Financial intermediation and the macroeconomy

Transcription

1 Financial intermediation and the macroeconomy Vincenzo Quadrini University of Southern California January 16, 2013 The financial crisis that developed starting in the summer 2007 has made it clear that macro studies need to assign a more prominent role to the financial sector not only for understanding the business cycle but also for understanding the long-term dynamics of the economy at the micro and macro levels. In this proposal I describe two main projects. The first project studies the role of the financial intermediation sector for the business cycle focusing on a novel transmission channel. The second project studies how some structural changes observed in the financial sector during the last three decades have contributed to the growth of the sector but also to greater income inequality. Broader impacts: The proposed research will have a broad scholarly impact in advancing our understanding of the interconnections between the financial sector and the real sector of the economy. In doing so, the research will be of interest for scholars and practitioners in both macroeconomics and finance. The broader impact of this research is also underscored by the fact that the proposal links two major strands of literature in macro: those focusing on the short-term dynamics and those focusing on the medium-term dynamics with a particular emphasis on heterogeneity. The proposal will help develop a new basis for research and teaching in macro-finance. It also offers new insights into the design of macro policies that could improve the functioning of financial markets. In particular, it will develop quantitative frameworks for studying the effects of macro-prudential policies and the desirability of redistributive policies. Project I - Bank asset channel Since the recent crisis, there has been a growing interest in embedding financial markets frictions in business cycles models. Even before the crisis, there was a well established tradition in macroeconomics adding financial market frictions in standard macroeconomic models. The seminal work of Bernanke and Gertler (1989) and later by Kiyotaki and Moore (1997) are the classic references for most of the work done in this area during the last 25 years. Although these contributions differ in many details ranging from the microfoundation of market incompleteness to the scope of the application, they typically share two common features. The first feature is that the role played by financial frictions in the propagation of shocks to the real sector of the economy is based on the typical credit channel. The idea is that various shocks can affect the financing capability of borrowers either in the volume of available credit or in the cost which in turn affects their economic decisions (consumption, investment, employment, etc.). The second common feature of pre-crisis models is that they assign a limited role to the financial intermediation sector. This is not to say that there were not contributions prior to the crisis that emphasized the role of banks for business cycle dynamics. The seminal paper by Holmstrom and Tirole (1997) provided a theoretical foundation for the central roles of banks in general equilibrium, inspiring subsequent contributions such as Van den Heuvel (2008) and Meh and Moran (2010). However, it is only after the recent crisis that the role of financial intermediaries has become central to the research agenda in macroeconomics. Recent contributions include Boissay, Collard, and Smets (2010), Brunnermeier and Sannikov (2010), Corbae and D Erasmo (2012), De Fiore and Uhlig (2011), Gertler and Karadi (2011), Gertler and Kiyotaki (2010), Mendoza and Quadrini (2010), Rampini and Viswanathan (2012). In the majority of recent contributions, the primary role of the intermediation sector is to channel funds to investors (borrowers). Because of frictions, however, the volume of funds that can be intermediated depends on the financial conditions of banks. When these conditions deteriorate, the volume of funds that 1

2 can be channeled to borrowers declines, which in turn affects investments and other economic decisions made by borrowers. Thus, the primary channel through which the financial intermediation sector affects real economic decisions is still the typical credit channel as in pre-crisis models without banks. The goal of this project is to study a second channel through which financial intermediaries can affect the real sector of the economy. Banks are not only important for channeling resources from agents in excess of funds to agents in need of funds (credit channel). They are also important for creating financial assets that can be used for insurance purposes. This point can be illustrated with an example. Suppose that a bank issues 1 dollar liability and sells it to agent A (bank deposit). The dollar is then used by the bank to make a loan to agent B. By doing so the bank facilitates a more efficient allocation of resources because, typically, agent B is in a condition to create more value than agent A (either because of higher productivity or higher marginal utility of consumption). However, if the bank is unable to issue the dollar liability, it cannot make the loan to agent B, who is forced to cut investments and/or consumption. This is the standard credit channel of financial intermediation. At the same time, when the bank issues the dollar liability, it creates a financial asset that can be held by agent A. The holding of the asset could affect the risky choices of agent A because the asset allows for better insurance. It is through the supply of liabilities, in addition to the supply of loans, that financial intermediaries could have important effects on real economic decisions. Thus, when the financial conditions of banks deteriorate and they are forced to reduce the supply of liabilities, agents in the non-financial sector become more risk-averse in their economic decisions, including investing and hiring. Through this mechanism, the difficulties in the financial intermediation sector are transmitted to the whole economy. I will refer to this channel as the bank asset channel. Although the example illustrates a possible channel through which difficulties in the financial intermediation sector are transmitted to the economy at large, it does not explain why the intermediation sector may face difficulties. The second goal of this project is to investigate the possibility that these problems are driven by pessimistic self-fulfilling expectations about the liquidity of the whole sector. The model features multiple equilibria in which the liquidity of banks is central to the multiplicity: when the market expects the intermediation sector to be liquid, banks can raise funds in financial markets and are ex-post liquid. On the contrary, when the market expects the intermediation sector to be illiquid, banks are unable to raise funds and face liquidity shortage. As we will see, this has very important policy implications. 1 Empirical motivation The focus on the banks asset channel and on self-fulfilling banking crises is of interest not only from a theoretical point of view but also from an empirical stand point. It is well known that during the last three decades, US corporations have increased the stock of liquid assets. Furthermore, some studies have shown that only a minority of corporations rely on external finance to fund investments. Although smaller firms seem to be more dependent on external financing, the economy-wide dependence is not very large. See, for example, Shourideh and Zetlin-Jones (2012). Along the same lines, Eisfeldt and Muir (2012) shows that corporations tend to raise external finance and to accumulate liquid assets simultaneously. Adrian, Colla, and Shin (2012) shows that, although bank credit contracted sharply during the recent crisis, corporations compensated part of the decline with direct market borrowing (corporate bonds). These studies suggest that, if the credit channel is the primary mechanism through which problems in the financial intermediation sector are transmitted to the rest of the economy, then the macroeconomic impact is unlikely to be large. The reason is because, even if firms are forced to cut their financing from banks, they can still use their sizable cash holdings to finance investment and employment. This point is especially important for the sluggish recovery in the aftermath of the recent crisis. Although the credit channel may have played an important role in the early stage of the crisis, there is skepticism about its impact on the labor market s sluggish recovery. As shown in Figure 1, the liquidity held by US businesses contracted during the crisis, which is consistent with the view of a credit crunch. However, after the initial drop, the liquidity of nonfinancial businesses quickly rebounded and, shortly after the crisis, firms were holding more liquidity than before the crisis. It is in this context that we can appreciate the potential relevance of the bank asset channel. One hypothesis is that firms have been unwilling to make more investments and hire more workers because, in the absence of a well functioning banking sector, they 2

