Environmental policy and the equilibrium rate of unemployment

ARTICLE IN PRESS

Journal of Environmental Economics and Management 49 (2005) 132–156 www.elsevier.com/locate/jeem

Environmental policy and the equilibrium rate of unemployment Thomas Wagner University of Applied Sciences Nuernberg, Bahnhofstrasse 87, 90402 Nuernberg, Germany Received 17 April 2000; received in revised form 23 June 2003 Available online 23 August 2004

Abstract This paper integrates environmental policy instruments with the theory of equilibrium unemployment. We investigate the question of whether a low equilibrium rate of unemployment and a high quality of the environment are complementary policy goals or must be traded off. It turns out that an interval exists for a tax on emissions where the two goals are indeed complementary. The tax stimulates the emergence of an abatement sector which provides pollution control and vacancies for the job seekers. For constrained efficiency, the policy maker operates five instruments to internalize the environmental and the search externalities. A tax on emissions, employment subsidies and recruiting allowances for the polluting industries are sufficient to implement the first-best. The optimal emission tax is an increasing function of the workers’ bargaining strength. For labor markets where workers have a strong bargaining position, the optimal pollution tax may easily exceed the Pigouvian tax. r 2004 Elsevier Inc. All rights reserved. Keywords: Environmental policy instruments; Emission tax; Equilibrium unemployment; Constrained efficiency

1. Introduction In recent years, public opinion—which, in the past, often regarded environmental regulations as ‘‘job killers’’—has gradually shifted towards supporting the hypothesis that a more stringent Corresponding author.

E-mail address: [email protected] (T. Wagner). 0079-610/$ - see front matter r 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.jeem.2004.03.006

ARTICLE IN PRESS T. Wagner / Journal of Environmental Economics and Management 49 (2005) 132–156

133

environmental policy not only promotes a country’s international competitiveness but may also improve its employment situation [5,19,23,31,32,39]. Discussions in the political arena have been preoccupied with conjectures about the employment effects of environmental policy, while environmental economics has rarely addressed the issue of the impact of environmental policy instruments on equilibrium unemployment. To investigate the relationship between the policy goals of a clean environment and low unemployment, the present paper integrates standard environmental policy instruments [3,8,20] with the theory of equilibrium unemployment [13,33,34]. The economy of the model consists of two sectors: a production sector with a dirty industry and a clean industry that emits an assimilative pollutant, and an abatement sector which provides cleaning services for the polluting industries and vacancies for the job seekers. Depending on the level of the tax rate, the emission tax causes either a trade-off or a complementarity between the two policy goals. Within the tax brackets where the goals are complementary, the tax reduces both the emissions and the equilibrium rate of unemployment. For low tax rates, on the other hand, we find a trade-off between the two policy goals. There are two reasons for this result. Firms in the polluting industries would rather pay the tax than control their emissions and workers faced with the low wages offered by the abatement sector do not find it attractive to search for cleaning jobs. Hence, an abatement sector, which could outweigh the job destruction effects of the pollution tax in the production sector, does not develop. We next show that, under conditions like those of the Pigouvian economy, the policy goals of a clean environment and a low rate of unemployment are complementary even in a command-andcontrol economy regulated by an emission standard. Empirical research has not produced clear cut evidence for the disputed trade-off [1–2,4,16,19,21,27]. However, the results of Berman and Bui’s [4] research into the employment effects of local ‘‘air quality regulations’’ in the Los Angeles area seem to confirm our analysis. They note that, despite considerable investment in ‘‘abatement capital, y we find no evidence that local air quality regulation substantially reduced employment, even when allowing for induced plant exit and dissuaded plant entry’’. According to Berman and Bui, all new regulations and every tightening of existing regulations induce large investments in abatement technology, and the measured employment effects of air quality regulations are generally positive although they are not statistically significant. They explain the adjustment of the demand for labor they observe in all polluting industries by the complementarities between abatement capital and labor in production that dominate the negative output effects of the air quality regulations. They also estimate the job destruction and creation effects of air quality regulations and again find no significant results, although they argue that the impact of new regulations on entry and exit is likely to be negative for the regulated industry. Although the extensive literature on the ‘‘double dividend’’ of an environmental tax reform focuses on the employment effects of environmental policy, there seems to be only one paper—by Bovenberg and v.d. Ploeg [10]—that describes the effects of such a reform within the framework of the theory of equilibrium unemployment. In their model, the government has a balanced budget and uses the revenue of an ad valorem tax on energy consumption to lower the firms’ payroll tax. The labor market is segmented. The natural rate of unemployment is positive in the official labor market which is a search market with a matching technology similar to the one we use. In the informal neoclassical labor market, however, any job seeker instantly finds a job and

ARTICLE IN PRESS 134

T. Wagner / Journal of Environmental Economics and Management 49 (2005) 132–156

the market clears at all times. The fiscal policy reform shifts the tax burden away from the official sector to the informal sector. Nevertheless, for a ‘‘double dividend’’ to develop, the pre-reform energy tax must be low. With a high initial tax rate the increase in the overall tax burden would make the aggregate employment effect of the tax reform negative. In contrast to [10], in our two-sector model real income during job search is an exogenous flat rate not indexed to the wages. Thus, the ‘‘double dividend’’ is neither a result of the assumptions about a job seeker’s utility function and the sources of his income during job search as in [10], nor does it stem from swapping environmental taxes for distortionary taxes as in most of the literature about the ‘‘double dividend’’. It emerges because—at a sufficiently high emission tax—an abatement sector develops which provides both abatement services to the polluting industries and vacancies for the job seekers. The paper is organized as follows. In Section 2, we present the overall equilibrium of the unfettered market with its search and environmental externalities. In Section 3 the polluters are forced to control their emissions and a market for pollution control services evolves. In Sections 4 and 5 emission taxes and emission standards are discussed. Section 6 analyzes the first-best allocation, Section 7 concludes. The appendix provides proofs of all propositions.1

2. The unfettered market The entrepreneurs in this model organize production, sell output, offer vacancies, and recruit workers. The workers employed carry out the production plans, the unemployed search for a vacancy. Firms and workers are risk neutral and have an infinite time horizon. The labor markets are search markets [13,35,11,17,36]. Frictions, heterogeneities, and informational imperfections— not explicitly modeled—force the market participants to search for matching partners. The labor force and the measure of jobs in the polluting industries are given [6–7,12]. The capacity of the abatement sector is endogenous, adapting to shocks through a perfectly elastic inflow of vacancies [30]. Job seekers are mobile between industries and move to the location where they earn the highest income. Vacancies and filled jobs are immobile.2 Jobs: There are two polluting industries i ¼ C; X, where i denotes the location or the characteristics of a differentiated product produced by the firms of industry i. The exogenous measure of jobs in industry i is ki . Each firm consists of one job which is either vacant or filled. A filled job produces the output yi and, as a by-product, the quantity Pi of a pollutant. Jobs in the industry C produce with a more advanced technology than jobs in the industry X, in particular we assume3 ðCXÞ PX 4PC 40 and yC XyX : These assumptions seem to be plausible because technologically improved process designs often pollute less and are more productive than less advanced technologies. For convenience, we will refer to the industries C and X as the clean and the dirty industry, respectively. 1

The appendix is available online as a supplement to this article at http://www.aere.org/journal/index.html. Hosios [18] is a two-sector model with completely mobile jobs; Mortensen and Pissarides [25] discuss a case in which even filled jobs are mobile between the sectors. 3 To prove the statements indexed by a* assumption (CX) is used. 2

ARTICLE IN PRESS T. Wagner / Journal of Environmental Economics and Management 49 (2005) 132–156

135

Matching technology: Time is continuous. The labor market is characterized by two-sided search [12,24,26,29,30,34]. Trade in the labor market and production are separate activities. Jobs (workers) either search, if vacant (unemployed), or produce, if filled (employed). Of all the ki jobs of industry i, ei are filled and vi are vacant, ki ¼ ei þ vi . The labor force l is exogenous. Of the l workers l P move to the economy’s production sector and l A to the abatement sector so that l ¼ l P þ l A . For the present we assume that l P ¼ l, see Fig. 1. Of the l P (exogenous) production workers l i move to the industry i, where ei are employed and ui search for a job, so that l i ¼ ei þ ui , i ¼ C; X, and l P ¼ l C þ l X . Vacant jobs and unemployed workers search for matching partners. All traders in the labor market act as atomistic competitors. The transaction technology is modeled by a matching function with the flow of matches mi per time unit as the dependent variable, and the measures of job seekers ui and vacancies vi as the independent variables, mi ¼ mðui ; vi Þ. Both industries i use the same matching technology [22]. The matching function is continuously differentiable and concave, has constant returns to scale, and strictly positive partial derivatives. The vacancies and job seekers that are matched are randomly selected from vi and ui . Hence, movement from unemployment to employment is a Poisson process with the transition rate mðui ; vi Þ=ui : From the homogeneity of the matching function it follows that mðui ; vi Þ=ui ¼ mð1; yi Þ, so that the transition rate pðyi Þ  mð1; yi Þ is a function of the labor market tightness, yi , where yi ¼ vi =ui is the ratio of the measure of vacancies and the measure of unemployed. The job seekers’ rate of arrival at a vacancy is qðyi Þ  mðui ; vi Þ=vi ¼ mð1=yi ; 1Þ, so that pðyi Þ ¼ yi qðyi Þ. With decreasing labor market tightness, the job seekers’ rate of transition into employment approaches zero, and their rate of arrival at a given vacancy approaches infinity: pð0Þ ¼ qð1Þ ¼ 0 and pð1Þ ¼ qð0Þ ¼ 1. A job is created when a vacancy and a job seeker meet. At each moment of time, pðyi Þui of the ui unemployed apply for a job. As soon as the worker is taken on, firm and employee begin to produce until an idiosyncratic shock destroys the match. The job becomes vacant, and the worker moves to the submarket i with the highest income for job seekers. Firm-specific demand or technology shocks occur at a frequency l, which is the result of an exogenous Poisson process and

Fig. 1. Equilibrium E of the unfettered market.

