1. 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 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; ${\mathrm{P}}_{\mathrm{t}}^{\mathrm{*}}$ 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, ${\mathrm{Y}}_{\mathrm{t}}^{\mathrm{d}}$ is real disposable income, and the α_i’s are coefficients to be estimated. ^1/ The short-run interest semi-elasticity of consumption is measured by the parameter α₁. ^2/ In this general specification are nested a number of alternative hypotheses about consumption. For example, if α₀ = α₁ = α₃ = α₄ = 0 and α₁ = 1, the simplest Hall (1978) version of the permanent income hypothesis with no liquidity constraints is obtained. ^3/ 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. ^4/ As a number of studies have shown, current disposable income would be important in an equation of this type (i.e., α₃ > 0) if liquidity constraints are binding for a significant portion of households. ^5/ Finally, the coefficient of the lagged disposable income term can also provide a test for the Blanchard hypothesis of finite horizons for private agents. ^6/

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 ${\mathrm{i}}_{\mathrm{t}}^{\mathrm{*}}$ 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 in a fairly standard way, that is as a linear function of the real interest rate, real output, and the beginning-of-period capital stock: ^7/

Taking first differences this becomes:

where ${\mathrm{k}}_3=1+{\mathrm{k}}_3^{\prime }$. 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 $\left(e_t\begin{array}{c}{\mathrm{P}}_{\mathrm{t}}^{\mathrm{*}}\mathrm{/}{\mathrm{P}}_{\mathrm{t}}\end{array}\right)$ and the level of real output abroad (Y*), with positive coefficients for both variables. ^8/ To incorporate partial adjustment, a lagged export term is included in the estimated equation. The export equation may therefore be expressed as follows: ^9/

Real imports are related negatively to the real exchange rate and positively to real domestic output. This specification is quite conventional. ^10/ Again, to capture partial adjustment behavior a lagged import term is included in the estimated equation. Furthermore, since foreign exchange availability is frequently a constraint on imports in developing countries, the reserve-import ratio lagged one period is often included in this regression. ^11/ The import equation can, therefore, be written as:

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

2. 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 θ_i (i = 0, 1, 2) are coefficients to be estimated. Estimation of the supply side of the model encounters the serious problem that few developing countries possess data on the aggregate capital stock. 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 K_o is the initial stock of capital. ^12/

Thus,

where

Note that (10) can be estimated for different values of δ over the interval (0,1), and optimal values of ${\theta }_{\mathrm{o}}^{\prime }$, θ₁ and θ₂ will correspond to that value of ρ which maximizes the ${\overline{R}}^2$ in (10). By imposing constant returns to scale (i.e., θ₁ + θ₂ = 1), (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.

3. Money market

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

While 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, hypothesized 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. ^13/

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 small open economy models, 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, on the other hand, 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 the time t of the exchange rate in period t+1, ĩ_t is the interest rate that would prevail if the capital account were closed, and ϕ is a capital mobility index. ϕ = 1 implies 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 ĩ—i.e., that which would emerge under a completely closed capital account. As ϕ increases from 0 to 1, 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 (i.e., one with no private capital flows), ĩ_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 $\tilde{\mathrm{M}}$) 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 i_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 i_t, the level of the domestic money supply required to clear the money market, say ${\overline{\mathrm{M}}}_{\mathrm{t}}$, is given by setting i = ī in the money-market equilibrium condition (15).

Given ${\overline{\mathrm{M}}}_{\mathrm{t}}$ 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-l yields the balance of payments (ΔR_t). Using the balance of payments identity:

where:

the authorities can derive the permissible level of private capital flows, ${\overline{\mathrm{\Delta F}}}_{\mathrm{p}\mathrm{,}\mathrm{t}}$, 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_{p, 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_t 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_{p, t} become endogenous. The domestic interest rate i_t will respond to factors affecting both the uncovered parity and the shadow interest rates. 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:

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

4. Government

The model’s dynamic specification is completed with a description of the behavior of the nonfinancial public sector. The public sector borrows in external markets (F_{G, t}) as well as from the domestic banking sector (D_{G, t}). For its revenues it relies on tax receipts, T_t, and 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:

5. 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. On the other hand, 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 which 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 model depends on the 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 level 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.