3 face lower insurability of risks. 1 8 Liquid assets/gdp Figure 1: Liquidity in the US nonfinancial business sector in percentage of GDP. Liquidity is the sum of foreign deposits, checkable deposits and currency, time and savings deposits. The choice to model banking crises as self-fulfilling equilibria is also motivated by empirical considerations. In particular, it is known that financial crises are sudden events that cannot be easily connected to unambiguous fundamental shocks. Furthermore, there is now a great deal of empirical evidence about the dynamics that proceed and follow a financial crisis. See, for example, Reinhart and Rogoff (2009) and Schularick and Taylor (2011). While economic booms are characterized by a gradual expansion of credit, recessions are more sudden and they are typically associated with a fast decline in credit. Furthermore, the higher the leverage of the banking sector, stronger is the contraction of the real economy. The next section describes a model with self-fulfilling bank crises capable of replicating the dynamics described here. 2 Model There are three sectors: the business sector, the household sector and the financial intermediation sector. I first describe the business and household sectors and show that in equilibrium there will be a flow of funds going from the household sector to the business sector. This allows me to illustrate the asset channel and to differentiate it from the credit channel. The importance of financial intermediaries emerges if the financial flows from the household sector to the business sector cannot take place without the intermediation of banks. I will then describe the structure and operations of financial intermediaries and show that the performance of the real sector depends on the financial conditions of banks. 2.1 Business sector There is a continuum of undiversified entrepreneurs with lifetime utility E 0 t=0 βt ln(c t ). Entrepreneurs are individual owners of firms, each operating the production function F (z t, h t ) = z t h t, where h t is the input of labor supplied by households at the market wage w t and z is an idiosyncratic productivity shock that is observed after the input of labor. The productivity shock is independently and identically distributed among firms and over time, with probability distribution Γ(z). Following Arellano, Bai, and Kehoe (2011), I assume that h t is chosen before observing z t and, therefore, the choice of labor is risky. This is an important property of the model and it is central for generating the asset channel described above. Entrepreneurs have access to a market for non-contingent bonds with gross interest rate Rt. b Entrepreneur i enters period t with risk-free bonds b i t and chooses the labor input h i t. After the realization of the idiosyncratic shock zt, i the entrepreneur chooses the next period bond b i t+1. The budget constraint is c i t + bi t+1 R b t = (z i t w t )h i t + b i t. (1) Because the choice of labor h i t is made before the realization of z i t while the saving decision is made after the observation of z i t, it will be convenient to define the entrepreneur s wealth after production 1 Risk can take the form of insolvency. Atkeson, Eisfeldt, and Weill (2012) find that the most recent recession was characterized by a collapse in financial soundness of all firms. 3

