Basic Setup

Households in country i supply a fixed amount of labor and maximize the following expected lifetime utility:

where δ is the discount factor, and C_iτ represents a consumption index for period τ. The consumption index is defined as

where $C_i^T$ and $C_i^N$ are the subindices for consumption bundles of traded and non-traded goods, γ_i is the share of traded goods in aggregate consumption, and time subscripts are dropped for simplicity. The traded-goods basket is also assumed to be a Cobb-Douglas index of m (> 1) goods:

where $C_i^{Tj}$ is the amount consumed of traded good j, and ${\theta }_i^j$ represents the share of the good in the basket.

Let P_i denote the consumer price index, and $P_i^T$ and $P_i^N$ the price indices for traded and nontraded goods. Using equations (1) and (2), we define P_i and $P_i^T$ as the cost-minimizing prices of C_i and $C_i^T$, which are given by

The pattern of production for traded goods is characterized by either diversification (with each country producing all traded goods) or specialization (with each country producing a different traded good). In the case of specialization, we use the same index for a country and its traded good (i.e., good i is produced by country i). Letting $Y_i^N$ and $Y_i^{\mathrm{Tj}}$ denote outputs of the nontraded and jth traded good, we assume the following Cobb-Douglas production function for these goods:⁹

where $K_i^N$ and $L_i^N$ represent the amounts of capital and labor used in the production of the nontraded good, while $K_i^{Tj}$ and $L_i^{Tj}$ are the corresponding amounts for the traded goodj. If there is specialization, $K_i^{Tj}=L_i^{Tj}=0\text{for}i\ne j$.

Let country 1 be the reference country, and define S_i as the exchange rate of country i (expressed as the price of country i's currency) with respect to country 1. We distinguish between the short and long run in the present model. The short run is characterized by nominal rigidities in the form of sticky wages and prices. The long run, on the other hand, represents steady-state equilibrium with full adjustment of wages and prices. In the short run, nominal rigidities can cause departures from the law of one price and the marginal productivity condition for labor. We assume below that there are no departures from these relations in steady state. We focus on the steady-state behavior of variables to derive Balassa-Samuelson effects. A tilde over a variable is used to denote the steady-state value of the variable.

Assuming that the law of one price holds in steady state, we can link steady-state prices of traded goods in different countries as follows:

Also, assume that the marginal productivity condition is satisfied in steady state. Thus, letting W_i denote the wage rate, and using equations (5) and (6), we have

where the second equality in equation (8) holds only for traded good i under specialization.

Key Relations

We now derive key relations in the log-linear form. Using lowercase letters to denote values in logs, we define the consumption-based log real exchange rate as

Next, we use equation (3) to decompose the log real exchange rate as

where $q_i^T\equiv s_i+p_i^T-p_1^T$ is the log real exchange rate for traded goods. Using equation (4), we can express this variable as

The traded-goods price in logs can be linked to export and import price indices as

where $p_i^X$ and $p_i^M$ are the price indices for goods for which country i is, respectively, a net exporter and net importer, and ${\theta }_i^X$ is the share of the export good in the traded-goods bundle.¹⁰ Note that in the specialization case, $p_i^X=p_i^{Ti}$ and ${\theta }_i^X={\theta }_i^i$.

Let rp_i denote the log relative price of nontraded goods to domestically produced traded goods. In the diversification case, $r{p}_i=p_i^N-p_i^T$, since all traded goods are produced domestically. Thus, for this case, equation (7) and the steady-state versions of equations (10) and (11) imply the following long-run relation for the real exchange rate:

The Balassa-Samuelson analysis is often simplified by the assumption that expenditure shares are the same everywhere. In this simple case, ${\theta }_i^j={\theta }_1^j$ for all j, γ_i = γ₁, and equation (13) can be expressed simply as q̃_i = (1 − γ₁)(rp̃_i − rp̃₁).

In the case of specialization, $r{p}_i=p_i^N-p_i^{Ti}$ since only traded good i is produced in country i. Using equation (12) and recalling that $p_i^{Ti}=p_i^X$, we obtain $r{p}_i=p_i^N-p_i^T-(1-{\theta }_i^X)(p_i^X-p_i^M)$ Then, letting $t{t}_i\equiv p_i^X-p_i^M$ denote the log terms of trade and using equation (7) along with equations (10) and (11) for steady state, we derive the following long-run relation for the specialization case:

Note that even if a country has the same expenditure shares as the reference country, the terms of trade differential (tt̰_i - tt̰₁) would affect the long-run real exchange rate in addition to the relative-price differential (rp̰_i − rp̰1). This effect arises because, in each country, the terms of trade influence the price of the traded-goods basket relative to that of the traded good produced at home.

