An Optimizing Model of Household Behavior Under Credit Rationing PETER MONT£ EL* T HAS LONG BEEN RECOGNIZED that the transmission mecha­ nism linking monetary policy to the real sector depends on certainI structural and institutional characteristics that may be spe­ cific to a particular country at a given moment in time. 1 The proper formulation of monetary policy therefore requires analysis of how the transmission mechanism can be expected to operate under the set of circumstances that happens to be relevant to the particular economy under review.2 For a typical developing country, it may often be appropriate to assume that the private sector has no access to international capital markets, that the assets available to savers are limited to money (that is, the liabil­ ities of the banking system) and physical capital, and that interest rates on loans from the banking system are controlled at below­ market levels (that is, that credit is rationed). The analysis of the transmission mechanism for monetary policy in such a setting, however, is not well developed. The purpose of this paper is to take a first step in the analysis of the mechanism by which monetary policy is transmitted to aggregate demand under these circumstances by analyzing the • Mr. Montiel, an economist in the Developing Country Studies Division of the Fund's Research Department when this paper was written, is now in the Macroeconomics Division of the Development Research Department, The World Bank. He is a graduate of Yale University and the Massachusetts Institute of Technology. 1 Such characteristics include the menu of available financial assets, the degree of substitutability among these assets, the extent to which various assets affect private net worth, the existence of various legal restraints such as interest rate ceilings or prohibitions on capital flows, and the exchange rate regime, among others. 2 Papers on the transmission mechanism for monetary policy under diverse circumstances include Modigliani (1963), Tobin (1978), Laidler (1978), Blanch­ ard (1980), and Modigliani and Papademos (1980}. 583 ©International Monetary Fund. Not for Redistribution 584 PETER MONTIEL behavior of a representative household under credit rationing in the general context set forth above. 3 The next section sets out a simple framework suitable for examining the issues involved. In Section II an optimizing model is developed for analyzing house­ hold behavior in the absence of credit rationing. The implications of imposing a constraint on the available supply of credit are examined in Section Ill. Section IV considers the effects of a change in the supply of credit and in the loan interest rate. A final section summarizes the main results. I. Monetary Policy, Credit to the Private Sector, and Aggregate Demand To investigate the issues, it is helpful to begin with a particularly simple framework. Consider a developing economy consisting of a government, a monetary authority, and a nonbank private sec­ tor. For simplicity, there is no commercial banking system. The government buys goods and services in the amount g, collects net revenues t, and covers any associated deficit in its budget by borrowing �da from the monetary authority and �fa from sources abroad. The government does not borrow directly from the do­ mestic private sector; its budget constraint4 is therefore �d � g - (1) G + �G = I. The private sector accumulates assets either by investing in physical capital, i, or by hoarding, �m0. It finances this accumu­ lation by saving, s, or borrowing from the monetary authority, �dp. The private sector's budget constraint is i + �m0=s + �dp. (2 ) FinaJiy, the monetary authority creates money, �m5, through the process of issuing credit to the public and private sectors, �da and �dp respectively, and acquiring foreign exchange reserves, �r. The behavior of the monetary authority is thus subject to the constraint (3) 3 Supply-side effects of credit policy are not considered here. For discussion of such effects in a developin� country setting, see Cavallo (1981), Taylor (1981), and van Wijnbergen (1983). 4 Interest payments by the government are not explicitly identified; for present purposes, they can be considered as already included in net revenues. ©International Monetary Fund. Not for Redistribution HOUSEHOLD BEHAVIOR UNDER CREDIT RATIONING 585 Changes in the central bank's foreign exchange reserves arise from transactions with the private sector and with the govern­ ment, D.rpand D.rc respectively. If one assumes for simplicity that all government spending is on domestic goods, then �=�; � that is, the proceeds of net foreign borrowing by the government are exchanged for domestic currency at the central bank.5 The accounts of the public sector can be consolidated by substi­ tuting identity (1) into identity (3) and using equation (4) to produce D.rp + [(g - t) + D.dp] = D.m5• (5) The expression in brackets is the exogenous component