A Marriage Between Fund and Bank Models?

Reply to Polak

This paper examines factors affecting saving, policy tools, and tax reform. The literature on factors affecting saving and capital formation in industrialized countries is reviewed, and measurement problems are examined. The effect on the saving rate of real rates of return, income redistribution, allocation of saving between corporations and individuals, growth of public and private pension plans, tax incentives, the bequest motive, energy prices, and inflation is considered. The limited tools available to policymakers to affect savings are discussed.


This paper examines factors affecting saving, policy tools, and tax reform. The literature on factors affecting saving and capital formation in industrialized countries is reviewed, and measurement problems are examined. The effect on the saving rate of real rates of return, income redistribution, allocation of saving between corporations and individuals, growth of public and private pension plans, tax incentives, the bequest motive, energy prices, and inflation is considered. The limited tools available to policymakers to affect savings are discussed.

In view of the central role that the Fund and the Bank jointly piay in the formulation of policies directed to adjustment and growth in developing countries, it is surprising that no attempt has been made to examine the relationship between the analytical approaches adopted by these institutions. Our recent paper (Khan and Montiel (1989)) attempted to help fill this gap by describing in formal terms the simplest versions of the Fund’s financial programming approach (FM) and the Bank’s RMSM model, with a view to exploring the relationship between these models.

A natural way to analyze this relationship in a formal manner is to merge these models in such a way that they become nested in a more general analytical framework. The fundamental insight to be gained from such an exercise is the identification of areas of conflict between the models. If no such conflict is found—that is, if the models are mutually compatible, as was found to be the case with regard to the financial programming model and RMSM—then it may be of interest to evaluate the usefulness of the resulting general framework (the “merged” model). The first step in such an evaluation is to identify the properties of the model using standard techniques, and a large part of our paper was devoted to this end.

Polak objects to our “merged” model, or if you like, to the “marriage” of FM and RMSM. We presume the objection is not directed to the marriage as an analytical device to examine the relationship between the models, but rather implicitly reflects his misgivings about the value of the merged model as a tool for analyzing adjustment with growth issues in developing countries.

We do not quarrel with this, and to some extent our exposition was intended precisely to elicit such evaluations. In his comment Polak acknowledges the relationship that we emphasized between FM and RMSM—that is, the monetary approach treats real output as exogenous, and RMSM essentially supplies the missing output equation, thus providing a way to close the financial programming model with endogenous output. We suspect, however, that Polak would simply prefer an alternative specification for output determination other than RMSM. As he puts it, “the absence of an equation does not mean that FM treats output as a loose end for which one can plug in just any number, such as the outcome of RMSM equations” (see p. 184, this issue). This is certainly true, but for the specific analytical purpose described above, the RMSM closure is the only one of interest. Alternative mechanisms are not, however, very hard to come up with, and we shall describe one such below.

First, though, we deal with a number of specific points made by Polak. Basically, we will show that most of Polak’s comments stem from a confusion between comparative-static exercises designed to show the effects of policy changes on the endogenous variables and solving the model in a “policy mode”; that is, finding a set of policies compatible with given macroeconomic targets. We shall consider each of the points in the order in which they appear in his Comment.

(1) Polak claims that the endogeneity of reserves in the merged model is incompatible with RMSM, and specifically that if “the country does not have the reserves, it cannot allow the payments deficit to develop; that is, the merged model is not applicable” (p. 184). In fact, as we indicate in the paper, the Polak model itself (Polak (1957)), as well as the merged model that incorporates it, is intended to handle just this situation. These models would typically be solved to obtain the policies that would yield a nonnegative balance of payments outcome because a country “does not have the reserves.” The endogeneity of reserves does not preclude treating them as a policy target, and the very purpose of models is to identify the policy measures required to achieve such targets. The calculation of credit ceilings in Fund-supported adjustment programs, for example, is done precisely in this fashion.

(2) Contrary to Polak’s claim, no particular technical problems arise in combining a model of short-run macroeconomic equilibrium with one of long-run growth. The problems we describe in the last section of our paper have to do with the shortcomings we perceive in the merged model as a description of macro economic reality in developing countries, not with technical problems of this sort. Adjustments are assumed to take place in a single period only for simplicity—to permit us to telescope ail interactions into one period and thus avoid complicating the exposition with dynamic analysis. Similarly, the starting point of zero inflation and zero growth simply implies that we chose to measure our variables as deviations from last period’s values. This simplifies certain derivatives, but has no substantive implications.1

(3) Polak addresses three issues under his third point. First, regarding our credit expansion exercise, Polak seems to be confusing a comparative-static result with a policy prescription. He claims that countries should be advised not to increase credit because that will raise prices and worsen the balance of payments. That conclusion is presumably based on a model of some sort—possibly the Polak model. The merged model also predicts precisely such an outcome. At no point were we suggesting that countries embark on a credit-expansion spree. We could just as easily have done the exercise for a reduction in credit, and all that would change would be the signs of the derivatives.

