The Simple IS-LM Model With Credit Rationing

This paper examines how the effects of credit rationing can be incorporated into the simple IS-LM model. When credit rationing occurs, firms are not able to sell all the bonds they desire at the current rate of interest. Therefore transactions take place and are finalized at a price at which the implicit bond market underlying the model fails to clear. The non-market-clearing analysis derived from Clower's dual decision hypothesis is used to analyze the impact of such non-market-clearing transactions on the IS and LM curves. INTRODUCTION Over 65 years have now passed since Hicks [8] first introduced the IS-LM model into the literature. In spite of the extensive criticism to which the model has been subjected on many different grounds, it continues to survive, both as an expository device and as an analytical tool. For example, Fischer [6, p. 35] has stated: “...it's still the basic model that people use – in fact I use it – in understanding the economy. ...I don’t think that there is a better model for getting the intuition of the short-run adjustment of the economy right.” Therefore it is essential that the model’s properties be fully understood. One of the features of the simple IS-LM model (that is, the version without an explicit labor market and a production function added to it) is that while it contains markets for commodities, money, and bonds (or credit), only the commodity and money markets are included in the explicit analysis. This raises the question of what the properties of the implicit bond market underlying the model are and how this market interacts with the money and commodity markets. It has been shown in the literature that Walras’ Law can be used to place a bond market equilibrium curve between the IS and LM curve, like the BB curve in Figure 1. However, when credit rationing occurs transactions take place and are finalized when the implicit bond market underlying the model does not clear, that is, at points below this BB curve, a condition under which Walras’ Law (which is based on the assumption of market clearing) does not hold. Therefore the properties of the model under conditions of credit rationing must be derived using an approach that explicitly permits transactions to take place and be finalized at prices at which markets do not clear. This can be done by making use of the non-market-clearing analysis based on the dual decision hypothesis developed by Clower [4]. This approach, as developed in the 1970s by Grossman [7] and Barro and Grossman [1], specifically analyzes the impact of non-market-clearing transactions in one market on all the other markets. We shall use it in this context to analyze the effects of credit rationing on the various markets in the model. In addition to examining the relationship of the impact of credit rationing on the various markets in the model, a second objective of this paper is to demonstrate the continuing relevance of the nonSouthwestern Economic Review 142 market-clearing analysis derived using Clower's dual decision hypothesis to macroeconomic modeling. A SIMPLE IS-LM MODEL In order to analyze the effects of credit rationing on the model we at this point specify a simple textbook version of the IS-LM model. In order to be able to analyze the interaction between the bond market, in which the credit rationing takes place, and the commodity market, the model must be specified in such a manner that changes in the stock of bonds and flows in the commodity market can interact at the relevant point in time. Therefore we specify a discrete end-of-period stock-flow version of the simple textbook model. It is important to note however that the analysis holds for any specification that permits changes in the stock of bonds and flows in the commodity market to interact at the relevant point in time. For example, the results also hold if the model is specified on a continuous pure flow basis, in which the supplies and demands for money and bonds are for instantaneous changes in the levels of asset holdings, as is done, for example, in the model in Grossman [7]. However, since the supply and demand for money in the simple IS-LM model are normally specified to be supplies and demands for stocks at a point in time, the endof-period stock-flow specification is more appropriate. The model confines itself to a single period of time. All markets explicitly included in the model are assumed to have cleared at the end of the previous period. There are two assets: money in the form of currency issued by the government and bonds issued by firms. The government issued the money during previous periods and does not change the money supply during the current period. Therefore the government sector can be omitted from the model and the supply of money at the end of the period is equal to the stock of money at the beginning of the period. The bonds are fixed-price, variable-coupon bonds that pay the rate of interest r. Firms pay out all of their profits to the household sector. Firms are assumed to purchase their investment goods from other firms, rather than producing these goods themselves. In consistency with the simple IS-LM model, it is assumed that the price level does not change during the current period. Therefore adjustment in the commodity market during the current period is brought about by adjustment in output. The model also makes the standard assumption made in the simple model that firms seek to sell the amount that they produce during the current period, so that the actual output produced represents aggregate supply, and therefore no separate aggregate supply function is required. The output produced is identical to the income generated, so that aggregate supply and aggregate income are identical. They will both be represented by the symbol Y. The model assumes that transactors make all transactions plans for the current period at the beginning of the period. In addition, all sales and purchases for the period are completed at the beginning of the period, but all deliveries and payments take place at a constant rate throughout the period. In the commodity market transactors’ plans are made with respect to the desired total values of the flows over the period and all variables represent the integrals of the flows from the beginning of the period to the end of the period. In the money and bond markets, since they are markets for stock aggregates, transactors’ plans are made with respect to the total amount of these assets that they wish to hold or have issued at the end of the period, and supplies and demands are therefore in terms of such desired end-ofperiod stocks. It is assumed that transactors desire to adjust their beginning-of-period assets to their desired end-of-period supplies and demands at a constant rate during the period, which results in flow supplies and demands for changes in the holdings of The Simple IS-LM Model with Credit Rationing 143 money and bonds during the period. It follows that changes in the money holdings of transactors must also take place continuously at a constant rate. We, at this point, specify a version of the model with notional supplies and demands based on the assumption that transactors expect to succeed in carrying out their transactions plans and derive notional market equilibrium curves from them. This model will serve as a benchmark against which the non-market-clearing results derived below can be compared. The notional supplies and demands are as follows: