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Testing a Disequilibrium Model of Lending Rate Determination

Author(s):
Barry Scholnick
Published Date:
September 1991
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I. Introduction

A large amount of literature has appeared following the seminal work of Stiglitz and Weiss (1981) (henceforth S&W) on informational asymmetries and equilibrium credit rationing in the market for loans. This paper falls within that literature, developing a new model which extends the S&W model of loan rate determination. The aim of the paper is to build and test a model that describes various stylized facts concerning the relative volatility of lending rates (IL). The model proposed by S&W is a static one that does not fully describe the dynamics of IL adjustment; thus it is unable to explain why IL rates are relatively volatile but not as volatile as interbank rates (IB). In order to explain the relative volatility of IL and IB, the new model combines some aspects of the S&W model, with a marginal cost pricing model that includes the interbank rate as a marginal cost of bank funds.

The first half of the paper describes fully both the S&W model and the combined model; while the second half is concerned with the empirical testing of the new model using Malaysian data. The econometric methodology used is based on Engle and Granger’s (1987) work on the relationship between cointegrating vectors and error correction mechanisms. Since the new model includes both long-run equilibrium and short-run disequilibrium components, these aspects of the model are tested using cointegration and error correction mechanisms respectively.

The model is tested on Malaysian data after 1982, when bank interest rates were liberalized. This condition is necessary, according to proponents of financial liberalization, for maximization of investment.

II. The Stiglitz and Weiss (S&W) Model

In this chapter the S&W model 1/ is developed in three stages. In section 1, it is argued that the relationship between expected profits of the banks may not be monotonic with respect to the lending rate (IL) under conditions of informational asymmetries. Section 2 shows how equilibrium credit rationing can exist if the IL rate is not monotonic, while Section 3 describes how monetary policy shocks are transmitted.

1. The nonmonotonic relationship between IL and profits

The following model of the nonmonotonic relationship is based on that described in Blanchard and Fisher (1989), although it produces the same result as S&W. Assume that there are many potential borrowers, each with a project that requires an initial indivisible investment of K. The borrowers each have an initial endowment of W < K, and thus they must borrow B = K - W from the banks, repaying (1 + IL)B if the project is successful.

Assume also that all projects yield the same expected return R, but have different risks of failing. A project (subscripted i) can either succeed, when it would yield Rsi, or fail when it would yield the common value Rf (e.g., zero). The probability of a project succeeding is pi, and of failing is (1 - pi). The distribution of pi across all projects is the density function g(pi).

From the assumption that the expected return of all projects is the same (R), the relationship between the probability of success of a project (pi) and the return from successful projects Ris is

There is thus an inverse relationship between pi and Ris. If (1) holds then those projects with higher expected returns will also have a lower probability of success--or greater risk of failure. From the above model it can also be assumed that

The expected return from successful projects is greater than the amount that borrowers have to repay to the banks which, in turn, is greater than the expected return from failed projects.

The asymmetric information assumption, in this part of the model, is that the borrower knows the probability of success of the project while the prospective lender (bank) does not. Thus the bank is not at this stage able to distinguish between “good” and “bad” borrowers. If both the borrower and the bank are risk neutral then the expected return to the borrower is

and the expected payoff to the lender (bank) is

The return to the bank is ρb = E(πb)/B

The relationship between IL and ρ is nonmonotonic because the greater the expected return from a project the smaller will be the probability of success (from (1)). This can be seen by substituting (1) into (3) to get

From (2) it can be seen that the expression in square brackets in (5) is positive. Thus, it can be concluded that there is a negative relationship between E(πi) and pi. Equation (5) also implies that high risk investors, who are prepared to have a lower value of pi, will be prepared to pay more than IL in order to earn E(πi). This can be investigated further by assuming that borrowers are able either to hold their wealth W in a safe asset with return ρρ or to borrow further for the proposed project. Thus borrowers will borrow for as long as

This implies that the higher the interest rate IL in (5), the lower will be the level of pi which will be required to ensure that E(πi) is high enough for the entrepreneur to proceed with the investment; that is, so that E(πi) satisfies (6). Thus,

which means that, as the banks increase IL, so the probability of success of proposed projects will decrease. The inequality (7) implies that, as the banks increase IL, they will attract borrowers whose projects have a lower probability of success. This will lower the expected income of the banks E(πb) by lowering the values of pi in (4).

According to S&W the increase in IL will lead to both an increase in the banks’ return from successful projects (called the “direct effect” in S&W), and a reduction in return from failed projects that do not repay B(1+IL) (called the “adverse selection effect”). Because these two effects have the opposite signs, there will be an interest rate (called IL*) where bank profits are maximised, i.e., where

If the bank increases IL above this point, then the higher returns from projects that do succeed will not outweigh the decline in returns from those that do not, where the latter were only attractive because of the higher IL in the first place.

Stiglitz and Weiss also discuss the notion of an excess supply of credit equilibrium to show why banks would not reduce IL to below IL*. This is also based on asymmetric information between banks and prospective new borrowers. S&W conclude that “[i]n equilibrium each bank may have an excess supply of loanable funds, but no bank will lower its interest rate.” 2/ S&W thus assert that (8) holds for situations of both excess supply of, and excess demand for credit.

2. Nonmarket-clearing equilibrium

The second part of the description of the S&W model concerns integrating the nonmonotonicity between IL and ρ into a model of nonmarket clearing equilibrium. 3/ The nonmarket clearing equilibrium is explained by use of figure 1, which has been used in both S&W and Blanchard and Fisher (1989). The nonmonotonic relationship between IL and ρ is shown in quadrant IV, where IL* is the rate at which bank profits are maximised from (8). Thus no lending takes place at levels above or below this rate.

Figure 1Stiglitz and Weiss (1981) Credit Rationing Model

Quadrant III contains the supply of funds function. In the S&W model it is assumed that the supply of funds is increasing in ρ, that is, as the returns to the bank increase so do the amounts that can be loaned out. Quadrant II contains a 45 degree line which allows the construction of a loan supply function in Quadrant I. The key point of the S&W model is that lending will only take place at IL* because the maximum return to the banks will be ρ*. This implies that the maximum supply of funds will be at point A on the supply curve in quadrant I.

If the demand curve for funds is drawn as in Figure 1, there will be credit rationing, because at IL* there will be a positive difference between B and A. The market clearing rate will be at point C but, as has been shown, the banks will not move to clear the market at that rate because they maximise their returns at IL*.

3. Monetary policy in the S&W model

An important conclusion in the S&W model is that if monetary policy is expansionary it will affect the level of investment “not through the interest rate mechanism but through the availability of credit.” 4/ They argue that if there is an increase in the money supply then this will increase the supply of loans at each interest rate. This would shift the supply of loans function in the third quadrant to the left, causing the Ls function in quadrant I to shift up. This would serve to close the gap between A and B. An increase in the money supply would thus increase the supply of loans but would not change the interest rate from IL*.

4. Assessment of the S&W model

There are three important problems with the S&W model. The first has been noted by Blanchard and Fisher (1989, p. 487): “The question remains however, to find the mechanism through which the loan supply curve in the third quadrant moved.” The S&W model does not explain how the banks received the increase in the money supply; it assumes implicitly that the banks received the injection from the central bank, in some kind of “helicopter drop.”

The second problem is that, as a static equilibrium model, the S&W model offers little explanation for the dynamic adjustment of the IL rate in response to monetary policy or other shocks. This closely relates to the third problem of the model, which is that S&W does not fit in with the stylized facts of the volatility of short-term interest rates. It is often noted that IL is relatively volatile, but not as volatile as the interbank rate IB

where σIB is the volatility of the interbank rate and σIL is the volatility of the lending rate. S&W argue that as long as there is a nonmarket clearing equilibrium then the IL rate will not shift from IL*

5/

The S&W model is important, however, in that it shows how the costs associated with adverse selection can affect the setting of IL rates. The new model that is built in this paper attempts to rectify the problems associated with S&W, while at the same time maintaining their key finding concerning the effect of adverse selection on lending rate determination.

The key elements of the combined model are the explicit modelling of the interbank market and the setting of the model in terms of an intertemporal dynamic optimization problem. The incorporation of the interbank market solves the “helicopter drop” problem of Blanchard and Fisher, while the dynamic optimization procedure explains the dynamics of IL adjustment. The specific functional form that is used has been chosen in order to accord with (9).

III. The Combined Model

This section develops a model that combines the S&W model with those that consider the IB rate as a marginal cost of funds. The first two parts examine the properties of the IB rate; the third develops the full dynamic specification for the model, while the fourth examines the effects of monetary policy.

1. Properties of the interbank (IB) rate

It is assumed in this model that the interbank rate (IB) instantly clears the market for interbank funds thus

where ESF is the excess supply of interbank funds. Participants in this market include the central bank, as it either injects or withdraws funds, and all commercial banks as they respond to shifts in the supply or demand for funds. Thus,

where S and D are the supply and demand of interbank funds from the central bank, and s and d are the supply and demand for interbank funds from all other participants in the interbank market. Based on (11), f is negative in (12), and g is positive.

Thus any monetary activity of the central bank will, ceteris paribus, cause the IB rate to shift. Any other shock to the economy which affects the supply and demand for short-term funds will also cause the IB rate to shift. This model will therefore include shifts in monetary policy in the analysis (through S and D), as well as all other shocks to short-term liquidity that affect the IB rate, such as shifts in exchange rates, income, etc. (through s and d).

2. The IB rate in marginal cost pricing (MCP) models

An important deficiency of the S&W model is that it ignores the role the IB rate plays as the marginal cost of funds for setting of bank interest rates. Indeed, many previous models of price setting behavior by the banking firm are based on the assertion that the IB rate serves as the marginal cost of funds for the commercial banks as they set their IL and ID rates. These models, collectively termed Marginal Cost Pricing (MCP) models, are based on the notion of mark-up pricing, which simply postulates that the IL rate is a mark up over the marginal cost of funds, i.e., the IB rate. Thus,

The deposit rate (ID) is also determined by a (perhaps different) mark up over marginal costs

where a and b are determined by the degree of monopoly power and any other conditions in the market that determines the sizes of the different mark-ups.

In the MCP models, therefore, the IB rate serves as the anchor for the spectrum of interest rates. In this type of model, any shift in the IB rate would shift all other Interest rates especially those quoted by the commercial banks. If a = b = 1 then the IL and ID rates would both be as volatile as the IB rate, i.e.,

Once again this does not accord with the stylised fact (9) that σIB > σIL > 0.

3. The combined model: S&W and MCP

Clearly both models of pricing behavior discussed above have important deficiencies. The S&W model argues that σIL = 0, and does not explain the dynamics of IL in response to exogenous shocks. The MCP model, on the other hand, argues that if there is a constant mark up (a = 1) then σIL = σIB. Neither of these models fit the stylised fact that σIB > σIL > 0. The model built in this section attempts to do this by combining aspects of both the S&W and the MCP models into a single dynamic model. It aims to show that, when banks set the IL rate, both the IB rate as the marginal cost of funds and the costs imposed by informational asymmetries are determinants in the bank’s profit function.

In integrating these two models the following assumptions are made.

Assumption[A1]In the long run (in the strict econometric sense), the MCP model as specified in (13) and (14) will be the only determinant of commercial bank interest rates.
Assumption[A2]In the short run (also in the econometric sense) both models influence the commercial bank in the determination of its interest rates.