ARTICLE IN PRESS 136

T. Wagner / Journal of Environmental Economics and Management 49 (2005) 132–156

is identical for all jobs and industries. Unemployment persists in the steady state, since before all unemployed job-worker pairs are matched lei of the ei filled jobs are destroyed. The process of job destruction produces a permanent inflow into the pools of unemployed and vacancies. In the steady state, the inflow into unemployment equals the outflow so that lei ¼ pðyi Þui since the measures for filled jobs and employed workers are identical. From this equation we derive4 the steady-state measures of vacancies, job seekers, filled jobs, and the size of the labor force in industry i as functions of the industry’s tightness yi and exogenous capacity ki .5 Asset equations: Denote by J i the net present value of a filled job, by V i the value of a vacancy, by W i the value of an employed worker, and by U i the value of a job seeker. In the steady state of industry i, the following asset equations hold: rJ i ¼ yi  wi þ lðV i  J i Þ;

ð1Þ

rV i ¼ c þ qðyi ÞðJ i  V i Þ;

ð2Þ

rW i ¼ wi þ lðU i  W i Þ;

ð3Þ

rU i ¼ b þ pðyi ÞðW i  U i Þ;

ð4Þ

W i  U i ¼ b½ðJ i  V i Þ þ ðW i  U i Þ ;

ð5Þ

where r is the real interest rate, b the UI benefit or the utility of leisure, l the separation rate, and c the hiring costs. The labor productivity yi , the bargained wage wi , and the labor market tightness yi of industry i are industry-specific. To interpret Eq. (1) note that a filled job with present value J i is an asset owned by the firm. If the job is destroyed, it moves into the pool of vacancies and the firm bears a loss equal to V i  J i . Therefore, the total return of the filled job is given by the sum of the current profit, yi  wi , and the expected capital loss lðV i  J i Þ. By investing the capital tied up in the job in the perfectly competitive capital market the firm could earn a permanent income equal to rJ i . In the steadystate, all arbitrage possibilities are exhausted. Therefore, in the steady state equilibrium of the labor market, the permanent income of a filled job in industry i must be equal to rJ i and the arbitrage Eq. (1) holds. Correspondingly, qðyi ÞðJ i  V i Þ in Eq. (2) is the expected gain for the firm if a vacancy is filled, an event which occurs with the endogenous flow-probability qðyi Þ. Taking into account the hiring costs c, in the steady state a vacancy at location i earns a permanent income rV i ¼ c þ qðyi ÞðJ i  V i Þ. The asset Eqs. (3) and (4) can be interpreted analogously. The process of job destruction changes the value of an employed worker from W i to U i with rate l. Hence the worker’s expected loss from the destruction of his job is lðU i  W i Þ and his permanent income, rW i , is equal to the sum of the negotiated wage wi and the loss lðU i  W i Þ. A job seeker’s expected gain from the transition to employment is pðyi ÞðW i  U i Þ. The job seeker’s return therefore equals the sum of the UI benefit b and the expected gain from a transition, see Eq. (4). Costly job search is the reason why a filled job earns a quasi-rent in the steady state. In the case of a match, firm and applicant form a bilateral monopoly and bargain over the distribution of the 4 5

See Lemma A.1 in Appendix A. For convenience we write l i ðyi Þ ¼ lðki ; yi Þ etc.

ARTICLE IN PRESS T. Wagner / Journal of Environmental Economics and Management 49 (2005) 132–156

137

rent. Eq. (5) describes the rule which governs the distribution of the present-discounted value of the match rent, ðJ i  V i Þ þ ðW i  U i Þ, between firm and worker. The worker’s share of the rent is a constant fraction b, 0obo1, where b reflects the exogenous bargaining strength of the worker. Eq. (5) can be interpreted as the first-order maximization condition derived from the generalized Nash solution for the wage rate wi ¼ arg maxðW i  U i Þb ðJ i  V i Þ1b . Reservation wage Y: Eqs. (1)–(5) contain six endogenous variables for each industry: the labor market tightness yi , the bargained wage wi , and the asset values J i , V i , W i , and U i . Solving for the endogenous variables we obtain the permanent income of a job seeker in i as a function of the labor market tightness:6 rU i ðyi Þ ¼ b þ gðyi Þpi ;

ð6Þ

where pi ¼ yi þ c  b is the current match rent of an occupied job. Note that the asset Eq. (4) and the income Eq. (6) are alternative expressions for a job seeker’s permanent income. In Eq. (4) the option value component of the permanent income is represented by the expected capital gain from transition into employment. By contrast, in the income Eq. (6) the option value is expressed as the share gðyi Þ of the current match rent pi for which gðyi Þ ¼ bpðyi Þ=dðyi Þp1, where dðyi Þ ¼ r þ l þ bpðyi Þ þ ð1  bÞqðyi Þ is a location-specific discount factor. The share gðyi Þ can be interpreted as the endogenous bargaining strength of a worker at location i. gðyi Þ is a strictly increasing function of b and the labor market tightness satisfying gð0Þ ¼ 0 and gð1Þ ¼ 1.7 Workers are free to move between the two industries. Accordingly, in overall equilibrium, the expected permanent income of job seekers in the two industries must be the same rU i ðyi Þ ¼ Y ;

i ¼ C; X

ð7Þ

where Y is the production sector’s reservation wage. Y is the minimum compensation a worker requires in order to give up search and accept a job. In view of the income Eq. (6) and the mobility condition (7), the tightness in the labor market of industry i, yi ðY Þ, can be shown to be a strictly increasing function of the production sector’s reservation wage Y.8 Assumption (CX) implies pC XpX . From this inequality and the Eqs. (6) and (7) it follows that workers in industry X have a bargaining strength at least as high as in industry C, gðyX ÞXgðyC Þ. Thus, due to the monotonicity of gð Þ, we find yX ðY ÞXyC ðY Þ for Y with bpY pb þ pX . If Y ob, no unemployed will search for a job. If on the other hand Y 4b þ pX industry X is not competitive and does not offer vacancies. Competitiveness: Industry i is competitive as long as its firms are willing to offer vacancies. Firms post vacant jobs if a vacancy’s permanent income is non-negative, rV i ðyi ÞX0. The permanent income of a vacancy is9 rV i ðyi Þ ¼ c þ dðyi Þpi ; 6

ð8Þ

See Lemma A.2 in Appendix A. See Lemma A.2. The worker’s endogenous bargaining strength, gðyi Þ, depends not only on b but also on the prevailing labor market conditions expressed through yi . The tighter the labor market, the longer the expected duration of a vacancy and the more resources a firm will have to invest in its hiring activities. Therefore, the tighter the labor market, the larger the share of the match rent the firm is willing to sacrifice during wage negotiations. 8 See Lemma A.3. 9 See Lemma A.2. 7

ARTICLE IN PRESS 138

T. Wagner / Journal of Environmental Economics and Management 49 (2005) 132–156

where the component representing the option value of the vacancy is expressed as the share dðyi Þ ¼ ð1  bÞqðyi Þ=dðyi Þp1 of the current match rent pi .10 Under the above assumptions, there are industry-specific reservation wages Y i , with boY i ob þ pi , where the value of a vacancy in i approaches zero, since dðyi ðY i ÞÞpi ¼ c.11 If Y 4Y i , industry i is not competitive because for the unemployed it is does not pay to search for vacancies in i which can only offer an income not exceeding Y i , see Fig. 1. If, on the other hand, Y pY i , the industry advertises vacancies and is frequented by a positive measure of job seekers. Given assumption (CX) clean firms are more competitive than dirty firms, Y C XY X —see also the vertical axis of Fig. 1. To prove this statement let Y be a sustainable reservation wage for both industries. Then we know that yX ðY ÞXyC ðY Þ, so that dðyX ðY ÞÞpdðyC ðY ÞÞ due to the monotonicity of dð Þ. Thus, taking into account pC XpX and Eq. (8), we get rV C ðyC ðY ÞÞXrV X ðyX ðY ÞÞ. Hence, by virtue of the monotonicity of yi ðY Þ the industry-specific reservation wage is higher in C than in X. Environmental damage and equilibrium: To close the model we introduce the excess supply function of the aggregate labor market. Since all endogenous variables now depend on the reservation wage, Y, we solve the two-industry model by determining the value of Y that clears the aggregate labor market, see Fig. 1. The labor force of industry i consists of the unemployed searching for a vacancy in i, ui ðyi Þ, and the workers employed in i, ei ðyi Þ, such that l i ðyi Þ ¼ ei ðyi Þ þ ui ðyi Þ. Since yi ¼ yi ðY Þ, the size of the labor force of industry i is a decreasing function of the reservation wage Y, l i ðyi ðY ÞÞ, see Fig. 1. Hence, given the (exogenous) labor force l P which stays in the economy’s production sector the excess supply of the sector’s aggregate labor market, El, is also a function of Y: ElðY Þ ¼ l P  l C ðyC ðY ÞÞ  l X ðyX ðY ÞÞ:

