Aggregate Demand

Real aggregate demand for domestic output is the sum of consumption, investment, government expenditure, and the trade balance:

The variables in equation (1) are defined as follows: Y_t is real gross domestic product (GDP); C_t, is real private consumption expenditure; I_t is real gross domestic investment expenditure; G_t is real government expenditure on the domestic good; X_t, denotes real exports; e_t is the nominal exchange rate (price of foreign currency in domestic currency terms); Z_t is real imports measured in units of the foreign good; $P_t^{*}$ is the foreign currency price of imports; and P_t is the domestic currency price of domestic output.

Turning to the components of demand, the consumption function is specified as follows:

where r_t is the domestic real rate of interest, $Y_t^d$ is real disposable income, and the α_i’s are coefficients to be estimated.² The short-run interest semi-elasticity of consumption is measured by the parameter α₁.³ In this general specification are nested a number of alternative hypotheses about consumption. For example, if α₀ = α₁ = α₃ = α₄ = 0, and α₂ = 1, the simplest Hall (1978) version of the permanent-income hypothesis with no liquidity constraints, in which current consumption is systematically related only to its own past value, is obtained (see Hall (1978)). If only the disposable income terms are rejected empirically, the specification would be consistent with more general Euler-equation approaches, which predict that, in the absence of new information, consumption grows from period to period at a rate that depends on the rate of interest (see Rossi (1988) and Giovannini (1985)). As a number of studies have shown, current disposable income would be important (that is, α₃ > 0) in an equation of this type estimated with instrumental variables if liquidity constraints are binding for a significant portion of households, since in this case aggregate consumption would include a portion that is attributable to liquidity-constrained households whose consumption is constrained by current income (see Flavin (1981)). Finally, the coefficient of the lagged disposable income term can also provide a test for the Blanchard hypothesis of finite horizons for private agents. As shown in Haque (1988), if the planning horizons of households that do not face liquidity constraints are effectively of infinite length, α₄ = 0; otherwise, α₄ will be negative (see also Haque and Montiel (1989)).

Consumer disposable income, a variable used in the consumption function above, is defined to be GDP plus the earnings on net assets held abroad, minus interest paid on domestic debt and taxes:

where $i_t^{*}$ is the (nominal) foreign interest rate, F_p,t is the stock of foreign assets held by the private sector (measured in foreign currency terms), DC_p,t is the stock of domestic bank credit held by the private sector, and T is real taxes. Disposable income and consumer expenditure are linked to the net change in consumer wealth by the private sector budget constraint:

where M_t denotes the money supply in period t. Disposable income is thus allocated to consumption, investment, and net changes in financial assets.

Investment is specified as a function of fairly standard variables—that is, the real interest rate, real output, and the beginning-of-period capital stock.⁴ We adopt a linear formulation, since this permits us to avoid the problem of the absence of capital stock data by first-differencing the equation. The investment function is

With first differences this becomes

where $k_3=1+k_3^{\prime }$. This transformation eliminates the capital stock, a variable for which no developing country data are available.

Exports are assumed to be a function of the real exchange rate $(e_t{P}_t^{*}/P_t)$ and the level of real output abroad (Y*), with positive coefficients for both variables.⁵ To incorporate partial adjustment, a lagged dependent variable is included in the estimated equation. The export equation may therefore be expressed as follows:⁶

Real imports are related negatively to the real exchange rate and positively to real domestic output. This specification is conventional.⁷ Again, to capture partial adjustment behavior a lagged import term is included in the estimated equation. Furthermore, since restricted foreign exchange availability frequently leads to the imposition of import controls and foreign exchange rationing, which act as a constraint on imports in developing countries, the reserve-import ratio lagged one period is often included in this regression (see Khan and Knight (1988)). The import equation can therefore be written as

where R_t, is the foreign exchange value of international reserves.

