Time-Varying Pollution Premium: Yin, Yu & Chen (2026)

What this is. The paper’s core results, the semiparametric factor model framework, and the estimation procedure with key equations: enough to understand what was found and how, without reading all 15 pages. To replicate or extend, read the full source at the original.

TL;DR

Using EPA Toxic Release Inventory (TRI) data matched to CRSP and Compustat for US common stocks (October 1992 to September 2018), the paper sorts firms into quintiles by annual toxic emission intensity scaled four ways (total assets, PP&E, sales, market cap) and constructs a long-short portfolio. In constant factor models (CAPM through HXZ) for the total-assets-scaled portfolio, the high-minus-low portfolio earns a statistically significant pollution premium of roughly 4 to 5 percent annually. A partially time-varying semiparametric model reveals, however, that the premium is concentrated before 2005: the nonparametric alpha estimate is statistically significant (90% confidence interval above zero) through approximately 2004-2005, then falls to a stable but indistinguishable-from-zero level. The paper identifies two channels associated with this time variation: time-varying risk exposures on the supply side (especially the HML value factor) and time-varying investor preferences on the demand side (consumer sentiment, natural disaster severity, sustainable fund flows, and environmental litigation risk). In univariate regressions on fully time-varying alphas, risk aversion is weakly positive for CAPM and negative for the other four factor models, while macroeconomic uncertainty is negative throughout. In the multivariate horse-race, risk aversion, macroeconomic uncertainty, natural disasters, and consumer sentiment emerge as the most robust predictors.

Core results

Magnitudes are as reported; *, **, and *** denote 10%, 5%, and 1% significance. Locators point into the source PDF.

#	Result	Locator	Magnitude
R1	Long-short portfolio earns positive raw returns across all four emission scalings	Table 1, Panel A, p. 4	H-L 4.57% annually (t=2.39, Sharpe=0.47, total-assets scaling); quintile raw returns increase almost monotonically from 6.82% (low) to 11.39% (high) (Q3=8.28% dips below Q2=10.60%)
R2	Long-short portfolio earns significant alpha in all constant factor models	Table 2, p. 5	FF3F alpha = 5.28%*** (t=3.56); CAPM 4.44%*** (t=3.10); FF4F 4.56%*** (t=3.29); FF5F 3.96%*** (t=2.70); HXZ 4.80%*** (t=3.44)
R3	Time-varying semiparametric alpha is significant only before 2005; statistically indistinguishable from zero thereafter	Figure 2, p. 6; §4.2	FF3F estimate approx. 0.40 monthly (4.8% annualized) in 1992, peaking near 1.0 around 2000; 90% CI above zero through approx. 2004-2005; falls to approx. 0.25 monthly and becomes insignificant post-2005
R4	HML (value factor) is the only risk factor consistently related to the pollution portfolio	Table 3, p. 7; §4.3	FF5F OLS: HML = -0.288 (SE=0.079, t approx -3.65); FF3F OLS: HML = -0.191 (SE=0.057, t approx -3.35); MKT and SMB insignificant across all specifications
R5	Consumer sentiment index is the strongest single economic-condition predictor of the time-varying alpha	Table 4, Panel C, p. 11	beta(ICS) = 0.009*** (t=14.25, FF3F partially time-varying); Adj. R-sq = 0.394
R6	Natural disaster severity is a positive and robust predictor of the time-varying pollution premium	Table 6, Panel A, p. 11	beta(Disasters) = 60.358*** (t=11.31, FF3F partially time-varying); Adj. R-sq = 0.554
R7	Multivariate horse-race: risk aversion, macroeconomic uncertainty, natural disasters, and consumer sentiment jointly explain most time variation	Table 9, Panel A, p. 12	Adj. R-sq = 0.770 (CAPM) to 0.819 (FF5F), partially time-varying model (Panel B, fully time-varying: up to 0.864)
R8	Return spreads vary across the alternative emissions scalings	Table 1, Panels B-D, p. 4	H-L annual excess return: PPENT 2.73% (t=1.54, Sharpe=0.30); sales 2.18% (t=1.29, Sharpe=0.25); market capitalization 5.41% (t=2.74, Sharpe=0.54)
R9	Fully time-varying estimates show changing factor exposures, especially a negative HML loading	Figure 4, p. 9; §5.2	FF3F alpha approx. 0.5 through 2000; MKT beta insignificant throughout; SMB beta significant only through the late 1990s; HML beta negative and significant in 1992-1998 and 2003-2013
R10	Sustainable fund flows correlate positively with the premium in partial-model regressions, while full-model estimates are mostly insignificant	Table 5, p. 11	Percentage-flow beta: FF3F 0.189***, FF4F 0.177***, FF5F 0.175***, HXZ 0.146*** (partial); amount-flow beta: 0.019***, 0.019***, 0.015***, 0.015*** in the same models; fully time-varying coefficients mostly insignificant
R11	Environmental litigation risk has a positive association with the premium	Table 7, p. 12	Partial-model beta ranges from 0.077** (CAPM, t=2.30) to 0.125*** (FF3F, t=3.08); full-model range 0.063 (FF5F, insignificant) to 0.126*** (FF4F, t=2.84)
R12	Risk aversion and uncertainty have distinct associations with the premium	Table 8, p. 12	Fully time-varying alpha: risk-aversion beta = 0.017* (CAPM), -0.024* (FF3F), -0.037*** (FF4F), -0.051*** (FF5F), -0.029*** (HXZ); monthly-variance uncertainty beta: -0.073** to -0.414***; annual-volatility uncertainty beta: -0.024** to -0.171***
R13	In the full-model horse race, risk aversion, uncertainty, fund flows, and consumer sentiment retain explanatory power	Table 9, Panel B, p. 12	Adj. R-sq = 0.743 (CAPM) to 0.864 (FF4F); risk aversion positive and significant in all five models; uncertainty negative and significant in all five; flow coefficients negative and significant in FF3F, FF4F, FF5F, and HXZ
R14	The emissions-return relation is concentrated in value stocks	§5.2, p. 8	The paper reports that the positive relationship between emissions and returns mainly exists for value stocks and is largely absent for growth stocks; no coefficient or spread magnitude is reported in the main text
R15	Shiller valuation and luxury-consumption measures also track the time-varying premium	Table 4, Panels A-B, p. 11	Shiller P/E beta is positive and significant in every model (0.010*** to 0.017***); luxury-consumption beta ranges from 0.525** to 0.645* in the partial model, while full-model estimates are significant in four of five specifications

