1. Households

Households supply labor inelastically and consume both traded and nontraded goods. Consumption decisions follow a two-step process: households first determine the optimal level of total consumption, and then allocate that amount between consumption of the two goods. Assuming that government expenditure does not yield direct utility, the representative household’s discounted lifetime utility can be written as

where ρ denotes the rate of time preference (assumed constant), c total consumption expenditure, and m real money balances, measured in terms of the price of the consumption basket, P. The parameter η is positive and different from unity. The instantaneous utility function is assumed to be additively separable in consumption and real money balances. Households hold three categories of financial assets in their portfolios: domestic money (which bears no interest), domestic government bonds (the real stock of which is 6), and foreign bonds b^*. Real wealth of the representative household a can thus be defined as

Both b and b^* are measured in terms of the price of the consumption basket. Specifically,b^* =B^*/P, where B^* represents foreign borrowing measured in foreign-currency terms.⁵ The flow budget constraint is given by⁶

where q denotes net factor income (derived below), т the real value of lump-sum taxes, i the domestic nominal interest rate, and π the domestic inflation rate. The term πa accounts for capital losses on total wealth resulting from inflation. The rate of return on foreign bonds i^* - θ consists of an exogenous, “base” (or risk-free) interest rate i^* and an endogenous discount θ, which captures liquidity or borrowing risk and is positively related to the outstanding level of foreign assets held by the household. Specifically, we use the linear approximation θ ≃ γb^*/2, where γ > 0. In the first stage of the consumption decision process, households treat π, q, i, i^* and т as given, internalize the effect of their portfolio decisions on θ, and maximize (1) subject to (2) and (3) by choosing a sequence $\{c,m,b,b*{\}}_{t=0}^{\infty }$. Let r = i - π denote the domestic (consumption-based) real rate of interest and σ = 1/η the intertemporal elasticity of substitution. The optimality conditions are given by:

together with the transversality condition $\underset{t\to \infty }{\text{lim}}\left(e^{-pt}{a}_t\right)=0$. Equation (4) is the money demand function, and is derived by equating the marginal rate of substitution between consumption and real money balances to the opportunity cost of holding money, the domestic nominal interest rate. Equation (5) indicates that holdings of foreign bonds are positively related to the difference between the risk-free foreign interest rate and the domestic interest rate. Equation (6) shows that total consumption rises or falls depending on whether the domestic real interest rate exceeds or falls below the rate of time preference.

In the second stage of the consumption decision process, the representative household maximizes a Cobb-Douglas sub-utility function V(C_N, C_T), where C_N denotes purchases of nontraded goods, and C_T expenditure on traded goods, subject to the budget constraint P_NC_N + P_TC_T =P_c, where P_N (P_T) denotes the price of the home (traded) good. The solution to this program yields the familiar result according to which the representative household sets the marginal rate of substitution between home and traded goods equal to their relative price z ≡ P_T/P_N, that is, the real exchange rate:

where δ denotes the share of home goods consumption in total consumption expenditure, which is allocated according to

The consumer price index P is thus:

so that

where π^* = Ṗ_T/P_T is the world inflation rate.

2. Supply side

Technology for the production of both traded and nontraded goods is characterized by decreasing returns to labor:

where y_h denotes output of good h (with h = N, T), and n_h the quantity of labor employed in sector h. From the first-order conditions for profit maximization, the labor demand functions can be derived as

where W_T is the product wage in the traded goods sector. Nominal wages are perfectly flexible.W_T is thus determined by the equilibrium condition of the labor market:

where n^s denotes the (exogenous) supply of labor. This equation implies that the equilibrium real wage (measured in terms of traded goods) is negatively related to the real exchange rate:

Substituting this result in equations (12), and noting that d(zw_T)/dz > 0 yields the sectoral supply functions:

3. Government and the central bank

The only function of the central bank is to ensure the costless conversion, at the official parity, of domestic money into foreign money, and vice versa. Since there is no credit, the real money stock is equal to

where R is the central bank’s stock of net foreign assets, measured in foreign currency terms. Real profits of the central bank consist of interest on its holdings of foreign assets, i^*z^δR, which are transferred to the government. The government consumes only home goods, in quantity g_N. For simplicity, it is also assumed to compensate private agents for the loss in interest income incurred as a result of imperfections on world capital markets. It balances its budget by levying lump-sum taxes on households. Setting the constant level of domestic bonds to zero, the budget constraint of the government is thus

4. Market-clearing conditions

To close the model requires specifying the equilibrium conditions for the home goods market and the money market. The former condition is given by

Using equation (4), the equilibrium condition of the money market can be solved for the market-clearing interest rate:

5. Dynamic structure and steady state

As described in detail by Agénor (1996), the dynamic structure of the model can be reduced to a first-order differential equation system involving two variables: private consumption c (which is a jump variable) and the economy’s net stock of foreign assets F = R + B^*, which evolves gradually over time as a result of changes in the current account balance:

The steady-state equilibrium of the model is depicted in Figure 2. The curve N N in the North-West panel of the figure shows the combinations of consumption and the real exchange rate that are consistent with equilibrium in the market for nontraded goods (equation (17)). In the North-East panel in the figure, the locus [Ḟ = 0] gives the combinations of c and F for which the current account is in balance (derived from equation (19)), whereas the locus [ċ = 0] depicts the combinations of c and F for which consumption does not change over time. Saddlepath stability requires that the [ċ = 0] curve be steeper than [Ḟ = 0] curve. The saddlepath SS slopes downward, so that a current account deficit, for instance, must be accompanied by a higher level of private consumption and an appreciating exchange rate. The steady-state solution is obtained by setting ċ = Ḟ = 0. From equation (4), π = π_N = π^*. From equation (6).