4 a i t = b i t + (zt i w t )h i t. The choice of h i t depends on b i t while the choice of b i t+1 depends on a i t. The following lemma defines some of properties of the firm/entrepreneur s policies. ( ) z w Lemma 2.1 Define φ t the solution to the condition E t z z w t+φ t = 0. The optimal policies are given by h i t = φ t b i t, c i t = (1 β)a i t, b i t+1 = βr b ta i t. According to the lemma, the demand of labor is linear in the initial wealth of the entrepreneur b i t. The factor of proportionality φ t changes over time but it is the same for all entrepreneurs since it depends, negatively, only on the wage rate. To make this dependence explicit, I will use the notation φ(w t ) where φ (w t ) < 0. I can then derive the aggregate demand of labor as H t = φ(w t ) b i t = φ(w t )B t. i The aggregate demand of labor depends negatively on the wage rate which is the typical property and positively on bonds which is a special property of this model. In a general equilibrium, the stock of bonds held by entrepreneurs depends on the ability of the system to supply bonds. The role of financial intermediaries is to facilitate the creation of these financial assets. Also linear is the consumption policy of entrepreneurs. This property allows for linear aggregation and makes the problem extremely tractable. Therefore, even if entrepreneurs are heterogeneous in asset holdings, for the aggregate dynamics of the model we only need to keep track of the average wealth B t. The last property I would like to emphasize is that in a stationary equilibrium in which B t converges to a constant value, the interest rate must be lower than the intertemporal discount rate, that is, R b < 1/β 1. To see this, consider the first order condition of an individual entrepreneur in the choice of b t+1. This is the typical euler equation that, with log preferences, takes the form, 1 c i t = βr b E t ( 1 c i t+1 Because c i t+1 is stochastic, E t (1/c i t+1) > 1/E t c i t+1. Therefore, if βr b = 1, we would have that E t c i t+1 > c i t and aggregate consumption would not be bounded. This violates the hypothesis of a stationary equilibrium. I will come back to this property after the description of the household sector. 2.2 Household sector and general equilibrium ) There is a continuum of households with lifetime utility E 0 t=0 βt ln (c t α h1+ν t 1+ν, where c t is consumption and h t is the supply of labor. Each household holds a non-reproducible asset available in fixed supply K. The asset is divisible and can be traded at the market price p t. Each unit produces χ units of consumption goods. We can think of the asset as housing and χ as the services from one unit of housing. Households can borrow but face the collateral constraint, ). l t+1 R l t ηk t+1 p t, where l t+1 is the loan contracted in period t and due in period t + 1, R l t is the gross interest rate and η is the fraction of the asset recovered by lenders if the household defaults. The budget constraint is c t + l t + (k t+1 k t )p t = l t+1 R l t + w t h t + χk t. Households do not face idiosyncratic risks and their policies satisfy the first order conditions, αh ν t = w t, U c (c t, h t ) βr l te t U c (c t+1, h t+1 ), U c (c t, h t ) βe t U c (c t+1, h t+1 )(χ + p t+1 ), 4

5 where the last two conditions are satisfied with inequality if the collateral constraint is binding. Before describing the financial intermediation sector, I first consider the general equilibrium where borrowing and lending is done without financial intermediaries and R l t = R b t = R t. Proposition 2.1 In a stationary equilibrium households borrow up to the limit and βr < 1. Since entrepreneurs face uninsurable risks, they would save and hold bonds if βr = 1. However, to induce households to issue bonds, the interest rate must decline. Once the interest rate is lower than the intertemporal discount rate, households will continue to borrow until the collateral constraint binds. The equilibrium in the labor market can be characterized as the simple intersection of aggregate demand and supply. The aggregate demand has been derived in the previous subsection and it is equal to H d t = φ(w t )B t, with φ (w t ) < 0 and B t are the financial assets (bonds) held by the business sector. The supply of labor is given by the households first order condition derived above and it is equal to H S t = (w t /α) 1/ν. The equilibrium in the labor market is depicted n Figure 2. H t Labor supply Ht S = ( w t ) 1 ν α Labor demand Ht D = φ(w t)b t Figure 2: Labor market equilibrium. The important property of the model is that the labor demand depends on B t. Suppose that the parameter η declines so that households are forced to cut their borrowing L t. Since in equilibrium L t = B t, this shifts the demand for labor inward and results in lower employment and wages. Importantly, the reason lower credit decreases the demand of labor is not because employers have less funds to finance hiring. In fact, there is no need of any financing for production. Instead, the reason is that the business sector does not have enough assets to insure the production risk. This mechanism, which I termed asset channel, is clearly distinct from the credit channel where firms are in need of funds to finance employment (for example because the wages are paid in advance) and a credit contraction impairs their ability to produce. Of course, if households could issue market securities directly, there is no need of financial intermediaries. However, if direct borrowing is not feasible or costly, financial intermediaries play an important role. It is under this assumption that I now introduce the banking sector. 2.3 Banking sector There is a continuum of investors with lifetime utility E 0 t=0 βt ln(c t ). They are the owners of banks and can trade shares with other investors. A difference between investors and entrepreneurs is that the latter are not diversified while investors own a diversified portfolio of banks. Since investors are homogeneous and earn only capital incomes, their consumption is equal to the dividends paid by banks, d t. Thus, he effective discount factor for investors is m t+1 = βd t /d t+1. This is also the discount factor for banks. Banks start the period with loans l t and liabilities (deposits) b t. During the period they choose new loans, l t+1, new liabilities, b t+1, and dividends, d t. The interest rates on loans and liabilities are, respectively, R l t and R b t. The bank also faces a convex operation cost ϕ(l t ) and the budget constraint is b t + ϕ(l t ) + l t+1 R l t 5 w t + d t = l t + b t+1 Rt b, (2)

6 Banks can default on their liabilities. Default takes place at the end of the period, after investing and paying dividends. At this stage the assets of the bank are l t+1. After defaulting, the creditors of the bank gain the right to liquidate the bank s assets. Suppose that the liquidation value is ξ t l t, where ξ t could be stochastic. To ensure that the bank does not default, the bank faces the enforcement constraint b t+1 R b t l t+1 ξ t Rt l. (3) The variable ξ t will be derived endogenously. For the moment, however, ξ t will be treated as an exogenous stochastic variable and, to illustrate the role played by fluctuations in ξ t, consider a pre-shock equilibrium in which the enforcement constraint is binding. Starting from this equilibrium, suppose that ξ t decreases. This forces the bank to reduce either dividends and/or investments. 2 The optimal choice depends on the relative cost of these two margins which, as we will see, depends on the stochastic discount factor m t+1 = βd t /d t+1. The optimization problem of the bank can be written recursively as { } V t (b, l) = max d,b,l d + Em V t+1 (b, k ) subject to: b + d + l b = l ϕ(l) + Rl R b (5) b ( ) l R b ξ R l, (6) where the prime denotes the next period variable. The first order conditions are R b Em = 1 µ, (7) R l Em = 1 µξ 1 ϕ l (l ), (8) where µ is the Lagrange multiplier for the enforcement constraint. These conditions are derived under the assumption that dividends are always positive, which will be the case when investors have log preferences. Equation (7) and (8) determine the interest rates on bank liabilities and loans. If we abstract from the operational cost and set it to ϕ(l) = 0, we can see that the two interest rates must be equal when the enforcement constraint is not binding. However, if the enforcement constraint is binding, the loan rate is higher than the interest rate on bank liabilities. Therefore, the multiplier µ determines the spread between the two rates: in periods in which banks face binding constraints, the spread increases. The characterization of the bank s problem provides insights about the property of the model once integrated in a general equilibrium. A decrease in ξ makes the enforcement constraint tighter. Because all banks reduce dividends, the consumption of investors decreases. This induces a decline in the discount factor m = βd/d and an increase in the multiplier µ (see equation (7)). From (8) we can then see that bank loans decline. In fact, since in the right hand side µ is multiplied by ξ < 1, the term 1 ϕ l (l ) must increase, which requires a reduction in l. Intuitively, when the credit conditions become tighter, banks need to rely more on equity and less on debt. This requires investors to cut consumption which is costly due to the concavity of the utility function. Because of this, in the short-term banks do not raise enough equity to maintain the pre-shock scale and cut lending. (4) Endogenous ξ t The variable ξ t is now interpreted as the liquidation price of bank assets and the endogeneity is based on the following two assumptions. 2 To see why, let s start with the case in which the firm does not change investments l t+1. Consequently, the only way to satisfy the enforcement constraint, equation (3), is by reducing b t+1. We can then see from the budget constraint (2) that the reduction in b t+1 requires a reduction in dividends. Thus, the bank is forced to substitute debt with equity. Alternatively, the bank could keep the dividends unchanged. However, if it chooses to do so, we can see from the budget constraint (2) that this would require the same b t+1. But keeping the same b t+1 and l t+1 would violate the enforcement constraint. 6

7 Assumption 1 In the event of liquidation, the bank s assets l are perfectly divisible and can be sold either to other banks or to other sectors (households or entrepreneurs). However, banks can recover a fraction ξ of the liquidated assets while other sectors can recover the smaller fraction ξ < ξ. Assumption 2 Banks can purchase the assets of liquidated banks only if they have liquidity. Thus, the sales of liquidated assets to other banks is more efficient. However, the sales to other banks is possible only if banks can raise additional funds (issue additional liabilities). To better understand this assumption, consider the enforcement constraint (3), where now ξ t is the end-of-period price of banks assets. If at the beginning of the period banks choose to borrow less than the limit, that is, the enforcement constraint is not binding, they have the option to raise additional funds at the end of the period to purchase the capital of defaulting banks. Therefore, ex-post, there will be banks that have the ability to purchase the investments of a defaulting bank. In this case the market price of liquidated assets is ξ t = ξ. However, if at the beginning of the period banks choose to borrow up to the limit, at the end of the period there will not be any bank with the required liquidity (unused credit). Thus, the liquidated assets can only be sold to non-banks and the price will be ξ t = ξ. Under assumptions 1 and 2, the value of liquidated assets depends on the financial choice of banks, which in turn depends on the expected liquidation value of their assets. This interdependence allows the model to generate self-fulfilling equilibria. Suppose that the expected liquidation price is ξ t = ξ. The low price makes the enforcement constraint (3) tighter, which may induce banks to borrow up to the limit in order to contain the reduction in dividends and/or loans. Then, if all banks borrow up to the limit, there will not be any bank, ex-post, that has the liquidity to purchase the assets of defaulting banks. Thus, the ex-post liquidation price will be ξ t = ξ, fulfilling the market expectation. Now suppose that the expected liquidation price is ξ t = ξ. Because the enforcement constraint (3) is not tight in the current period but could become tight in the future, banks may choose not to borrow up to the limit for precaution. But then, in case of liquidation, there will be banks with liquidity needed to purchase the liquidated capital and the market price will be ξ t = ξ. So also in this case we have that the ex-ante expectation of a high liquidation price will be fulfilled by the banks borrowing choice. Whether both equilibria with tight and loose credit are possible depends on the aggregate states s t = (B t, L t ). Three cases are possible: 1. The liquidation price is ξ with probability 1. This arises if we are in a state s t in which banks borrow up to the limit independently of the expected price ξ t. 2. The liquidation price is ξ with probability 1. This arises if we are in a state s t in which banks do not borrow up to the limit independently of the expected price ξ t. 3. The liquidation price is ξ with some probability p (0, 1). This arises in a state s t in which banks borrow up to the limit when the expected price is ξ t = ξ but do not borrow up to the limit when the expected price is ξ t = ξ. The third case allows for sunspot equilibria. Denote by ε {0, 1} a non-fundamental shock (sunspot). This variable takes the value of zero with probability p (0, 1) and it is serially uncorrelated. We then define p(s t ) the probability of an equilibrium with binding enforcement constraints and low liquidation price ξ t = ξ. The economy will then fluctuate between tight and loose credit equilibria in response to changing expectations about the liquidation price ξ t. 3 Extension and policy implications The model presented above is very stylized. This has been a deliberate choice to facilitate the presentation of the theory. The next step, however, would be to use the model to address quantitative questions such as the importance of the asset channel for the propagation of shocks that affect directly the banking sector. For that purpose I plan to extend the model with the ingredients that are now common in macroeconomic models. For example, the extension with capital accumulation. The quantitative analysis will also explore 7

8 the ability of the model to capture the key dynamic features of financial crises as characterized, for example, in Reinhart and Rogoff (2009) and Schularick and Taylor (2011). Another important goal of this project is to conduct a normative analysis with special attention to macro-prudential policies. In particular, the project will explore: Minimum capital requirement. As it is typically the case in models with multiple equilibria, government interventions could prevent the economy from switching to bad equilibria. In the model described here, this can be easily achieved by imposing limits to bank leverage: the reason the economy switch to a bad equilibrium is because banks choose too much leverage 3 and because of this, pessimistic expectations can place them in an illiquid state. However, in recommending restrictions to bank leverage, we also have to consider that lower leverages reduce the assets held by entrepreneurs which reduce the demand of labor. This is also inefficient. Therefore, macroprudential policies have to trade-off the benefits of avoiding bank crisis from the benefits of a more efficient allocation of resources allowed by larger financial markets. Price guarantees. Another type of policy would be for the government to stand ready to purchase bank assets in the eventuality of a crisis. This policy is specific to the multiplicity of equilibria. By committing to buy bank assets at the price ξ, the government insures the uniqueness of the equilibrium. In fact, by standing ready to purchase bank assets, the low price ξ cannot be an equilibrium outcome. This would have the advantage not only of avoiding crisis, but will also improve the allocation in the good equilibrium. In fact, by insuring that the price will never fall to ξ, banks are willing to issue more liabilities which increases the demand of labor through the asset channel described earlier. Effectively, banks will borrow up to the limit because they do not fear a fall in ξ t. Without the government price guarantee, this would not be an equilibrium because, by borrowing to the limit, banks become illiquid. However, government intervention guarantees the liquidity of the market even if the banking sector is not. 4 Government debt. Banks are not the only institutions that can create financial assets used as saving vehicles. The government also creates safe financial assets when it finance expenditures with public debt. The role of the government as a provider of safe assets has also been explored in Azzimonti, de Francisco, and Quadrini (2012) but in a model with exogenous labor supply and without aggregate uncertainty. The model developed here shows that the counter-cyclicality of government debt could motivated not only by the standard tax smoothing arguments but also by the need to compensate the reduction in the supply of assets from the financial sector during crises. Another extension is the consideration of asset bubbles. Financial intermediaries could also be important for creating bubbles. In this economy, bubbles could be efficient because they represents saving vehicles. At the same time, however, bubbles can burst and when that happens it could have significant macroeconomic consequences. As part of the project I plan to explore asset bubbles created by the banking sector following the approach proposed by Miao and Wang (2011) and Miao and Wang (2012). I will then study the design of desirable policies in the presence of bubbles. Project II - Risky financial investments, growth and inequality This project, which is in collaboration with Thomas Cooley and Ramon Marimon, is motivated by the observation that the size and structure of the financial sector have changed dramatically during the last three decades. As shown in the first panel of Figure 5, the financial industry accounted for roughly 4% of GDP in 1970 but reached 8.2% in 2006; employment in the financial sector increased from 4.5% of total nonfarm employment to about 6%. The increase in size was associated with a sharp increase in compensation. Clementi and Cooley (2009) show that between 1980 and 2007 the average compensation in the financial sector increased from parity 3 Therefore, the model features over-borrowing as in Bianchi (2011). 4 In reality, of course, this policy is not easy to implement because of moral hazard problems: if the government guarantees a fixed price, what prevents banks from selling bad assets to the government? Nevertheless, the theoretical analysis hinted here provides some insights about the preferred structure of macroprudential policies. 8

9 9 Economy wide contribution of Finance and Insurance 60 Income share of top 5 percent Value added (% Total GDP) Employment (% Nonfarm) Managerial occupations in financial sector Other occupations Figure 3: Size of financial sector and Share of income of the top 5%. to 181% of other sectors of the economy. At the same time, the compensation of managers became more unequal in the financial sector. This is clearly shown in the second panel of Figure 5 which plots the evolution of the income share of the top 5% of managers in the sector as compared to other occupations. This period was also characterized by important changes in the organizational form of financial firms. Historically, it was common for investment firms to be organized as partnerships. Many argued that this was a preferred form of organization because in a partnership, the managers and investors were the same entities. Thus, when risks were taken, the partners own assets were at risk. In fact, a partnership can be interpreted as an organizational structure where the separation between ownership and investment control is minimized and with it the typical agency issues studied in contract theory. Public companies, by contrast, are organizational structures with a separation between ownership (shareholders) and investment control (managers) and are characterized by significant agency problems. As the structure of financial firms changed, so did the evaluation of them. The market does not seem to value highly the large complex financial institutions that characterize world financial markets today. Figure 4 plots the evolution of the ratio of average market value of equity to book value of equity and shows that, since the early 1980 s, for financial firms the ratio has been flat while for non-financial firms it has continued to grow. Average Market Equity to Book Equity Ratio Financial Firms (dash), Non-Financial Firms (solid) Ratio Year Figure 4: Average Market Value of Equity/Book Values of Equity To understand these changes, this project develops a model where investors compete for managers to run investment projects, with each investor-manager pair representing a financial firm. A key feature of the model is that production depends on the human capital of the manager which can be enhanced within the firm with costly investment. Since part of the accumulated human capital can be transferred outside the firm by the manager, there is a conflict of interest between the investor and the manager. In this environment, the investment desired by the investor may be smaller than the investment desired by the manager because the cost is incurred by the firm while the benefits are shared. This implies that, if the 9

10 investor cannot control the investment policy either directly or indirectly through a credible compensation scheme, the manager has an incentive to deviate from the optimal policy simply because it does not internalize the full cost of the investment. By embedding the financial sector in a general equilibrium model, the project investigates the importance of the organizational changes for explaining 1) Higher risk-taking; 2) Increased size of the financial sector; 3) Lower stock market valuation of financial institutions; 4) Greater income inequality within and between sectors (financial and nonfinancial). 1 The model The financial sector is characterized by firms regulated by a contract between an investor (the owner) and a manager. The expected lifetime utility of managers is Q 0 = E t t=0 β t[ ] ln(c t ) e(λ t ), where C t is consumption and e(λ t ) is the dis-utility from effort required for the implementation of investment projects as described below. The period utility satisfies u > 0, u < 0 and e > 0, e > 0, e(0) = 0 and e(1) =. Investors are risk neutral with expected lifetime utility V 0 = E t t=0 The income generated by the firm in period t is equal to the human capital of the manager, h t. Human capital can be increased over time by investing in risky projects of size λ t [0, 1]. Given the choice of λ t, the firm incurs the investment cost κh t λ t and the next period human capital evolves according to β t C t. h t+1 = (1 + λ t ε t+1 )h t. The variable ε t+1 {0, ε} is an iid stochastic variable with probability distribution {1 p, p}. The stochastic nature of ε t+1 implies that investment is risky. To use a compact notation, we define y(λ t ) = 1 κλ t the income per unit of human capital net of the of the investment cost, and g(λ t, ε t+1 ) = 1 + λ t ε t+1 the gross growth rate of human capital. Then the net income generated by the firm and the evolution of human capital are, respectively, Y t = y(λ t )h t, h t+1 = g(λ t, ε t+1 )h t. The cost of the investment has two components. The first is the pecuniary cost κh t λ t incurred by the firm. The second is the dis-utility e(λ t ) incurred by the manager. If the manager chooses to quit, the pecuniary cost is paid by the firm but the benefit goes to the manager in the form of higher human capital. This creates a conflict of interest between investors and managers. Managers have the option to quit and search for an offer from a new firm/employer. If they choose to quit, they will receive an offer with probability ρ [0, 1]. The probability ρ captures the degree of competition for managers, that is, the easiness to start a new contract after quitting the current firm. Higher values of ρ denote more competitive economies. Denote by Q t+1 (h t ) the outside value without an external offer and by Q t+1 (h t+1 ) the outside value with an offer. Thus, the expected outside value after the realization of ε t+1 is D(h t, h t+1, ρ) = (1 ρ) Q t+1 (h t ) + ρ Q t+1 (h t+1 ). For the moment we take ρ and Q t+1 (h t ) and Q t+1 (h t+1 ) as given. However, in the later extension to a general equilibrium, they will be derived endogenously. 5 5 Notice that the outside value without an offer depends on h t while the outside value with an external offer depends on h t+1. This is motivated by the assumption that the new project will increase the human capital of the manager only if the project is implemented. However, if the manager decides to quit and does not receive an external offer, the new project will not be implemented and the human capital of the manager remains h t. 10

11 The manager has also the control of the investment and, therefore, she could choose λ t different from the value that maximizes the surplus of the partnership. This generates a second source of contractual frictions. Definition 1 (Contract) A contract is a sequence of payments to the manager {C t } t=0 and investments {λ t } t=0 conditional on the initial human capital h 0 and the history of shocks {ε t } t=1. Implicit in this definition is the assumption that the payments made to the manager in period t, cannot be conditional on the actual investment λ t chosen by the manager also in period t. 1.1 The normalized contract To simplify the exposition, we make special assumptions about the outside values of managers. properties will actually hold in the extension to a general equilibrium. These Assumption 3 The outside values of managers take the form ( ) 1 Q t+1 (h t ) = q + ln(h t ), 1 β ( ) 1 Q t+1 (h t+1 ) = q + ln(h t ). 1 β Since h t grows on average over time, the values of the contract for investors and managers are in general non-stationary. Therefore, it becomes convenient to use a transformation that makes all variables stationary in levels. We can then write the contractual problem following the promised utility approach. When the investor commits to the contract (one-side limited commitment), the optimal contract maximizes the investors value subject to the promise-keeping, limited enforcement and incentive-compatibility constraints. In normalized form this can be written as v(q) = max λ,c,q(ε ) { y(λ) c + βeg(λ, ε )v subject to [ ( ) ] q = ln(c) + α ln(1 λ) + βe B ln g(λ, ε ) + q ( ) q(ε) (1 ρ)q + ρ q (1 ρ)b ln g(λ, ε ) ( βe t [q + B ln g(λ, ε )) ] α ln ( 1 ˆλ 1 λ ( q(ε )) } (9) ) + βe (10) (11) [ ( (1 ρ)q + ρ q + ρb ln g(ˆλ, ε )) ] (12) where B = 1 1 β. Lower letters denote stationary (normalized) values6 and ˆλ is the investment that maximizes the manager outside value net of the dis-utility from effort. Constraint (12) insures that the manager does not chooses ˆλ (incentive-compatibility). Constraint (11) is the enforcement constraint and insures that the manager does not quit the firm. Constraint (10) is the promise-keeping condition. If there is limited commitment also from the investor (double-sided limited commitment), promised utilities q(ε ) that exceed the outside value of the manager will be renegotiated. Because of this, the objective of the manager is always to maximize the outside value net of the dis-utility of effort. Thus, λ = ˆλ and the contract solves the problem { ( v(q) = max y(ˆλ) c + βeg(ˆλ, ε)v q(ε)) } (13) c,q(ε) subject to q = ln(c) + α ln(1 ˆλ) [ ( ) ] + βe B ln g(ˆλ, ε) + q(ε) ( ) q(ε) = (1 ρ)q + ρ q (1 ρ)b ln g(ˆλ, ε), for all ε. 6 The values of the contract for the investor and the manager are normalized, respectively, as v = V/h and q = Q B ln(h). 11

12 This problem is a special case of (9) where we have replaced the incentive-compatibility constraint (12) with λ = ˆλ. Furthermore, we have imposed that the enforcement constraint (11) is always satisfied with equality since any promises that exceed the outside value of the manager will be renegotiated down. 1.2 Contract properties The top panels of Figure 5 depict the values of next period (normalized) continuation utilities, q(ε), as a function of current period (normalized) utility, q, for two environments: one-side limited commitment (where the investor commits but the manager does not) and double-sided limited commitment (where both the investor and the manager do not commit to the long-term contract). Figure 5: Continuation utilities and investment. Consider first the case of one-sided limited commitment (first panel). The utility received when the investment succeeds, ε = ε, is lower than the utility when the investment fails, ε = 0. These, however, are normalized utilities: The next period non-normalized utility is higher when ε = ε. The fact that q( ε) < q(0) simply means that the non-normalized utility grows less than the growth of h t+1, which is a consequence of the insurance provided by the optimal contract. Therefore, the value of the contract for the manager, relatively to human capital h, declines on average over time. As the normalized utility reaches a minimum and the lower bound on q(ε ) binds, the contract can no longer provide insurance and consumption grows at the same rate as h. In terms of normalized utilities this means that q( ε) = q(0). The case with double-sided limited commitment is depicted in the second panel of Figure 5. In this environment the manager always receives the outside value, with the exception of the first period as indicated by the vertical line. Therefore, q jumps immediately to the outside value after the initial period. After that it fluctuates between two values. The fact that the initial q is higher than subsequent values implies that in the first period the manager receives a higher initial payment (consumption) relatively to the human capital h. The third panel of Figure 5 plots the innovation variable λ. In the environments with one-sided limited 12

13 commitment, λ first increases with promised utility, and then gradually declines. The increasing section can be explained as follows. The investor would like to keep λ low because this increases the outside value of the manager which requires higher promised utility. The cost of the higher utility in terms of consumption is greater than the benefit from higher production. Thus, the optimal investment is inefficiently low. However, the manager strategically chooses higher λ s in order to increase the value of the contract through the increase in the outside value. This mechanism, of course, is relevant only when the enforcement constraint is binding. If the promised utility is above a certain threshold, the enforcement constraint is no longer binding, and λ is chosen efficiently. The subsequent declines is a consequence of the income effect in the supply of effort: as manager s consumption increases, she requires higher compensation for effort. In the environment with double-sided limited commitment λ is independent of q. Given the limited commitment from the investor, the manager knows that her value is always equal to the outside value. Since she is not constrained in the choice of λ, the objective of the manager is to choose the investment that maximizes the outside value net of the dis-utility of effort. In doing so, the manager does not take into account that innovations also imply the cost κλh for the firm. Thus, investment is inefficiently high. 2 General model There are two sectors in the model financial and nonfinancial and three types of agents a unit mass of investors, a unit mass of skilled workers, and a mass N of unskilled workers. Unskilled workers are only employed in the nonfinancial sector while skilled workers can be employed in either sectors. Investors are the owners of firms. All agents have the same utility ln(c t ) + α ln(1 λ t ). To simplify the analysis, we assume that only managerial occupations in the financial sector require effort λ t. Therefore, the utilities of investors, unskilled workers and skilled workers employed in the nonfinancial sector reduce to ln(c t ). All agents survive with probability 1 ω. In every period there are newborn agents of each type so that the population size and composition remain constant over time. Newborn skilled workers are endowed with initial human capital h 0 while the human capital of unskilled workers is normalized to 1. The motivation for adding this particular demographic structure is to prevent the distribution of h t to become degenerate. The assumption of a constant h 0 together with the finite lives of skilled workers guarantee that the distribution of h t across financial managers converges to an invariant distribution and the model is stationary in level. For notational convenience we define the effective discount factor as ˆβ = β(1 ω). Investors are the owners of firms in the financial sector. Since they are risk averse, they hold a diversified portfolio of firms. Thus, the assumption of risk neutrality for investors made in the previous section is justified by portfolio diversification. By further specializing to steady states, we can use ˆβ to discount future payments to investors. Only skilled workers can become managers in the financial sector. We denote by S the mass of skilled workers that are employed in the nonfinancial sector. Thus, 1 S is the mass of skilled workers employed in the financial sector (financial managers). The non-financial sector produces output with the technology Y t = F (N, H), where N is the number of unskilled workers and H is the aggregate efficiency units of labor supplied by skilled workers employed in the non-financial sector. This results from the aggregation of human capital of all skilled workers employed in the nonfinancial sector. In equilibrium, the human capital of skilled workers employed in the nonfinancial sector is h 0. Therefore, H = h 0 S. The production function is strictly increasing and concave in both arguments and homogeneous of degree 1 (constant returns). In equilibrium, the wages earned in the non-financial sector by unskilled and skilled workers per efficiency unit of labor are, respectively, w N = F N (N, H), w S = F H (N, H). Skilled workers can find occupation in the financial sector if matched with vacancies funded by investors. Denote by ρ t+1 the probability for a skilled worker to be matched with an open vacancy. Then, the lifetime utility of a skilled worker with human capital h currently employed in the non-financial sector is Q t (h) = ln(w S h) + ˆβ [ ] (1 ρ t+1 ) Q t+1 (h) + ρ t+1 Q t+1 (h). (14) In the general model, the value for a manager of not finding an occupation in the financial sector, Q t+1 (h), is the value of being employed in the nonfinancial sector. The function Q t+1 (h) is the value of a 13