The first term on the righthand side of equations (13) and (14) represents the log real exchange rate for traded goods in steady state, ${\stackrel{\sim }{q}}_i^T$. This term will not equal zero and may exhibit nonstationary behavior if the composition of a country's traded-goods basket differs from that of the reference country. In the case of heterogeneous expenditure shares, ${\stackrel{\sim }{q}}_i^T$ represents an additional channel through which the terms of trade influence the real exchange rate, regardless of whether there is diversification or specialization.¹¹ In our empirical analysis based on panel data, however, we do not link ${\stackrel{\sim }{q}}_i^T$ to the terms of trade; instead, we use time effects to control for variations in this variable.

Next, the relative price of nontraded goods can be related to the productivity differential between domestically produced traded and nontraded goods. We define the log labor productivity in the two sectors as

where ${\omega }_i^j$ is the weight for good j's labor productivity in the aggregate labor productivity index for traded goods. In the specialization case, ${\omega }_i^j$ equals one for j = i and zero otherwise. Let $l{p}_i\equiv l{p}_i^T-l{p}_i^N$ denote the labor productivity differential between traded and nontraded goods. In defining the diversification labor productivity index in steady state, we use the same weights as those in the price index for traded goods. Thus, let ${\omega }_i^j={\theta }_i^j$ under diversification; and ${\omega }_j^i=1$ for j = i and ${\omega }_i^j=0$ for j ≠ i under specialization. Using equation (8) and steady-state versions of equations (4), (15), and (16), we can express the steady-state relative price as

where ϑ equals $\sum {}_{j=1}^m{\theta }_i^j$ in the case of diversification and logβ_i - logβ_N in the case of specialization.

Data

We use a number of sources to put together a developing economies panel-data set that includes time series from 1976 to 1994 for 16 countries.¹² Traded goods are assumed to consist of manufacturing and agriculture sectors. Nontraded goods represent all other sectors. The United States is chosen as the reference country. The real exchange rate is based on consumer price indices and represents the real value of a currency in terms of U.S. dollars.

Although our classification of the traded- and nontraded-goods sectors is similar to the one used for industrial countries, one potential problem is that a substantial portion of the agriculture sector (and possibly of the manufacturing sector) in developing countries may consist of traditional activities producing nontraded goods. Another problem is that the quality of labor is likely to vary considerably across sectors in developing countries, and our labor productivity measure (based on employment figures unadjusted for quality changes) does not account for this variation.¹³ We are unable to address these issues because of data limitations. However, we explore below certain implications of these measurement problems for the estimation of the empirical model.

Empirical Model

To undertake panel-data tests of the Balassa-Samuelson relations, we assume that long-run parameters are the same across our developing country set (D).¹⁴ Thus, we set ${\theta }_i^X={\theta }^X$ and γ_i = γ for i € D. However, to allow for possible differences in expenditure shares between developing and industrial countries, we do not require U.S. (country 1) parameters to be the same as those for our developing country sample.

The following two equations are estimated to test for Balassa-Samuelson effects:

where rpd_it = rp_it − rp_1t, ttd_it = tt_it − tt_1t, and lpd_it = lp_it − lp_1t are, respectively, the log differences in the relative price of nontraded goods, the terms of trade, and the traded-nontraded productivity ratio between developing country i and the United States; μ_i and Ψ_i are country-specific fixed effects while κ_t and ϰ_t are common time effects; and u_it and v_it are error terms. Time effects represent the influence of common time-specific (short- and long-run) factors, and error terms capture the effects of short-term deviations from steady state (that are not included in time effects).

Equation (18) is derived from equations (13) and (14). Under our assumption that ${\theta }_i^j=\theta j$ for i € D, time effects in equation (18) would control for movements in ${\stackrel{\sim }{q}}_{it}^T(=\sum {}_{j=1}^m({\theta }_i^j-{\theta }_1^j){\stackrel{\sim }{q}}_1^{Tj})$ arising from parametric differences between developing countries and the United States. In the presence of time effects, equation (18) nests the diversification and specialization cases with τ = 0 under diversification and τ = (1 − θ^X)(1 − γ) > 0 under specialization.¹⁵ In both cases, π = (1 − γ) > 0. Equation (19) is based on equation (17). In this equation, λ = 1. The absence of Balassa-Samuelson effects would imply that π = τ = λ = 0.¹⁶

Although the long-run parameters in equations (18) and (19)—π, τ, and λ—are constrained to be the same across developing countries, these relations allow the short-run dynamics (reflected in the time-series behavior of the error terms) to be different across countries. The explanatory variables—rpd_it, ttd_it, and lpd_it—can be stationary, trend-stationary, or nonstationary. In the case of trend-stationary behavior, equations (18) and (19) can be modified to include a time trend. Coefficients of time trends in the two relations would be homogeneous across countries and depend on the long-run parameters.¹⁷ Note that if the explanatory variables are integrated or trend-stationary, then q_it would also be integrated or trend-stationary. In this case, Balassa-Samuelson effects would cause permanent departures from the purchasing power parity.