Overall (paper’s conclusion). The pollution premium is not a stable, time-invariant phenomenon: it reflected a priced systematic risk tied to environmental policy and investor preferences before 2005, but the abnormal returns became statistically indistinguishable from zero after that. The time variation is associated with changing factor exposures, particularly HML, as well as macroeconomic conditions and investor preferences on the demand side.

Theory / model

The paper proposes no formal economic model. The economic object is the abnormal return (pollution premium) of a long-short portfolio sorted on toxic emission intensity, studied through two related semiparametric factor models adapted from Ang and Kristensen (2012) and Chen and Hong (2012).

Hypotheses tested. The null is that pollution exposure is not priced at all (alpha=0 in constant models), and the secondary null is that any pricing is time-invariant (alpha is constant over time). The paper rejects both nulls pre-2005 but fails to reject the second null post-2005.

Identification. The design is descriptive: no exogenous variation is exploited and no causal claim is made. The semiparametric model relaxes the constant-coefficient assumption, letting the data reveal the temporal shape of alpha without imposing a functional form (linear, structural-break, or otherwise). Driver regressions (Sections 5-6) establish associations between the estimated time-varying alpha and proxy variables; they do not identify causal effects.

Method

Partially time-varying factor model

The paper’s baseline model has a time-varying intercept and constant factor loadings (Eq. 1, p. 2):

$$r_t = \alpha_t + \sum_{j=1}^{J} \beta_j x_{jt} + \varepsilon_t, \qquad \varepsilon_t = \sigma_t e_t, \quad t = 1, \ldots, T; \quad j = 1, \ldots, J \tag{1}$$

where $r_t$ is the long-short portfolio excess return, $x_{jt}$ are observable common risk factors, $\alpha_t$ is the time-varying pollution premium, and $\beta_j$ is the constant factor loading. In matrix notation (Eq. 2):

$$r_t = \alpha_t + Z_t^\top \beta + \varepsilon_t, \quad t = 1, \ldots, T \tag{2}$$

This compact form is Eq. 2 on p. 3.

The stacked model (Eq. 3, p. 3) and the adjusted-return equation used in the first estimation step (Eq. 4, p. 3) are:

$$r = \alpha + \mathbf{Z}\beta + \varepsilon \tag{3}$$ $$\tilde{r}_t = \alpha_t + \varepsilon_t, \qquad \tilde{r}_t = r_t - Z_t^\top \beta \tag{4}$$

Semiparametric profile estimation

Following the semiparametric-profile-estimation approach of Fan and Huang (2005) and Chen and Hong (2012), $\alpha_t$ is estimated as a smooth function of rescaled time $\tau_t = t/T \in [0,1]$ by local linear kernel regression. Step 1 treats $\beta$ as known, computes the adjusted return $\tilde{r}_t = r_t - Z_t^\top \beta$, and minimizes the loss function (Eq. 5, p. 3):

$$\sum_{t=1}^T \left[ \tilde{r}_t - \alpha(\tau) - \alpha^{(1)}(\tau)(\tau_t - \tau) \right]^2 K_h(\tau_t - \tau) \tag{5}$$

where $K_h(u) = K(u/h)/h$ is the Epanechnikov kernel with bandwidth $h$ selected by leave-one-out cross-validation, and $\alpha^{(1)}(\tau)$ is the local linear slope. The infeasible local linear estimator of $\alpha(\tau)$ is Eq. 6, p. 3:

$$\tilde{\alpha}(\tau) = [1,0] \left( D(\tau)^\top K_h(\tau) D(\tau) \right)^{-1} D(\tau)^\top K_h(\tau)(r - Z\beta) \tag{6}$$

Stacking the local estimates gives the smoother representation in Eq. 7 (p. 3):

$$\tilde{\alpha} = S(r - \mathbf{Z}\beta), \qquad S = [S(\tau_1)^\top, S(\tau_2)^\top, \ldots, S(\tau_T)^\top]^\top \tag{7}$$

Step 2 substitutes $\tilde{\alpha}$ back into the original model and partials out the intercept path (Eq. 8, p. 3):

$$(I-S)r = (I-S)\mathbf{Z}\beta + \tilde{\varepsilon} \tag{8}$$

OLS on the transformed regression gives the constant factor loading estimate (Eq. 9, p. 3):

$$\hat{\beta}_{\text{ols}} = (\tilde{X}^\top \tilde{X})^{-1}\tilde{X}^\top \tilde{Y}, \qquad \tilde{X}=(I-S)\mathbf{Z}, \quad \tilde{Y}=(I-S)r \tag{9}$$

The feasible semiparametric estimator is then Eq. 10, p. 3:

$$\hat{\alpha}_{\text{semi}}(\tau) = S(\tau) \left( r - Z \hat{\beta}_{\text{ols}} \right) \tag{10}$$

where $S(\tau)$ stacks the local-linear kernel smoothing matrices. Confidence bands are obtained by a wild bootstrap (5,000 replications; Appendix B), using the reflection method of Chen and Hong (2012) at boundary points to correct for boundary bias.

To correct for heteroscedasticity in the errors, the paper also constructs a weighted least-squares (WLS) estimator of $\beta$ (Appendix D), with weights $\hat{\sigma}^2(\tau)$ estimated from the kernel-local residuals.

For the WLS estimates reported alongside OLS in Table 3, the coefficient estimate is (Appendix D, p. 14):

$$\hat{\beta}_{\text{wls}} = (\tilde{X}^\top \hat{W}^{-1}\tilde{X})^{-1}\tilde{X}^\top\hat{W}^{-1}\tilde{Y}, \qquad \hat{W}=\operatorname{diag}(\hat{\sigma}^2(\tau_1),\ldots,\hat{\sigma}^2(\tau_T))$$

Table 3 reports standard errors in parentheses for OLS and WLS loadings on the monthly October 1992-September 2018 sample.

