**A**BILITY TO DETERMINE the effect of changes in government policy variables on the balance of payments and income has been of major concern to policymakers in developing countries. A prerequisite to evaluating these effects is showing how income and the balance of payments are determined, since it is only then that a study can be made of the channels through which policy variables act. This paper presents a theoretical specification of a model considered relevant for analyzing the behavior of nominal income and the balance of payments in developing countries and tests the resulting model for a group of such countries. Since the model centers on the monetary aspects of income and balance of payments determination, it can be described essentially as a “monetary” model.^{1}

The model in this paper will attempt to analyze the determination of income and the balance of payments within the monetary framework for ten developing countries over the period 1952-70. The countries in the sample are Argentina, Colombia, the Dominican Republic, India, Mexico, Pakistan, Peru, the Philippines, Thailand, and Turkey. The common features among these geographically distinct countries are that they are all defined as “developing,” are small,^{2} are open, and—except Argentina, and Thailand up to 1954—maintained fixed exchange rates throughout the period specified. The Dominican Republic was studied for a shorter period, 1953-70, because of difficulties in obtaining data.

The model is formulated in disequilibrium form, as this procedure provides more information, especially on possible lags in adjustment, than would an equilibrium model. In addition, from a statistical standpoint, it is necessary to have a disequilibrium formulation in order to determine whether or not the system is in equilibrium; if the observations are in fact generated by a disequilibrium structure, performing the estimation in equilibrium form would result in a bias caused by incorrect specification. The model is estimated for each of the ten countries in continuous form as a linear stochastic differential equation system. The main reason for considering a set of differential equations, rather than a discrete system of difference equations, is based on the proposition that the behavior of the economic system can be represented more accurately by a continuous model. This is especially true of the monetary approach to determination of income and the balance of payments,^{3} for which, despite the lack of continuous observations, it would be useful from the point of view of the policymaker to have a continuous prediction of these key variables.

Section I of this paper describes the basic model and shows the derivation of each of the functional relationships. Section II discusses the results obtained from estimating the model, and Section III discusses some policy implications. The Appendix describes the techniques used in estimating the model.

## I. Description of Model

The model specified is a six-equation one, containing three behavioral relationships—for imports, exports, and aggregate expenditure—and three identities—for nominal income, the balance of payments (change in net foreign assets), and the money supply. Each of these is discussed.

### IMPORTS

The demand for aggregate nominal imports in time period *t* is generally specified to be a positive function of domestic income. However, the demand for foreign goods and services should be related to total domestic expenditure on all goods and services and not to purchases of domestic goods and services by both domestic and foreign residents, which the use of income as an explanatory variable would involve.^{4}

Therefore, in general, imports should be related to domestic demand for all goods including imports, namely, to aggregate expenditure.

However, particularly for developing countries, relating imports to aggregate domestic expenditure might involve some incorrect specification, as no account would be taken of the existing quantitative restrictions and controls on imports. In order to correct for this, the inclusion of a variety of proxies in the import equation—such as the level of international reserves, of exports, or of overseas assets—have been suggested by Islam (1961), Dutta (1964), and Turnovsky (1968). The basic assumption behind the use of such variables is the implied existence of a government policy-reaction function relating the imposition of controls inversely to one of them. The authorities in the country concerned are assumed to ease and to tighten restrictions on imports as their capacity to import increases or decreases. The most suitable proxy for such capacity would seem to be the level of net foreign assets, and this is used in the formulation.

Import demand is thus specified as a linear function of the level of net foreign assets and aggregate expenditure in time period *t*:

where *M ^{d}* is demand for nominal imports,

*NFA*is the level of net foreign assets, and

*AE*is aggregate nominal expenditure; u is a random error term with “white noise” properties.

^{5}

The expected pattern of signs is as follows:

^{6}

Because of the assumption that the countries are small and have fixed exchange rates, a relative price argument in (1) is impossible, since domestic and foreign prices would be equal, and the relative price ratio would be constant.

Actual imports in period *t* are assumed to adjust to excess demand for imports, that is, to the difference between demand in period *t* and actual supply in the same period:

where *D* is an operator equivalent to some form of stochastic differentiation (i.e., it is equivalent to *d/dt*). A further assumption is that import supply is equal to actual imports:

Formulations of this type have been applied to studies of import behavior on the grounds that imports of many countries, especially developing ones, consist mostly of durable goods, the demand for which has been shown to fit into this type of framework.^{7} This specification introduces an explicit distributed lag structure, through costs of adjustment, into the determination of imports.

Substituting (1) into (1), the estimating equation becomes:

### EXPORTS

In the small-country case, exporters are generally price takers in the world market and can sell whatever they produce. The volume of exports is therefore determined by supply conditions present in the export sector. An increase in the capacity to produce in the export sector should lead to an increase in exports.

