Environmental Regulation and U.S. State-Level Production

Environmental Regulation and U.S. State-Level Production Daniel J. Henderson State University of New York at Binghamton Department of Economics Daniel L. Millimet Southern Methodist University Department of Economics July 2004 Abstract Using data from the U.S. over the period 1977-1986, we estimate the impact of environmental policy on state-level output using both parametric and nonparametric techniques. We find that while the added flexibility of the nonparametric approach yields much insight, the lack of a relationship between environmental regulation and output is quite robust. JEL: C14, C33, D24 Keywords: Generalized Kernel Estimation, Environmental Regulation, Cobb-Douglas, Translog Daniel J. Henderson, Department of Economics, State University of New York, Binghamton, NY 13902. Tel: (607) 777-4480. Fax: (607) 777-2681. E-mail: djhender@binghamton.edu. The authors wish to think Eric Maskin, an anonymous referee, and Léopold Simar for helpful suggestions. The usual caveats apply. Corresponding address: Daniel Millimet, Department of Economics, Box 0496, Southern Methodist University, Dallas, TX 75275-0496. Tel: (214) 768-3269. Fax: (214) 768-1821. E-mail: millimet@mail.smu.edu.

1 Introduction Policymakers, business leaders, and workers have long perceived stringent environmental regulation as a serious threat to U.S. competitiveness as measured by net exports and/or domestic production. 1 Empirical evidence surrounding this claim, however, has been mixed. On the one hand, Jaffe et al. (1995, p. 157) conclude after an extensive review: Overall, there is relatively little evidence to support the hypothesis that environmental regulations have had a large adverse effect on competitiveness.... On the other hand, more recent evidence suggests that environmental regulation does influence competitiveness by influencing trade patterns and firm location decisions (e.g., Ederington et al. 2003; Fredriksson et al. 2003; List et al. 2004). Building on this previous work, this paper assesses the impact of environmental regulation on U.S. state-level output using panel data from 1977 1986 using both parametric and recently developed nonparametric techniques. The results indicate considerable advantages in using nonparametric methods in general. However, the parametric and nonparametric methods both suggest that environmental stringency has little to no impact on state-level output. The remainder of the paper is organized as follows. Section 2 discusses the estimation framework and data. Section 3 presents the results. Section 4 concludes. 2 Empirical Methodology 2.1 Generalized Kernel Estimation The model we wish to estimate is a reduced form production model, where output, y, is determined by (i) a vector of inputs (private capital, public capital, and labor), (ii) the unemployment rate (capturing business cycle effects; see Baltagi and Pinnoi 1995), (iii) environmental regulations, (iv) state and time effects, and (v) unobserved idiosyncratic shocks. 2 The analysis of this model proceeds using Li-Racine Generalized Kernel Estimation (Li and Racine 2004; Racine and Li 2004). To detail the technique, it is useful to express the reduced form production model as y i = m(x i )+ε i, i =1,...,NT (1) where m is the unknown smooth production function with argument x i =[x c i,xu i,xo i ], xc i is a vector of continuous covariates (private capital, public capital, labor, environmental regulation, and the unemployment rate), x u i is a vector of regressors that assume unordered discrete values (state effects), x o i is a vector of 1 The notion that stricter environmental regulation will shift production abroad to countries with more lax regulation has become known as the Pollution Haven Hypothesis. 2 The presence of environmental regulation in the reduced form production function follows from the treatment of emissions, whichinturndependonthestringencyofregulation, as an input (see, e.g., Cropper and Oates 1992). 1