ð9Þ

Using the measure of filled jobs, we obtain the emissions of industry i, Di ðY Þ ¼ ei ðyi ðY ÞÞPi . The aggregate emissions, D, and the equilibrium rate of unemployment, u, are: DðY Þ ¼ DC ðY Þ þ DX ðY Þ;

uðY Þ ¼ uC ðyC ðY ÞÞ þ uX ðyX ðY ÞÞ:

ð10Þ

The pollutant generated in the process of production is a public bad and reduces the welfare of all job seekers and workers alike. Environmental damage Z is measured in units of output and is a function of the aggregate flow of pollutants D. The workers’ utility functions are assumed to be additively separable with respect to their income and the damage Z(D). Hence the net utility of the employed and the unemployed is rWi  ZðDÞ and rUi  ZðDÞ; respectively. Since workers are risk neutral and the environmental damage is not location-specific, the externality does not influence the equilibrium allocation of the unfettered market [9–10,14,15,28]. The overall equilibrium of the unfettered market is characterized by a reservation wage Y  for which ElðY  Þ ¼ 0. Y  determines, in turn, the natural rate of unemployment u ¼ uðY  Þ, and the aggregate emissions D ¼ DðY  Þ. In view of assumption (CX) an overall equilibrium with an active dirty and clean industry exists, see Fig. 1 point E, if we assume that the excess supply 10 The share dðyi Þ reflects the endogenous bargaining strength of the firm and is a strictly increasing function of ð1  bÞ and a strictly decreasing function of the labor market tightness with the limits dð0Þ ¼ 1 and dð1Þ ¼ 0. We will assume throughout that the current match rent is higher than the hiring costs, pi 4c. Then there always exist labor market conditions with yi 40 where firms in industry i are willing to post vacancies (see Fig. A.2 in Appendix A). 11 See Lemma A.3 and Fig. A.2 in Appendix A.

ARTICLE IN PRESS T. Wagner / Journal of Environmental Economics and Management 49 (2005) 132–156

139

function (9) for the industry-specific reservation wage Y X satisfies ElðY X ÞX0. Since the excess supply function is continuous and strictly monotone, the overall equilibrium is characterized by an unique reservation wage Y  , with boY  pY X .

3. The market for pollution control As a waste sink, the environment provides inputs which are overused if nature’s assimilation capacity is free or legally assigned to the polluting industries without obligation to process emissions. In an economy where a regulator has the right to exclude polluters from (over-)using nature’s services, firms are forced to control their emissions and therefore demand abatement services. We now extend the model by introducing an abatement sector which provides pollution control and vacancies for the job seekers. First, we focus again on the economy’s production sector and deal with the cleaning service as a factor of production, which is traded on a competitive market. Next, we present the model of the abatement sector. Third, we discuss the overall equilibrium. We establish that there exists a lower bound to the price for abatement services kl , see Fig. 2, below which it does not pay for the job seekers to leave the polluting industries and move to the abatement sector. For cleaning prices above kl , the abatement sector is active and supplies emission control and posts vacancies in the labor market. Next we show, that there exists a cleaning price kn , see Fig. 2, at which the market for pollution control services clears. Finally we prove that the equilibrium duration of job search is shorter in the abatement sector than in the production sector. 3.1. The production sector At a price k for each unit of pollution control, the abatement costs of a filled job in industry i with pollution Pi are kPi . In the income Eqs. (6) and (8), the current match rent of a job in industry i is now pi ðkÞ ¼ yi  kPi þ c  b. In the equilibrium of an economy where the regulator

Fig. 2. Equilibrium E.

ARTICLE IN PRESS 140

T. Wagner / Journal of Environmental Economics and Management 49 (2005) 132–156

forces polluting firms to clean their emissions the tightness of the labor market of industry i is a strictly increasing function of the reservation wage Y and—given Y—of the cleaning price k.12 If k40, assumption (CX) implies the strict inequality pC ðkÞ4pX ðkÞ. From this inequality, and from the workers’ mobility between the industries C and X, it follows that the equilibrium labor market tightness of the dirty industry X is strictly larger than that of industry C, yX ðY ; kÞ4yC ðY ; kÞ. Competitiveness: The process of job creation depends on the firms’ willingness to open vacancies and search for job applicants. Opening a vacancy in industry i pays only if its permanent income (8) is non-negative. Using the labor market tightness yi ðY ; kÞ in industry i we get the permanent income of a vacancy as a function of the reservation wage and the cleaning price, rV i ðY ; kÞ. From rV i ðY ; kÞ ¼ 0 we derive the industry-specific reservation wage Y i at which industry i loses its competitiveness as a function of k, Y i ðkÞ, and its inverse, the ‘‘shutdown cleaning price’’ for industry i, ki ðY Þ, as a function of Y. Lemma 1*. (1) Given the production sector’s reservation wage Y, industry i is competitive at the cleaning price k if kpki ðY Þ. (2) Due to the assumption (CX), kC ðY Þ4kX ðY Þ for all Y at which industry X is viable. Equilibrium: Accounting for yi ¼ yi ðY ; kÞ, we replace (9) by the following excess supply function for the production sector’s aggregate labor market ElðY ; kÞ ¼ l P  l C ðyC ðY ; kÞÞ  l X ðyX ðY ; kÞÞ:

ð11Þ

Lemma 2. Given the cleaning price k40 and the labor force l P staying at the economy’s production sector, their exists a unique reservation wage Y ðk; l P Þ at which ElðY ðk; l P Þ; kÞ ¼ 0. The equilibrium reservation wage is as shown in Fig. 2 a decreasing function of k and l P . Since yi ¼ yi ðY ; kÞ and Y ¼ Y ðk; l P Þ, the following equations hold for the equilibrium flow of emissions and rate of unemployment: Dðk; l P Þ ¼ DC ðk; l P Þ þ DX ðk; l P Þ;

uðk; l P Þ ¼ uC ðyC ðk; l P ÞÞ þ uX ðyX ðk; l P ÞÞ;

ð12Þ

where Di ðk; l P Þ ¼ ei ðyi ðk; l P ÞÞPi is the emission or the demand of industry i for abatement services. Shutdown price: In view of assumption (CX) both the clean and dirty industry are competitive at the reservation wage Y ðk; l P Þ if the cleaning price k does not exceed the shutdown cleaning price for industry X, kpkX ðY ðk; l P ÞÞ. For a given labor force l P , the shutdown price kX ðY ðk; l P ÞÞ is a strictly increasing contraction mapping.13 The intuition for this result is as follows. Increasing the cleaning price k reduces the reservation wage Y ðk; l P Þ which clears the labor market of the production sector. But the reservation wage Y ðk; l P Þ is the return on the unemployed worker’s human capital and therefore the job seekers ‘‘threat point’’ during wage negotiations. As a higher cleaning price reduces the ‘‘threat’’, the bargained wages and the wage costs decline in both industries. Therefore, both industries can sustain higher expenses for abatement activities, so that the shutdown prices move up. From the observation that the shutdown cleaning price is a contraction, it follows that there exists a unique fix point, i.e. a cleaning price knX such that knX ¼ kX ðY ðknX ; l P ÞÞ [37]. Given the labor 12 13

See Lemma A.4*. See Lemma A.5 in Appendix A.

ARTICLE IN PRESS T. Wagner / Journal of Environmental Economics and Management 49 (2005) 132–156

141

force l P staying at the economy’s production sector, despite the burden caused by the pollution control costs, the dirty industry and a fortiori the clean industry are both viable as long as kpknX . Remark. 1. Notice that for the equilibrium reservation wage Y n of the unfettered market Y  ¼ Y ð0; lÞ, see Fig. 2. 2. To secure kX ðY ðkX ; l P ÞÞ40, it is sufficient to assume that the shutdown cleaning price for industry X at the equilibrium reservation wage of the unfettered market economy, Y ð0; l P Þ, is strictly greater than zero, kX ðY ð0; l P ÞÞ40. 3. The fact that a growing labor force l P in the production sector reduces the reservation wage Y ðk; l P Þ implies that the shutdown cleaning price for the dirty industry is indeed an increasing function of l P , kX ðl P Þ ¼ kX ðY ðkX ðl P Þ; l P ÞÞ (see Lemma A.5). 4. Further below in the section on the overall equilibrium it will be shown that the equilibrium labor force staying at the economy’s production sector is a decreasing function of the cleaning price k. Industry i is competitive at k if and only if kpki ðl P ðkÞÞ, where like l P ðkÞ, ki ðl P ðkÞÞ is a decreasing function of the price for the cleaning service. Lemma A.6* establishes that for ki ðl P ðkÞÞ there is a fixed point K i ¼ ki ðl P ðK i ÞÞ, such that the industry i is viable at all k, for which kpK i . 3.2. The abatement sector An abatement firm is conceptualized along the lines of the theory of equilibrium unemployment. Firms consist of one job. The job is vacant or occupied. Each occupied job rents a capital good and produces cleaning services. Each vacancy is actively searching for job applicants. As soon as a worker is taken on, the firm starts production and offers its output on the market for the abatement service. There are two conditions for the abatement sector to become active. First, a vacancy in the sector must earn a non-negative income. Second, the income offered to job seekers must induce them to move to the abatement sector. Jobs and matching technology: Each abatement job is either vacant or filled with a worker who produces the quantity of pollution control a measured in units of the pollutant. For the moment, we assume the cleaning price k as given and investigate only the abatement sector’s labor market. The UI benefit, b, the separation rate, l, the discount rate, r, the hiring costs, c, and the bargaining strength of the workers, b, are the same as in the production sector of the economy. Moreover, yA ¼ vA =uA is the tightness in the abatement sector’s labor market where uA job seekers and vA vacancies are searching for each other. The abatement sector uses the same matching technology as the production sector, qðyA Þ is the arrival rate of job seekers at a given vacancy, and pðyA Þ ¼ yA qðyA Þ is an unemployed worker’s rate of transition to employment. Income equations: The asset equations for the value of a filled job, a vacancy, an employed worker, and a job seeker, and the equation for the distribution of the match rent have the same structure as Eqs. (1)–(5). The Eqs. (6) and (8) for the permanent income of a job seeker and a vacancy in the abatement sector, reproduced here for easier reference, are rU A ðyA Þ ¼ b þ gðyA ÞpA ðkÞ;

ð13Þ

rV A ðyA Þ ¼ c þ dðyA ÞpA ðkÞ;

ð14Þ

where pA ðkÞ ¼ ka þ c  b is the current match rent of an occupied abatement job.