Aggregate Supply

We assume a Cobb-Douglas production function relating labor and capital to output:

where K and L are measures of the aggregate capital stock and employment and the θ_i’s(i = 0, 1, 2) are coefficients to be estimated. As with the investment function, estimation of the supply side of the model is hampered by the shortage of data on aggregate capital stock for developing countries. The following procedure was therefore adopted. The solution to the difference equation K_t = (1–ρ) K_t-1 + I_t, where ρ is the rate of depreciation, can be written (after taking logs) as

where K₀ is the initial stock of capital.⁸ Thus,

where

Note that equation (10) can be estimated for different values of ρ over the interval (0,1), and optimal values of ${\mathrm{\theta }}_0^{\prime }$, θ₁, and θ₂ will correspond to that value of ρ which maximizes the ${\overline{R}}^2$ in equation (10). By imposing constant returns to scale (that is, θ₁ + θ₂ = 1), equation (10) can be written in per capita terms as

To allow for lagged adjustment and technical progress over time, we also included log (Y/L)_t-1 and a time trend, t, as additional explanatory variables in our final specification. Thus, the empirical production function becomes

The degree of wage-price flexibility in developing countries is an unsettled issue. The present model is estimated on the assumption of complete wage-price flexibility. Under these circumstances, equation (12) also represents the economy’s aggregate supply function.

Money Market

The supply of money (M) in the economy consists of reserves and domestic credit, with the latter denoted as DC:

Whereas reserves are determined endogenously by the balance of payments (see below), domestic credit, both to the private sector (DC_P,t) and to the public sector (DC_G,t), is determined by policy:

The demand for money is, as usual, taken to be related negatively to the nominal rate of interest and positively to the level of income, with a partial adjustment mechanism introduced to capture lagged responses:

The lagged term in Y allows for different speeds of adjustment of the demand for money to changes in interest rates and income.⁹

The specification of the determination of the domestic nominal interest rate allows us to test for the effective degree of capital mobility in the economy. If capital is perfectly mobile, as is frequently assumed in models of small open economies, nominal interest rates are determined by the interest parity condition that equates the domestic nominal interest rate to the sum of the nominal rate prevailing abroad and the expected change in the value of the domestic currency (uncovered interest parity). In a completely closed economy, nominal interest rates have no relationship to external rates and are determined purely in domestic markets. Our formulation follows Edwards and Khan (1985) in specifying the domestic interest rate as a linear combination of these two polar cases:

Here, E_te_t+1 is the expectation at time t of the exchange rate in period t + 1; ī_t is the interest rate that would prevail if the capital account were closed; and φ is a capital mobility index ranging between zero and unity. When φ = 1, it is implied that the domestic interest rate is determined by the uncovered interest parity condition, and thus corresponds to perfect capital mobility, whereas φ = 0 implies that the domestic interest rate is ī—that is, the rate that would emerge under a completely closed capital account. As φ increases from zero to unity, the degree of capital mobility increases, since i approaches its uncovered parity value. In these intermediate cases the equilibrium interest rate is determined by a combination of domestic and external factors.

The interest rate that would prevail in an economy with a closed capital account (that is, one with no private capital flows), ī_t, can be determined by equating the money supply that would be observed in this case to the demand for money. This “shadow” money supply (denoted by $\tilde{M}$) differs from the supply of money given by equation (13), in that the effects of current private capital flows on the central bank’s stock of foreign exchange reserves are removed:

Thus, the “shadow” domestic interest rate ī_t can be obtained by solving the following equation:

In this model the authorities use capital controls to pursue an independent monetary policy, as follows: for a desired level of the domestic interest rate, say ī_t, the level of the domestic money supply required to clear the money market, say ${\overline{M}}_t$, is given by setting i = ī in the money-market equilibrium condition (15).

Given ${\overline{M}}_t$, from equation (15) and the supply of credit DC_t, equation (13) determines foreign exchange reserves R_t. Subtracting the previous period’s reserves, R_t-1, yields the balance of payments (ΔR_t). Using the balance of payments identity

where

the authorities can derive the permissible level of private capita) flows, ${\overline{\mathrm{\Delta }F}}_{p,t}$, conditional on the current account, CA_t, and public capital outflows, ΔF_G,t.

The authorities could choose to administer this system in a number of ways. If either i_t or ΔF_ρ,t is treated as an exogenous variable, the other becomes endogenous and equation (16) drops out of the model. With i_t exogenous, the authorities announce a domestic interest rate, solve for the value of ΔF_p,t required to support it, and permit this degree of capital mobility. Equation (16) becomes unnecessary, useful only for calculating a period-by-period index φ, of the degree of capital mobility. Alternatively, the authorities could choose ΔF_p,t exogenously, with (19) determining R_t, (13) determining M_t, and (15) the domestic interest rate. The role of (16) would then be as in the previous case.