regressors that assume ordered discrete values (time effects), ε is an additive error, N is the number of cross-sectional units, and T is the number of periods in the sample (N = 48, T = 10 in the application). Taking a first-order Taylor expansion of (1) with respect to x j yields y i m(x j )+(x c i x c j)β(x j )+ε i (2) where β(x j )isdefined as the partial derivative of m(x j ) with respect to x c.ify and x are both expressed in logarithmic form, then β(x j ) is interpreted as an elasticity. The estimator of δ(x j ) m(x j ) β(x j ) is given by ³ µ bm(xj ) bδ(x j ) = = X 1 x c 1 i Kb h xc j ³ ³ ³ 0 bβ(x j ) i x c i xc j x c i xc j x c i xc j X µ Kb ³ 1 h x c i i y i, (3) xc j where Kb h = Π q b h 1 s w x c si xc r ³ sj s=1 b Π l u x u hs s=1 si,xu sj, λ c ³ s pπ u l o x o s=1 si,xo sj, λ c o s. K h is the commonly used product kernel (Pagan and Ullah 1999), where w is the standard normal kernel function with window width h s = h s (NT) associated with the s th component of x c. l u is a variation of Aitchison and Aitken s (1976) kernel function which equals one if x u si = xu sj and λu s otherwise; l o is the Wang and Van Ryzin (1981) kernel function which equals one if x o si = xo sj and (λo s) xo si xo sj otherwise. See Racine and Li (2004) for further details. Estimation of the bandwidths (h, λ u,λ o ) is typically the most salient factor when performing nonparametric estimation. Although there exist many selection methods, we choose Hurvich et al. s (1998) Expected Kullback Leibler (AIC c ) criteria. 3 This method chooses smoothing parameters using an improved version of a criterion based on the Akaike Information Criteria. AIC c has been shown to perform well in small samples and avoids the tendency to undersmooth as often happens with other approaches such as Least Squares Cross-Validation. Specifically, the bandwidths are chosen to minimize where AIC c =log bσ 2 + bσ 2 = j=1 1+tr(H)/N T 1 [tr(h)+2]/n T 1 XNT (y j bm j (x j )) 2 NT where bm j (x j ) is the commonly used leave-one-out estimator of m(x). = y 0 (I H) 0 (I H)y/NT, (5) 3 We have run several other methods for selecting window widths and have found our results to be robust to the choice of bandwidth selection criteria. Further, we tried the Robust Cross-Validation procedure suggested by Henderson and Kumbhakar (2004) and find that our results are unaffected. (4) 2

2.2 Parametric Estimation For comparison we estimate several standard parametric versions of (1) nested in the following specification: y it = λ t + Ã! KX x 2 ijt θ 1k x ikt + θ 2k 2 k=1 K 1 X + KX k=1 l=k+1 θ 3kl x ikt x ilt + µ i + ε it, i =1,...,N; t =1,...,T (6) where y is now subscripted with i and t explicitly, λ t are time fixed effects, µ i is either a state fixed or random effect, θ [θ 1,θ 2,θ 3 ] is the vector of parameters of interest, k =1,...,K indexes inputs, and ε it is an error term which is identically distributed within states and independent between states. The most parsimonious version of (6) we estimate restricts θ 2k = θ 3kl =0 k, l, µ i =0 i, andλ t = λ t. Thus, (6) reduces to a simple pooled OLS Cobb-Douglas model. Allowing λ t and µ i to vary by t and i, respectively, but maintaining θ 2k = θ 3kl =0 k, l, yields a Cobb-Douglas specification with either fixed or random state effects, depending on the treatment of µ i. Allowing θ 2k and θ 3kl to be non-zero for all k, l, but restricting µ i =0 i and λ t = λ t, yields a pooled OLS translog model. Finally, allowing θ 2k, θ 3kl, λ t,andµ i to all be free parameters gives rise to a translog specification with either fixed or random state effects, again depending on the treatment of µ i. In the Cobb-Douglas case, θ 1 are output elasticities assuming all variables are measured in logarithmic form; in the translog specifications, the elasticities are observation-specific (Greene, 1993, p. 210). 3 Data The data span 1977 1986 for the 48 contiguous U.S. states. Output is measured by gross state product (GSP), public capital is total expenditure on highways and streets, water and sewer facilities, and other public buildings and structures, the stock of private capital is obtained from the Bureau of Economic Analysis (BEA), and labor is measured as employment in non-agricultural payrolls. Environmental regulation is measured using Levinson s (2001) industry-adjusted index of environmental stringency, computed for each state-year observation as the ratio of actual pollution costs per dollar of output to predicted pollution costs per dollar of output based on the distribution of industries within the state-year. A value greater (less) than one indicates that industries in the state spend relatively more (less) per dollar of output on pollution abatement than identical industries located in other states. The index has been utilized in several previous studies. 4 See Levinson (2001) and Baltagi and Pinnoi (1995) for further details on the environmental 4 The Levinson index measures enviromental stringency within the manufacturing sector. As such, we must assume that environmental stringency in other sectors is proportional to environmental stringency within the manufacturing sector for each state. 3