14 new contract for the financial manager. The probability ρ t+1 and the outside values Q t+1 (h) and Q t+1 (h) are now endogenous and determined in the general equilibrium. Investors hold diversified portfolios of financial firms and in every period they search for managers (skilled workers) by posting vacancies. The funding of vacancies is also shared among investors in the sense that each investor holds a diversified portfolio of new vacancies. A vacancy specifies the human capital h and provides a value Q t (h) to the manager. This is the value of the long-term contract signed between the firm and the manager. The cost of posting a vacancy for a manager with human capital h is τh. Let I t (h) be the number of vacancies posted for managers with human capital h and U t (h) the number of skilled workers with human capital h in search of ( a managerial ) position in the financial sector. The number of matches is determined by the function m I t (h), U t (h) = mi t (h) η U t (h) 1 η. The probabilities that a vacancy is filled and a worker finds occupation are, respectively, φ t (h) = m(i t (h), U t (h))/i t (h) and ρ t (h) = m(i t (h), U t (h))/u t (h). 2.1 The impact of organizational changes We are now using the general model to study the impact of the organization changes described in the Introduction. These changes had two effects. The first is to facilitate the entry of new financial firms. The separation between investors and managers enlarged the base of potential investors who could fund new financial firms or expand existing ones. In the context of our model this is captured, parsimoniously, by a reduction in the vacancy cost τ. This generates more entry and, therefore, more competition for managers. The second effect of the changes in organizational structure is that it weakened the commitment of investors. In fact, while the limited commitment of managers was also a feature of the traditional partnership (each manager was not restrained from leaving the partnership), the commitment of investors was much stronger since investors and managers were, effectively, the same entities. Even from a legal stand point, it was difficult for a partnership to replace a partner without a consensual agreement. A feature of a corporation, instead, is the clearer separation between investors and managers. Once this separation takes place, investors (shareholders) can always replace managers and use this as a threat for the renegotiation of existing agreements. In the context of our model, this change is captured by a shift from the environment with one-sided limited commitment to the environment with double-sided limited commitment. Proposition 2.1 Consider the environment with double-sided limited commitment. The steady state associated with lower τ is characterized by 1) Higher risk-taking; 2) Larger size of the financial sector; 3) Lower stock market valuation; 4) Higher income inequality within and between sectors. Therefore, the model with double-sided limited commitment captures some of the salient features observed in the US economy during the last three decades. Table 1 reports the steady state values of some key variables for two values of τ. As can be seen from the table, the probability of receiving offers increases with more competition. Since this increases the outside value for the manager, a larger share of the return from the innovation must be shared with the manager. Therefore, innovations become less attractive for the investor. In contrast, when neither managers or investors commitment, more competition leads to more innovation. Also in this environment the probability of external offers increases, which raises the external value of financial managers and makes innovation less attractive for investors. Thus, it would be preferable for investors to promise adequate future compensation in order to implement the optimal λ. The problem is that future promises are not credible in this environment and the only way the manager can increase his/her contract value is by increasing the outside value. This is achieved by choosing higher λ, which is true for any value of τ. However, with a lower τ, the probability of an external offer ρ increases, which raises the manager s incentive to choose a higher ˆλ. So far we have shown that the environment with double-sided limited commitment can generate higher risk-taking as a result of higher competition. We now show that this environment can also capture other important changes observed in the US economy. As shown in Table 1, a lower τ is associated with a larger fraction of financial managers, implying an expansion of the sector. Also, a lower τ is associated with a lower value for investors (relative to human capital). These two properties are consistent with the observed expansion of the financial sector and the decline in stock market valuation of financial institutions. 14