Steady-State Equilibrium

Citation: IMF Working Papers 1996, 137; 10.5089/9781451855876.001.A001

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Steady-State Equilibrium

Citation: IMF Working Papers 1996, 137; 10.5089/9781451855876.001.A001

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Substituting this result in (5) yields

and from (4) and (20):

Finally, from equation (19),

Thus, the steady-state solution of the model is such that the current account must be in equilibrium, domestic inflation and the rate of inflation in the price of home goods are equal to world inflation, the real interest rate is equal to the rate of time preference—so that the domestic nominal interest rate is equal to the rate of time preference plus world inflation. Real holdings of foreign bonds are proportional to the difference between the world real interest rate and the rate of time preference, indicating that in the long run domestic private agents are net creditors (debtors) if their rate of time preference is lower (greater) than the foreign discount rate.

6. Shocks, capital flows, and relative prices

To illustrate the functioning of the model, consider a permanent, unanticipated increase in government spending on home goods financed by an increase in lum-sum taxes (equation (16)). This shock has no long-term effect on the domestic nominal interest rate (as implied by equation (20)), no effect on private holdings of foreign assets (as implied by equation (21)). Private consumption is “crowded out”, and the real exchange rate appreciates to maintain equilibrium of the market for nontraded goods. The fall in private spending is associated with a reduction in real money balances, since domestic interest rates do not change (equation (22)). But the shock has an ambiguous effect on the economy’s stock of net foreign assets. The reason is that the appreciation of the real exchange rate has an adverse effect on output of traded goods. Since both production and consumption of traded goods fall, the net effect on the trade balance cannot be ascertained a priori; thus, whether the service account surplus (and thus the economy’s stock of net foreign assets) must increase or not cannot be determined unambiguously.⁷ The two panels in Figure 3 illustrate the two cases.

Increase in Government Spending on Home Goods

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Increase in Government Spending on Home Goods

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On impact, private consumption always falls, but the movement in the real exchange rate is now ambiguous and depends on the strength of consumption smoothing effects. If the degree of intertemporal substitution is low (so that private consumption changes by a relatively small amount, implying that net absorption of home goods rises), the real exchange rate will appreciate. Real money balances also fall on impact. But since both private consumption and money holdings fall, the domestic nominal interest rate (and thus the interest rate differential) may either rise or fall on impact; with a low degree of intertemporal substitution it tends to rise—as illustrated in both panels of Figure 3. The increase in the rate of return on domestic assets implies that holdings of foreign bonds must fall, so that the economy experiences capital inflows. Because of the monotonicity of the adjustment path toward the new long-run equilibrium, the stock of net foreign assets continuously rises or falls during the transition according to whether it rises or falls in the new steady state. During the transition, consumption rises (falls), and the real exchange rate appreciates (depreciates), if net foreign assets increase (decline).

Consider now the effects of a permanent reduction in the world interest rate, and suppose that the country is initially a net creditor $(\tilde{F}>0)$.⁸ The long-run effects are a reduction in aggregate consumption, a depreciation of the real exchange, rate and a reduction in total holdings of foreign assets. At the initial level of the real exchange rate, the reduction in the world interest rate lowers interest income. To maintain external balance, consumption must therefore fall. At the same time, the reduction in the rate of return on foreign assets reduces private demand for foreign bonds. Since consumption falls, real money balances—with the nominal interest rate remaining constant—must also fall. Thus, at the initial level of relative prices, the overall stock of foreign assets falls—compounding the initial negative effect on interest income and the current account. The reduction in consumption expenditure lowers demand for nontraded goods and leads to a depreciation of the real exchange rate, together with an increase in output of traded goods. The fall in consumption of traded goods and the expansion of output of tradables bring about the required improvement in the trade balance, which restores external equilibrium.

Since the steady-state stock of foreign assets falls, the transition (given the permanent nature of the shock and the monotonic nature of the adjustment path) must involve a sequence of current account deficits. However, on impact the real exchange rate may either appreciate or depreciate. The initial effect of a reduction in the rate of return on foreign assets is a fall in interest income for the economy as a whole (since overall holdings of foreign assets cannot change on impact), a reduction in the private demand for foreign bonds and an increase in the demand for domestic currency holdings. This instantaneous portfolio shift takes place through an inflow of capital (a discrete reduction in private holdings of foreign bonds) and an offsetting movement in central bank holdings of foreign assets, which leads (under unsterilized intervention) to a discrete increase in the real money stock. However, whether domestic interest rates rise or fall to maintain equilibrium in the money market cannot be ascertained a priori, because the real exchange rate (and thus aggregate consumption) may appreciate or depreciate on impact.

Intuitively, the ambiguity emerges as a result of conflicting wealth and intertemporal effects on consumption. On the one hand, the expected future reduction in interest income (induced by the reduction in the world interest rate and the level of financial wealth) tends to reduce immediately (at the initial level of the real exchange rate) private expenditure and increase saving. On the other, a reduction in the world interest rate encourages agents to save less (and consume more) today, since the rate of return on foreign assets has fallen (intertemporal effect). Because the initial effect on aggregate consumption is ambiguous, the real exchange rate may either appreciate or depreciate on impact.

If the degree of intertemporal substitution is large, aggregate consumption will rise on impact, and the real exchange rate will appreciate. This is the case characterized in the upper panel in Figure 4. Because consumption of both home and traded goods increase, the trade balance (which, in the initial equilibrium, is characterized by a deficit equal in absolute value to interest income on net foreign assets) tends to deteriorate. The real appreciation leads to a reduction in output of traded goods, which compounds the effect of the increase in consumption on the trade deficit. Since interest income received on the initial stock of assets always falls, the economy generates a current account deficit on impact. Real money balances unambiguously increase whereas private holdings of foreign bonds fall. The increase in the domestic money stock (induced by the discrete portfolio adjustment) tends to lower the domestic interest rate on impact, but the increase in consumption tends to raise it. The net effect is in general ambiguous. The increase in domestic interest rates, of course, reinforces the effect of a reduction in the world interest rate on the demand for foreign bonds, and further stimulates capital inflows.