Second, that devaluation must worsen growth when it improves the current account is indeed a model-specific result, but not one that arises from “quirks” in the merged model. As we pointed out in the paper, this is a characteristic of open-economy Harrod-Domar models, of which the RMSM is one.

Finally, regarding the effects of an increase in government saving, Polak has again confused a comparative-static exercise with a policy prescription. Certainly conducting separate comparative-static exercises in isolation in a theoretical analysis does not imply that combinations of policies should not be used in actual applications. But one needs a model to identify the appropriate combinations. It may be worth noting that the accommodative credit policy that Polak recommends as an adjunct to increased public saving requires that, in setting credit ceilings for the period ahead (for example, in a Fund-supported program), the authorities be able to predict the output consequences of the increase in public saving. This means that output cannot be taken to be exogenous, as in the financial programming model, but rather the “missing equation” must be supplied, as in the merged model.

As indicated above, we suspect that Polak would prefer an alternative “missing equation.” It is not difficult to provide one that does not involve “setting the growth rate in [FM] equal to that produced by [RMSM].” For example, suppose that the “growth” component of the merged model explains capacity growth, while the “monetary” component (equation (23) in Khan and Montiel (1989, p. 289)) explains the growth of actual output. Lety¯ denote capacity output, and y denote actual output. This notation requires rewriting the production function (equation (8), p. 283) as


Substituting for dk as in Khan and Montiel yields


By allowing actual output to deviate from capacity, we have in effect introduced an additional unknown into the merged model. To close the model, therefore, an additional equation is needed. A natural missing equation is an aggregate supply relationship—for example, one that links domestic inflation to the gap between actual and capacity output:


where PD is the price of domestic goods, taken to be unity in the previous period, and -y is a positive parameter. This equation states that the price of domestic goods will change in proportion to the change in the ratio of actual output y to capacity output y¯

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The properties of the model with this form of closure can be established directly. Rewrite (3) as


By substituting into (3a) from equation (2) above, a modified “growth component” is derived, which can be combined with the “monetary component” (equation (23), p. 289) to solve the new model. The new growth component is


Except for the first term in the numerator, equation (4) is identical to equation (22) in the merged model of Khan and Montiel (p. 288) for (y/y¯)0=1. The positive relationship between dPD and dy in the merged model’s equation (22) is preserved in (4) above, so the implied GG locus in the modified model has a positive slope, as in Khan and Montiel (p. 290). Similarly, the qualitative effects of policies on the position of this locus are the same under equation (4) above as under equation (22) in Khan and Montiel. Though the magnitude of the comparative-static multipliers would be affected, the properties of the model would be qualitatively the same. As such, Polak’s misgivings about the properties of the merged model cannot be attributed to our defining the “output” that appears in the monetary model with that which is explained by RMSM.

In conclusion, we can certainly sympathize with Polak’s reluctance to marry his model with the RMSM model, and we also share his view that the merged model is not ideal, for the reasons we outlined in Section III of Khan and Montiel. But at the same time, we feel that it would be premature to pronounce the marriage a failure until we have seen the quality of the offspring. The model we have outlined, as we stressed in our article, can serve as a basis for the development of more realistic models that capture the complexities of growth and adjustment, if only by focusing the discussion on precise identification of the model’s shortcomings, thereby permitting superior, but equally policy-relevant, alternatives to emerge.


  • Khan, Mohsin S., and Peter J. Montiel, “Growth-Oriented Adjustment Programs: A Conceptual Framework,” Staff Papers, International Monetary Fund (Washington), Vol. 36 (June 1989).

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  • Polak, Jacques J., “Monetary Analysis of Income Formation and Payments Problems,” Staff Papers, International Monetary Fund (Washington), Vol. 6 (November 1957).

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Mohsin S. Khan is Assistant Director in the Research Department. He is a graduate of Columbia University and the London School of Economics and Political Science.

Peter J. Montiel is Assistant Chief of the Developing Country Studies Division of the Research Department. He is a graduate of Yale University and the Massachusetts Institute of Technology.


In any financial programming exercise one would typically start with last period’s values. Furthermore, evaluating derivatives around an arbitrary point such as zero is standard procedure.


Note thatd(y/y¯)=dy/y¯0(y0/y¯02)dy¯=y¯01[dy(y/y¯)0dy¯].