Capacity to produce in the export sector is related directly to the capacity to produce in the entire economy, and an increase (decrease) in the latter capacity would lead to an increase (decrease) in exports. If income is considered a suitable indicator of capacity to produce, exports can be specified as a positive function of domestic income. Whether exports will increase more than in proportion to income will depend on the supply elasticity of domestic goods relative to the supply elasticity of exports.^{8}

An indicator of the capacity to produce that would be more appropriate than current income is “permanent,” or expected, income. Exports are specified as a function of this long-run concept, rather than the shortrun concept of current income:

where *X* is the nominal value of exports and Y^{*} is the concept of permanent nominal income in time period *t*; *v* is a random error term.

The parameter bx is expected to be positive.

Permanent income is generated in the following way:

Permanent income in time period *t* adjusts to the difference between permanent income and actual income (*Y*) in period *t*.

Equation (5) can be rewritten as:

and solving for *DX(t)*:

where *ε(t) = (D + β), v(t)* is a moving-average process of order one.^{9}

The estimating equation (8) could also have been derived through a partial-adjustment hypothesis, although the error term would be different.

### AGGREGATE EXPENDITURE

In the standard Keynesian model of a closed economy, aggregate expenditure (consumption *plus* investment) depends on the level of domestic income and the domestic interest rate. The familiar IS-LM framework considered within a disequilibrium framework shows how a change in monetary policy affects expenditure, through the impact of changes in the interest rate on investment expenditure. Rather than introducing the rate of interest, which represents the yield on only one asset, it may be more appropriate to include in the expenditure function the stock of liquid assets that the public desires to hold directly. Given this stock, an increase in the money supply would raise it above the desired level. This would create an excess demand for goods and services and would lead to higher expenditure as the public attempted to reduce its excess cash balances. Increases in nominal income could also be expected to increase nominal expenditure.

The equation for “desired” expenditure can be specified as follows:

where *AE ^{d}* is desired aggregate nominal expenditure,

*M*is the stock of money representing the stock of liquid assets, and

_{o}*Y*is nominal income; w is a random error term, and c1 and c2 are parameters having the following pattern of signs:

The cash balances variable, *M _{o}*, included in equation (9) is defined as broad money, comprising currency, demand deposits, and time and savings deposits. In developing countries, with a limited range of financial assets, the use of Mo to represent all liquid assets would not be too unrealistic. The expenditure variable, AE, includes government expenditure, so that an implicit assumption is that the fiscal authorities are constrained in their deficit financing by the monetary authorities.

A behavioral equation such as (9), although outwardly different, has been shown by Fleming (1938) and Rhomberg (1965) to be entirely consistent with the general Keynesian formulation.

The actual value of expenditure is assumed to adjust to the difference between “desired” expenditure and actual expenditure:

By substituting (9) into (10), the differential equation in DAE(t) is obtained:

This is the equation that will be estimated.

### NOMINAL INCOME

Nominal domestic income is equal to nominal aggregate domestic expenditure *plus* nominal exports *minus* nominal imports:

This identity must hold, *ex post*.

### BALANCE OF PAYMENTS

The balance of payments in nominal terms is equal to the trade balance (exports minus imports) plus all other items in the balance of payments account; it is also equal to the change in a country’s net foreign assets.^{10} Therefore, the identity can be written as:

where *DK(t)* represents the nontrade variable that contains services, short-term and long-term capital flows (including official), and all types of foreign aid receipts or repayments. For the purpose of the model, this item (i.e., *DK*) is assumed to be determined outside the system.

### THE MONEY SUPPLY

The stock of money in an economy is equal to the stock of net foreign assets and domestic credit of the consolidated banking system:

where *C* is the stock of domestic credit. This concept of money, as will be recalled, is the broad one, including time and savings deposits.

*C* is treated in this study as a monetary policy instrument. For this to be justified, either of two related assumptions must be satisfied: the authorities must be able to control the instrument directly, or the money multiplier relating the money supply to the monetary base—*Mo = m H*, where *H* is the stock of high-powered money (reserve money) and *m* is the multiplier—must be constant. It can be shown that the relationship between domestic credit and the assets of the central bank can be expressed as:

so that the monetary authorities can control total credit in the economy by controlling the stock of net domestic assets (NDA). In the countries under consideration, the multiplier was, in general, relatively stable over the period.^{11}

### SUMMARY OF MODEL

Combining equations (3), (8), and (11) and identities (12), (13), and (14), the basic model is specified in linear form.

where the variables are defined in domestic currency terms as follows:

*M*= nominal value of imports*X*= nominal value of exports*AE*= aggregate nominal domestic expenditure*Y*= nominal domestic income*DNFA*= change in net foreign assets of the consolidated banking system*Mo*= nominal money supply*DK*= all items in the balance of payments other than the trade balance*C*= domestic credit of the consolidated banking system.

The causal sequence of the model can be outlined as follows.^{12} An increase in the stock of net domestic assets (an expansionary monetary policy) would result in an expansion of the stock of money,^{13} from the identity (14). This expansion would increase the rate and the level^{14} of nominal domestic expenditure as the public attempted to get rid of its excess liquidity, from equation (11). This rise in nominal domestic expenditure would have two effects: it would lead to an increase in domestic nominal income, from the identity (12), and it would also increase imports above their pre-expansionary monetary policy level, from equation (3). Naturally, this rise in imports would lower income. Assuming, however, that the effect on the income that is due to an increase in expenditure is greater than that due to the increase in the level of imports,^{15} overall income could be expected to rise. This rise would increase expenditure further and would also increase the rate of change and the level of exports, from equation (8). The ensuing rise in the level of imports would tend to worsen the balance of payments, from identity (13); if this rise exceeded that in exports, the balance of payments would worsen. If sterilization policies were not put into effect, the money supply would then decline. A once-and-for-all increase in C would have a temporary effect on the economy in the short run, but in the absence of sterilization policies, in the longer run the effects would be completely reversed.

The process just outlined is a direct extension of the monetarist approach to an open economy. Theoretical arguments of a similar nature can be found in Prais (1961), Laffer (1968), Johnson (1972), and Guitian (1973). An empirical application of this type of model has been made by Polak (1957) and Rhomberg (1965) for a number of countries.

## II. Results

The model outlined in Section I was estimated for the period 1952-70 for each of the countries in the sample except the Dominican Republic, for which the period was 1953-70. The method of estimation was three-stage least-squares, and various transformations were made to approximate the differential equations.^{16} All data were obtained from the IMF Data Fund.

For each country the estimates of the structural equations with *t* values of the estimated coefficients are shown in parentheses, and the within-sample predictions of the trade balance (capital flows are assumed to be exogenous) and changes in nominal income obtained from the calculated “reduced form” are also presented. Although the level of nominal income is determined in the model, since actual values of the lagged endogenous variables are used, the predicted values of the current level of nominal income would be expected to be accurate. Therefore, it was felt that comparing first-differences of the predicted and actual values of nominal income would be more informative. The results are discussed individually for each country.

### Argentina

Table 1 shows the structural equation estimates. In the import equation (1), all estimated coefficients have the expected signs and are significant at the 5 per cent level. Net foreign assets appear to impose a large constraint on the change in imports, with a rise of, say, $a 1 million in *NFA* increasing the change in imports by roughly half a million. Aggregate nominal expenditure has a positive effect on imports, as expected in theory. The lag in adjustment of imports to desired levels is fairly long,^{17} as the estimate of the coefficient of adjustment is on the low side.

Current nominal income has a positive effect on the change in exports, and the estimated coefficient is significant at the 1 per cent level. The estimated coefficient of the level of exports also has the correct sign and is highly significant in equation (2).

In the aggregate expenditure equation, the estimated coefficient of the stock of money is fairly large and has the correct positive sign. However, the coefficient of current income is not significantly different from zero even at the 10 per cent level. This is an unusual result, since it implies that neither consumption nor investment expenditure is influenced by current income. This may be due to a high degree of multicollinearity between *M _{o}* and

*Y*, leading to a high variance for the estimated coefficient of income. The estimate of the coefficient of adjustment is significant at the 1 per cent level and has the expected negative sign. The mean-time lag in the adjustment of actual expenditure to desired levels is a little more than one year.

The estimates of the structural equations show that the model appears to fit Argentine data fairly well, with only one estimated coefficient turning out to be insignificant. Chart 1 shows the plots of the actual and simulated values of the balance of trade and changes in nominal income. These within-sample predictions are derived from a reduced form equation relating the endogenous variables to the exogenous or policy-determined variables.

Chart 1 shows that the model appears to track the change in income reasonably well, although substantial differences between the actual and simulated values do appear toward the latter part of the period.

For the trade-balance simulations, the model captures most of the changes that took place. Errors of about $a 200 million are found

**Argentina**

**Argentina**

**Argentina**

in the period 1963-67, while they are generally much smaller in the years up to 1963.

### COLOMBIA

In the structural model, estimates shown in Table 2 (the estimated coefficients in the import equation) are all significantly different from zero and have the expected signs. A unit increase in the net foreign asset holdings of the authorities will lead to a change in imports of 0.962 unit, and a similar increase in aggregate expenditure will change imports by only 0.035 unit. The coefficient of adjustment implies that importers adjust to the desired level in about three years.

Current nominal income has a positive and significant effect (at the 5 per cent level) on the change in exports, but the estimate of the coefficient of adjustment of permanent income, although having the correct sign, is not significantly different from zero. A suitable proxy for capacity to produce in Colombia seems to be current rather than permanent income.

