ and the event-study dynamics suggest that the observed post-policy differences stem from ongoing structural and environmental disparities rather than the effectiveness of the NCAP.

Control Strategy 3: Regionally Stratified Urban Controls

Given the failure of parallel trends in national-level comparisons, we employ Control Strategy 3 (defined in Section 3.2.2.3) to match treated cities exclusively to demographically similar urban units within the same airshed. Table 4.5 reports the resulting regional DiD estimates.

The findings from the regional analysis strongly suggest an aggregate null result. In the IGP, the coefficient is -0.360 but statistically indistinguishable from zero, indicating no divergence from the business-as-usual trend even in the region most critically targeted by the policy. In the South, a significant positive coefficient ($1.055^{***}$) suggests that treated cities are on a steeper emissions growth trajectory than their regional counterparts, which the policy has failed to arrest.

Figure 4.8 presents the event-study plots for these regions. The South (Panel b) shows a distinct upward pre-trend, confirming that treated southern metropolises were growing faster than controls well before 2019. In contrast, the IGP (Panel a) shows relatively flat pre-trends but no structural break after 2019. The visible instability in pre-treatment trends across most regions further motivates the use of the SDiD estimator in the subsequent section to correct for these underlying differences.

(a)

(b)

(c)

(d)

(e)

Robustness Check Results: Placebo Treatment-Year Tests

To evaluate the credibility of the TWFE Difference-in-Differences estimates, a series of placebo treatment-year exercises were conducted by artificially shifting the intervention date to pre-policy years (2015–2017) on the analysis based on Control Group 1. Under a valid parallel trends assumption, these placebo specifications should yield coefficients that are statistically indistinguishable from zero, as no policy intervention occurred in these years. However, the placebo regressions produce positive and highly significant interaction terms ranging from 1.47 to 1.72 $\mu$g/m$^{3}$, closely mirroring the magnitude of the main DiD estimate.

These results corroborate the violations observed in the event-study analysis figures, where several pre-treatment coefficients diverged from zero, indicating that treated and control cities followed systematically different pollution trajectories long before 2019. The placebo evidence therefore provides strong additional confirmation that the parallel trends assumption does not hold in this setting, rendering the TWFE DiD estimator unsuitable for credible causal inference.

4.2.2 Synthetic Difference-in-Differences Results

Motivation and Overview

The DiD results in the previous section showed that treated NCAP cities follow systematically different pre-treatment trajectories than their controls, violating the parallel trends assumption even under refined control definitions. This motivates the use of the SDiD estimator, which explicitly reweights donor units and time periods to match pre-exposure trends.

National SDiD Results

Weight Structure

Table 4.6 summarises the structure of the weights underlying the national SDiD estimator. The algorithm assigns non-zero weights to 1,669 donor units, producing a high effective sample size ($N_{eff} \approx 1,359$)¹¹. The maximum unit weight is very small (approximately 0.0015 for Chorasi in Surat district, Gujarat), demonstrating that the synthetic counterfactual is not driven by a narrow subset of cities but instead reflects a broadly diversified combination of control units.

The time-weight distribution is particularly informative. The years 2008, 2017, and 1999 carry the greatest predictive importance, suggesting that these periods capture structural features in pollution dynamics that extend into the post-intervention period. Later pre-treatment years with limited predictive content are effectively downweighted or assigned zero weight, which is consistent with the SDiD objective of learning the counterfactual from the most informative segments of the historical record rather than mechanically treating all pre-2019 years as equally relevant.

Estimated Treatment Effect

Figure 4.9 displays the trajectories of the average PM$_{2.5}$ concentration for the treated NCAP cities (solid line) and the synthetic counterfactual (dashed line) constructed using the estimated weights. The pre-treatment alignment between the two series is close over 1998–2018: the treated and synthetic trends co-move tightly, especially in the high-weight years identified in Table 4.6. This visual impression is corroborated quantitatively by the detrended root mean squared prediction error, $RMSPE^{trend}$, which is 0.242¹². Such a low value indicates that the SDiD estimator closely replicates the underlying pollution dynamics of treated cities prior to the NCAP, lending credibility to the constructed counterfactual.

The visual evidence in Figure 4.9 therefore provides strong support for the identification strategy. In contrast to the diverging pre-trends observed in the standard DiD specifications (Figures 4.6 and 4.7), the reweighted synthetic control trajectory tracks the treated path closely throughout the pre-policy period. While some residual variation remains due to idiosyncratic annual shocks ($E_{it}$), the counterfactual successfully captures the main turning points and the secular evolution of pollution in the treated cities.

The corresponding estimates of the ATT are reported in Table 4.7. The SDiD estimator yields a coefficient of 0.853 with a jackknife standard error of 0.249, implying a 95% confidence interval of $[0.365, 1.340]$. Similar to the earlier DiD estimates from Control 1 and Control 2 — albeit smaller in magnitude — this result indicates a statistically significant increase in PM$_{2.5}$ concentrations, roughly 0.9 $\mu g/m^3$ higher than the synthetic counterfactual in the post-2019 period. At the same time, the magnitude of the SDiD estimate is markedly lower than the TWFE DiD coefficients (1.79 and 3.06). This suggests that once latent trend heterogeneity is accounted for, the apparent adverse effect of the NCAP is attenuated but not eliminated. Taken together with the strong pre-treatment fit documented above, the SDiD evidence points to an absence of meaningful air-quality improvements in the early years of the programme, consistent with a slight relative deterioration in treated cities compared to similar untreated areas.

Regional Heterogeneity

While the national SDiD estimate suggests no detectable average effect of the NCAP, it is plausible that the policy operates differently across India’s major airshed regions. Differences in baseline pollution levels, industrial composition, meteorology, and institutional capacity may produce heterogeneous treatment effects. While the SDiD estimator accounts for these structural differences to construct valid counterfactuals, these factors may also act as effect modifiers, determining how responsive a region is to the policy intervention. To assess this, the SDiD estimator is re-estimated separately for each of the five regions defined in Section 3.2.2.3 using the annual panel for 1998–2023 and the same donor-construction rules as in the national specification.

Table 4.8 reports the ATT, jackknife standard errors, confidence intervals, and the effective sample size for each regional donor pool. The corresponding Figures 4.10–4.12 display the treated and synthetic trajectories for each region, enabling a visual assessment of pre-treatment alignment and post-treatment divergence.

