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Dynamic Evolution of Corporate Emissions Determinants
Over the past three decades, environmental regulation and public scrutiny have transformed the way firms internalise pollution externalities becker2000effects,greenstone2002impacts,greenstone2003estimating,shapiro2018pollution,gaganis2021informal. What was once treated primarily as a compliance cost is increasingly embedded in firms’ investment strategies, organisational capabilities, and innovation decisions. Emissions outcomes today reflect not only regulatory stringency, but also how firms adapt technologically and financially to evolving policy regimes and macroeconomic conditions. Understanding these adaptive processes is central to debates in innovation and industrial policy, where regulation is often viewed not merely as a constraint, but as a potential catalyst for technological change and organisational learning porter1995toward.
A growing body of research argues that environmental policy can stimulate innovation by altering relative prices, inducing process improvements, and accelerating capital-vintage turnover porter1995toward,shapiro2018pollution. Meanwhile, firms differ markedly in their ability to respond. Financial structure, investment capacity, and managerial characteristics shape whether regulation leads to technological upgrading, organisational change, or delayed compliance konar2001does,tomar2023greenhouse. Recent evidence further highlights the role of intrinsic motivation and place-based preferences in shaping corporate pollution abatement, underscoring that adaptation to environmental challenges is mediated by internal organisational factors as well as external policy constraints andrikogiannopoulou2025not.
These heterogeneous responses imply that the relationship between firm characteristics and emissions is unlikely to be stable over time. Instead, it should evolve as regulatory regimes mature, technologies diffuse, and macroeconomic conditions change. Despite this, much of the empirical literature still relies on static models that impose constant effects over long horizons or focus on discrete policy shocks. Such approaches obscure the dynamic nature of firm adaptation. A factor that is strongly associated with emissions in an early regulatory phase—such as scale or investment intensity—may weaken, reverse, or disappear as firms learn, innovate, or face new financial constraints. Capturing these evolving relationships is therefore essential for understanding when regulation induces genuine technological change rather than short-run adjustment.
This paper studies the dynamic evolution of emissions determinants using a uniquely long and granular panel of U.S. industrial facilities from 1992 to 2023, drawn from the U.S. Environmental Protection Agency’s Toxics Release Inventory (TRI). The resulting balanced panel comprises 204 facilities observed over 32 years. By linking facility-level emissions to parent-firm financial characteristics, managerial attributes, local labour-market conditions, and aggregate macroeconomic indicators, we examine how firm-level drivers of pollution change across distinct regulatory and economic regimes. Rather than treating emissions as a static outcome, we interpret them as a revealed measure of firms’ evolving production technologies, investment choices, and organisational responses to policy and market conditions.
Methodologically, we employ a time-varying mean-group (TVMG) estimator that allows regression coefficients to evolve smoothly over time while accommodating heterogeneity across facilities robinson1989nonparametric,robinson1991time,pesaran1995estimating,giraitis2014inference,giraitis2018inference,giraitis2021time. The approach combines kernel-weighted local estimation at the unit level with cross-sectional aggregation, yielding a time path of average effects. This framework is particularly well suited to studying innovation and adaptation, as it does not require prespecifying breakpoints or policy dates and can capture gradual transitions in firm behaviour as regulations tighten, technologies diffuse, and macroeconomic conditions shift.
Our results reveal pronounced dynamics in the determinants of emissions. In the baseline single-regressor specification, investment intensity and cash holdings are significant for a few years, sales exhibit more persistent significance, CEO age shows only brief significance, and local unemployment is significant in two distinct periods. Conditioning on aggregate economic conditions using a bi-regressor model preserves these patterns while sharpening their timing. The joint multi-variable model shows stage-like dynamics. In the early part of the sample, emissions growth is closely linked to firm scale, valuation, and managerial characteristics, consistent with a period in which environmental performance largely reflects production intensity and organisational heterogeneity. From the late 2000s through the late 2010s, aggregate macroeconomic conditions dominate, suggesting a phase in which emissions responses become more synchronised across firms, potentially reflecting common regulatory constraints and widespread diffusion of abatement technologies. In the most recent period, managerial attributes re-emerge as salient correlates, indicating that adaptation capacity and corporate strategy matter most when firms face heightened uncertainty and adjustment pressures.
These findings contribute to the innovation and policy literature in three ways. First, they provide long-run evidence on how firm-level adaptation to environmental regulation unfolds over multiple decades, highlighting that the relevance of innovation, investment, and organisational characteristics is inherently time-dependent. Second, they show that financial conditions and organisational factors play a crucial role in shaping environmental outcomes, reinforcing the link between innovation policy, access to finance, and organisational decision-making konar2001does,tomar2023greenhouse,andrikogiannopoulou2025not,yang2021real. Third, by demonstrating that aggregate conditions and firm-specific drivers dominate in different phases, the paper underscores the importance of time-aware policy design: regulatory instruments and complementary innovation policies are likely to be most effective when aligned with firms’ evolving adaptive capacities.
From a policy perspective, these dynamics have direct implications for innovation-oriented environmental regulation. If emissions outcomes reflect firms’ evolving technological, organisational, and financial capacities, then uniform regulatory instruments are unlikely to generate uniform responses over time. Policies that are effective in inducing adjustment in one phase may have limited impact in another, depending on firms’ access to finance, managerial incentives, and the prevailing macroeconomic environment. This suggests that environmental regulation may be most effective when complemented by policies that support investment in cleaner technologies, relax financial constraints, and account for heterogeneity in firms’ adaptive capacity. Understanding when and how firm-level drivers dominate emissions outcomes is therefore central to the design of policies that aim not only to reduce pollution, but also to foster sustained technological change.
To provide a disciplined interpretation of these time-varying reduced-form estimates, we also draw on a simple economic framework in which total emissions depend on both production scale and emissions intensity, while firms can lower future emissions intensity through environmentally oriented investment whose effective cost depends on internal liquidity, financial constraints, and broader financing conditions. This interpretation is consistent with evidence that environmental performance affects firm value and financing conditions, and with a growing climate-finance literature showing that investor demand and the pricing of climate risk have become increasingly salient konar2001does,chava2014environmental,krueger2020importance,bolton2021do,pastor2021sustainable. The purpose of this framework is not to identify structural parameters. Rather, it provides a coherent way to understand why the association between emissions growth and variables such as sales, investment intensity, cash holdings, and macroeconomic conditions may itself evolve over time.
We emphasise that our results are descriptive of evolving relationships rather than causal estimates of specific regulatory interventions, but they provide systematic evidence on the timing and nature of firm adaptation to environmental and economic conditions.
The remainder of the paper proceeds as follows. Section 2 outlines the empirical framework and data. Section 3 presents the main results, moving from single-variable specifications to joint firm-level and macroeconomic analyses. Section 4 concludes with implications for innovation-oriented environmental policy.
To interpret empirical estimates, it is important to have an economic framework that guides the interpretation of results. It is useful to start by distinguishing between a scale margin and an adjustment margin. Suppressing firm subscripts for expositional clarity, let total emissions be denoted by $\mathcal{E}_t$ and write
where $q_t$ denotes current activity and $m_t$ denotes emissions intensity, that is, emissions per unit of activity. Taking log differences gives
Equation (ref) provides the basic economic lens for the empirical analysis. Emissions growth may be high because activity expands, because emissions intensity rises, or because emissions intensity does not decline sufficiently quickly.
We assume that firms can lower future emissions intensity through environmentally oriented investment, which may include cleaner capital replacement, pollution-control equipment, process redesign, or other forms of operational adjustment. Let $G_t$ denote such investment. Emissions intensity then evolves according to
so that higher environmentally oriented investment reduces next period's emissions intensity. This interpretation is consistent with evidence that long-run declines in industrial pollution are driven to an important extent by falling emissions intensity rather than by output contraction alone shapiro2018pollution.
A simple way to embed financial structure is to assume that firms choose current activity $q_t$ and environmentally oriented investment $G_t$ to maximise
subject to (ref). Here $A_t$ is an aggregate demand or productivity shifter, $\lambda_t$ is the effective shadow cost of emissions, $c_t$ is internal liquidity, and $\psi_t$ is a financing wedge that raises the effective cost of environmentally oriented investment. We assume
where $d_t$ denotes leverage and $\xi_t$ denotes aggregate financing tightness. In this formulation, internal liquidity facilitates environmental adjustment, whereas leverage and tighter macro-financial conditions make such adjustment more costly.
This setup also clarifies the interpretation of the observed investment-intensity variable used in the empirical analysis. Let total observed investment be denoted by $I_t$, and let the share of that investment directed toward emissions-reducing adjustment be $\omega_t \in [0,1]$. Then
where $\text{Invint}_t = I_t/K_{t-1}$ is observed investment intensity and $K_{t-1}$ is a scale variable such as lagged PP&E. Equation (ref) implies that the reduced-form coefficient on investment intensity need not be constant over time. When the environmentally oriented share of investment is small, investment intensity mainly reflects ordinary expansionary investment; when that share rises, the same observed variable increasingly proxies emissions-reducing adjustment.
The framework yields four qualitative implications that are directly relevant for the empirical analysis. First, holding emissions intensity fixed, higher activity raises emissions, so variables that proxy current scale, such as sales, are more likely to be positively associated with emissions growth when the scale channel dominates. Second, greater environmentally oriented investment lowers future emissions intensity and therefore tends to reduce subsequent emissions growth. Third, internal liquidity facilitates such adjustment, whereas leverage and tighter aggregate financing conditions hinder it by raising its effective cost. Fourth, because the state variables $(A_t,\lambda_t,\xi_t,\omega_t)$ evolve over time, the reduced-form relationship between emissions growth and firm characteristics need not be stable across periods. The role of the empirical specification is therefore not to estimate structural parameters of (ref), but to document how the visibility of these economic margins changes over time. The appendix provides more detail on this framework.