stringency index and the remaining data, respectively. 5 4 Results The results are displayed in Tables 1 3. Table 1 presents the nonparametric results. 6 Tables 2 and 3 present the parametric results from the Cobb-Douglas and translog specifications, respectively. Tables 1 and 3 present the mean output elasticity with respect to each (continuous) input, as well as the elasticities at the 25 th,50 th,and75 th percentiles (labelled Quartiles 1, 2, and 3). Table 2 presents the elasticity estimates from the Cobb-Douglas specifications, which are constant across observations. Prior to examining the specific results, we conducted three sets of specification tests for the parametric models. First, a Hausman test of (state) fixed versus random effects rejects the random effects specification in both the Cobb-Douglas and translog models (p = 0.00 in both cases). Second, an F-test rejects the null that the state fixed effects are jointly insignificant in both cases as well (p =0.00 for both). Third, in all three parametric specifications (pooled OLS, fixed effects, and random effects), the restrictions implied by the Cobb-Douglas model (i.e., θ 2k = θ 3k = 0) are rejected (p =0.00 in all cases). Thus, the preferred parametric specification is the translog model with state fixed effects (Panel II in Table 3). In terms of the primary result of interest, both the nonparametric and preferred parametric approaches find predominantly negative and statistically insignificant effects of regulatory stringency on state output. Specifically, at least 75% of the observations have an output elasticity with respect to environmental stringency above -0.039 (-0.017) according to the nonparametric (parametric) estimation. Thus, while recent research documents that stricter environmental regulation may adversely affect trade flows and the location decisions of manufacturing plants, aggregate state-level output remains unaffected. Such a result is consonant with a simple general equilibrium theoretical model with two or more sectors. Although the nonparametric and parametric techniques reach similar conclusions regarding the impact of environmental regulation on state output, the two methods provide a number of contrasting results in terms of the remaining inputs. First, the nonparametric model finds a positive and statistically significant effect of public capital, whereas the parametric model yields the converse: a negative and statistically significant relationship for many observations. The ability of the nonparametric model to find a positive impact of public capital on state output, potentially solving this productivity puzzle, was first noted in Henderson and Kumbhakar (2004). Second, the nonparametric model yields a highly significant elasticity of output with respect to physical capital of roughly 0.3. The parametric model, on the other hand, fails 5 To conserve space, summary statistics are not provided, but are available upon request. 6 All nonparametric calculations are performed using N c. 4

to find a statistically significant relationship between physical capital and state output. Third, while the parametric models reports a (precisely estimated) elasticity of output with respect to labor greater than unity for the majority of observations, the nonparametric model finds more reasonable values in the range of 0.6 to 0.7. Finally, the nonparametric approach yields a negative and statistically significant association between unemployment and state output (although small in magnitude), whereas the parametric model obtains point estimates much closer to zero and always statistically insignificant. Each of these contrasts suggests that the translog specification is not sufficiently flexible to capture the data. 5 Conclusion Employing both parametric and nonparametric techniques, we estimate several U.S. state-level production functions using panel data from 1977 1986. While the added flexibility of the nonparametric approach yields elasticities with respect to public capital, physical capital, and labor that appear more reasonable, the lack of an observed association between the stringency of environmental regulation and state-level output is robust across all estimation methods. 5

References [1] Aitchison, J. and C.B.B. Aitken (1976), Multivariate Binary Discrimination by Kernel Method, Biometrika, 63, 413-420. [2] Baltagi, B.H. and H. Pinnoi (1995), Public Capital Stock and State Productivity Growth: Further Evidence from an Error Components Model, Empirical Economics, 20, 351-359. [3] Cropper, M.L. and W.E. Oates (1992), Environmental Economics: A Survey, Journal of Economic Literature, 30, 675-740. [4] Ederington, J., A. Levinson, and J. Minier (2003), Footloose and Pollution-Free, Review of Economics and Statistics, forthcoming. [5] Fredriksson, P.G., J.A. List, and D.L. Millimet (2003), Corruption, Environmental Policy, and FDI: Theory and Evidence from the United States, Journal of Public Economics, 87, 1407-1430. [6] Greene. W.H. (1993), Econometric Analysis, 2 nd Edition, Englewood Cliffs, NJ, Prentice Hall. [7] Henderson, D.J. and S.C. Kumbhakar (2004), Public and Private Productivity Puzzle: A Nonparametric Approach, unpublished manuscript, State University of New York at Binghamton. [8] Hurvich, C.M., J.S. Simonoff, and C.-L. Tsai (1998), Smoothing Parameter Selection in Nonparametric Regression Using an Improved Akaike Information Criterion, JournaloftheRoyalStatistical Society, Series B, 60, 271-293. [9] Jaffe, A.B., S.R. Peterson, P.R. Portney, and R.N. Stavins (1995), Environmental Regulations and the Competitiveness of U.S. Manufacturing: What does the Evidence Tell Us? Journal of Economic Literature, 33, 132 163. [10] Levinson, A. (2001), An Industry-Adjusted Index of State Environmental Compliance Costs, in C. Carraro and G.E. Metcalf (eds.) Behavioral and Distributional Effects of Environmental Policy, Chicago, University of Chicago Press. [11] Li, Q., and J. Racine (2004), Cross-Validated Local Linear Nonparametric Regression, Academia Sinica, 14, 485-512. [12] List, J.A., D.L. Millimet, P.G. Fredriksson, and W.W. McHone (2003), Effects of Environmental Regulations on Manufacturing Plant Births: Evidence from a Propensity Score Matching Estimator, Review of Economics and Statistics, 85, 944-952. 6