The reasoning behind these assumptions is as follows. It is argued that, in the long run, the marginal cost of funds is the only determinant of IL. This is because--owing to adverse selection--the cumulative costs of not responding to changes in the marginal cost of funds will exceed the possible costs incurred by the banks by keeping IL at IL*. In the short run, however, it is asserted that both the marginal cost pricing model and the adverse selection model influence the decisions of the banks in the determination of their IL rates. The exact form of this interaction is the most important issue in building the combined model. The assertion that the IL and ID rates are determined in the long run by the IB rate is empirically tested later. The remainder of this section considers the nature of the short-term combined model.

a. A short-term disequilibrium model of IL determination

It was asserted above that in the short run the effects of both adverse selection problems and the marginal cost pricing models would influence the setting of the IL rate. This section develops an intertemporal optimization model that includes both of these phenomena in an econometrically tractable way.

The model is set up in terms of costs faced by the banks when setting the IL rate. The MCP model argues that the banks face costs if they do not shift their IL rate following a change in the IB rate; yet they also face adverse selection costs if they shift do IL away from IL*. If the banking system is not perfectly competitive, and banks are price setters, those banks that are first to adjust IL following shocks to IB will bear adverse selection costs because they will attract the risky borrowers that serve to lower the banks’ rate of return. There will thus be a benefit to banks in delaying their adjustment to exogenous shocks and thus keeping the volatility of IL lower than the volatility of IB. The following model will formally set up all of these possible costs in terms of the well known quadratic loss function.

Whenever the quadratic loss function approach is adopted, the model has to specify both the long-run desired or target variable of the agent as well as the choice variable, which the agent can adjust in order to minimise the loss function. In this case the agents are the commercial banks. From assumption [1] it is asserted that the long-run target or desired variable is the IB rate. The choice variable of the banks is the IL rate.

The dynamic optimization problem will be derived in terms of the well known Error Correction Model (ECM) framework developed by Davidson et al. (1978), Nickell (1985) and many others. This sets the agents’ loss function in the following form.

where M1 is a constant mark-up.

The loss function forming the basis of the ECM is made up of three components. The first states that agents face a loss if they are not at the target or desired level. The second states that they face a loss if they move too rapidly towards the desired level. The third states that agents benefit if they move in the correct direction towards the desired level. The intertemporal solution to this type of model is that, following an exogenous shock, the agents adjust slowly towards the long-run target or equilibrium level; hence the name Error Correction Mechanism. Thus this model includes both short-run disequilibrium and long-run equilibrium components.

The MCP model is clearly represented by the first element in the loss function (16). In terms of (13) and (14), the banks (agents) would prefer to set their IL rates at the level of the IB rate plus a mark-up, and thus the IL rate would respond to any shift in the IB rate. In the loss function (16), this phenomenon is modelled as the cost imposed on the bank when the control variable IL is not equal to the target variable IB plus a constant mark-up, these costs being measured by c1 and determined by the first quadratic in (16).

The second element of the loss function states that the agents face a cost in shifting the IL rate at too rapid a pace; the greater the change between the previous periods IL and the present IL, the greater the cost associated with c2 in (16). This element models the adverse selection problems faced by the banks that are associated with changing IL. In an oligopolistic environment, banks would gain by not adjusting IL. Hence this equation measures the costs associated with having to adjust IL. 6/

The third component of (16) states that the agents face a benefit if they adjust their control variable in the direction of the target variable, i.e., the disequilibrium “error” from the exogenous shock is “corrected” in the correct direction of the long run equilibrium. This is the term that differentiates an ECM from other specifications and enables the integration of short-run disequilibrium and long-run equilibrium components. If both of the bracketed terms have the same sign, i.e., IL moves in the same direction as IB, then the banks face a decrease in costs because of the negative sign associated with c3. From assumption [A1] it is asserted that the banks shift their IL rates towards the target IB rate. This process will be modelled by the third component of (16).

An important derivation of (16) is that in the long run the agent will always approach the desired or target variable. Whether the control variable actually reaches the target variable or only approaches it asymptotically is a matter for debate (see Salmon, 1982 and Nickell, 1985). In terms of this model, however, it can be clearly stated that if (16) holds then in the long run IL will at least approach IB. It is for this reason that assumption [A1] was introduced.

It is therefore possible to incorporate both the costs associated with adverse selection, as well as the costs incurred by not adjusting to changes in the marginal cost of funds, into a dynamic optimization problem which produces the quadratic loss function (16). There are two reasons for modelling the banks’ behavior in this way. The first concerns the econometric tractability of such models. The second is that a loss function such as (16) is clearly useful in its own right as a technique for modelling the actions of the banks when faced with the different costs described above.

The main attraction of a formulation such as (16) is that it can be shown to fit into the stylized facts in (9). In the combined model IB is a market clearing rate; thus there is no limit on the volatility of σIB. According to (16), however, IL will respond slowly to shocks in IB, and will only approach IB in the long run, therefore σIB > σIL. There will, however, be some dynamic response from IL in response to changes in IB, which means that σIL > 0. It is thus clear that (16) does indeed accord with (9) in that σIB > σIL > 0.

It can be noted that an attempt has been made in the literature to explain (9) by using implicit contract type models. 7/ In such models banks form an implicit contract to share risk with their borrowers by keeping σIB > σIL. It is argued that banks are less risk averse than individual borrowers because of banks’ ability to diversify risk and also because of lender of last resort facilities. The argument is that banks can afford to keep σIL low in an attempt to increase the probability of borrowers’ projects succeeding. The problem with this type of model becomes evident if there are any changes in the economy which leads to an expected change in σIB. In such cases the banks would be less prepared to enter into the implicit contract that kept σIL at a lower level. This is because the banks will only be able to afford to enforce the implicit contract if σIB is expected to be relatively constant. Thus any factor that created instability in the system could lead to a breakdown in the implicit contract and thus in this explanation of (9).

In the model built in (16), however, (9) can be explained no matter what shock affects the economy or how volatile σIB is. This is because the volatility of IB is built into the model through (11) and (12). The banks act to solve the problem in (16) by letting IL respond slowly to changes in IB no matter how volatile IB is or how σIB changes.

4. Monetary policy in the combined model

The combined model (16) can be used to show how shifts in monetary policy affect the IL rate through shifts in the IB rate. In the following section the same four quadrant diagram used by S&W (Figure 2) is examined to show how the new model reacts to changes in monetary policy.

Figure 2Dynamic Lending Rate Model

Assume, for example, that the central bank tightens its monetary policy which, according to (10), leads to an increase in the market clearing IB rate. If the banks’ problem is set up in terms of (16) then the optimal solution will be for the banks to increase IL slowly toward the target rate, i.e., the error correction response. This response will be a dynamic disequilibrium response which only leads to an equilibrium in the long run. This is very different from S&W where a new static equilibrium is reached instantly following any exogenous shock.

In terms of Figure 2, (16) implies that the whole curve in quadrant IV will move slowly to the right. As explained above this shift will be dynamic and intertemporal and will not reach an equilibrium in the short run. There will be a new and increasing level of IL* due to the increase in IB, but not because of any shift in any of the variables that determine the result in (8). There will still be a relationship such as (8), but if the banks’ problem is set up according to (16) then (8) will only form part of the disequilibrium mechanism that determines IL*. Thus, in terms of the figure the whole curve in quadrant IV will be shifting to the right which will in turn be shifting the Ls curve in quadrant I to the right. The functions in quadrants IV and I will have a new maximum point at each time period (see Figure 2).

The combined model thus leads to very different conclusions from the S&W model. In the combined model a tightening of monetary policy leads to a slow increase in the IL with the Ls curve shifting slowly to the right. In comparison the S&W model concludes that a tightening of monetary policy will increase the amount of credit rationing, but will not affect the IL rate. The Ls curve moves instantly downward.

The combined model thus improves on all three deficiencies of S&W, while maintaining their important finding concerning the effect of adverse selection on lending rate determination. It is able, first, to explain the relationship between the central and commercial banks without recourse to “helicopter drops”, and second, to explain the dynamics of IL adjustment in response to exogenous shocks. The model in (16) also accords better with the stylised facts in (9) than either the S&W model or the MCP model.

IV. Lending and Deposit Rates in the Combined Model

In the S&W model of commercial bank behavior, no mention is made of the deposit rates paid by banks to depositors. This is because no adverse selection problems exist in the market for deposits. While the banks act as price setters, it is depositors who face any possible risk of default on the part of the banks.

The deposit rate does, however, play an important role in the MCP model; equations (13) and (14) show that both the IL and ID rates are functions of the IB rate. The fact that the banks do not face adverse selection problems in the market for deposits is of some importance in the econometric measurement of the combined model. If, following a shock to the IB rate, the ID rate responds faster than the IL rate then this could signify that adverse selection may be a factor in the market for loans. 8/

This section first develops the short-run dynamic relationship between IB and ID (to be compared with the relationship between IB and IL in Chapter III, Section 3(a), and then develops the long run relationship between IB, IL, and ID.

1. Short-run dynamics between IB and ID

As shown above, there is no reason for the ID rate to exhibit inertia on grounds of informational asymmetry concerning depositors, i.e., no adverse selection can exist in the market for deposits. However it must be recalled that both the ID and IL rates are set by the banks as price setters, while the IB rate is a market clearing rate. Even in a situation of no information asymmetries, the banks would face menu costs in adjusting their ID rates instantly, following any change in the target IB rate. The important distinction is that, if banks face the costs of adverse selection, then total costs in changing the IL rate will be much larger than menu costs involved in changing the ID rate. Thus the overall speed of response of IL will be slower than of ID.

The model of the short-term dynamics of ID is developed for its economic tractability in order to fit into the Error Correction Mechanism framework described above. It is argued that banks set the ID rate in terms of the dynamic optimization technique of the error correction mechanism as in (16). Such a model can be parameterised as

where M2 is a constant mark-up.

As usual the loss function (17) is made up of three factors. The first reflects the MCP model in (13) and (14), where there is a constant mark-up between IB and ID. Thus, in terms of this model the banks face costs if there is a difference between ID and IB. In (17) this is modelled by d1. The second term in (17) is a reflection of the menu costs faced by banks in changing ID. Menu costs are the small costs involved when banks actually change their interest rates (“reprinting their menus”). The second term in the ECM is the main difference between the lending rate model (16) and the deposit rate model (17). In (16), the c2 term is hypothesized to be large due to adverse selection costs. The corresponding d2 term in (17) is relatively small and can approach zero. The d3 term once again measures the fact that ID approaches IB in the long run and that it benefits the firm to move in that direction, i.e., to follow an error correction solution to the intertemporal problem.

This section has thus argued that in the market for deposits the banks are price setters and that the IB rate indicates a long-run desired position for the ID rate because it indicates shifts in the market for loanable funds. Further it is argued that menu costs can be imposed on banks when adjusting their ID rates. In the market for loans any menu costs are added to the costs imposed by adverse selection problems.