The non-parametric time-varying model, which employs kernel-based weights and assigns different weights to observations based on a rolling window following giraitis2014inference and giraitis2021time, takes the form of
where $y_{it}$ denotes the explained variable, $x_{it}=(x_{1,it}, ..., x_{p,it})'$ is a $p \times 1$ set of explanatory variables. $\beta_{it}=(\beta_{1,it}, ..., \beta_{p,it})'$ is a $p \times 1$ coefficient vector that can change with time $t$ based on rolling window, and $u_{it}$ is a $1 \times 1$ noise.
The estimation of time-varying $\beta_{it}$ mathematically can be defined, following giraitis2021time and bai2023mean, as
with kernel weights $b_H,|j-t|$ and bandwidth parameter $H$ defined as
where $H$ is the bandwidth parameter that controls the smoothness of weights, and $K(.)$ is a kernel function that takes in distance and gives out the weight. We assume $K(.)$ is non-negative and continuous, with either compact support or sufficiently fast tail decay, and that $K$ and $K'$ are bounded by $C(1 + |x|^v)^{-1}$ for some $C > 0$, $v \ge 2$ (examples include the uniform, Epanechnikov, and Gaussian kernels). The bandwidth satisfies $H \rightarrow \infty$ and $H = o(T)$ as $T \rightarrow \infty$, ensuring a standard bias-variance trade-off, where the effective sample around $t$ grows (variance shrinks) while the window remains local (time variation is preserved). For the typical Gaussian kernel used in many empirical research, $K(x) \propto exp(-cx^\alpha)$.
We adopt a mean-group estimation rather than pooled OLS, for each time $t$, the period coefficient $\hat{\beta}_t$ is a simple average of all individual estimators:
as pesaran1995estimating, and similar to bai2023mean without the instrumental variable (IV) part. For each individual regression within the mean-group, we add a constant term to include an intercept in the estimation.
\paragraph{Remark 1.} In all unit-specific local regressions we include a constant, $x_{1,it} = 1$. The associated time-varying coefficient, $\beta_{1,it}$, plays the role of a unit effect $\alpha_{it}$ that is allowed to drift slowly over $t$, under the same smoothness conditions imposed on the other coefficients. An equivalent treatment would be to first partial out the intercept by regressing $y_{it}$ and each element of $x_{it}$ on a constant within unit-either fixed over time (if $\alpha_i$ is truly constant) or estimated via a kernel-smoothed “time-varying constant" (if $\alpha_{it}$ drifts), and then to run the TVMG regression on the residuals without an intercept. Under our assumptions, this preliminary step does not affect the subsequent theoretical analysis or inference for the slope paths, so adopting the in-model time-varying intercept is without loss of generality. Practically, this choice accommodates slowly evolving unit baselines (e.g., facility-specific emission levels) while avoiding an additional filtering step, and we do not interpret the intercept path itself. \paragraph
Next, we outline relevant assumptions on $x_{it}$ and $u_{it}$, following giraitis2014inference, giraitis2021time, and bai2023mean.
\paragraph{Assumption 1.} Elements of $x_{it}$ and $u_{it}$ have the following properties.
\paragraph{Assumption 2.} With $e_i$ being the random-coefficient deviation $\beta_{i} = \beta_{0} + e_{i}$, $(x_i, u_i, e_i)$ are mutually independent across $i$, where $x_i = (x'_{i1}, x'_{i2}, ..., x'_{iT})'$, $u_i = (u_{i1}, u_{i2}, ..., u_{iT})'$, and $e_i = (e_{i1}, e_{i2}, ..., e_{iT})'$.
\paragraph{Assumption 3.} The coefficients $\beta_{it}$ follow the random coefficient model
we have
\paragraph
Assumption 1(i) imposes high-order moment bounds on regressors and errors. These conditions control tail behavior and ensure concentration for the kernel-weighted sums used in the unit-level local regressions. In particular, the requirement that $E|x_{\ell,it}|^\theta$ and $E|u_{\ell,it}|^\theta$ are uniformly bounded (for some $\theta > 4$) allows us to apply exponential/maximal inequalities to obtain uniform consistency rates for the local estimators and to derive pointwise asymptotic normality at interior dates. The moment bound is mild, where typical firm-level variables satisfy it after standard scaling or log transforms. Assumption 1(ii) places strong-mixing ($\alpha$-mixing) conditions on the time series. This permits serial correlation and conditional heteroskedasticity while ruling out long memory. The geometric decay of the mixing coefficients guarantees that observations sufficiently far apart in time are nearly independent, which underpins the law of large numbers and CLTs for kernel averages. Together with 1(i), these conditions yield tight control of the stochastic part of the local OLS fits across all $t$. Assumption 1(iii) is the exogeneity condition for local OLS. It ensures that, at each date $t$, regressors are mean-independent of the structural disturbance and that the local estimators target the true unit-specific coefficients $\beta_{it}$. The assumption is compatible with rich dynamics in the data (including serial correlation in $u_{it}$) and with a time-varying intercept treated as one element of $x_{it}$. Assumption 1(iv) is a no near-multicollinearity condition. The regressor covariance matrices $\Sigma^i_{xx,t} = E[x_{it}x'_{it}]$ are uniformly nonsingular, which keeps the local design well-conditioned for all $t$ and prevents explosion of variances. In practice, this amounts to excluding pathological cases where some regressors become almost perfectly collinear within the local kernel window.
Regarding cross-sectional behavior, Assumption 2 formalizes the random-coefficient mean-group setting and the cross-section structure. Each unit’s coefficient path is written as $\beta_{i} = \beta_{0} + e_{i}$, where $\beta_{0}$ denotes the deterministic target of interest. $e_{i}$ captures unit-specific deviations. Stacking time paths, we assume $(x_i, u_i, e_i)$ are independent across units, allowing for unrestricted heterogeneity in distributions across $i$. This delivers a cross-sectional CLT for the mean-group estimator $\hat{\beta}_{MG} = N^{-1}\sum_i \hat{\beta}_{i}$ with asymptotic variance driven by the cross-sectional dispersion of $e_{i}$.
Assumption 3 introduces the random-coefficient structure $\beta_{it} = \beta_{0,t} + e_{it}$ and regulates how coefficients vary over time. Part (i) defines the estimand: $\beta_{0,t} = E(\beta_{it})$ is the cross-sectional mean coefficient path, treated as non-random in $t$. The mean-group estimator targets this sequence. Part (ii) imposes smooth time variation on $\beta_{0,t}$, where the component is H\"older-continuous. This bounds how fast the target can drift and implies that, in a local window of width $H$, the deterministic bias of the kernel estimator is $O((H/T)^{\gamma_1})$. Part (iii) lets unit-specific deviations $e_{it}$ evolve idiosyncratically but also slowly, via the analogous H\"older bound with thin-tailed random moduli $q_{\ell,i,ts}$. The thin-tail condition rules out rare, explosive jumps and ensures uniform control of stochastic errors. Together, (i)–(iii) guarantee that kernel smoothing recovers a well-defined, slowly varying mean path, that local bias can be made negligible relative to sampling variation, and that the mean-group estimator admits uniform consistency and pointwise asymptotic normality at interior times.
\paragraph{Remark 2.} Under Assumptions 1–3, let $H \rightarrow \infty$ and $H = o(T)$. Then, as $(N,T) \rightarrow \infty$, we have uniform consistency where
For pointwise asymptotic normality, if the bias is negligible relative to $N^{-1/2}$, i.e. $(H/T)^{\gamma_1} = o(N^{-1/2})$, then for any interior time $t$,
With $\hat\beta_{it}$ the unit-level local OLS at t,
\paragraph{Bandwidth selection}
In choosing the bandwidth $H$, with $H \rightarrow \infty$ and $H = o(T)$, and enforce inference condition $(H/T)^{\gamma_1} = o(N^{-1/2})$, as giraitis2014inference, giraitis2018inference, and giraitis2021time, appropriate setting can be $H = T^{\alpha}$ with $0 < \alpha < 1$. For choosing $\alpha$, two methods can be adopted: (1) use a technique called leave-one-unit-out cross-validation to choose $\alpha$ value from a discrete grid search, which is used and described in bai2023mean as well with $\alpha \in \{0.3, 0.35, ..., 0.8, 0.85\}$; and (2) via rule-of-thumb set $\alpha = \frac{1}{2}$ as the bandwidth, where giraitis2018inference and giraitis2021time found that this setting leads to overall best finite sample performance. \paragraph
Overall, the model applied to emissions data can be written as
where $x_{J(i,t)}$ is the set of proposed explanatory variables, with $J(i,t)$ the function that identifies company (or “county" for unemployment) $j$ owning facility $i$ at time $t$, and also points out time $t$. $\beta_{t}$ is the mean-group slope, $\alpha_{it}$ is unit effects as described in Remark 1, and $u_{it}$ is the idiosyncratic component. $\beta_t$ is obtained by first estimating unit-specific coefficients via kernel smoothing and then averaging them across units as Equation (ref). The explained variable following andrikogiannopoulou2025not is the percentage change of emissions as defined in greenstone2003estimating as
This measure of percentage change, which takes values in the interval $[-2,2]$, is constructed to reflect expansions and contractions symmetrically. Emissions included are on-site only, with three discharge channels: air, water, and ground.