of the flow supply of money-that is, it is the portion of this flow that is directly controlled by the authorities under a fixed exchange rate regime. One can denote this exogenous component D.m5:6 D.m5= (g-t) + D.dp. (6) Identity (6) helps to illuminate the options faced by the authorities in this economy. They can choose to target the supply of money (through D.m5), the fiscal deficit, or the volume of credit to the private sector. However, targets for only two of these variables can be chosen independently. The third will be determined by identity (6). Whatever the combination of variables chosen as targets by the authorities, identity (6) makes clear that the supply of credit to the private sector is the key policy instrument that allows mon­ etary policy to be conducted independently of fiscal policy in this type of economy. For example, if the authorities set targets for those variables which dominate macroeconomic policy discussions in industrial countries-the supply of money and the fiscal defi­ cit-then the supply of credit to the private sector must be set as a residual to reconcile these policy objectives. Of course, the combination of instruments that should in prin­ ciple be targeted by the authorities depends on the relationships 5 Allowing for government spending on foreign goods, government receipts of income from abroad (for example, through transfers), or for both would merely clutter up equation (6) without adding anything of substance. 6 Identity (6) can also be written as 5 !:1m = 6.d + 6.fc; that is, the exogenous component of the flow supply of money differs from the flow of domestic credit by the amount of external government borrowing. ©International Monetary Fund. Not for Redistribution 586 PETER MONTIEL of these policy instruments to the ultimate goals of macroeco­ nomic policy. The supply of credit to the private sector has not, in fact, typically been relegated to a residual role but has become an important policy instrument in its own right. One role of fiscal subceilings under domestic credit ceilings in Fund-supported ad­ justment programs, for example, is to promote availability of credit to the private sector. This concern is based on the suppo­ sition that, in a context in which the supply of domestic bank credit is rationed and in which the private sector has no access to external funds, private aggregate demand will be constrained by the availability of bank credit (see Keller (1980)). More impor­ tant, a strategic component of private demand-private invest­ ment-is believed to be particularly sensitive to the supply of bank credit.7 According to this view, therefore, in this type of economy monetary policy works at least partially through a direct effect of the supply of credit to the private sector on private spending, specifically on private investment. 8 There are theoretical reasons to believe that, in a regime of credit rationing, the quantity of credit extended to the private sector would appear directly in private demand functions. Such a conclusion derives from the general principle discussed by Clower (1965) and Patinkin (1965), and extended by Barro and Grossman (1971), that under rationing the quantity constraints faced by agents will become arguments in their behavioral functions. Moreover, the argument can be made that private investment in particular can be expected to increase when the supply of credit expands: as long as the credit constraint is binding, the marginal product of capital exceeds the opportunity cost of funds, creating an incentive to expand the capital stock when the credit constraint is eased. In this setting, therefore, the transmission mechanism from monetary policy to aggregate demand would be relatively simple. The supply of bank credit to the private sector would itself appear as an argument in the private investment and consumption functions. But to say that the transmission mechanism from monetary policy to aggregate demand in the setting under scrutiny takes the form of the direct appearance of the supply of credit to the private sector in consumption and investment functions is obviously not 7 Empirical evidence of the sensitivity of private investment to the availability of cred1t has recently been provided by Blejer and Khan (1984). 8The effect is "direct" in that the effect on aggregate demand from supplying credit to the private sector is not transmitted simply through the money supply. ©International Monetary Fund. Not for Redistribution HOUSEHOLD BEHAVIOR UNDER CREDIT RATIONING 587 enough to satisfy the policymaker. One would also want to know what determines the total impact on aggregate demand of a given change in the supply of credit to the private sector as well as the components of this total effect-that is, the extent to which the effect on aggregate demand operates through changes in consump­ tion instead of changes in investment. These points can be illus­ trated by rewriting identity (2) as i(t::..dp, .