2. Long-run equilibrium relationship between IB. IL and ID

In this section the long-run equilibrium relationships of variables used in the combined model are developed. The examination of long-run relationships is important for two reasons. First, the notion of long-run equilibrium is useful for purposes of empirical testing and thus differentiating between competing models. The second reason concerns the relationship between long-run equilibrium and short-run disequilibrium. According to Engle and Granger (1987), if a long-run equilibrium exists in the form of a cointegrating vector, then a short-run dynamic relationship must exist in the form of an error correction mechanism. Thus the notion of a long-run equilibrium used here strictly follows that used in the time series econometric literature. The section examines the long-run equilibrium positions which should theoretically exist in the three models discussed above, i.e., the S&W model, the MCP model and the combined model. It also examines a fourth case of interest that is often encountered in models of financial liberalization.

Case 1: S&W model

As there is no IB rate in the S&W model, there is obviously no long-run equilibrium involving the IB rate. The key proposition of the S&W model is that the IL rate is set by banks with reference to adverse selection problems, while there are no such problems affecting ID. Because the ID and IL rates are determined so differently there can be no long-run equilibrium relationship between them. Thus an important empirical test for the S&W model is the absence of a cointegrating vector between IL and ID.

Case 2: MCP model

In the simple MCP model described in (13) and (14), there are clear relationships between both IB and IL, and IB and ID. It can thus be concluded that cointegrating vectors exist between these two variable sets. It is possible that if a is proportional to b in (13) and (14) then there can be a third cointegrating vector between IL and ID. This third relationship however is not critical to the MCP model.

Case 3: Combined model

The combined model developed in this paper assumes [A1] that, in the long run, both IL and ID are determined by the IB rate. Thus tests for cointegrating vectors between IB and IL, and between IB and ID, are important tests of assumption [A1] and of the model. The long-run relationship between IL and ID is not clear according to this model. As it is constructed on the assumption that IL and ID are determined quite differently, it would seem plausible that no long-run relationship exists between them. This conclusion is in contrast to that sometimes derived in models of financial liberalization.

Case 4: Perfectly competitive banking model--an aside

In the context of developing countries much interest has been expressed in differences between S&W type credit rationing models and models of financial liberalization (see Fry 1988). Broadly speaking the latter argues that if commercial banks are allowed to set market clearing interest rates, then investment will be maximised. If adverse selection or credit rationing exists, however, then constraints on investment can still operate even if full liberalization has occurred. Important to the financial liberalization literature has been the development of perfectly competitive, zero cost banking models. A key assumption of such models is that the IL and the ID rates are related:

where q is the required reserve ratio. Because these models are obviously very different from models that include adverse selection problems, such as S&W and the combined model, it is possible to compare these two types of models by testing if IL and ID are cointegrated. This test will be carried out in this paper. Cointegration would support the perfectly competitive financial liberalization models (18), while its absence would support the adverse selection type models.

V. Some Aspects of the Econometric Methodology

The econometric methodology used in this paper draws on recent developments in time series econometrics concerning cointegration in nonstationary time series. As Engle and Granger (1987) show, the existence of a cointegrating (CI) vector between two series signifies the existence of both a long-run equilibrium 9/ and a short-run error correction mechanism (ECM) between them. They also show the reverse argument that, if an ECM representation is shown to explain a dynamic process, then a cointegrating vector must exist to explain the long-run relationship. The intuitive reason for this relationship is that the ECM forces the short-run shocks to be “corrected” in the direction of the long-run equilibrium relationship. The econometrics used in this paper will thus be of two types. First, tests are run for the existence of long-run equilibria in order to examine if there are cointegrating vectors between the various interest rates under discussion. Second, the short-run dynamics between vectors that do have a long-run relationship are examined.

1. Cointegration

It has long been noted that if OLS regressions are conducted on non-stationary time series, this leads to the so-called spurious regression problem (see Hendry, 1986). Accordingly much recent econometric work has focused on the estimation and testing of variables that are not stationary. Based on the work of Hendry (1987) and Engle and Granger (1987), the important notion of cointegration has been developed.

If a series is stationary then it is termed I(0) which broadly means that it has a constant mean and a constant variance over time. However, if the series needs to be differenced once in order to be made stationary then it is termed I(1). Such a series is defined as being integrated of order 1. 10/ When dealing with series that are I(1), one approach is to difference all such series, so that all series in the equation are I(0). The problem in dealing with a “differences” econometric methodology, is that all long-term information in the series is lost. It therefore becomes important to develop techniques that include both “levels and differences” to capture long-run information in the series, which at the same time deal with the spurious regression problem. The cointegration procedure has been developed to address both of these problems.

If two (or more) series are I(1) then it is possible that a linear combination of the two series are I(0). In such cases (and only in such cases) does a cointegrating vector exists between the two I(1) series. If, for example, two I(1) variables can form a linear combination that is I(0), e.g.,

then it is clear that the relationship between the variables xt and yt will be a series zt that is stationary, i.e., has a constant mean and variance. The series formed by the linear relationship of the two I(1) variables will return to a stable mean in the long-run, because the variance of the series is constant. Accordingly, if a cointegrating vector exists, then the linear relationship between the two variables will return to a constant mean value in the long-run. This relationship defines the long-run equilibrium between the two series. 11/

2. Error correction mechanisms (ECM)

The ECM representation of short-run dynamics, which predates the cointegration literature, was developed in Davidson, Hendry, Srba and Yeo (1978) (DHSY). It has been further developed by Salmon (1982) and Hendry (1986). 12/ The ECM is important for three reasons. First, if a cointegrating vector exists, then an ECM will also exist to describe the dynamics. Second, the combined model of IL determination in the short run can be described in terms of ECMs. Thus, a congruent ECM model will support the description of the combined model (16). 13/ Third, it is possible to compare the speed of adjustment in the model of IL dynamics with the model of ID dynamics for specific evidence that IL is more inert than ID.

