Limited Market Participation, Financial Intermediaries, And Endogenous Growth

Review of Economics & Finance Submitted on 02/May/2011 Article ID: 1923-7529-2011-04-53-10 Hiroaki OHNO Limited Market Participation, Financial Intermediaries, And Endogenous Growth Hiroaki OHNO Department of Economics, Tokyo International University 1-13-1 Matoba-Kita, Kawagoe, Saitama, 350-1101, JAPAN Tel: +81-49-232-1111, E-mail: hiohno@tiu.ac.jp Abstract This paper analyzes the role of imperfect asset markets and financial intermediaries in determining the equilibrium growth rate of the capital stock by incorporating exogenous market participation constraints into an overlapping generation s economy. Economic growth and social welfare monotonically increase with the degree of market participation. Hence, economies with financial intermediaries have a stronger potential for a higher growth rate than economies with imperfect markets lacking such institutions. JEL Classifications: E21; G20; O16 Keywords: Limited market participation, Financial intermediaries, Endogenous growth model 1. Introduction This study examines the relationship between imperfect asset markets and financial intermediaries in determining the equilibrium growth rate of capital stock and social welfare. This is accomplished by incorporating exogenous limited market participation into an overlapping generations economy. Empirical analyses support the positive impact of financial innovation on economic growth. 1 However, it is difficult to derive this relationship from the theoretical analysis. Several studies discuss the important issue of whether financial innovation promotes economic growth. One typical example is that precautionary motives for uninsured idiosyncratic risks promote capital accumulation. In this case, financial sophistication reduces the equilibrium growth rate. 2 However, in light of the critical issue raised in Angeletos and Calvet (2006) and Bencivenga and Smith (1991), as to how the progress in financial technologies contributes to economic growth, these studies analyze the economic dynamics in reference to the risk aversion parameter. In the present study, we focus on the degree of limited market participation. The issue that limited market participation in asset markets affects consumption and asset prices was first discussed by Mankiw and Zeldes (1991). They estimated Euler equations for stockholders and nonstockholders using data from the Panel Study of Income Dynamics. According to Mankiw and Zeldes (1991), stockholders only comprise a small proportion of consumers (27.6 percent among a sample of 2998 families). 3 We consider the effect of exogenous market participation constraints on economic growth and social welfare. 1 For example, see King and Levine (1993) and Levine (1997). 2 The literature on uninsured idiosyncratic risks models includes, inter alia, Aiyagari (1994) Devereaux and Smith (1994), and Huggett (1993). 3 The literature examining the effect of market participation constraints includes Allen and Gale (1994); Cao, et al. (2005); Ohno (2010); Vissing-Jorgensen (2002a, 2002b, 2003); Weil (1992); and Williamson (1994), among others. These studies analyzed incomplete market participation generated by ~ 51 ~

ISSNs: 1923-7529; 1923-8401 2011 Academic Research Centre of Canada It can also be argued that in the aftermath of the Second World War, economic reconstruction was largely achieved through bank-based financial systems. Given that some economies were market-oriented before the war, the increased reliance on bank financing during the post-war period makes it difficult to understand the factors underlying salient post-war achievements and the economic function of banking institutions. As noted in Allen and Gale (2000), there are discrepancies between economies with bank-based financial systems (e.g., Germany, France, and Japan, among others) and those with market-oriented financial systems (e.g., the United Kingdom and the United States). Thus, it is important to assess the economic rationale underlying bank-based financial systems, which can also assist in discerning this system from the market-oriented alternative. The present analysis is based on the work of Diamond and Dybvig (1983), who illustrated that financial intermediaries provide risk-sharing opportunities for consumers with preference shocks in financial autarky. Using the Diamond and Dybvig model, Bencivenga and Smith (1991) provide a theoretical framework in which financial intermediaries play an important role in achieving a higher equilibrium growth rate. The Bencivenga and Smith (1991) model assumes that all consumers cannot access the secondary market. By incorporating the secondary market into the Bencivenga and Smith model, we reexamine the role of banking institutions under the coexistence of financial intermediaries and asset markets. Introducing perfect secondary markets, however, financial intermediaries cannot affect the resource allocation and economic growth. Given this factor, the exogenous participation constraint is considered. This approach has the advantage of investigating the role of financial intermediaries on economic growth and social welfare, treating the degree of market participation as a parametric variable. The raison d' tre of the present study lies in the need to address the relationship between imperfect asset markets and financial intermediaries for economic growth and social welfare. We illustrate that the growth rate and social welfare monotonically increase in market participation. In addition, economies with financial intermediaries have a stronger potential for a higher growth rate than those with incomplete market participation and lacking such institutions. However, economies allowing for full participation will grow no less than those characterized by a bank-intensive system. The subsequent sections examine the behavior of economic agents. Section 2 describes the theoretical setting. Section 3 considers asset markets with limited market participation. Section 4 introduces the financial intermediaries. Section 5 discusses our conclusion in the context of literature. Section 6 concludes the study. 2. The Model The model developed in this study is an extension of the Bencivenga and Smith (1991) and Diamond (1997) models, in which the economy consists of a sequence of two- or three-period overlapping generations. Time is indexed by. In period, there is an initial old generation, endowed with an initial per firm capital stock of, as well as an initial middle-aged generation, endowed with a per firm capital stock of units in period. Except for the initial old and middle-aged generations, agents have no endowment of the capital good (or consumption) at any given time. There are two goods in this economy a consumption good and a capital good. The consumption good is produced by capital and labor. For reasons to be discussed, all capital is owned by old agents, henceforth called entrepreneurs. Letting denote the capital held by an individual entrepreneur in period, an entrepreneur who employs units of labor in period produces the consumption good according to the production function, where, represents an external transaction cost, liquidity (Allen and Gale, 1994; Williamson, 1994), fixed participation cost (Weil, 1992), model uncertainty (Cao, et al., 2005), and risk-sharing externalities (Ohno, 2009, 2010). ~ 54 ~

Review of Economics & Finance effect that acts as the Harrod-neutral technology growth parameter. Following Romer (1986, 1987), we assume that in the equilibrium and no capital wastage occurs. There are two assets in this economy. There is a short-term investment, where one unit of the consumption good invested in t yields one unit of consumption good at either or. Thus the return on the short-term investment does not depend on the date of liquidation. Moreover, there is an irreversible capital investment, in which one unit of the capital good invested in t yields units of the capital good in period. The number of new generations is a continuum and normalized to one (no population growth is assumed). Each young agent is endowed with a single unit of labor when young, which is supplied inelastically. There is no labor endowment at middle or old ages. Because young agents do not undertake consumption, all of their income is saved. The t-generations turn out to be the types, and at the end of each period as the young generation. The type comprise early consumers who only consume in period. In addition, types comprise late consumers who consume in period. The distinction between is whether they can participate in the secondary market. More specifically, type- can trade with type-, but type- cannot trade assets with anyone. We interpret type- consumers as facing infinite transaction costs. We also assume that the probability for types is given by where. 4 These probabilities are constant over time. Therefore, the risks of this economy are based on the types of agents. 5 Assume that the new generations have the following expected utility: We assume a logarithmic utility function and focus our attention on incomplete market participation. 6 All capital resides in the hands of old entrepreneurs for each date given an inherited capital stock of where represents the agents type. An entrepreneur chooses a quantity of labor and capital to maximize profits, that is (1) Here and denote the real wage rate and the real interest rate, respectively. First-order conditions are given by the following equations: (2) Hence, the discussion of labor-market and capital-market clearing remains. In this case, each young agent supplies one unit of labor. Since type- agents do not consume in old age, they liquidate all assets at middle age and hire no labor. Only a fraction of old agents are entrepreneurs, each of whom hires units of labor. The labor market requires the following equilibrium condition: 4 We assume that,. 5 This exogenous market participation setting is derived from Diamond (1997). 6 Assuming logarithmic utility function, the model does not reflect the effect of the utility curvature against preference shocks. For more details, see Diamond and Dybvig (1983). ~ 55 ~ (3) (4)

