Socially responsible investment in an environmental overlapping generations model

Socially responsible investment in an environmental overlapping generations model

Resource and Energy Economics 33 (2011) 1015–1027 Contents lists available at ScienceDirect Resource and Energy Economics journal homepage: www.else...

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Resource and Energy Economics 33 (2011) 1015–1027

Contents lists available at ScienceDirect

Resource and Energy Economics journal homepage:

Socially responsible investment in an environmental overlapping generations model Lammertjan Dam * University of Groningen, Department of Economics, P.O. Box 800, 9700 AV Groningen, The Netherlands



Article history: Received 24 August 2007 Received in revised form 20 May 2009 Accepted 20 August 2010 Available online 30 August 2010

One of the problems associated with the conservation of the environment is that short-lived individuals fail to account for the long-term effects of pollution, which implies that future generations bear the costs imposed by the current generation. Such intergenerational externalities are usually tackled by (Pigovian) taxes, fiscal policy or environmental regulation. Alternatively, we propose that socially responsible investment funds create a role for the stock market to deal with intergenerational environmental externalities. We analyze the role of the stock market in an environmental overlapping generations model of the Diamond-type, in which agents choose between investing in ‘‘clean’’ government bonds or ‘‘polluting’’ firm equity. We show that although socially responsible investors are short-lived, the forward-looking nature of stock prices can help to resolve the conflict between current and future generations. ß 2010 Elsevier B.V. All rights reserved.

JEL classification: D11 D21 D62 Q01 Q20 Keywords: Overlapping generations Environmental quality Socially responsible investment Corporate social responsibility Sustainability Stock market

1. Introduction The externality associated with the conservation of the environment exhibits two dimensions. First, there is an intra-generational dimension. The environment is a public good and as such its conservation suffers from the standard free rider problem. Second, there is an inter-generational dimension. Since pollution usually accumulates, future generations bear the costs of the actions of the

* Tel.: +31 050 363 6518; fax: +31 050 363 7337. E-mail address: [email protected] 0928-7655/$ – see front matter ß 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.reseneeco.2010.08.002


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current generation. Various studies have proposed tax and/or fiscal policy measures to manage this long-term threat of pollution to the environment in order to achieve sustainable development (see e.g. John and Pecchenino, 1994; Bovenberg and Heijdra, 1998). This paper proposes an alternative mechanism to deal with the inter-generational aspect of the pollution externality, namely by making an appeal on the forward looking nature of asset prices in stock-markets. In particular, socially responsible investment, or ‘‘green screening’’, allows the stock market to function as a tool in dealing with environmental externalities. Typically, short-lived agents do not internalize the long-term effects of pollution. However, in the presence of a forward looking stock market, we show that proper valuation induced by socially responsible investment can help to resolve the coordination failure between current and future generations. Socially responsible investment is a portfolio management ‘‘style’’ that does not only rely on financial returns. In fact, the main focus of socially responsible investment is on non-financial characteristics of the companies associated with the shares in the portfolio. The notion nowadays is that many investors do not only care about cash flows, but also about how these cash flows are generated. An investor might, for example, oppose to investing in firms that adopt heavily polluting technologies or use child labor. The historical development of socially responsible investment is partly rooted in investment behavior of churches and charities, which have personal objections to investing their money in certain types of companies. One empirical finding in this context that illustrates a drop in demand for certain types of equity is the positive abnormal return that has been observed on socalled ‘‘sin stocks’’ (Hong and Kacperczyk, 2009) which comprise of, among a few other categories, shares of tobacco, gambling, pornography, and alcohol companies. Moreover, Fama and French (2007) also recently acknowledged that there exists ‘‘taste for assets’’, as if the assets are consumption goods themselves. Socially responsible investment has increasingly witnessed attention and experienced large growth figures. There are numerous examples to illustrate this claim. For example, in 2005 about one out of every ten dollars under professional management in the United States was subject to some form of socially responsible screening, that is, about 10% of the mutual funds screened out certain stocks on non-financial grounds.1 Also, the popular magazine ‘‘Institutional Investor’’ of April 2008 reports that investor groups in the U.S. have filed 54 resolutions on climate change, up from 43 a year before. Many resolutions call on firms to disclose their greenhouse gas emissions. The most common form of socially responsible investment used in practice is straightforward screening, i.e. stocks of companies that ‘‘misbehave’’ – according to some threshold measure – are eliminated from the portfolio. Although simple screening is the most common form of socially responsible investment, more subtle forms of socially responsible investment exist. Rating agencies like KLD Research and Analytics, Inc., and Ethical Investment Research Services (EIRIS) provide scores on various aspects of social and environmental performance and policy.2 Investors balance these social and environmental scores with financial performance when constructing their portfolio. The particular focus on environmental issues in socially responsible investment is sometimes referred to as ‘‘green screening’’. Within the broad range of subjects that socially responsible investment deals with we focus on environmental socially responsible investment to study how the stock market can help in resolving inter-generational conflicts that arise due to accumulating pollution. To capture the conflict between generations, we study the environment in a Diamond type overlapping generations (OLG) model, in line with John and Pecchenino (1994). Agents live for two periods. They work when they are young, retire and derive utility from consumption and environmental quality when they are old. We adapt the model of John and Pecchenino (1994) such that, instead of choosing between consumption and environmental maintenance, agents choose between investing in ‘‘clean’’ government bonds and ‘‘dirty’’ corporate shares. The novelty of our 1