ARTICLE IN PRESS 142

T. Wagner / Journal of Environmental Economics and Management 49 (2005) 132–156

The capacity of the abatement sector is endogenous, the inflow of vacancies continues until their value is driven to zero. Using Eq. (14) and V A ¼ 0, we obtain the job creation condition for the abatement sector pA ðkÞ  c=dðyA Þ ¼ 0:

ð15Þ

For the cleaning price k, (15) gives the tightness at which the inflow of vacancies into the abatement sector ceases and the job creation process stops. Note that as a consequence of the free entry condition the equilibrium tightness does not depend on the labor force staying in the abatement sector. If we substitute the current match rent pA ðkÞ from (15) into (13), we obtain the equilibrium reservation wage of the sector, rU A ðyA Þ ¼ b þ byA c=ð1  bÞ:

ð16Þ

Supply of pollution control services: The first vacancy entering the labor market of the abatement sector faces the market tightness yA ¼ 0, and therefore can expect the return rV ð0Þ ¼ ka  b, as dð0Þ ¼ 1. From this condition for the ‘‘extensive margin’’ of the job creation process we derive the shutdown price of the abatement sector kA ¼ b=a, see Fig. 2. Given the labor force l A and the cleaning price k4kA the aggregate supply of cleaning services is14 Sðk; l A Þ ¼ mðyA ðkÞÞl A a:

ð17Þ

In (17), mðyA Þ  pðyA Þ=ðl þ pðyA ÞÞp1, with mð0Þ ¼ 0 and mð1Þ ¼ 1, denotes the abatement sector’s equilibrium rate of employment which is a strictly increasing function of the labor market tightness. Equilibrium: For a given cleaning price k4kA and a given labor force l A the equilibrium in the labor market of the abatement sector is a state ðyA ; rU A ; S  Þ —with the tightness yA ¼ yA ðkÞ, the reservation wage rU A ¼ rU A ðkÞ, and the supply of abatement services S  ¼ Sðk; l A Þ —which satisfies the job creation condition (15), the income Eq. (16), and the supply function (17). For ðyA ; rU A ; S  Þ the following lemma holds: Lemma 3. (1) The labor market tightness, the reservation wage of the sector (see Fig. 2), and the supply of abatement services are increasing functions of the cleaning price k. (2) The supply of abatement services is, moreover, an increasing function of the labor force l A employed in or seeking employment in the sector. 3.3. Overall equilibrium The market for pollution control is a Walrasian auction market with perfectly informed participants behaving as atomistic price takers. The production sector’s aggregate demand for pollution control services, Dðk; l P Þ, is determined by emissions (12), while the supply of the abatement sector, Sðk; l A Þ, is given by the aggregate supply function (17). The steady-state equilibrium in the three labor markets of the economy and in the market for pollution control is a 14

Use (A.1), Appendix A, to calculate the measure of filled jobs as a function of the labor force, e ¼ ml, with m ¼ p=ðl þ pÞ; then, take into account the fact that a filled job produces the quantity of pollution control a, and obtain S ¼ mla.

ARTICLE IN PRESS T. Wagner / Journal of Environmental Economics and Management 49 (2005) 132–156

143

state ðk ; l P ; l A Þ where k is the cleaning price, and l A and l P , respectively, denote the labor force in the abatement sector and the production sector15 which satisfies the following conditions: Sðk; l A Þ ¼ Dðk; l P Þ

ð18Þ

rU A ðkÞ ¼ Y ðk; l P Þ

ð19Þ

l ¼ lP þ lA:

ð20Þ 16

Condition (18) requires that the market for pollution control clears. The mobility condition (19) implies that in equilibrium the job seekers are indifferent between the production sector and the abatement sector. Finally, condition (20) requires that the aggregate labor market clears. Moreover, at the production sector’s reservation wage, Y ðk; l P Þ, the sector’s labor markets clear, and the excess supply (11) approaches zero. Is there an overall equilibrium with an active abatement sector for a regulated market economy? Vacancies for abatement services are offered only if the cleaning price exceeds the sector’s shutdown price kA , see Fig. 2. On the other hand, for cleaning prices exceeding ki ðlÞ—where ki ðlÞ is the shutdown cleaning price for the industry i when a labor force of size l is staying in the production sector17—industry i is not viable, and its demand for pollution control falls to zero. Since kC ðlÞ4kX ðlÞ under assumption (CX), kC ðlÞ4kA is necessary for the two-sector model to have a non-trivial solution. Mobility rent: The mobility rent EY ðk; l P Þ ¼ rU A ðkÞ  Y ðk; l P Þ is continuous and strictly increasing in k. Hence, for a total labor force of size l staying at the production sector, a unique cleaning price kl with kA okl okC ðlÞ exists, for which the mobility rent is zero, EY ðkl ; lÞ ¼ 0,18 see Fig. 2 point B. Therefore, in an economy with a total labor force of size l a general equilibrium with an active abatement sector can only develop at cleaning prices kXkl . At lower prices the mobility rent is negative, and no job seeker would move to the abatement sector. Let kXkl . If the cleaning price rises, the reservation wage offered to job seekers in the abatement sector, rU A ðkÞ, increases, see Fig. 2, the job creation process attracts a growing labor force l A and the complementary job destruction in the production sector reduces the labor force l P .19 Recall that the production sector’s equilibrium reservation wage, Y ðk; l P Þ, is decreasing in both of its arguments.20 Thus, the increasing cleaning price reduces Y ðk; l P Þ. Therefore, the decline of the production sector and its labor force l P must compensate first the negative effect of the increase in k and second raise Y ðk; l P Þ, such that the mobility condition (20) is fulfilled. Equilibrium: With a rising abatement price, the labor force moves to the abatement sector, attracted by the newly opened vacancies and the growing labor income. But this reallocation of the labor force leads to a drop in the shutdown cleaning prices for the industries C and X.21 15

Recall that the production sector consists of the polluting industries C and X implying that l P ¼ l C þ l X . Note that equilibrating supply and demand for abatement services does not necessarily mean that polluters abate all of their emissions! The surviving jobs clean that part of their emissions, for which, for example, pollution control is technically feasible or legally required. 17 See Remark 3 and Lemma A.5. 18 See Lemma A.6*. 19 See Lemma A.6*. 20 See Lemma 2. 21 See Lemma A.6*. 16

ARTICLE IN PRESS 144

T. Wagner / Journal of Environmental Economics and Management 49 (2005) 132–156

Hence, an equilibrium with an active abatement sector exists only if we can find a cleaning price kXkl at which at least the clean industry C is competitive, so that kpK C .22 Provided that at K C the excess supply of the abatement market is positive there indeed exists a unique kn , with kl ok pK C , at which the market for the abatement service clears.23 In the overall equilibrium ðk ; l P ; l A Þ the clean industry is competitive and demands abatement services. Whether the dirty industry survives depends on the industry’s shutdown price K X . If k pK X , as we will assume in the following, industry X is also viable. For cleaning prices k, with kl pkpk , for which the equilibrium conditions (19) and (20) are satisfied we are now prepared to prove: Lemma 4*. At k the labor market tightness of the abatement sector is at least as high as that of the clean and dirty industry. In particular, it is true that yA ðkÞXyX ðk; l P Þ4yC ðk; l P Þ, where l P ¼ l P ðkÞ is the equilibrium labor force of the production sector. Moreover, the current match rents at the three locations satisfy the inequalities pA ðkÞppX ðkÞopC ðkÞ. From Lemma 4* it follows that the average duration of unemployment, 1=pðyÞ, is shortest in the abatement sector and longest in the clean industry, while the expected duration of a vacancy, 1=qðyÞ, is longest in the abatement sector and shortest in C. Thus a reallocation of the marginal worker from C to A would reduce the aggregate rate of unemployment, since the aggregate duration of unemployment declines and the job destruction rate l is the same at all locations. What is the intuition for Lemma 4*? The result is a consequence of the model’s mobility and entry assumptions. While job seekers are perfectly mobile, jobs are not. Therefore, in equilibrium, the expected income of an unemployed worker is the same everywhere, while the income of a vacancy differs between sectors and locations. In particular, the income in the production sector is at least as high as that in the abatement sector, rV i X0 ¼ rV A , i ¼ C; X. Workers have rational expectations. They anticipate that immediately after the separation from the job, the job owner will open a new vacancy with an income equal to rV i X0. This expectation is reflected in the option value component of the return from the search. From (6) we know that the income of an unemployed worker in industry i is rU i ¼ b þ gðyi Þpi , while, according to (8), the income from a vacancy is rV i ¼ c þ dðyi Þpi . Substituting for the current match rent in the job seeker’s income equation and rearranging terms we find that rU i ¼ b þ byi ðc þ rV i Þ=ð1  bÞ. Hence, the higher the asset value of a vacancy in industry i the higher is, ceteris paribus, the income of an unemployed worker searching for a job in that industry. The mobility rent the job seekers can expect attracts the unemployed of the other labor markets to the industry i, and the tightness at i declines until the mobility rents vanish. Since in the steady state we have rV A ¼ 0, the unemployed in the abatement sector in fact do not benefit from a positive asset value of the sector’s vacancies. Therefore, if the job seekers looking for an abatement job were not compensated they would leave the sector and move to the industries C or X. The tightness of the labor market for abatement services would increase, the 22 23

See Remark 4. Lemma A.6* shows that for K C the strict inequalities kl oK C oknC ðlÞ hold. See Lemma A.7.