The regional results reveal a mixed pattern. In the IGP, the largest and most polluted airshed, the ATT is modestly positive (0.474 $\mu g/m^3$) with a confidence interval that comfortably includes zero. Figure 4.10 shows that the synthetic trajectory closely tracks the treated units prior to 2019, while the post-treatment gap remains small and statistically indistinguishable from zero. Even in this region of severe and persistent pollution, the NCAP does not appear to have shifted the aggregate PM$_{2.5}$ trajectory in a measurable way. However, it is important to note that the IGP region exhibits instability in placebo tests (see Appendix C.3), with several pre-treatment years showing statistically significant “effects.” This suggests that even the SDiD estimator struggles to fully correct for the complex trend heterogeneity in this specific airshed, and consequently, the null result for the IGP should be viewed with caution.

(a) Arid West (Significant Increase)

(b) North-East & East (Significant Decrease)

A more concerning pattern emerges in the Arid West, where the ATT is 1.096 $\mu g/m^3$ and statistically significant at the 5% level. As illustrated in Figure 4.11, the treated and synthetic series are reasonably well aligned before 2019, but the treated cities drift above their counterfactual path in the post-treatment period. This suggests that, relative to comparable urban areas in the same airshed, NCAP cities in Rajasthan and Gujarat experienced a deterioration in air quality rather than an improvement. The effective sample size for this region ($N_{eff} \approx 109$) is smaller than in the IGP but still sufficiently large to warrant attention, even though the result should be interpreted cautiously given the limited number of treated cities and the region’s strong dust-related variability.

By contrast, the North-East and Eastern cluster shows a statistically significant negative effect, with an ATT of $-0.851$ $\mu g/m^3$ and a relatively tight confidence interval. Figure 4.12 displays a clear post-treatment separation in which treated cities fall persistently below their synthetic counterparts after 2019. This suggests that, in this region, NCAP implementation coincided with modest but measurable improvements in air quality relative to the regional counterfactual.

(a) Southern India (Null Result)

(b) Central India (Null Result)

In Central India, the ATT is slightly negative ($-0.310$ $\mu g/m^3$) but far from statistically significant, and Figure 4.15 shows only modest post-2019 separation between the treated and synthetic series. The effective sample size ($N_{eff} \approx 79$) is the smallest among the regions, reflecting a relatively limited donor pool and contributing to the wide confidence interval and larger standard errors. Overall, there is no compelling evidence that the NCAP has altered PM$_{2.5}$ trends in this transitional airshed.

The Southern region, which in the TWFE specification exhibited a large and statistically significant positive effect, now shows a more moderate and statistically insignificant ATT of 0.436 $\mu g/m^3$. Figure 4.14 confirms that once pre-treatment trend differences are explicitly corrected using SDiD, the synthetic trajectory closely mirrors the treated series throughout the pre-policy period and no systematic divergence emerges after 2019. This attenuation underscores the extent to which the earlier TWFE result was driven by biased pre-trend comparisons rather than genuine policy effects.

Taken together, the regional SDiD estimates and the corresponding trend plots indicate that the NCAP has not produced any generalised improvements in urban air quality. Most regions display effects that are small relative to their confidence intervals and statistically indistinguishable from zero. The two notable exceptions point in opposite directions: a deterioration relative to the synthetic counterfactual in the Arid West and an improvement in the North-East and East. This pattern reinforces the national conclusion that, in its current form, the NCAP has not shifted the overall trajectory of PM$_{2.5}$ concentrations in a substantive way, while also highlighting substantial geographic heterogeneity that motivates the city-level analysis in the next section.

City-Level SDiD Results

The regional analyses presented thus far suggest a predominant lack of policy effectiveness across India’s major airsheds. To subject this finding to rigorous scrutiny, we estimate city-specific SDiD treatment effects for all 129 non-attainment cities, restricting each city’s donor pool to its respective airshed to ensure meteorological comparability. Given the dimensionality of these results, we first visualise the distribution of effect sizes before examining the statistical significance of individual estimates.

Figure 4.13 displays the density of estimated treatment effects ($\hat{\tau}_{city}$) across the five airshed regions and the "other" region. An initial visual inspection reveals that estimates are distributed across both negative and positive values, seemingly supporting the hypothesis of heterogeneous policy impacts. However, this interpretation warrants caution. The magnitude of these deviations is contained largely within the range of $[-5,8]~\mu g/m^3$—a variation that is relatively small compared to the high baseline pollution levels characteristic of Indian cities. Consequently, what appears to be heterogeneity may simply reflect stochastic variation around a null mean rather than substantive divergence in policy efficacy.

Furthermore, the density plot does not account for estimation uncertainty. A non-zero point estimate is economically meaningless if the associated standard error is large enough to encompass zero. To address this, the statistical significance of the estimates is examined after applying a rigorous quality filter. Attention is restricted to the subset of cities where the synthetic control provides a reliable pre-treatment trajectory. Specifically, matches are classified as having an "excellent fit" if the RMSPE¹³ is less than 0.5, and a "very good fit" if the RMSPE falls between 0.5 and 1. This filtering ensures that inferences are drawn only from cities where the counterfactual is demonstrably robust.

Table 4.9 presents the results for the selected cities from the high-quality subset of city-level SDiD estimates. Among these ten cities with well-fitted counterfactuals, the pattern is heterogeneous. In the South, Madurai, Davanagere and Anantapur exhibit statistically significant improvements in air quality, while Hyderabad, Nalgonda and Bangalore show significant worsening. Kurnool’s estimate is small in magnitude and statistically indistinguishable from zero. In Central India, Pune shows a modest but significant improvement, whereas Akola records a statistically significant deterioration. The only city from the IGP in this subset, Gaya, displays a small but statistically significant reduction in PM$_{2.5}$.

Despite this mix of positive and negative effects, the magnitudes are generally modest: apart from Nalgonda, Hyderabad and Madurai, the absolute value of the ATT remains well below $1\,\mu g/m^3$. This granular analysis therefore suggests that pockets of improvement and deterioration exist but are scattered and limited in size, and thus do not overturn the national and regional conclusion that the NCAP has not substantively altered the overall trajectory of urban PM$_{2.5}$. The complete set of estimates, standard errors, and fit diagnostics for all 129 treated non-attainment cities, are reported in Appendix Table C.4.