The estimated coefficients of the money supply and income are both significant and positive in the expenditure equation. A unit increase in the stock of money will have a proportionately greater effect on the change in nominal expenditure, leading to an increase of 1.387 units. A similar increase in income will change expenditure by 0.816 unit. Nominal expenditure will adjust to its desired level in approximately 16 months after the money supply or income changes.

Chart 2 shows the within-sample predictions for the change in income and the trade balance. The model is not able to capture changes in income at all well, as is evident from the first half of the chart; major fluctuations of about Col$2 billion appear to have taken place on occasion. The predictions of the trade balance, however, are much more accurate except for 1969, for which the model predicted a further worsening and the deficit in fact remained constant. The model does well in capturing the major movements, in the trade balance that took place from 1964 onward, including the sharp cycle from 1964 to 1968.^{18}

### DOMINICAN REPUBLIC

Table 3 shows the estimates of the structural model for the period 1953-70. The estimated coefficients of net foreign assets and aggregate

**Colombia**

**Colombia**

**Colombia**

**Dominican Republic**

**Dominican Republic**

**Dominican Republic**

nominal expenditure are both significantly different from zero at the 1 per cent level and have the expected positive signs in equation (1). A 1-unit increase in each of these two variables would increase the change in imports by 0.7 unit.^{19} Imports appear to adjust fairly rapidly to eliminate excess demand, reaching their desired position in little more than a year and a half, as calculated from the estimated coefficient of the level of imports.

The level of current nominal income has a positive and significant effect on the value of exports, and the coefficient of adjustment of permanent income is also significant. Permanent nominal income adjusts in approximately two years.

All estimated coefficients in the nominal expenditure equation are significantly different from zero at the 5 per cent level and have the expected signs. A simultaneous increase of one unit in the stock of money and the level of current income would lead to an increase in imports of 2.6 units. The estimated coefficient of adjustment of nominal expenditure to its desired level is 0.764, implying a mean-time lag in adjustment of slightly more than 16 months.

The model appears to fit the Dominican Republic data fairly well, as all estimated coefficients had the correct signs and were significantly different from zero at the 5 per cent level.

Chart 3 shows the plots of the actual and simulated values of the change in income and the trade balance. Changes in nominal income fluctuate quite substantially, and the fitted and actual values diverge frequently. The largest error appears in 1966, for which the model overestimated the change by about RD$150 million; the actual level of nominal gross domestic product was about RD$1 billion, so that the error was approximately 15 per cent. The movements in the trade balance, however, are very accurately tracked. This occurs despite the fact that the plot of the actual trade balance shows substantial cyclical variation. The largest error was approximately RD$20 billion (1969).

### INDIA

Table 4 shows the structural model estimates. In the import equation, the level of aggregate expenditure has a positive effect as expected and the estimated coefficient is significant at the 1 per cent level. The surprising result is that the level of net foreign assets has no effect on the change in imports. In the framework of the model this has one of two

**India**

**India**

**India**

possible implications: either restrictions are not important in the determination of imports in India or the authorities do not look to the country’s net foreign asset position when changing the level of restrictions; since restrictions were operative in India over the period 1952-70, the latter implication would seem to be more relevant. The mean-time lag in adjustment of imports is just over one year.

The results of the export equation show that a unit increase in current income will lead to an increase of 0.228 unit in exports. The estimated coefficient of income is highly significant. The estimated coefficient of the adjustment of permanent income has the correct sign and is also significantly different from zero.

Both the nominal stock of money and nominal income exert a positive effect on the change in aggregate nominal expenditure. The effect of a simultaneous increase of one unit each in both these variables would raise imports by 2.207 units. The adjustment of actual nominal expenditure to a desired level is fairly rapid, with the mean-time lag being marginally greater than one year.

Chart 4 shows the simulated and actual values of the change in income and in the trade balance. Changes in income are not very well predicted, with substantial errors appearing especially in the latter part of the period.^{20} Except for the years 1958 and 1967, the direction in which income is changing is tracked well by the model; so is the direction of trade balance movements, with the predicted values being close to the actual, especially in the period after 1965.

### MEXICO

Table 5 gives the estimates of the structural model. All estimated coefficients in the import equation are significantly different from zero at the 5 per cent level. Net foreign assets and aggregate nominal expenditure both have a positive impact on the change in nominal imports. The adjustment of imports takes almost three years to complete.

In the export equation, both of the estimated coefficients are significantly different from zero and have the expected signs. An expansion in current nominal income of one unit will lead to an increase in nominal imports of 0.019 unit. The estimated coefficient of the adjustment of permanent nominal income, that is, the “expectations coefficient,” is 0.270.