Reduction in the World Interest Rate

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The transition period is characterized by a continuous reduction in the stock of foreign assets (associated with current account deficits), a fall in consumption, and a depreciation of the real exchange rate. The fall in consumption and the expansion in output of traded goods (resulting from the real depreciation) tend to reverse over time the adverse effect of the initial appreciation on the trade balance. The trade deficit falls over time, eventually turning into a trade surplus. However, because interest payments continue to fall with the reduction in the stock of assets, improvements in the trade balance are not large enough to prevent the current account from remaining in deficit until the new steady state is reached. Since the devaluation rate does not change, the nominal interest rate must fall in order to return to its initial value and ensure equality between the real interest rate and the rate of time preference. And since the domestic interest rate falls, holdings of foreign assets by the private sector tend to increase during the transition, thereby leading to capital outflows and lower reserve accumulation by the central bank. The domestic money stock is thus falling during the transition.

If the degree of intertemporal substitution is sufficiently small, consumption will fall on impact and the real exchange rate will depreciate. This is the case characterized in the lower panel in Figure 4. Although the fall in consumption of traded goods and the expansion of output of these goods (resulting from the real depreciation) lead initially to an improvement in the trade balance, the reduction in interest income is large enough to generate a current account deficit. The net effect on the domestic interest rate is now unambiguously negative, since consumption falls. This tends to increase the demand for foreign bonds. However, since both the world interest rate and the domestic interest rate fall, whether the net effect on real money balances and the demand for foreign bonds is positive or negative cannot be determined a priori. Thus, the economy may experience either capital inflows or capital outflows. If the reduction in the world interest rate is larger than the induced reduction in the domestic interest rate, holdings of foreign bonds will fall and the economy will experience capital inflows on impact. Real money balances in this case will rise. Despite the reduction in private expenditure on both categories of goods and the depreciation of the real exchange rate (which stimulates output of traded goods), the fall in interest income ensures that the current account remains in deficit. The domestic interest rate rises gradually toward its initial level, stimulating further capital inflows. With consumption falling and domestic interest rates increasing, real money balances tend to fall over time.

Consider now the case of a net debtor country $(\tilde{F}<0)$. The long-run effects of a permanent reduction in the world interest rate are again a reduction in consumption, a depreciation of the real exchange rate, and a reduction in total holdings of foreign assets—that is, an increase in foreign debt. The initial effect of the reduction in the cost of borrowing on world capital markets is an increase in private foreign indebtedness, which results in higher interest payments and a deterioration of the service account. To maintain external balance in the long run, the initial trade surplus (which is just equal, in absolute terms, to the initial deficit in the service account) must increase. Consumption must therefore fall. This leads to a depreciation of the real exchange rate, which in turn stimulates output of traded goods and further improves the trade balance. Since the nominal interest rate remains constant, real money balances—and thus official reserves—fall also. With foreign borrowing by private agents increasing, and net foreign assets held by the central bank falling, the economy’s external debt unambiguously rises.

The impact effects of a permanent reduction in the world interest rate on private spending and relative prices are, in contrast to the case where the economy is initially a net creditor, can be signed unambiguously. As illustrated in Figure 5, consumption increases, and the real exchange rate appreciates. This is because the wealth and intertemporal effects operate now in the same direction: the reduction in the world interest rate not only encourages agents to save less (and consume more) today, but it also lowers the debt burden and generates a positive wealth effect. Although the trade balance and the service account move in opposite direction (the former deteriorates, whereas the latter improves), the net effect is a current account deficit on impact; and if the degree of intertemporal substitution is sufficiently low, the domestic interest rate will rise on impact, and the economy will experience a capital inflow. Because of the permanent nature of the shock and the monotonic nature of the adjustment process, the current account remains in deficit throughout the transition period, with consumption falling towards its new, lower steady-state level, and the real exchange rate depreciating—with both effects contributing to a gradual reversal of the initial deterioration in the trade deficit. During the transition, with the domestic interest rate returning to its initial value, the economy experiences capital outflows.

Reduction in the World Interest Rate

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1. Methodology

The specific variables that are included in our near-VAR model are a broad measure of capital inflows in proportion of aggregate output (denoted ky), changes in the uncovered interest rate differential (idiff), government expenditure as a proportion of aggregate output (gy), money-base velocity (veloc), the change in the “world” interest rate (iw), and the temporary component of the real exchange rate (lzc), which is denoted TCRER and whose derivation is explained below. The near-VAR approach allows us to treat the government spending-output ratio and changes in the world interest rate as block-exogenous variables. The endogenous block consists therefore of capital flows, changes in the interest rate differential, TCRER and velocity. Precise definitions of all variables are given in the Appendix. In particular, the world interest rate is proxied by U.S. interest rates. In line with the analytical model described in the previous section, where the stock demand for foreign assets is related to the level of the interest rate differential, we relate changes in the interest rate differential to capital flows in the empirical model. Our empirical specification—whose statistical adequacy is established below—captures the key feature of our theoretical framework, namely, the view that capital movements respond not only to external factors (such as changes in world interest rates) but also to changes in domestic macroeconomic conditions—as captured by movements in domestic interest rates and fiscal policy. The addition of money-base velocity plays the role of a “control” variable, which is meant to capture indirect effects of changes in the money supply on capital flows, through their effect on domestic interest rates. The focus on the TCRER is motivated by two considerations. First, from a statistical point of view, the real exchange rate in the group of countries considered here is not stationary (as indicated by the unit root tests discussed below), while the other variables described above are stationary. Detrending the real exchange rate therefore is a necessary first step to avoid mixing stationary and nonstationary variables in our econometric model. From an economic point of view, focusing on the TCRER is related to the assumption that, in line with the analytical framework described in the previous section, it is the stock of net foreign assets, rather than changes in this stock (capital flows), that affect the trend (or steady state) value of the real exchange rate. The (stationary) temporary component can be interpreted as transitory deviations from the long-run path, resulting from short-term cyclical and speculative factors.¹⁰