Social Investment Forum, 2005 Report on Socially Responsible Investing Trends in the United States. EIRIS, for example, provides a portfolio management tool, the Ethical Portfolio Manager, in which over a 150 questions are answered and used to give companies from all over the world individual scores. One example of such a question and its default scores is: ‘‘What level of improvements in environmental impact can the Company demonstrate? (Nodataorinadequatedata ¼ 1; Noim pro ¼ 0; Minorim pro ¼ 1; Signi ficantim pro ¼ 2; Ma jorim pro ¼ 3Þ’’. The investor can choose which questions to include to calculate companies’ total scores and can also manually alter the values of the default scores that are assigned to each answer. As such, users of the investment tool are actually defining their ‘‘utility function’’. KLD uses a similar scoring mechanism and provides yearly ratings for U.S. firms with data going back to 1990. 2

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model is that (some) investors prefer investing in clean assets, and thus require a higher return on ‘‘dirty’’ assets. The change from a consumption into an investment decision allows us to introduce and analyze the role of a stock market. Magill and Quinzii (2003) point out that when corporate ownership rights are traded separately from real capital on a stock market, externalities or frictions can push the value of equity away from the value of real capital goods. In our context of socially responsible investment, the value of firm equity may depend on both the level of capital goods and the level of environmental quality. The introduction of this ‘‘missing market’’ can potentially deal with the intergenerational externality of pollution in a natural way, as especially the stock market can be characterized by its forward-looking nature. Our paper relates to the literature that analyzes the threat to the environment in a Diamond-type OLG model (John and Pecchenino, 1994; John et al., 1995; Guruswamy Babu et al., 1997; Zhang, 1999; Seegmuller and Verche`re, 2004). This literature shows that a social optimum will arise if (1) market failures are corrected using Pigovian taxes or environmental regulations and (2) an optimal distribution of welfare is achieved using lump-sum transfers or the accumulation/repayment of public debt. The proposed tax programs are usually not straightforward, because they often require the use of various instruments. The reason is that even without environmental externalities the decentralized economy need not be Pareto-optimal.3 However, the fact that in the presence of market frictions the value of financial equity is not necessarily equal to the replacement value of physical capital (Magill and Quinzii, 2003) is a possibility that has not been explored in the literature mentioned above. Our paper is also related to the literature on socially responsible investment. There exists an abundance of empirical literature on socially responsible investment that is particularly interested in the relationship between corporate social and financial performance. Two widely cited survey articles on this literature are Margolis and Walsh (2001) and Orlitzky et al. (2003). There is, however, only a small theoretical literature on socially responsible investment. Heinkel et al. (2001) study a static model with ‘‘green screening’’ in the portfolio selection (see also Beltratti, 2005). Their model is mathematically similar to the asymmetric information model by Merton (1987), in which stocks are ‘‘screened’’ simply because they are not known to some investors. Preferences over green goods in the models mentioned above are extreme, there are simply two types of investors; a group who are indifferent about pollution, and a group who are only willing to buy ‘‘clean’’ shares. Both Baron (2008) and Zivin and Small (2005) present models in which preferences are explicitly defined and are ‘‘smooth’’. Zivin and Small (2005) justify these preferences by means of a ‘‘warm glow’’ effect (see Andreoni, 1990), defined as utility that is derived from the act of giving as distinct from the value one might derive from a public good. Baron – who has written an impressive series of articles with principal-agent type of models on corporate social responsibility – gives several justifications for the way socially responsible investment is modeled. What the theoretical literature on socially responsible investment has in common is that investors have a higher willingness to pay for (i.e. require a lower return on) ‘‘green shares’’, which may be due to altruistic or warm glow preferences. We adopt the warm glow approach to model socially responsible investment, as in Zivin and Small (2005). As such, this paper can also be related to the literature on ‘‘green consumerism’’ (see e.g., Bansal and Gangopadhyay, 2003; Cremer and Thisse, 1999). In fact, the literature on socially responsible investment tries to push this type of modeling in the direction of investment behavior. As far as we are aware of, the literature has mainly examined static (one-period) partial equilibrium models of socially responsible investment, whereas this paper analyzes socially responsible investment in a discrete time dynamic overlapping generation framework. In a companion paper, Dam and Heijdra (2008) analyze the effects of socially responsible investment and the interaction with public abatement by the government in a continuous time representative agent general equilibrium model. The introduction of dynamics raises some intriguing questions about investor behavior. In particular, it matters whether the warm glow preferences depend on the level of environmental quality or on the change of environmental quality (the pollution flow). Instead of choosing for one specification, we explore both possibilities. 3 This is the well known result of Diamond (1965) that agents can over- or under invest in physical capital compared to the Golden Rule solution.

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In Section 2 we present the core of the model. We introduce socially responsible investment and its consequences for corporate valuation and investments in real capital. In Section 3 we briefly discuss equilibrium and dynamics. We also calculate allocations for two benchmark scenarios: A socially planned economy and an economy for which the warm glow preference depends on pollution flows. We show that when introducing a stock market, proper valuation can partially resolve the coordination problem. We conclude in Section 4. 2. The model We introduce environmental quality in a standard Diamond (1965) overlapping generations (OLG) model. Environmental quality Et is modeled as a renewable resource and contemporaneous pollution Pt due to production decreases the ‘stock’ of environmental quality (see John and Pecchenino, 1994): Etþ1 ¼ ð1  bÞEt  Ptþ1 ;


with 0 < b < 1 representing the rate of natural recovery. Without pollution, environmental quality will return to its virgin value which is equal to zero. Note that Et takes only non-positive values; Et  0. Basically, environmental quality is the negative of a stock of pollution, so that we can treat the negative of an economic bad as a good. 2.1. Consumers At each date t a generation of finitely-lived consumers of fixed size L is born. Since there is no population growth we can normalize the number of consumers to one. Consumers live for two periods, but only have preferences defined at old age. This simplification is quite common in OLG models which include environmental quality (see Guruswamy Babu et al., 1997; John and Pecchenino, 1994). Since we focus on intergenerational conflicts due to investment choice (how are savings used), and not due to savings behavior (how much is saved), we can make this simplifying assumption without loss of generality. The representative consumer’s preferences at old age can be characterized by the following utility function: uðctþ1 ; g tþ1 ; Etþ1 Þ;


where ct+1 is consumption, gt+1 is an index of the environmental impact caused by firms that the consumer owns shares of, and Et+1 is the stock of environmental quality (see also Dam and Heijdra, 2008). Consumers do not fully internalize the environmental externality, but they do experience a ‘‘warm glow’’, as in Andreoni (1990), defined as utility that is derived from the act of contributing to the public good as distinct from the value they derive from the public good itself. In the utility function (2), Et+1 is the external effect on utility, while gt+1 accounts for the warm-glow effect. The warm glow is channeled through socially responsible investment, which is described in more detail below.4 We assume that the utility function is separable in its arguments, i.e. we can write u(c, g, E) = U1(c) + U2(g) + U3(E). Furthermore every argument is modeled as a good; uc > 0, ug > 0, uE > 0, ucc < 0, ugg < 0, uEE < 0. Finally we assume U2(g) = U3(E) , g = E, which is not really a restriction at all since g is a function itself, but this convention turns out to be useful when comparing equilibria. Socially responsible investment is modeled by assuming that the consumer feels partly responsible for the pollution generated by firms in which it holds shares. Even though an investor recognizes that he is ‘‘small’’ and his individual actions will have an insignificant impact on environmental quality, he experiences a warm-glow from investing in ‘‘clean’’ assets, and hence prefers investing in these. In terms of the traditional warm glow: the ‘‘contribution’’ of the investor is thus that he is willing to limit the set of investment opportunities for the sake of environmental quality. This limitation implies an (opportunity) cost, but the investor receives a warm-glow from the idea that he only facilitates investment in ‘‘clean’’ firms. We assume that there are two types of financial claims in the economy, 4 Nyborg et al. (2006) use a comparable approach in the context of socially responsible consumers and present a detailed discussion of the psychological background of ‘‘green consumerism’’.

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namely ‘‘clean’’ government bonds and ‘‘dirty’’ corporate shares.5 For simplicity, we assume that firms do not issue new equity. We can thus normalize the number of outstanding shares to one. Also, there are no corporate bonds.6 Since government bonds are clean, the consumer only derives disutility from the share of corporate equity he holds from t to t + 1, denoted by nt: g tþ1 ¼ GðEtþ1 ; P tþ1 Þ  nt ;

with GðEtþ1 ; P tþ1 Þ < 0;


so the warm-glow effect is determined by the shareholdings nt and the strength of the warm-glow effect is represented by G(  ) and can, in principle, depend on the stock of environmental quality, Et+1, or the flow of pollution Pt+1, or both. In Appendix A we give as an illustration some micro-economic foundations that justify this particular preference structure of the representative agent. For now, we assume that the strength of the warm-glow motive depends only on the level of environmental quality in a simple multiplicative way, G(E, P) = gE, so that: g tþ1 ¼ g Etþ1  nt ;

with 0 < g < 1; Etþ1  0:


Since environmental quality Et+1 takes only non-positive values, investors prefer holding clean government bonds over dirty corporate equity, ceteris paribus. The constant parameter g drives the strength of the warm-glow motive and thus the extent to which investors internalize the externality. For g = 0 investors would be indifferent between the two assets, whilst g = 1 implies that investors fully internalize the environmental externality in equilibrium (where demand of shares equals supply; nt = 1), since then the warm glow moves one-to-one with the external effect, U2(g) = U3(E). Investors take the level of environmental quality as given and so they can only influence gt+1 by changing their shareholdings. In a different section we will explore the implications of an alternative specification where the warm glow only depends on the flow of pollution, instead of the stock of environmental quality. 2.2. Consumers’ maximization problem Consumers inelastically supply one unit of labor when young at a real wage rate wt , save all their wages, invest in either government bonds or firm shares, and consume when old. The price of the consumption good is the numeraire. The young agent at time t takes as given: the rate of return on bonds rt+1 at t + 1 and environmental quality Et+1, the current price pt and future price pt+1 per share and dividends dt+1 per share. He constructs a portfolio of bt government bonds and nt corporate shares to maximize his utility (2) subject to: ctþ1 ¼ bt ð1 þ r tþ1 Þ þ nt ð ptþ1 þ dtþ1 Þ;


wt  zt ¼ bt þ nt pt :