**Mexico**

**Mexico**

**Mexico**

A change in the stock of money has a strong impact on the change in aggregate nominal expenditure, and the estimated coefficient is significantly different from zero at the 1 per cent level. Current income, however, appears to have no effect on expenditure; this result is similar to the one obtained for Argentina. In both cases the coefficient has the correct positive sign but is not significantly different from zero, perhaps because of a high degree of multicollinearity between the stock of nominal money and the flow of nominal income. The mean-time lag in the adjustment of aggregate expenditure to a desired position is a little more than one year.

Chart 5 shows the plots of the actual and simulated values of the change in nominal income and in the trade balance. The model captures the direction of change in income except for the years 1965, 1967, and 1969; in the earlier part of the period the predicted values are fairly close to the actual. The movements in the trade balance are tracked accurately, especially from 1961.

### PAKISTAN

Table 6 gives the results for the structural model. The estimated coefficients of net foreign assets and aggregate nominal expenditure are both significantly different from zero at the 5 per cent level in equation (1) and both have the expected positive signs. A unit increase in net foreign assets would increase imports by 0.798 unit. A similar increase in aggregate expenditure would increase the change in imports by 0.015 unit. Although the effect of aggregate expenditure is small, nevertheless it is significant. Actual imports appear to adjust fairly slowly to eliminate excess demand, taking almost four years to reach the desired level of equilibrium.

The level of current nominal income has a positive and significant effect on the change in value of exports. The expectation coefficient is also significantly different from zero and has the postulated sign.

All estimated coefficients in equation (3) are significant and have the correct signs. The estimate of the effect of a change in the money supply on the change in nominal expenditure is less than 1; and, while theoretically there is no reason to expect the coefficient to be anything other than positive, Pakistan is the only country in the sample where this occurs. The reasons for this are not immediately obvious. The estimate for the coefficient of adjustment of actual expenditure to a desired level is fairly low, implying a fairly long mean-time lag of nearly two

**Pakistan**

**Pakistan**

**Pakistan**

years (1.927). Again, Pakistan is the only country where the lag is greater than 18 months. The length of this lag provides some information on why the impact coefficient of money on the change in nominal expenditure was low.

The model appears to explain the Pakistan economy fairly well, as all estimated coefficients have the expected signs and are statistically significant. Chart 6 shows the actual and simulated values for the change in nominal income and in the trade balance. Considerable fluctuations are evident in the behavior of income, and the model does not perform very well in this respect. Movements in the trade balance, however, are tracked rather accurately, although the deterioration in the two years following the military take-over in 1958 is underestimated by the model, as is the sharp improvement in 1963. The error for 1963, approximately PRs 200 million, was the largest.

### PERU

Table 7 shows the structural estimates for the model. The estimated coefficients for net foreign assets and aggregate expenditure are significantly different from zero at the 5 per cent level. A simultaneous increase of one unit in net foreign assets and in aggregate expenditure would result in an increase of 1.017 units in imports. The coefficient of adjustment has the correct sign and is significant at the 10 per cent level.

In the export equation, the estimated coefficients for current income and exports both have the expected signs and are significantly different from zero.

In the aggregate expenditure equation, the estimated coefficients of both the stock of money and current nominal income are fairly large and have positive signs. Both coefficients are statistically significant. A simultaneous increase in the stock of money and in current income would have a larger impact on aggregate expenditure in Peru than in any other country covered in this study. A unit increase in both variables would result in an increase of 3.498 units in the rate of nominal expenditure. Actual expenditure adjusts to the desired level fairly rapidly, in just over one year.

Chart 7 shows the actual and simulated values for the change in income and in the trade balance. The model performs fairly well, with substantial errors appearing only in the period 1962-66. The sharp deterioration in income from 1962 to 1963 is badly underestimated;

**Peru**

**Peru**

**Peru**

in attempting to correct for this, the model also misses the improvement in 1965. The movement in the trade balance is accurately tracked by the model, with a sizable error appearing only in 1965. Even cycles in the trade balance are depicted well; in fact, the predictions for the trade balance of Peru are the best of the countries studied here.

### PHILIPPINES

Table 8 shows the structural model estimates. All estimated coefficients in the import equation are significantly different from zero at the 5 per cent level and have the correct signs. The coefficient of aggregate expenditure is the highest obtained for any of the countries in this sample, that is, slightly more than 0.1. A unit increase in net foreign assets and in aggregate expenditure raises imports by 0.896 unit. The estimate for the coefficient of adjustment implies that imports would take about two years to adjust to the desired level.

The effect of nominal income on the change in nominal exports also appears to be the strongest in the Philippines, relative to the other countries in the sample. Both coefficients have the correct signs and are significantly different from zero at the 5 per cent level.