ISSNs: 1923-7529; 1923-8401 2011 Academic Research Centre of Canada The equilibrium condition of the capital market requires In the equilibrium, the real wage and real interest rates are not influenced by individual i. Therefore, the following condition is satisfied: From Equations (4), (5) and (6), the per capita capital stock is given as follows: Finally, substituting Equation (7) into Equations (2) and (3), it is possible to derive the real wage and net interest rates. Thus, the return on long-term investment can be obtained by stock is assumed not to depreciate. 3. Limited Participation and Endogenous Growth (5) (6) (7) (8), since the capital This section investigates consumers optimization problem with limited market participation and derives the equilibrium growth rate of the capital stock. 3.1 Constrained optimal consumptions The consumption of an agent born at time is denoted by, of types and, respectively. Let and be the spot price at of illiquid and liquid assets, respectively. Given the risks of early withdrawal and limited market participation, they maximize Equation (1) introducing the budget constraints. New generations have long-term and liquid assets for future consumption upon their arrival in this economy. They hold the proportions in the liquid asset, and in the illiquid asset, respectively. This implies that However, after learning one s type, the long-term assets are wasted for any type-, because of the limited prospects of living until maturity. Therefore, type- sells long-term assets to type- and purchases additional short-term assets. On the other hand, type- would be interested in investing in long-term assets using short-term assets, because they can live for three periods and that the return from long-term assets is superior to that from short-term assets. Hence after their types are known, type- and type- trade with each other using their own assets. Thus, the budget constraints are given by Equation (9) and the following equations: (9) As type- cannot participate in the secondary market, he/she holds the liquid asset until maturity. Hence, the first-order condition can be obtained as follows: where. ~ 56 ~

Review of Economics & Finance The secondary financial market equilibrium conditions remain to be discussed. Type- purchases units of short-term assets. Moreover, type- buys units of long-term assets. On the other hand, type- offers units of short-term assets. Hence, in per capita terms, type- can obtain units of short-term assets. In the same way, type- can obtain units of longterm assets. Thus, in the equilibrium, the following clearing condition is given: The first order condition for the individual maximization problem and the equilibrium condition yield the following:., where and In the economy, all agents who have experienced participation constraints have no other choice than to possess liquid assets. Hence, young generations have an additional demand for illiquid assets against limited market participation, while they have an incentive to hold liquid assets to prepare for the risk of type- consumers, since these consumers cannot survive until maturity. 3.2 Market Equilibrium This section analyzes the equilibrium growth rate of capital stocks with limited market participation. In the equilibrium, Substituting Equation (8) into Equation (10) yields the equilibrium growth rate of the capital stock: Equation (11) yields the equilibrium growth rate of output. In particular, (10) (11) The capital stock in period depends on the wage rate in period, since capital formation takes two periods and the return on long-term investment is time-invariant. Here we introduce the following proposition: Proposition 1 (Market Participation) The equilibrium growth rate and social welfare monotonically increase with the degree of market participation. The proof is given in the Appendix. We consider participation constraints as a parametric parameter. If the fraction is equal to zero, the first-order condition and the equilibrium conditions characterize the following consumption pattern: ~ 57 ~

ISSNs: 1923-7529; 1923-8401 2011 Academic Research Centre of Canada In a full market participation economy, the above allocation can be obtained. It should be noted that if risk aversion is larger, then agents have an incentive to smooth their consumptions more than shown in our model. This effect may induce a decrease in capital accumulation. 4. Financial Intermediaries and Endogenous Growth In this context, limited market participation represents an economy where a group of agents cannot participate in the markets due to the fixed participation cost. In such an environment, efficient intermediation with lower costs of access may allow for the participation of constrained agents. In particular, financial intermediaries resembling those shown in Diamond (1997) are now introduced. These intermediaries accept deposits from young savers and invest in both liquid assets and illiquid capital goods. Investment in liquid assets is a form of reserve holding by banks. The financial intermediaries are viewed as a risk-sharing group formed by young agents in period t. They maximize Equation (1) subject to Financial intermediaries resource constraints must satisfy Equation (12). These financial intermediaries maximize the utility functions of any new generations under the budget constraint that endowments are invested in both short-term and long-term assets. The optimum consumptions denoted by for each type are as follows: (12) This allocation coincides with the case of a full market participation economy. In the equilibrium, the capital stock is characterized by (13) Consequently, Equations (8) and (13) imply that Equation (14) yields the equilibrium rate of the growth of output. In particular, (14) We are mainly interested in examining the relationship between and. The relationship is the necessary condition for satisfying the relationship >. When, this condition is always satisfied. Here, we obtain the following proposition: Proposition 2 (Financial Intermediaries) If limited market participation exists, then financial intermediaries bring higher equilibrium growth rates and improve social welfare. However, if full market participation is achieved, then financial intermediaries cannot influence resource allocation. The proof is given in the Appendix. Proposition 2 implies that if the degree of limited market participation increases, then the economy with financial intermediaries grows larger than the market- ~ 58 ~