To decompose the real exchange rate into a nonstationary (trend) component and a stationary one, two commonly-used techniques are implemented here. The first is the Beveridge-Nelson (BN) approach, the second the Hodrick-Prescott (HP) filter. To highlight the main features of these techniques, suppose that the observed variable X_t has no seasonal component and can be expressed as the sum of a trend $x_t^{*}$ component and a cyclical component, $x_t^c$

At period t, the econometrician can observe x_t but cannot measure either $x_t^{*}$ or $x_t^c$. The BN approach is motivated by the observation that many macroeconomic time series are well-captured by ARIMA processes. Specifically, suppose that the series x_t follows an ARIMA(p, 1, g) process. Beveridge and Nelson (1981) showed that any such process can be represented in terms of a stochastic trend plus stationary component, where the former is a random walk (possibly with drift) and the latter is an ARIMA(p, 0, q)or, more compactly, ARMA(p, q) process.¹¹

Formally, the model for ${\left\{x_t\right\}}_{t=0}^T$, where T is the sample size, can be written as

where L is the lag operator, $\mathrm{\psi }\left(L\right)={\mathrm{\Sigma }}_{h=0}^p{\mathrm{\Phi }}_h{L}^h,\mathrm{\Theta }\left(L\right)={\mathrm{\Sigma }}_{h=0}^q{\theta }_h{L}^h,\mu$ a constant term, and et is an i.i.d. error. Inverting ѱ(L) gives (1 -L)x_t = γ + B(L)ε_t where $\gamma =({\mathrm{\Sigma }}_{h=0}^p{\mathrm{\Phi }}_h{)}^{-1}\mu$, and B(L) = ѱ(L)^-1Θ(L). Recursively substituting for x_t and assuming that x₀ = ε_T = 0 (for т < 0) yields

which can be rewritten as (Blackburn and Ravn, 1991):

where $b={\mathrm{\Sigma }}_{h=0}^{\infty }{b}_h,G\left(L\right)={\mathrm{\Sigma }}_{k=0}^{\infty }{ɡ}_k{L}^k,\text{and}{\mathit{ɡ}}_k=-{\mathrm{\Sigma }}_{h=k+1}^{\infty }{b}_h$. The trend and cyclical components are given respectively by $x_t^{*}=\gamma t+b{\mathrm{\Sigma }}_{\tau =1}^t{\epsilon }_{\tau }$ and $x_t^c$ = G(L)ε_t. Thus, the trend component follows a random walk with drift. The equivalent representation is therefore

The second technique used here to defining the cyclical component of the real exchange rate is the Hodrick-Prescott (HP) filter.¹² The technique consists essentially in specifying an adjustment rule whereby the trend component of the series x_t moves continuously and adjusts gradually. Formally, the unobserved component $x_t^{*}$ is extracted by solving the following minimization problem:

Thus, the objective is to select the trend component that minimizes the sum of the squared deviations from the observed series, subject to the constraint that changes in $x_t^{*}$ vary gradually over time. The Lagrange multiplier λ is a positive number that penalizes changes in the trend component. The larger the value of λ, the smoother is the resulting trend series.¹³ By manipulating the first-order condition of the minimization problem (see King and Rebelo, 1993), a time domain representation of the HP filter can be developed in which the trend component $x_t^{*}$ is represented by a two-sided symmetric moving average expression of the observed series:

where the parameters α_|h| depend on the value of the Lagrange multiplier λ. Both of the above decomposition techniques have their limitations. The difficulty with the BN approach results precisely from its flexibility: in practice, identifying the polynomials ѱ(L) and Θ(L) requires considerable judgment, and choosing among alternative parameterizations can be arbitrary. The HP filter has also been the subject of criticism (see Stadler, 1994, pp. 1768-69). In particular, it has been argued that it removes potentially valuable information from time series (King and Rebelo, 1993), and that it may impart spurious cyclical patterns to the data (Cogley and Nason, 1995). Nevertheless, using both procedures here provides a way of testing the sensitivity and robustness of the econometric results described below.

2. Unit Root tests and ARMA models

Figure 6 shows the TCRERs derived by using both the BN and HP techniques. An ARMA process for the first-differences of (the logarithm of) the real exchange rate was selected on the basis of conventional criteria, starting from an ARMA(2,2) to economize on degrees of freedom. The models selected were an ARMA(0,1) for Korea, ARMA(2,0) for Mexico, ARMA(2,2) for the Philippines, and an ARMA(1,1) for Thailand. As shown in the figure the two series that for Thailand they are fairly similar throughout the sample period. For the other countries these series show similar movements of the TCRER during the 1990s. In the early part of the sample, however, these series show different accounts of movements of the TCRER. For example, the HP filter suggests that the TCRER depreciated from 1985 through 1987 for these other countries, while the BN filter suggests the reverse. Note further that the HP filter seems to identify a fairly regular cyclical movement for Korea and Mexico.