The estimate of the coefficient of the money stock in the aggregate expenditure equation has the expected positive sign and is highly significant. Current nominal income, however, though having the correct sign, appears to have no significant effect on the change in nominal expenditure; this may be a result of multicollinearity between the nominal stock of money and nominal income. Expenditure will adjust to its desired level in approximately five quarters following a change in the money supply.

Apart from the estimated coefficient of income in equation (3), all other coefficients are significant and have the expected signs.

The within-sample predictions for the change in income and in the balance of trade are shown in Chart 8. The income predictions are affected by fairly large errors in 1961, in 1965, and especially in 1970, when there was a major increase in income that the model badly underestimates. The trade balance predictions are fairly accurate, with appreciable errors appearing only in 1957 and 1963. The error for 1963 can perhaps be explained through the improvement in the trade balance following the devaluation of the peso in 1962.

**Philippines**

**Philippines**

**Philippines**

### THAILAND

Table 9 shows the estimates of the structural model. The estimated coefficients of net foreign assets and aggregate nominal expenditure are both significantly different from zero at the 5 per cent level, and have the expected positive signs in the import equation. However, the combined effect of a simultaneous change in each of these variables on the change in nominal imports is somewhat weak. Imports take more than two years to adjust to a desired level, with the mean-time lag calculated at 2.387.

Neither of the two estimated coefficients in the export equation is significantly different from zero, although they have the correct expected signs. Thus, nominal exports can be treated as entirely exogenous for Thailand.

The stock of money has a strong effect on the change in nominal expenditure, with the estimated coefficient turning out to have the correct sign and being significantly different from zero at the 1 per cent level. The estimated coefficient of nominal income, though having the expected positive sign, is significant only at the 10 per cent level. Nominal expenditure adjusts to a desired level in approximately six quarters (the mean-time lag being 1.590).

Thailand is the only country in the sample for which neither current nor permanent income has any effect on the change in nominal exports. Three of the estimated coefficients were insignificant at the 5 per cent level—the largest number for any of the countries studied.

Chart 9 shows the plots of the actual and simulated values of changes in income and in the balance of trade. The predicted values of changes in income are reasonably accurate, with substantial errors appearing only in 1959 and 1966. The trade balance predictions are accurate for the period up to 1962, including the years (1952-54) when the exchange rate was flexible. After 1962 the movement of the trade balance is captured with respect to direction if not to magnitude.

### TURKEY

Table 10 shows the estimates obtained for the structural model. The estimated coefficients of net foreign assets and aggregate expenditure are both significantly different from zero at the 5 per cent level and have the expected signs. However, similarly to the results for Thailand, the combined effect of a unit increase in both of these variables yields only a rather small increase (0.278 unit) in imports. The lag in adjust-

**Thailand**

**Thailand**

**Thailand**

**Turkey**

**Turkey**

**Turkey**

ment of actual imports to eliminate any excess demand is also rather large, as imports adjust to a desired equilibrium level in about three and a half years.

Both coefficients in the export equation have the expected signs and are significant at the 1 per cent level. Permanent income seems to be a reasonable proxy for capacity to grow in Turkey.

The impact of the money supply on the change in aggregate expenditure appears to be the strongest in Turkey; the coefficient is positive and significant even at the 0.05 per cent level. The estimated coefficient of current income, however, has the wrong sign and is insignificant. It could of course be that, because of multicollinearity, the money supply variable is picking up the effect of nominal income as well. The adjustment of nominal expenditure to a desired level is fastest in Turkey among the countries studied, with a mean-time lag of only 0.987.

Chart 10 shows the plots of the actual and simulated values for the change in nominal income and in the trade balance. Apart from the period after 1966, the model tracks changes in income rather accurately, with a large error occurring only in 1958. The trade balance predictions, on the other hand, are more accurate after 1966. Prior to that, the sharp movements that occurred in 1956, 1961, and 1964 were all badly underestimated. The worsening of the position after 1966, when imports grew quite dramatically, was picked up.

## III. Conclusion

The basic purpose of this study has been to show how two key macroeconomic variables—the balance of payments and nominal income—in developing countries can be explained within a monetary framework. To achieve this purpose, a small aggregative model was constructed. This model was designed to show the channels through which monetary policy operates in an open economy and affects domestic activity and the balance of payments. The monetary model was then tested for ten developing countries for the period 1952-70. Certain common results emerge from the estimates of the model for individual countries. Despite some obvious dissimilarities between countries, most of the estimated coefficients in this study appear to be of the same order of magnitude. In the import equation estimates, the coefficient for net foreign assets ranges from approximately 0.3 to 0.9 and the coefficient of aggregate expenditure from 0.02 to 0.10, with most figures at the lower end. The lag in adjustment of imports to a desired level varies from 1.340 (for India) to 6.098 (for Peru). The current-income coefficients in the export equation lie between 0.02 and 0.1 and the expectations coefficients between 0.1 and 0.7, with most between 0.3 and 0.5. With the exception of the results for Pakistan, the stock of money has a greater than proportionate effect on nominal expenditure, with the estimated coefficients ranging from 1.4 to 2.2. Differences among countries as to the estimated income coefficient in the nominal expenditure equation are much greater. The lag in the adjustment of expenditure to a desired level is generally similar among countries, varying from one to two years; if Pakistan is removed, the lag varies from four to six quarters.