Review of Economics & Finance oriented system with limited market participation. However, the equilibrium growth rates for a fullparticipation economy and bank-based financial systems are identical. The intuition underlying this proposition is as follows: type- agents are restricted from purchasing additional long-term assets in an imperfect market. Therefore, capital investment is not sufficiently promoted. When financial intermediation is introduced, however, they can obtain a first-best allocation. Therefore, the funding within type- is effectively used to invest in long- term assets. Hence, the growth rate of the economy is higher than the model, where the participation constraint exists. 5. Discussion Our conclusion suggests that all consumers should participate in the asset market or hold a deposit in banking institutions in terms of economic growth and risk sharing. However, market participants and bank depositors coexist in the real economy. More specifically, the condition of full participation is not realized. In this regard, Ohno (2009, 2010) examines an economy where multiple risk-sharing mechanisms provide risk-sharing opportunities and consumers must decide either to participate in asset markets or hold a deposit. It can be shown that market participants and bank depositors coexist in the equilibria under certain conditions. The empirical evidence presented by Levine (2002), analyzing the impact of the strength of banking institutions on economic growth, illustrates that financial intermediaries are scarcely able to influence economic growth. This conclusion is not inimical to our conclusion: if the financial market is substantially developed, then financial intermediaries cannot bring about drastic changes for economic growth. In terms of economic growth, our conclusion supports the fact that there is little difference between the economies with high-intensity banking systems and developed asset markets, where the degree of market participants is sufficiently large. On the other hand, it can be expected that the introduction of a banking system contributes to substantial advances in economic growth in the economy, where consumers cannot sufficiently obtain risk-sharing opportunities. Hence, it is possible to argue that the economy that lacks developed asset markets should depend on banking systems. 6. Conclusion Our analysis has examined the relationship between asset markets with participation constraints, financial intermediaries, and the equilibrium growth rate in a two- or three-period overlapping generations economy. Under limited market participation, financial intermediaries are effective vehicles for resource allocation and economic growth. However, a full participation economy enables consumers to skip the deposit contract with financial intermediaries. Thus, our conclusion implies the positive impact of financial sophistication on growth and social welfare. This study opens new avenues for theoretical and empirical research by discussing the relationship between the degree of limited market participation and financial intermediaries. Acknowledgements: An earlier version of this paper was presented at the Biannual Meeting of the Japanese Economic Association, Chuo University, and at a seminar at Osaka University. I am very grateful to Kazuhiko Nishina, Yoshiro Tsutsui, Yuzo Honda, Chiaki Hara, Shinsuke Ikeda, Yuichi Fukuta, Maghrerebi Nabil, Hiroshi Nakaota, Takayuki Ogawa and the seminar participants at Osaka University for their invaluable suggestions. I am especially indebted to the anonymous referees of REF for many constructive comments. All remaining errors are mine. ~ 59 ~