Eq. (5) simply states that the total return on bonds and equity are used for consumption at t + 1. Eq. (6) is the budget constraint in which zt is a lump-sum tax paid to the government. We assume that consumers have perfect foresight. The first-order optimality condition of the consumer problem takes the form of a pricing equation: pt ¼

ptþ1 þ dtþ1 þ Dtþ1 Etþ1 : 1 þ r tþ1


The current price equals the discounted future price plus dividends plus the stock of environmental quality times the marginal rate of substitution between warm-glow and consumption, u Dtþ1 Etþ1  gtþ1 g Etþ1 < 0; uctþ1 5 This means that investors assume that the government does not engage in polluting activities. The assumption of a representative agent, a single dirty asset, and a single clean asset is sufficient to characterize the mechanism of socially responsible investment, and at the same time it keeps the model tractable without significant loss of generality. One can easily generalize the model by recognizing heterogeneous firms and heterogeneous consumers. In such a setting, the average investor portfolio will determine equilibrium prices, and dirtier firms will have a higher rate of return. 6 If there were corporate bonds, we assume that investors would treat them as dirty assets, i.e. equivalent to equity, and under this assumption there is no loss of generality since there is no uncertainty.


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which can be viewed as a negative dividend and we define it as the ‘‘pollution’’ premium. We label this e a premium since the firm has to deliver a return on equity rtþ1 that is larger than the return on bonds: e rtþ1  r tþ1 ¼

ptþ1 þ dtþ1  pt Dtþ1 Etþ1  r tþ1 ¼   0; pt pt


which shows that socially responsible investment induces a higher cost of capital for ‘‘dirty’’ assets. We can also see this from Eq. (7): a lower environmental quality (larger stock of pollution) lowers the value of the dirty asset such that the return will be larger. The government issues one period bonds Bt at time t and faces the following budget constraint: Btþ1 þ ztþ1 L ¼ Bt ð1 þ r tþ1 Þ;


so the government issues new bonds or collects taxes to pay interest plus principal on old bonds. The Q government must remain solvent, and the solvency condition reads lim T ! 1 BT Tt¼0 1=ð1 þ r tþt Þ ¼ 0. 2.3. Firms Output is represented by a linear homogeneous production function F(Kt, Lt) where Kt denotes the capital stock and Lt labor used at time t. Capital invested at t, denoted It, becomes productive at t + 1. Firms depreciate capital at a uniform rate d: K tþ1 ¼ ð1  dÞK t þ It :


Because of constant returns to scale, we can rewrite output as a function of per capita capital kt: F(Kt, Lt) = f(kt)Lt where f(kt) is production per capita. We use lower case letters, it, kt, ct, to denote per capita investment, capital, and consumption. Capital Kt creates contemporaneous pollution Pt. We assume there is a linear relation between capital and pollution and as a consequence we are free to choose our unit of account of pollution. We normalize such that one unit of capital creates one unit of pollution, that is Pt = Kt. Recall that firms do not issue new equity, nor issue bonds, so a firm finances it investment by retained earnings. We have: FðK tþ1 ; Ltþ1 Þ  wtþ1 Ltþ1 ¼ Itþ1 þ Dtþ1 :


A firm can use its production net of labor payments to finance its real capital investments or to pay out dividends Dt+1. Rewriting (11), in per capita form using dt = Dt/L, and rearranging we find: dtþ1 ¼ f ðktþ1 Þ  wtþ1  itþ1 :


Since we have normalized the number of consumers and shares to one, using the pricing Eq. (7) we find in equilibrium for the stock market value of the firm:

vt ¼

vtþ1 þ dtþ1 þ Dtþ1 Etþ1 1 þ r tþ1



Substituting the expression for dividends we find:

vt ¼

vtþ1 þ f ðktþ1 Þ  wtþ1  itþ1 þ Dtþ1 Etþ1 1 þ r tþ1



which shows that dividends do not matter to the value of the firm, i.e. the Modigliani–Miller Theorem holds. 2.4. Firms’ maximization problem A firm makes investments in real capital to maximize shareholder value according to (14). We let the optimal investment it at time t depend on the state variables kt and Et, such that for the firm’s market value vt ¼ v ðkt ; Et Þ we have:

vt ¼

f ðktþ1 Þ  wtþ1  i ðkt ; Et Þ þ Dtþ1 Etþ1 þ vtþ1 ; 1 þ r tþ1


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which is a Bellman Equation. The maximum principle then gives the following first-order conditions7: 1b 0 0 ½ f ðktþ1 Þ  ðr tþ1 þ dÞ ¼ f ðkt Þ  ðr t þ dÞ  Dt ; 1 þ r tþ1 0

f ðkt Þ  f ðkt Þkt ¼ wt :