Temporary Component of the Real Exchange Rate

Citation: IMF Working Papers 1996, 137; 10.5089/9781451855876.001.A001

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Prior to estimating the near-VAR model, each set of series was tested for stationarity. Augmented Dickey-Fuller (ADF) and Phillips-Perron (PP) unit root tests were employed (see Dickey and Rosanna, 1994). The results of these tests—based on a unit-root null versus a trend-stationary alternative—are reported in Table A1 of the Appendix. In general, both test statistics give similar results, although in a few cases differences exist and the significance level is not always large. In almost all cases, the results supports the assumption that the “world” interest rate (proxied by the U.S. Treasury bill rate) is differenced stationary, whereas all the other variables are stationary in levels. Note that for Korea, there appears to be only weak evidence of stationarity of the TCRER obtained by the HP filter; this feature of the data is accounted for in the estimation of the near-VAR, as indicated below.

3. Variance decompositions

The near-VAR model (with seasonal dummies in each equation) was estimated using the two different measures of the TCRER discussed previously over the period 1982:Q1 through 1994:Q3 for Korea, Mexico, and the Philippines, and over 1986:Q3-1994:Q3 for Thailand.¹⁴ For consistency across countries and to conserve degrees of freedom, estimation for each country was performed with 2 lags.¹⁵ The near-VAR model for Mexico includes a dummy variable (equal to one from 1988:Q4 onward) to account for the stabilization program implemented in the late 1980s; this dummy is statistically significant. We also tried adding a dummy variable for NAFTA (one from 1993:Q4 onwards) but this variable was not statistically significant.

The statistical adequacy of the near-VAR models used in this study was tested with a multivariate generalization of the Granger causality test. This generalization is essentially a multivariate likelihood ratio test and the resulting test statistic is distributed as X² with degrees of freedom equal to the number of regressors excluded in the null hypothesis. Specifically, we test the null hypothesis that iw and gy are jointly block exogenous against the alternative hypothesis that iw and gy are part of the “endogenous” VAR system. The resulting X₂ with 20 degrees of freedom (5 variables with 2 lags each excluded from 2 equations) did not reject the null hypothesis at conventional level of significance in any of the countries considered in this study.

The estimated models were used to perform “generalized” VAR analysis, as proposed by Koop, Pesaran, and Potter (1996). An attractive feature of this approach is that it does not suffer from the “compositional effect” inherent in standard VAR analysis. As is well known, variance decompositions and impulse response functions derived from standard VAR analysis, depend on the ordering of the variables used to obtain the orthogonal shocks.¹⁶ This dependence reflects the fact that changing the ordering changes the implicit linear combination of the VAR innovations used to obtain the orthogonal shock, that is, changing the ordering changes the “composition” of the orthogonal shock.

Generalized VAR analysis is based on re-thinking what is to be “recovered” from the estimated VAR (or near-VAR) model, specifically consider impulse responses. Typically a VAR is subjected to an orthogonal shock, and the impulse responses trace out the dynamic response of the model to that shock. Note that implicitly these impulse responses compare the evolution of the model following the shock to a baseline model not subject to the shock. Generalized impulse responses (GIR) build upon this idea and propose to look instead at a “typical” historical shock. GIR compares the “average” dynamic responses of the model given a “typical” historical shock and the history of the model, compared to the “average” baseline model not subject to the shock given the history of the model. Specifically, GIR compares the conditional expectation of a variable in the model given an arbitrary currrent shock υ_t and history ω_t, to the conditional expectation of that variable given history:

For example, consider an economy where the real exchange depends only on fiscal policy and world interest rates. Suppose further that in this economy the data shows that when a negative world interest rate shock is observed, the authorities respond with a contractionary fiscal shock. The GIR of the real exchange rate to a world interest rate shock in this economy would trace out, on average, the evolution of the real exchange rate to a typical world interest rate shock—given the historically observed fiscal shocks. It should be clear that since the GIR captures the historically-observed information regarding shocks in the data, it does not pretend to recover the responses to a “pure” world interest rate shock.

Likewise, the generalized variance decompositions (GVD) measures does not pretend to measure the percentage of the variance attributed to “pure” shocks. Specifically, in our example, the percentage of the variance of the real exchange rate attributed to the typical world interest rate would also capture the historically observed information regarding shocks in the data. Note that to the extent that historical shocks are in fact correlated, the GVD will typically not add up to 100 percent.

Table 2 presents the GVD of the TCRER at 4-quarter intervals (up to 16 quarters). At short forecasting horizons, the importance of composite shocks to the TCRER dominate movements of TCRER. Note, however, that composite shocks associated with idiff play a fairly substantive secondary role in Korea and Thailand at the 4-quarter horizon, explaining somewhere in the order of 20 and 40 percent respectively. The evidence for Mexico and Philippines on this issue is less clear and depends on the filter used to measure the TCRER. In particular, the evidence from the BN filter in both countries suggests that shocks associated with idiff plays a substantive role in explaining movements of TCRER at the 4-quarter horizon—30 and 50 percent respectively in Mexico and Philippines—but the evidence from the HP filter does not find this secondary role. With the notable exception of Korea,¹⁷ at this forecasting horizon composite shocks associated with gy also appear to explain movements in the TCRER, but the magnitude of this effect is filter dependent. Although in Thailand the effect of composite shocks associated with gy explain fairly stable share of the movements of the TCRER (15 and 10 percent respectively with the BN and HP filters), this is not the case in Mexico or in Philippines. In Mexico, these composite shocks explain about 20 percent of the movements of the TCRER when measured with the BN filter but only about 5 percent when measured with the HP filter. In Philippines, filter dependence is also evident, when the BN filter is used 10 percent of the movements of TCRER are explained by shocks associated with gy and 30 percent when the HP filter is used. At 16 quarters, the bulk of the movements of the TCRER are no longer associated with “own” composite shocks, and suggest that the other composite shocks in the model play a role in explaining TCRER. Composite shocks associated with iw explain roughly about 10 of the movements of TCRER in Korea, Mexico and Philippines at this forecasting horizon, and in Thailand they appear to explain about 20 percent. Composite shocks in Thailand they appear to explain about 20 percent. Composite shocks associated with idiff explain about 15 and 40 percent of the movements of the TCRER in Korea and Thailand respectively, whereas these shocks explain somewhat less in Mexico and Philippines when the HP filter is used to calculate the TCRER and higher percentage when the BN filter is used. Composite shocks associated with ky appear to explain about 10 percent of the movements of the TCRER in Korea, Mexico and Thailand—with some filter dependence evident—but a negligible amount in Philippines. Composite shocks associated with gy appear to explain between 10 and 15 percent of the movements of the TCRER in all countries (except in Korea and Philippines where the BN filter suggests a small percentage). And finally, composite shocks associated with veloc explain about 15 percent of the movements of TCRER in Thailand, about 10 percent in Philippines, about 5 to 20 percent for Korea, and a smaller amount for Mexico. Table 3 presents the GVD of ky at 4-quarter intervals (up to 16 quarters). Perhaps the most striking feature is the high degree of autonomy exhibited by these capital flows, that even after 16 quarters the “own” composite shock still explains somewhere between 60 and 70 percent in all countries. Composite shocks associated with zw, gy and veloc explain a much smaller amount of the movements in the TCRER at 16 quarters, each accounting for roughly 10 percent.