As discussed above, our measure for the traded-goods sector (i.e., agriculture plus manufacturing) may be too broad for developing countries and could include nontraded goods. As discussed in Appendix I, the measured relative price of non-traded goods in this case would understate the true relative price and bias the relative-price coefficient upward in equation (18). This measurement problem would not lead to a systematic bias in the estimation of equation (19), since the measured value of the traded-nontraded productivity differential would also understate its true value. A more serious problem for estimating equation (19) is that the labor productivity measure is not adjusted for quality variation. Appendix I also shows that the estimated effect of the measured labor productivity differential would be biased downward if there is a positive association between the average labor quality and the true labor productivity.

Estimation

Before estimating equations (18) and (19), we examine whether the variables in these relations contain a unit root or not. Table 1 shows the results of two tests of a unit root in panel data. In the first test (LL), based on Levin and Lin (1993), the null hypothesis of a unit root is tested against the alternative of a homogeneous auto-regressive coefficient. The second test (IPS), based on Im, Pesaran, and Shin (2003), tests the unit root null against a more general alternative of a heterogeneous autoregressive coefficient. Both tests indicate that q_it contains a unit root (with or without a time trend).¹⁸ For the remaining variables, the tests are sensitive to whether a time trend is included or not. In the absence of a trend, the unit root hypothesis is not rejected for rpd_it and ttd_it by both the LL and IPS tests, and for lpd_it by the LL test. However, if a trend is present, both tests indicate that rpd_it and lpd_it are not integrated, and the IPS test indicates that ttd_it is also not integrated.

Table 1

Unit Root Tests

Notes: q_it is country i's dollar real exchange rate in logs, while rpd_it, ttd_it, and lpd_it represent, respectively, log differences in the relative price of nontraded goods, the terms of trade, and the traded-nontraded labor productivity ratio between country i and the United States.

^*indicates significance at the 5 percent level, and ** at the 1 percent level.

Table 1

Unit Root Tests

	Levin-Lin Test Statistic		Im-Pesaran-Shin Test Statistic
Variable	Without trend	Without trend	Without trend	Without trend
q it	0.478	-1.008	-1.513	-1.480
rpd it	0.231	-3.730**	-0.358	-6.615**
ttd it	-0.070	-1.327	-0.388	-1.987*
lpd it	0.604	-3.297**	-2.059*	-6.169**

Notes: q_it is country i's dollar real exchange rate in logs, while rpd_it, ttd_it, and lpd_it represent, respectively, log differences in the relative price of nontraded goods, the terms of trade, and the traded-nontraded labor productivity ratio between country i and the United States.

^*indicates significance at the 5 percent level, and ** at the 1 percent level.

View Table

Table 1

Unit Root Tests

	Levin-Lin Test Statistic		Im-Pesaran-Shin Test Statistic
Variable	Without trend	Without trend	Without trend	Without trend
q it	0.478	-1.008	-1.513	-1.480
rpd it	0.231	-3.730**	-0.358	-6.615**
ttd it	-0.070	-1.327	-0.388	-1.987*
lpd it	0.604	-3.297**	-2.059*	-6.169**

Notes: q_it is country i's dollar real exchange rate in logs, while rpd_it, ttd_it, and lpd_it represent, respectively, log differences in the relative price of nontraded goods, the terms of trade, and the traded-nontraded labor productivity ratio between country i and the United States.

^*indicates significance at the 5 percent level, and ** at the 1 percent level.

We first consider the basic form of equations (18) and (19), which does not include a time trend. In this case, since there is indication of nonstationary behavior for variables in these relations, we also undertake tests for co-integration. We use two parametric tests, the panel t-test and the group t-test, suggested by Pedroni (1999). The panel t-test rejects the hypothesis that there is no co-integration for the vector (q_it, rpd_it), but does not reject this hypothesis for vectors (rpd_it, lpd_it) and (q_it, rpdit, ttdi_t). The group t-test rejects the no-co-integration hypothesis for all three vectors.¹⁹ The group t-test (unlike the panel t-test) does not constrain the first-order correlation in the residuals to be homogeneous under the alternative hypothesis and is more relevant for our model, which allows the short-run dynamics to vary across countries. The test's failure to reject the hypothesis of no co-integration for the above vectors supports the Balassa-Samuelson model's implication that a long-run relation exists between the real exchange rate and relative prices (and possibly the terms of trade) as well as between relative prices and productivity ratios. We next estimate Balassa-Samuelson effects in these relations.

We estimate equations (17) and (18) by Dynamic Ordinary Least Squares (DOLS), which is an appropriate framework for estimating and testing hypotheses for homogeneous co-integrating vectors.²⁰ The relations are estimated in the following form:

where n is the number of lags and leads used for the first-difference terms. Coefficients of these terms capture the short-run dynamics. We allow the short-run dynamics to be heterogeneous (i.e., let ξ_ir, ζ_ir, and Õ_ir differ across i). We test the null hypotheses that π = τ = 0 in equation (20) and λ = 0 in equation (21) against the alternative hypotheses that these variables are positive.

