Does Air Pollution Lower Productivity? Evidence

from Manufacturing in India

Jamie Hansen-Lewis

Brown University

March 2, 2018

Abstract

I estimate the effect of air pollution on firms in India using wind velocity as an instru-

ment for pollution. With satellite-derived pollution and firm panel data, I detect sensitivity

among labor intensive industries yet I find no meaningful average effect. To explain this

variance, I estimate a model of profit maximization that incorporates pollution into produc-

tion. The model implies varying input intensities contribute to heterogeneity. I estimate a

one unit increase in aerosols diminishes returns to labor by 14 percent relative to other in-

puts. I show excess pollution results in costly output reductions among sensitive industries

but little reduction overall.

I would like to thank Andrew Foster, Matt Turner, Jesse Shapiro, Ken Chay, Lint Barrage, Daniel Bjorkegren,

David Glick, Stefano Polloni, Will Violette, and participants of the Brown Development Economics Break-

fast and Applied Microeconomics Lunch for helpful feedback. All mistakes are my own. Contact: jamie_

hansen-lewis@brown.edu.

1

1 Introduction

Counteracting negative externalities is a primary rationale for government regulation. It is often

the case that the burden of an externality is not shared equally. When the burden is severe for

particular groups, lack of knowledge of how the costs are distributed and which groups are

adversely affected could lead to inaccurate assessments that overstate the cost or fail to find any

cost. Moreover, the social costs of correcting such externalities could be substantially lower

under policies that target groups with the greatest marginal social benefit relative to policies

that ignore the distribution of marginal social benefits.

An important externality with these features is air pollution from manufacturing. Among

manufacturing firms exposed to air pollution, many face losses from sick workers even as others

benefit from foregoing abatement investments. Air pollution may present little overall cost to

industry if the sensitive firms account for a small portion of output or invest in adaptations.

Alternatively, air pollution may be very costly to industry if output reductions amplify the shock

of unhealthy workers. Thus, to understand the economic costs of air pollution it is important to

consider the diverse effects across industries over time.

In this paper, I ask whether air pollution affects manufacturing productivity in India and

how much industries vary in their sensitivity to air pollution. In this setting, exposure to high

pollution is so prevalent that firms from a wide range of industries risk losses from unhealthy

workers. Air quality does not meet the World Health Organization (WHO) standards for 99.5

percent of the population and the pollution results in premature deaths totaling 2.1 billion life

years (Greenstone et al., 2015). The health toll of air pollution in India is estimated to be around

8 percent of GDP (World Bank, 2016). Further, public and political attention to improving air

quality is considerable.1 Existing regulations are weak (Duflo et al., 2013, 2014) and industries

stand to benefit from productivity improvements because productivity lags behind developed

countries (Bloom et al., 2010; Hsieh and Klenow, 2009).

While it is plausible the economic implications of air pollution in India are meaningful, I

model how health damages from pollution are reflected in manufacturing production to deter-

mine an appropriate benchmark. A challenge of assessing the costs is defining a reasonable

measure of sensitivity. Candidate measures such as changes in output or average output per

unit labor conflate the impact of pollution on production with changes in input prices. To un-

derstand sensitivity, I present a model of production where the returns to inputs are a function

1Economic Times Bureau (2014); Moham (2015)

2

of air pollution. Assuming a Cobb Douglas form of production, air pollution is allowed to re-

duce the portion of each input that contributes to output. The model shows that the effect of air

pollution on total factor productivity reflects its impact on input returns without the additional

price effects present in the effect of air pollution on output and average product of labor. The

key prediction of the model is that the overall effect of pollution on productivity is its effect on

the return to each input to production weighted by the factor shares.

To estimate the model, I use a panel survey of manufacturing firms in India. I observe firms

annually from 2001 to 2010 in the Annual Survey of Industries (ASI). While the data report the

value of output and inputs, productivity is not readily observable. I use methods developed in

Ackerberg et al. (2015) to obtain estimates of the factor shares and calculate productivity. The

approach relies on the assumption that firms determine the optimal capital inputs without full

knowledge of future productivity.

Given an appropriate definition of sensitivity, the measurement of how air pollution affects

productivity is not straightforward. Poor measures of air quality and confounding factors are

two challenges I address. Comprehensive measures of air pollution are not generally available

during the period of study. The network of public air pollution monitors in India is limited to

140 cities before 2008, leaving large geographic areas where pollution might take effect unob-

served (Greenstone and Hanna, 2014; Greenstone et al., 2015). In lieu of monitor data, I use

satellite derived measures of air quality from Moderate Resolution Imaging Spectroradiometer

(MODIS) Aerosol Optical Depth (AOD). AOD is a strong proxy of particulate matter over India

(Dey et al., 2012) and daily measurements at fine spatial resolution are available for the entire

firm sample.

Moreover, even with perfect data, it is difficult to estimate the causal effect of pollution on

productivity. Pollution and production are both functions of productivity. For example, after a

productivity rise a polluting firm would increase production, which in turn increases pollution.

In the same vein, low productivity firms plausibly use outdated production technology that

lowers productivity and increases pollution regardless of the incidence of pollution from other

sources. To accurately measure the impact of pollution, the econometrician requires a source of

variation in pollution intensity that is plausibly exogenous to productivity.

I measure the impact of air quality on productivity with an instrumental variables estimation

strategy. I isolate variation in pollution unrelated to industrial productivity with annual average

wind speed. The wind data come from an atmospheric reanalysis model, the European Centre

for Medium-Range Weather Forecasts (ECMWF) ERA-Interim (Dee et al., 2011). The data

3

show that wind velocity is strongly negatively correlated with aerosols because wind disperses

emitted particulates. I perform additional tests to show that the wind velocity is not correlated

with productivity except through its effect on pollution.

Last, I allow the impact of pollution to differ across industries and quantify how hetero-

geneity in sensitivity affects the predicted costs of air pollution. With industry-level sensitivity

parameters, I perform an empirical Bayes shrinkage to determine the underlying sensitivity dis-

tribution. Further, I estimate the effect of air pollution on the returns to labor relative to capital

and materials from the industry-level sensitivity parameters. I test the hypothesis that labor

inputs are the most sensitive to air pollution. Finally, I examine the impact of air pollution on

input demand and output.

The results indicate that the impact of air pollution on productivity is diverse and occurs

primarily via labor inputs. I fail to detect a significant average effect of air pollution on pro-

ductivity. The confidence interval is precise enough to exclude previous estimates of the effect

of air pollution on labor productivity. Estimation of the sensitivity distribution shows variation

in sensitivity across industries and indicates that industries accounting for 39 percent of output

are sensitive. I find that sensitivity is significant among labor intensive firms. Industries with

large labor shares are the most susceptible to air pollution because pollution lowers the returns

to labor. I find that a one percent increase in aerosols reduces the portion of hired labor that

contributes to output around 15 percent relative to other inputs. Further, I find evidence that

pollution results in adjustments to input, output, and wages. Across all manufacturing indus-

tries, reducing air pollution to the WHO standard would not have led to a significant increase in

output, but among sensitive industries it would have led to increases as high as 1.5 percent.

This paper contributes the first evidence of impacts of air pollution representative of the

entire manufacturing sector. To substantiate this contribution, the paper makes four primary

advances from prior studies. First, it considers how pollution affects the production function

and production function estimation. In contrast to previous research, the model permits firms

to adjust the quantity of pollution-sensitive inputs. Second, rather than examining the instanta-

neous impact of pollution on output, this paper explores the effect of increasing the annual mean

pollutant concentration measured over a decade. Third, previous literature relies on the premise

that short-term fluctuations in pollution are quasi-random; however, this does not address the

possibility that firms sensitive to average pollutant exposure locate away from sources or oth-

erwise adapt. The instrumental variables approach in this paper addresses selection bias from

firms’ anticipation of damages. Last, the evidence of long term manufacturing-wide impacts in

4

this paper is an important improvement because the set of industries in an economy exhibits a

broad range of production technologies and each industry faces unique risks from air pollution.

I show that studies of a particular industry are not representative of the overall manufacturing

sector.

While wind has been previously used as an instrumental variable, the formulation I employ

is novel. Schlenker and Walker (2015); Sullivan (2015) use the direction of wind at pollution

sources as variation for pollutant concentration at downwind destinations; by contrast, I rely

on the wind velocity at particular location for variation in pollutant concentration at the same

location. This approach draws on the same meteorological principals as Broner et al. (2012)

with only differences in the application. First, whereas I isolate wind velocity, Broner et al.

(2012) combine wind velocity with other meteorological factors for more generalized variation.

Second, Broner et al. (2012) use a long-term average of meteorological factors as an excluded

instrument for cross-sectional variation in countries’ regulation; however, I use annual wind

velocity as an excluded instrument for panel-variation in within-country air quality.

This paper joins two central questions in the study of development and environmental eco-

nomics. In development economics, much concern has been placed on the causes for low pro-

ductivity in Indian manufacturing (Allcott et al., 2016; Hsieh and Klenow, 2009; Bloom et al.,

2012), and this paper adds to evidence of barriers to production in the developing country con-

text. In environmental economics, a key concern has been measuring the costs of poor air qual-

ity. Hedonic methods have been central in quantifying these impacts (Chay and Greenstone,

2003, 2005) and demonstrated that home-buyers perceive substantial risks from air pollution.

Previous research on worker productivity has further substantiated the premise that air pollu-

tion has meaningful impacts on how workers perform in the United States (Chang et al., 2016;

Graff Zivin and Neidell, 2012; Walker, 2013; Shapiro and Walker, 2015), China (Chang et al.,

2016), Mexico (Hanna and Oliva, 2015), and India (Adhvaryu et al., 2014). While existing

work has demonstrated a pollution productivity relationship in diverse settings, prior estimates

report the impact of pollution for individual workers with detailed data at a single firm and short

term exposure to air pollutants. By contrast, this paper comprehensively estimates the effect of

pollution on productivity across all manufacturing industries in a developing country.

5

2 Data and Background

2.1 Firm Survey

Data on firms are from the Annual Survey of Industries (ASI), a large administrative survey on

firms in India. The ASI is a panel of all registered firms for 1995-2011. I employ a 10 year

sample from 2000-2001 to 2009-2010 inclusive. While unregistered firms evade the sampling

frame, the sample covers roughly 42 percent of firms and the missing firms tend to be small and

contribute little to value added (Nagaraj, 2002). Further, the ASI provides the most comprehen-

sive source available on firm attributes in this context. The data have been used previously to

study the productivity of Indian industry in Allcott et al. (2016) and Hsieh and Klenow (2009).

I made several important decisions in the preparation of the data.2 First, the data do not

distinguish a plant from a firm so I assume they are equivalent. Second, I weighted the data to

be representative of the firm population. For the most part, firms with over 100 employees were

surveyed every year and smaller firms were surveyed according to a random sample. However,

the details of the sampling design changed from year to year. As a result, I weight firms by the

average value of the weighting variable over the time periods. I report robustness checks to show

that the results are not sensitive to the firm weights. Third, the classification of industries and

industry codes changed twice during the sample so I aligned them manually. Fifteen industries

did not include enough firms to estimate the capital factor share. After this procedure, my

sample included 138 unique industries.

From the firm observations, I construct the location, inputs, and output of each firm for

each year. The firm observations can be located geographically in one of 520 districts, the

administrative division below a state. I map all observations to 2001 administrative districts via

name and 2001 census code because the district boundaries changed during the period of study.

After 2009-2010, the ASI no longer reports the district so I include only the prior periods in

the analysis. The main variables are the gross revenue, capital stock, labor cost, input materials

cost, investment, and number of workers. Since firms report the monetary values of inputs and

outputs instead of quantities, I deflated monetary amounts to quantities. Further, outliers were

removed to correct irregularities. I report firm descriptive statistics of firms in the sample in

Table A1.

2I replicate the preparation of Allcott et al. (2016). I repeat their procedures to align industrial codes to the

classification of 1987 at the 3-digit level, deflate values to quantities, and remove outliers.

6

2.2 Air Quality

Information on air quality was obtained from Moderate Resolution Imaging Spectroradiometer

(MODIS) Aerosol Optical Depth Product 3. Aerosols are measured from the MODIS Terra and

Aqua platforms. MODIS features a 2330km wide swath, twice daily coverage, and high spectral

resolution which enables it to detect clouds and aerosols better than previous instruments. The

data have a spatial resolution of 10 km per pixel. MODIS reports AOD on a log scale of 0 to

5. AOD below 0.1 is considered to be clear and the maximum possible of 5 means that sunlight

cannot pass through the air. Since AOD is already on a log scale, I do not perform a subsequent

log transformation of the data.

There are several important differences between AOD and traditional air quality monitor

data. First, while air quality monitors track a variety of pollutants, aerosols measure only sus-

pended particulates. AOD is not representative of other pollutants such as ozone or sulfur and

nitrogen oxides. Relatedly, satellite observations only make coarse characterizations of the

aerosol type, such as dust, sulfate, smoke, or mixed. Second, whereas monitors are on the sur-

face, a high measurement of AOD does not necessarily imply that there was high exposure to

aerosols at the surface. AOD data do not resolve the distribution of aerosols in the atmospheric

column. Last, monitors are available for only a limited set of locales in India; by contrast, AOD

offers universal spatial coverage at a high temporal frequency.

Despite the differences, AOD is a valid and well-established proxy for surface air quality.

Research in atmospheric science has validated MODIS AOD as a measure of ground-level fine

particulate matter globally as well as over India.4 To supplement these studies, I conducted a

validation where I demonstrate strong correlation between the AOD and the level of suspended

particulate matter (SPM) from the air pollution monitor sample in Greenstone and Hanna (2014)

(see Figure 1). These findings indicate that AOD captures the variation in air quality of primary

interest with the additional advantages of consistent measurement and universal spatial coverage

over the period of study.5 Furthermore, economics research on the health effects of air pollution

and other topics has previously employed MODIS AOD (Foster et al., 2009; Greenstone et al.,

2015; Gendron-Carrier et al., 2017).

As further grounds for using AOD, I find that the AOD data are consistent with the main

3I used data from Gendron-Carrier et al. (2017). See Gendron-Carrier et al. (2017) for additional documenta-

tion.4See Remer et al. (2005, 2006); Ten Hoeve et al. (2012); Guazzotti et al. (2003); Dey et al. (2012).5In A1.2, I provide intuition for the aerosols calculation method and details of the construction of Figure 1.

7

Figure 1: Relationship Between AOD and Suspended Particulate Matter

02

00

40

06

00

80

0C

ity Y

ea

r M

ea

n S

PM

(m

icro

gra

m p

er

cu

bic

me

ter)

0 200 400 600 800 1000Mean AOD Within 10k

Note: Each dot represents a city and year observation from 2001-2014. SPM data from 140 cities in sample

from Greenstone and Hanna (2014). AOD data from MODIS. Non-parametric regression in solid line and linear

regression depicted with 95 percent confidence interval shaded.

descriptive features of air pollution in India. Figure 2 depicts the district mean AOD during the

period of study. Across India, AOD exceeds the clear air level of 0.1. The mean AOD is 0.41

(Table 1). Due to inversions and accumulation near the Himalayan mountains, air pollution is

much worse in the north. Urban centers also have poor air quality: the highest annual averages

are consistently in Delhi. Further, AOD data indicate that air quality has worsened substantially

during the period of study. Figure 3 depicts 2010 district mean AOD net the 2001 district

mean AOD. On average, AOD rose over 20 percent and many districts experienced even greater

increases.

2.3 Weather

I use atmospheric reanalysis data to measure annual mean wind velocity in lieu of weather

station monitors. Atmospheric reanalysis data are gridded records of meteorological variables

derived from both observational data and a meteorological model. The traditional approach to

construct wind data would be to collect observational data from weather stations and interpolate

the observations with a statistical procedure. Like the network of air quality monitors, public

weather station data for this setting is limited: wind is measured at least once per year at less

8

Figure 2: District Mean AOD 2001 - 2010

Note: Boundaries depict the 2001 districts of India. Shading represents the average of annual district AOD means

for ASI years 2000-2001 to 2009-2010. AOD data from MODIS.

Table 1: Summary of AOD and Weather

mean sd p10 p50 p90 count

AOD 0.41 0.17 0.22 0.37 0.67 4932

Wind Velocity (m/s) 1.70 0.83 0.78 1.46 2.83 4932

Precipitation (cm/month) 10.03 7.28 3.98 8.28 17.95 4922

Temperature (deg C) 25.43 2.90 23.53 25.83 27.58 4922

Vapor Pressure (hPa) 20.89 4.26 16.55 20.57 26.84 4932

Note: The unit of observation is the district-year. The sample includes all districts with a firm in the ASI panel years

2001-2010. AOD data are from MODIS. Wind velocity data are from Wentz and J. Scott (2015). Precipitation and

temperature data are from Willmott and Matsuura (2015). Vapor pressure data are from Harris et al. (2014).

than 150 stations in India in some years of the sample.6 Interpolation across stations could yield

substantial measurement error Dell et al. (2014).

6Available at http://www7.ncdc.noaa.gov/CDO/cdoselect.cmd.

9

Figure 3: Change in District Mean AOD 2001 - 2010

Note: Boundaries depict the 2001 districts of India. Shading represents the district mean AOD in ASI year 2009-

2010 minus the district mean AOD in 2000-2001. AOD data from MODIS.

Given the drawbacks to wind station data, there are two distinguishing advantages of reanal-

ysis data. First, while traditional gridded data interpolate observations with a statistical proce-

dure, reanalysis data interpolate observational data with a climate model (Dell et al., 2014). Sec-

ond, reanalysis data integrate more observational sources than an individual researcher could

possibly collect. The sources include radiosonde, satellite, buoy, aircraft and ship reports, and

other sources from within the area of interest and elsewhere (Dee et al., 2016). Reanalysis

data provide comparable measurements over the entire sample and are well-vetted in scientific

research (Dee et al., 2016, 2011).

Several surface wind products are available so I consult multiple sources to ensure accu-

racy. For the main dataset, annual mean surface wind velocity was constructed from ECMWF

10

Figure 4: District Average Absolute Percent Deviation From Mean Wind Velocity 2001-

2010

Note: Boundaries depict the 2001 districts of India. Shading represents the average percent of absolute deviation

from the district mean wind velocity from ASI year 2001-2001 to 2009-2010. Wind velocity data are from Wentz

and J. Scott (2015).

ERA-Interim (Dee et al., 2011).7 The dataset provides the monthly mean component vectors of

wind at 10 meters above the surface at approximately 0.75 degree girds. I calculate the mag-

nitude of the wind vector, wind speed, in each grid cell and average over the ASI year and

geographic district. As a robustness exercise, I repeat all the results with annual mean wind

velocity constructed from another prominent product, the National Centers for Environmental

Prediction (NCEP) and the National Center for Atmospheric Research (NCAR) Reanalysis 1

(Kalnay et al., 1996). Output reported in Appendix A1.3.

Annual variation is an important feature of wind in this setting. As with unseasonably warm

7I obtain the ERA-Interim monthly mean surface-wind from Wentz and J. Scott (2015).

11

or cold years, annual periods exhibit substantial variation in the average wind velocity. Figure

4 reports the average annual deviation from the mean wind velocity in the sample. The data

suggest that annual average wind velocity is fairly variable. The average annual percent change

in wind velocity was 3.6%. The annual wind velocity often deviated by over 10 percent of the

nine-year mean for many districts in the sample.

To improve the analysis of wind and air quality, I also employ data on temperature, precip-

itation, and vapor pressure. Temperature and precipitation were obtained as monthly mean and

monthly total respectively in 0.5 degree grids from Willmott and Matsuura (2015). Monthly

vapor pressure was also obtained in 0.5 degree grids from CRU TS Harris et al. (2014). The

process to obtain ASI year district means of the grids was the same as for wind and AOD. Table

1 reports descriptive statistics of wind and weather controls.

3 Production Model and Estimation

In this section, I model a Cobb-Douglas production function with pollution as a tool to un-

derstand how air pollution alters output and productivity. In the model, pollution distorts pro-

duction via the returns to inputs and the total factor returns. The observed total factor revenue

productivity is the underlying total factor revenue productivity net the effect of pollution on the

returns to inputs to production.

3.1 Production and Effective Inputs

Each firm f is a member of industry i, located in district d, and observed in year t. The inputs

to production are labor L, capital K, and materials M . Pollution, represented as aerosols A,

depletes the effectiveness of employed inputs. Production of observed revenue, Y , follows a

Cobb-Douglas function of inputs, aerosols, and TFPR Ω.

Yfidt =(

Aγ0Ωfidt

)

(AγLdt Lfidt)

βLit (AγKdt Kfidt)

βKit (AγMdt Mfidt)

βMit . (1)

The key alteration from the standard model in Equation 1 is that pollution determines the

returns to hired inputs to production. The portion of employed inputs that contribute to observed

output differed from hired inputs. For example, the labor contribution to output, AγLdt Lfidt, dif-

fers from hired labor Lfidt in that it is adjusted for distortions in the returns to labor. Distortion

in the returns to labor occurs when some of the hired labor does not contribute to production

12

(Greenstone et al., 2012). For example, if a salaried worker suffers from asthma on the job and

needs additional breaks, their contributing, or effective, labor is a portion AγLdt of their hired

labor.

The quantity of aerosols, A, and the elasticity of effective inputs with respect to pollution

γ determine the portion of hired inputs that contribute to output. For example, as aerosols

increase, AγLdt changes at rate γL, so a one percent increase in aerosols yields a γL percent

change in the portion of hired labor that contributes to output. I do not impose an assumption

that γ < 0. In addition to depleting the returns of inputs to production, pollution may affect non-

input components of production. Specially, pollution also affects the returns to productivity:

portion Aγ0 of TFPR Ωfidt contributes to output.

Pollution may still change aspects of firm behavior that are not reflected in production func-

tion parameters. For instance, as pollution rises firms might respond with a change in the quan-

tity of employed labor or reallocate from old to young workers. I outline the effect of pollution

on quantity of inputs, output, and profits in a subsequent section.

To define the effect of pollution on TFPR, I rewrite the production function after collecting

terms for aerosols:

Yfidt = Aλit

dt ΩfidtLβLit

fidtKβKit

fidt MβMit

fidt (2)

where

λit = γ0 + γLβLit + γKβKit + γMβMit. (3)

It follows that the observed TFPR is defined:

Ωfidt =Yfidt

LβLit

fidtKβKit

fidt MβMit

fidt

= Aλit

dt Ωfidt (4)

I rewrite the expression for TFPR in logs. I use lowercase variables to denote the log of each

quantity.

ωfidt = λitadt + ωfidt (5)

This equation shows that the measured log TFPR, ωfidt, is the log TFPR in absence of pollution,

ωfidt, net the effect of pollution on productivity via the effectiveness of inputs, λitadt. Formally,

impact of pollution on observed log TFPR is:

dωfidt

dadt= λit. (6)

This indicates that we can interpret the overall effect of pollution on TFPR, λit, as composed of

the impact on each input to production weighted by the factor shares.