Fully time-varying factor model

An alternative model allows both $\alpha_t$ and factor loadings $\beta_{jt}$ to be time-varying (Eq. 11, p. 7):

$$r_t = \alpha_t + \sum_{j=1}^{J} \beta_{jt} x_{jt} + \varepsilon_t, \quad t = 1, \ldots, T; \quad j = 1, \ldots, J \tag{11}$$

Both functions are approximated locally by linear polynomials. The compact form in Eq. 12 and local weighted least-squares objective in Eq. 13 are given in Appendix A, p. 13:

$$r_t = X_t^\top \beta_t + \varepsilon_t, \qquad X_t=(1,x_{1t},\ldots,x_{Jt})^\top, \quad \beta_t=(\alpha_t,\beta_{1t},\ldots,\beta_{Jt})^\top \tag{12}$$ $$\sum_{t=1}^{T}\left[r_t-X_t^\top\left\{\beta(\tau)+\beta^{(1)}(\tau)(\tau_t-\tau)\right\}\right]^2 K_h(\tau_t-\tau) \tag{13}$$

This fully time-varying local-linear objective lets the authors study changes in both the pollution-premium level and the portfolio’s exposure to common risk factors (Figures 3 and 4).

Empirical specifications

Portfolio construction

Following Hsu et al. (2023), the paper sorts firms into quintiles by annual toxic emission intensity, grouping firms relative to their Fama-French 49 industry peers each October (when updated TRI data become available). Emissions are scaled four ways: total assets (Panel A), property, plant and equipment (Panel B), sales (Panel C), and market capitalization (Panel D). Portfolios are value-weighted. The H-L long-short portfolio takes a long position in Quintile 5 (highest emission) and short in Quintile 1 (lowest emission).

Sample restrictions: common stocks (SHRCD = 10/11) on NYSE, AMEX, or NASDAQ; non-missing data in all three databases (CRSP, Compustat, EPA TRI); at least two years of Compustat history; financial firms (SIC 6000-6999) excluded.

Constant factor model tests (Table 2)

For each sorted portfolio return, the constant-coefficient factor specification is:

$$R_{p,t}-R_{f,t}=\alpha_p+\sum_{j=1}^{J}\beta_{p,j}F_{j,t}+\varepsilon_{p,t}$$

This is estimated by OLS separately by portfolio and model, with no fixed effects; standard errors use Newey-West adjustments with 12 lags. The sample is monthly October 1992-September 2018. The five models use CAPM (MKT); FF3F (MKT, SMB, HML); FF4F (MKT, SMB, HML, UMD); FF5F (MKT, SMB, HML, RMW, CMA); and HXZ (MKT, SMB, I/A, ROE). Alphas are annualized by multiplying by 12. The H-L alpha from FF3F is 5.28% annually (t=3.56, Table 2, Panel B).

Time-varying estimation (Figure 2; §4.2)

The partially time-varying model (Eq. 1) is estimated for each factor model. The semiparametric estimate $\hat{\alpha}(\cdot)_{\text{semi}}$ is plotted with 90% wild-bootstrap confidence bands (Figure 2). The FF3F-based estimate peaks near monthly alpha of 1.0 around 2000, then declines; the 90% CI lower bound is above zero from 1992 through approximately 2004-2005, after which the band crosses zero and the premium is statistically insignificant. The pattern holds across CAPM, FF4F, FF5F, and HXZ models.

Time-varying betas from the fully time-varying model (Figure 3 for CAPM; Figure 4 for FF3F) confirm that MKT beta is effectively zero throughout the sample, size beta is short-lived (significant only through the late 1990s), and HML beta is the key driver: significantly negative from 1992 to 1998 and from 2003 to 2013. Bansal et al. (2016) provide the baseline climate-risk-pricing motivation; Bekaert et al. (2022) provide the risk aversion and uncertainty indices used in the driver analysis.

Driver regressions (Tables 4-9; §§5-6)

For each proxy variable $Z_t$, the paper estimates the following time-series regression (Table 4, p. 11; Tables 5-9, pp. 11-12):

$$\hat{\alpha}_t = c + \beta Z_t + u_t$$

The horse-race specification includes all proxy variables together:

$$\hat{\alpha}_t = c + \beta_{RA}RA_t + \beta_{Unc}Unc_t + \beta_{LR}LR_t + \beta_D Disasters_t + \beta_F Flows_t + \beta_{PE}ShillerPE_t + \beta_{ICS}ICS_t + \beta_L LuxuryCons_t + u_t$$

These are aggregate time-series regressions with no fixed effects. The reported tables provide t-statistics but do not state a separate serial-correlation correction for these regressions. The source frequency and sample vary by proxy: monthly October 1992-September 2018 for Shiller P/E, sentiment, litigation, and risk aversion/uncertainty; quarterly 2007:Q4-2018:Q3 for sustainable fund flows; quarterly 1992:Q4-2018:Q3 for natural disasters; and annual observations for luxury consumption. Table 9 uses annual observations from 1992 to 2018 to align the proxies. The paper also estimates monthly and annual-volatility versions of uncertainty.