Table 2.

Generalized Variance Decomposition of TCRER

Note: Based on the estimated near-VAR models discussed in the text. The percentage of the variance attributed to the historical shocks associated with each variable do not necessarily add up to 100.

Table 2.

Generalized Variance Decomposition of TCRER

	HP filter						BN filter
Quarters	iw	idiff	lzc	ky	gy	veloc	iw	idiff	lzc	ky	gy	veloc
Korea
1	0.2	24.0	100.0	1.1	0.9	0.5	0.4	18.7	100.0	0.1	0.1	0.0
4	10.9	29.0	69.0	9.6	2.4	6.4	8.5	12.4	62.8	19.1	5.3	3.9
8	14.9	22.7	46.4	10.7	3.5	18.0	8.4	12.0	60.7	20.3	5.5	5.1
12	11.5	17.5	36.7	8.3	9.3	22.0	8.4	12.0	60.5	20.4	5.5	5.2
16	10.4	15.0	31.5	7.6	13.4	22.9	8.4	12.0	60.4	20.4	5.5	5.3
Mexico
1	0.0	17.4	100.0	11.2	1.9	0.0	0.0	2.3	100.0	7.8	2.8	0.3
4	5.0	5.9	50.3	27.3	4.5	0.6	12.1	28.8	49.0	11.3	20.3	7.3
8	9.8	4.2	46.8	24.6	8.4	0.6	11.7	29.5	47.0	10.9	21.8	7.2
12	11.2	4.0	45.5	23.8	8.9	0.8	11.5	30.0	46.5	10.9	22.2	7.3
16	11.6	3.9	45.2	23.5	9.2	0.8	11.5	30.0	46.4	10.8	22.2	7.3
Philippines
1	4.3	5.0	100.0	0.4	3.0	6.5	5.3	0.1	100.0	0.9	8.6	3.8
4	6.0	17.5	32.0	3.0	30.6	2.8	12.2	50.1	34.4	0.5	10.2	12.9
8	9.7	13.4	20.1	2.3	42.8	5.0	146	48.4	32.7	1.4	9.8	13.0
12	10.9	13.7	20.4	2.4	41.2	6.0	14.6	48.3	32.6	1.4	9.9	13.0
16	11.1	13.7	20.5	2.4	40.8	6.3	14.6	48.3	32.6	1.4	9.9	13.1
Thailand
1	5.5	25.9	100.0	1.8	9.3	1.5	8.9	15.6	100.0	3.6	22.2	8.1
4	22.7	32.3	19.4	16.5	11.6	31.0	21.9	53.7	28.6	5.1	15.6	26.3
8	21.6	32.1	16.6	21.0	13.6	27.6	21.8	52.0	27.7	6.9	15.9	26.0
12	21.9	32.0	16.3	21.0	14.0	27.2	21.9	52.0	27.7	6.9	15.9	26.0
16	21.9	32.0	16.3	21.0	14.0	27.2	21.9	52.0	27.7	6.9	15.9	26.0

Note: Based on the estimated near-VAR models discussed in the text. The percentage of the variance attributed to the historical shocks associated with each variable do not necessarily add up to 100.

View Table

Table 2.

Generalized Variance Decomposition of TCRER

	HP filter						BN filter
Quarters	iw	idiff	lzc	ky	gy	veloc	iw	idiff	lzc	ky	gy	veloc
Korea
1	0.2	24.0	100.0	1.1	0.9	0.5	0.4	18.7	100.0	0.1	0.1	0.0
4	10.9	29.0	69.0	9.6	2.4	6.4	8.5	12.4	62.8	19.1	5.3	3.9
8	14.9	22.7	46.4	10.7	3.5	18.0	8.4	12.0	60.7	20.3	5.5	5.1
12	11.5	17.5	36.7	8.3	9.3	22.0	8.4	12.0	60.5	20.4	5.5	5.2
16	10.4	15.0	31.5	7.6	13.4	22.9	8.4	12.0	60.4	20.4	5.5	5.3
Mexico
1	0.0	17.4	100.0	11.2	1.9	0.0	0.0	2.3	100.0	7.8	2.8	0.3
4	5.0	5.9	50.3	27.3	4.5	0.6	12.1	28.8	49.0	11.3	20.3	7.3
8	9.8	4.2	46.8	24.6	8.4	0.6	11.7	29.5	47.0	10.9	21.8	7.2
12	11.2	4.0	45.5	23.8	8.9	0.8	11.5	30.0	46.5	10.9	22.2	7.3
16	11.6	3.9	45.2	23.5	9.2	0.8	11.5	30.0	46.4	10.8	22.2	7.3
Philippines
1	4.3	5.0	100.0	0.4	3.0	6.5	5.3	0.1	100.0	0.9	8.6	3.8
4	6.0	17.5	32.0	3.0	30.6	2.8	12.2	50.1	34.4	0.5	10.2	12.9
8	9.7	13.4	20.1	2.3	42.8	5.0	146	48.4	32.7	1.4	9.8	13.0
12	10.9	13.7	20.4	2.4	41.2	6.0	14.6	48.3	32.6	1.4	9.9	13.0
16	11.1	13.7	20.5	2.4	40.8	6.3	14.6	48.3	32.6	1.4	9.9	13.1
Thailand
1	5.5	25.9	100.0	1.8	9.3	1.5	8.9	15.6	100.0	3.6	22.2	8.1
4	22.7	32.3	19.4	16.5	11.6	31.0	21.9	53.7	28.6	5.1	15.6	26.3
8	21.6	32.1	16.6	21.0	13.6	27.6	21.8	52.0	27.7	6.9	15.9	26.0
12	21.9	32.0	16.3	21.0	14.0	27.2	21.9	52.0	27.7	6.9	15.9	26.0
16	21.9	32.0	16.3	21.0	14.0	27.2	21.9	52.0	27.7	6.9	15.9	26.0