Our data consist of three parts: facility-level data from the Toxics Release Inventory (TRI) by the U.S. Environmental Protection Agency (EPA), firm-level data from Compustat and Execucomp, as well as macroeconomic data from the FRED-QD dataset.
Data preprocessing is conducted prior to the empirical analysis to ensure consistency in the panel structure. The raw dataset contains 32 years of annual observations from 1992 to 2023. Facility-level unit data with missing essential information such as lacking facility emissions records or parent firms without reported sales in a given year are excluded, to maintain a balanced panel. After applying first-difference transformations, such as computing percentage changes in emissions or constructing lagged PP&E, the resulting balanced dataset contains $T = 31$ years of facility-level observations.
To link facilities to their parent companies, we first assign each facility a Compustat identifier (GVKEY) based on its associated firm, which then enables the merging of firm-level variables with facility-level records. We follow the matching algorithm as andrikogiannopoulou2025not. In addition, the GVKEY assignment is carried out by matching either the “standard parent company name" or the “parent company name" in the TRI dataset to the “company name" field in the Compustat fundamentals dataset. When a valid match is identified, the corresponding GVKEY is attributed to the facility.
Facility-level emission data are sourced from the Toxics Release Inventory (TRI) established by the U.S. Environmental Protection Agency (EPA), under the Emergency Planning and Community Right-to-Know Act (EPCRA) of 1986.\footnote{TRI webpage: https://www.epa.gov/toxics-release-inventory-tri-program.} It collects and publicly releases data on the management and environmental release of certain toxic chemicals from industrial and federal facilities across the United States. Facilities in manufacturing, energy, mining, and other sectors must annually report the quantities of listed chemicals they release into the air, water, and land, as well as those managed through recycling, energy recovery, or treatment. The aims of TRI include increasing transparency, supporting community awareness, and encouraging pollution prevention by providing detailed, facility-level data that help policymakers, researchers, and the public track trends in chemical management and environmental performance over time. The TRI dataset provides annual information on the quantities of over 650 listed chemicals released or managed by facilities, along with detailed attributes such as facility location, industry classification (NAICS/SIC codes), parent company identifiers, and types of waste management activities. The data cover a wide range of manufacturing and processing sectors and span several decades, allowing for consistent longitudinal analysis. Because facilities are required to report under standardized EPA guidelines, the TRI provides comparable and verifiable measures of toxic releases that can be linked to other datasets, such as firm-level financial information, which is one of the focuses of this study.
TRI primarily uses “TRIFID" as its unique facility identifier, while also having “FRS ID" to align with other EPA programs. TRIFID together with year entry can point out a specific facility-year observation, which forms our panel data sample. TRI categorizes emissions into three aspects based on the channel of emission: air, water, and ground. Air emissions include fugitive and stack air. Water emissions consist of releases to streams and other surface bodies of water. Ground emissions include waste disposed in underground injection wells, landfills, surface impoundments, or spills and leaks released to land. For representing the total emissions of facilities, we use the sum of air, water, and ground emissions on-site only (i.e., excluding recycling, recovery, and treatment). All emission quantities are converted to units of pounds.
This study utilizes firm-level data from Compustat “North America Fundamentals Annual" and Execucomp “Annual Compensation", both provided by S&P Global Market Intelligence. The Compustat database contains standardized financial statement information for publicly listed firms in the United States and Canada, covering key accounting variables. These data are widely used to construct measures of firm performance and capital structure. The Execucomp database complements this financial information by providing comprehensive data on executive characteristics and compensation, such as CEO identity, age, gender, and tenure. Together, these datasets offer a consistent and reliable source for firms’ financial conditions and managerial characteristics, which we aim to examine their impacts on facility emissions.
The study also incorporates county-level unemployment data obtained from the U.S. Bureau of Labor Statistics (BLS).\footnote{BLS data webpage: https://www.bls.gov/data/.} The BLS provides consistent and publicly available measures of labor market conditions through its Local Area Unemployment Statistics (LAUS) program, which reports monthly and annual estimates of unemployment and other labor force statistics for each U.S. county. These data are constructed using a combination of household and establishment surveys, administrative records, and statistical models, ensuring comparability across counties and over time.
Table (ref) presents potential variables and their definition. Most of the variables are calculated from raw Compustat and Execucomp data, which are displayed in Table (ref) in Appendix (ref). In addition, Table (ref) introduces the corresponding effect channels.
For broad macroeconomic indicators at the country level, we draw on the FRED-QD dataset compiled by mccracken2020fred. The Federal Reserve Economic Data – Quarterly Database provides a comprehensive and consistently updated collection of U.S. macroeconomic and financial time series, sourced primarily from the Federal Reserve Bank of St. Louis. It contains over 200 quarterly variables covering real activity, labor markets, prices, money and credit, interest rates, and asset prices, all organized with standardized mnemonics and transformations suitable for empirical macroeconomic research. The dataset facilitates the construction of aggregate economic indicators, which together provide an overview of macroeconomic conditions. Table (ref) presents all entries of the FRED-QD dataset with descriptions. The dataset is in quarterly frequency. To align it with our yearly data, we average the four quarters for each year and then apply PCA to extract the common factor. Since we want PCA factors to represent cyclical macro conditions, most series need to be transformed into a stationary form. The original paper provides the corresponding appropriate transformations for each macro variable, indicated by the “T-Code", as displayed in Equation (ref).
We primarily use the first Principal Component (PC-1) extracted from the FRED-QD macro dataset as a summary indicator of overall economic conditions. Principal Component Analysis (PCA) provides a systematic way to condense information from a large set of correlated macroeconomic variables into a smaller number of orthogonal components that capture the dominant sources of variation in the data. Formally, if $X_t = (x_{1t}, x_{2t}, ..., x_{pt})'$ represents a vector of standardized macroeconomic variables at time $t$, the first principal component is defined as
where $a_1$ is the eigenvector associated with the largest eigenvalue of the covariance matrix of $X_t$. The coefficients in $a_1$ are chosen to maximize the variance of $PC_{1,t}$, subject to the constraint that $a'_1 a_1 = 1$. In practice, this component captures the largest common movement across macroeconomic indicators such as output or major stock market indexes, generally reflecting the business cycle, thereby summarizing the state of the aggregate economy in a single index. This approach allows the analysis to control for cyclical macroeconomic fluctuations without introducing multicollinearity from multiple correlated macro variables. Figure (ref) shows the trend of the principal component factor score estimated from FRED-QD. Two troughs appear at the 2008 financial crisis and the 2020 pandemic.
Our balanced panel data sample contains 6528 facility-years that are matched across TRI, BLS, and the principal component constructed from FRED-QD. With a time span of 32 years from 1992 to 2023, there are 204 facilities. In total, there are 92 parent firms and 297 CEOs corresponding to the facilities, with Berkshire Hathaway Inc. owning the most facilities, totaling 29. Most firms own 1 to 3 facilities. There are 42 states in which facilities are located, and Ohio (OH) has the highest number of facilities, totaling 19. The transformed annual FRED-QD dataset used for PCA contains 237 series within the 32-year time span.
The 6528 facility-year count refers to the matched facility-level panel over 1992–2023, while the TVMG estimation samples are smaller because the percentage-change outcome uses the previous year’s emissions as well as differencing variables, and thus begins in 1993. The experimental dataset therefore contains 6324 observations, obtained by excluding the 204 first-year facility observations from the original 6528 observations.
Table (ref) reports summary statistics for facility-level emissions. On average, a facility releases roughly 326 thousand pounds of pollutants per year, with air emissions constituting the largest share at approximately 216 thousand pounds. Median emissions to water and ground are zero, indicating that more than half of facilities do not discharge into these media in a given year. Emissions distributions are highly skewed, as reflected in the large standard deviations relative to the means. Consistent with long-run declines in industrial pollution, total emissions decrease over time at an average annual rate of about 4.9%, driven primarily by reductions in air emissions. Water emissions exhibit a slight positive trend, while ground emissions decrease modestly. Figure (ref) further illustrates these dynamics: aggregate total and air emissions fall sharply in the early 1990s and continue declining gradually thereafter, whereas water emissions rise substantially in the initial years before stabilizing, and ground emissions decline early in the sample and then level off. Together, these patterns suggest sustained improvements in facility environmental performance, particularly with respect to air releases.
Table (ref) summarizes key financial and executive characteristics of parent firms, along with county-level unemployment rate. On average, firms in the sample are large, with mean lagged total assets of \$27.9 billion (median \$4.4 billion), and mean sales of \$18.0 billion (median \$4.5 billion), indicating a right-skewed size distribution. Firms exhibit moderate leverage, with a mean ratio of 0.27, and maintain average cash holdings of approximately 9.2% of total assets. Investment intensity averages 0.18, while the mean Tobin's Q is 1.76, suggesting that firms generally have positive growth opportunities. Executive characteristics show that female CEOs are rare, representing about 1.7% of firm-years, whereas approximately 42% of CEOs are at or above age 60, highlighting an older leadership structure among publicly traded firms. Finally, the average county unemployment rate during the sample period is 5.7%, with substantial variation across counties and over time. These statistics reflect a sample of large, financially established firms with relatively stable financial positions and infrequent female representation in CEO roles.
Guided by the economic framework presented earlier, the baseline single-regressor specifications can be viewed as making one economic margin more visible at a time. Variables such as sales are most naturally linked to the scale margin, whereas investment intensity and cash holdings are more closely connected to the adjustment margin through their association with environmentally oriented investment and the firm's ability to finance it. In this sense, the baseline analysis is useful not because it assigns a fully structural interpretation to any one coefficient, but because it shows when each of these margins appears most clearly in the data.
In the baseline univariate TVMG analysis, each proposed determinant is estimated using a variable-specific balanced panel. This design preserves the balanced time-series structure required for the time-varying mean-group estimator while avoiding the loss of observations that would arise from imposing a single common sample across all covariates. Thus, for each coefficient path, the estimating sample includes the facilities and parent firms with complete usable observations for the dependent variable and the regressor under consideration. The baseline results should therefore be read as variable-specific evidence: differences across coefficient paths reflect both the economic channel associated with each variable and the largest balanced facility-firm panel available for estimating that channel. Table (ref) presents the relevant sample information.
We start with testing the relationship between facility emissions and each proposed variable with the TVMG model. Equation (ref) is estimated with a single regressor, where
following Equation (ref) as the explained variable, and different characteristic variables shown in Table (ref) as the explanatory variable. The estimation uses a Gaussian kernel for smoothing. $\beta_t$ is estimated via mean-group as Equation (ref).
We select bandwidth via two different methods: leave-one-unit-out cross-validation, as well as a fixed bandwidth. The results show that a fixed bandwidth, regardless of explanatory variable, yields better performance. Thus, for this study we use fixed bandwidth $H = \sqrt{T} \approx 5.57$. The confidence intervals are set at 90% level. Figure (ref) shows the time-varying coefficients across the time span of 1993 to 2023. Five variables display statistically significant periods, with their significant periods and directions of correlation presented in Table (ref). As comparison, results from a cross-validation selection of bandwidth are reported in Table (ref) and Figure (ref).
Our model shows a short period of statistically significant negative association for investment intensity from 2009 to 2014. In 2011, the Greenhouse Gas Reporting Program (GHGRP) initiated by EPA started the first wave of data reporting, covering emissions from 2010. This marked a huge event for emissions control in the US. Large plants emitting more than 25 kt CO2 had to publish their numbers from 2011. They cut emission rates by about 7% while owners simultaneously trimmed expansion spending and shifted activity to smaller sites yang2021real. Transparency and investor/shareholder pressure in the 2010s made corporate managers more sensitive to emissions when planning capital investments. Many U.S. companies (especially large public ones) were actively trying to decouple growth from emissions – either by investing in cleaner processes or by limiting expansion of emissions-heavy operations, which results in a higher ratio of capital expenditures to lagged PP&E, but a lower change in emissions. shapiro2018pollution. tomar2023greenhouse finds that once GHGRP data became public (2012-13), facilities lowered GHGs by 7.9% and their parent firms raised CapEx by 2.5% of assets to fund abatement projects. fell2018fall show that cheap shale gas plus fast-growing wind generation cut coal-fired output 25% from 2007 to 2013, accounting for “the vast majority" of power-sector CO2 reductions. Utilities were pouring CapEx into new combined-cycle gas turbines and wind farms (small PPE base, low on-site CO2) while retiring coal units (large PPE, high CO2, little new CapEx). Thus, higher CapEx / PPE shows up at lower emission-growth facilities. davis2022coal document that almost one-third of the U.S. coal fleet retired during the early-2010s, with a quarter of the remaining capacity has announced plans to retire. Retiring plants keep a large legacy PPE denominator but virtually zero new CapEx, and their absolute emissions plunge once mothballed. This intensifies the negative correlation found.
A negative regression coefficient is found between the percentage change of emissions and cash holding during 1998 to 2004. For financial performance, waddock1997corporate posits that financially healthy firms with abundant slack (extra resources like cash) can invest in discretionary initiatives such as environmental improvements. Environmental protection often requires up-front costs (for cleaner technology, pollution control equipment, process upgrades, etc.), which are easier to bear for cash-rich firms. By contrast, financially constrained firms may delay or forego such investments, focusing on immediate survival or core operations. konar2001does, orlitzky2003corporate, and huang2019chemical all argue that a negative association exists between toxic emissions / environmental disadvantage and firm's financial performance. For the period 2000 to 2002, attention on environmental protection and corporate transparency gradually increases. Many Clean Air Act programs had major milestones around 2000. Notably, Phase II of the Acid Rain Program took full effect in 2000, dramatically tightening SO2 and NOx emission caps for power plants. konar2001does showed capital markets started to reward good environmental performance and penalize poor performance around the period.
A positive correlation was found for the parent firm log of sales from 1993 to 1997, and 2006 to 2013 after a few years of borderline insignificance. It was generally assumed (and often observed) with many literature supports that increases in a firm’s economic activity would lead to increases in environmental harm (see, e.g., hertwich2010assessing). At a later stage, the coefficient loses its statistical significance from 2014. This was primarily due to technological advances and stronger regulations. shapiro2018pollution finds evidence on manufacturing and lacount2021reducing on power sector that, despite growth in production or trading etc..., during the period companies managed to reduce emissions (whether in pollution per unit base or in total), because of technological innovation and stronger regulation by the EPA and government.
With our TVMG model, only the year 1993 shows a statistically significant positive coefficient for the dummy variable indicating whether the age of the parent firm’s CEO is older than 60. To explain this, CEO characteristics have been found to have an impact on decision-making and attitude towards sustainable and social development manner2010impact, huang2013impact. It is plausible that older CEOs in 1993 (many of whom began their careers decades earlier, in a time of loose environmental oversight) were less responsive or slower to adapt to these rising environmental expectations, whereas younger CEOs were more willing to innovate and proactively reduce emissions. hossain2023does argue that CEO's tendency toward risk aversion can frequently result in unethical consequences, such as environmental degradation, and is often a significant factor influencing firm-level carbon emissions. Before 1993, environmental concerns were not a central focus for most firms, with limited regulatory pressure and low public awareness contributing to minimal corporate attention to sustainability. However, starting in the mid-1990s, growing environmental movements, emerging climate science, and the introduction of stricter environmental regulations by the EPA began to shift this dynamic. Over time, environmental responsibility became an increasingly important consideration in corporate strategy, and managerial characteristics like CEO age lost explanatory power in later periods.
From 1993 to 1996, and 2013 to 2016, the model shows that there was a statistically significant negative correlation between the percentage change in a facility’s emissions and the unemployment rate of its county. The U.S. entered the 1990s coming off a recession (1990–91) that hit manufacturing and heavy industry hard. Many counties still had elevated unemployment in the 1993–1996 window as they struggled to regain jobs. In such places, factories often ran at lower capacity, produced less pollution, or even shut down facilities, directly reducing emissions. Empirical evidence backs this: arora1999community examined toxic release changes around 1993 and found that releases decline in neighborhoods with high unemployment. In their data, communities with unemployment rates above about 10% saw a drop in toxic releases, whereas some economically better-off areas saw smaller changes. As for the later timeframe – a period of stable and economic growth in many U.S. counties, the common pattern of the “Environmental Phillips Curve"(EPC) shows clearly, i.e., inverse association between unemployment and emissions. Many studies have documented this relationship (see, e.g., azimi2024examining, davis2010economic).
The baseline results are most coherent when read as different moments in the framework's channel hierarchy. Sales is the direct proxy for $q_t$, the activity margin. Its positive coefficient periods from 1993 to 2013 imply that, for much of the sample, higher parent-firm operating scale translated into higher facility emissions growth because $\Delta \log q_t$ dominated any offsetting decline in $\Delta \log m_t$. The loss of significance after 2013 is therefore not just a weakening of sales as a variable; it is evidence that the link between activity and emissions became less mechanical. By then, cleaner capital, fuel substitution, disclosure, and regulatory pressure had raised the importance of the intensity margin. This is consistent with shapiro2018pollution, who show that U.S. manufacturing emissions fell mainly through within-product reductions in emissions intensity rather than output contraction, and with lacount2021reducing, who describe long-run Clean Air Act implementation in the power sector.
\paragraph{Economic framework interpretation} Investment intensity enters the framework through $G_t = \omega_t I_t$. The key is $\omega_t$, the share of observed investment directed toward emissions-reducing adjustment. The negative investment-intensity coefficient in 2009-2014 indicates that $\omega_t$ rose enough for investment to proxy cleaner capital replacement, abatement equipment, fuel switching, or process redesign rather than ordinary capacity expansion. The timing fits the early GHGRP reporting period, when $\lambda_t$, the effective shadow cost of emissions, increased through public disclosure and investor scrutiny. yang2021real find emissions-rate reductions after mandatory GHGRP disclosure, and tomar2023greenhouse shows that disclosure and benchmarking induced abatement-related investment. Energy-market adjustment reinforced this channel: fell2018fall link emissions reductions to shale gas and renewables, while davis2022coal document major coal retirements during the 2010s. In framework terms, the negative coefficient appears when rising $\lambda_t$ and $\omega_t$ make investment intensity an adjustment-margin variable rather than a scale-margin variable.
Cash holdings are the empirical counterpart of $c_t$, internal liquidity. The negative coefficient in 1998-2004 suggests that liquidity mattered most when firms faced a discrete increase in compliance pressure, especially around Phase II of the Acid Rain Program and broader Clean Air Act implementation. Cash-rich firms could absorb upfront costs of pollution-control equipment, process retrofits, and operational interruption without relying on external finance. In the framework, higher $c_t$ lowers the effective cost of $G_t$, allowing firms to reduce future $m_t$. This aligns with the slack-resources argument in waddock1997corporate and with xu2022financial, who show that financial constraints increase toxic releases. The short window is plausible because liquidity is most visible exactly when adjustment costs are high and compliance timing is sharp; once control routines diffuse, $c_t$ becomes less distinguishable in a single-regressor specification.