(16) (17)

Iteratively substitute (16) and find: 0

(18) f ðkt Þ ¼ ðr t þ dÞ þ Qt ; P1 t Qt where we define Qt ¼ t ¼0 ð1  bÞ = s¼0 ð1 þ r tþs ÞDtþt . Eq. (18) states that the marginal product of one unit of capital today should equal the familiar (rt + d) plus Qt, which is the discounted sum of the pollution premia Dt of all future generations. Since pollution due to investment today yields a change in the warm glow of (1  b) one period ahead we have a discount rate equal to (1  b)/(1 + rt) for the future pollution premia. We solve Eq. (14) by repeated substitution and find:

vt ¼

1 X f ðktþt Þ  wtþt  itþt þ Dtþt Etþt ; Rðt þ t Þ t ¼1


Q with Rðt þ t Þ ¼ ts¼1 r tþs and we require that the standard transversality (no bubble) condition holds: QT lim T ! 1 vT t ¼0 1=ð1 þ r tþt Þ ¼ 0. Substituting (17) and (18) and recognizing that Etþs ¼ ð1  bÞs Et þ Ps ðst Þ ktþt , we find after some tedious steps the value of the firm along the optimal path: t¼1 ð1  bÞ

vt ¼ kt ð1  dÞ þ it þ Qtþ1 Et ;


vt ¼ ktþ1 þ Qtþ1 Et :


The market value of the firm is equal to the value of its capital stock plus the valuation of current environmental quality. The valuation of current environmental quality consists of the pollution premia of the current and all future generations. The forward looking nature of the stock market ensures that the current value of the firm contains the valuation of all future generations for the level of environmental quality today, reflected by Qt+1. A way to interpret this result is that the stock market assures that current generations pay every future generation for the ‘‘right’’ to reduce current environmental quality. The payment to every generation is equal to the present value of the pollution premium (using the discount rate (1  b)/(1 + rt)). So if the current generation decides to pollute heavily, the value of the firm at old age will be lower. The firm thus becomes cheaper for the new generation(s), reflecting the fact that future generations want to be compensated for the additional pollution. If the value of the firm at old age is lower, it reduces the amount of funds available for consumption at retirement. This mechanism creates an incentive to reduce pollution and take into account the effect of pollution on future generations. The main model equations are summarized in Table 1 by Eqs. (T1.1)–(T1.7). Eq. (T1.1) is the accounting identity. Eq. (T1.2) states that labor is rewarded with its marginal product. Eq. (T1.3) characterizes the dynamic investment decision of the firm. Eq. (T1.4) is the per capita production function. Eq. (T1.5) states that the pollution premium depends on the warm-glow effect. Eq. (T1.6) is the government’s budget constraint. Finally, Eq. (T1.7) characterizes the dynamic evolution of environmental quality. 3. Dynamics and comparison of equilibria In equilibrium all markets clear, and utility and firm value are maximized. To be able to study dynamic effects we study a scenario in which the government implements a simple fiscal policy. The 7 To solve the maximization problem, it is useful to rewrite (1) as Et+1 = (1  b)Et  (1  d)kt  it and note that the firm takes into account the direct effect on the pollution premium DtEt, but not second-order effects, i.e. it treats Dt as a price. See Appendix B for a detailed derivation.

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1022 Table 1 Main model equations. ktþ1 ¼ yt  ct  dkt



wt ¼ f ðkt Þ  f ðkt Þkt 1b 1þr tþ1




½ f ðktþ1 Þ  ðrtþ1 þ dÞ ¼ f ðkt Þ  ðr t þ dÞ  Dt


yt ¼ f ðkt Þ u


ðc ;E Þ

Dt ¼ g ugc t ðctt ;Ett Þ


Btþ1 þ ztþ1 L ¼ Bt ð1 þ r tþ1 Þ


Etþ1 ¼ ð1  bÞEt  ktþ1



Notes: ct is consumption, wt is the wage rate, rt is the interest rate, kt is the per capita capital stock, L is labor supply, d is the depreciation rate of capital, Dt is the pollution premium (warm glow), Et is environmental quality, yt is per capita output, zt is the lump-sum tax per agent, and Bt is the stock of government bonds.