If a linear trend is included, unit root tests suggest that the explanatory variables in equations (18) and (19) are not integrated. We, thus, also consider the trend-stationary setting for estimating these relations. DOLS is a useful estimating procedure even in this case. Since first-difference terms are included in this procedure, the coefficients of level terms represent long-run effects. Therefore, we estimate equations (20) and (21) with trend variables to identify long-run Balassa-Samuelson influences in the trend-stationary case.

Basic Results

Tables 2 and 3 present DOLS estimates of different variants of the real exchange rate equation with one lag and one lead of the first-difference terms.²¹ Table 2 shows the estimates of the equation for the diversification case excluding the terms of trade variable, and Table 3 for the specialization case including this variable. For both cases, we report the results for homogeneous as well as heterogeneous short-run dynamics. Regressions 1 and 4 in these tables show estimates of the basic form of the equation without a time trend. In all of these cases, the effect of the relative-price variable is positive and significant. The predicted value of this variable's coefficient equals 1 − γ (which represents the share of the nontraded-goods sector). The estimated value, however, is greater than unity in most cases. The small size of our sample (based on only 19 years of data for each country) is a concern; it could be a source of bias in DOLS estimates. As discussed above, however, the discrepancy between the predicted and estimated values could reflect an upward bias arising from defining the traded-goods sector too broadly.²² The results also show that the terms of trade variable exerts a positive and significant effect when introduced in the real exchange rate equation (see Table 3). This finding is consistent with the specialization version of the model, in which each country produces a different good.

Table 2

The Exchange Rate Relation Without the Terms of Trade

Notes: The dependent variable is q^it(see notes to Table 1 for the definitions of variables). All regressions include country-specific and time-specific dummy variables as well as first differences of each explanatory variable at time t, t - 1, and t + 1. Coefficients of the first-difference terms are constrained to be the same across countries under homogeneous dynamics, and unconstrained under heterogeneous dynamics. White heteroskedasticity-consistent errors are shown in parentheses. D is a dummy variable, which equals one for low-income developing countries and zero for others. The number of observations equals 256. * indicates significance at the 5 percent level, and ** at the 1 percent level (using a one-sided test for rpd^it and a two-sided test for other variables).

Table 2

The Exchange Rate Relation Without the Terms of Trade

		Coefficient Estimates
Variable		(1)	(2)	(3)	(4)	(5)	(6)
		Homogeneous short-run dynamics			Heterogenecous short-run dynamics
rpdit		0.962**	0.962**	0.790**	1.066**	1.066**	0.846**
		(0.146)	(0.146)	(0.161)	(0.156)	(0.156)	(0.173)
Trend			0.057			0.071
			(0.055)			(0.060)
rpdit*D				0.329*			0.401*
				(0.129)			(0.156)
Adjusted R2		0.997	0.997	0.997	0.997	0.997	0.997
Standard error		0.154	0.154	0.152	0.160	0.160	0.158
	of regression

Notes: The dependent variable is q^it(see notes to Table 1 for the definitions of variables). All regressions include country-specific and time-specific dummy variables as well as first differences of each explanatory variable at time t, t - 1, and t + 1. Coefficients of the first-difference terms are constrained to be the same across countries under homogeneous dynamics, and unconstrained under heterogeneous dynamics. White heteroskedasticity-consistent errors are shown in parentheses. D is a dummy variable, which equals one for low-income developing countries and zero for others. The number of observations equals 256. * indicates significance at the 5 percent level, and ** at the 1 percent level (using a one-sided test for rpd^it and a two-sided test for other variables).

View Table

Table 2

The Exchange Rate Relation Without the Terms of Trade

		Coefficient Estimates
Variable		(1)	(2)	(3)	(4)	(5)	(6)
		Homogeneous short-run dynamics			Heterogenecous short-run dynamics
rpdit		0.962**	0.962**	0.790**	1.066**	1.066**	0.846**
		(0.146)	(0.146)	(0.161)	(0.156)	(0.156)	(0.173)
Trend			0.057			0.071
			(0.055)			(0.060)
rpdit*D				0.329*			0.401*
				(0.129)			(0.156)
Adjusted R2		0.997	0.997	0.997	0.997	0.997	0.997
Standard error		0.154	0.154	0.152	0.160	0.160	0.158
	of regression

Notes: The dependent variable is q^it(see notes to Table 1 for the definitions of variables). All regressions include country-specific and time-specific dummy variables as well as first differences of each explanatory variable at time t, t - 1, and t + 1. Coefficients of the first-difference terms are constrained to be the same across countries under homogeneous dynamics, and unconstrained under heterogeneous dynamics. White heteroskedasticity-consistent errors are shown in parentheses. D is a dummy variable, which equals one for low-income developing countries and zero for others. The number of observations equals 256. * indicates significance at the 5 percent level, and ** at the 1 percent level (using a one-sided test for rpd^it and a two-sided test for other variables).