Five categories of proxy variables are tested: (1) economic conditions (Shiller P/E ratio, luxury goods consumption, consumer sentiment index ICS; Table 4); (2) sustainable fund flows from Morningstar (percentage and dollar-amount; Table 5); (3) natural disaster severity from SHELDUS, defined as total fatalities and injuries relative to US population, scaled by 1,000 (Table 6); (4) environmental policy uncertainty via firm-level litigation risk, aggregated as total EPA civil cases filed against firms from year $t+1$ to $t+5$ (Table 7); (5) risk aversion and macroeconomic uncertainty indices from Bekaert et al. (2022), measured in monthly variance units and annual volatility percentage (Table 8).

The multivariate horse-race (Table 9) includes all proxies simultaneously. For the partially time-varying model (Panel A), risk aversion, macroeconomic uncertainty, natural disasters, and consumer sentiment are significant across most factor models; risk aversion is positive in these multivariate regressions even though its univariate association with fully time-varying alphas is mixed. Macroeconomic uncertainty exhibits the strongest negative coefficient (e.g., -6.094 for FF5F, t=-2.48) and natural disasters the strongest positive effect. The adjusted R-sq reaches 0.819 (FF5F) in Panel A and 0.864 (FF4F) in Panel B (fully time-varying model).

Datasets used

Dataset	Role in paper	Wiki page
EPA Toxic Release Inventory (TRI)	Annual firm-level toxic emission intensity (pounds released per year, 1991-2018); scaled four ways for emission-sorted quintile construction	EPA TRI
CRSP monthly returns and market data	Stock returns, market capitalization, exchange codes; monthly Oct 1992-Sep 2018	WRDS / CRSP (licensed)
Compustat annual fundamentals	Total assets, PP&E, sales for scaling; book values and firm characteristics for sample filters	WRDS / Compustat (licensed)
Fama-French factors (Kenneth French library)	FF3F, FF4F, FF5F factor returns; FF 49-industry classification for within-industry quintile sorts	Ken French library
HXZ q-factors (Global-Q)	MKT, SMB, I/A, ROE factors for the HXZ model tests	No page yet (data:global-q)
Morningstar sustainable fund database	Quarterly total net assets, holdings, and returns for sustainable and ESG funds; 2007:Q4-2018:Q3	No page yet
SHELDUS natural disaster database	County-level hazard event data (fatalities + injuries relative to US population), quarterly 12-quarter moving average; Arizona State University	No page yet
Bekaert et al. (2022) risk aversion and uncertainty indices	Monthly time-varying risk aversion and macroeconomic uncertainty indices (available at nancyxu.net)	No page yet
EPA ICIS enforcement and FRS data	Annual aggregate count of civil cases against firms from EPA Enforcement and Compliance History Online; matched to TRI via Facility Registry Service	No page yet

Sample: October 1992 to September 2018 (312 months, monthly). TRI data are annual (from 1991), matched to stock data in October of each year.

When to read the full paper

Use the original if you are: studying whether and how the pollution or ESG premium varies over time in the US; applying semiparametric partially or fully time-varying factor models to other long-short portfolios; investigating the supply-side (risk exposure) versus demand-side (investor preference) decomposition of time-varying premia; or seeking formal asymptotic derivations for the local-linear kernel estimator (Appendices A-D). The locators above point to exact tables and figures.

Attribution and rights

Source: peer-reviewed, Journal of Banking and Finance vol. 187 (2026). This distillation was extracted by an LLM on 2026-06-25 and is not human-verified or independently reproduced. The article is paywalled; this page contains extracted text only and is not a redistribution of the work.

Yin, Ximing, Deshui Yu, and Li Chen. “The time-varying pollution premium.” Journal of Banking and Finance 187 (2026): 107693. DOI: 10.1016/j.jbankfin.2026.107693. © 2026 Elsevier B.V. All rights reserved.