1. Unobserved variables

The first estimation issue to be confronted is the absence of data on the relevant market-determined interest rate i_t and, of course, the shadow interest rate ī_t. This problem can be addressed by solving equation (18) for ĩ_t, and then substituting the resulting expression for ī_t into (16) to solve for i_t. The expression for i_t can be substituted into (21) to obtain the real interest rate r_t. The solution for the nominal interest rate can be used to eliminate i_t from the money-demand function (15), while the solution for the real interest rate can be used to eliminate r_t from both the consumption function (2) and the investment function (5). 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 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). The equations to be estimated are presented in Table 1.

Table 1.

Behavioral Equations of the Model

Table 1.

Behavioral Equations of the Model

$\begin{array}{cc}log{\mathrm{C}}_{\mathrm{t}}={\alpha }_o+{\alpha }_1{\mathrm{r}}_{\mathrm{t}}+{\alpha }_{2}log{\mathrm{C}}_{\mathrm{t}\mathrm{-}\mathrm{1}}+{\alpha }_{3}log{\mathrm{Y}}_{\mathrm{t}}^{\mathrm{d}}+{\alpha }_{4}log{\mathrm{Y}}_{\mathrm{t}\mathrm{-}\mathrm{1}}^{\mathrm{d}}& \left(2\right)\end{array}$

$\begin{array}{cc}{\mathrm{I}}_{\mathrm{t}}\mathrm{=}{\mathrm{k}}_{\mathrm{1}}\mathrm{\left(}{\mathrm{r}}_{\mathrm{t}}\mathrm{-}{\mathrm{r}}_{\mathrm{t}\mathrm{-}\mathrm{1}}\mathrm{\right)}\mathrm{+}{\mathrm{k}}_{\mathrm{2}}\mathrm{\left(}{\mathrm{Y}}_{\mathrm{t}}\mathrm{-}{\mathrm{Y}}_{\mathrm{t}\mathrm{-}\mathrm{1}}\mathrm{\right)}\mathrm{+}{\mathrm{k}}_{\mathrm{3}}{\mathrm{I}}_{\mathrm{t}\mathrm{-}\mathrm{1}}\mathrm{,}& \left(5\right)\end{array}$

$\begin{array}{cc}log{\mathrm{X}}_{\mathrm{t}}={\tau }_{\mathrm{o}}+{\tau }_{1}log\frac{{\mathrm{e}}_{\mathrm{t}}{\mathrm{P}}_{\mathrm{t}}^{\mathrm{*}}}{{\mathrm{P}}_{\mathrm{t}}}+{\tau }_{2}log{\mathrm{Y}}_{\mathrm{t}}^{\mathrm{*}}+{\tau }_{3}log{\mathrm{X}}_{\mathrm{t}\mathrm{-}\mathrm{1}}& \left(6\right)\end{array}$

$\begin{array}{cc}log\left({\mathrm{Y}}_{\mathrm{t}}\mathrm{/}{\mathrm{L}}_{\mathrm{t}}\right)={\theta }_{\mathrm{o}}^{\prime }+{\theta }_1\left({\mathrm{K}}_{\mathrm{t}}^{\mathrm{\prime }}\mathrm{-}\log {\mathrm{L}}_{\mathrm{t}}\right)+\mathrm{g}\mathrm{.}\mathrm{y}+{\theta }_{3}log{\left(\mathrm{Y}\mathrm{/}\mathrm{L}\right)}_{t-1}& \left(12\right)\end{array}$

$\begin{array}{cc}\log \frac{{\mathrm{M}}_{\mathrm{t}}}{{\mathrm{P}}_{\mathrm{t}}}-{\beta }_{o+}{\beta }_1{\mathrm{i}}_{\mathrm{t}}+{\beta }_2\log {\mathrm{Y}}_{\mathrm{t}}+{\beta }_3\log {\mathrm{Y}}_{\mathrm{t}\mathrm{-}\mathrm{1}}+{\beta }_4\log \frac{{\mathrm{M}}_{\mathrm{t}\mathrm{-}\mathrm{1}}}{{\mathrm{P}}_{\mathrm{t}\mathrm{-}\mathrm{1}}}& \left(15\right)\end{array}$

$\begin{array}{cc}{\mathrm{i}}_{\mathrm{t}}\mathrm{=}\mathit{\phi }\mathrm{\left(}{\mathrm{i}}_{\mathrm{t}}^{\mathrm{*}}\mathrm{+}\frac{{\mathrm{E}}_{\mathrm{t}}{\mathrm{e}}_{\mathrm{t}\mathrm{+}\mathrm{1}}\mathrm{-}{\mathrm{e}}_{\mathrm{t}}}{{\mathrm{e}}_{\mathrm{t}}}\mathrm{\right)}\mathrm{+}\mathrm{\left(}\mathrm{1}\mathrm{-}\mathit{\phi }\mathrm{\right)}{\tilde{\mathrm{i}}}_{\mathrm{t}}& \mathrm{\left(}\mathrm{16}\mathrm{\right)}\end{array}$

View Table

Table 1.

Behavioral Equations of the Model

$\begin{array}{cc}log{\mathrm{C}}_{\mathrm{t}}={\alpha }_o+{\alpha }_1{\mathrm{r}}_{\mathrm{t}}+{\alpha }_{2}log{\mathrm{C}}_{\mathrm{t}\mathrm{-}\mathrm{1}}+{\alpha }_{3}log{\mathrm{Y}}_{\mathrm{t}}^{\mathrm{d}}+{\alpha }_{4}log{\mathrm{Y}}_{\mathrm{t}\mathrm{-}\mathrm{1}}^{\mathrm{d}}& \left(2\right)\end{array}$

$\begin{array}{cc}{\mathrm{I}}_{\mathrm{t}}\mathrm{=}{\mathrm{k}}_{\mathrm{1}}\mathrm{\left(}{\mathrm{r}}_{\mathrm{t}}\mathrm{-}{\mathrm{r}}_{\mathrm{t}\mathrm{-}\mathrm{1}}\mathrm{\right)}\mathrm{+}{\mathrm{k}}_{\mathrm{2}}\mathrm{\left(}{\mathrm{Y}}_{\mathrm{t}}\mathrm{-}{\mathrm{Y}}_{\mathrm{t}\mathrm{-}\mathrm{1}}\mathrm{\right)}\mathrm{+}{\mathrm{k}}_{\mathrm{3}}{\mathrm{I}}_{\mathrm{t}\mathrm{-}\mathrm{1}}\mathrm{,}& \left(5\right)\end{array}$

$\begin{array}{cc}log{\mathrm{X}}_{\mathrm{t}}={\tau }_{\mathrm{o}}+{\tau }_{1}log\frac{{\mathrm{e}}_{\mathrm{t}}{\mathrm{P}}_{\mathrm{t}}^{\mathrm{*}}}{{\mathrm{P}}_{\mathrm{t}}}+{\tau }_{2}log{\mathrm{Y}}_{\mathrm{t}}^{\mathrm{*}}+{\tau }_{3}log{\mathrm{X}}_{\mathrm{t}\mathrm{-}\mathrm{1}}& \left(6\right)\end{array}$

$\begin{array}{cc}log\left({\mathrm{Y}}_{\mathrm{t}}\mathrm{/}{\mathrm{L}}_{\mathrm{t}}\right)={\theta }_{\mathrm{o}}^{\prime }+{\theta }_1\left({\mathrm{K}}_{\mathrm{t}}^{\mathrm{\prime }}\mathrm{-}\log {\mathrm{L}}_{\mathrm{t}}\right)+\mathrm{g}\mathrm{.}\mathrm{y}+{\theta }_{3}log{\left(\mathrm{Y}\mathrm{/}\mathrm{L}\right)}_{t-1}& \left(12\right)\end{array}$