Table 3

The Exchange Rate Relation with the Terms of Trade

Notes: The dependent variable is q^it (see notes to Table 1 for the definitions of variables). All regressions include country-specific and time-specific dummy variables as well as first differences of each explanatory variable at time t, t - 1, and t + 1. Coefficients of the first-difference terms are constrained to be the same across countries under homogeneous dynamics, and unconstrained under heterogeneous dynamics. White heteroskedasticity-consistent errors are shown in parentheses. D is a dummy variable, which equals one for low-income developing countries and zero for others. The number of observations equals 246. * indicates significance at the 5 percent level, and ** at the 1 percent level (using a one-sided test for lpd^it and ttd^it, and a two-sided test for other variables).

Table 3

The Exchange Rate Relation with the Terms of Trade

		Coefficient Estimates
Variable		(1)	(2)	(3)	(4)	(5)	(6)
		Homogeneous short-run dynamics			Heterogeneous short-run dynamics
rpd it		1.111**	1.111**	0.851**	1.217**	1.217**	0.834**
		(0.143)	(0.143)	(0.163)	(0.204)	(0.204)	(0.251)
ttd it		0.300**	0.300**	0.477**	0.332**	0.332**	0.565**
		(0.091)	(0.091)	(0.103)	(0.129)	(0.129)	(0.141)
Trend			0.063			0.111
			(0.054)			(0.075)
rpdit*D				0.407**			0.601*
				(0.143)			(0.271)
ttdit*D				-0.348**			-0.407
				(0.123)			(0.209)
Adjusted R2		0.997	0.997	0.998	0.997	0.997	0.997
Standard error		0.142	0.142	0.139	0.152	0.152	0.148
	of regression

Notes: The dependent variable is q^it (see notes to Table 1 for the definitions of variables). All regressions include country-specific and time-specific dummy variables as well as first differences of each explanatory variable at time t, t - 1, and t + 1. Coefficients of the first-difference terms are constrained to be the same across countries under homogeneous dynamics, and unconstrained under heterogeneous dynamics. White heteroskedasticity-consistent errors are shown in parentheses. D is a dummy variable, which equals one for low-income developing countries and zero for others. The number of observations equals 246. * indicates significance at the 5 percent level, and ** at the 1 percent level (using a one-sided test for lpd^it and ttd^it, and a two-sided test for other variables).

View Table

Table 3

The Exchange Rate Relation with the Terms of Trade

		Coefficient Estimates
Variable		(1)	(2)	(3)	(4)	(5)	(6)
		Homogeneous short-run dynamics			Heterogeneous short-run dynamics
rpd it		1.111**	1.111**	0.851**	1.217**	1.217**	0.834**
		(0.143)	(0.143)	(0.163)	(0.204)	(0.204)	(0.251)
ttd it		0.300**	0.300**	0.477**	0.332**	0.332**	0.565**
		(0.091)	(0.091)	(0.103)	(0.129)	(0.129)	(0.141)
Trend			0.063			0.111
			(0.054)			(0.075)
rpdit*D				0.407**			0.601*
				(0.143)			(0.271)
ttdit*D				-0.348**			-0.407
				(0.123)			(0.209)
Adjusted R2		0.997	0.997	0.998	0.997	0.997	0.997
Standard error		0.142	0.142	0.139	0.152	0.152	0.148
	of regression

Notes: The dependent variable is q^it (see notes to Table 1 for the definitions of variables). All regressions include country-specific and time-specific dummy variables as well as first differences of each explanatory variable at time t, t - 1, and t + 1. Coefficients of the first-difference terms are constrained to be the same across countries under homogeneous dynamics, and unconstrained under heterogeneous dynamics. White heteroskedasticity-consistent errors are shown in parentheses. D is a dummy variable, which equals one for low-income developing countries and zero for others. The number of observations equals 246. * indicates significance at the 5 percent level, and ** at the 1 percent level (using a one-sided test for lpd^it and ttd^it, and a two-sided test for other variables).

Table 4 shows the results for estimating the relative-price relation by DOLS. Regressions 1 and 4 in this table estimate the basic form of the relation without a time trend. The effect of the labor productivity index in both regressions is positive and significant. But the estimated values of its coefficients in the two regressions are substantially below the predicted value of unity. One possible explanation of this result, suggested above, is that measuring employment without adjustment for quality changes leads to a downward bias in the productivity coefficient.²³ Other limitations of employment data and the small sample size could also have contributed to a bias in the estimates of the productivity coefficient.

Table 4

The Relative-Price Relation

Notes: The dependent variable is rpd^it (see notes to Table 1 for the definitions of variables). All regressions include country-specific and time-specific dummy variables as well as first differences of each explanatory variable at time t, t - 1, and t + 1. Coefficients of the first-difference terms are constrained to be the same across countries under homogeneous dynamics, and unconstrained under heterogeneous dynamics. White heteroskedasticity-consistent errors are shown in parentheses. D is a dummy variable, which equals one for low-income developing countries and zero for others. The number of observations equals 256. * indicates significance at the 5 percent level, and ** at the 1 percent level (using a one-sided test for lpd^it and a two-sided test for other variables).