Robustness Check: Placebo Treatment-Year Tests for Regional S-DiD

To assess the validity of the regional S-DiD estimates, placebo treatment-year tests were conducted by shifting the NCAP intervention to pre-policy years (2010–2017). Under a correctly specified design, these placebo regressions should yield coefficients close to zero. The results, summarised briefly here and reported in detail in Appendix C.3, show that the Central, South, West, and North-East & East airsheds exhibit placebo effects that are small and statistically insignificant, indicating that the regional donor pools successfully reproduce pre-treatment pollution dynamics. In contrast, the Indo-Gangetic Plain displays several sizeable and statistically significant placebo effects, reflecting persistent trend heterogeneity that the estimator cannot fully correct.

These findings also inform the credibility of the city-level S-DiD estimates, which rely on the same regional donor structure. In regions where the placebo tests confirm that pre-treatment dynamics are well-matched, city-level counterfactuals constructed from the same donor pools can be interpreted with greater confidence, provided that each treated city has a sufficiently large set of high-quality untreated donors. For the IGP, however, the placebo evidence signals that latent trend heterogeneity remains problematic, and city-level estimates for this airshed should therefore be interpreted with caution.

4.3 Does Money Buy Clean Air? A Mechanism Check

The results in Table 4.9 and the distribution shown in Figure 4.13 indicate that even among cities with the most reliable counterfactuals, the majority of estimated treatment effects are very small. This suggests that the NCAP has not produced the widespread structural shifts in PM$_{2.5}$ concentrations that the programme set out to achieve.

This raises an important question. Is the null effect due to weak implementation in the sense that cities did not meaningfully deploy their NCAP funds, or is it a deeper issue of policy design, meaning that the interventions funded by NCAP are ineffective even when executed? If implementation failure is responsible, then cities with higher fund utilisation ratios should show more negative treatment effects. If policy design is the issue, then fund utilisation should have no systematic relationship with estimated air quality changes.

To test this mechanism, the treatment effects are regressed on each city’s NCAP fund utilisation ratio. Figure 4.14 visualises this relationship, where each point corresponds to a treated city, bubble size reflects statistical precision, and the fitted line is obtained from WLS with weights $w_i = 1/SE(\hat{\tau}_i)^2$.

The corresponding regression results are reported in Table 4.10. The coefficient on fund utilisation ($R_i$) is small, positive, and statistically insignificant. This indicates that cities which spent a larger share of their NCAP allocations did not exhibit better pollution outcomes. The intercept is positive and statistically significant, meaning that the average treatment effect remains positive even when reported utilisation is zero. Furthermore, the regression yields an $R^2$ of merely 0.004, with a negative adjusted $R^2$ of -0.004. This effectively zero explanatory power indicates that differences in fund utilisation explain virtually none of the cross-city variation in treatment effects. In other words, cities that exhausted their allocated budgets were no more likely to achieve pollution reductions than those with substantial unspent balances.

Three distinct patterns emerge from the combined graphical and regression evidence. First, high fund utilisation does not correspond to improved outcomes; several cities reporting utilisation rates near or above 100 percent show either no improvement or statistically significant increases in PM$_{2.5}$, indicating that spending alone does not correlate with better air quality. Second, a large cluster of cities exhibits both moderate to high utilisation and near-zero treatment effects. This pattern suggests that NCAP interventions are often implemented but fail to shift the underlying pollution trend, likely because commonly funded activities—such as mechanical sweeping, road paving, or equipment procurement—do not meaningfully address the processes driving PM$_{2.5}$ formation. Finally, cities that do exhibit improvements do not systematically occupy the upper end of the utilisation distribution. The absence of a positive association implies that these gains are not linked to programme spending, but may instead reflect unrelated industrial adjustments or idiosyncratic local policies.

Overall, the evidence suggests that the NCAP struggles not only because of slow or incomplete implementation, but also because the interventions it funds do not tackle the major drivers of PM$_{2.5}$ in Indian cities. Even when financial resources are deployed, the underlying policy design is insufficient to materially influence air quality trajectories. This conclusion is based on the assumption that the funds are actually "utilised" for specific interventions in the treated cities with high fund utilisation. The possibility of corruption, fund misallocation and outright fund stealing could dilute the case for design failure. However, under the assumption that these kinds of political issues are not present, this mechanism check strengthens the broader conclusion that the NCAP, in its current form, is not delivering measurable improvements in ambient particulate pollution due to policy design failures.

4.4 Discussion

This chapter evaluated the impact of the NCAP through a progression of empirical strategies, moving from standard TWFE DiD to the more robust SDiD. The initial DiD models yielded positive and statistically significant coefficients, ostensibly suggesting that air quality in treated cities worsened following policy implementation. However, the event study diagnostics revealed that these estimates were driven by persistent pre-existing trend divergence rather than the policy itself. Treated non-attainment cities were already on a steeper pollution trajectory than their urban counterparts long before the intervention began — a structural difference that simple unweighted control groups failed to capture.

To correct for this bias, the SDiD estimator was employed to construct valid counterfactuals by explicitly reweighting control units to match the pre-treatment dynamics of the treated group. Once this latent trend heterogeneity was accounted for, the estimated treatment effect attenuated considerably (falling from $1.79 \mu g/m^3$ to $0.85 \mu g/m^3$). This correction confirms that the earlier “adverse” effects were largely artifacts of selection bias. The regional SDiD analysis further decomposed this national aggregate, revealing statistically insignificant results in three of the five airsheds. The exceptions were the Arid West (deterioration) and the North-East & East (improvement), though even here, the magnitudes were economically small relative to the region’s severe baseline pollution. Notably, the null result for the Indo-Gangetic Plain (IGP) must be interpreted with caution, as placebo tests indicated that high spatial autocorrelation in this region makes the construction of a perfect counterfactual challenging, potentially reducing the precision of the estimator.