¯ and lump-sum taxes are also government issues a fixed number of government bonds Bt ¼ Btþ1 ¼ B, held constant, ztþ1 ¼ zt ¼ z. ¯ We can write wages, consumption, per capita output, and the pollution premium (T1.1), (T1.2), (T1.4) and (T1.5) in terms of the state variables capital and environmental 0 quality, i.e. wt ¼ wðkt Þ ¼ f ðkt Þ  f ðkt Þkt , ct = c(kt, kt+1)) = f(kt) + (1  d)kt  kt+1, and Dt ¼ Dðkt ; ktþ1 ; Et Þ ¼ g ðugtþ1 =uctþ1 Þ. Government policy fixes the interest rate and according to (T1.6) it is equal to ¯ 8 t. Eqs. (T1.7) and (T1.3) can then be used to study dynamic behavior. The paths of the state r t ¼ z= ¯ b; variables kt, Et thus fully determine all other variables. Once these paths are known, Qt can also be calculated and the path for firm value follows vt ¼ ktþ1 þ Qtþ1 Et . In a steady state we have: ˆ ¼rþdþ f ðkÞ 0

1þr ˆ D; rþb


kˆ Eˆ ¼  ;



ˆ Eqs. (22) and (23) and the steady state value of the firm is equal to vˆ ¼ ð1  ðð1  bÞ=bðr þ bÞÞDÞk. uniquely8 determine the steady state values for kt and Et, from which the steady state value for vt follows directly. We turn to the stability of the system by log-linearizing Eqs. (1) and (16) around the steady state. A variable with a tilde denotes a percentage change from its initial value e.g. k˜t ¼ dlog kt 2 3 2 3     ˆ kˆ 0 ˆ 1b ˆ ˆ k½ f 0 ðkÞ ˆ ˆ ekl  s c D ˆ þ ð1  dÞ 6  f ðkÞ 0 7 k˜tþ1 ¼ 4  f 0 ðkÞ e  sc D  s D kl g 5 k˜t ; 4 5 ˜ 1þr cˆ cˆ Etþ1 E˜t 0 ð1  bÞEˆ kˆ Eˆ (24) ˆ k= ˆ f ðkÞ ˆ the elasticity of substitution between capital and labor, sc = uccc/uc the with ekl ¼ f ðkÞ elasticity of marginal utility to consumption, and sE = uggg/ug the elasticity of marginal utility to warm glow. Since government policy can fix any interest rate, we analyze stability in the case for which the classic Diamond economy is steady-state efficient, r = 0. The log-linearized system can be rewritten as: 00



ˆ 0 ˆ ˆ k½ f 0 ðkÞ ˆ þ ð1  dÞ ekl  s c D  f ðkÞ ˜tþ1 16 k cˆ ½ ¼ 6 4 ˜ ˆ A Etþ1 0 ˆ ˆ k½ f 0 ðkÞ ˆ þ ð1  dÞÞ bð f ðkÞ ekl þ s c D cˆ



  7 k˜ 7 t ; 5 E˜ t ˆ ð1  bÞA  bs g D ˆ s g D



Eq. (23) is a downward sloping curve and using implicit differentiation we find for (22) that dE=dk ¼ ½ f ðkÞ 

ˆ d½ðucc =uc Þ=ðugg =ug Þ þ ðr þ bÞ=ð1 þ rÞ f 00 ðkÞ=ðu gg =ug Þðug =uc Þ which is positive for all k  0 and E  0 satisfying (22), so that (22)

ˆ The implied single crossing property of the two functions defines a implicitly defines Eˆ as a strictly increasing function in k. unique steady state.

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0 ˆ ˆ . The absolute value of the determinant of this matrix is less with A ¼  f ðkÞð1  bÞ=ð1 þ rÞekl  s c D 0 ˆ than one if f ðkÞ  d < b=ð1  bÞ; a necessary condition for stability since in general the determinant of ˆ =bÞ < b=ð1  a matrix is equal to the product of its eigenvalues. In a steady state this is equivalent to ðD bÞ which implies that we require that the marginal rate of substitution between warm-glow and consumption should not be too large. Furthermore we need that sc and sg should not be too large.

3.1. Benchmark 1: alternative warm-glow specification We now consider a case for which the warm-glow depends on the flow of pollution only, that is: g tþ1 ¼ g Ptþ1  nt ;

with 0 < g < 1; Ptþ1  0:


The pricing equation is similar in this case and we have pt ¼

ptþ1 þ dtþ1  Dtþ1 Ptþ1 : 1 þ r tþ1


Optimal investment now yields first order conditions in line with John and Pecchenino (1994), namely 0

f ðkt Þ ¼ r t þ d þ Dt


and Eq. (17). Now the marginal product of capital covers only the pollution premium of the current generation. Setting g = 1 is equivalent to John and Pecchenino (1994) who assume that there is a form of intragenerational coordination to establish optimal provision of the public good for agents alive at time t, but no intergenerational coordination. Furthermore, we find that if the warm-glow only depends on the flow of pollution, the value of the firm is equal to its replacement value, vt ¼ ktþ1 . It implies that there are no intergenerational transfers. This makes sense, since only changes in environmental quality are valued by the stock market, and these changes happen within the lifetime of one generation. Every generation is simply compensated by its own pollution premium. Since the required marginal product of capital in Eq. (28) is lower compared to Eq. (18), the capital stock will be relatively higher when the warm glow only depends on pollution flows. As a result, environmental quality will be lower. 3.2. Benchmark 2: a centrally planned economy We calculate both the optimal transition path and the long-run efficient steady state benchmark equilibrium for the case of a central planner. There is quite some debate whether to include the warmglow preferences in the calculation of a social optimum (see e.g. Chilton and Hutchinson, 1999). We choose not to include the warm-glow since we feel that including the warm-glow in the planner’s allocation is ‘‘double-counting’’. In the end, all consumers really care about is the environment. When a planner allocates resources, consumers know that the pollution is internalized, and warm-glow becomes meaningless. Therefore, we assume the planner does not allocate property rights, but simply allocates consumption and investment. As such, the warm glow is equal to gt = 0, 8 t. Whether this is theoretically the ‘‘right’’ benchmark is beyond the scope of this paper. Consider a central planner that maximizes a social welfare function that assigns a fixed weight 1/ (1 + R) to the utility of each generation, with the planner’s discount rate R > 0. The planner maximizes: max