Table 4

The Relative-Price Relation

		Coefficient Estimates
Variable		(1)	(2)	(3)	(4)	(5)	(6)
		Homogeneous short-run dynamics			Heterogeneous short-run dynamics
lpd it		0.287**	0.287**	0.345**	0.302**	0.302**	0.397**
		(0.042)	(0.042)	(0.051)	(0.048)	(0.480)	(0.062)
Trend			0.000			-0.004
			(0.028)			(0.028)
lpdit*D				-0.152*			-0.229**
				(0.076)			(0.086)
Adjusted R2		0.833	0.833	0.835	0.832	0.832	0.838
Standard error		0.073	0.073	0.072	0.073	0.073	0.072
	of regression

Notes: The dependent variable is rpd^it (see notes to Table 1 for the definitions of variables). All regressions include country-specific and time-specific dummy variables as well as first differences of each explanatory variable at time t, t - 1, and t + 1. Coefficients of the first-difference terms are constrained to be the same across countries under homogeneous dynamics, and unconstrained under heterogeneous dynamics. White heteroskedasticity-consistent errors are shown in parentheses. D is a dummy variable, which equals one for low-income developing countries and zero for others. The number of observations equals 256. * indicates significance at the 5 percent level, and ** at the 1 percent level (using a one-sided test for lpd^it and a two-sided test for other variables).

View Table

Table 4

The Relative-Price Relation

		Coefficient Estimates
Variable		(1)	(2)	(3)	(4)	(5)	(6)
		Homogeneous short-run dynamics			Heterogeneous short-run dynamics
lpd it		0.287**	0.287**	0.345**	0.302**	0.302**	0.397**
		(0.042)	(0.042)	(0.051)	(0.048)	(0.480)	(0.062)
Trend			0.000			-0.004
			(0.028)			(0.028)
lpdit*D				-0.152*			-0.229**
				(0.076)			(0.086)
Adjusted R2		0.833	0.833	0.835	0.832	0.832	0.838
Standard error		0.073	0.073	0.072	0.073	0.073	0.072
	of regression

Notes: The dependent variable is rpd^it (see notes to Table 1 for the definitions of variables). All regressions include country-specific and time-specific dummy variables as well as first differences of each explanatory variable at time t, t - 1, and t + 1. Coefficients of the first-difference terms are constrained to be the same across countries under homogeneous dynamics, and unconstrained under heterogeneous dynamics. White heteroskedasticity-consistent errors are shown in parentheses. D is a dummy variable, which equals one for low-income developing countries and zero for others. The number of observations equals 256. * indicates significance at the 5 percent level, and ** at the 1 percent level (using a one-sided test for lpd^it and a two-sided test for other variables).

Tables 2–4 also report the results for the trend-stationary case, in which a homogeneous linear trend (with the same coefficient across countries) is included in the two relations. The tables show (see regressions 2 and 4 in each table) that the coefficient of the trend variable is insignificant in all cases, and the introduction of this variable in the regressions makes no difference to the estimates of Balassa-Samuelson parameters. We also introduced heterogeneous trends in the two relations, but this variation made little difference to the results.

Further Analysis

Our empirical model includes time effects to allow the effect of U.S. variables to be different from that of developing countries variables because of parametric differences. Time effects are, in fact, significant in both relations. Nevertheless, we also estimated the two relations without time effects but did not find a substantial difference in results. We further examined whether the results are sensitive to variation in income levels across countries. To explore this question, we divided the developing country sample into high- and low-income groups, and tested whether coefficients of Balassa-Samuelson variables differ between the two groups.²⁴ Regressions 3 and 6 in Tables 2–4 show the results of these tests. These regressions include interactions between explanatory variables and a dummy variable for the low-income group. Thus, coefficients of the variables show the effects for the high-income group, and interaction terms represent the additional effects for the low-income group. Interestingly, the results show that the effect of the relative-price variable (in the real exchange rate regressions) is significantly higher for the low-income group, while the effect of the labor productivity differential (in the relative-price regressions) is significantly lower. The departures from predicted values are, thus, more pronounced for low-income countries. Since data problems are likely to be more severe for the developing countries at the lower end of the income scale, this finding supports our suggested explanation that the estimates of Balassa-Samuelson effects are biased because of measurement errors. The results also indicate that the terms of trade effect is smaller for the low-income group.²⁵

The conventional tests of Balassa-Samuelson effects are based on a single relation that links the real exchange rate directly to the labor productivity index. To derive such a relation, we combine equations (18) and (19) to obtain

where ${\mu }_i^{\prime }=u_i+\pi {\psi }_i,+{\kappa }_t^{\prime }={\kappa }_t+\pi {\chi }_t$ and ${\mu }_{it}^{\prime }=u_{it}+\pi v_{it}$. For the purpose of comparison with the existing literature, we also present results for the single-equation version of our two relations. Table 5 reports DOLS estimates of six variants of equation (22), which are similar to those shown in Tables 2–4. Note that the estimates of the coefficients of the labor productivity and terms of trade variables in the DOLS version of equation (22) need not fully conform to the estimates of these variables in equations (20) and (21) because of the use of different variables to control for short-run dynamics.²⁶ The results indicate that the labor productivity coefficient in the single-equation version is significant in all cases, but its value tends to be smaller than the product of the estimates of π and λ (obtained from regressions of equations (20) and (21)). The terms of trade coefficient also differs somewhat from the estimate of τ based on equation (20) and is significant in all cases except regression (6) in the table. The effect of the two variables is no longer significantly different between the high- and low-income groups. For the labor productivity variable, this result (that its coefficient, πλ, does not differ between the two income groups) is consistent with the earlier findings that π is higher and λ is lower for the low-income group.

