The Macroeconomics of Credit Market Imperfections (Part I): Static Models

The Macroeconomics of Credit Market Imperfections (Part I): Static Models Jin Cao 1 1 Munich Graduate School of Economics, LMU Munich Reading Group: Topics of Macroeconomics (SS08)

Outline Motivation Bridging finance towards macro What s new Static Partial Equilibrium Models Homogeneous agents Heterogeneous agents More complicated cases Static General Equilibrium Models A model with depositors An open economy extension An international trade extension

Problem: Introducing financial sector in macro It is extremely desired to introduce financial sector in macro: Financial sector is gaining importance in economy, one of main resources of funding; Micro foundation for better understanding of macro, e.g. economic growth, monetary policy, financial globalization, etc. However, it s not straight forward to do so: Financial sector is too complicated, reality versus tractability; Severe technical problems, especially in dynamic macro Heterogeneity: challenging representative agent modelling; Discontinuity and non-monotonicity: challenging dynamic optimization.

New framework of finance in a macro context Compact, stylized model of credit market capturing key effects Credit market imperfections, and resulting financial constraints; The effects of lender & borrower s book value Capital deepening effect versus net worth effect. Tractable ways of bridging finance with macro Heterogeneities? Inequalities, open economy macro, etc; Dynamic? Augmented OLG models (credit market between young & old). Rich extensions in economic growth, international trade, financial globalization, economic transitions, etc.

Preferences, technology, and timing A Continuum of homogeneous agents with unit mass, prefer to consume at T = 1. T = 0: The agent is endowed with ω < 1 unit of input Non-divisible investment project, converting one unit of the input into R units of capital in period 1, by borrowing 1 ω at the market rate r. Then produce consumption goods with NC technology y = f (k), with f > 0 > f ; Lending ω input and receive rω units of consumption good in period 1 Profitability constraint (PC): Rf (k) r. T = 1: The agent consumes, with utility function U = Rf (k) r(1 ω), if she runs the project (entrepreneur, borrower); U = rω, if she lends her endowment (lender).

Credit market imperfection: borrowing constraint ω: Entrepreneur s net worth, firm s balance sheet, the borrower s creditworthiness... The agent can borrow and invest only if borrowing constraint (BC) satisfied: λrf (k) r(1 ω). Measure of agency problem: λ < 1 Reasons: Strategic default, renegotiation, and inalienable human capital (Hart & Moore, 1994); Moral hazard (hidden action), etc. Interpretations: Institutional quality; The state of financial development, etc.

Example: Motivating λ by incomplete contract In T = 0 a borrower needs to borrow 1 ω to kick off her project, promising the lender a rate weakly higher than market rate r. And the project is used as collateral; Inalienable human capital: The project yields Rf (k) in T = 1 if run by the borrower, but λrf (k) (λ < 1) if run by anybody else; Then in T = 1 the borrower may want to renegotiate and bargain down r A credible threat; Therefore in the first place, the lender would never lend more than the value of collateral borrowing constraint (BC) λrf (k) r(1 ω).

Aggregate capital formation in equilibrium Both BC: λrf (k) r(1 ω) and PC: Rf (k) r satisfied, { Rf (k) = max 1, 1 ω } r λ If λ + ω < 1, then BC is tighter than PC, Rf (k) = 1 ω λ r > r Too little investment; Credit market imperfection Net worth effect, i.e. ω f (k) k. If λ + ω > 1, then PC is tighter than BC, Rf (k) = r > 1 ω λ r Optimal investment; No net worth effect.

Appealing features in equilibrium Endogenized entrepreneurs / lenders If λ + ω > 1, Rf (k) = r, indifferent between being entrepreneurs and lenders; If λ + ω < 1, Rf (k) > r, agents prefer being entrepreneurs. However, BC makes it a mixed strategy equilibrium. The role of indivisibility of investment If, instead, we start from heterogeneous agents, i.e. assume entrepreneurs / lenders, then usually difficult to find equilibria; However, ex ante homogenous agent plus indivisibility endogenized heterogeneity ex post! Easier to introduce heterogeneities in other dimemsions, e.g. heterogeneities in endowment ω or / and profitability R.

Introducing heterogeneities Suppose λ + ω < 1 (developing countries, countries with poor financial institutions, etc), with Rf (k) = 1 ω λ r > r. Who will become entrepreneurs? Agents are heterogeneous in endowments, ω G(ω). Define ω c such that Rf (k) = 1 ω c λ r, ω c = 1 λrf (k) r, and only (richer) agents with ω > ω c become entrepreneurs. [ ( )] Capital stock k = R 1 G 1 λrf (k) r finding the fixed point! Comparative statics: Capital market imperfections: λ k ; Market rate: r k ; Net worth effect: First order stochastic dominance shift in G k.

Introducing heterogeneities (cont d) Finding fixed point of k

Introducing heterogeneities (cont d) Distributional effects of improving credit market? Suppose λ increases from λ 1 to λ 2, then k increases from k1 to k 2 ; ωc = 1 λ Rf (k) r decreases from ωc 1 to ωc 2. Welfare of the agents? Mixed effects For ω < ω 2 c, U 2 (ω) = U 1 (ω) = rω; For ωc 2 < ω < ωc 1, U 1 (ω) = rω < U 2 (ω) = Rf (k 2 ) r(1 ω); For ω > ωc 1, U 2 (ω) = Rf (k 2 ) r(1 ω) < U 1 (ω) = Rf (k 1 ) r(1 ω). The middle class gains, the rich loses The rich benefits from credit market imperfections...