1 X ð1 þ RÞt uðct ; g t ; Et Þ



subject to ct ¼ f ðkt Þ þ ð1  dÞkt  ktþ1


Et ¼ ð1  bÞEt1  kt


nt ¼ 0


L. Dam / Resource and Energy Economics 33 (2011) 1015–1027


and given initial values k1, E1. The third restriction is the assumption that there are no property rights, and thus the planner does not consider the warm-glow in calculating the optimum. Along the optimal path the following first-order condition must hold: 1b uE 0 0 ½ f ðktþ1 Þ  ðrtþ1 þ dÞ ¼ f ðkt Þ  ðrt þ dÞ  t ; 1 þ rtþ1 uc t


with ð1 þ rtþ1 Þ  ð1 þ RÞuct =uctþ1 the inverse of the marginal rate of intertemporal substitution. Eq. (33) provides the planner with a simple investment rule. A hat on a variable denotes its steady state value. The steady state associated with Eq. (33) reads: ˆ ¼ Rþdþ f ðkÞ 0

1 þ R uEˆ : R  b ucˆ


We see that when the discount rate R goes to infinity, f0 (k) goes to infinity, implying (assuming Inada conditions) a steady state with zero production. In this case the planner allocates all capital in the first period to the old generation to use for consumption. Next we turn to steady state efficiency. We substitute the steady state values of capital, ˆ  dk; ˆ bÞ, and choose the ˆ 0; k= consumption and environmental quality in the utility function, uð f ðkÞ ˆ E; ˆ c) ˆ is steady state optimal if it satisfies the level of capital that maximizes utility. A steady state (k; following first-order condition: ˆ ¼dþ f ðkÞ 0

1 uEˆ

b ucˆ



We can see that the optimal path will lead to the efficient steady state if the planner’s discount rate R = 0, since then the steady state solution of (34) is equal to (35), which is not very surprising since there is no time preference nor uncertainty in the model. 3.3. Comparison of equilibria In Fig. 1 the line 0  A  JP  B is associated with Eq. (23); this line represents steady states which are technically possible. First we consider equilibria for which the warm-glow depends on the level of

Fig. 1. Comparison of steady state equilibria. The line 0  A  JP  B is associated with Eq. (23) and any point on this line can be a steady state economic outcome. The curve Emin  A is associated with Eq. (23). Point A is the steady-state equilibrium in a stockmarket economy with socially responsible investors. The stock-market assures intra and intergenerational coordination with respect to environmental quality. The arrows reflect the dynamic forces of this equilibrium. Point JP is the steady-state equilibrium of the economy of John and Pecchenino (1994) in which there is only coordination within each generation with respect to environmental quality. Point B reflects an economy without any coordination.

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environmental quality. The curve Emin  A is associated with Eq. (22) and point A with the steady state of this system, for the case g = 1. Point A also reflects the first-best optimal steady state equilibrium, Eq. (35), since the externality is fully internalized for g = 1. For 1 < g < 0 we can end up anywhere on the line A  JP  B. We also depict the John and Pecchenino (1994) steady state as defined by Eq. (28), for g = 1; an equilibrium in which the warm-glow depends only on the pollution flow. For various values of g associated with Eq. (28), the steady state is a point on the line JP-B. In these equilibria environmental quality is always too low and invested capital is too high, even for g = 1. Finally, if firms maximize pure profits instead of value – which is equivalent to an economy in which investors are not socially responsible(g = 0) – the economy will end up in point B and environmental quality will be even lower, naturally. Finally, apart from a parameter shift, the social planner finds the same allocation rule as the competitive economy. Therefore, we argue that the introduction of a stock market does not bring additional restrictions in terms of stability requirements. 4. Conclusion One of the key issues in achieving sustainable development is managing the impact of economic activity on the environment. In the last decade, corporations have increasingly put sustainable development on their agendas, creating the possibility of socially responsible investment. This paper argues that the stock market can play a role in achieving sustainable development. We analyze this in an Diamond-type overlapping generations model with short-lived consumers that care about environmental quality, comparable to John and Pecchenino (1994). A lack of coordination between old and young agents leads to over accumulation of pollution. We show that introducing an equity market that allows for trade of property rights can partially resolve the coordination failure. The intuition is straightforward: since the stock market is forward looking, equity allows for trade in future valued capital, incorporating the welfare loss of pollution of future generations. One of the contributions of this paper is to show that, in a dynamic overlapping generations setting, the way in which socially responsible investment is modeled is important. Such behavior can only lead to the social optimum if the stock of externalities is considered in firm valuation, not the flow. This is intuitive once one realizes that in this case environmental quality hardly differs from real capital when it comes to market values. Finally, it would be interesting to see whether it makes a difference if the government finances pollution abatement by issuing more bonds or by increasing taxes. This is an extension which we leave for future research. Acknowledgements I am indebted to Ben Heijdra for providing me with very useful suggestions and feedback on some crucial modeling choices. I wish to thank Bert Scholtens, Elmer Sterken and two anonymous referees for detailed comments on earlier drafts and useful suggestions. I am also grateful to Martine Quinzii, Sjak Smulders, Richard Tol, Jose´ Luis Moraga Gonza´lez, and Pim Heijnen for helpful comments. Gratitude also goes to participants of the IEE Brown Bag Seminar held in Groningen, the Netherlands, 2003, participants of the ‘‘Forschungsseminar’’ Quantitative Wirtschafst-forschung held in Hamburg University, Germany, May 2005, participants of the SURED conference held in Ascona, Switzerland, June 2004 and June 2006, participants of the CORE conference held in Milan, Italy, June 2007, and the participants of the Osaka University Forum, held in Groningen, the Netherlands, June 2007, for inspirational discussions. Appendix A. A note on the preferences of the representative agent Since the preference structure is novel in our model, it may be useful to motivate this preference structure with some micro-economic foundations by giving an example. In static models of vertical product differentiation the following is a common set-up: Consider a mass of heterogeneous consumers of size one. Suppose each individual consumer i has an indirect utility function Vi = R  uiP, with R the (excess) return on a stock, P pollution associated with the stock, and ui the private taste


L. Dam / Resource and Energy Economics 33 (2011) 1015–1027

parameter for the environment of consumer i with distribution F(ui). For sake of the argument, we assume that if the consumer chooses to buy stocks, there is a minimum (discrete) amount of stocks he is able to buy, say, one stock. Furthermore, the benefits of financial diversification may limit the total amount of shareholdings a single consumer holds in one firm. We can simplify this situation such that a consumer buys at most one stock, and hence, we have a discrete choice model. In such discrete choice models, a consumer buys one stock only if Vi  0, i.e. screens out stock if Vi < 0. The indifferent consumer is determined by ui = u$ = R/P. It follows that aggregate demand for shares is equal to n = F(R/P) and the pollution elasticity of demand is equal to @ n/@P(P/n) = u$f(u$)/F(u$). Aggregate preferences thus imply a trade-off between the aggregate demand for shares n and the level of pollution P, and this trade-off depends on the distribution of the consumers. This illustrates that the proposed preference specification of our representative agent has micro-economic foundations and can account for possible heterogeneous investor groups, in which some investors may not care about the environment at all. Alternatively, if socially responsible investment is not operationalized by the mechanism of screening out stock, but by a more subtle mechanism with ‘‘social scoring’’, the preference specification of this paper follows more directly, irrespective of whether investors are heterogeneous or not. To this extent see also the example in Footnote 2 about more subtle forms of socially responsible investment used in practice, where consumers base their portfolio choices on ratings by rating agencies. Appendix B. Derivation of firm’s maximization problem The optimal investment it at time t depends on the state variables kt and Et. The value function

vt ¼ v ðkt ; Et Þ yields the following Bellman Equation: vt ¼

f ðktþ1 Þ  wtþ1  ð1 þ r tþ1 Þi ðkt ; Et Þ þ Dtþ1 Etþ1 þ vtþ1 ; 1 þ r tþ1


with it = kt+1  (1  d)kt and Et+1 = (1  b)Et  (1  d)kt  it. Taking the derivative of the value function with respect to the control variable gives the first order condition:   dvtþ1 dvtþ1 dvt 1 0 ¼ f ðk Þ  ð1 þ r Þ  D þ  (37) ¼ 0: tþ1 tþ1 tþ1 1 þ r tþ1 dit dktþ1 dEtþ1 Note that the firm takes into account the direct effect on the externality premium DtEt, but not secondorder effects, i.e. it treats Dt as a price. To solve we take the derivative of the value function with respect to the state variables:   d v dv dvt 1d 0 ¼ f ðktþ1 Þ  Dtþ1 þ tþ1  tþ1 ; (38) dkt 1 þ r tþ1 dktþ1 dEtþ1   dv dvt 1b ¼ Dtþ1 þ tþ1 ; dEt 1 þ r tþ1 dEtþ1


where we have applied the envelope theorem. Combining (37) and (38) gives: dvt ¼ ð1  dÞ; dkt


which can be led one period and substituted in (37) to find: dvtþ1 0 ¼ f ðktþ1 Þ  ðr tþ1 þ dÞ  Dtþ1 : dEtþ1


Substituting (41) and (41) lagged in (39) and rearranging gives 1b 0 0 ½ f ðktþ1 Þ  ðr tþ1 þ dÞ ¼ f ðkt Þ  ðr t þ dÞ  Dt ; 1 þ r tþ1 which is the implicit difference equation that characterizes the optimal path, Eq. (16).


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