Table 5

The Combined Exchange Rate Relation

Notes: The dependent variable is q^it (see notes to Table 1 for the definitions of variables). All regressions include country-specific and time-specific dummy variables as well as first differences of each explanatory variable at time t, t? 1, and t + 1. Coefficients of the first-difference terms are constrained to be the same across countries under homogeneous dynamics, and unconstrained under heterogeneous dynamics. White heteroskedasticity-consistent errors are shown in parentheses. D is a dummy variable, which equals one for low-income developing countries and zero for others. The number of observations equals 246. * indicates significance at the 5 percent level, and ** at the 1 percent level (using a one-sided test for lpd^it and ttd^it, and a two-sided test for other variables).

Table 5

The Combined Exchange Rate Relation

		Coefficient Estimates
Variable		(1)	(2)	(3)	(4)	(5)	(6)
		Homogeneous short-run dynamics			Heterogeneous short-run dynamics
lpd it		0.177*	0.177*	0.205**	0.212*	0.212*	0.302**
		(0.080)	(0.080)	(0.087)	(0.109)	(0.109)	(0.124)
ttd it		0.357**	0.357**	0.388*	0.432**	0.432**	0.203
		(0.089)	(0.089)	(0.102)	(0.135)	(0.135)	(0.184)
Trend			-0.007			-0.014
			(0.047)			(0.078)
lpdit*D				-0.080			-0.157
				(0.169)			(0.271)
ttdit*D				-0.085			0.347
				(0.120)			(0.224)
Adjusted R2		0.997	0.997	0.997	0.997	0.997	0.997
Standard error		0.154	0.154	0.155	0.155	0.155	0.154
	of regression

Notes: The dependent variable is q^it (see notes to Table 1 for the definitions of variables). All regressions include country-specific and time-specific dummy variables as well as first differences of each explanatory variable at time t, t? 1, and t + 1. Coefficients of the first-difference terms are constrained to be the same across countries under homogeneous dynamics, and unconstrained under heterogeneous dynamics. White heteroskedasticity-consistent errors are shown in parentheses. D is a dummy variable, which equals one for low-income developing countries and zero for others. The number of observations equals 246. * indicates significance at the 5 percent level, and ** at the 1 percent level (using a one-sided test for lpd^it and ttd^it, and a two-sided test for other variables).

View Table

Table 5

The Combined Exchange Rate Relation

		Coefficient Estimates
Variable		(1)	(2)	(3)	(4)	(5)	(6)
		Homogeneous short-run dynamics			Heterogeneous short-run dynamics
lpd it		0.177*	0.177*	0.205**	0.212*	0.212*	0.302**
		(0.080)	(0.080)	(0.087)	(0.109)	(0.109)	(0.124)
ttd it		0.357**	0.357**	0.388*	0.432**	0.432**	0.203
		(0.089)	(0.089)	(0.102)	(0.135)	(0.135)	(0.184)
Trend			-0.007			-0.014
			(0.047)			(0.078)
lpdit*D				-0.080			-0.157
				(0.169)			(0.271)
ttdit*D				-0.085			0.347
				(0.120)			(0.224)
Adjusted R2		0.997	0.997	0.997	0.997	0.997	0.997
Standard error		0.154	0.154	0.155	0.155	0.155	0.154
	of regression

Notes: The dependent variable is q^it (see notes to Table 1 for the definitions of variables). All regressions include country-specific and time-specific dummy variables as well as first differences of each explanatory variable at time t, t? 1, and t + 1. Coefficients of the first-difference terms are constrained to be the same across countries under homogeneous dynamics, and unconstrained under heterogeneous dynamics. White heteroskedasticity-consistent errors are shown in parentheses. D is a dummy variable, which equals one for low-income developing countries and zero for others. The number of observations equals 246. * indicates significance at the 5 percent level, and ** at the 1 percent level (using a one-sided test for lpd^it and ttd^it, and a two-sided test for other variables).