The city-level analysis reinforced the conclusion of limited efficacy. While individual cities exhibited heterogeneous outcomes, the aggregate picture remains one of policy stagnation. A subset of cities in the North-East & East with high-quality counterfactual fits (low RMSPE) did show statistically significant reductions, but these gains were modest in absolute terms. Conversely, the mechanism analysis presented in Section 4.3 offers a critical insight into why the broader programme has failed. The complete absence of correlation between fund utilisation ratios and treatment effects challenges the narrative that null results are driven solely by administrative bottlenecks. Instead, the data reveal that even cities reporting near-complete fund utilisation failed to diverge from their counterfactual trends. This pattern is consistent with a failure of policy design rather than implementation: the specific interventions prioritised under the NCAP (such as road dust management and mechanical sweeping) appear unable to address the fundamental sources of emissions driving the crisis.

Given that the average post-2019 PM$_{2.5}$ concentration in treated cities remains $\approx 49\mu g/m^3$, achieving the NCAP’s target of a 40% reduction would require an annual decline of roughly $20 \mu g/m^3$. None of the empirical estimates obtained in this study come remotely close to this threshold. Instead, the significant positive intercept in the mechanism regression suggests that treated cities are industrialising at a pace that outstrips the scale of current mitigation efforts. Taken together, the evidence indicates that the NCAP, in its present form, is structurally misaligned with the dynamics of particulate pollution in urban India, rendering the policy insufficient to achieve its stated objectives.

5 Conclusion

This thesis sought to determine whether the NCAP brought about measurable improvements in fine particulate pollution across India’s cities. The evidence presented, established through a robust SDiD framework, indicates that the programme did not produce a detectable reduction in PM$_{2.5}$ concentrations during the period from 2019 to 2023. By correcting for the pre-treatment trend divergence that biased earlier standard DiD estimates, this study confirms that the apparent "effects" of the policy were largely artefacts of structural urban growth rather than effective mitigation. From a policy standpoint, this is a major finding: approximately US$ 1.6 billion of taxpayer money has been allocated towards this cause without yielding statistically significant benefits to date.

Implications for Policy and Political Economy

The disconnect between financial allocation and environmental outcome raises critical questions regarding the transparency of fund utilisation and the efficacy of city action plans. The failure of the NCAP cannot be viewed solely as a technical shortcoming; it is deeply embedded in the political economy of India’s federal structure. There is a considerable risk that funding allocations are influenced by political considerations rather than pollution urgency. The selection of NCAP cities and the disbursement of aid warrant scrutiny under a political lens. Concerns regarding fiscal federalism have emerged, with accusations that central aid is sometimes contingent on political alignment. A pertinent parallel is observed in the SSK, where states governed by opposition parties reportedly faced funding delays compared to states aligned with the central administration (Brittas, 2025). If similar dynamics influence NCAP allocations, the programme’s ability to target pollution hotspots objectively is severely compromised.

This lack of political accountability is reinforced by public perception. Findings from Bala et al. (2025) reveal a “perception gap”: even when presented with evidence of policy ineffectiveness, surveyed citizens maintained that the government was taking sufficient action. This public acceptance, even in the absence of tangible progress, suggests there are minimal political consequences for programme failure. This disconnect helps explain the government’s stance on health data, exemplified by the recent admission in Parliament that the Union government possesses no comprehensive data on pollution-linked mortality (FPJ, 2024). This denial, combined with controversial measurement standards where Indian monitors often cap AQI readings at 500, suggests a systemic reluctance to acknowledge the true scale of the crisis.

Beyond political will, the structural design of the NCAP merits critique. The programme relies largely on command-and-control regulations without the legal teeth to enforce them. As discussed in Singhal (2018), while CAC instruments are politically attractive because they offer control over distributional outcomes, they often lack the efficiency of market-based instruments. The current NCAP framework occupies an unhappy middle ground where it is not legally enforceable like a strict command-and-control regime, while also lacking the flexibility and cost-efficiency of market mechanisms.

A critical operational failure identified is the lack of scientific grounding in expenditure. The minutes of the 17th meeting of the Implementation Committee state that as of late 2024, only 50 cities had completed source apportionment studies (CPCB, 2024). This implies that the majority of cities are utilising funds for pollution control without a scientific understanding of their specific pollution sources. Blind spending on generic solutions — such as mechanical sweepers — without source-specific targeting is a recipe for inefficiency.

Contributions, Limitations, and Future Research

This study contributes to the literature on environmental economics in developing countries by demonstrating the limitations of standard TWFE models in heterogeneous airsheds. It highlights that standard econometric evaluations often fail to account for the structural divergence in pollution trends driven by differential rates of industrialisation and urban growth. Without explicitly correcting for this latent trend heterogeneity—as demonstrated through the SDiD framework—evaluations may yield spurious results. Furthermore, this research represents one of the first comprehensive city-level assessments of the NCAP, providing critical empirical evidence that identifies policy design failure, rather than mere implementation gaps, as the primary driver of the programme’s ineffectiveness.

However, this thesis is not without limitations. First, the analysis was constrained by administrative data limitations. Specifically, the prolonged inaccessibility of the official government data portal during the research period restricted the scope of the treated sample. A stricter selection of the geographical extent of the treated group might have helped isolate effects more continuously; however, manual data collection was not feasible within the master’s thesis timeline. Second, the study lacks certain high-resolution covariates, such as sub-district-level fuel consumption or industrial density, which could better explain pollution variance. Finally, the instability of the placebo tests in the IGP underscores the limitations of counterfactual construction in highly polluted airsheds. The extreme spatial autocorrelation in Northern India presents a structural challenge that even advanced estimators cannot fully overcome.

Future research could extend this work by examining longer post-treatment periods, incorporating satellite retrievals for other pollutants (such as NO$_x$ or SO$_2$), or assessing the effectiveness of individual NCAP interventions rather than the aggregate policy. Additionally, a rigorous political economy analysis linking specific party alignments to fund disbursement delays would provide valuable empirical evidence on the fiscal federalism hypothesis raised in this discussion.

Concluding Remarks

As a policy, the NCAP in its current form can be considered a failure in both design and implementation. This does not imply that the objective was misguided, but rather that the conditions necessary for meaningful change — institutional capacity, depoliticised funding, and scientific rigour — were not in place. The broader challenge facing India’s air-quality policy lies in the structure of urban growth and the regional nature of pollution. Local-level interventions are unlikely to generate substantial improvements without parallel changes in energy systems and regional coordination. As India continues its rapid urban transformation, shifting from discretionary spending to evidence-informed, legally enforceable mandates will be central to safeguarding public health and ensuring the long-term habitability of its cities.