ARTICLE IN PRESS T. Wagner / Journal of Environmental Economics and Management 49 (2005) 132–156

145

rate of transition from unemployment to employment would follow suit, and, finally, the option value of the human capital of a job seeker would be driven up. 4. The emission tax In the Pigouvian economy, the government regulates the flow of pollutants through a tax on emissions [20]. The tax rate, t, is defined in units of output per unit of the pollutant. A filled job in industry i which does not control pollution must pay the tax tPi . Two intervals of the tax rate can be distinguished with regard to the impact of the tax on the equilibrium rate of unemployment. Tradeoff: The first interval is ½0; kl Þ. Recall that for l P ¼ l, the upper support kl is the cleaning price at which the mobility rent equals zero (see Fig. 2 point B). Hence, for cleaning prices k 2 ½0; kl Þ the mobility rent is negative and no job seeker will move to the abatement sector. Producers must pay the tax, and—if assumption (CX) holds—society is confronted with the well known trade-off between employment and environmental quality. Proposition 1*. (1) If the government levies a tax t 2 ½0; kl Þ on emissions, job seekers move from the dirty industry X to the clean industry C, such that the labor market tightness increases in X and decreases in C. (2) In the dirty industry the unemployment rate is a decreasing function and in the clean industry it is an increasing function of t. The reallocation of the labor force induced by an increase in the emission tax causes the equilibrium rate of unemployment to rise and the quantity of emissions to fall. The reason for this result is that the rising labor market tightness in X increases the rate of transition into employment and reduces the pool of job seekers in industry X, while the decreasing tightness in C has just the opposite effects on the industry-specific transition and unemployment rates. Since the labor market tightness at X is strictly higher and the average duration of unemployment strictly lower than in industry C (see Lemma 4*), the reallocation of the labor force induced by an increasing emission tax raises the aggregate rate of unemployment. Complementarity: The second tax rate interval ½kl ; k Þ is bounded from above by the cleaning price k which clears the market for pollution control. A tax rate t 2 ½kl ; k Þ has the effect of a price ceiling. In particular a cleaning price k4t cannot be sustained because paying the tax is the least-cost strategy. On the other hand, at kot producers prefer to control their emissions and, due to kotok , an excess demand for abatement services develops. The abatement price begins to rise until k ¼ t. Hence, in the equilibrium of the Pigouvian economy, producers are indifferent between paying taxes and controlling emissions, and we assume that they choose the environmentally sound strategy. If assumption (CX) holds, the employment and the environmental policy goal of emission reduction are complementary at tax rates t 2 ½kl ; k Þ: Proposition 2*. At tax rates t 2 ½kl ; k Þ the abatement sector offers vacancies to job seekers and pollution control services to producers. As t increases, the cleaning capacity of the abatement sector grows and workers move from the industries C and X into the abatement sector. The unemployment rates decrease in C and X and increase in A. Since the average duration of unemployment in the abatement sector is strictly shorter than in the production sector, this reallocation of the labor force causes the equilibrium rate of unemployment to decrease.

ARTICLE IN PRESS 146

T. Wagner / Journal of Environmental Economics and Management 49 (2005) 132–156

5. The emission standard In the Pigouvian economy, the government regulates the flow of pollutants through a tax on emissions; in the command-and-control economy the regulator intervenes directly in the decisions of the firms through binding performance standards [3]. The emission standard E is defined in units of the pollutant and indicates the permitted quantity of emissions per job and time unit. Clean jobs for which PC  Ep0 have a free but non-tradable right to pollute. Dirty jobs with PX  E40 are obliged to control PX  E40 of the discharge volume PX and therefore demand abatement services. Thus, only the X-firms enter the market for pollution control, each occupied job demanding PX  E units of the service. At the cleaning price k, each firm in industry X faces the abatement costs kðPX  EÞ. Therefore, the current match rent is pX ðk; EÞ ¼ yX  kðPX  EÞ þ c  b for a filled job in industry X, while, for a job with advanced technology, the rent is as in the unfettered market economy pC ¼ yC þ c  b. From the assumption (CX) it follows that pC 4pX ðk; EÞ if k40. In the equilibrium of the regulated sector, the income Eq. (6) and the mobility condition (7) hold, and the excess supply (11) is zero. Consequently, the labor market tightness, the reservation wage, and the regulated sector’s demand for abatement services are functions of the cleaning price k, the labor force located in the production sector l P , and the emission standard E. In view of yX ¼ yX ðk; l P ; EÞ we write the aggregate demand for pollution control as DX ðk; l P ; EÞ ¼ eX ðyX ðk; l P ; EÞÞðPX  EÞ;

ð21Þ

where eX ðyX ðk; l P ; EÞÞ is the measure of filled jobs in industry X. Given the cleaning price k and the labor force l P , the following lemma holds: Lemma 5. If the regulator tightens the emission standard, workers move from the dirty industry into the clean industry, the tightness in the labor market of industry X (C) increases (decreases), and the production sector’s reservation wage, Y ðk; l P ; EÞ, declines, while the reaction of the demand for pollution control, DX ðk; l P ; EÞ, is ambiguous. Changes in the standard E cause two opposing reactions of the demand for abatement services. If the regulator cuts down the permitted quantity of emissions, demand increases, since filled jobs in the dirty industry must undertake additional efforts to control their emissions; on the other hand, a stricter standard reduces the match rent of the X-jobs and induces job seekers to move to industry C so that the tightness in the labor market of industry X grows. The rate of job seekers arriving at a vacancy in X declines, jobs are destroyed and the actively used part of the production capacity in X shrinks. How far can the regulator tighten the standard without threatening the competitiveness of industry X? The shutdown cleaning price k X for industry X is implicitly defined by the equation rV X ðk X ; l P ; EÞ ¼ 0. k X is an increasing function of the labor force l P and the standard E, k X ðl P ; EÞ.24

24

See Lemma A.8.

ARTICLE IN PRESS T. Wagner / Journal of Environmental Economics and Management 49 (2005) 132–156

147

An overall equilibrium in the three labor markets of the command-and-control economy and in the market for abatement services is a state ðk ; l P ; l A Þ which satisfies the conditions: Sðk; l A Þ ¼ DX ðk; l P ; EÞ;

ð22Þ

rU A ðkÞ ¼ Y ðk; l P ; EÞ;

ð23Þ

l ¼ lP þ lA:

ð24Þ

Whether an equilibrium with an active abatement sector exists depends on the viability of the dirty industry. From the mobility condition (23) and the allocation rule (24) it follows that l P and l A are functions of the cleaning price k and the standard E, where l P ½l A decreases [increases] when the performance standard is tightened.25 As in Lemma A.6* it can be shown that for industry X there exists a shutdown cleaning price, K X ðEÞ, beyond which the industry is no longer competitive. The shutdown cleaning price is an increasing function of the standard E. Therefore, in the command-and-control economy, an equilibrium with an active abatement sector exists only if the excess supply of the abatement sector is positive at the cleaning price K X ðEÞ. Intuitively, one would expect the equilibrium cleaning price to increase if the regulator tightens the standard. Since the excess supply of the market for pollution control, ESðk; EÞ, is an increasing function of k, the conjecture follows from the implicit function theorem if, and only if, ESðk; EÞ is increasing in E. But, in general, the excess supply does not adjust unambiguously to changes in the performance standard. However, if S , the (negative of the) elasticity of the supply of abatement services with respect to the standard, exceeds the corresponding elasticity of the demand, D , ESðk; EÞ is, at least locally, an increasing function of E. The determinants of the difference between these elasticities are spelled out in Lemma 6. The excess supply in the market for pollution control is an increasing function of the standard E if the supply and demand elasticities of the standard satisfy S  D 40, where S  D ¼

E=PX  aX qX  kA : 1  E=PX

ð25Þ

The difference between the elasticities (25) depends on the fraction of free emissions, E=PX o1, on the fraction of the vacant capacity in the dirty industry, aX ¼ vX =kX o1, on the elasticity of the job seekers’ rate of arrival at a vacancy in industry X with respect to E, qX 40, and on the elasticity of the abatement sector’s capacity with respect to E, kA 40. Other things being equal, the difference (25) is higher, the higher the fraction of free emissions and the lower the fraction of vacant capacity in X. If assumption (CX) holds, the policy goals of a low equilibrium rate of unemployment and a high equilibrium quality of the environment are complementary even in a command-and-control economy regulated with an emission standard. Proposition 3*. If the clearing price of the market for pollution control in the command-and-control economy increases when the regulator tightens the standard E, then the quantity of emissions is an 25

See Lemma A.9.

ARTICLE IN PRESS T. Wagner / Journal of Environmental Economics and Management 49 (2005) 132–156

148

increasing function of E. Moreover, the environmental and the employment goals are complementary, and the tightening of the standard leads to a reduction in the equilibrium rate of unemployment and an increase in the equilibrium quality of the environment.

6. Efficiency The equilibria of the unfettered and the regulated market economies that we analyzed in the preceding sections suffer from search and environmental externalities. In this section, we focus on the optimal control problem and the implementation of the first-best allocation. 6.1. Social welfare function The planner optimizes subject to the same matching technology and the same technologies of the production and the abatement jobs as firms and workers. Per unit time, ðki  yi ui Þ occupied jobs in industry i produce the aggregate output ðki  yi ui Þyi and the quantity of emissions ðki  yi ui ÞPi . The abatement sector removes ðkA  yA uA Þa units of the pollutant. The number of jobs ki , i ¼ C; X, is exogenous, whereas the capacity of the abatement sector, kA , and the tightness yi , i ¼ A; C; X, of the three labor markets are controlled by the planner. P Each job seeker derives utility of leisure b and thus the aggregate flow of utility per unit time is ui b. Each vacancy P costs society c. Hence, in view of the yi ui vacancies at location i, the aggregate hiring costs are yi ui c. An amount NE of net emissions causes a per capita damage of ZðNEÞ. The damage function is continuously differentiable, convex, and monotonically increasing, Z 0 40 and Z 00 X0, and we have ZðNEÞ ¼ 0 for NEp0. The perfectly informed planner has an infinite time horizon and uses the control variables ðy; kA Þ, with y ¼ ðyA ; yC ; yX Þ, to maximize the social welfare function # Z 1" X X X O¼ ðki  yi ui Þyi þ ui b  yi ui c  lZðNEÞ ert dt ð26Þ 0

i¼C;X

i¼A;C;X

i¼A;C;X

subject to the following four constraints. First, the net emissions satisfy X ðki  yi ui ÞPi  ðkA  yA uA Þa: NE ¼

ð27Þ

i¼C;X

Second, the planner is constrained by the transition equations of the state variables u_ i ¼ lðki  yi ui Þ  pðyi Þui ;

i ¼ A; C; X;

where u_ i ¼ dui =dt. Third, the planner observes the resource constraint X ½ki  ðyi  1Þui ; l¼

ð28Þ

ð29Þ

i¼A;C;X

where l i ¼ ki  ðyi  1Þui is the labor force at location i, i ¼ A; C; X. Finally, the planner must take into account the capacity restrictions yi ui pki , i ¼ A; C; X. Solution: We consider solutions of the optimal control problem with the following two characteristics: first, at each location there exists a positive number of occupied jobs, such that

ARTICLE IN PRESS T. Wagner / Journal of Environmental Economics and Management 49 (2005) 132–156

149

yi ui oki , and, second, the planner utilizes the entire capacities ki , i ¼ A; C; X.26 Since the planner is not only restricted by the transition Eq. (28) but must also take account of the resource constraint (29), we need to solve an optimal control problem (26)–(29) of the Bolza-Hestenes type [38] with the Lagrangian function in present value terms " # X X X ðki  yi ui Þyi þ ui b  yi ui c  lZðNEÞ ert Lðu; y; kA ; m; rÞ ¼ i¼C;X

þ

X

i¼A;C;X

i¼A;C;X

"

mi ½lðki  yi ui Þ  pðyi Þui þ r l 

i¼A;C;X

X

# ½ki  ðyi  1Þui

ð30Þ

i¼A;C;X

where u ¼ ðuA ; uC ; uX Þ and m ¼ ðmA ; mC ; mX Þ. The co-state variable mi indicates the marginal social costs of an additional job seeker at location i ¼ A; C; X. The Lagrange multiplier r associated with constraint (29) is the shadow price of the labor force l. In the following, the shadow prices are denoted in current value terms, with r~ ¼ ert r and m~ i ¼ ert mi . The FOCs of the optimal control problem are given in Appendix A. From the FOCs we get Lemma 7. (1) The planner chooses the labor market tightness at the three locations such that the location-specific marginal social revenue from filling an additional vacancy at location i equals the shadow price of labor: r~ ¼ b þ pi ðlZ 0 Þ þ m~ i fl þ qðyi Þ½1  Zðyi Þ g; 0

i ¼ A; C; X;

0

0

ð31Þ 0

where pi ðlZ Þ ¼ yi  lZ Pi þ c  b, i ¼ C; X, and pA ðlZ Þ ¼ lZ a þ c  b are the current social match rents and lZ 0 with labor force l is the marginal social damage of the pollutant. (2) The capacity of the abatement sector satisfies the job creation condition: r~ ¼ lZ 0 a þ m~ A l

ð32Þ

(3) The social revenue of the marginal job seeker at location i equals his location-specific marginal social costs, so that b  m~ i ½r þ pðyi Þ ¼ ð1  yi Þr~ þ yi ½pi ðlZ 0 Þ þ b þ m~ i l ;

i ¼ A; C; X:

ð33Þ

Interpretation: The RHS of Eq. (31) denotes the marginal social revenue of filling an additional vacancy at location i given the location’s capacity ki , i ¼ A; C; X. pi ðlZ 0 Þ is the current social match rent of the occupied job, while the term m~ i fl þ qðyi Þ½1  Zðyi Þ g represents the expected social costs of job destruction and creation. m~ i , with m~ i o0, are the social costs of an additional job seeker at location i, l is the rate with which occupied jobs are destroyed, and p0 ðyi Þ ¼ qðyi Þ½1  Zðyi Þ is the search externality caused by posting or filling an additional vacancy. Thus, m~ i lo0 are the expected social costs of job destruction, while m~ i qðyi Þ½1  Zðyi Þ o0 are the social costs of filling an additional vacancy at location i. Zðyi Þ is the elasticity of the hirings at location i, mðui ; vi Þ, with respect to the number of job seekers, ui . By the homogeneity of mðui ; vi Þ, Zðyi Þ is a function of the labor market tightness only, and—because of Euler’s Theorem—we have Zðyi Þ 2 ð0; 1Þ. 26

In view of ki ¼ ei þ vi þ I i , where I i is the idle capacity in i, the planner utilizes the entire capacity ki , if I i ¼ 0.

ARTICLE IN PRESS 150

T. Wagner / Journal of Environmental Economics and Management 49 (2005) 132–156

The job creation condition (32) says that, for the first-best capacity of the abatement sector, the social revenue of the marginal occupied cleaning job equals the shadow price of labor. The social revenue of an additional occupied cleaning job, given the number of cleaning vacancies, is the difference between the environmental damage avoided through the pollution control services of that job, lZ 0 a, and the expected social costs of job destruction, m~ A lo0. The social revenue of an additional job seeker at location i consists of his utility of leisure, b, and the avoided social costs of unemployment, m~ i ½r þ pðyi Þ 40, which together form the LHS of Eq. (33). The cost savings occur, first, because an additional worker added to the pool of unemployed at the given tightness yi , will increase the number of job seekers who move from unemployment into employment by pðyi Þ and, second, because the interest lost on the human capital tied up in the pool of unemployed decreases by the amount r of the discount rate. On the other hand, the labor force located at i increases with the new job seeker by ð1  yi Þ. To keep the labor market tightness constant, the planner must increase the number of vacancies by yi , which, at a given capacity, necessitates the destruction of yi occupied jobs. The increase in the labor force ~ and the destruction of yi occupied jobs brings about additional causes social costs of ð1  yi Þr, costs of yi ½pi ðlZ 0 Þ þ b þ m~ i l . ^ k^A Þ, where y^ ¼ We denote the steady-state solution of the optimal control problem by ðy; ðy^ A ; y^ C ; y^ X Þ is the vector of the efficient labor market tightness in the abatement sector and the polluting industries, respectively, while k^A is the first-best measure of vacant and producing abatement jobs. Given the assumption (CX) we obtain from the FOCs of the control problem: Corollary 1*. The current social match rent of an occupied job in the clean industry is strictly larger than in the dirty industry, pC ðlZ 0 Þ4pX ðlZ 0 Þ, while the socially efficient tightness of the labor market in the clean industry is strictly smaller than in the dirty industry, y^ X 4y^ C . Comparing Corollary 1* with Lemma 4*, the similarity between the first-best solution and the market solution is obvious. In both cases the tightness of the labor market in the dirty industry is strictly larger than in the clean industry. But, as Lemma 4* shows, in addition, in the economy regulated with the emission tax, the tightness of the labor market in the abatement sector is greater than the tightness in the producing industries. Whether the inequality y^ A Xy^ i also holds for the first-best allocation, however, depends on the parameters of the model. Assume that the marginal environmental damage is a constant such that Z 00 ðNEÞ ¼ 0. Then the comparative static analysis of the first-best allocation provides the following results. Lemma 8. (1) An incremental change in the productivity of an abatement job, a, has the following impact on the first-best allocation: d y^ i =da40, i ¼ A; C; X, and d k^A =da40. (2) A small change in the productivity of a polluting job at the industry i, yi , has the following effects: d y^ i =dyi o0, d k^A =dyi o0, i ¼ C; X, and d y^ j =dyi ¼ 0, where j ¼ A; C; X and jai. (3) A marginal change in the quantity of pollution per occupied job at industry i, Pi , implies: d y^ i =dPi 40, d k^A =dPi 40, i ¼ C; X, and d y^ j =dPi ¼ 0, where j ¼ A; C; X and jai. Hence, an increase in the productivity of the jobs in industry i, yi , or a decrease in the quantity of pollution, Pi , will reduce the industry-specific tightness y^ i , without effecting the first-best tightness of the other two labor markets. Therefore, whether or not y^ A Xy^ i depends in particular on the industry-specific parameters ðyi ; Pi Þ, i ¼ C; X.