13

3.2 Input Choice, Timing, and Production Function Estimation

The goal of this section is to outline the measurement of ω, βLit, βKit, βMit. I use the method

developed in Ackerberg et al. (2015) and Collard-Wexler and De Loecker (2016) with the main

assumptions are that firms maximize profits, labor and materials are a static inputs, capital takes

one period to build, and productivity follows AR(1) evolution.

Firms maximize profits:

Πfidt = Yfidt − pLfidtLfidt − pKt Kfidt − pMfidtMfidt (7)

where pLfidt, pKt , p

Mfidt represent prices for labor, capital, and materials respectively. For labor

and materials, firms maximize profits assuming perfectly competitive factor markets and no

adjustment costs. By contrast, firms need time to adjust capital inputs.

Static Inputs

At the optimal levels of labor and materials, the profit maximization first order conditions imply:

βLfidt =pLfidtLfidt

Yfidt

,

βMfidt =pMfidtMfidt

Yfidt

,

Since I observe cost of labor and materials for every firm, I computed the parameters βLfidt and

βMfidt directly from the formula for each firm. In the analysis that follows, I assign each firm

the industry median factor share with a time trend βLit and βMit to smooth over idiosyncratic

constraints to static profit maximization (Allcott et al., 2016; Syverson, 2011).

Non-Static Inputs

I wish to measure βKit; however, several sources introduce bias in the estimation. To begin,

the ASI does not include firm-level interest rates so the first-order condition approach would

introduce noisy proxies of investment costs. Relatedly, capital inputs are inherently difficult to

measure and measurement error in capital can introduce bias in productivity estimates (Collard-

Wexler and De Loecker, 2016). Further, any exit of unproductive firms would imply selection

bias. Data limitations aside, the assumption that firms create and destroy capital instantaneously

is implausible: it requires time to accumulate. It is also implausible to assume under profit max-

imization that capital inputs and productivity are exogenous. Under these conditions, neither

14

the first-order condition approach nor a regression of log output on log capital would produce

an unbiased estimate of the capital factor share.

To address these concerns, I use the instrumental variables approach of Olley and Pakes

(1996); Ackerberg et al. (2015) and Collard-Wexler and De Loecker (2016) to estimate the

capital share. I assume that the returns to capital do not change over time, βKit = βKi and I

take advantage of unanticipated productivity shocks and past investment to identify βKi.

I impose three assumptions on the joint evolution of productivity and capital accumulation.

First, capital takes one year to build. Current capital is a function, κ, of the previous period’s

capital and investment, ι, in logs.

kfidt = κ(kfidt−1, ιfidt−1). (A1)

(A1) is similar to the first-stage of an instrumental variables approach. Past investment predicts

future capital. Second, productivity follows an AR(1) process, with unanticipated shocks ξfidt:

ωfidt = ρωfidt−1 + ξfidt. (A2)

(A2) isolates the shocks to productivity ξfidt that firms are not aware of when they set capital

investment. While the AR(1) assumption is more restrictive than assuming capital follows a

first-order Markov process or generic non-linear process, it is common in previous estimation

with the ASI (see Collard-Wexler and De Loecker (2016); Allcott et al. (2016)). Last, firms

invest without full knowledge of transitory productivity shocks:

E(ξfidtιfidt−1) = 0. (A3)

(A3) is akin to the exclusion restriction of an instrumental variables approach. An important

implication of (A2) and (A3) for the research design is that the components of ξfidt cannot be

deterministic nor related to prior investment decisions.

Under these conditions, I estimate βKi for each industry i with Generalized Method of

Moments (GMM). I first rewrite production net the contributions of labor and materials:

yfidt = yfidt − βLitℓfidt − βMitmfidt

and I substitute so that for a given βKi

ωfidt = yfidt − βKikfidt.

15

Table 2: Estimation of Production Function Parameters

mean sd p5 p50 p95 count

ωfidt 2.45 1.16 0.57 2.38 4.51 207176

βLit 0.07 0.03 0.02 0.07 0.13 207176

βMit 0.70 0.10 0.55 0.69 0.91 207176

βKi 0.17 0.07 0.06 0.17 0.27 207176

CRS coef 0.95 0.05 0.85 0.95 1.01 207176

Note: The unit of observation is a firm-year. Data from Annual Survey of Industries 2001-2010. All statistics use

survey weights. CRS coefficient is the sum of βLit, βMit, and βKi.

Second, I estimate the AR(1) coefficient of productivity with ordinary least squares

ωfidt = ρωfidt−1 + ξfidt,

and compute the residuals ξfidt. Finally, drawing from the moment condition (A3), I select βKi

to minimize the criterion

Q(βKi) = (ι′ξ)′(ι′ι)−1(ι′ξ)

with ι = matrix of constant and ιfidt−1 and ξ = vector of ξfidt.8

Production Function Parameters

Table 2 summarizes the estimates of the production function parameters. The median labor

coefficient βLi is 0.07. The median capital coefficient βKi is 0.17. The average log total factor

revenue productivity, ωfidt, is 2.45. These estimates closely replicate prior estimates in this

sample (Allcott et al., 2016; Collard-Wexler and De Loecker, 2016).

3.3 Identification Using Wind Velocity

I wish to test whether λit < 0; however, a measurement problem arises. Specifically, were I

to estimate λit from a regression of equation 5, I would expect the residuals to be correlated

with pollution adt because higher productivity results in greater production and pollution is a

by-product of production. To address concern that pollution is a product as well as determinant

of productivity, I use wind velocity for as-if random assignment of air pollution. In this section,

I summarize the validity of this approach.

8The estimation is completed separately for each three digit industry. For example, for garment making, NIC =

265, there are 6573 firm-years of which 3639 have lagged capital, investment, and predicted productivity ω. Thus

ιfidt−1 is 3639 × 2 and ξfidt is 3639 × 1.

16

First Stage

There is a strong scientific rationale that wind velocity is a key factor in the atmospheric concen-

tration of particulates. Wind patterns determine how pollutants are disbursed both horizontally

and vertically once emitted. First, strong winds disburse pollutants over a wider horizontal area

than weak winds.9 Higher dispersion need not result in a linear relationship between wind ve-

locity and pollutants. For example, high winds might spread pollutants to locations excluded

from the sample, resulting in lower aerosol concentrations. They might also bring in more

pollutants from neighboring sources, resulting in higher aerosol concentration. Second, weak

winds enable the formation of steep temperature gradients that abate the vertical circulation

of air and keep pollutants trapped near the surface, called inversions (Jacob (1999), Chapter 4).

Thus, strong winds result in lower aerosol concentrations because they diminish the temperature

gradient at the location. Previous studies of air quality and meteorology in India and elsewhere

give credence to these principles (Guttikunda and Gurjar, 2012; Larissi et al., 2010; Arceo et al.,

2016).

Figure 5 displays histograms of log annual aerosol concentration for district years with

below the median log wind velocity and above the median log wind velocity respectively. The

figures show that the frequency of high AOD concentration observations is lower in the half of

the sample with high wind speeds. Moving from below to above the 50th percentile of log mean

annual wind velocity results in a 0.95 standard deviation decrease on average in annual mean

AOD.

Table 3 reports a robust negative correlation between annual mean wind velocity and AOD

in logs. I included additional controls, Xdt for the annual mean rain, temperature, and polyno-

mials of rain and temperature as well as fixed effects for the district, year, and state and linear

state trends. I found a significant negative effect of log annual wind velocity on log AOD: the

estimate implies that a one percent increase in log annual wind velocity results in an 0.11 per-

cent decrease in AOD. The effects are significant at the 1 percent level when clustering standard

errors by district.

For the main analysis, I use a semi-parametric instrumental variables method because the

relationship between air quality and wind velocity is not linear a priori. I estimate a non-

parametric first stage to determine the appropriate parametric specification. I provide the details

of the approach, which follows Robinson (1988), in Section A2.1. Figure 6 depicts the non-

9An accessible overview of atmospheric particulate transport, including the “Puff” model, in Jacob (1999)

Chapter 3.

17

Figure 5: Distribution of AOD By Low and High Wind Districts

0.5

11

.50

.51

1.5

-2 -1 0

Above median log wind velocity

Below median log wind velocity

De

nsity

Log AODGraphs by lwind_lo

Note: The unit of observation is a district-year. The sample includes all districts with a firm in the ASI panel years

2001-2010. AOD data are from MODIS. Wind velocity data are from Dee et al. (2011). The plot shows a histogram

of the district annual mean AOD for i) district-years above the median wind velocity and ii) district-years below

the median wind velocity.

parametric estimation of the relationship between air quality and wind velocity conditional

on the controls. The effect of log wind on log AOD is roughly linear and negative in the

range of most observations, -0.5 to 0.5, yet varies in steepness is not monotonic. Figure 6

also depicts the parametric relationship between wind velocity and AOD fitted with an eight

degree polynomial. While I reject the null that the nonparametric relationship and a parametric

eight degree polynomial relationship are equivalent (p = 0.02), the choice of polynomial degree

did not yield qualitative differences in the end results. To minimize misspecification bias and

improve precision, I employ an eight degree polynomial of log wind velocity in the first stage

of the subsequent results in lieu of a linear specification. The semi-parametric instrumental

variables did yield qualitative differences relative to the standard linear specification. I provide

comparisons with linear instrumental variables estimates for the main results and additional

robustness checks in Section A2.2.

18

Table 3: Linear First Stage Relationship Between AOD and Wind Velocity

(1) (2) (3)

Log AOD Log AOD Log AOD

Log Wind Velocity (m/s) -0.113 -0.113 -0.102

(0.0138) (0.0365) (0.0202)

Observations 4,922 4,922 2,732

R-squared 0.970 0.970 0.975

Weather controls Yes Yes Yes

Yield controls No No Yes

District fixed effects Yes Yes Yes

Year fixed effects Yes Yes Yes

State * year trends Yes Yes Yes

Clustering District State District

Note: The unit of observation is a district-year. The sample includes all districts with a firm in the ASI panel years

2001-2010. The dependent variable is the district annual mean AOD. Robust standard errors in parenthesis are

clustered by district.

Exclusion Restriction

The assumption underlying the instrumental variables approach is that annual mean wind ve-

locity is not correlated with productivity through channels other than air pollution. While it is

not possible to formally test the exclusion restriction, the assumption is justified for several rea-

sons. To begin, firms, politicians, and people cannot manipulate wind velocity. Even if sensitive

firms avoid pollution by locating upwind from a source, they cannot avoid changes in pollution

that arise from variable wind speeds. Furthermore, changes in wind velocity are difficult to

accurately predict. Some unpredictability is necessary because firms might still adjust produc-

tion based on the expected wind velocity even if they cannot change location. In the context

of the model, the annual mean wind velocity is part of the unanticipated shock to productivity

ξfidt. Since productivity shocks are unknown to firms when they determine capital investment,

annual mean wind velocity must be somewhat unpredictable and uncorrelated with investment

to be consistent with (A3).

Table 4 reports evidence that air quality, number of firms, and investment changes are not

predicted from past changes in wind velocity despite a modest degree of predictability in wind

velocity. In each column, I report the results of a regression with controls and lagged changes

19

Figure 6: Semi-Parametric Relationship Between AOD and Wind Velocity

-1.1

-1-.

9-.

8C

on

ditio

na

l L

og

AO

D

-1 -.5 0 .5 1 1.5Log Wind Velocity (m/s)

Binned Values Non-Parametric Predicted Values

Parametric Predicted Values

Note: The unit of observation is a district-year. The sample includes all districts with a firm in the ASI panel years

2001-2010. The dependent variable is AOD where variation from all control variables besides log wind velocity

was removed non-parametrically as in Robinson (1988). The diagram depicts i) scatter plot of conditional log

AOD and log wind velocity in bins of 20 observations, ii) non-parametric estimated relationship between log AOD

and log wind velocity, iii) eight-degree polynomial estimated relationship between log AOD and log wind velocity.

in log wind velocity as the explanatory variables of interest. Columns 1 and 2 report the effect

of the lags on the change in log wind velocity. Column 2 shows that the changes in log wind

velocity from t − 1 and t − 2 are significant predictors of the change in log wind velocity in t.

Still, the change in wind velocity from the past two periods along with the controls leaves

a substantial portion, about 45 percent, of the observed variation in wind velocity changes

unexplained. As further evidence of unpredictability, Columns 3 and 4 report the effect of

the lags on current change in log AOD. I observe that lagged changes in log wind velocity do

not provide consistent information on current changes in air quality: the model including an

additional lag of log wind velocity in t − 2 (Column 4) weakened the R2 relative to one lag

(Column 3). Additionally, Columns 5 and 6 report the effect of the lags on changes in district

mean firm investment. Analogously, Columns 7 and 8 show the effect for changes in the number

of firms. I failed to find evidence that investment decisions and firm presence were related to

changes in wind velocity. This evidence supports the assumption that knowledge of past wind

velocity does not change firms’ expectations of the future and resulting production decisions

20

Figure 7: The Effect of Wind Velocity on Productivity

-.6

-.4

-.2

0.2

.4L

og

win

d c

oe

fficie

nt

< -0.05 -0.05 - 0.25 0.25 - 0.65 0.65 - 0.85 0.85 - 0.95 0.95 - 1.05 1.05 - 1.15 > 1.15

Log Wind Interval

Point Estimate 95% CI

Note: The unit of observation is a firm-year. The sample includes firms in the ASI panel years 2001-2010. Each

point depicts the coefficient of log wind velocity from a regression of log TFPR for the subset of firms with mean

log wind velocity from 2001-2010 in the corresponding interval. Each regression includes controls for temperature,

precipitation, vapor pressure, and corresponding polynomials, and and fixed effects for the firm, year, state, and

state by year trends. All regressions use survey weights. Robust standard errors were clustered at the district level.

The error bars are ± 1.65 standard errors. A solid line at zero shows estimates that are significant at the 10% level.

(A3).

Another possible concern is that changes in wind velocity are related to meteorological or

socioeconomic factors that also affect productivity. I failed to find evidence that wind veloc-

ity is related to observable socioeconomic characteristics of districts that could influence total

factor productivity (Table A5). The most plausible channel to address is that wind is correlated

with temperature and rainfall and these variables influence productivity independently of air

quality. To account for such an effect, I include controls for flexible functions and interactions

of precipitation temperature in the analysis.

4 Impact of Air Pollution on Productivity

4.1 Reduced Form Estimates

Figure 7 shows the effect of wind velocity on TFPR. Each point depicts the coefficient from

a regression of TFPR, ωfidt, on log annual mean wind velocity for firms with average wind

21

Table 4: Statistical Properties of Wind Instrumental Variable

(1) (2) (3) (4)

Panel A: Log Wind Velocity Log Wind Velocity Log AOD Log AOD

Log Wind Velocity (m/s) t− 1, -0.425 -0.674 -0.0318 0.00922

(0.0118) (0.0171) (0.00838) (0.00935)

Log Wind Velocity (m/s) t− 2, -0.469 0.0453

(0.0151) (0.00976)

Observations 3,808 3,298 3,808 3,298

R-squared 0.399 0.552 0.340 0.314

(5) (6) (7) (8)

Panel B: Log Investment Log Investment Log Firm Count Log Firm Count

Log Wind Velocity (m/s) t− 1, -0.0359 -0.0631 -0.0206 0.0297

(0.252) (0.298) (0.0617) (0.0757)

Log Wind Velocity (m/s) t− 2, -0.265 0.0479

(0.273) (0.0589)

Observations 3,594 3,127 3,808 3,298

R-squared 0.080 0.102 0.177 0.192

Weather controls Yes Yes Yes Yes

District fixed effects Yes Yes Yes Yes

Year fixed effects Yes Yes Yes Yes

State * year trends Yes Yes Yes Yes

Note: The unit of observation is a district-year. The sample includes all districts with a firm in the ASI panel years

2001-2010. All models are estimated in differences and include fixed effects for the district, year, and linear state

by year trend. Controls for precipitation, temperature, vapor pressure, and their polynomials also included. The

dependent variable is indicated at the top of the column. Annual district investment is the sum of investment for

all firms located in d during year t in millions of Rupees adjusted for capital inflation. The independent variables

of interest are change in district annual mean log wind velocity in t− 1 in all columns and district annual mean log

wind velocity in t − 2 in columns (2), (4), (6), and (8). Robust standard errors in parenthesis are clustered at the

district level.

22

velocity in the corresponding interval. The plot shows that high winds significantly increased

TFPR in the range of around 0.85 to 1.05. In this interval, a one percent increase in wind

yielded a 0.13% increase in TFPR. At log wind velocity above 1.15, the same range where the

first stage is weak and positive, the plot shows that the reduced form is weak and potentially

negative. The correspondence in the functional forms is evidence that wind affects TFPR via

AOD because other factors are less likely to demonstrate this specific pattern. However, log

wind did not have a significant effect on TFPR in the interval of -0.05 to 0.85. Since the first

stage relationship is especially strong in this range (Figure 6) and the confidence intervals of

the reduced form estimates seem precise, this pattern indicates that wind does not effect TFPR

even if has a strong effect on AOD.

4.2 Instrumental Variables Estimates

To measure the average effect of pollution on productivity, I estimate the coefficient λ in the

regression:

ωfidt = α0 + λadt + α1φ(rdt) + α2Xidt + ffid + ǫfidt (8)

with log TFPR ωfidt, district-year log AOD adt, control function of first stage residuals φ(rdt),

firm fixed effects ffid, and other controls Xidt. I test if λ < 0 to evaluate if AOD reduces TFPR.

Several features of this specification are valuable to ensure consistent estimates. Following,

(Garen, 1984; Blundell and Powell, 2003), I present results with a control function of residu-

als from the eight degree parametric first stage estimation, rdt. Analogously, φ(rdt) is an eight

degree polynomial of the first stage residuals and interactions of residuals with AOD.10 The

inclusion of polynomials of residuals from the non-linear first stage ensures the estimates are

consistent relaxing the assumption that the relationship between unobserved variables contribut-

ing to pollution and the treatment is linear. Further, the addition of interactions of AOD with

polynomials of the residuals ensures the function controls for selection whereby the firms most

affected by pollution are exposed to less pollution.

In addition to the control function, the regression model includes firm fixed effects ffid

and controls Xidt. Firm fixed effects control for time invariant features of each firm that affect

productivity and might be correlated with air pollution, for example, the location and fixed

infrastructure. Fixed effects estimates reflect the impact of air pollution on productivity within

each firm over time. I also include the control variables Xidt for weather as well as fixed effects

10φ(rdt) = (1 + adt)∑8

k=1 rkdt

23

Table 5: Impact of AOD on Productivity

(1) (2) (3)

λ p-value N

(1) Baseline 0.08 0.49 202,053

(0.11)

(2) Linear IV -0.12 0.41 202,053

(0.15)

(3) No selection correction 0.09 0.45 202,053

(0.11)

(4) 2001 survey weights 0.04 0.72 202,053

(0.12)

(5) 2010 survey weights 0.08 0.48 202,053

(0.11)

(6) Constant returns to scale 0.03 0.76 202,053

(0.11)

(7) Ackerberg et al. (2015) 0.08 0.50 202,053

(0.11)

(8) Labor adjustment cost 0.10 0.38 201,660

(0.11)

(9) Low working days 0.14 0.58 46,979

(0.26)

(10) High working days 0.04 0.70 155,074

(0.11)

(11) Low AOD -0.00 0.99 113,771

(0.26)

(12) High AOD 0.25 0.10 88,282

(0.15)

Note: The unit of observation is the firm-year. The sample includes firms in the ASI panel years 2001-2010. Row (1) reports the AOD coefficient (column 1), p-

value (column 2), and sample size (column 3) from a regression of log TFPR (Equation 8). The coefficient standard error is reported in parenthesis beneath. Robust

standard errors were clustered at the district level. Row (2) repeats row (1) with a linear control function. Row (3) repeats row (1) without selection corrections in

the control function. Row (4) repeats row (1) with the firm survey weights from ASI 2000-2001. Row (5) repeats specification (1) with the firm survey weights

from ASI 2009-2010. Row (6) replicates row (1) under the assumption of constant returns to scale, βKi = 1 − βLi, with βLi computed as in the main body

of the text. Row (7) repeats specification (1) with the computation of capital factor share in Ackerberg et al. (2015). Row (8) repeats specification (1) with the

computation of the labor factor share with adjustment cost in Collard-Wexler and De Loecker (2016). Row (9) repeats row (1) with the subsample of firms in the

lowest 25% of days open and row (10) does so with the subsample of firms in the highest 75% of days open. Row (11) repeats row (1) with the subsample of firms

below the median air pollution and row (12) does so with the subsample of firms above the median air pollution. All regressions include controls for temperature,

precipitation, vapor pressure, and corresponding polynomials, and fixed effects for the firm, year, state, and state by year trends. All regressions use survey weights.

for the year, state, and state-time trends.

24

Table 5 presents the results of estimating λ. It begins with the main estimate from Equation

8 in Row 1. The estimated value implies a one percent increase in AOD resulted in a 0.08

percent increase in productivity. While the direction of the effect is counter-intuitive, the effect

is not statistically distinguishable from zero. Firm adaptations could result in a positive impact

of air pollution on measured productivity. For example, suppose a firm facing a pollution shock

has capital or labor stocks of heterogeneous quality. A possible adjustment would be for the

firm to keep the most healthy and unimpeded workers and retire its least efficient capital. These

contractions would increase the measured TFPR during a pollution shock.

The estimated λ remains statistically insignificant under several alternative assumptions. In

rows 2-11, I repeat the main regression given a linear control function, alternative definitions of

the survey weights, alternative assumptions while computing productivity, high and low work-

ing days, and high and low AOD in subsequent rows. Splitting the sample by high and low

working days shows that differences between seasonal and year-round firms are not driving the

result. Relatedly, similar estimates when splitting the sample by high and low AOD shows that

linear approximation of the AOD-productivity relationship is reasonable. In all scenarios, I fail

to detect a significant effect of AOD on manufacturing productivity.

Although statistically indistinguishable from zero, the estimated effect is informative. The

sample is large enough to distinguish small estimates from zero. As a general reference, un-

der a mean log productivity of 2.45 and standard deviation of 1.16, the minimum detectable

coefficient with 95 percent power and district clustering is 0.059, roughly three-quarters of the

estimate. So even with adequate power to detect a small effect and attention to eliminating the

main sources of bias, the data did not bear evidence that AOD lowers TFPR. It is necessary

to reference a benchmark to assess the precision of the 95 percent confidence interval (-0.14,

0.30). I outline comparisons to two estimates in the literature: the impact of electricity short-

ages on TFPR and the impact of particulate matter on worker productivity. In both cases, I find

the lower bound impact of an AOD shock on TFPR is of smaller absolute magnitude than the

comparison.

The confidence interval indicates air quality shocks have small effects on TFPR in compar-

ison to electricity shortages. I focus on the comparison to electricity shortages in Allcott et al.

(2016) because the setting, firm data, and definition of TFPR in Allcott et al. (2016) are nearly

identical to those in Table 5. With ASI data from an additional eight years, 1992-2010, Allcott

et al. (2016) find that a one percentage point increase in the probability of an electricity short-

age resulted in a -0.304 percent decrease in log TFPR, ω, with a 90 percent confidence interval

25

from -0.69 to 0.085.11 Taking the -0.304 percent decrease in log TFPR as the true effect of a

one percent point increase in the probably of a shortage, I note that this is below the analogous

lower bound elasticity estimate of -0.14 percent decrease in log TFPR for a one percent increase

in AOD. However, units of AOD are difficult to gauge. From the estimation of the relationship

between log AOD and ground-based particulate measures in Brauer et al. (2015), a one unit

increase in log AOD corresponds to a 0.7 increase in log fine particulate matter (PM2.5) µgm−3

concentration. The typical annual concentration of PM2.5 in Indian cities is about 46 µgm−3

(Greenstone et al., 2015; World Bank, 2016). This indicates that a rise of at least 0.7 µgm−3,

a 1.5 percent increase, in annual mean PM2.5 concentration has roughly the same detriment to

productivity as a one percentage point rise in the probability of an electricity shortage. Under

these assumptions, the confidence intervals exclude the possibility that increasing particulate

concentration up to 1.5 percent reduces productivity by as much as a one percentage point in-

crease in the probability of an electricity shortage.

Further, under some assumptions, the confidence interval excludes previous estimates of the

effect of air pollution on manufacturing worker productivity. I assess the estimate relative to

the effect of PM2.5 on pear packers in Chang et al. (2016) because it exemplifies the existing

research worker productivity impacts in manufacturing. There are still several important dif-

ferences to account for in a comparison. The setting is notably different: Chang et al. (2016)

consider the effect of PM2.5 at the level of the worker-day for a single firm at a single location

in California. Moreover, Chang et al. (2016) measure the effect of air quality on the average

revenue product of labor, denoted LP, whereas the outcome in Table 5 is total factor revenue

productivity, TFPR.12

To understand the differences between LP and TFPR estimates, I use the model for an

analytical comparison. The impact of log AOD on log LP is:dlog(LPfidt)

dadt=

d(yfidt−ℓfidt)dadt

. By

definition, LP differs from TFPR because the intensity of use of capital and materials alters LP

although TFPR is invariant (Syverson, 2011). Moreover, the derivative of LP with respect to

log AOD combines the impact of log AOD on log TFPR, λ, and the effects of log AOD on

input prices. The setting of Chang et al. (2016) indicates that the input prices did not change

in response to air pollution as input prices are unlikely to adjust over the course of a single

day. Assuming there is (1) no change in input prices as a result of air pollution and (2) constant

returns to scale, the impact of log AOD and log LP effects are equivalent. λ. I provide details

11For example, a rise of shortages from 7 percent of the time to 8 percent of the time.12LPfidt =

Yfidt

Lfidt.

26

of the comparison and an analytical derivation of the effects in A3.1.

The confidence interval excludes the possibility that TFPR effect is equivalent to the LP

effect in Chang et al. (2016). Chang et al. (2016) find that a one µgm−3 rise in PM2.5 con-

centration resulted in a 0.6 percent decrease in LP. Assuming (1) and (2), a decrease in LP is

equivalent to λ. The lower bound of the baseline in Table 5 indicates that a one µgm−3 rise

in PM2.5 concentration would yield at most 0.3 percent decrease, an effect roughly half the

magnitude of Chang et al. (2016).13

A zero effect does not imply that air quality is economically inconsequential. Several sce-

narios would result in an estimate of zero and it is necessary to disentangle these scenarios to

evaluate the impact of AOD. The first possibility is that there exists a mixture of sensitive and

insensitive firms in the sample. Supposing λ varies across industries, the average treatment ef-

fect could be zero. Such a scenario would mask economically important sensitivity to AOD if

the sensitive firms account for a disproportionate share of output. A second possibility is that

AOD is of such little detriment to capital and materials that a negative γL is offset by large

materials and capital shares. Equation 3 implies λ is the aggregate impact of aerosols on ωfidt

via effective input elasticities, (γA + βLitγL + βKitγK + βMitγM). Thus λ need not be signif-

icantly negative for aerosols to substantially deplete the effectiveness of labor inputs when the

capital and materials factor shares outweigh the labor factor share. A final possibility is that

firms employ costly adaptations, such as reducing output, even when the the effect of AOD on

TFPR over the course of a year is modest.14 Profit maximization implies that a small TFPR

shock could result in an even greater shock to output if input prices do not compensate. These

possibilities are not mutually exclusive.

For the remainder of the paper, I assess these hypotheses and evaluate the economic impact

of air pollution on manufacturing. I provide evidence on the extent of heterogeneity in the

effect of AOD on TFPR. I measure the elasticity of effective inputs with respect to pollution,

γL, γK , γM, and examine the importance of the factor shares in regulating these channels.

Last, I summarize the effect of an AOD productivity shock on input demand, output, and profit

and provide a rough estimate of aggregate cost of air pollution.

13I also estimateddlog(LPfidt)

dadtfrom a regression of log(

Yfidt

Lfidt) on AOD with ASI data (Table A6). I fail to reject

the estimate of Chang et al. (2016). I find a 0.13 percent decrease in LP for a one µgm−3 rise in PM2.5, just over

twice the 0.6 estimate of Chang et al. (2016).14Other unobserved and costly adaptations are also possible. Consider the manager reallocation of workers

across tasks during periods to high particulate matter at a South Asian textile firm in Adhvaryu et al. (2014).

27

5 Factors that Determine Variation in Pollution Sensitivity

5.1 Variance Estimation

In this section, I focus on quantifying the extent of heterogeneity in sensitivity to air pollution

across industries. I first measure the industry-specific impact of pollution on productivity for all

industries observed in the sample. I then present the distribution of the industry sensitivities.

To obtain industry-sensitivities, I repeat Equation 8 separately for each industry. This pro-

duces N = 132 coefficients λi.15 Among the industry-level sensitivities, the industries with the

most significantly negative sensitivity was sugar refining.

With the λi estimates, I estimate the distribution of λi. I employed the empirical Bayes

(EB) shrinkage method of (Morris, 1983) that is common in the value-added literature (Kane

and Staiger, 2002; Jacob and Lefgren, 2007; Chandra et al., 2016). Whereas the distribution of

the λi would include outliers that likely reflect noise; by contrast, the EB shrinkage of the λi

accounts for estimation error in the individual estimates to more accurately extrapolate the mean

and standard deviation of the underlying population. The EB estimates of industry sensitivity,

denoted λEBi , are the weighted average of λi and the overall mean.16 The weight on each

component varies by industry depending on the uncertainty of λi: the larger the standard error

of λi the more weight that is placed on the mean in lieu of λi.

Figure 8 reports the estimated distribution of λi weighting each industry by output. On

average there is no effect of AOD on TFPR. The general pattern observed is a symmetric distri-

bution around mean zero. Bootstrap samples of the EB estimation indicated an underlying data

generating process of mean λi of 0.08, with 95 percent confidence interval (-0.16, 0.25), and

standard deviation of 0.38, with 95 percent confidence interval (0.09, 0.75). The mean of the

distribution aligns with the IV estimate of the average effect, 0.08, and has nearly the same de-

gree of precision. Taking the EB estimates as the true values, the distribution implies industries

accounting for roughly that 39 percent of output are sensitive to air pollution (ie λEBi < 0).

15Some industries did not have enough unique firms or firm-years to estimate Equation 8. The estimate of

industry 286, manufacture of bank notes, postage stamps, and related products, was an order of magnitude lower

than the next lowest estimate and is excluded in the main results for precision.16The mean is 1

N

∑i=N

i=1 λi weighting each industry by its portion of output.

28

Figure 8: Distribution of the Effects of Air Pollution on Productivity

0.2

.4.6

.81

De

nsity

-1.5 -1 -.5 0 .5 1λ

iEB

kernel = epanechnikov, bandwidth = 0.1317

N = 131, Mean = 0.08, Standard Deviation = 0.38

Note: The unit of observation is the three-digit industry. The sample includes manufacturing industries in the ASI

panel years 2001-2010. Industry 286 excluded. The plot shows the estimated distribution of industry sensitiv-

ity to air pollution, λi, with industries weighted by their total output. See Section 5 for details on the variable

construction.

5.2 Determinants of Sensitivity

To distinguish the characteristics that make some industries more sensitive to air pollution than

others, I turn to comparing the effect of log AOD on the effectiveness of each input to produc-

tion. Intuition suggests that labor is the most vulnerable to pollution because of the substantial

human health impacts of exposure to particulate matter. However, when comparing two firms

with the same number of employees, we could expect to observe differences in their sensitivity

if one uses labor more intensely than capital and materials. The model captures this balance of

input sensitively and intensity of use: the pollution sensitivity λi, is composed of the impacts on

each input to production weighted by the factor shares (Equation 3). More broadly, the finding

that AOD has little effect on TFPR would be compatible with findings that pollution greatly

harms workers in a world where the detriments to labor are outweighed by intensive use of

capital and materials.

To investigate the effect of air pollution on the inputs to production, I estimate the following

regression based on Equation 3:

λi = (γ0 − γM) + (γL − γM)βLi + (γK − γM)βKi. (9)

29

In this regression, βLi is the average labor factor share for each industry. I note that the data

exhibit constant returns to scale (Table 2) so the explanatory variables are nearly collinear.

Thus, thus I identify γ0 − γM , γL − γM , γK − γM respectively. I continue to use the sample

of N = 132 industry sensitivity estimates; however, I remove outlying estimates in the baseline

results. I weight the industries by their total output so that the estimates are representative of

the manufacturing sector.

Table 6 presents the estimates of the elasticity of returns labor and capital. Row 1 contains

the estimate with λi obtained from the method in Table 5 row 1. Column 1 indicates that

a one percent increase in AOD reduces the portion of labor that contributes to output by 14

percent relative to the materials, the omitted factor. The estimate is statistically significant (p-

value = 0.024). Column 2 shows the elasticity of capital returns relative to materials returns

is not significantly different than zero. In row 2 I employ λEBi as the outcome in lieu of λi

and in row 3 I include the outlying observations. In row 4, I repeat row 1 with capital as the

omitted factor in lieu of labor. In rows 5-11, I repeat the estimation with λi obtained from

alternative productivity assumptions and alternative sample weights. The specifications repeat

the assumptions of 5 rows 2-7. I find consistent evidence that γL is negative relative to the

omitted factor. This evidence shows that labor is the most sensitive input to production.

The magnitude of the estimated input sensitivities along with the factor shares predict that

the impact of AOD on TFPR is modest. Averaging industries in Equation 3 suggests λ =

γ0 + γLβL + γKβK + γMβM . Supposing that materials are insensitive to pollution, γM = 0,

and substituting in the values of the factor shares from Table 2, the model and parameters imply

λ = 0.16 − 14 ∗ .07 + 4 ∗ .17 = −.14, this is within the confidence interval of Table 5 row 1

and Figure 8.

The model and parameters predict a larger effect of log AOD on log TFPR in industries

with greater labor factor shares. In Figure 9, I plot the λ estimates of the impact of log AOD

on productivity from Equation 8 against the labor factor share. Each plot of λ is for the sub-

sample of firms with the labor factor share βLit in the designated interval. I find that log AOD

has a significant negative impact on TFPR for firms with especially high labor shares. Pollution

negatively affects productivity for firms with labor share in the highest approximately 15%. I

find a consistent trend in an analogous plot of reduced form estimates (Figure A3). This finding

demonstrates that the labor intensity plays a critical role in impact of air pollution on firms.

Agricultural sectors (Graff Zivin and Neidell, 2012) and garment making (Adhvaryu et al.,

2014) will be more sensitive to air pollution than the average manufacturing firm because they

30

Table 6: Input Contributions to λi

(1) (2) (3) (4) (5)

γL γK γ0 γM N

(1) Baseline -13.85 4.22 0.16 129

(6.04) (3.48) (0.42)

(2) EB adjusted -5.94 1.14 0.25 131

(2.17) (1.17) (0.17)

(3) Outliers included -15.40 5.02 0.09 132

(6.03) (3.45) (0.43)

(4) Capital omitted -14.68 2.47 -2.15 129

(8.01) (2.02) (2.30)

(5) Linear IV -16.82 7.50 -0.57 128

(7.52) (4.22) (0.52)

(6) No selection correction -14.61 4.90 0.06 129

(5.94) (3.35) (0.42)

(7) 2001 survey weights -15.43 4.81 0.24 129

(6.05) (3.43) (0.44)

(8) 2010 survey weights -12.08 3.66 0.13 128

(5.85) (3.39) (0.40)

(9) Constant returns to scale -12.43 2.38 0.26 129

(5.94) (2.37) (0.35)

(10) Ackerberg et al. (2015) -14.44 4.26 0.22 130

(6.08) (3.17) (0.34)

(11) Labor adjustment cost 1.34 0.89 -0.38 127

(1.77) (1.71) (0.65)

Note: The unit of observation is the three-digit industry. The sample includes manufacturing industries in the

ASI panel years 2001-2010. The sample size is 132. Outliers more than 3.5 standard deviations from median

are removed unless otherwise noted. The cells of row (1) report the coefficients of estimating Equation 9. The

outcome industry sensitivity to air pollution and the explanatory variables are the factor shares. The coefficient

robust standard error is in parenthesis beneath. Row (2) repeats row (1) with λEBi as the outcome in lieu of λi.

Industry 287 is excluded. Row (3) repeats row (1) including outliers. Row (4) repeats the specification of (1) with

the capital factor share omitted in lieu of the materials factor share. Rows (5) to (11) repeat the specification of

row (1) with the outcome variable defined as in rows (2) to (8) of Table 5. All regressions weight industries by

their total output.

are comparatively labor intensive in addition to potential biological channels, such as increasing

31

Figure 9: Labor Share βL And Productivity Sensitivity λ Trend

-4-3

-2-1

01

λ E

stim

ate

< 0.045 0.045 - 0.06 0.06 - 0.075 0.075 - 0.09 0.09 - 0.105 0.105 - 0.12 0.12 - 0.135 > 0.135

β Labor Interval

Point Estimate 95% CI

Note: The unit of observation is a firm-year. The sample includes firms in the ASI panel years 2001-2010. Each

point depicts the coefficient of AOD from Equation 8 for the subset of firms with labor factor share in the cor-

responding interval. Each regression includes controls for temperature, precipitation, vapor pressure, and corre-

sponding polynomials, and fixed effects for the firm, year, state, and state by year trends. All regressions use survey

weights. Robust standard errors were clustered at the district level. The error bars are ± 1.65 standard errors. A

solid line at zero shows estimates that are significant at the 10 percent level.

the respiratory rate worsening the effects Chang et al. (2016). The differences reflect biological

responses as well as labor intensity.

6 Cost of Production Adjustments

To assess the overall cost of air pollution on manufacturing it is necessary to consider how

productivity shocks are incorporated into firms’ optimal input demand and output. The full

impact of air pollution on producers reflects the sensitivity, changes in market prices, and the

extent of adjustment in firm input and output. In this section, I analyze these effects of pollution

to gauge the adjustments and costs.

Returning to the model of profit maximization with pollution (Equation 7), the impact of

pollution on optimal inputs and output depends on both the sensitivity of and adjustment in

input prices. Assuming there are no adjustment constraints, the effect of an increase in log

32

Table 7: Impact of AOD on Input Use

(1) (2) (3)

Log AOD Coef p-value N

(1) Log labor -0.12 0.41 202,053

(0.15)

(2) Log materials -0.49 0.11 202,053

(0.31)

(3) Log capital 0.40 0.10 202,053

(0.24)

(4) Log wage -0.32 0.01 202,053

(0.12)

Note: The unit of observation is the firm-year. The sample includes firms in the ASI panel years 2001-2010. Row

(1) reports the AOD coefficient (column 1), p-value (column 2), and sample size (column 3) from a regression of

Equation 8 with log labor as the explanatory variable in lieu of log TFPR. The coefficient standard error is reported

in parenthesis beneath. Robust standard errors were clustered at the district level. Row (2) repeats row (1) with

log materials as the explanatory variable. Row (3) repeats row (1) with log capital as the explanatory variable.

All regressions include controls for temperature, precipitation, vapor pressure and corresponding polynomials, and

fixed effects for the firm, state, district, and state by year trends. All regressions use survey weights.

AOD on the demand of log input j ∈ ℓ, k,m is:

djfidt

dadt= λi −

dpJ

dadt(10)

Without adjustment in input prices, a productivity shock from pollution will lead demand for

each input to adjust according to the sensitivity. All inputs respond to the productivity shock

even if pollution has no effect on some inputs. Prices might adjust to offset the productivity

shock and firms might be constrained in their ability to adjust each input, especially for capital.

To measure the input effects, I repeat Equation 8 with the log of each input as the explana-

tory variable in lieu of log productivity. Table 7 reports the estimated coefficients. I find a

significant positive effect of air pollution on capital inputs, a marginal decrease in materials, an

no significant effect on labor. I hypothesize that the greater adjustment of capital and materials

relative to labor occurs because i) the price of these inputs is set on the world market and will

not adjust for the air pollution productivity shock in India and ii) materials can be adjusted at

relatively low cost. I fail to reject the hypothesis that the adjustment labor, materials, and capital

are equal. The negative effect of air pollution on materials inputs indicates that firms decrease

33

inputs to mitigate the effect of pollution on profits.

Given that managers are knowledgeable and able to adjust inputs in response to pollution,

pollution should cause wages should fall to reflect the decline in marginal product, all else

equal. In Table 7 row 4, I tested for a relationship between wages and pollution and found

pollution causes a significant decrease in wages. While this evidence is consistent with the

finding that pollution affects health and workers, other plausible scenarios suggest the pollution-

wage relationship could be weaker than expected. For example, wages will not reflect changes

in labor productivity if sensitive plants are wage takers. Another possibility is that wages will

not reflect labor sensitivity when labor is mobile because worker movement will equalize wages

across locations in equilibrium and polluting firms may offer compensation that counteracts the

productivity shock on wages.

All else equal, fewer inputs result in lower output. Comparing the effect of pollution on

output with the effect on TFPR, λ, I expect the output effects to be greater than or equal to the

TFPR effects. The effect of pollution on log output is:

dyfidt

dadt= λi +

∑

J

βJit

(

λi −dpJ

dadt

)

(11)

Equation 11 imparts bounds on the effect of air quality on output. If input prices perfectly adjust

to offset the productivity loss, or adjustment costs prevent reductions in input, the second term

in Equation 11 is zero and the output effect and TFPR effect are equivalent. If input prices do

not change and there are no input adjustment costs, the impact of log AOD on log output will

be roughly twice the magnitude of the effect on log TFPR.

To gauge the impact of air pollution output, I first repeat Equation 8 with output as the ex-

planatory variable. Figure 10 depicts the output sensitivity coefficients for the subset of firms

in intervals of the labor factor share. The reduced form is reported in Figure A4. I expect the

trend in output sensitivity to mirror the trend in TFPR sensitivity and have greater magnitude.

As expected, I find a negative effect of pollution on output for firms with high labor factor

shares. Industries with the greater labor factor shares βL are increasingly sensitive to air pollu-

tion. Further, while the confidence intervals are considerable, the point estimates are of greater

magnitude than those for productivity (Figure 9). This aligns with my hypothesis that output is

more sensitive to pollution than productivity in a setting where prices do not adjust to perfectly

offset productivity shocks and inputs are flexible.

Table 8 reports the effect on manufacturing output in India of reducing annual mean PM2.5

to the World Health Organization standard. To achieve the standard, India must reduce annual

34

Figure 10: Labor Share βL And Output Sensitivity

-6-4

-20

2

AO

D c

oe

fficie

nt

< 0.045 0.045 - 0.06 0.06 - 0.075 0.075 - 0.09 0.09 - 0.105 0.105 - 0.12 0.12 - 0.135 > 0.135

β Labor Interval

Point Estimate 95% CI

Note: The unit of observation is a firm-year. The sample includes firms in the ASI panel years 2001-2010. Each

point depicts the coefficient of log AOD from Equation 8 with log output as the explanatory variable in lieu of

log TFPR for the subset of firms with labor factor share in the corresponding interval. Each regression includes

meteorological controls for temperature, precipitation, vapor pressure, and corresponding polynomials, and fixed

effects for the firm, year, state, and state by year trends. All regressions use survey weights. Robust standard errors

were clustered at the district level. The error bars are ± 1.65 standard errors. A solid line at zero shows estimates

that are significant at the 10 percent level.

Table 8: Percent Change in Output of Reducing AOD to WHO Standard

(1) (2)

Price adjustment No price change

(1) All industries 0.01 -0.04

(-0.32,0.49) (-0.38,0.44)

(2) Sensitive industries 1.27 1.49

(0.77,2.08) (0.99,2.31)

Note: The unit of observation is the three-digit industry. The sample includes manufacturing industries in the ASI

panel years 2001-2010. The sample size is 134. The cell in row (1) column (1) reports Equation 11 multiplied

by -0.65 with dpJ

dadt= 0.07 for all inputs J . The cell in row (1) column (2) reports Equation 11 with dpJ

dadt= 0 for

all inputs J . The cell in row (2) column (1) reports repeats the estimate in row (1) column (1) with the subset of

industries with λEBi < 0 and dpJ

dadt= -0.57. The cell in row (2) column (1) repeats the estimate in row (1) column

(2) with the subset of industries with λEBi < 0. All estimates weight industries by their total output. 95 percent

confidence intervals reported in parenthesis. Standard errors obtained from 1000 bootstrap samples.

35

mean PM2.5 by roughly 36 µgm−3, or around 78 percent.17 I present the estimate in the sce-

nario where prices adjust (Column 1) separately from the scenario where prices do not change

(Column 2). In Column 1, in lieu of assuming that input prices adjust in each industry to per-

fectly offset that industry’s unique productivity shock, I assume all input prices adjust by the

average productivity shock for all industries. Given this imperfect price adjustment, the effects

under price changes are not strictly lower than under no price changes. Assume some price

adjustment, I find that manufacturing output would rise 0.01 percent for all industries and 1.27

percent were the manufacturing sector composted entirely of sensitive industries. In a scenario

with no price changes and no costs to adjusting inputs, I estimate that bringing air quality to the

standard would result in a 0.04 percent decline in output overall and a 1.49 percent rise were

the manufacturing sector composed entirely of sensitive industries.