CEO age and local unemployment map to different framework channels. The positive CEO-age result in 1993 reflects the managerial allocation channel: leadership affects $\omega_t$ and the willingness to respond to rising $\lambda_t$ before environmental management becomes routinized. Older CEOs in the early 1990s may have been more attached to legacy production practices, so managerial discretion mattered when formal disclosure and compliance systems were less mature. manner2010impact, huang2013impact, and hossain2023does support the broader view that CEO traits and risk preferences shape sustainability outcomes. Unemployment, by contrast, proxies local $q_t$. Its negative association in 1993-1996 and 2013-2016 means weak local labor markets coincide with lower utilization and slower emissions growth. arora1999community provide TRI-based evidence on community conditions and toxic releases, while heutel2012should shows emissions are procyclical in a business-cycle model.
\paragraph{Static estimation} To assess whether time-varying coefficients are substantively important, we also estimate a static mean-group OLS model as a benchmark, thereby obtaining time-invariant coefficient estimates for comparison. The model takes the form
where $\beta$ estimated via mean-group
Table (ref) presents the static OLS mean-group estimation results, where coefficients are assumed to be constant over time. Results show that most variables exhibit no statistically significant association with changes in facility emissions over the full sample period. Most regressors yield small and statistically insignificant coefficients, indicating no detectable effect when the model imposes a time-invariant structure. The only two significant variables are sales and unemployment, with a positive coefficient at the 5% level and a negative coefficient at the 10% level, respectively, consistent with a scale effect where larger firms or more activity tend to increase emissions on average. Apart from this association, the static OLS framework suggests a largely weak relationship between firm-level characteristics (or unemployment) and emission dynamics.
Static OLS results largely reflect the limitations of static estimation. By forcing coefficients to be constant across nearly three decades, the model effectively averages across periods in which the effect of a variable may strengthen, weaken, or reverse. This averaging masks episodic but economically meaningful patterns, leading to attenuation and loss of significance. In contrast, the time-varying method uncovers specific periods during which variables may have statistically significant explanatory power. The comparison therefore indicates that while static OLS identifies only a persistent scale effect through sales, dynamic estimation reveals richer temporal structure and more nuanced firm–environment interactions. This highlights the importance of allowing coefficients to vary over time when studying emission behaviors in evolving regulatory and economic environments.
\paragraph{Structural coefficient-shift}
We conduct a structural coefficient-shift exercise around 2009 to assess whether the relationships estimated in the TVMG analysis exhibit a discrete post-2009 break. The year 2009 is used as a theoretically meaningful boundary because it coincides with the aftermath of the Great Recession and a major shift in the U.S. climate-regulatory environment, including EPA's 2009 greenhouse-gas reporting and endangerment actions. The test is therefore designed to capture whether firms' emissions-related responses changed after a period of substantial macroeconomic disruption and increased regulatory salience.
For each explanatory variable, we estimate a facility-level interaction specification. The detailed framework is presented in Appendix (ref). The results provide limited evidence of a sharp and uniform structural break in 2009. Most variables have post-2009 shift estimates whose confidence intervals include zero. Unemployment provides the clearest weak evidence of change: its coefficient remains negative but becomes less negative after 2009, with a shift of $0.004$ significant at the 10 percent level ($p=0.090$). Overall, the test suggests that the post-2009 change in emissions determinants was not primarily a discrete regime break. This supports the use of the kernel-smoothed TVMG approach in the main analysis, since that method allows coefficients to evolve gradually over time without imposing a predetermined structural break.
\paragraph{Sectoral analysis}
To further examine the baseline time-varying mean-group (TVMG) relationships with particular industrial structures, we conduct a sectoral analysis that exploits the NAICS classification of firms. While the baseline results pool all industries, emissions processes are inherently tied to production technologies, energy use, and regulatory exposure, which vary across sectors. As a result, the same firm characteristic, such as financial or managerial traits, may reflect different underlying mechanisms depending on the production environment.
To address this heterogeneity, we restrict attention to the individual sectors where the sample coverage is sufficiently rich to support reliable TVMG estimation. We first present results for the broad manufacturing group and then further disaggregate into major three-digit subsectors. This allows us to distinguish between common patterns that persist across sector-specific dynamics that may be masked in the aggregate.
The detailed sector-level estimation results, including specific figures and extended interpretation, are provided in the Sectoral Analysis Appendix (ref). The appendix documents how the timing, sign, and persistence of estimated associations differ across industries, and links these patterns to differences in production technologies, scale versus technique effects, and sector-specific adjustment processes.
To assess the stability and credibility of the baseline time-varying mean-group (TVMG) estimates, we conduct a sequence of complementary robustness checks that address potential sources of sensitivity in both cross-sectional influence and time-series smoothing. First, we implement a leave-one-firm-out (LOFO) procedure to examine whether the estimated average time-varying coefficients are disproportionately driven by any single parent firm, particularly large firms with multiple facilities. Second, we evaluate the sensitivity of the estimated coefficient paths to the assumed degree of temporal smoothness by re-estimating the model under alternative bandwidths and kernel functions, thereby assessing whether the results depend on a particular bias–variance trade-off or weighting scheme inherent in kernel-based local estimation. Finally, we adopt a duration-based criterion that restricts attention to effects that remain statistically significant for at least three consecutive years, providing a conservative filter that emphasizes economically meaningful and persistent time-varying relationships.
To examine whether the baseline time-varying mean-group (TVMG) results are unduly driven by any single parent firm, we conduct a leave-one-firm-out (LOFO) robustness check. The design directly targets potential concerns that large firms with many facilities, or firms exhibiting idiosyncratic emission dynamics, may exert disproportionate influence on the estimated average time-varying coefficients. Specifically, the full estimation procedure is repeated multiple times, each time excluding all facilities associated with one parent firm from the sample:
where $f$ indicates firms through GVKEY identifiers. This exclusion is implemented at the firm level rather than the facility-year level, ensuring that all observations belonging to a given firm are removed simultaneously. For each LOFO iteration, we re-estimate the model at the facility level and then recompute the mean-group aggregation across the remaining firms, yielding a sequence of alternative time-varying coefficient paths. These paths are compared to the baseline estimates obtained from the full sample. Stability of $\hat{\beta}^{(-f)}_{MG,t}$ across $f$ supports robustness. In particular, we examine whether excluding any single firm leads to substantial changes in the magnitude of the estimated effects or sign reversals, given by
respectively.
Table (ref) presents the LOFO robustness check results, showing as Maximum Deviation Ratio (MDR) and Sign Flip Ratio (SFR), on the left and right of each variable-year, respectively. Most MDR values during the significant periods fall within the range of 0.4–0.7, indicating a moderate influence of large firms. Nevertheless, there are no sign flips in the significant periods, representing a stable estimation of directions. Significance periods coincide with relatively low MDR and SFR over the time span for each variable. Taken together, these findings confirm that the baseline TVMG results are not largely driven by a small subset of influential parent firms. Instead, the estimated time-varying relationships reflect common patterns across firms, reinforcing the credibility and representativeness of the main empirical conclusions.
For evaluating the sensitivity of the estimated time-varying relationships to the assumed degree of smoothness, we conduct a smoothness robustness check by re-estimating the baseline TVMG models using alternative bandwidths and kernel functions. The bandwidth governs the extent of temporal smoothing by controlling the width of the local estimation window, while the kernel determines how observations are weighted as a function of their distance from each evaluation point in time. Because both choices directly affect the bias–variance trade-off inherent in kernel-based estimation, examining alternative specifications provides an important check on whether the results are driven by a particular smoothing assumption rather than by underlying data patterns.
Specifically, we vary the bandwidth around the baseline choice $H=\sqrt{T}$ with $T^{0.4}$ and $T^{0.6}$, respectively. A smaller bandwidth places greater weight on nearby observations and allows for more local fluctuation, while a larger bandwidth imposes stronger smoothness by borrowing information from a wider time window. Figure (ref) and (ref) display the time-varying coefficient results. Across the two alternative specifications, the estimated coefficient paths remain qualitatively consistent with the baseline in terms of overall shape, direction, and timing of major movements. Using the smaller bandwidth $H=T^{0.4}$ produces slightly more pronounced local variation and wider confidence bands in certain periods, reflecting higher estimation variance, whereas the larger bandwidth $H=T^{0.6}$ yields smoother trajectories with attenuated short-run fluctuations and narrower relative changes over time. Importantly, the main patterns—such as persistent sign behavior and the broad timing of periods with stronger or weaker effects—are preserved under both bandwidth choices.
For an alternative kernel function choice, we re-estimate the models using the Epanechnikov kernel in place of the Gaussian kernel, with
While the Gaussian kernel assigns strictly positive weights to all observations, the Epanechnikov kernel has compact support, placing zero weight on observations outside the bandwidth window and relatively more weight on observations close to the evaluation point. Figure (ref) presents the estimations using Epanechnikov kernel with fixed bandwidth. Relative to the baseline Gaussian specification, the Epanechnikov kernel produces coefficient paths that are broadly consistent in sign and overall shape, indicating a degree of kernel invariance in the estimated relationships. As expected given the kernel’s compact support, the estimates exhibit sharper local movements and somewhat wider confidence intervals in periods with fewer effective observations. Nevertheless, despite often shorter significance periods, the dominant temporal patterns—such as shifts in coefficient levels and the persistence of some economically meaningful periods remain intact.