ARTICLE IN PRESS T. Wagner / Journal of Environmental Economics and Management 49 (2005) 132–156

151

6.2. Implementation We assume that the policy maker regulates the flow of emissions and the job creation and destruction process with the policy instruments ðt; j; sÞ, where t is a tax on emissions, j ¼ ðjC ; jX Þ is a vector of employment subsidies (taxes), and s ¼ ðsC ; sX Þ is a vector of recruiting cost allowances. A recruiting allowance is a flow si paid to the vacancies in industry i during the time of search and recruiting job applicants. The employment subsidy is a flow ji paid to the occupied jobs in industry i, i ¼ C; X. In the equilibrium of the abatement sector all profit opportunities from creating new jobs are exhausted, so that V A ¼ 0. The private job creation condition of the abatement sector (15) follows from the income Eq. (14) and V A ¼ 0. The job creation condition (15) in turn implicitly defines the equilibrium price for the abatement service as a strictly increasing function of the equilibrium tightness of the labor market for abatement workers, tðyA Þ. Given that the equilibrium price for the abatement service, k, satisfies k ¼ t^ , the first-best tightness y^ A can be implemented by levying a tax on emissions t^ at rate: b 1  dðy^ A Þ c : t^ ¼ tðy^ A Þ  þ a ðþÞ dðy^ A Þ a

ð34Þ

Next, we prove that the equilibrium price for the abatement service indeed satisfies k ¼ t^ . Suppose that ko^t were true. Then the equilibrium tightness of the labor market for abatement workers would be too small, yA oy^ A , and the net emissions of the economy would be ^ But by virtue of the properties of the damage function the first-best too high, NE4N E. ^ ^ net emission of the pollutant is non-negative, NEX0. Given that NE4N EX0 and ko^t the polluting jobs could increase their profits through additional abatement efforts and hence an excess demand would develop in the market for the abatement service—a contradiction which proves that k ¼ t^ . In equilibrium, the job seekers who move to the abatement sector earn an income equal to rU A ðy^ A Þ, which is determined by the income Eq. (16). In the overall equilibrium of the regulated economy, the mobility rent is zero, so that rU A ðyA Þ ¼ Y , where Y is the reservation wage of the production sector. Thus, in equilibrium, the job seekers in the production sector earn a wage income Y^ , which satisfies Y^ ¼ rU A ðy^ A Þ. In the market economy firm and worker bargain over the distribution of the match rent inclusive of the employment subsidy, pi ðtÞ þ ji , i ¼ C; X. Consequently for the economy regulated by the instruments ðt; j; sÞ we must modify the income Eqs. (6) and (8) of the job seekers and the vacancies of the production sector, respectively, as follows: rU i ðt; yi ; ji Þ ¼ b þ gðyi Þ½pi ðtÞ þ ji ; rV i ðt; yi ; ji ; si Þ ¼ c þ dðyi Þ½pi ðtÞ þ ji þ si ;

ð35Þ i ¼ C; X:

ð36Þ

Given the reservation wage Y, the tightness of the labor market in the industry i, yi , and the cleaning price t, the mobility condition for industry i follows from (35) with: ^ i necessary to Y ¼ b þ gðyi Þ½pi ðtÞ þ ji , i ¼ C; X. Solving for ji we get the employment subsidy j

ARTICLE IN PRESS T. Wagner / Journal of Environmental Economics and Management 49 (2005) 132–156

152

implement the first-best labor market tightness of industry i: Y^  rU i ð^t; y^ i ; 0Þ ^ i ¼ ji ð Y^ ; t^ ; y^ i Þ  j ; ðþÞ ðþÞ ðÞ gðy^ i Þ

i ¼ C; X:

ð37Þ

^ is not sufficient to implement the first-best solution as a In general, the policy scheme ð^t; jÞ ^ the income of a vacancy in the production sector market equilibrium. The reason is that with ð^t; jÞ might turn out to be negative, so that no vacancy is supplied. To guarantee the participation of the vacancies, the planner employs the recruiting allowances. The recruiting allowance that induces a positive supply of vacancies in industry i follows from (36) by virtue of the fact that rV i ðt; yi ; ji ; si Þ ¼ 0 is necessary and sufficient to stimulate the profit maximizing firms to supply vacancies at i. Assume that rV i ðt; yi ; ji ; 0Þo0. Then the minimal allowance that ensures the vacancies’ participation is si ð t ; yi ; ji Þ ¼ rV i ðt; yi ; ji ; 0Þ:

ð38Þ

ðþÞ ðþÞ ðÞ

To implement the first-best solution as a market equilibrium the policy maker must subsidize the vacancies of industry i with a recruiting allowance s^ i X0, for which ^ i Þg; s^ i ¼ maxf0; si ð^t; y^ i ; j

i ¼ C; X:

ð39Þ

^ sÞ, ^ that satisfies the implementation conditions (34), (37) and (39), The policy vector ð^t; j; ensures that the private equilibrium is efficient and, moreover, that the participation conditions of the jobseekers and vacancies are fulfilled. 6.3. Evaluation First, we show that the optimal emission tax is an increasing function of the workers’ bargaining strength. Next, we discuss conditions, that ensure that the policy maker needs no recruiting allowances to induce the first-best allocation. Finally, we demonstrate that the emission tax can generate a double dividend exactly under these conditions. From the FOCs of the optimal control problem we find that the first-best allocation fulfills the job creation condition ^ y^ A Þ ¼ 0; pA ðlZ 0 Þ  c=dð

ð40Þ

where ^ A Þ and dðy ^ A Þ ¼ r þ l þ ZðyA ÞpðyA Þ þ ½1  ZðyA Þ qðyA Þ: ^ A Þ ¼ ½1  ZðyA Þ qðyA Þ=dðy dðy Comparing the private job creation condition (15) with the social job creation condition (40) we obtain: Corollary 2. The optimal emission tax, t^ , that the government imposes to induce the first-best pollution, is a strictly increasing function of the workers’ bargaining strength b. In particular, t^  lZ 0 o iff b  Zðy^ A Þ. o

Whether the government should levy the Pigouvian tax on emissions to stimulate the first-best solution, that is whether t^ ¼ lZ0 , depends on the workers’ bargaining strength, as shown by

ARTICLE IN PRESS T. Wagner / Journal of Environmental Economics and Management 49 (2005) 132–156

153

Corollary 2. The threshold value for the bargaining strength is the first-best elasticity of the number of hirings in the abatement sector with respect to the sector’s unemployment. In particular, for labor markets where, as a consequence, for example, of the prevailing labor law, workers have a strong bargaining position, the optimal pollution tax may easily exceed the Pigouvian tax. Next, we state two corollaries with results concerning the recruiting allowances for the polluting industries. Corollary 3*. Given the assumption (CX), the optimal recruiting allowance for the dirty industry is at least as large as the allowance for the clean industry, s^ X Xs^ C X0. Whether the policy maker must employ all five instruments to reap the efficiency gains of a transition to the first best depends on the structure of the efficient allocation. In particular, the recruiting allowances are not always necessary to steer the economy into the first-best. Corollary 4. The optimal allowance for the vacancies at industry i is equal to zero, s^ i ¼ 0, if and only ^ i , i ¼ C; X. if y^ A Xy^ i , or equivalently, if and only if pA ð^tÞppi ð^tÞ þ j Therefore, whether or not s^ i ¼ 0 depends in particular on the industry-specific parameters ðyi ; Pi Þ, i ¼ C; X, as Corollary 4 and Lemma 8 show. Consider the market economy from Section 4 and assume that it is regulated with an emission tax t 2 ½kl ; k Þ. Recall that k is the cleaning price that clears the market for abatement services ½NEðk Þ ¼ 0 , and that kl is the price at which the mobility condition (19) is fulfilled for a given labor force of size l being located in the economy’s production sector. From Proposition 2 we know that an increase in the tax rate t 2 ½kl ; k Þ raises the environmental quality and reduces the equilibrium unemployment. In an economy regulated by the policy instruments ðt; jÞ the boundaries of the above tax interval, ½kl ðjÞ; k ðjÞÞ, are—strictly increasing—functions of the employment subsidies j. ^ sÞ, ^ with s^ X ¼ 0. Moreover, suppose that the assumption Consider now an optimal policy ð^t; j; ^ suffice to (CX) holds. Then, in view of Corollary 3*, s^ C ¼ 0. Hence, the instruments ð^t; jÞ implement the first-best solution and in addition, we can apply Lemma 4* and Proposition 2 to ^ k ðjÞÞ. ^ Given that the first-best net the economy regulated with the emission tax t 2 ½kl ðjÞ; ^ ^ k ðjÞÞ, ^ and we emission of the pollutant is strictly greater than zero, NE40, we have t^ 2 ðkl ðjÞ; can state without proof: ^ t^ Þ raises social welfare, Corollary 5*. (1) An incremental increase in the emission tax t 2 ½kl ðjÞ; enhances the quality of the environment and reduces the aggregate unemployment; hence the society reaps a double dividend. ^ reduces social welfare, (2) In contrast, a marginal increase in the emission tax t 2 ð^t; kn ðjÞÞ despite the fact that the environmental quality improves and the equilibrium unemployment declines.