In addition to this, the ECM can be set up so that the coefficients of the dynamic equation have economically sensible coefficients. From the loss function (16), it is possible to set ∂L/∂IL = 0 which can be reparameterized to form a econometrically tractable model (see Cuthbertson 1985, p.67 for derivation, and Nickell 1985, for a discussion). This takes the form of the following “levels and differences equation” (20)

In terms of these parameters β0 is referred to as the impact effect, (α-1) as the feedback effect, and k as the long-run relationship between the two I(1) variables--i.e., the cointegrating vector in (19). After an initial shock to the independent variable, there will be an impact effect on the dependent variable which creates the initial disequilibrium. This initial impact is measured by β0. This effect will, however, be counteracted by a feedback response in which the system moves towards the new long-run equilibrium point. This is measured by the (α - 1) coefficient. The term (ILt-1 - k IBt-1) measures the disequilibrium in the past period and the coefficient -(α - 1) measures the feedback or the amount by which agents correct the disequilibrium in each period. The long-run position is determined by k which is exactly the long-run cointegrating vector discussed above.

The coefficients of the ECM equation can therefore be used to measure both the impact and the feedback effects following an initial shock. It is also possible to develop the mean lag between the initial shock to the independent variable and the full response over time of the dependent variable. This is defined (Hendry 1989) as

Thus, it is easy both to distinguish between the feedback and impact effects, and to measure the average length of time for the dependent variable to react fully to a shift in the independent variable. This is very useful information when considering speed of adjustment issues.

The ECM formulation has been used extensively in many macroeconomic interpretations, especially money demand equations (see Domowitz and Hakkio, 1990). This paper uses this formulation in a new application--that of testing a dynamic model of IL determination that incorporates both adverse selection problems and MCP criteria for interest rate determination.

VI. Financial Liberalization in Malaysia

Malaysia has been considered one of the success stories of financial liberalization (see Villanueva and Mirakhor, 1990). It embarked on a rapid process of financial liberalization but has not endured the major financial crises that followed the liberalization process in some South American countries. Villanueva and Mirakhor argue that the reasons for this success were the stable macroeconomic environment at the time, as well as adequate bank supervision by the authorities which served to avoid moral hazard problems.

Despite this, it is still possible that adverse selection may be a factor in lending rate determination, even if the banking system is relatively stable, and there are no moral hazard problems. While not leading to financial crises, the presence of this factor would still be contrary to the assumptions of the perfectly competitive financial liberalization models. Thus, the period after financial liberalization in Malaysia will be used as a test of the above model of lending rate determination.

In the 1970s, both deposit and lending rates were set by the central bank. In 1978, banks were able to determine their own deposit rates, but were still forced to maintain low lending rates for “priority” customers, who comprised a large proportion of bank lending. This led to lending rates being lower than deposit rates. It was only in 1982 that banks were able to set their own lending rates, which resulted in lending rates rising above deposit rates.

The authorities tried to intervene in the long-term interbank market while targeting the exchange rate. Short-term rates were volatile because of the rigid reserve requirement regime and market-determined rediscount rate (set above the highest interbank rate during the day). The level of short-term interest rates was allowed to shift to new levels from time to time based on broader money and credit indicators.

In the econometric section that follows, tests will only be conducted for the period after 1982. This does pose econometric problems concerning the limited sample size but, under the circumstances, longer sample periods cannot be used. The model is tested on monthly data from 1983 (1) to 1988 (12), leading to a data set of 72 months.

VII. Results

Based on the above sections there are four hypotheses that need to be tested empirically to support the combined model. These are:

  • 1. The existence of a long-run equilibrium between IB and IL, and between IB and ID

  • 2. The lack of a long-run equilibrium between IL and ID

  • 3. A congruent ECM representation between IB and IL

  • 4. The short-run dynamic speed of adjustment of IL must be significantly slower than ID.

This section tabulates results for the case of Malaysia in two subsections. Subsection 7.1 tests for the existence of cointegrating vectors, while subsection 7.2 tests the short-run dynamic specification in cases where long-run equilibria exist.

1. Cointegration tests

Three well-known tests were conducted on the time series under discussion to determine if they contained a unit root. 14/ Results are given for the Cointegrating Durbin-Watson Test (CIDW), the Dickey-Fuller Test (DF) and the Augmented Dickey-Fuller (ADF) test.

VARIABLECIDWDFADF
IL.0510-.5-.33
ID.0362-.5-.5
IB.3441-2.1-1.7
ΔIL2.42 ***-6.3 ***-3.2 **(n=4)
ΔID1.72 ***-5.6 ***-3.1 **
ΔIB2.50 ***-5.2 ***-3.4 **
Note. *** indicates acceptance of stationarity at 1 percent, and ** indicates acceptance at 5 percent.
Note. *** indicates acceptance of stationarity at 1 percent, and ** indicates acceptance at 5 percent.

The critical values are those produced in Engle and Granger (1987) (Table II, p. 296); these are developed using Monte Carlo methods based on the bivariate case. From the above table it can be concluded that all of the level variables are I(1) while the differenced variables are I(0). This indicates that it is possible to form cointegrating vectors with all of the level variables.

Tests were then conducted for the existence of a long-run equilibrium between all three interest rates, along the lines suggested by Granger and Engle (1987). They propose that, if the residuals of an OLS regression are I(0) while all the regressors are I(1), a cointegrating vector and a long-run equilibrium exists. The following table shows the usual tests of stationarity of the residuals of the regressions from OLS equations of unlagged levels.