Taken together, these results indicate that the baseline findings are not driven by a specific smoothness assumption. While the degree of smoothness affects the volatility and precision of the estimated paths, the substantive time-varying relationships remain stable across reasonable bandwidth and kernel choices. This reinforces the interpretation that the observed dynamics reflect genuine temporal variation rather than artifacts of selection.
Building on the baseline TVMG results in Table (ref), we further evaluate robustness using a duration-based criterion, requiring statistically significant effects to persist for at least three consecutive years (i.e., significance lasting $\ge$ 3 years) to be interpreted as economically meaningful. This approach filters out isolated or short-lived significance and focuses attention on sustained relationships. Table (ref) shows the strict results under this criterion.
Under this criterion, the effect of investment intensity, cash holdings, and sales remains robust, as their significant periods comfortably exceed the three-year threshold. This indicates a persistent association rather than a transitory episode. The negative association with unemployment also satisfies the duration requirement, with two episodes that are slightly shorter than the others, each lasting four years. Finally, the positive effect associated with CEO age 60, which appears only in 1993, fails the duration criterion and is therefore not considered robust under this stricter standard.
Overall, the duration-based analysis reinforces the robustness of the results for investment intensity, cash holdings, sales, and unemployment, while downgrading the interpretive weight placed on short-lived findings for CEO age. This exercise treats most reliable time-varying relationships as those that persist over multiple years, supporting a conservative and economically grounded interpretation of the TVMG estimates.
While the baseline analysis provides a transparent benchmark by documenting the time-varying association between facility-level emissions and individual parent-firm characteristics in isolation, such estimates may reflect not only firm-specific behavior but also broader economic forces that shape corporate decisions over time. Firm balance-sheet conditions, investment intensity, and operational scale are well known to co-move with the business cycle, credit conditions, and aggregate demand. As a result, single regressor estimates may confound firm-level mechanisms with economy-wide fluctuations that simultaneously influence production activity and emissions. To address this concern and to sharpen the economic interpretation of the estimated coefficients, this section augments the baseline TVMG framework with an additional regressor capturing aggregate economic conditions. Specifically, we consider a bi-regressors specification in which facility-level emissions depend on a single parent-firm characteristic of interest and a principal component extracted from a set of macroeconomic indicators. The principal component summarizes the dominant common variation across macroeconomic conditions and serves as a parsimonious control for economy-wide forces affecting firms’ production and abatement behavior. By including this factor alongside the firm-level variable, the estimated time-varying coefficient on the firm characteristic can be interpreted as its conditional marginal effect, holding constant the prevailing economic environment. This approach allows us to distinguish firm-specific emission responses from those driven by aggregate fluctuations.
Our economic framework also suggests that some firm-level variables may partly proxy for aggregate conditions. Sales, investment intensity, and cash holdings can all co-move with the business cycle and with aggregate financing conditions, while the effective shadow cost of emissions may itself vary with the broader macroeconomic environment. Conditioning on an aggregate factor therefore helps distinguish more clearly between firm-level and macroeconomic components of the observed time variation.
With the additional regressor, the model becomes
where $PC_t$ is the first principal component estimated from the FRED-QD dataset, and the rest are the same as Equation (ref). This experiment also utilizes a rolling variable setup as Table (ref).
With a fixed bandwidth $H = \sqrt{T} = 5.57$ and 90% significance level, plots of coefficients are displayed in Figure (ref). Table (ref) shows the five variables that are statistically significant. The bi-regressor estimation reveals that all baseline relationships remain robust, after conditioning on aggregate conditions, while different variables shift in timing - either intensify or attenuate. The pattern suggests that all baseline associations reflect some of the firm-level channel forces, in control of the economic environment.
Several firm attributes, including investment intensity, cash holdings, and CEO age 60, exhibit longer statistically significant periods once aggregate economic conditions are accounted for. Relative to the baseline single variable specifications, the expansion of significant windows for investment intensity and cash holdings suggests that these firm-level variables capture emission-relevant mechanisms that operate independently of macroeconomic fluctuations. In particular, investment intensity is generally pro-cyclical, where economic growth, easy credit, and high confidence lead to a greater willingness to invest in long-term assets. Corporate cash holdings are often argued to move counter-cyclically, reflecting precautionary motives and heightened uncertainty during economic downturns. In any case, the two financial variables are correlated with macro conditions, which are potentially related to the change in emissions.\footnote{In this section, we do not interpret the relationship between macroeconomic conditions itself and firm-level change of emissions. An aggregate level study follows in section (ref)} By controlling for broad macroeconomic variation through the inclusion of the principal component, we find that investment intensity and cash holdings exhibit statistically significant associations with changes in emissions that are orthogonal to general economic conditions. The behavior of CEO age 60 highlights the distinction between firm-specific governance effects and macro-driven correlations. Relative to the baseline results, the bi-regressors specification identifies one additional year of statistical significance for CEO age 60, indicating that the association between managerial age and emissions is not entirely driven by macroeconomic co-movements. Although the effect remains concentrated in the early part of the sample, its persistence after controlling for economic conditions suggests a modest but non-negligible firm-specific governance channel.
In contrast, the statistically significant periods associated with sales and unemployment become noticeably shorter once aggregate economic conditions are controlled. The two variables are generally treated as highly correlated with macroeconomic fluctuations, consistent with the difference of our estimation results. In the baseline specification, sales exhibits positive associations with emissions over two windows of the sample, reflecting the close link between firm output scale and pollution. However, after controlling for macroeconomic conditions, the significance of sales is largely confined to earlier years, indicating that a substantial share of the long-run association observed in the baseline model is driven by economy-wide demand fluctuations rather than firm-specific expansion alone. A similar pattern emerges for unemployment. While the baseline results identify multiple periods in which unemployment is negatively associated with emissions, the bi-regressor model reveals a more limited window of statistical significance once macroeconomic conditions are included. This contraction implies that the baseline unemployment association partially arises from aggregate economic forces.
\paragraph{Economic framework interpretation} The macro-conditioned specification is directly motivated by the framework's aggregate state variables $A_t$ and $\xi_t$. $A_t$ shifts demand and productivity, while $\xi_t$ shifts aggregate financing tightness and therefore the financing wedge $\psi_t$. In the baseline model, firm variables partly absorb these states: sales captures firm scale and aggregate demand, investment captures expansion and adjustment, cash captures firm liquidity and precautionary macro conditions, and leverage captures firm balance-sheet pressure and common credit cycles. Adding the FRED-QD macro PC separates the common macro component from the firm-specific channel. Following the factor logic in stock2002forecasting and mccracken2020fred, the PC acts as a parsimonious control for common variation across output, prices, financial conditions, and labor-market indicators.
This explains why the investment-intensity window expands from 2009-2014 to 2004-2017. Once $A_t$ is held constant, investment intensity no longer mainly reflects procyclical capital spending. The remaining variation is closer to $\omega_t I_t$, the environmentally oriented part of investment. Its negative coefficient over a wider period indicates that cleaner adjustment began before formal GHGRP disclosure and persisted after the initial reporting shock. The macro PC removes demand-driven investment cycles, letting the technique channel appear earlier and longer. In framework terms, controlling for $A_t$ reveals that firms with higher $\omega_t$ used investment to lower $m_t$, while the common business cycle no longer masks this relationship.
Cash holdings also become significant over 1997-2005 because conditioning on macro conditions isolates $c_t$ from precautionary cash accumulation associated with the cycle. In the unconditioned model, cash mixes two meanings: liquidity available for adjustment and cash held because uncertainty is high. After controlling for the macro PC, the negative cash coefficient is more plausibly the internal-finance channel in the framework. Cash lowers the effective cost of $G_t$ and helps firms respond to higher $\lambda_t$ around regulatory tightening and rising transparency. konar2001does show that environmental performance was capital-market relevant, and huang2019chemical link chemical releases with corporate cash holdings. The broadened window therefore suggests that internal liquidity supported a longer adjustment phase than the baseline result alone revealed.
The one-year extension of the CEO Age 60 effect of 1994 after conditioning on the macro PC suggests that the early managerial-age association is not entirely driven by the broader post-recession macro environment. In the framework, CEO age operates through the managerial allocation channel: leadership characteristics can affect the share of investment directed toward emissions-reducing adjustment, $\omega_t$, and the willingness to respond to a rising shadow cost of emissions, $\lambda_t$. Once aggregate conditions are controlled for, the continued significance into 1994 indicates that older CEOs may still have been associated with slower adaptation to emerging environmental expectations during the early phase of regulatory and social transition. This interpretation is consistent with evidence that CEO characteristics influence corporate environmental and sustainability outcomes manner2010impact, huang2013impact, hossain2023does.
Sales and unemployment contract after macro conditioning because these variables are closest to the scale channel. Sales significance narrows once $A_t$ absorbs aggregate demand, sales remains informative only in the period when facility emissions were still tightly linked to current activity $q_t$. After the early 2000s, sales becomes a mixed proxy for output, product mix, technology, market power, and cleaner operating capacity, so its conditional coefficient loses precision. Unemployment similarly contracts to 1993--1995 because the macro PC absorbs much of the general cyclical labor-market information. Only the early local recovery period remains distinct enough to identify county-level utilization effects.
Overall, extending the baseline TVMG framework to include aggregate economic conditions changes the timing of some of the estimated relationships, while demonstrating robustness, as the overall pattern and direction of the estimations do not diverge.
This subsection extends the baseline and bi-regressors specifications by estimating a joint multiple-regressor TVMG model in which all testing variables are included simultaneously, together with the principal component summarizing aggregate macroeconomic conditions. The objective is to assess the time-varying conditional effects of individual variables on facility-level emissions while controlling for both covariates and economy-wide forces. Unlike the earlier specifications, which examine each variable in isolation or alongside a single macro factor, this joint framework allows the estimated coefficients to be interpreted as conditional marginal effects, thereby mitigating potential confounding arising from correlations among variables tested.
In the joint specification, the relative visibility of different coefficients can be interpreted as reflecting shifts in the importance of the scale, adjustment, and macroeconomic channels over time. For that reason, we interpret the changing pattern of significance not as evidence of sharply identified structural regimes, but as indicative of changes in the dominant correlates of emissions growth across periods.
For facility-level percentage change of emissions, the joint multiple regression model follows:
where $k \in K$ indexes the set of variables proposed in Table (ref). $PC_t$ is the first principal component estimated from the FRED-QD dataset, and the rest are the same as Equation (ref).
For the joint multiple-regressor TVMG estimation, a fully balanced dataset is required because all coefficients are estimated within the same estimation equation and therefore must be identified from the same facility-year observations. After imposing this requirement, the fully balanced joint-estimation sample contains 179 facilities, 81 parent firms, and 5,728 facility-year observations over 1992-2023.
Using a fixed bandwidth $H = \sqrt{T} = 5.57$ and at 90% significance level, Table (ref) presents the 6 variables with statistically significant periods and directions. Figure (ref) displays the multiple TVMG model results. Given the joint nature of the multiple-regressor TVMG specification, individual coefficients capture conditional marginal associations that vary in relative importance over time. To facilitate interpretation, we therefore also summarize the results using a time-centric table (ref), which highlights the most salient associations in each period rather than emphasizing variables in isolation. Similarly, we discuss the results in a timewise manner.
During the early sample period (1993–1997), the joint TVMG results indicate that emissions growth is most strongly associated with firm-level heterogeneity in scale, operating activity, valuation-related measure, and managerial characteristics. The negative associations with lagged assets and Tobin’s Q, together with a positive association with sales, suggest that emissions dynamics during this period are more closely aligned with contemporaneous production intensity than with firm size or forward-looking valuation measures. In this environment, firms with higher sales tend to exhibit higher emissions growth, consistent with emissions being closely tied to current operating scale, whereas larger or more highly valued firms are associated with comparatively lower emissions growth, potentially reflecting larger or more highly valued firms being correlated with more mature production structures, newer capital stock, or greater organizational capacity for standardization and compliance, all of which are associated with comparatively lower emissions growth. In addition, the positive association with the indicator for CEOs aged 60 or above suggests that emissions outcomes are correlated with managerial attributes in this period, potentially reflecting systematic differences in experience, risk tolerance, or organizational conservatism that coincide with leadership age. Taken together, these patterns characterize the early 1990s as a phase in which emissions outcomes vary substantially across firms and are closely correlated with operating scale, organizational and managerial heterogeneity, rather than being primarily synchronized with aggregate macroeconomic conditions.
Moving into the late 1990s and early 2000s (1998–2007), the joint estimates indicate a rebalancing between firm-level and macroeconomic associations. While valuation-related measure (Tobin's Q) and managerial attribute (CEO age) remain statistically relevant, aggregate economic conditions begin to play a more prominent role. This pattern suggests that emissions dynamics during this phase are shaped by a combination of firm-specific positioning and broader economic expansion, with neither dimension fully dominating the other. The joint significance of these variables highlights a transitional period in which emissions outcomes appear increasingly synchronized with the macroeconomic environment, while still retaining some firm-level differentiation.
From the late 2000s through 2019 (2008-2019), the results point to a marked concentration of statistical significance in the macroeconomic component. In this period, conditional associations between emissions growth and firm-specific characteristics largely attenuate once aggregate conditions are accounted for. This shift suggests that emissions behavior becomes more closely aligned with economy-wide fluctuations, reducing the relative explanatory role of cross-firm heterogeneity. Interpreted descriptively, this period reflects a phase in which firms’ emissions responses appear more uniform, potentially reflecting common constraints, shared regulatory environments, or broadly synchronized economic conditions.
In the most recent years (2020–2023), the re-emergence of managerial characteristics as statistically significant correlates coincides with a period of heightened economic uncertainty and rapid structural change. The association between emissions growth and CEO age suggests that differences in leadership attributes regain relevance when firms face unprecedented shocks and adjustment pressures. It indicates that emissions outcomes during this period are more strongly correlated with internal decision-making characteristics than in the preceding macro-dominated phase.
\paragraph{Economic framework interpretation}
The joint TVMG model is the closest empirical counterpart to the paper's framework because it allows $q_t$, $m_t$, $G_t$, $c_t$, $d_t$, $A_t$, $\xi_t$, $\lambda_t$, and managerial allocation to operate simultaneously. Coefficients now represent conditional marginal associations: which channel remains visible after the other channels are held constant. This is why the joint results should be interpreted as a shifting hierarchy of mechanisms rather than as standalone effects for individual variables. A variable becomes significant when its channel is the marginal constraint on emissions growth in that period.
In 1993-1997, positive sales appears together with negative lagged assets and negative Tobin's Q. In framework terms, sales captures $q_t$, while assets and Q capture organizational maturity, capital quality, expected profitability, and possibly lower environmental liability. Conditional on assets and valuation, higher sales means higher current utilization and therefore higher $\Delta \log q_t$. Conditional on sales, larger asset bases may indicate more standardized production systems, greater compliance capacity, and lower emissions growth through a lower $m_t$ path. The negative Tobin's Q coefficient suggests that high-valuation firms were not merely large producers; they may have had cleaner technologies, better expected compliance, or lower perceived environmental liabilities. This interpretation fits konar2001does, chava2014environmental, and bolton2021do, who connect environmental performance or carbon risk to valuation and financing.
The early CEO-age coefficient interacts with this scale-valuation configuration. It indicates that when $q_t$ was important and formal environmental routines were still developing, managerial choices affected $\omega_t$ and the response to $\lambda_t$. Higher sales raised emissions growth, but high-Q or asset-rich firms could partly offset that through better systems. Older leadership may have slowed the shift from expansionary investment toward environmentally oriented $G_t$. The one-year Female CEO association should be treated cautiously because heavy-industry female CEO observations were likely sparse and selected; in the framework it is safer to read it as a governance-allocation signal, not as a universal gender effect.
The 1998-2007 period is a transition in which Tobin's Q and CEO age remain significant while the macro PC becomes positive. This means both firm-level $\omega_t$ choices and aggregate $A_t$ conditions matter. The positive PC coefficient suggests that common macro expansion raised $q_t$ across firms, while the negative Q coefficient indicates that higher-valued firms were better able to prevent activity growth from translating into emissions growth. CEO age remaining positive implies that managerial inertia continued to matter when firms needed to convert regulatory pressure into concrete changes in $G_t$. The synergy is therefore between market discipline, managerial allocation, and macro demand: high demand raises emissions pressure, while valuation and leadership determine how much of that pressure is offset by intensity improvements.
From 2008-2019, the macro PC dominates. In framework language, $A_t$ and $\xi_t$ become the primary visible state variables, while cross-firm differences in $c_t$, $d_t$, and $\omega_t$ become less statistically distinct. The global financial crisis, recovery, shale-gas expansion, renewable deployment, GHGRP disclosure, coal retirements, and tightening environmental expectations were broad enough to synchronize facility emissions. This does not mean firm channels disappeared; rather, their marginal contribution is harder to identify after common shocks and common regulatory pressures are included. heutel2012should and annicchiarico2022business provide the macro-environmental logic: emissions are procyclical, but regulation and technology can dampen the raw activity-emissions link.
The 2022-2023 re-emergence of CEO age shows that the managerial channel becomes visible again when the state variables are unstable. The late period involves pandemic recovery, inflation, energy-price uncertainty, supply-chain disruption, and pressure to maintain production. Under those conditions, firms must make discretionary choices about whether to maintain old assets, delay abatement, accelerate cleaner replacement, or protect short-run liquidity. CEO age can proxy differences in how firms set $\omega_t$ and respond to $\lambda_t$ under uncertainty.
The joint interpretation is therefore a staged framework narrative: early years are governed by $q_t$, valuation, and managerial discretion; the transition period combines $q_t$, Q, and leadership; 2008--2019 is dominated by $A_t$ and $\xi_t$; and the post-pandemic period again makes managerial allocation salient. Overall, the joint multiple-regressor TVMG analysis reveals that the conditional associations between facility-level emissions and firm-level as well as macroeconomic variables evolve substantially over time, highlighting the evolving structure of emissions associations and underscoring the value of a joint, time-varying framework for capturing such temporal shifts.
Macroeconomic conditions can impact facility emissions on an aggregate level. Using estimated principal components, we investigate the association between macro environment and aggregate facility emissions. For this experiment, we test three categories (air, water, ground) separately as well as the total release. The explanatory variables used are principal components estimated from the FRED-QD dataset described in Section (ref). In this study we do not interpret the PCs themselves. The explained variable is the aggregate-level percentage change of emissions described as in Equation (ref).
The aggregate analysis can be viewed as the macroeconomic counterpart to the facility-level framework. Whereas the micro-level regressions distinguish between scale and adjustment margins at the firm level, the aggregate regressions ask whether broad macroeconomic conditions are sufficiently important to generate time-varying co-movement in overall emissions. The exercise is therefore descriptive of macro-emissions linkages rather than a structural model of aggregate emissions determination.