Appendix A Supplementary Data

This appendix provides supplementary reference material to contextualize the empirical analysis, specifically detailing the full list of cities targeted by the NCAP.

A.1 List of NCAP cities

Appendix B Supplementary Methodology

This appendix presents supplementary mathematical derivations and technical details supporting the estimation strategies outlined in Chapters 3 and 4.

B.1 Spatial Autocorrelation Methodology

This section details the methodological foundations of the spatial analysis presented in Section 4.1.3.

Spatial Weight Matrix ($W$)

The calculation of Moran’s I requires the definition of a spatial weight matrix, $W$, which formalises the concept of “neighbourhood.” For this analysis, we employed Queen Contiguity weights (Anselin, 1988). Under this definition, two sub-districts $i$ and $j$ are considered neighbours ($w_{ij} = 1$) if they share any common boundary point, including vertices. This approach is preferred over Rook contiguity (which requires a shared edge) because it captures the continuous nature of atmospheric dispersion, where pollutants can spread diagonally across administrative corners.

The weight matrix was row-standardised, such that $\sum_j w_{ij} = 1$. This normalisation ensures that the spatial lag term represents the average pollution level of a unit’s neighbours, preventing units with many neighbours from dominating the global statistic (Cliff & Ord, 1981).

Global Moran’s I Statistics

The Global Moran’s I statistic (Moran, 1950) is calculated as: $$I = \frac{N}{\sum_i \sum_j w_{ij}} \frac{\sum_i \sum_j w_{ij} (x_i - \bar{x})(x_j - \bar{x})}{\sum_i (x_i - \bar{x})^2}$$(B.1) where $N$ is the number of spatial units indexed by $i$ and $j$, $x$ is the variable of interest (PM$_{2.5}$), $\bar{x}$ is the mean, and $w_{ij}$ are the elements of the spatial weight matrix.

B.2 SDiD Weights, Estimator & Standard Errors

The Synthetic Difference-in-Differences (SDiD) estimator, proposed by Arkhangelsky et al. (2021), improves upon standard difference-in-differences (DiD) by relaxing the parallel trends assumption. It achieves this by reweighting the control units and the pre-treatment time periods to construct a counterfactual that more accurately tracks the trajectory of the treated units. This appendix section outlines the mathematical formulation and intuitive logic behind the two sets of weights - unit weights ($\hat{\omega}$) and time weights ($\hat{\lambda}$) - used in the analysis.

B.2.1 Unit Weights and Time Weights

Unit Weights ($\hat{\omega}$): Constructing the Synthetic Control

The unit weights, denoted as $\hat{\omega}_i$, determine the contribution of each untreated city to the synthetic counterfactual. Unlike the standard DiD estimator, which assigns equal weight ($1/N_{co}$) to all control units, SDiD seeks a weighted combination of controls that minimises the difference in pre-treatment trends relative to the treated units.

Formally, let $Y_{it}$ denote the outcome for unit $i$ at time $t$. Let $N_{co}$ be the number of control units and $T_{pre}$ be the number of pre-treatment periods. The unit weights are obtained by solving the following regularised optimisation problem:

$$(\hat{\omega}_0, \hat{\omega}) = \operatorname*{argmin}_{\omega_0 \in \mathbb{R}, \omega \in \Omega} \left\{ \sum_{t=1}^{T_{pre}} \left( \omega_0 + \sum_{i=1}^{N_{co}} \omega_i Y_{it} - \bar{Y}_{tr,t} \right)^2 + \zeta^2 T_{pre} \sum_{i=1}^{N_{co}} \omega_i^2 \right\}$$(B.2)

where $\bar{Y}_{tr,t}$ is the average outcome of the treated units at time $t$, and $\Omega = \{ \omega \in \mathbb{R}^{N_{co}}_+ : \sum_i \omega_i = 1 \}$ ensures the weights sum to one and are non-negative.

The objective function in Equation (B.2) consists of two components:

1. Trend Matching: The first term minimises the squared distance between the treated trend and the weighted control trend. The inclusion of the intercept $\omega_0$ is a critical distinction from the traditional Synthetic Control Method (SCM). It allows the synthetic control to match the slope (trend) of the treated unit without needing to match the absolute level. This makes the estimator invariant to additive unit-fixed effects, essentially performing a "parallelizing" operation.

2. Regularisation (Ridge Penalty): The second term, weighted by the hyperparameter $\zeta$, is an $L_2$ regularisation (ridge) penalty. In traditional SCM, weights are often sparse (i.e., relying on very few donors), which can lead to over-fitting and high variance. The regularisation term encourages dispersion, spreading the weights across a larger number of donor units. This ensures that the counterfactual is constructed from a broad, stable base of untreated cities rather than relying on idiosyncratic shocks in a handful of towns.

Time Weights ($\hat{\lambda}$): Balancing the Pre-Treatment Period

Standard DiD assumes that the average outcome in the pre-treatment period is a good proxy for the systematic component of the outcome. However, if pollution trends are non-linear or subject to time-varying shocks, specific pre-treatment years may be more predictive of the post-treatment era than others. SDiD addresses this by calculating time weights $\hat{\lambda}_t$.

The time weights are found by minimizing the discrepancy between the weighted pre-treatment outcomes and the average post-treatment outcome for the control units:

$$(\hat{\lambda}_0, \hat{\lambda}) = \operatorname*{argmin}_{\lambda_0 \in \mathbb{R}, \lambda \in \Lambda} \left\{ \sum_{i=1}^{N_{co}} \left( \lambda_0 + \sum_{t=1}^{T_{pre}} \lambda_t Y_{it} - \bar{Y}_{i,post} \right)^2 \right\}$$(B.3)

where $\bar{Y}_{i,post}$ is the average outcome for control unit $i$ in the post-treatment period, and $\Lambda = \{ \lambda \in \mathbb{R}^{T_{pre}}_+ : \sum_t \lambda_t = 1 \}$.

The optimization in Equation (B.3) seeks to identify which pre-treatment years (e.g., 2017, 2014) best predict the average outcome in the post-treatment years (2019–2023) for the control group.