Note: Based on the estimated near-VAR models discussed in the text. The percentage of the variance attributed to the historical shocks associated with each variable do not necessarily add up to 100.

4. Dynamic Response to Shocks

As discussed above, the transitional dynamics induced by a temporary change in any variable in the near-VAR model can be traced using GIRs. Here we examine shocks to government spending and the world interest rate.¹⁸ We view these two experiments as particularly useful (in light of the discussion provided in section II) to assess the effect of “pull” (internal) and “push” (external) factors.

a. World interest rate shock

GIRs and their one-standard error bands for the TCRER and capital inflows associated with a one-standard deviation reduction in the world interest interest iw are illustrated in Figures 7 and 8, for both measures of the TCRER.¹⁹ Since the world interest rate variable enters in first-differenced form, this shock is tantamount to a permament shock to the level of the variable, and matches closely the experiment performed in the first part of the paper. To save space, movements in the other variables of the system are not shown, although the behavior of the (change in) interest rate differentials is described below.

Generalized Impulse Responses to a Fall in iw, HP filter

Citation: IMF Working Papers 1996, 137; 10.5089/9781451855876.001.A001

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Generalized Impulse Responses to a Fall in iw, HP filter

Citation: IMF Working Papers 1996, 137; 10.5089/9781451855876.001.A001

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Generalized Impulse Responses to a Fall in iw, HP filter

Citation: IMF Working Papers 1996, 137; 10.5089/9781451855876.001.A001

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Generalized Impulse Responses to a Fall in iw, BN filter

Citation: IMF Working Papers 1996, 137; 10.5089/9781451855876.001.A001

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Generalized Impulse Responses to a Fall in iw, BN filter

Citation: IMF Working Papers 1996, 137; 10.5089/9781451855876.001.A001

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Generalized Impulse Responses to a Fall in iw, BN filter

Citation: IMF Working Papers 1996, 137; 10.5089/9781451855876.001.A001

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Table 3.

Generalized Variance Decomposition of ky

Note: Based on the estimated near-VAR models discussed in the text. The percentage of the variance attributed to the historical shocks associated with each variable do not necessarily add up to 100.

Table 3.

Generalized Variance Decomposition of ky

	HP filter						BN filter
Quarters	iw	idiff	Izc	ky	gy	veloc	iw	idiff	lzc	ky	gy	veloc
Korea
1	0.4	6.0	1.1	100.0	17.8	2.2	0.0	2.0	0.1	100.0	20.6	0.6
4	2.5	7.5	6.5	84.4	15.8	5.6	3.6	3.0	3.4	85.2	18.8	3.0
8	3.1	7.2	6.2	74.9	15.2	12.0	3.7	2.8	3.7	78.4	17.8	8.6
12	2.9	6.5	6.4	64.7	16.7	15.5	3.9	2.6	3.6	74.3	16.2	11.9
16	3.3	6.3	7.0	57.0	18.2	17.0	4.0	2.4	3.5	72.1	15.1	13.6
Mexico
1	6.6	3.8	11.2	100.0	0.6	2.4	6.8	1.9	7.8	100.0	0.2	1.6
4	11.0	6.4	8.4	73.2	9.8	7.3	11.8	6.7	5.3	70.6	12.8	3.0
8	13.7	6.2	9.3	69.9	10.5	7.0	22.4	7.1	4.9	61.8	15.9	2.6
12	13.9	6.2	9.5	69.1	10.8	6.9	22.4	7.1	4.9	61.5	16.3	2.6
16	13.9	6.2	9.6	68.9	10.8	6.9	22.4	7.1	4.9	61.4	16.4	2.6
Philippines
1	3.1	5.5	0.4	100.0	0.4	36	3.4	4.1	0.9	100.0	0.4	4.2
4	2.9	4.7	2.4	83.6	5.4	11.5	3.4	3.6	2.0	85.7	4.9	9.3
8	6.1	8.1	4.0	72.3	7.9	16.5	5.3	8.0	2.2	75.4	7.9	14.6
12	6.2	8.2	5.4	69.0	10.1	17.2	5.3	9.0	2.3	72.1	9.5	16.6
16	6.3	8.3	5.7	68.2	10.4	17.6	5.3	9.5	2.3	70.5	10.2	17.7
Thailand
1	0.7	6.4	1.8	100.0	0.8	0.7	2.1	1.4	3.6	100.0	1.3	8.1
4	3.5	13.7	3.7	63.2	13.9	6.1	12.6	15.1	16.1	61.0	13.6	7.8
8	5.1	13.8	3.7	60.5	16.3	6.2	13.0	15.0	16.2	58.3	14.6	9.0
12	5.1	13.9	3.7	60.4	16.3	6.3	13.1	15.0	16.1	58.1	14.8	9.0
16	5.1	13.9	37	60.3	16.3	6.3	13.2	15.0	16.1	58.1	14.8	9.0

Note: Based on the estimated near-VAR models discussed in the text. The percentage of the variance attributed to the historical shocks associated with each variable do not necessarily add up to 100.