VARIABLECIDWDFADF
Z-DL.11-1.7-1.0
Z-BL.69***-3.3**-2.2
Z-BD1.18***-4.7***-3.81**
Note. “Z-DL” is the residuals formed from the equation IL = α1 ID + ν1; “Z - BL” is the residuals formed from the equation IL = α2 IB + ν2; “Z-BD” is the residuals formed from the equation ID = α3 IB + ν3] where ** indicates acceptance at 5 percent, and *** indicates acceptance at 1 percent that the series is stationary. Critical values are those produced by Engle and Granger, 1987, p. 296, Table II.
Note. “Z-DL” is the residuals formed from the equation IL = α1 ID + ν1; “Z - BL” is the residuals formed from the equation IL = α2 IB + ν2; “Z-BD” is the residuals formed from the equation ID = α3 IB + ν3] where ** indicates acceptance at 5 percent, and *** indicates acceptance at 1 percent that the series is stationary. Critical values are those produced by Engle and Granger, 1987, p. 296, Table II.

From these tests it can be concluded unambiguously that IL and ID do not form a cointegrating vector, and that ID and IB do. All three tests accept the hypothesis that ID and IB cointegrate at a 1 percent significance level, while rejecting the hypothesis of cointegration between IL and ID even at the 10 percent significance level. Both of these results are supportive of the combined model developed above. However, it is not possible to assert unambiguously that IL and IB form a cointegrating vector. While the CIDW test accepts the hypothesis of cointegration at 1 percent, and the DF test accepts the hypothesis at 5 percent, the hypothesis is rejected in the ADF test.

The main reason why the existence of a cointegrating vector between IL and IB is so important is the fact that if such a vector exists, then it can be presumed that a dynamic specification of the error correction mechanism class exists. If the ECM is the correct specification, then not only can that specification be supported on theoretical grounds, but it is possible to compare the speed of adjustment of IL and ID. For this reason this paper will, for the moment, assume that a cointegrating vector does indeed exist between IL and IB, and will determine if the short-run dynamic ECM is correctly specified. This procedure has been followed by Hendry and Ericsson (1989, p. 17) who after finding similarly conflicting results of unit root tests “cautiously proceed under the assumption of cointegration.”

The following section tests for the significance of the ECM specification in the relationship between IL and IB, and ID and IB.

2. Short-run dynamics

There are two reasons for testing the short-run dynamics of the relationship between the interest rates under discussion. The first is to test if the ECM is a congruent representation which would confirm that the combined model could be modelled as (16). The second is to measure the speed of adjustment of IL and ID after an exogenous shock. Two ECM models were tested based on (16) and (17).

The short term dynamic model between IB and ID is as follows.

R2 = 0.27F(2,69) = 12.99σ = .45
BOX-PIERCE(16)F = .93[.4982]
AR (5,66)51F = 1.17[.3354]
ARCH (10,51)F = 1.55[.1492]
HET(4,66)F = 1.22[.3096]
FUNCTIONAL FORM (5,65)F = 1.92[.1034]

The short-term dynamic model between IB and IL is as follows.

R2=.21F(2,69) = 9.46σ = .36
B0X-PIERCE(16)F = .97[.4688]
AR (5,66)51F = 1.49[.2055]
ARCH(10,51)F = .99[.4676]
HET(4,66)F = .70[.5972]
FUNCTIONAL FORM(5,65)F = .95[.4537]

The test statistics indicate that both of the models are well specified. In both models, the ECM term (Z-..) is clearly significant, which is what would be expected if a cointegrating vector existed in the levels equation. It will be recalled that there was some doubt as to whether a cointegrating vector existed between IL and IB. In the model (22), however, the ECM is clearly significant; further indication that IL and IB do indeed form a cointegrating vector. Both of these dynamic models pass a range of diagnostic tests concerning the residuals: the existence of autoregression, ARCH and heteroscedasticity of the residuals, as well as functional form misspecification. These procedures are explained in Appendix II.

The ECM dynamic specification can also be examined by considering the results of recursive tests on (21) and (22). A recursive system can test a given model for parameter consistency because it recalculates the model for each succeeding time period. Thus, a model that is well specified will have relatively constant parameters over time. Hendry and Ericsson (1989, p.15) argue that “recursive estimation of an equation provides an incisive tool for investigating parameter constancy.” They note that if the final recursive estimate lies outside the initial confidence interval, then this would refute the hypothesis of parameter constancy. Both (21) and (22) were tested recursively and the results are displayed in Charts 1 to 4. In these graphs, the middle line is the recursive coefficient, and the outer lines are confidence intervals measured by the coefficient ± 2 standard errors.

Chart 1Malaysia: Deposit Rate Model: Recursive Estimation of the IB Coefficient

Source: Equation 22.

Chart 2Malaysia: Deposit Rate Model: Recursive Estimation of the Z-BD Coefficient

Source: Equation 22.

Chart 3Malaysia: Lending Rate Model: Recursive Estimation of the IB Coefficient

Source: Equation 23.

Chart 4Malaysia: Lending Rate Model: Recursive Estimation of the Z-BL Coefficient

Source: Equation 23.

The parameters in model (21), as displayed in Charts 1 and 2, are remarkably constant over the period of the recursive system. Both the ΔIB and the Z - BD coefficients are very stable even after the regime change of the Malaysian authorities in 1987. For both coefficients of this model, the change in regime is evident in the recursive residuals, but in both cases the coefficients returns to the levels that existed before the regime shift. This would seem to emphasise how well the ECM model acts in describing the short term dynamics between IB and ID.

The parameters of model (22) are also displayed in Charts 3 and 4. In the case of the ΔIB variable, the coefficient is once again very stable over the whole recursive system, except for the period during the regime change. In the case of the Z - BL variable, the coefficient is stable in the period before and after the regime change. However, there does seem to have been a shift in the value of the ECM coefficient because of the regime change. On the whole though, it appears that the short-term dynamic models are satisfactory. In none of the reported recursive estimates does the final coefficient fall outside the initial confidence interval, thus the hypothesis of parameter constancy can be accepted according to the criteria set out in Hendry and Ericsson above.

Once it can be concluded that the above models have been well specified, it is possible to draw conclusions concerning the speeds of adjustment of the IL and ID rates using the formula (21) for the mean lag of adjustment.