The stark differences in the impact for sensitive industries in comparison to the full sector

underscore the external validity challenge for studies with data from a single firm. Estimates

of a single industry are not representative of the overall cost of air pollution. While most of

the settings of previous research, such as call centers and cargo packaging, cannot be intuitively

mapped to ASI industry codes, garment production (Adhvaryu et al., 2014) is a stark example.18

Garment production is in roughly the 75th highest percentile of sensitivity so extrapolating from

any estimates of air quality shocks on firms in this industry would overstate the average effect

for the whole of manufacturing.

7 Conclusion

This study examines the costs of pollution for the manufacturing sector in India. It estimates

a model of production where air pollution reduces the portion of each input that contributes

to output. The model demonstrates that the overall effect of a shock, such as air pollution, on

productivity depends how much the shock affects the returns to each input and the intensity of

use of each input. Since high winds dissipate pollution, wind velocity generates as-if random

assignment of pollution by which the impacts are measured.

I find the effect of air pollution on productivity is very small in comparison to previous

estimates of similar productivity shocks. Guided by the model, I argue this finding reflects

two features of the setting: low labor factor shares and high sensitivity of labor returns to air

17The World Health Organization guideline for annual mean PM2.5 is 10 µgm−3. This assumes an annual mean

PM2.5 of 46 µgm−3.18NIC87 classification of garment production is 265.

36

pollution relative to other inputs. Consistent with a prior that air pollution leads to unhealthy

workers, I find the impact of air pollution reduces the returns to labor 14 percent more than it

reduces returns to materials. In firms that use labor intensively, I measure significant sensitively

to air pollution even though the impacts are modest on average. Last, I show that while output

costs of air pollution are substantial for sensitive industries, the effects on sensitive industries

are not representative of the overall manufacturing sector.

The implications of these findings are relevant for assessing the welfare cost and incidence

of air pollution. In prior work, such as Copeland and Taylor (1999), an industry is either pollut-

ing or environmentally insensitive. These findings underscore that when emissions and sensi-

tivity are not mutually exclusive, multiple forms of heterogeneity contribute to the equilibrium

location of firms. Specifically, the results of this study predict that pollution externalities and

location sorting are a much greater force in a world where highly polluting industries tend to

be insensitive than in a world where highly polluting industries tend to be sensitive. The cor-

relation of labor intensity and emissions is key to predicting externalities and location sorting.

Given a prior that sensitivity and emissions are negatively correlated, a promising direction for

future research is to consider the cost to firms of locating away from their ideal location in a

world without excess air pollution.

37

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42

Appendix

A1

A1 Data

A1.1 Annual Survey of Industries

Table A1 presents descriptive statistics of the firms in the sample. In total, there are 207,176

observations of 53,902 unique firms. The median firm earns 20 million rupees in a year and

employs 25 people. The distributions of number of workers, value of output, output per worker,

and labor cost in the sample closely match previous research with the dataset (Allcott et al.,

2016).

Table A1: Summary of ASI Firm Characteristics

mean sd p5 p50 p95 count

Revenues (million Rupees) 165.69 658.53 1.14 20.54 671.79 207176

Number of Employees 94.11 266.52 6.00 25.00 390.00 207176

Capital Stock (million Rupees) 49.08 363.28 0.12 2.95 164.95 207176

Materials Cost (million Rupees) 106.55 416.25 0.69 14.19 434.16 207176

Note: Data from Annual Survey of Industries 2001-2010. The unit of observation is the firm-year. All statistics

use survey weights.

A1.2 MODIS Aerosol Optical Depth

MODIS Aerosol optical depth (AOD) is developed with advanced versions of basic physical

principals of remote sensing I describe here. As electromagnetic radiation travels through the

atmosphere, it can be deflected off atmospheric particles, called scattering, or it can be trans-

formed into kinetic energy, called absorption. AOD is defined as the extent to which aerosols

attenuate the transmission of light by absorption or scattering. The degree of attenuation de-

pends on the size and composition of particles in the atmosphere, the wavelength of light, and

the distance through the atmosphere that the light passed, which in turn depends on the angles

of the sun and the sensor.

Thus, the model of potential paths of light from the sun to the sensor allows for absorption

and scattering to abate the radiance measured at the sensor from the target pixel and for atmo-

spheric upwelling to increase radiance at the sensor. MODIS AOD products are derived from an

algorithm that builds on this model of light-atmosphere interaction, but also accounts for how

aerosol particle size and total amount, or load, affect the amount of light transmitted (see Re-

mer et al. (2006) page 26 for the equation). The algorithm relies on a large database where the

radiance at the sensor is calculated for many combinations of potential aerosols, angles of sun

and sensor, elevation, etc over which the algorithm “inverts” the data. The process is described

in detail in Remer et al. (2006). The following is a very simplified version:

A2

1. Discard pixels identified as water, clouds, snow, extremely dark, or extremely light.

2. Calculate path radiance from remaining dark pixels and calculate surface reflectance.

3. Match observed path radiance to most likely aerosol combination.

In Figure 1, I present evidence that MODIS AOD is commensurate with the existing air

quality data sets in India. I obtained the replication files of Greenstone and Hanna (2014). I

matched the 140 cities for which they organized the annual mean government pollution monitor

data to the census. I then computed the annual mean AOD in a 10 kilometer radius of the census

coordinates. The graph depicts the scatter of the 10k mean AOD and the mean suspended

particulate matter for the cities over 2001-2014. The graph also depicts a linear fit and a non-

parametric regression. Over the majority of the AOD domain, the non-parametric relationship

is within the confidence interval of the linear model. This fit is strong evidence that AOD is an

appropriate measure of suspended particulate matter.

A1.3 Reanalysis wind product robustness

I repeated the main tables with wind velocity constructed from NCEP Reanalysis 1 (Kalnay

et al., 1996) in lieu of Wentz and J. Scott (2015). At 2.5 degree spatial resolution, the NCEP

data is substantially more coarse than Wentz and J. Scott (2015). The change in source of wind

velocity data did not result in any substantive changes in the conclusions on the average effect

of wind on productivity. In the heterogeneity analysis, although the data no longer shows a

significant contribution of the labor factor share to the industry sensitivity, the direction of the

coefficients are consistent. Measurement error from the coarse spatial resolution plausibly bi-

ased the coefficients towards zero and the small sample size of industry level analysis decreased

the statistical power in these results.

A1.3.1 First stage

A1.3.2 Outcomes

A3

Table A2: Robustness Test of Linear First Stage Relationship Between AOD and Alterna-

tive Wind Velocity

(1) (2)

VARIABLES Log AOD Log AOD

Log Wind Velocity (m/s) NCEP -0.0452 -0.0452

(0.0142) (0.0374)

Observations 4,922 4,922

R-squared 0.969 0.969

Weather controls Yes Yes

District fixed effects Yes Yes

Year fixed effects Yes Yes

State * year trends Yes Yes

Clustering District State

Note: Replication of Table 5 with wind data from NCEP. The unit of observation is a district-year. The sample

includes all districts with a firm in the ASI panel years 2001-2010. The dependent variable is the district annual

mean log AOD. Robust standard errors in parenthesis are clustered by district.

A4

Table A3: Robustness Test of Impact of AOD on Productivity With Alternative Wind

(1) (2) (3)

λ p-value N

(1) Baseline 0.05 0.63 202,053

(0.10)

(2) Linear IV -0.41 0.23 202,053

(0.34)

(3) No selection correction 0.06 0.57 202,053

(0.10)

(4) 2001 survey weights 0.02 0.84 202,053

(0.10)

(5) 2010 survey weights 0.06 0.57 202,053

(0.10)

(6) Constant returns to scale -0.04 0.63 202,053

(0.08)

(7) Ackerberg et al. (2015) 0.05 0.63 202,053

(0.10)

(8) Labor adjustment cost 0.11 0.28 201,660

(0.10)

(9) Low working days -0.09 0.64 43,034

(0.18)

(10) High working days 0.08 0.42 158,900

(0.10)

(11) Low AOD 0.11 0.43 113,771

(0.14)

(12) High AOD -0.12 0.38 88,282

(0.13)

Note: Replication of Table 5 with wind data from NCEP. The unit of observation is the firm-year. The sample includes firms in the ASI panel years 2001-2010.

Row (1) reports the log AOD coefficient (column 1), p-value (column 2), and sample size (column 3) from a regression of log TFPR (Equation 8). The coefficient

standard error is reported in parenthesis beneath. Robust standard errors were clustered at the district level. Row (2) repeats row (1) with a linear control function.

Row (3) repeats row (1) without selection corrections in the control function. Row (4) repeats row (1) with the firm survey weights from ASI 2000-2001. Row

(5) repeats specification (1) with the firm survey weights from ASI 2009-2010. Row (6) replicates row (1) under the assumption of constant returns to scale,

βKi = 1 − βLi, with βLi computed as in the main body of the text. Row (7) repeats specification (1) with the computation of capital factor share in Ackerberg

et al. (2015). Row (8) repeats specification (1) with the computation of the labor factor share with adjustment cost in Collard-Wexler and De Loecker (2016). Row

(9) repeats row (1) with the subsample of firms in the lowest 25% of days open and row (10) does so with the subsample of firms in the highest 75% of days

open. Row (11) repeats row (1) with the subsample of firms below the median air pollution and row (12) does so with the subsample of firms above the median air

pollution. All regressions include controls for temperature, precipitation, vapor pressure, corresponding polynomials, and fixed effects for the firm, year, state, and

state by year trends. All regressions use survey weights.

A5

Table A4: Robustness Test Of Input Contributions to λi With Alternative Wind

(1) (2) (3) (4) (5)

γL γK γ0 γM N

(1) Baseline -1.55 -1.04 0.31 122

(2.27) (1.28) (0.17)

(2) EB adjusted -3.01 0.03 0.19 132

(2.46) (1.31) (0.19)

(3) Outliers included -3.15 0.25 0.17 132

(3.19) (1.77) (0.22)

(4) Capital omitted 2.62 -1.64 2.12 122

(2.93) (0.87) (0.99)

(5) Linear IV -8.07 -4.85 1.05 122

(11.27) (5.93) (0.93)

(6) No selection correction -1.48 -1.43 0.35 123

(2.09) (1.10) (0.17)

(7) 2001 survey weights -3.80 -0.52 0.39 123

(2.15) (1.26) (0.19)

(8) 2010 survey weights -1.81 -0.96 0.31 125

(2.73) (1.29) (0.21)

(9) Constant returns to scale 0.70 -2.24 0.47 121

(2.37) (1.04) (0.18)

(10) Ackerberg et al. (2015) -0.96 -1.36 0.29 123

(2.38) (1.14) (0.15)

(11) Labor adjustment cost -0.91 -1.37 0.43 120

(0.61) (1.00) (0.20)

Note: Replication of Table 6 with wind data from NCEP. The unit of observation is the three-digit industry. The

sample includes manufacturing industries in the ASI panel years 2001-2010. The sample size is 132. Outliers

more than 3.5 standard deviations from median are removed unless otherwise noted. The cells of row (1) report

the coefficients of estimating Equation 9. The outcome industry sensitivity to air pollution and the explanatory

variables are the factor shares. The coefficient robust standard error is in parenthesis beneath. Row (2) repeats

row (1) with λEBi as the outcome in lieu of λi. Row (3) repeats row (1) including outliers. Row (4) repeats

the specification of (1) with the capital factor share omitted in lieu of the materials factor share. Rows (5) to (11)

repeat the specification of row (1) with the outcome variable defined as in rows (2) to (8) of Table 5. All regressions

weight industries by their total output.