• If pollution levels in 2015 were anomalously high due to a specific meteorological event (e.g., a severe El Niño year) that did not recur in the post-treatment period, the algorithm will assign a low or zero weight ($\lambda_{2015} \approx 0$) to that year.

• Conversely, years that exhibit structural pollution dynamics similar to the post-2019 period will receive higher weights.

This process essentially creates a "synthetic pre-treatment period" that is structurally balanced with the post-treatment period, removing bias caused by transient time-specific shocks.

B.2.2 The SDiD Estimator

Combining these two sets of weights, the final SDiD estimator is a localized difference-in-differences estimator:

$$\hat{\tau}^{sdid} = \left( \bar{Y}_{tr, post} - \sum_{t=1}^{T_{pre}} \hat{\lambda}_t \bar{Y}_{tr,t} \right) - \left( \sum_{i=1}^{N_{co}} \hat{\omega}_i \bar{Y}_{i, post} - \sum_{i=1}^{N_{co}} \sum_{t=1}^{T_{pre}} \hat{\omega}_i \hat{\lambda}_t Y_{it} \right)$$(B.4)

Here, the first term represents the change in the treated units (post-treatment vs. weighted pre-treatment), and the second term represents the change in the synthetic control unit (weighted post-treatment vs. weighted pre-treatment). By utilizing $\hat{\omega}$ and $\hat{\lambda}$, SDiD ensures that this double-difference is calculated between groups that are comparable in both their unit-specific trends and their time-specific dynamics.

B.2.3 Bootstrap Inference for City-Level SDiD Estimates

When estimating the effect of the NCAP at the level of a single city, the treated group contains only one observational unit. In such cases, standard asymptotic results for the SDiD estimator do not apply, since consistency and normality require a growing number of treated units. As noted by Arkhangelsky et al. (2021), the jackknife variance estimator proposed for multi-unit treatment is therefore unsuitable in this context. Instead, inference must rely on resampling methods that emulate the sampling uncertainty arising from the donor pool.

To conduct valid inference for city-specific estimates, this study employs a cluster bootstrap in which untreated sub-districts within the same airshed form the resampling clusters. This design preserves the spatial dependence structure inherent in Indian air pollution, which is shaped by regional meteorological and topographical conditions. The bootstrap procedure proceeds in four steps:

1. Resampling. For each replication $b = 1, \ldots, B$, a new donor pool is drawn by sampling untreated units from the same airshed with replacement. This resampling produces a synthetic donor set of the same size as the original, but with some clusters repeated and others omitted.

2. Re-estimation. Using this resampled donor pool, the SDiD estimator is recomputed, yielding a bootstrap estimate $\hat{\tau}_b$. Each replication reflects how the estimated treatment effect might differ if the donor pool were altered due to sampling variation.

3. Variance estimation. The bootstrap standard error is calculated as the sample standard deviation of the $B$ bootstrap estimates (Efron & Tibshirani, 1993): $$\widehat{SE}_{boot} = \sqrt{ \frac{1}{B - 1} \sum_{b = 1}^{B} \left( \hat{\tau}_b - \bar{\tau} \right)^2 },$$ where $\bar{\tau} = \frac{1}{B} \sum_{b=1}^{B} \hat{\tau}_b$. This formulation provides a direct approximation of the estimator’s sampling variability (Arkhangelsky et al., 2021).

4. Confidence intervals. Ninety-five per cent confidence intervals are constructed using the normal approximation, $$\hat{\tau} \pm 1.96 \cdot \widehat{SE}_{boot},$$ which is appropriate when the bootstrap sampling distribution is approximately symmetric. Simulation evidence in related applications suggests that this approximation performs well for city-level SDiD estimation.

This bootstrap procedure serves two functions. First, it provides a principled approximation of the sampling variability of the SDiD estimator when the treated sample contains only one unit. Second, by resampling at the airshed level, it preserves the regional correlation patterns that characterise Indian pollution dynamics, ensuring that inference remains robust to spatial dependence. The resulting standard errors thus represent the uncertainty associated with constructing a synthetic counterfactual for each treated city given the available donor pool and the underlying meteorological structure.

B.3 Fit Check for Synthetic Controls

The use of the $RMSPE^{trend}$ statistic, rather than the standard RMSPE calculated on raw outcome levels, is motivated by the specific algebraic properties of the Synthetic Difference-in-Differences (SDiD) estimator.

As defined in Arkhangelsky et al. (2021) [4089], the SDiD estimator obtains the treatment effect ($\tau$) by solving a weighted two-way fixed effects regression problem: $$(\hat{\tau}^{sdid}, \hat{\mu}, \hat{\alpha}, \hat{\beta}) = \operatorname*{argmin}_{\tau, \mu, \alpha, \beta} \left\{ \sum_{i=1}^{N} \sum_{t=1}^{T} \left( Y_{it} - \mu - \alpha_i - \beta_t - W_{it}\tau \right)^2 \hat{\omega}_i^{sdid} \hat{\lambda}_t^{sdid} \right\}$$ Crucially, this specification includes a unit fixed effect, $\alpha_i$. Arkhangelsky et al. (2021) [4102] explicitly note that this inclusion makes the estimator invariant to additive unit-level shifts. That is, if the underlying systematic component of the outcome $L_{it}$ is modified such that $L_{it} \leftarrow L_{it} + \nu_i$ for any unit-specific constant $\nu_i$, the resulting estimator $\hat{\tau}^{sdid}$ remains unchanged.

This property implies that the SDiD estimator does not require the synthetic control to match the levels of the treated unit, provided it matches the trends (dynamics). A standard RMSPE calculation on raw levels would penalise a synthetic control that tracks the treated unit’s slope perfectly but sits at a different intercept (a constant vertical gap). Such a penalty would be econometrically invalid in this context, as the $\alpha_i$ term in the regression stage automatically absorbs this intercept difference.

Therefore, the $RMSPE^{trend}$ statistic is the appropriate diagnostic for this specific estimator. By removing the linear trend (or unit-specific means) from the pre-treatment series before calculating the error, this metric isolates discrepancies in the slope and curvature of the trajectory. A low value for $RMSPE^{trend}$ confirms that the unit weights ($\hat{\omega}$) have successfully constructed a counterfactual that satisfies the parallel trends assumption, which is the necessary condition for identification in difference-in-differences designs.