View Table

Table 3.

Generalized Variance Decomposition of ky

	HP filter						BN filter
Quarters	iw	idiff	Izc	ky	gy	veloc	iw	idiff	lzc	ky	gy	veloc
Korea
1	0.4	6.0	1.1	100.0	17.8	2.2	0.0	2.0	0.1	100.0	20.6	0.6
4	2.5	7.5	6.5	84.4	15.8	5.6	3.6	3.0	3.4	85.2	18.8	3.0
8	3.1	7.2	6.2	74.9	15.2	12.0	3.7	2.8	3.7	78.4	17.8	8.6
12	2.9	6.5	6.4	64.7	16.7	15.5	3.9	2.6	3.6	74.3	16.2	11.9
16	3.3	6.3	7.0	57.0	18.2	17.0	4.0	2.4	3.5	72.1	15.1	13.6
Mexico
1	6.6	3.8	11.2	100.0	0.6	2.4	6.8	1.9	7.8	100.0	0.2	1.6
4	11.0	6.4	8.4	73.2	9.8	7.3	11.8	6.7	5.3	70.6	12.8	3.0
8	13.7	6.2	9.3	69.9	10.5	7.0	22.4	7.1	4.9	61.8	15.9	2.6
12	13.9	6.2	9.5	69.1	10.8	6.9	22.4	7.1	4.9	61.5	16.3	2.6
16	13.9	6.2	9.6	68.9	10.8	6.9	22.4	7.1	4.9	61.4	16.4	2.6
Philippines
1	3.1	5.5	0.4	100.0	0.4	36	3.4	4.1	0.9	100.0	0.4	4.2
4	2.9	4.7	2.4	83.6	5.4	11.5	3.4	3.6	2.0	85.7	4.9	9.3
8	6.1	8.1	4.0	72.3	7.9	16.5	5.3	8.0	2.2	75.4	7.9	14.6
12	6.2	8.2	5.4	69.0	10.1	17.2	5.3	9.0	2.3	72.1	9.5	16.6
16	6.3	8.3	5.7	68.2	10.4	17.6	5.3	9.5	2.3	70.5	10.2	17.7
Thailand
1	0.7	6.4	1.8	100.0	0.8	0.7	2.1	1.4	3.6	100.0	1.3	8.1
4	3.5	13.7	3.7	63.2	13.9	6.1	12.6	15.1	16.1	61.0	13.6	7.8
8	5.1	13.8	3.7	60.5	16.3	6.2	13.0	15.0	16.2	58.3	14.6	9.0
12	5.1	13.9	3.7	60.4	16.3	6.3	13.1	15.0	16.1	58.1	14.8	9.0
16	5.1	13.9	37	60.3	16.3	6.3	13.2	15.0	16.1	58.1	14.8	9.0

Note: Based on the estimated near-VAR models discussed in the text. The percentage of the variance attributed to the historical shocks associated with each variable do not necessarily add up to 100.

Consider first the behavior of capital inflows. The results obtained with the HP filter (Figure 7) suggest that a significant increase in capital inflows occurs on impact in the case of Korea and one quarter after the shock in the case of the Philippines; in the latter case, an increase in inflows also occurs in the fifth and sixth periods.²⁰ In both countries, the movement in inflows reflects a significant increase in (the change in) the interest rate differential between domestic and foreign assets, which improves the attractiveness of domestic assets. The results obtained with the BN decomposition (Figure 8) also suggest that capital inflows in Korea and the Philippines increase significantly on impact and in the first quarter after the shock—with no discernible effet in the subsequent periods in the case of Korea, despite a significant increase in the interest rate differential in the third quarter after the shock. They also indicate a significant increase in the interest rate differential in the Philippines after two quarters, with capital inflows increasing significantly and showing some persistence. For Thailand, the results with the HP filter indicate that capital inflows do not appear to be very responsive to the interest rate shock, although a slightly significant effect can be detected in the second quarter after the shock—mirroring a significant improvement in the interest rate differential at that period. The results obtained with the BN decomposition show a more signifcant effect in the second quarter (which again mirrors the movement in the interest rate differential) and a slight recovery in the third quarter. The response of capital movements in Mexico is some what counterintuitive: with both filtering methods, there is a significant reduction in capital inflows on impact (despite the fact that the interest rate differential shows no significant movement during that period). Results obtained with the BN filter indicate another fall between the third and sixth quarters. However, those obtained with the HP suggest a slightly positive effect in the first quarter after the shock.

Consider now the movements in the TCRER. In Korea and Mexico, both filtering methods indicate that there is no significant effect on the TCRER on impact. After one quarter, however, there is a slight real appreciation (which does not persist), whereas in Korea, two quarters the shock, the TCRER depreciates, with the effect showing some persistence (notably with the HP filter) until the sixth quarter. The TCRER subsequently appreciates with the HP filter, but a comparison with the results obtained with the BN filter suggests that this effect is not robust. In both Thailand and the Philippines, the GIRs show a slight depreciation of the TCRER, followed by a statistically more significant appreciation in the first and second quarters after the shock. The response of the TCRER in both countries is more short-lived with the BN filter. For the Philippines, and in line with the drop in capital inflows noted earlier, the TCRER depreciates after the fourth quarter—a movement that displays some persistence over time.