Judged by the simulations, the model was able to explain a good deal of the behavior of the trade balance over the period in most of the countries. This occurred even when the improvement was presumably a result of a change in the exchange rate (which is outside the model). The model thus gave good results both for countries where devaluation occurred frequently over the period (1952-70), namely, Argentina and Colombia, and for countries where the exchange rate was fixed, that is, the Dominican Republic. The model was also able to explain the behavior of the changes in nominal income for all countries reasonably well.

In an open economy, monetary policy affects prices, output, and the balance of payments in the short run. This study aggregated prices and output into one variable, nominal income, and this may be considered somewhat unrealistic. A more disaggregated model would have to deal with the effects of monetary policy on output and domestic prices separately. The present model can therefore be viewed as a starting point on which to build by incorporating particular institutional features present in individual countries so as to attain a greater degree of realism. The purpose of this study was to develop a framework for model building in developing countries, and it appears from the results that an approach centering on the monetary aspects of balance of payments and nominal income determination is a useful one to take.

## APPENDIX

### Estimation of Linear Stochastic Differential Equation Systems

This Appendix presents a short summary of the technique used in estimating the models in the paper and a description of the computer programs used. The presentation relies almost exclusively on the work by Sargan (1968) and Wymer (1972 a and 1972 b).

A recursive model of rth order differential equations is as follows:

where *D* is an operator equivalent to stochastic differentiation, *y(t)* is a vector of endogenous variables, *z(t)* a vector of exogenous variables, *u{t)* a vector of disturbances, and A and B matrices of coefficients.

The disturbances u(t) are assumed to be generated by a stationary process with constant spectral density, so that the integral

is a homogeneous random process with uncorrelated increments. Since ε(*t*) is “white noise” and nondifferentiable, *u(t)* cannot be rigorously defined. As Wymer (1972 b) has shown, it is necessary therefore to consider (1) as

where *u(t)* is replaced by the mean-square differential of ε(*t*). This may be written as the first-order system:

The exact discrete model derived from the solution to (3) is as follows:

The derivation of (4) and the definition of *w ^{*}(t)* are given in Wymer (1972 b).

If the observations are generated by (2), they will satisfy (4) irrespective of the length of the interval between successive observations, so that the sampling properties of (2) may be studied by considering the sampling properties of (4). Generally the variables *z{t)* will not be analytic functions of time, so that the integral *ds* cannot be evaluated directly. This integral can be evaluated directly, however, if *z(s)* is a linear or quadratic function of *s*. See Wymer (1972 b) and Sargan (1968).

Since it is computationally expensive to estimate (4) subject to general a priori restrictions on *A ^{*}* and

*B*,

^{*}^{21}an approximation that maintains the structural form and requires less computing time to estimate can be used as an alternative.

This approximation to (2) is a nonrecursive discrete model derived by integrating over the interval *(t—1, t)* and using the approximations

where Δ=1-L and *M= 0.5(1+L)* and *L* is the lag operator.

The approximate model is

where *V ^{*}t* is a vector of disturbances depending on the errors in (2) and the errors of approximation. The approximate estimating equation is

where *V ^{t}* is a moving-average process of order

*r*—1 and depends on the coefficients of (5) and

*V*. This may, however, be approximated by a moving-average system, again of order r—1, that is independent of the parameters of the model. The estimates obtained for

^{*}t*A*from (6) are biased, but the bias is known—Wymer (1972 b)—and generally will be small provided the eigenvalues of

^{*}*A*are small.

^{*}The estimation technique can be extended to a system of mixed-order linear differential equations, where the structural equations are of any order including zero, by redefining *A ^{*}* in (3) to allow for this—Wymer (1972 b). Although the approximation to the continuous system has been derived under the assumption that the variables in the model are either all instantaneous (that is, variables whose value can be measured at a point in time) or all flows, the mixed-order system allows the analysis to be extended to a mixed stock/flow model.

