does air pollution lower productivity? evidence from
TRANSCRIPT
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_
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
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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.
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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