We will assume instead that the system is run somewhat less flexibly. The severity of capital controls, as measured by the parameter φ in equation (16), is taken as a structural (institutional) feature of the economy. In this case, both i_t, and ΔF_ρ,t become endogenous. The domestic interest rate i, will respond to factors affecting both the uncovered parity and the shadow interest rate. For the money market to clear, ΔF_p,t must be adjusted in response to these factors as well. Notice that the structural interpretation of φ permits its magnitude to be estimated empirically, in a manner to be discussed in the next section.

The real interest rate enters the model in both the consumption and investment functions. It is given by

that is, the real interest rate is the nominal interest rate minus the expected rate of inflation.

Government

The model’s dynamic specification is completed with a description of the behavior of the nonfinancial public sector. The public sector acquires assets in external markets (F_G,t) as well as from the domestic banking sector (D_G,t).¹⁰ For its revenues it relies on tax receipts, T_t, and on interest on its foreign asset holdings. Expenditures (G_t) consist of purchases of domestic goods for consumption purposes and interest payments on domestic debt. Combining these elements, the government budget constraint can be written as

Overall Structure of the Model

The model that emerges from this specification is essentially a flexible-price dynamic variant of the traditional Mundell-Fleming model with specific developing country features. A single good is produced domestically, which can be sold at home or abroad. The home country has some monopoly power over the price of its output in world markets. It is a price-taker, however, in the market for its imports. However, as is common in developing countries, private agents may not be able to satisfy their notional demand for imports, because the authorities impose quantitative import restrictions that depend on the adequacy of their foreign exchange reserves. On the financial side, the degree of integration of the home economy with the rest of the world depends on the degree of severity with which capital controls are enforced. In principle, this can range from financial autarky to perfect capital mobility. The dynamics of the model arise from forward-looking expectations, partial adjustment in the behavioral relationships, and stock accumulation. Since the levels of investment and the current account are endogenous, the model can explain medium-term growth and external debt accumulation. Since expectations are forward-looking, these phenomena will depend not just on present, but also on future, values of the policy and exogenous variables.

Unobserved Variables

The first estimation issue to be confronted is the absence of data on the market-determined interest rate i_t and, of course, the shadow interest rate ī_t. In developing countries the relevant market-determined interest rate is typically that for loans in informal, or “curb” markets. Time-series data on such interest rates are very rare. Published developing country interest rate data typically refer to central bank discount rates or to official interest rates on deposits or bank credit. Such interest rates have almost invariably been set by administrative fiat and do not adequately capture the marginal cost of funds.

This problem can be addressed by solving equation (18) for the shadow interest rate ī_t, and then substituting the resulting expression for ī_t, into (16) to solve for i_t. The result is an equation for the domestic market-determined interest rate that expresses this variable as a function of domestic money-market conditions as well as of the external interest rate. The solution for the nominal interest rate can be used to eliminate i_t from the money-demand function (15), permitting that equation to be expressed in terms of observable variables. The expression for i_t can also be substituted into (21) to solve for the real interest rate r_t. This solution for the real interest rate can be used to eliminate r_t from both the consumption function (2) and the investment function (5), rendering these equations in terms of observable variables. The revised equations (2), (5), and (15) are nonlinear in the structural parameters and subject to cross-equation restrictions among these parameters. This procedure has the virtue of not only making it possible to estimate the parameter φ, but also of permitting us to extract estimates of interest rate elasticities in consumption, investment, and money demand, which do not, as is common in much of the developing country literature, depend on proxies for market interest rates such as administered interest rates or inflation rates. The resulting system to be estimated consists of the revised versions of equations (2), (5), and (15)—with associated nonlinear parameter and cross-equation restrictions—as well as equations (6), (7), and (12).

Expectations

The next issue concerns the treatment of expectations in the estimation procedure. The assumption of rationality in our model implies that forward expectations are based on all available information, including the structure of the model. This implies the property that prediction errors should be nonsystematic:

where ε_i,t+1 is a serially uncorrected random disturbance term. For estimation a reasonable proxy is needed for E_tP_i,t+1, which now appears in the revised versions of equations (2) and (5). One such observable proxy for the unobservable price-expectation variable E_tP_i,t+1, according to equation (23). is the actual P_i,t+1. The associated estimation procedure must take account of the errors-in-variables problem implied by (23). This errors-in-variables method (EVM), in which the expected forward price is replaced by the realized (observed) value, and the latter is treated as an additional endogenous variable of the model, is a well-known approach to estimation under rational expectations.¹² An alternative approach that has been used for estimation of simultaneous equation models with rational expectations is the so-called substitution method (SM) where the rationally expected variables are replaced by forecasts based on a restricted reduced form.¹³ Wickens (1982, 1986) emphasizes many advantages of the EVM approach over the SM method. He shows that in a nonlinear model such as ours, the additional non-linearity in the parameters introduced due to SM will make the estimation technique hopelessly complicated. Wickens (1982, 1986) also demonstrates that EVM is in general more robust than SM in cases where the variables in the information set (Ω_t) are incomplete. Moreover, EVM is relatively easy to implement, making it more amenable to repeated experimentation with different specifications of the model. In addition, Wickens (1986) shows that until the type of rational expectations solution exhibited by the model is known, it will not be possible to select the appropriate fully efficient SM estimator.

The reduced-form equation for P_t in country i can be obtained by linearizing the model, solving it for P_t, advancing it one period, taking expectations conditional on Ω_t, and solving for E_tP_i,t+1. If we write

where X_it is the set of instruments belonging to Ω_t, and П is a vector of reduced-form coefficients, then (23) becomes

This equation can be used to generate the instruments for P_i,t+1. In estimating the behavioral equations of the revised model, therefore. E_tP_i,t+1 was replaced by P_i,t+1; and C_it, I_it, X_it. Z_it, M_it. Y_it. P_it, and P_i,t+1 were treated as endogenous variables (that is, not part of the set of instruments). This yields consistent estimates of the structural parameters. Note that in order to identify and estimate all the structural parameters, we have to estimate the system of equations together, incorporating the nonlinear restrictions both within and across equations.

Treatment of Country Heterogeneity

The use of pooled cross-section, time-series data means that the issue of country heterogeneity has to be confronted. Most studies that use such data for empirical estimation rely on a fixed-effects model, using dummy variables to deal with country heterogeneity, primarily for ease of estimation (see, for example, Khan and Knight (1981)). In this study we adopted the alternative approach of variance components. Under this assumption, the error term of the jth equation, η_j, is composed of two terms: η_ji, the country-specific effect, which varies only across countries and not across time; and ε_jit, an individual random effect which may differ for all observations. The approach has the advantage that it recognizes the possibility that country-specific effects may be correlated across equations.

Method of Estimation

As is well known, variance-components characterization of country heterogeneity implies that generalized least-squares (GLS) estimation techniques can be used to consistently estimate the model parameters as well as the variance components of the random error term. In order to deal with the error-component structure of the variance of the random error term in the model, generalized estimation techniques were implemented using a two-step procedure.¹⁴ At the first stage, the vector of residuals was calculated from two-stage least-squares (2SLS) estimates of the model. These residual estimates were used to calculate the variance and covariance components. See Wallace and Hussain (1969) and Maddala (1988).

With the variance components estimated, the variance-covariance matrix of the disturbance term can be constructed to allow generalized two-stage or three-stage least squares to be used for consistent estimation of the model parameters. Anderson and Hsiao (1982) and Sevestre and Trognon (1985) have shown that this estimator is consistent and, for dynamic models, independent of initial conditions. In our case, a generalized, nonlinear, three-stage-least-squares estimator was used due to the presence of nonlinearities and cross-equation restrictions. Following Breusch, Mizon, and Schmidt (1989), the instruments used were the within-country variables $(X_{jit}-{\overline{X}}_{ji})$ and the between-country variables (X_ji); they have shown that the use of this procedure allows efficient estimation in models with panel data.¹⁵

Consumption

The estimated coefficients of the consumption function are all of the anticipated signs. In magnitude, these coefficients also conform well to theory as well as to consumption function estimates that are available in the literature. Interestingly enough, α₁ is negative and significant at the 10 percent level, verifying a negative relationship between consumption and the interest rate. Most studies of the consumption function have found this relationship to be statistically insignificant. Our results suggest that the use of inappropriate proxies for domestic real interest rates (for example, the rate of inflation) may have contributed to this result.¹⁷ The estimated coefficient is, however, quite small, suggesting that changes in interest rates would not induce substantial changes in consumption. This result confirms Rossi’s (1988) finding of a significant but small real interest rate elasticity in the consumption function.