Interest RateMean Lag of Adjustment to IB Shocks
IL19.32 months
ID5.09 months

The mean lag of the ID rate is about three and a half times shorter than the IL rate lag. This provides important support for the notion that rates in the lending market are more prone to inertia than those in the deposit market, which could be interpreted that the banks faced adverse selection costs in the market for loans in Malaysia after 1982.

VIII. Conclusion

The aim of this paper has been twofold: to extend the S&W model into a dynamic model and to test the latter for the case of Malaysia. The new model combines the S&W model and the MCP model, and is set in disequilibrium framework. The combined model is based on the stylised fact that the IL rate is relatively volatile, but not as volatile as the IB rate. It is argued that S&W does not fully explain IL dynamics (and volatility) in response to exogenous shocks, while the MCP model leads to the conclusion that the IL (and ID) rates can be as volatile as the IB rate.

The key element of the combined model has been the use of the Error Correction Mechanism to integrate the different costs that are faced by a bank when it sets the IL rate. This resulted in a model that contains short-run disequilibria as well as a long-run equilibrium components. The use of an ECM has also facilitated the use of cointegration techniques to test various aspects of the combined model in the case of Malaysia.

It was found that there exists long-run equilibrium relationships between IB and IL, as well as IB and ID--both important aspects of the combined model. On the other hand no long-run relationship existed between ID and IL in the case of Malaysia. This result refutes an important proposition in some financial liberalization models which assume a perfectly competitive banking system.

This paper also shows that a congruent ECM model, based on the above theoretical propositions, is able to describe IL rate determination in Malaysia. It is therefore concluded that the use of an ECM to describe the combined model may indeed be valid. A congruent ECM model was also found to explain ID rate determination. This means that the speed of response of the IL rate can be compared to that of the ID rate. It is shown that the IL rate is more inert than the ID rate, a conclusion that also supports the combined model of IL determination.

Appendix I: Data Sources

All data is from International Financial Statistics (IFS), published by the IMF.

IB: line 60b IFS (Daily average overnight interbank lending rates of 10 banks for the last week in the month)

ID: line 601 IFS (Mode of the range of rates quoted for three month time deposits)

IL: line 60p IFS (Mode of the range of rates quoted for base lending rates)

Appendix II: Diagnostic Test Statistics

Tests in this paper are those reported by the PC-GIVE package. Full derivations of all these tests can be found in Hendry (1989, pp. 54-58). Each statistic is reported with its five percent critical value in square brackets. Following Hendry, all results are reported in F-test format.

Autocorrelation

BOX-PIERCE Residual Correlogram Statistic, based on sum of squares of the coefficient of residual autocorrelation.

AR Lagrange Multiplier test for residual autocorrelation for lags 1 to 5. Test is based on regression of residuals on lagged residuals.

Heteroscedasticity

ARCH Lagrange Multiplier test for 10th order autoregressive conditional heteroscedasticity. The test is based on a regression of squared residuals on lag squared residuals up to lag 10.

HET Lagrange Multiplier test for Heteroscedasticity associated with squares of the explanatory variables. The test is based on a regression of squared residuals on the original regressors and their squares.

Test of Specification of Functional Form

FUNCTIONAL FORM White test based on a regression of squared residuals on all squares and cross products of the original regressors.

Bibliography

Much of the research for this paper was undertaken when the author was a Summer Intern in the Central Banking Department of the IMF. The author is indebted to Maxwell J. Fry for his detailed comments on many previous drafts of this paper. I would also like to thank Sergio Pereira Leite and Reza Vaez-Zadeh for their help, and for introducing me to the topic. Useful comments were provided by K. Hughes, S. Szabo, and seminar participants at the University of Cambridge.

The S&W model has also been developed for use in the broader debate concerning the origin and propagation of business cycles. The emphasis in this paper, however, is the specific implications of the model for lending rate determination.

See S&W, page 409.

Following S&W, the emphasis in this exposition is on the excess demand for credit, but as has been shown, the model also holds for excess supply of credit.

See S&W, page 409.

S&W do state that when the increase in money supply is greater than the amount of credit that is rationed, then IL will shift. As long as credit is rationed, however, quantities will adjust but not prices (IL).

For simplicity it will be assumed in this model that the banks face the same costs when raising IL to above IL*, as they face when lowering IL to below IL*. This then means that c2 in (15) can be used to measure the costs faced by the banks if they shift IL in either direction. It has been shown by Nickell (1985, p. 127) that it is quite possible in an ECM to aggregate “two components of some variable to a common target but with different adjustment costs” but by assuming that c2 is the same for both excess supply and excess demand, Nickell’s approach is not necessary in this case.

See Villanueva and Mirakhor (1990, p. 519)

It is, of course, possible that IL can be sticky for other reasons.

Dolado and Jenkinson (1988 p. 3) note that “the concept of cointegration is, in many ways, a statistical definition of equilibrium.”

If a series xt is I(1) then Δxt is I(0).

If a cointegrating vector exists, Dolado and Jenkinson (1988) note that “whereas the individual economic variables involved in a theory may all be non-stationary, the deviations from a given equilibrium may be bounded” (p. 21).

In this connection, an important distinction can be made between the ECM and partial adjustment models (PAM). The main problem with the PAM is that the model does not include lags of the independent variables--even though such information is available to agents. A further problem, according to Hendry (1989), is that the distribution is highly skewed. This is because when the coefficient on the lagged dependent variable is close to unity the mean lag becomes very large.

According to Hendry and Ericsson (1989, pp. 11-13), a model is congruent if it successfully passes diagnostic tests for correct specification. These include all the usual diagnostic tests on the residuals of equations as well as tests of parameter constancy.

A nonstationary I(1) series contains a unit root.

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