Introducing heterogeneities (cont d) Effects of improving credit market

Heterogeneities in two dimensions Keeping λ + ω < 1, and agents are heterogeneous in both endowment and projects, (ω,r) G(ω,R). Who will become entrepreneurs? Again (1) PC: Rf (k) r; (2) BC: ω ω c = 1 λrf (k) r. 1

Heterogeneities in two dimensions (cont d) Effects of improving credit market? A & B are worse off, but C better off. 1

Adding depositors in the baseline model Now endogenize the investment decisions (market rate r). Suppose there are two types of agents: A unit continuum of entrepreneurs, with endowment ω < 1. Capital investment with return rate R, then production f (k) and consume only in T = 1; A unit continuum of depositors, with endowment ω 0 and no access to either storage or investment technology. Consume in both T = 0 and T = 1 with max U 0 = V (ω 0 S 0 (r)) + C 0 1, s.t. C 0 1 = rs 0 (r) Depositor s supply of funds from FOC: V (ω 0 S 0 (r)) = r, i.e. S 0 (r) = ω 0 (V ) 1 (r).

Aggregate supply and demand of funds Resource constraint of the economy determines the aggregate supply of funds S(r) = ω + S 0 (r), k = RS(r) k R := S(r) = ω + ω 0 ( V ) 1 (r); Aggregatre demand determined by both PC and BC { Rf (k) = max 1, 1 ω } r λ k R := I (r) = 1 ( f ) [ { 1 r R R max 1, 1 ω }]. λ

Finding equilibrium market rate 1 max 1,1

Capital deepening effect of higher lender s book value ω 0 1 max 1,1

Net worth effect of higher borrower s book value ω To make it interesting, suppose that λ + ω < 1 1 1

Extension: Modelling international capital flow Now suppose two countries (North & South) with own entrepreneurs & depositors, having identical f (k) and R, differ in λ, ω and ω 0. More assumptions: Input and consumption goods are tradeable, motivating international borrowing / lending; R is substantially lower when operating abroad: ruling out FDI. World equilibrium with full financial integration World resource constraint: k N + k S = R [ ω N + ωn 0 + ω S + ωs 0 (V )(r) ] ; PC and BC: { } { Rf λ (k N )min 1, N 1 ω = r = Rf (k S )min 1, N λ S 1 ω }. S

Pattern 1: Neoclassical view Suppose λ N = λ S, ω N = ω S, and ωn 0 > ω0 S : North s saving helps finance South s production 1 2 1 1

Pattern 2: Capital flight to quality 1 1 Suppose λ N > λ S, ω N = ω S, and ωn 0 = ω0 S : South s saving leaves for high quality projects in North 1 2 1 1 1 1

Pattern 3: Net worth attraction Suppose λ N = λ S, ω N > ω S, and ωn 0 = ω0 S : North s projects credit worthiness attracts South s saving 1 2 1 2 1 1 1 1

Extension: Modelling international trade Consider two countries (North & South) involved in trading consumption goods: A continuum of tradeable consumption goods indexed by z [0,1]; In each country, unit mass homogeneous agents each endowed with ω < 1 labor, utility from consumption: U = ( 1 0 zε dz) 1 ε ; z are produced in the projects run by some of the agents (entrepreneurs) Each agent runs at most one project; Each project in sector z converts unit labor into R units z. Threshold value: An entrepreneur has to hire 1 ω labor at market wage rate w from the workers. No flow of labor.

Introducing credit market imperfections Agents income: (1) I e = p(z)r w(1 ω) if she s entrepreneur; (2) I w = wω if she s worker; PC: One is willing to run project z if Ie I w p(z)r w; BC: Two dimension imperfections λ of the economy, and project specific Λ(z) (suppose it is continuously increasing in z). Then λλ(z)p(z)r w(1 ω). In closed economy, both{ constraints } hold for all sectors in both countries: p(z) w = 1 R max 1, 1 ω λλ(z). The credit market imperfection restricts entry to the lower-indexed sectors.

Introducing credit market imperfections (cont d) 1 1 Λ

North s absolute advantage in autarky Suppose λ N > λ S, ω N > ω S. North (South) has absolute advantage (disadvantage) in low-indexed goods. 1 1 1 Λ

Comparative advantage in international trade North s absolute advantage translates into a higher wage in North, which implies North s (South s) comparative advantage in low (high)-indexed sectors. 1 1 Λ 1 Λ 1 Λ

Summary What have we done so far? Static models Modelling credit market imperfections. Key factors: λ measure of imperfection; ω net worth; Market economy fails to allocate the credit to its most productive use; Net worth / balance sheet conditions play crucial roles in allocating the credit. Partial equilibrium models with homo- / heterogeneous agents; General equilibrium models with open economy extensions. To be discussed next time: Dynamic models Models with homo. agents: Persistence, volatility, and growth; Models with hetero. agents: (Open economy) extensions.

For Further Reading... I Hart, O. and J. Moore A theory of debt based on the inalienability of human capital. Quarterly Journal of Economics, 109, 841 879, 1994. Matsuyama, K. Aggregate implications of credit market imperfections. in D. Acemoglu, K. Rogoff, and M. Woodford. (eds.) NBER Macroeconomics Annual 2007. Cambridge: MIT Press, 2008. Agion, P. and A. Benerjee Volatility and Growth (Clarendon Lectures in Economics) New York: Oxford University Press, 2005.