^{22}

Consider a simple model:

where *x*: is a stock and *y* a flow. Integrate twice over the interval (t—1, *t*) to obtain

By defining

(8) may be written as follows:

and (9) is approximated as follows:

or

where *y ^{*}{t)* is measured

*y(t)*over the observation period. Thus,

*y*refers to (say) quarterly or yearly observations of some flow variable and xt refers to stocks at the end of period;

^{*}_{t}*x*refers approximately to stocks at midperiod. The double integration does lead, however, to a first-order moving-average process in the disturbances, which can be approximated by using a moving-average process:

^{*}_{t}and truncating after a few terms. The program used to estimate *A ^{*}* and

*B*in (5) was SIMUL, which estimated by two-stage least-squares, three-stage leastsquares, and full-information maximum likelihood methods. A related program,

^{*}TRANSF, performs the necessary transformation for the approximations to continuous time. The program PREDIC uses (5) to forecast or simulate the continuous system at discrete intervals. These intervals may be smaller or greater than the intervals in the sample used for estimation. In the models of this paper, the prediction intervals were made to coincide with the actual intervals, namely, annual.

All three programs were written by C.R. Wymer and have been adapted at the Fund by Niranjan Arya and Mohsin Khan.

## BIBLIOGRAPHY

Dutta, Manoranjan, “A Prototype Model of India’s Foreign Sector,”

5 (January 1964), pp. 82—103.*International Economic Review*,Fleming, J. Marcus, “The Determination of the Rate of Interest,”

5 (August 1938), pp. 333—41.*Economica*, New Series,Guitian, Manuel, “Credit Versus Money as an Instrument of Control,”

20 (November 1973), pp. 785—800.*Staff Papers*,Islam, Nurul, “Experiments in Econometric Analysis of an Import Demand Function,”

11 (September 1961, pp. 21—38, and December 1961, pp. 1—19).*Pakistan Economic Journal*Johnson, Harry G.,

(Amsterdam, 1972).*Inflation and the Monetarist Controversy*Laffer, Arthur B., “The Anti-Traditional General Equilibrium Theory of the Rate of Growth and the Balance of Payments Under Fixed Exchange Rates”(unpublished, Chicago, 1968).

Mundell, Robert A.,

(Pacific Palisades, California, 1971).*Monetary Theory: Inflation, Interest and Growth in the World Economy*Polak, J.J., Monetary Analysis of Income Formation and Payments Problems,“

6 (November 1957) pp. 1—50.*Staff Papers*Prais, S.J., “Some Mathematical Notes on the Quantity Theory of Money in an Open Economy,”

8 (May 1961), pp. 212—26.*Staff Papers*Rhomberg, Rudolf R., “Money, Income, and the Foreign Balance,”

*in*18 to 28 July 1962, ed. by E.F. Jackson (Oxford, 1965), pp. 254—75.*Economic Development in Africa: Papers Presented to the Nyasaland Economic Symposium Held in Blantyre*Robichek, E.W., “Financial Programming: Stand-By Arrangements and Stabilization Programs” (mimeographed, Washington, January 6, 1971).

Sargan, J.D., “Some Discrete Approximations to Continuous Time Stochastic Models” (unpublished, London School of Economics and Political Science, 1968).

Turnovsky, Stephen John, “International Trading Relationships for a Small Country ry: The Case of New Zealand,”

1 (November 1968), pp. 772—90.*Canadian Journal of Economics*,UNCTAD, “Developing Countries in Project LINK” (unpublished, New York, 1972).

Wymer, C.R., (1972 a), “Econometric Estimation of Stochastic Differential Equation Systems,”

40 (May 1972), pp. 565—77.*Econometrica*,Wymer, C.R., (1972 b), “Estimation of General Linear Differential Equation Systems” (unpublished, London School of Economics and Political Science, 1972).

^{}1

This distinguishes the model from one constructed by the United Nations Conference on Trade and Development (UNCTAD) for the Project LINK study. (See UNCTAD, in the Bibliography, p. 274.) For a complete exposition of the monetary approach, see Robichek (1971), Johnson (1972), and Guitian (1973).

^{}2

“Small” is defined here in relation to the rest of the world. Specifically, in this context a country is small if it is a price taker for both imports and exports.

^{}6

In the continuous model (but not in the discrete model), a may take any positive value, and if the rate of adjustment is fast, a will be large. Since the mean-time lag is 1/a, if the time unit in the continuous model is (say) one year (i.e., the unit in which time is measured in the continuous model and not to be confused with the observation period, which need not be the same) and the mean-time lag is two weeks, then α = 26. As α→ ∞ the adjustment process tends more and more toward a jump discontinuity, which would occur if the system were always in equilibrium.

^{}10

Since

^{}11

See International Monetary Fund, *International Financial Statistics, Supplement 1972*, pp. xviii and xix.

^{}12

This is done for purposes of exposition, since the effects that are traced take place simultaneously although the mean-time lag varies.

^{}13

Again, for expositional purposes, assume that the expansion in *C* is reflected fully in an expansion in *M _{o}*, with the effects on

*NFA*being completely offset initially.

^{}14

If a variable x is affected by a variable y, so is the integral of

^{}17

The mean-time lag in continuous systems is calculated as 1/A, where A is the coefficient of adjustment.