References ISSNs: 1923-7529; 1923-8401 2011 Academic Research Centre of Canada [1] Aiyagari, S. R. (1994). Uninsured Idiosyncratic Risk and Aggregate Saving, Quarterly Journal of Economics, 109: 659 684. [2] Allen, F. and D. Gale (1994). Limited Market Participation and Volatility of Asset Prices, American Economic Review, 84: 933 955. [3] Allen, F. and D. Gale (2000). Comparing Financial Systems, Cambridge: MIT Press. [4] Angeletos, G. and L. Calvet (2006). Idiosyncratic Production Risk, Growth and the Business Cycle, Journal of Monetary Economics, 53: 1095 1115. [5] Bencivenga, R. and B. Smith (1991). Financial Intermediation and Endogenous Growth, Review of Economic Studies, 58: 195 209. [6] Cao, H. H., T. Wang, and H. H. Zhang (2005). Model Uncertainty, Limited Market Participation, and Asset Prices, Review of Financial Studies, 18: 1219 1251. [7] Devereux, M. B. and G. W. Smith (1994). International Risk Sharing and Economic Growth, International Economic Review, 35: 535 550. [8] Diamond, D. and P. Dybvig (1983). Bank Runs, Deposit Insurance, and Liquidity, Journal of Political Economy, 91: 401 419. [9] Diamond, D. (1997). Liquidity, Banks, and Markets, Journal of Political Economy, 105: 928 956. [10] Huggett, M. (1993). The Risk Free Rate in Heterogeneous-agent, Incomplete Insurance Economies, Journal of Economic Dynamics and Control, 17: 953 970. [11] King, R. G. and R. Levine (1993). Finance, Entrepreneurship, and Growth: Theory and Evidence, Journal of Monetary Economics, 32: 513 542. [12] Levine, R. (1997). Financial Development and Economic Growth: Views and Agenda, Journal of Economic Literature, 35: 688 726. [13] Levine, R. (2002). Bank-based or Market-based Financial Systems: Which is Better?, Journal of Financial Intermediation, 11: 398 428. [14] Mankiw, N. G. and S. P. Zeldes (1991). The Consumption of Stockholders and Nonstockholders, Journal of Financial Economics, 29: 97 112. [15] Ohno, H (2009). Incomplete Market Participation, Endogenous Endowment Risks and Welfare, Journal of Economics and Business, 61 (5): 392 403. [16] Ohno, H (2010). Risk-Sharing Externalities and Its Implications for Equity Premium in an Infinite-Horizon Economy, AUCO Czech Economic Review, 4 (2): 168 188. [17] Romer, P. M. (1986). Increasing Returns and Long-run Growth, Journal of Political Economy, 94: 1002 1037. [18] Romer, P. M. (1987). Growth Based on Increasing Returns Due to Specialization, American Economic Review, 77: 56 62. [19] Vissing-Jorgensen, A. (2002a). Limited Asset Market Participation and the Elasticity of Intertemporal Substitution, Journal of Political Economy, 110: 825 853. [20] Vissing-Jorgensen, A. (2002b). Towards an Explanation of Household Portfolio Choice Heterogeneity: Nonfinancial Income and Participation Cost Structures, NBER Working Paper, No.8884. [21] Vissing-Jorgensen, A. and O. P. Attanasio (2003). Stock Market Participation, Inter-temporal Substitution, and Risk Aversion, American Economic Review, 93: 383 391. [22] Weil, P. (1992). Hand-to-mouth Consumers and Asset Prices, European Economic Review, 36: 575 583. [23] Williamson, S. (1994). Liquidity and Market Participation, Journal of Economic Dynamics and Control, 18: 629 670. ~ 60 ~

Appendix A1. Proof of Proposition 1 Review of Economics & Finance First, we illustrate that. The assumption ensures the following calculus: Now, Therefore, if the relationship is satisfied, then and are decreasing in. To prove the relationship, let us assume the following inequality: Squaring both sides, the following relationship is satisfied: Substituting the relationship relationship is satisfied: into the above inequality, the following Therefore, is smaller than. This implies that the variables and are decreasing in. In addition, if financial intermediaries allocate constrained-optimum consumption to consumers, the budget constraint of financial intermediaries can be obtained by We illustrate that is decreasing in : ~ 61 ~

ISSNs: 1923-7529; 1923-8401 2011 Academic Research Centre of Canada Since is the interior solution in, this implies that has negative values. Moreover, as illustrated above, is a negative value, which implies that is decreasing in. Hence, if financial intermediaries provide a market equilibrium allocation for consumers, financial intermediaries only use a partial resource. Consequently, a monotonic increase in the utility function implies Proposition 1. Q.E.D. A2. Proof of Proposition 2 Economic growth: This proof is based on the calculus. Here, and Subtracting from, we get Because of and, we only have to prove the following relationship: Squaring both sides, the LHS minus the RHS yields Hence, the relationship is satisfied. Social welfare: If financial intermediaries allocate to the consumers, the following expression is satisfied: As is smaller than one and, must be smaller than one. Hence, if financial intermediaries provide constrained optimum allocation for consumers, financial intermediaries can leave over resources. Consequently, a monotonic increase in the utility function implies Proposition 2. However, when ; this implies that the social welfare achieved with competitive financial intermediaries is equivalent to that achieved with complete market participation. Q.E.D. ~ 62 ~