The estimation, as it turns out, supports a number of important hypotheses relating to the consumption function that were discussed above. The specification is very similar to the Haque and Montiel (1989) version of the permanent income model. The coefficient of lagged consumption is close to unity and significant, as expected in the Hall (1978) specification of the permanent income hypothesis. However, contrary to the Hall hypothesis, disposable income is significant in explaining consumption behavior. The coefficient of disposable income, α₃, which is statistically significant, suggests that about 15 percent of consumers in developing countries are liquidity constrained, which is on the low end of the range of estimates reported in Haque and Montiel (1989).

Investment

The specification of the investment function was a relatively simple one. Nevertheless, it seems to provide a reasonably good explanation of investment behavior in developing countries. Most studies of investment behavior in such countries do not include interest rates as an explanatory variable because of lack of adequate information (see Blejer and Khan (1984a, 1984b)). Our approach to modeling capital mobility allows the identification of the effect of the real interest rate on investment. Although small, the coefficient of the real interest rate, k₁, is negative as expected, and significant at the 5 percent level. Growth in income also affects investment positively and significantly, in keeping with the flexible-accelerator family of investment theories. The coefficient of lagged investment, k₃, is close to but less than unity, indicating both a stable investment function as well as a fairly protracted period of adjustment. Using this estimate, the long-run interest rate and output elasticities can be calculated—they turn out to be 0.59 and 1.02, respectively. Thus, as can be expected, in the long run, when all adjustments have been completed, the interest elasticity is substantially larger than it is on impact. Moreover, the steady-state property that per capita output and investment grow at the same rate is satisfied.

Aggregate Supply

All the variables in the estimated aggregate supply (production) function are significant and of the right sign.¹⁸ Since ${\mathrm{\theta }}_0^{\prime }$ contains log K₀, which is an initial-value parameter representing the initial stock of capital for each country, equation (12) was estimated from the “within” dimension of the data. The parameter ρ was estimated to be 0.05, although estimates of θ₁, g, and θ₃ were not particularly sensitive to values of ρ in the vicinity of 0.05.¹⁹ The per capita stock of capital affects current output significantly and positively with a short-run elasticity of 0.12 and of close to unity in the long run. At the sample means, our results, which are derived from a log-linear specification, compare quite favorably to the estimates of Dadkhah and Zahedi (1986). Nevertheless, the supply equation provided the least satisfactory empirical results. The coefficient on the lagged dependent variable is implausibly high, suggesting that some of our maintained hypotheses (for example, regarding the form of the production function or the degree of wage-price flexibility) require further investigation.

Foreign Trade

The estimated export function fits the data well, with all coefficients bearing the expected signs and reasonable magnitudes. The fitted equation exhibits a significant export response to relative price changes, although one that is somewhat smaller in magnitude than other available estimates.²⁰ The long-run elasticity of 0.66, though considerably higher than the short-run elasticity, still suggests a fairly inelastic response. In the estimated (foreign) function for the demand for exports, the coefficient of foreign income is positive and significant, with a long-run elasticity of 1.12. A fair amount of persistence in the level of exports appears to be indicated by the coefficient of lagged exports, which is both significant and close to unity, so that the response to changes in relative prices and foreign income tends to be quite prolonged over time.

In the import equation the estimated coefficients also bear the right signs and are all significant at conventional levels. Imports are responsive to real exchange rate changes with a short run elasticity of–0.157 and a long-run elasticity of about–0.94. Growth in the domestic economy increases imports, with an elasticity of 0.16 in the short run and about 0.96 (not significantly different from unity) in the long run. Reflecting foreign exchange constraints, the coefficient of the lagged reserve-import ratio is significant and positive. These estimates are similar to those in Khan and Knight (1988).

Our results suggest that the trade equations are not as responsive to real exchange rate changes and income growth as other studies have previously estimated. However, when these results are being compared, it must be borne in mind that most available estimates of such equations were constructed in a partial equilibrium setting. The estimates presented here, by contrast, are in the context of a complete macroeconomic model.

Money and Capital Mobility

The coefficients of the estimated money-demand function are all significant and of the expected sign. Money demand, in keeping with expectations, is quite interest-inelastic, with the short-run interest elasticity estimated to be about—0.04 and the long-run elasticity estimated at about—0.26. The estimated income elasticities are much higher: the short- and long-run elasticities turn out to be 0.22 and 1.82, respectively.²¹