B.3.1 Formal Definition of $RMSPE^{trend}$ & Interpretation

Let $T_{pre}$ denote the number of pre-treatment periods and $N_{co}$ the number of control units. The average treated series ($Y^{tr}_t$) and the synthetic control series ($Y^{syn}_t$) in the pre-treatment period are defined as:

$$Y^{tr}_t = \frac{1}{N_{tr}} \sum_{i=N_{co}+1}^{N} Y_{it}, \qquad Y^{syn}_t = \sum_{j=1}^{N_{co}} \hat{\omega}_j Y_{jt}, \qquad t = 1,\dots,T_{pre}.$$(B.5)

Step 1: Remove linear trends

To isolate the temporal dynamics from the level differences, each series is detrended by regressing it on a linear time trend using Ordinary Least Squares (OLS).

For the treated series: $$Y^{tr}_t = \hat{\alpha}_{tr} + \hat{\beta}_{tr} t + \hat{\varepsilon}^{tr}_t,$$(B.6)

and for the synthetic series: $$Y^{syn}_t = \hat{\alpha}_{syn} + \hat{\beta}_{syn} t + \hat{\varepsilon}^{syn}_t.$$(B.7)

The estimated detrended residuals are given by: $$\hat{\varepsilon}^{tr}_t = Y^{tr}_t - (\hat{\alpha}_{tr} + \hat{\beta}_{tr} t), \qquad \hat{\varepsilon}^{syn}_t = Y^{syn}_t - (\hat{\alpha}_{syn} + \hat{\beta}_{syn} t).$$

These residuals correspond exactly to the output of the resid() function in the R implementation used in this study.

Step 2: Compute the divergence between detrended series

The detrended RMSPE is then defined as the root mean squared difference between these residuals:

$$RMSPE^{trend} = \sqrt{ \frac{1}{T_{pre}} \sum_{t=1}^{T_{pre}} \left( \hat{\varepsilon}^{tr}_t - \hat{\varepsilon}^{syn}_t \right)^2 }.$$(B.8)

Interpretation

The $RMSPE^{trend}$ statistic quantifies the average deviation between the temporal dynamics of the treated and synthetic series, ignoring static level differences. A value close to zero confirms that the pre-treatment trends are parallel, thereby satisfying the specific identification condition required for the SDiD estimator.

Given the average baseline PM$_{2.5}$ concentration of 56.4 $\mu g/m^3$ for Control Group 1, this study establishes quantitative benchmarks to assess the quality of the synthetic counterfactual. Specifically, we define an $RMSPE^{trend} \leq 0.5$ as an "Excellent Fit", corresponding to a relative deviation of less than 0.9% from the mean pollution levels. Similarly, a value falling within the range $0.5 < RMSPE^{trend} \leq 1.0$ is classified as a "Very Good Fit", representing a relative error of approximately 1.8%. These statistical thresholds, supplemented by visual identification of the trajectories, confirm that the synthetic control reproduces the slope and curvature of the treated series with high fidelity, ensuring the validity of the causal inference.

B.4 Derivation of the Weighted Least Squares Estimator

B.4.1 Motivation: The Problem of Heteroskedasticity

In the meta-regression analysis, the dependent variable is not a raw observation but an estimated parameter, $\hat{\tau}_i$ (the SDiD treatment effect for city $i$). Because these estimates are derived from synthetic controls with varying goodness-of-fit and different underlying sample sizes, they possess different degrees of statistical precision.

Let the true relationship between the treatment effect $\tau_i$ and the fund utilisation ratio $R_i$ be linear: $$\tau_i = \alpha + \beta R_i + u_i$$(B.9) However, we do not observe $\tau_i$; we observe an estimate $\hat{\tau}_i = \tau_i + e_i$, where $e_i$ is the sampling error. Substituting this into the model yields: $$\hat{\tau}_i = \alpha + \beta R_i + (u_i + e_i) = \alpha + \beta R_i + \varepsilon_i$$(B.10) Here, the composite error term $\varepsilon_i$ includes the sampling error $e_i$. Since the variance of the sampling error depends on the precision of the SDiD estimate for city $i$ (denoted as $SE_i^2$), the variance of $\varepsilon_i$ is not constant across cities: $$\text{Var}(\varepsilon_i) = \sigma^2_i$$(B.11) This violation of the homoskedasticity assumption ($\text{Var}(\varepsilon_i) = \sigma^2$) renders the standard Ordinary Least Squares (OLS) estimator inefficient, although it remains unbiased (Wooldridge, 2020263). OLS treats a noisy estimate from a city with a poor synthetic fit as equal to a precise estimate from a city with an excellent fit. To correct for this and obtain the Best Linear Unbiased Estimator (BLUE), we employ Weighted Least Squares (WLS).

B.4.2 Derivation of the WLS Estimator

The WLS estimator minimises the weighted sum of squared residuals (WSSR), assigning higher influence to observations with lower variance (higher precision). Let $w_i$ be the weight assigned to city $i$. The objective function to minimise is: $$S(\alpha, \beta) = \sum_{i=1}^{N} w_i \left( \hat{\tau}_i - \alpha - \beta R_i \right)^2$$(B.12) In our specific application, following standard meta-analytic practice (Stanley & Doucouliagos, 201261), we define the weights as the inverse of the variance of the estimated treatment effect: $$w_i = \frac{1}{SE(\hat{\tau}_i)^2}$$(B.13) This weighting scheme ensures that cities with precise estimates contribute more information to the regression line.

Solving for the Coefficients

To find the optimal estimators $\hat{\alpha}_{WLS}$ and $\hat{\beta}_{WLS}$, we take the partial derivatives of $S(\alpha, \beta)$ with respect to $\alpha$ and $\beta$ and set them to zero (First Order Conditions).