A6

Figure A1: Robustness Test Of Labor Share βL And Productivity Sensitivity λ Trend With

Alternative Wind

-3-2

-10

1

λ E

stim

ate

< 0.045 0.045 - 0.06 0.06 - 0.075 0.075 - 0.09 0.09 - 0.105 0.105 - 0.12 0.12 - 0.135 > 0.135

β Labor Interval

Point Estimate 95% CI

Note: Replication of Figure 9 with wind data from NCEP. The unit of observation is a firm-year. The sample

includes firms in the ASI panel years 2001-2010. Each point depicts the coefficient of AOD from Equation 8 for

the subset of firms with labor factor share in the corresponding interval. Each regression includes controls for

temperature, precipitation, vapor pressure, and corresponding polynomials, and fixed effects for the firm, year,

state, and state by year trends. All regressions use survey weights. Robust standard errors were clustered at the

district level. The error bars are ± 1.65 standard errors. A solid line at zero shows estimates that are significant at

the 10 percent level.

A7

A2 Instrumental Variables Research Design

A2.1 Semi-Parametric First Stage

I examine variants of the following first stage relationship for each district d and year t:

adt = 0 + φ(vdt) + θ′1Xdt + rdt (A1)

vdt is log of annual average wind velocity. I include additional controls, Xdt, for the annual

mean meteorological controls (precipitation, temperature, vapor pressure), and polynomials of

meteorological controls, as well as fixed effects for the state, year, and state by year trends.

Theory does not ensure the relationship between air quality and wind velocity is linear. For

this reason, I evaluate wind velocity as an instrument for air quality with a semi-parametric

approach.

Following Robinson (1988), I use a two-step procedure to estimate φ(vdt) in equation A1.

The first step of the procedure to perform nonparametric estimation of gx(vdt) of the influence

of wind velocity on each explanatory variable and the outcome variable, xdt, in equation A1:

xdt = gx(vdt) + ex,dt, ∀xdt ∈ adt, x1dt, ..., xKdt.

To complete the first step, I transform the data to remove the predicted variation in wind velocity

from each variable xdt and estimate θ2 using the transformed data:

adt − ga(vdt) = θ0 + θ′1[Xdt − g′X(vdt)] + edt.

In the second step, I use the estimates θ2 to remove from aerosol optical depth the variation

from controls, accounting for the influence of wind velocity on the controls, and recover non-

parametrically φ:

adt − θ′1Xdt = θ0 + φ(vdt) + rdt.

I plot the estimated φ(vdt) in Figure 6 to evaluate the relationship between log wind and AOD

and to compare the trend to a linear relationship.

A2.2 First Stage Robustness Check

Atmospheric models predict an instantaneous relationship between meteorological conditions

and air quality; however, an instantaneous relationship does not imply annual averages reflect

the same relationship. One concern is that the instantaneous relationship between air quality

and wind velocity does not scale into annual averages and the observed pattern is instead re-

flects anomalies in data availability, such as seasonal missing AOD data. Since firm outcomes

are measured annually, I cannot relate pollution to productivity more frequently than annually.

Instead, to ensure that the annual pattern is consistent across the year and across locations, I

repeated the first stage with monthly data. Figure A2 shows that monthly mean wind veloc-

A8

Figure A2: Conditional Wind and AOD for Each Month

-50

050

100

150

aod_

r

-2 -1 0 1 2wind_spd_r

Month = 1, t = -7.574083137882213

-150

-100

-50

050

aod_

r

-2 -1 0 1 2wind_spd_r

Month = 2, t = -10.03864528816386

-150

-100

-50

050

aod_

r

-3 -2 -1 0 1 2wind_spd_r

Month = 3, t = -12.3086235695266

-150

-100

-50

050

aod_

r

-2 0 2 4wind_spd_r

Month = 4, t = -22.65185929792262

-40

-20

020

4060

aod_

r

-2 -1 0 1 2 3wind_spd_r

Month = 5, t = -7.804645266518454

-100

010

020

030

0ao

d_r

-2 -1 0 1 2 3wind_spd_r

Month = 6, t = -14.03656862560196

010

020

030

040

0ao

d_r

-2 0 2 4wind_spd_r

Month = 7, t = -4.034401993144588

-100

-50

050

100

150

aod_

r-2 -1 0 1 2 3

wind_spd_rMonth = 8, t = 1.112100400755984

-150

-100

-50

aod_

r

-2 -1 0 1 2wind_spd_r

Month = 9, t = .5644962416164555

-100

-50

050

aod_

r

-4 -2 0 2wind_spd_r

Month = 10, t = .2281249450580358

-100

-50

050

100

aod_

r

-3 -2 -1 0 1 2wind_spd_r

Month = 11, t = -4.262507852627019

-50

050

100

150

aod_

r

-2 -1 0 1 2wind_spd_r

Month = 12, t = -11.28517892985861

Note: Each point represents binned of averages of district-month mean wind velocity and mean AOD. Line depicts

a linear regression of AOD on log wind velocity conditional on rain, temperature, district and year fixed effects.

A9

ity is significantly correlated with monthly mean AOD conditional on controls for weather in

all months except the rainy season, August, September, and October. This pattern is consis-

tent with expectations: since rain deposits aerosols, wind has little effect aerosol concentration

conditional on rain when rain is very high.

A2.3 Exclusion Restriction Robustness Check

Table A5: Cross-Sectional Properties of Wind Instrumental Variable

(1) (2) (3) (4) (5) (6) (7)

VARIABLES N HHs Population SC ST Literate Illiterate Workers

Log Wind Velocity -127,720 -1.126e+06 -563,627 -124,357*** -334,158 -791,343 -228,998

(312,643) (1.632e+06) (520,953) (42,754) (963,277) (670,656) (531,834)

Observations 385 385 385 385 385 385 385

Robust standard errors in parentheses

*** p<0.01, ** p<0.05, * p<0.1

Note: The unit of observation is the district. Data from 2001 Indian Census. SC is scheduled castes, ST is

scheduled tribes. Outcomes are number of households in column (1), population in column (2), Scheduled Caste

population in column (3), Scheduled Tribe population in column (4), literate population in column (5), illiterate

population in column (6), number of workers in column (7).

A10

A3 LP and TFPR comparison

A3.1 Analytical comparison

Define labor productivity LPfidt:

LPfidt =Yfidt

Lfidt

.

The impact of AOD on log LP is:

dlog(LPfidt)

dadt=

d (yfidt − ℓfidt)

dadt(A2)

I derive each component separately. First, rearranging the first order condition for labor yields:

dℓfidt

dadt= λit −

dpLfidt

daat. (A3)

The derivatives of materials and capital with respect to pollution are analogous. Further, the

derivate of log output with respect to pollution is:

dyfidt

dadt= λit + βLit

dℓfidt

dadt+ βKi

dkfidt

dadt+ βMit

dmfidt

dadt. (A4)

Substituting (A3) and (A4) into (A2):

d (yfidt − ℓfidt)

dadt= λitβLit+(1−βLit)

(

dpLfidt

daat

)

+βKi

(

λit −dpKfidt

daat

)

+βMit

(

λit −dpMfidt

daat

)

(A5)

Thus the effect of a productivity shock on LP is not generally comparable to the effect on TFPR.

LP is a function of the intensity of use of non-labor inputs. Since we expect a productivity

shock to affect demand for inputs and input prices, the impact of a shock on LP will reflect

these changes in addition to the impact on TFPR.

There are two cases that make the LP and TFPR derivatives equivalent. First, if prices for

every input adjust to perfectly mirror the TFPR shock, iedpJ

fidt

daat= λit∀J ∈ L,K,M, then the

log LP and log TFPR derivatives are both λit. Second, assuming the are no adjustment in prices

and constant returns to scale implies that the effect of AOD on log LP is equivalent to the effect

on log TFPR. Specifically, given (1)dpJ

fidt

daat= 0∀J ∈ L,K,M and (2) βMit + βKi + βLit = 1

∀ i and t, then the expression simplifies:

d (yfidt − ℓfidt)

dadt= λit =

dωfidt

dadt.

A11

A3.2 Impact of AOD on LP

Table A6: Impact of AOD on Labor Productivity Use

(1) (2) (3)

Log AOD Coef p-value N

(1) Log(output/person-day) -0.06 0.77 199,960

(0.21)

Note: The unit of observation is the firm-year. The sample includes firms in the ASI panel years 2001-2010. Row

(1) reports the AOD coefficient (column 1), p-value (column 2), and sample size (column 3) from a regression

of Equation 8 with log(Yfidt

Lfidt) as the explanatory variable in lieu of log TFPR. The coefficient standard error is

reported in parenthesis beneath. Robust standard errors were clustered at the district level. The regression includes

controls for temperature, precipitation, vapor pressure, and corresponding polynomials, and fixed effects for the

firm, year, state, and state by year trends. The regression uses survey weights.

Table A6 depicts the results of estimating the impact of log AOD on log LP. The regression

equation is Equation 8 with log(Yfidt

Lfidt) as the outcome in lieu of log TFPR. Rounding down on

the lower bond of the 95 percent confidence interval, I find that a one percent increase in AOD

decreased the output per worker day the at worst by 0.06 percent. Converting the estimate to

PM2.5, the lower bound indicates that a 1 µgm−3 increase in the concentration of PM2.5 would

yield at worst a 1.03 percent decrease inYfidt

Lfidt.

A12

A4 Reduced Form Plots

Figure A3: Reduced Form: Labor Share βL And Productivity Sensitivity Trend

-.1

0.1

.2.3

.4L

og

win

d c

oe

fficie

nt

< 0.045 0.045 - 0.06 0.06 - 0.075 0.075 - 0.09 0.09 - 0.105 0.105 - 0.12 0.12 - 0.135 > 0.135

β Labor Interval

Point Estimate 95% CI

Note: The unit of observation is a firm-year. The sample includes firms in the ASI panel years 2001-2010. Each

point depicts the coefficient of log wind, vdt, from a regression of log TFPR ωfidt = τ0+τλvdt+τ1Xidt+ffidt+ǫfidt for the subset of firms with labor factor share in the corresponding interval. Each regression includes controls

for temperature, precipitation, vapor pressure, and corresponding polynomials, and fixed effects for the firm, year,

state, and state by year trends. All regressions use survey weights. Robust standard errors were clustered at the

district level. The error bars are ± 1.65 standard errors. A solid line at zero shows estimates that are significant at

the 10 percent level.

A13

Figure A4: Reduced Form: Labor Share βL And Output Sensitivity Trend

-.2

0.2

.4.6

Lo

g w

ind

co

effi

cie

nt

< 0.045 0.045 - 0.06 0.06 - 0.075 0.075 - 0.09 0.09 - 0.105 0.105 - 0.12 0.12 - 0.135 > 0.135

β Labor Interval

Point Estimate 95% CI

Note: The unit of observation is a firm-year. The sample includes firms in the ASI panel years 2001-2010. Each

point depicts the coefficient of log wind, vdt, from a regression of log output yfidt = τ0+τλvdt+τ1Xidt+ffidt+ǫfidt for the subset of firms with labor factor share in the corresponding interval. Each regression includes controls

for temperature, precipitation, vapor pressure, and corresponding polynomials, and fixed effects for the firm, year,

state, and state by year trends. All regressions use survey weights. Robust standard errors were clustered at the

district level. The error bars are ± 1.65 standard errors. A solid line at zero shows estimates that are significant at

the 10 percent level.

A14