During our sample period, currency crises involving large exchange rate depreciations occurred in a number of countries. Adverse economic conditions during crisis times could have caused comovements in exchange rates, labor productivity, and relative prices. This paper uses an estimation procedure that attempts to disentangle long-run Balassa-Samuelson effects from short-run correlations produced by temporary shocks (such as those leading to currency crises). However, to address the concern that our method may not have adequately removed the influence of crisis shocks, we explore the sensitivity of our results to inclusion of crisis periods. To identify crisis periods, we follow Kaminsky, Reinhart, and Vegh (2004), who define a crisis year as a year in which there is a 25 percent or higher monthly depreciation that is at least 10 percent higher than the previous month's depreciation.²⁷ Using their crisis data, we reestimate our basic regressions, excluding the observations for crisis years.²⁸ Note that since our regressions include one lag and one lead of each explanatory variable's first differences (which are not available for the year of the crisis and the following year), the exclusion window for these regressions is generally four years for a single crisis.²⁹ Longer periods are excluded for countries with multiple crises. In fact, for three countries—Ecuador, Turkey, and Venezuela—there were not enough observations to estimate country-specific dynamics. These countries were, thus, excluded from regressions with heterogeneous dynamics.

Table 6 presents the results of basic regressions based on data for crisis-free periods for both the two- and one-equation versions of the model (see columns 1–2 and 4–5 of the table for the two-equation version and columns 3 and 6 for the one-equation version). As the table shows, the effect of the basic Balassa-Samuelson variables—the relative-price and labor productivity indices—remains robust even after excluding crisis periods. The effect of the labor productivity variable, in fact, becomes stronger. The terms of trade effect, however, becomes weaker and is insignificant in most cases. Thus, the results on the influence of the terms of trade on the real exchange rate are sensitive to whether crisis periods are included or not. Although our regressions generally exclude four years for a crisis, this period may not be considered long enough to fully remove the effect of a crisis shock.³⁰ To deal with this concern, we explored additional variations that introduced longer exclusion windows or excluded all the data for countries that faced multiple crises within the sample period.³¹ These variations further reduced the sample size but still did not much affect our results about the robustness of the effect of the labor productivity and relative-price variables.

Table 6

Basic Regressions, Excluding Crisis Years

Notes: The dependent variable is rpdit for regressions in columns (1) and (4), and qit for other regressions (see notes to Table 1 for the definitions of variables). All regressions include country-specific and time-specific dummy variables as well as first differences of each explanatory variable at time t, t - 1, and t + 1. Coefficients of the first-difference terms are constrained to be the same across countries under homogeneous dynamics, and unconstrained under heterogeneous dynamics. White heteroskedasticity-consistent errors are shown in parentheses. * indicates significance at the 5 percent level, and ** at the 1 percent level (using a one-sided test).

Table 6

Basic Regressions, Excluding Crisis Years

		Coefficient Estimates
Variable		(1)	(2)	(3)	(4)	(5)	(6)
		Homogeneous short-run dynamics			Heterogeneous short-run dynamics
lpd it		0.342**		0.247**	0.337**		0.240*
		(0.042)		(0.093)*	(0.044)		(0.123)
ttd it			0.152	0.222*		0.130	0.161
			(0.098)	(0.105)		(0.196)	(0.141)
rpd it			1.153**			1.099**
			(0.135)			(0.192)
Adj.R2		0.861	0.998	0.997	0.877	0.997	0.997
Standard error		0.069	0.132	0.150	0.065	0.144	0.140
	of regression
No. Obs.		215	205	205	215	190	190

Notes: The dependent variable is rpdit for regressions in columns (1) and (4), and qit for other regressions (see notes to Table 1 for the definitions of variables). All regressions include country-specific and time-specific dummy variables as well as first differences of each explanatory variable at time t, t - 1, and t + 1. Coefficients of the first-difference terms are constrained to be the same across countries under homogeneous dynamics, and unconstrained under heterogeneous dynamics. White heteroskedasticity-consistent errors are shown in parentheses. * indicates significance at the 5 percent level, and ** at the 1 percent level (using a one-sided test).

View Table

Table 6

Basic Regressions, Excluding Crisis Years

		Coefficient Estimates
Variable		(1)	(2)	(3)	(4)	(5)	(6)
		Homogeneous short-run dynamics			Heterogeneous short-run dynamics
lpd it		0.342**		0.247**	0.337**		0.240*
		(0.042)		(0.093)*	(0.044)		(0.123)
ttd it			0.152	0.222*		0.130	0.161
			(0.098)	(0.105)		(0.196)	(0.141)
rpd it			1.153**			1.099**
			(0.135)			(0.192)
Adj.R2		0.861	0.998	0.997	0.877	0.997	0.997
Standard error		0.069	0.132	0.150	0.065	0.144	0.140
	of regression
No. Obs.		215	205	205	215	190	190

Notes: The dependent variable is rpdit for regressions in columns (1) and (4), and qit for other regressions (see notes to Table 1 for the definitions of variables). All regressions include country-specific and time-specific dummy variables as well as first differences of each explanatory variable at time t, t - 1, and t + 1. Coefficients of the first-difference terms are constrained to be the same across countries under homogeneous dynamics, and unconstrained under heterogeneous dynamics. White heteroskedasticity-consistent errors are shown in parentheses. * indicates significance at the 5 percent level, and ** at the 1 percent level (using a one-sided test).