$\begin{array}{cc}\log \frac{{\mathrm{M}}_{\mathrm{t}}}{{\mathrm{P}}_{\mathrm{t}}}-{\beta }_{o+}{\beta }_1{\mathrm{i}}_{\mathrm{t}}+{\beta }_2\log {\mathrm{Y}}_{\mathrm{t}}+{\beta }_3\log {\mathrm{Y}}_{\mathrm{t}\mathrm{-}\mathrm{1}}+{\beta }_4\log \frac{{\mathrm{M}}_{\mathrm{t}\mathrm{-}\mathrm{1}}}{{\mathrm{P}}_{\mathrm{t}\mathrm{-}\mathrm{1}}}& \left(15\right)\end{array}$

$\begin{array}{cc}{\mathrm{i}}_{\mathrm{t}}\mathrm{=}\mathit{\phi }\mathrm{\left(}{\mathrm{i}}_{\mathrm{t}}^{\mathrm{*}}\mathrm{+}\frac{{\mathrm{E}}_{\mathrm{t}}{\mathrm{e}}_{\mathrm{t}\mathrm{+}\mathrm{1}}\mathrm{-}{\mathrm{e}}_{\mathrm{t}}}{{\mathrm{e}}_{\mathrm{t}}}\mathrm{\right)}\mathrm{+}\mathrm{\left(}\mathrm{1}\mathrm{-}\mathit{\phi }\mathrm{\right)}{\tilde{\mathrm{i}}}_{\mathrm{t}}& \mathrm{\left(}\mathrm{16}\mathrm{\right)}\end{array}$

2. 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:

where ε_{i, t+1} is a serially uncorrelated random disturbance term. Consequently, for estimation one needs a reasonable proxy for E_t P_{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} is the actual P_{i, t+1}. The associated estimation procedure is the errors-in-variables (EVM) method, 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. ^15/ 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. ^16/ Wickens (1982, 1986) emphasizes many advantages of the EVM approach over the SM method. He shows that in a non-linear model such as ours, the additional non-linearity in the parameters introduced due to the SM will make the estimation technique hopelessly complicated. Wickens (1982, 1986) also demonstrates that the 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, leading it one period, taking expectations conditional on Ω_t, and solving for E_tP_it+1. If we write

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

This equation can be used to generate the instruments for P_it+1. In estimating the behavioral equations of the revised model, therefore, E_tP_it+1 was replaced by P_it+1 and C_it, I_it, X_it, Z_it, M_it, Y_it, P_it and P_it+1 were treated as endogenous variables (i.e., 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 non-linear restrictions both within and across equations.

3. Tests of heterogeneity and serial correlation

In using pooled cross-section, time-series data the issue of country heterogeneity has to be confronted. Most studies that use such data for empirical estimation rely on dummy variables to deal with country heterogeneity, primarily for ease of estimation. ^17/ 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. Consequently, the error term is written as:

for t - 1, 2, …, T; i - 1, 2, …, N and j - 1, 2, …, M. Moreover,

for t, t’ = 1, 2, … T; i, i’ = 1, 2, … N; j, j’ = 1, 2, … M.

Together these assumptions imply that the variance structure of the composite disturbance term μ is given by:

The variance-covariance matrix of the disturbance term for the jth equation can therefore be written as follows:

where $\mathrm{A}\mathrm{=}{\mathrm{I}}_{\mathrm{N}}\otimes {\mathrm{\ell }}_{\mathrm{T}}{\mathrm{\ell }}_{\mathrm{T}}^{\mathrm{\prime }}$ with ⊗ defining the Kronecker product and ℓ_T being a T-vector of ones. Denoting the M x M variance-covariance matrix for η and ε for the system of equations by Σ_η and Σ_ε respectively, the MNT x MNT variance covariance matrix for the system-wide vector of disturbances $\mathrm{u}\mathrm{=}{\mathrm{\left(}{\mathrm{u}}_{\mathrm{1}}^{\mathrm{\prime }}\mathrm{\dots }{\mathrm{u}}_{\mathrm{m}}^{\mathrm{\prime }}\mathrm{\right)}}^{\mathrm{\prime }}$ may be written as:

As is well known, variance-components characterization of country heterogeneity has the advantage that 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. ^18/ At the first stage, the vector of residuals was calculated from 2SLS estimates of the model. These residual estimates, denoted ${\hat{\mathrm{u}}}_{\mathrm{jit}}$, were used to calculate the variance components as follows: ^19/

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 (1983) and Sevestre and Tragnon (1986) have shown that this estimator is consistent and, for dynamic models, independent of initial conditions. In our case, a generalized non-linear three-stage least squares estimator was used due to the presence of non-linearities and cross-equation restrictions. Following Breusch, Mizon and Schmidt (1989), the instruments used were the within-country variables $\mathrm{\left(}{\mathrm{X}}_{\mathrm{jit}}\mathrm{-}{\overline{\mathrm{X}}}_{\mathrm{ji}}\mathrm{\right)}$ and the between-country variables (X_ji). They have shown that the use of this procedure allows efficient estimation in models with rational expectations and panel data.

Before proceeding to the model estimation, we tested the error components structure assumed above against the alternative of no country-specific effects. In order to perform this test, unrestricted two-stage least squares (2SLS) estimates of the behavioral equations were initially obtained based on pooled data, as well as within-country and between-country data. ^{20/ 21/} All predetermined variables of the model (except for the lagged endogenous variable for the equation being estimated) were used as instruments. 2SLS estimates based on pooled data were obtained in order to test for the presence of country-specific error terms in each equation. We used the Lagrange multiplier (LM) test due to Breusch and Pagan (1980) to test for the significance of σ_ηjj (j = 1,…,6) in each equation. The LM statistic is given by:

where Û_it is the 2SLS residual from each of the estimated equations. Estimates of the LM statistic are presented in Table 2. The LM statistic is distributed x² (1). The estimates suggest that the null hypothesis, σ_ηjj = 0, can be rejected for each of the equations. Based on estimated residuals, values of λ_j = 1 - [σ_εjj/σ_εjj + Tσ_εjj)]^½ were calculated for each equation. ^22/ Except for the money demand equation, these estimates of λ_j were fairly large. In the case of the money demand equation σ_ηjj was only 0.0003, whereas σ_εjj was calculated to be 0.0085. Thus, of all the behavioral equations the money demand equation was found to be most homogenous across countries, but in each of the equations our assumption of a country-specific error term is supported by the data.

Table 2.

Estimated Test Statistics for the Lagrange-Multiplier (LM) Test, Values of λ, and d_p Statistic

^1/Critical value for x² (1) at the 1% significance level = 6.63

Table 2.

Estimated Test Statistics for the Lagrange-Multiplier (LM) Test, Values of λ, and d_p Statistic

Equation	LM 1/	λ	dp
Consumption	62.4	0.49	1.95
Investment	70.2	0.52	1.90
Exports	85.2	0.94	2.04
Imports	102.3	0.91	1.75
Money demand	12.9	0.26	1.94
Production function	120.8	1.0	1.76

^1/Critical value for x² (1) at the 1% significance level = 6.63

View Table

Table 2.

Estimated Test Statistics for the Lagrange-Multiplier (LM) Test, Values of λ, and d_p Statistic

Equation	LM 1/	λ	dp
Consumption	62.4	0.49	1.95
Investment	70.2	0.52	1.90
Exports	85.2	0.94	2.04
Imports	102.3	0.91	1.75
Money demand	12.9	0.26	1.94
Production function	120.8	1.0	1.76

^1/Critical value for x² (1) at the 1% significance level = 6.63