[13] N c, Nonparametric software by Jeff Racine (http://faculty.maxwell.syr.edu/jracine). [14] Pagan, A. and A. Ullah (1999), Nonparametric Econometrics, Cambridge, Cambridge University Press. [15] Racine, J. and Q. Li (2004), Nonparametric Estimation of Regression Functions with Both Categorical and Continuous Data, Journal of Econometrics, 119, 99-130. [16] Wang, M.C., and J. Van Ryzin (1981), A Class of Smooth Estimators for Discrete Estimation, Biometrika, 68, 301-309. 7

Table 1. Elasticity of Output with Respect to Inputs: Nonparametric Estimates. Public Physical Labor Unemployment Environmental Capital Capital Rate Regulation Mean 0.084 0.307 0.662-0.009-0.021 (0.03) (0.02) (0.04) (0.002) (0.02) Quartile 1 0.025 0.277 0.608-0.013-0.039 (0.03) (0.02) (0.03) (0.002) (0.02) Quartile 2 0.089 0.305 0.666-0.009-0.019 (0.03) (0.03) (0.03) (0.002) (0.02) Quartile 3 0.138 0.326 0.709-0.005-0.001 (0.03) (0.02) (0.04) (0.002) (0.01) NOTES: Output measured by state-level Gross State Product (GSP). Estimates obtained from equation (3). Standard errors in parentheses. AICc used for bandwidth selection. Controls for state and time effects also included. Table 2. Elasticity of Output with Respect to Inputs: Parametric Cobb-Douglas Estimates. Model Public Physical Labor Unemployment Environmental Capital Capital Rate Regulation Pooled OLS 0.110 0.298 0.646-0.010-0.023 (0.06) (0.05) (0.07) (0.004) (0.028) State Fixed Effects -0.262-0.007 1.102-0.003-0.009 (0.10) (0.05) (0.10) (0.003) (0.01) State Random Effects -0.104 0.191 0.924-0.005-0.009 (0.03) (0.03) (0.03) (0.001) (0.007) Hausman Test: FE v. RE χ 2 (14) = 132.86 p = 0.00 NOTES: Output measured by state-level Gross State Product (GSP). Estimates obtained from equation (6). Standard errors in parentheses. Controls for time effects included in both fixed and random effects models.

Table 3. Elasticity of Output with Respect to Inputs: Parametric Translog Estimates. Model Public Physical Labor Unemployment Environmental Capital Capital Rate Regulation I. Pooled OLS Mean 0.133 0.251 0.674-0.012-0.014 (0.06) (0.03) (0.06) (0.004) (0.02) Quartile 1 0.054 0.146 0.585-0.017-0.052 (0.05) (0.05) (0.15) (0.005) (0.15) Quartile 2 0.170 0.216 0.666-0.012-0.020 (0.05) (0.04) (0.08) (0.004) (0.08) Quartile 3 0.250 0.328 0.776-0.009 0.021 (0.16) (0.05) (0.07) (0.005) (0.07) II. State Fixed Effects Mean -0.272 0.004 1.111 0.001-0.007 (0.07) (0.05) (0.08) (0.002) (0.01) Quartile 1-0.380-0.049 1.047-0.002-0.017 (0.12) (0.05) (0.09) (0.003) (0.09) Quartile 2-0.298-0.003 1.111 3.560E-05-0.005 (0.13) (0.07) (0.08) (0.003) (0.08) Quartile 3-0.175 0.053 1.202 0.003 0.009 (0.17) (0.06) (0.08) (0.002) (0.08) III. State Random Effects Mean -0.084 0.207 0.893-0.002-4.221E-04 (0.03) (0.03) (0.04) (0.002) (0.01) Quartile 1-0.158 0.149 0.846-0.006-0.011 (0.06) (0.04) (0.04) (0.002) (0.04) Quartile 2-0.083 0.208 0.908-0.003 0.004 (0.04) (0.04) (0.05) (0.002) (0.05) Quartile 3-0.014 0.256 0.954 6.910E-05 0.016 (0.04) (0.04) (0.07) (0.002) (0.07) Hausman Test: FE v. RE NOTES: See Table 2. χ 2 (28) = 254.80 p = 0.00