7. Conclusions The paper integrates instruments of environmental policy into the theory of equilibrium unemployment. The labor markets are characterized by two-sided search. Spatial and other heterogeneities, informational imperfections and market institutions are implicitly contained in

ARTICLE IN PRESS 154

T. Wagner / Journal of Environmental Economics and Management 49 (2005) 132–156

the matching technology of the labor markets. Two production technologies are available. For each of these there is an exogenous number of jobs which are either filled or advertised as vacancies in the job market. Each job is associated with a capital good, the design of which determines the emitted quantity of a pollutant produced as a by-product and in fixed proportions of the output. Clean jobs use an advanced technology and hence enjoy a higher productivity than jobs in the dirty industry. The environmental damage is a public bad that reduces the welfare of job owners and job seekers alike. Under certain conditions, an abatement sector develops which offers vacancies to job seekers and supplies pollution control services to the polluting industries. The analysis yields the following results. First, in an economy where a regulator imposes a tax on the emission of pollutants, we can distinguish two intervals of the tax rate differing in their employment effects: in the first interval the tax is so low that an abatement sector is not viable. In view of the sector’s low wage income, job seekers have no incentive to leave the polluting industries and move to the abatement sector. Society is faced with the well-known trade-off between employment and environmental quality. In the second interval, an abatement industry develops which provides vacancies for the job seekers and cleaning services for the polluting industries. With an increasing emission tax, gross and net emissions decline and so too does the equilibrium rate of unemployment. Aggregate employment and environmental quality are complementary policy goals. Second, if the market price for pollution control services increases with the strictness of the emission standard, then the effects of a command-and-control approach are very similar to those we observe in a Pigouvian economy: reducing the equilibrium rate of unemployment and increasing the equilibrium quality of the environment are complementary policy goals. Third, in general, five policy instruments are necessary for the government to internalize the environmental and search externalities and to induce the participation of job seekers and vacancies. In our model, in addition to the pollution tax, for the production sector the policy maker uses employment subsidies for the occupied jobs and recruiting allowances for the vacancies. The optimal emission tax is a strictly increasing function of the workers’ bargaining strength and may easily exceed the Pigouvian tax rate. The normative analysis reveals that, with respect to the tax interval where the policy goals of a clean environment and a low unemployment are complementary, we can distinguish two different segments. In the lower segment an increase in the emission tax produces efficiency gains, environmental quality increases and equilibrium unemployment declines. However, in the upper segment of the tax interval an incremental tax increase causes efficiency losses, although the quality of the environment increases and the number of unemployed workers declines. For future research, it seems worthwhile to analyze the effects of environmental policy within a search model with endogenous job destruction and wage posting. Other important research topics are the implementation of second-best environmental policy instruments and the analysis of the impacts of tax recycling.

Acknowledgments Especially I want to thank Ru¨diger Pethig for his tremendous help. Furthermore, I am grateful to the editors and two anonymous referees, to Ge´rard Gaudet and Christopher Pissarides, to the

ARTICLE IN PRESS T. Wagner / Journal of Environmental Economics and Management 49 (2005) 132–156

155

participants at the EARE 2000 conference, Crete, the EEA 2000 Conference, Bolzano and the EALE/SOLE 2000 conference, Milan. Finally, I thank Elke J. Jahn and Peter Mottershead for their helpful comments.

References [1] A.J. Barbera, V.D. McConnell, The impact of environmental regulations on industry productivity—direct and indirect effects, J. Environ. Econ. Manage. 18 (1990) 50–65. [2] A.P. Bartel, L.G. Thomas, Predation through regulation: the wage and profit effects of the occupational safety and health administration and the environmental protection agency, J. Law Econ. 30 (1987) 239–264. [3] W.J. Baumol, W.E. Oates, The Theory of Environmental Policy, Cambridge University Press, Cambridge, UK, 1992. [4] E. Berman, L.T. Bui, Environmental regulation and labor demand: evidence from the South Coast Air Basin, J. Pub. Econ. 79 (2001) 265–295. [5] R.H. Bezdek, Environment and economy. What’s the Bottom Line?, Enviroment 35 (7–11) (1993) 25–32. [6] O.J. Blanchard, P.A. Diamond, The Beveridge Curve, Brooking Pap. Econ. Act. 1 (1989) 1–60. [7] O.J. Blanchard, P.A. Diamond, The Flow Approach to Labor Markets, Amer. Econ. Rev. 82 (1992) 354–359. [8] P. Bohm, C.S. Russell, Comparative analysis of alternative policy instruments, in: A.V. Kneese, J.L. Sweeney (Eds.), Handbook of Natural Resource and Energy Economics, Vol. I, Elsevier Science, Amsterdam, 1985. [9] A.L. Bovenberg, F.v.d. Ploeg, Optimal taxation, public goods and environmental policy with involuntary unemployment, J. Pub. Econ. 62 (1996) 59–83. [10] A.L. Bovenberg, F.v.d. Ploeg, Tax reform, structural unemployment and the environment, Scand. J. Econ. 100 (1998) 593–610. [11] G.R. Butters, Equilibrium distributions of sales and advertising prices, Rev. Econ. Stud. 44 (1977) 465–491. [12] P.A. Diamond, Wage determination and efficiency in search equilibrium, Rev. Econ. Stud. 49 (1982) 217–227. [13] M. Friedman, The role of monetary policy, Amer. Econ. Rev. 58 (1968) 1–17. [14] L.H. Goulder, Environmental taxation and the double dividend: a reader’s guide, Int. Tax Pub. Fin. 2 (1995) 157–183. [15] L.H. Goulder, I.W.H. Parry, D. Burtraw, Revenue-raising vs. other approaches to environmental protection: the critical significance of pre-existing tax distortions, Rand. J. Econ. 28 (1997) 703–708. [16] W.B. Gray, R.J. Shadbegian, Environmental regulation and manufacturing productivity at the plant level, NBER Working Papers No. 4321, 1993. [17] A.J. Hosios, On the efficiency of matching and related models of search and unemployment, Rev. Econ. Stud 57 (1990) 279–298. [18] A.J. Hosios, Factor market search and the structure of simple general equilibrium models, J. Polit. Econ. 98 (1990) 325–354. [19] A.B. Jaffe, S.R. Peterson, P.R. Portney, R.N. Stavins, Environmental regulation and the competitiveness of US manufacturing: what does the evidence tell us?, J. Econ. Lit. 33 (1995) 132–163. [20] C.D. Kolstad, Environmental Economics, Oxford University Press, New York, 2000. [21] S. K. Majumdar, A. A. Marcus, Do Environmental regulations retard productivity? Evidence from US electric utilities, Working Paper, University of Michigan, 1998. [22] E.R. Moen, Competitive search equilibrium, J. Polit. Econ. 105 (1997) 385–411. [23] R.D. Mohr, Technical change, external economics, and the porter hypothesis, J. Environ. Econ. Manage. 43 (2002) 158–168. [24] D.T. Mortensen, Property rights and efficiency in mating, racing, and related games, Amer. Econ. Rev. 72 (1982) 968–979. [25] D.T. Mortensen, C.A. Pissarides, Technological progress, job creation and job destruction, CEPR, London, 1995. [26] D.T. Mortensen, C.A. Pissarides, New developments in models of search in the labor market, in: O. Ashenfelter, D. Card (Eds.), Handbook of Labor Economics, Vol. IIIB, Elsevier Science, Amsterdam, 1999.

ARTICLE IN PRESS 156

T. Wagner / Journal of Environmental Economics and Management 49 (2005) 132–156

[27] OECD, Environmental Policies and Employment, OECD, Paris, 1997. [28] I.W.H. Parry, A.M. Bento, Tax deductions, environmental policy, and the ‘‘Double Dividend’’ hypothesis, J. Environ. Econ. Manage. 39 (2000) 67–96. [29] C.A. Pissarides, Efficient job rejection, Econ. J. 94 (1984) 97–108. [30] C.A. Pissarides, Equilibrium Unemployment Theory, MIT Press, Cambridge, 2000. [31] M.E. Porter, America’s green strategy, Sci. Am. 264 (1991) 168. [32] M.E. Porter, C.v.d. Linde, Towards a new conception of the environment-competitiveness relationship, J. Econ. Perspect. 9 (1995) 97–118. [33] R. Rogerson, Theory ahead of language in the economics of unemployment, J. Econ. Perspect. 11 (1997) 73–92. [34] R. Rogerson, R. Wright, Search-theoretic models of the labor market: a survey, PIER Working Paper 02-041, 2002. [35] M. Rothschild, Models of market organization with imperfect information: a survey, J. Polit. Econ. 81 (1973) 1283–1308. [36] G.J. Stigler, The economics of information, J. Polit. Econ. 69 (1961) 213–225. [37] N.L. Stokey, R.E. Lucas Jr., Recursive Methods in Economic Dynamics, Harvard University Press, Cambridge, 1989. [38] A. Takayama, Mathematical Economics, Cambridge University Press, Cambridge, 1985. [39] A. Xepapadeas, A. de Zeeuw, Environmental policy and competitiveness: the Porter hypothesis and the composition of capital, J. Environ. Econ. Manage. 37 (1999) 165–182.