For this experiment, we use a time-varying model where
To investigate different principal components, we estimate, using the FRED-QD, 3 PCs and apply them with one additional PC at a time, and perform multiple time-varying regressions. As we are analyzing the aggregate sum of emission, without facility units, the mean-group method as Equation (ref) is not applicable. Further, in this setting, serial dependence in both emissions and explanatory variables, together with the use of kernel-based local estimation, renders conventional confidence intervals unreliable. In particular, standard errors that assume independent observations do not account for local estimation error or the non-standard sampling distribution of time-varying coefficient estimators, especially in finite samples. We therefore construct confidence bands using a moving-block bootstrap (MBB) procedure, which resamples contiguous blocks of observations to preserve temporal dependence while naturally incorporating the effects of kernel smoothing. Let $\ell = [cT^{1/3}]$ denote the block length and define overlapping blocks $B_j = \{(y_j, x_j), ..., (y_{j+\ell-1}, x_{j+\ell-1})\}$ for $j = 1, ..., T-\ell+1$. For each bootstrap replication $b = 1, ..., B$, we sample $m = [T/\ell]$ blocks with replacement, concatenate them to form $\{(y^{*(b)}_t, x^{*(b)}_t)\}^T_{t=1}$, re-estimate $\hat{\beta}^{*(b)}_t$, and obtain pointwise percentile bands:
applied componentwise for each element of $\beta_t$. This moving-block bootstrap procedure yields confidence bands that appropriately reflect serial dependence and the local nature of TV estimation. We set $\alpha$ to 0.10 thus 90% confidence level.
Because the confidence bands are constructed using percentile quantiles of the moving-block bootstrap distribution, they are not constrained to be centered on the point estimates. In finite samples, the sampling distribution of the kernel-based time-varying coefficient estimator can be asymmetric and affected by local smoothing bias and boundary effects, so that the empirical bootstrap distribution may be shifted relative to $\hat{\beta}_t$. As a result, the point estimate may lie asymmetrically within the confidence band or, in some cases, fall outside the band altogether. This behavior is a standard feature of percentile bootstrap confidence intervals and reflects the non-standard sampling distribution of time-varying estimators rather than an error in implementation.
Figure (ref), (ref), and (ref) present the coefficient paths and moving-block bootstrap confidence bands for one, two, and three principal components, respectively. With only one PC, all four emission categories show no significance. When adding an additional second PC, the first principal component does not exhibit statistically distinguishable effects over the sample. In contrast, the second principal component shows statistically significant associations in the mid-sample period for air emission types, and across the whole sample period for water emission. For air emissions, the estimated coefficient on PC-2 turns positive and remains statistically significant for several consecutive years before gradually declining toward zero. For water emissions, PC-2 is associated with a large negative effect early in the sample that attenuates over time. No significant association for the remaining two categories: total and ground. Finally, adding the third principal component does not help as there are no significant periods for all four categories.
The aggregate-emissions exercise is the macro counterpart of the same framework. At the facility level, $\mathcal{E}_t = m_t q_t$ can be decomposed across firms and channels. At the aggregate level, cross-sectional heterogeneity is removed, so the question becomes whether common macro factors move aggregate $q_t$ or aggregate $m_t$ strongly enough to generate significant time-varying co-movement. PC-1 is not significant, and this is substantively useful: the broadest macro factor is too general to map cleanly onto aggregate TRI emissions. Aggregate output, financial conditions, and labor markets may move together, but emissions also depend on regulation, fuel mix, abatement capital, media-specific reporting, and substitution across firms and pollutants.
The significance of PC-2 for air and water emissions suggests that the relevant macro channel is not the broad level of economic activity but a secondary dimension orthogonal to it. Because principal components are statistical objects and we do not report detailed loadings here, we avoid assigning a specific economic label to PC-2. Instead, we interpret the result as evidence that certain emissions media co-move with a secondary macroeconomic factor in particular periods. PC-2 exhibits a mid-sample association with air emissions. fell2018fall and davis2022coal show how fuel prices, renewables, and coal retirements reshaped air emissions during the relevant period, which could also be linked to macro situations. Water emissions have the opposite pattern: PC-2 is negative early and attenuates over time. Without further interpreting the principal component here, keiser2019consequences show that water-quality improvements are closely connected to large regulatory and infrastructure investments. The attenuation over time implies that, once treatment and permitting systems become embedded, water emissions become less sensitive to macro-state variation and more governed by facility-level process choices.
The lack of significance for total emissions follows naturally from the framework because total emissions aggregate multiple media with different $q_t$ and $m_t$ sensitivities. A macro factor can raise air emissions through utilization while lowering water emissions through infrastructure or composition effects. Aggregation can therefore cancel media-specific channels. Ground emissions are also less likely to respond smoothly to annual macro factors because they often reflect disposal choices, waste-management practices, classification rules, and episodic events rather than continuous combustion or production flow. This is why the paper should emphasize that the aggregate evidence supports selective macro-emissions linkages, not a uniform macro effect.
The absence of PC-3 significance reinforces the parsimonious factor interpretation. Later principal components capture less common variation and may mix narrower subchannels or noise. stock2002forecasting and mccracken2020fred justify using a small number of factors because the first few components contain the systematic macro information. Here, PC-1 is too broad, PC-2 captures the relevant secondary state for air and water, and PC-3 adds no robust explanatory content.
For comparison, we also present, in Figure (ref), (ref), and (ref), the conventional normal confidence bands at 90% level with $\hat{\beta}_t \pm 1.645 \ \mathrm{SE}(\hat{\beta}_t)$. Relative to the moving-block bootstrap bands, the normal bands also indicate statistically significant associations between the second principal component and aggregate air and water emissions, while suggesting additional periods of statistical significance for some other coefficients. However, because they do not account for serial dependence or the local estimation error inherent in kernel-smoothed time-varying coefficients, such normal bands are likely to overstate precision in aggregate time-series settings. Accordingly, while the normal confidence bands provide a useful benchmark for illustrating the sensitivity of the results to the inference method, we rely on the moving-block bootstrap confidence bands for formal inference throughout, as they offer a more appropriate characterization of uncertainty.
This paper has examined the long-run evolution of the firm-level determinants of industrial emissions using a uniquely long and granular panel of U.S. facilities spanning 1992–2023. By combining facility-level emissions data from the Toxics Release Inventory with firm financial characteristics, managerial attributes, local labour-market conditions, and aggregate macroeconomic indicators, we have documented how the correlates of pollution evolve across regulatory and economic regimes. Methodologically, the analysis exploits a time-varying mean-group framework that allows relationships to change smoothly over time while accommodating persistent heterogeneity across production units.
Three broad conclusions emerge. First, the determinants of emissions are inherently time-dependent. Variables that are strongly associated with emissions in one phase of the regulatory or macroeconomic environment often lose relevance, reverse sign, or re-emerge later. This finding highlights a limitation of static empirical approaches: by averaging across heterogeneous regimes, they risk obscuring the dynamics of firm adaptation and technological change. A simple corporate finance interpretation helps organise these dynamics. Emissions growth reflects both a scale margin and an adjustment margin, and the relative importance of those margins depends on firms' financial conditions, the effective shadow cost of emissions, and the broader macroeconomic environment. In that sense, the time variation documented in the estimates is economically natural in an environment where regulation, disclosure, and financing conditions evolve jointly over time. Time-aware empirical methods are therefore essential for understanding how firms respond to environmental policy over long horizons.
Second, the results underscore the central role of firm-level adaptation capacity. Financial structure, investment intensity, and managerial characteristics are repeatedly shown to matter for emissions outcomes, but their relevance varies across periods. These patterns are consistent with an interpretation in which emissions reflect firms’ evolving production technologies, organisational choices, and ability to finance adjustment. In this sense, environmental performance is not solely a function of regulatory stringency, but also of firms’ internal capabilities and incentives. This perspective complements recent evidence emphasising the importance of organisational factors and managerial motivations in shaping environmental and investment decisions.
Third, the joint multivariate analysis shows that aggregate macroeconomic conditions play a dominant role in explaining emissions dynamics during a specific intermediate phase of the sample. In particular, in the period from the late 2000s to the late 2010s, aggregate factors account for a substantially larger share of the variation in emissions relative to firm-level characteristics. This dominance emerges only in the joint specification and is not present uniformly across the full sample. Outside this period, firm-specific financial and managerial variables regain explanatory importance, indicating that the relevance of aggregate conditions is both time-specific and context-dependent rather than a general feature of emissions dynamics.
Taken together, these findings have implications for innovation-oriented environmental policy. Policies designed to induce technological change are unlikely to be equally effective at all times. Their impact depends on firms’ financial conditions, organisational characteristics, and the broader macroeconomic environment in which they operate. Regulatory instruments may therefore be most effective when complemented by policies that relax financing constraints, support investment in cleaner technologies, and account for heterogeneity in managerial incentives and adaptation capacity.
More broadly, the analysis illustrates the value of long-run, facility-level evidence for understanding the interaction between regulation, innovation, and firm behaviour. By documenting how emissions determinants evolve over multiple decades, the paper contributes to a growing literature that views environmental outcomes as the result of dynamic organisational and technological processes rather than static compliance decisions. Future research could build on this approach by linking emissions more directly to measures of innovation output, technology adoption, or organisational change, further illuminating the mechanisms through which environmental policy shapes firm behaviour over time.
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