1. Derivative with respect to $\alpha$: $$\frac{\partial S}{\partial \alpha} = -2 \sum_{i=1}^{N} w_i (\hat{\tau}_i - \hat{\alpha} - \hat{\beta} R_i) = 0$$(B.14) Dividing by $-2$ and rearranging: $$\sum w_i \hat{\tau}_i = \hat{\alpha} \sum w_i + \hat{\beta} \sum w_i R_i$$(B.15) Dividing by $\sum w_i$, we obtain the solution for the intercept in terms of the weighted means: $$\hat{\alpha} = \bar{\tau}_w - \hat{\beta} \bar{R}_w$$(B.16) where $\bar{\tau}_w = \frac{\sum w_i \hat{\tau}_i}{\sum w_i}$ and $\bar{R}_w = \frac{\sum w_i R_i}{\sum w_i}$ are the weighted averages of the treatment effects and utilisation ratios, respectively.

2. Derivative with respect to $\beta$: $$\frac{\partial S}{\partial \beta} = -2 \sum_{i=1}^{N} w_i R_i (\hat{\tau}_i - \hat{\alpha} - \hat{\beta} R_i) = 0$$(B.17) Substituting $\hat{\alpha}$ from Equation (B.16) into this expression: $$\sum w_i R_i (\hat{\tau}_i - (\bar{\tau}_w - \hat{\beta} \bar{R}_w) - \hat{\beta} R_i) = 0$$(B.18) Rearranging terms to group by $\hat{\beta}$: $$\sum w_i R_i (\hat{\tau}_i - \bar{\tau}_w) = \hat{\beta} \sum w_i R_i (R_i - \bar{R}_w)$$(B.19) Solving for $\hat{\beta}_{WLS}$: $$\hat{\beta}_{WLS} = \frac{\sum_{i=1}^{N} w_i R_i (\hat{\tau}_i - \bar{\tau}_w)}{\sum_{i=1}^{N} w_i R_i (R_i - \bar{R}_w)}$$(B.20) Alternatively, this can be written using centered variables as: $$\hat{\beta}_{WLS} = \frac{\sum_{i=1}^{N} w_i (R_i - \bar{R}_w)(\hat{\tau}_i - \bar{\tau}_w)}{\sum_{i=1}^{N} w_i (R_i - \bar{R}_w)^2}$$(B.21)

B.4.3 Economic Interpretation

The derived coefficient $\hat{\beta}_{WLS}$ provides a precision-weighted estimate of the policy’s implementation elasticity. Specifically, it measures the expected change in PM$_{2.5}$ concentration ($\hat{\tau}$) associated with a marginal increase in fund utilisation ($R$), conditional on the statistical reliability of the underlying city-level estimates.

By explicitly down-weighting observations with large standard errors, this estimator isolates the signal from the noise. A statistically significant negative $\hat{\beta}_{WLS}$ would imply that financial execution is a binding constraint on air quality improvement. Conversely, a null result ($\hat{\beta}_{WLS} \approx 0$) would indicate that the effectiveness of the NCAP interventions is uncorrelated with the intensity of their funding, suggesting structural limitations in the policy design itself rather than failures of implementation capacity.

Appendix C Supplementary Results

This appendix presents supplementary empirical findings and extended robustness checks to further validate the primary analysis.

C.1 Moran’s I Test Results

Table C.1 reports the full statistical output for the Global Moran’s I test. The extremely high Z-score (116.8) confirms that the clustering of PM$_{2.5}$ across Indian sub-districts is statistically significant and highly unlikely to be the result of a random spatial process.

C.2 Placebo Treatment-Year Diagnostics for the TWFE DiD Model

As an additional robustness diagnostic for the identification strategy underlying the TWFE DiD estimator, a series of placebo treatment-year regressions were performed on the Control Group 1 (Population > 100,000 & Population Density > 400). In these exercises, the actual intervention year of 2019 was replaced with placebo treatment years in the pre-policy period (2015, 2016, and 2017), while maintaining identical sample restrictions, fixed effects, and estimation procedures as used in the equation (3.2). If the parallel trends assumption were satisfied, these placebo regressions should return coefficients that are statistically indistinguishable from zero, since no policy was implemented in those years.

Table C.2 summarises the estimated placebo ATTs. The placebo ATTs are both large in magnitude and highly statistically significant, despite the fact that the NCAP had not yet been introduced during these years. Moreover, their values closely align with the main DiD estimate (1.79 $\mu$g/m$^{3}$), demonstrating that the TWFE model would have detected a “treatment effect” even in a period where no policy existed. This behaviour indicates that treated and control cities were already on systematically diverging trends in the pre-intervention period.

These findings reinforce the evidence presented in the event-study analysis in Chapter 4, which likewise displayed substantial pre-treatment deviations from zero and provide clear confirmation that the parallel trends assumption is violated. The TWFE DiD estimator therefore attributes long-standing structural differences in pollution trajectories to the NCAP, and therefore cannot credibly identify the causal impact of the programme.

C.3 Placebo Treatment-Year Diagnostics for Regional SDiD

This appendix presents placebo treatment-year diagnostics for the regional SDiD estimates. For each airshed region, the actual NCAP treatment year (2019) was replaced with fictitious treatment dates in the pre-policy period (2010, 2012, 2014, 2015, 2016, and 2017). Under a valid identification strategy, these placebo interventions should yield treatment effects that are statistically indistinguishable from zero, as no treatment occurred in those years.

Table C.3 reports the estimated placebo Average Treatment Effects (ATTs), standard errors, and 95% confidence intervals for all regions. The results demonstrate that the Central, South, West, and North-East & East regions exhibit placebo ATTs that are small in magnitude and imprecisely estimated, with confidence intervals consistently overlapping zero. This pattern indicates that the regional donor pools provide credible counterfactuals and that SDiD effectively reproduces the pre-treatment evolution of PM$_{2.5}$ in these regions.

In contrast, the IGP displays several statistically significant placebo effects, ranging from 0.33 to 0.85 $\mu$g/m$^{3}$, which is consistent with the substantial pre-trend divergence documented in Chapter 4. This behaviour suggests that the IGP remains too heterogeneous for SDiD to fully reconstruct the underlying pollution trajectory, even after regional stratification.

The placebo results demonstrate that, with the exception of the IGP, regional S-DiD models satisfy the key identifying assumption that no spurious “effects” should be detected in pre-treatment periods. This strengthens the credibility of the regional estimates presented in Section [subsub:sdid_regional].

C.4 City-level SDiD Results

Complete City-Level SDiD Estimates