Creating Business Cycles Through Credit Constraints

Business cycles appear to be large, persistent, and asymmetric relative to the shocks hitting the economy. This observation suggests the existence of an asymmetric amplification and propagation mechanism, which transforms the shocks into the observed movements in aggregate output. This article demonstrates, in a small open economy, how credit constraints can be such a mechanism. The article also shows, however, that the quantitative significance of the amplification which credit constraints can provide is sensitive to the quantitative specification of the underlying economy (especially factor shares). The views expressed herein are those of the author and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System. Over the past two centuries, aggregate output in the United States has grown steadily, but not in a straight line; it has fluctuated around its upward trend. These output fluctuations have had three key properties: • Size. Movements in aggregate output have been large. In an economy as big and varied as that of the United States, movements in various sectors might be expected to cancel each other, leaving only small movements in aggregate output. This is not what has happened. • Persistence. The output movements have been highly persistent. Once output has fallen below its usual trend growth, for example, it has stayed below this trend for some time. • Asymmetry. Output’s movements have been asymmetric: downward movements have been sharper and quicker than upward movements (Falk 1986, Acemoglu and Scott 1997). Economists have labeled the recurrent movements in aggregate output business cycles, but they have not yet satisfactorily explained why the movements have the particular properties they do. At least two types of explanations have been offered. One is simply that the economy has been frequently hit with aggregate shocks which have these properties. The problem with this explanation is that sufficiently large shocks like these are hard to find in the data (Summers1986,Cochrane1994).Candidates likesudden changes in government policy, the weather, and oil supplies have not been large enough to account for the large movements in aggregate output. The other potential explanation for the business cycle properties is that the economy has some as yet unidentified mechanism which transforms small, barely detectable, shocks to some or all parts of the economy into large, persistent, asymmetric movements in aggregate output. This economic mechanism propagates and amplifies shocks in a downwardly biased fashion. Here I argue that the mechanism might be credit constraints, or limits on how much economic agents can borrow. Before turning to the formal specifics of my argument, let me explain the intuition behind it. Think of an entrepreneur who is the owner and manager of a firm which has two types of assets: savings in a bank account and computer equipment. Assume that the entrepreneur cannot borrow. However, note that the firm’s scale of production is optimal; otherwise, the entrepreneur would use some of the firm’s savings to buy more computer equipment. Suppose this entrepreneur receives an unanticipated upward temporary shock to income. Will the entrepreneur use this income to buy more computers? No, the firm’s scale of production is already optimal, so the extra income will simply be consumed or saved. Now suppose instead that the entrepreneur receives a downward shock to income. If the shock is small, the entrepreneur will absorb it by reducing the firm’s savings or consuming less or both. But if the shock is big enough to swamp the firm’s savings, then the entrepreneur must lower the firm’s scale of production by selling off some computer equipment. Note that in this instance, the entrepreneur would prefer to borrow, but cannot. If the marginal returns to computer equipment are diminishing, and the entrepreneur’s marginal utility is diminishing, then returning to the firm’s optimal scale of production will take many periods. Thus, for an entrepreneur who faces credit constraints, upward shocks and small downward shocks to income have little or no effect on production. However, sufficiently large downward shocks can have persistent negative effects on production. Credit constraints (of virtually any form) are an asymmetric propagation mechanism. Still, little in this intuition explains why credit constraints should amplify shocks. This is because only certain types of credit constraints do so. We just considered an entrepreneur who could not borrow at all. Now suppose instead that the entrepreneur also owns land, which is a complementary input with the computer equipment. We have seen that a downward income shock can lead a credit-constrained entrepreneur to reduce a firm’s computer equipment. Suppose a large number of entrepreneurs are in this situation. Then, because computers and land are complementary inputs, land prices must fall. This fall will shrink the debt capacity of the entrepreneurs and lead to a further shrinkage in production. In this way, certain types of credit constraints can amplify the effects of income shocks. I formalize this argument below. I construct a simple model in which productive agents use capital and land to produce output. The agents face a limit on how much they may borrow and an interest rate that is exogenously specified. I consider the effects of unanticipated increases or decreases in the agents’ income. I show that unanticipated increases have no impact on output. However, sufficiently large unanticipated decreases in income reduce output, and after such reductions, output returns only slowly to its original level. I then consider two types of credit constraints. First, I allow agents to borrow up to a fixed exogenous limit. I show that in this setting, the effects of income shocks are not amplified. Second, I allow agents to borrow up to the value of their land. In this setting, the effects of income shocks may be greatly amplified. However, the degree of amplification depends crucially on the shares of capital and land in the production function: if these shares sum to less than 40 percent (as is approximately true in the U.S. data), then the effects of income shocks are not amplified at all. My work here is essentially a simpler presentation of ideas originally presented elsewhere, by me and by others. Many studies have pointed out that in economies with credit constraints, temporary income shocks can have persistent effects. (See, for example, Scheinkman and Weiss 1986, Kocherlakota 1996, and Cooley, Marimon, and Quadrini 2000.) Kiyotaki and Moore (1997) and Kiyotaki (1998) have emphasized the importance of borrowing limits that depend on asset values as an amplification mechanism. A Simple Model To start the analysis, I describe a simple model with a credit constraint. In technical terms, the model is essentially a small open economy version of a neoclassical growth model with complete depreciation. I model a group of farmers. The farmers grow a special type of corn, which can be used equally well for food or for seed. In each period of time t, a farmer produces corn according to this production function: