I. INTRODUCTION

The empirical investigation of the import demand function has been one of the most active research areas in international economics. This is evidenced by the many surveys on this topic, although most focus on industrial countries.² Perhaps one of the main reasons for its popularity is its application to a wide range of important macroeconomic policy issues such as the international transmission of domestic disturbances, where these elasticities are a crucial link between economies; the impact of expenditure-switching through exchange rate management and commercial policy on a country’s trade balance; and the degree to which the external balance affects a country’s growth.

The traditional import demand function is specified as a log-linear function of the relative price of imports and real income. Because of data constraints and the empirical success of this specification, it has dominated the empirical literature for more than a quarter century. But, questions about its microeconomic foundation arise since it has not been derived from utility maximization. Another issue that has been largely ignored in the literature is the problem of nonstationarity, which is found present in most macroeconomic variables and which invalidates classical statistical inference. Thus, if the variables that enter the import demand equation contain a unit root, ignoring nonstationarity in these variables may cause serious inference problems.

The objective of this paper is twofold. First, the paper seeks to address the two problems discussed above by deriving an empirically tractable import demand equation that can be estimated for a large number of countries, using recent time series techniques that address the issue of nonstationarity present in the data. Second, because the statistical properties of the different estimators have been derived only asymptotically, econometric theory does not offer any guidance when it comes to comparing the performance of different estimators in small samples. Consequently, the paper derives the small sample properties of both the Ordinary Least Squares (OLS) and the Fully-Modified (FM) estimators of the short- and long-run elasticities, using Monte Carlo methods. It is shown that the FM estimators dominates the OLS estimators, even in small samples.

The derived aggregate import demand equation is log-linear in the relative price of imports and an activity variable defined as GDP minus exports.³ An important insight from the explicit derivation of the aggregate import demand equation is that the definition of the activity variable depends on the aggregation level.⁴ The model predicts a unique cointegrating vector among imports, the relative price of imports and the activity variable. This prediction is not rejected by the data, and the cointegrating vector is estimated efficiently by the Phillips-Hansen FM estimator. Two recent papers follow a similar methodology. Clarida (1994) derives a similar import demand function for U.S. nondurable consumption goods from explicit intertemporal optimization, carefully taking into account data nonstationarity. Similarly, Reinhart (1995) estimates both structural import and export demand functions for twelve developing countries using Johansen’s cointegration approach.

The results underscore the presence of nonstationarity in the data and the adverse consequences of neglecting it. Both price and income elasticities generally have the expected sign and are precisely estimated. The average price elasticity is close to zero in the short run but is slightly higher than one in the long run. It takes five years for the average price elasticity to achieve 90 percent of its long-run level. A similar pattern holds for income elasticities in the sense that imports react relatively slowly to changes in domestic income. The short-run income elasticities are on average less then 0.5, while the long-run income elasticities are close to 1.5. Industrial countries have both higher income and lower price elasticities than do developing countries. On average, these estimates are relatively close to Reinhart’s.⁵

Empirical researchers are generally interested in two statistical properties of their estimates of import elasticities. First, they are interested in the magnitude of these elasticities. A relevant question, then, is how close the estimates are to their true value. The systematic deviation of estimates from their true value is measured by the bias of the estimates. Second, they are interested in inference, that is, hypotheses testing, about these estimates. For example, are the price and income elasticities significantly different from one? Testing such hypotheses requires knowing the distribution of the t-statistic (defined as the coefficient estimate divided by its standard deviation). The asymptotic distribution of this statistic is unknown for the long-run elasticities because these elasticities are nonlinear transformations of the import demand coefficients. In addition, the definition of the long-run elasticities includes the lagged dependent variable whose t-statistic follows a nonstandard distribution in the nonstationary case. In light of this, using the critical values of the t-distribution for hypothesis testing may be misleading. Consequently, the small sample distribution of the t-statistic for both the short- and long-run elasticities are computed using Monte Carlo methods.

The analysis shows that the OLS bias is significantly higher than the FM bias for both the short- and long-run elasticity estimates. The FM bias reaches its minimum when the relative price of imports and the activity variable are exogenous. Strong endogeneity of the explanatory variables (that is, high correlation between the import demand innovations and the explanatory variables innovations) may induce substantial bias. But for most countries—being “small” relative to the rest of the world—the relative price of imports and the activity variable are only weakly endogenous, leading to a relatively small bias. The bias of long-run elasticities is generally much lower than the bias of short-run elasticities. For the benchmark case in which both explanatory variables are assumed to be exogenous, the t-statistics of the short-run elasticities are symmetric around zero but are flatter than the asymptotic t-distribution. This implies that an inference based on the usual t-or F-statistic may be misleading. For example, the exact confidence intervals are wider than those based on the t-statistic. The t-statistic distribution of the short-run elasticities become skewed and flatter when the relative price of imports and/or the activity variable is allowed to be endogenous. The stronger the endogeneity, the larger is this departure from the asymptotic t-distribution.

II. THE MODEL

Assume that the import decision in each country is made by an infinitely lived representative agent who decides how much to consume from the domestic endowment (d_t) and from the imported good (m_t).⁶ The home good is the numeraire. The intertemporal decision can be formalized by the following problem:

subject to:

where δ is the consumer’s subjective discount rate; r is the world interest rate; b_t+1 is the next period stock of foreign bonds if positive, and the next period’s debt level if negative; e_t is the stochastic endowment which follows an AR(1) process with unconditional mean $\overline{e}$ and an unconditional variance σ²/(l-ρ²), where σ² is the variance of the iid innovation ξ_t and ρ determines the degree of persistence of the endowment shocks; and p_t, is the relative price of the foreign good, that is, the inverse of the usual definition of terms of trade. In this two-good economy, p_t also represents the relative price of imports.Equation (2) is the current account equation, equation (3) is the stochastic process driving the endowment shock, and equation (4) is the transversality condition that rules out Ponzi games. The first order conditions of this problem are:

where λ_t is the Lagrange multiplier on the current account equation. From equation (5), λ_t is the marginal utility of the domestic good. Following Clarida (1994, 1996) and Ogaki (1992), it is assumed that the instantaneous utility function u is addilog:⁷

where A_t and B_t are exponential stationary random shocks to preferences, ∈_{A, t} and ∈_{B, t} are stationary shocks and α and β are curvature parameters. Substituting equation (8) into equations (5) and (6) yields:

Substituting equations (9)-(11) into equation (12) and taking logs yields:

where c₀ = (1/β)(b₀ − a₀), and ∈_t = (1/β)(∈_{B, t} − ∈_{A, t}). A tilde indicates the log of the corresponding variable. In this model, x_t = e_t − d_t = GDP_t − d_t, where x_t is exports. Consequently, d_t = p_t − x_t. Thus, the model yields an equation for import demand that is close to the standard import demand function except that the correct activity variable is GDP_t − x_t rather than GDP_t.Equation (13) can be rewritten as:

Taking logs of equation (11) yields:

Because each of the three variables in the import demand equation (13) can either be trend-stationary (TS) or difference-stationary (DS), four cases need to be considered (Table 1). In the next section, results from unit root tests show that the first case is the most common, with some countries falling into the second category. The prime interest is the estimates of the standard price and income elasticities for import demand, defined (respectively) as the coefficients of the log of the relative price of imports (−1/β) and the log of the activity variable (α/β). Note that ${\tilde{m}}_t$ and ${\tilde{p}}_t$ are, in general, endogenously determined by import demand and import supply (not modeled here). Therefore, ${\tilde{p}}_t$ is likely to be correlated with the error term ∈_t in equation (14). Thus OLS would yield biased estimates of the price and income elasticities. The Phillips-Hansen FM estimator corrects for this potential simultaneity bias, as well as for autocorrelation, in the cointegration framework.

Table 1:

The four possible model specifications

^1/${\tilde{{p}}}_{{t}}$ is either exogenous under a perfectly elastic import supply or is endogenously determined by the interaction of the demand and supply of imports. The supply of imports is not modeled explicitly here.

^2/See Stock and Watson (1988).

Table 1:

The four possible model specifications

Model Specification		Model predictions and testing strategy
1.	All three variables are difference-stationary (DS)
In the model, the following three assumptions are necessary to achieve DS for all three variables:		Under assumptions (a) − (c), equation (13) implies that ${\tilde{{m}}}_{{t}}$, ${\tilde{{d}}}_{{t}}$, and ${\tilde{{p}}}_{{t}}$ are cointegrated with cointegrating vector (1 1/β −α/β) Furthermore, this cointegrating vector is unique (up to a scale factor) since the import demand equation (13) has three I(1) variables and two common stochastic trends.2/If a cointegration relation between these three variables does note exist, estimation of the import demand equation (13) will result in a spurious regression. Hence, to detect this potential spuriousness, a residual-based cointegration test will be performed on equation (13).
(a)	For ${\tilde{{d}}}_t$ to be DS, we must assume r = δ. Then the Euler equation (7) becomes: $\begin{array}{ccc}{{\lambda }}_{{t}}={{E}}_{{t}}{{\lambda }}_{{t}+1}& & (18)\end{array}$
	Thus, λt can be written as: λt = λt+1 + et, where et is such that Et et = 0. In other words, λt has a unit root and, therefore, ${\tilde{{d}}}_{{t}}$ will also inherit a unit root since ${\tilde{{A}}}_{{t}}$ is stationary. If ${\tilde{{d}}}_{{t}}$ has a unit root, then, from equation (13), ${\tilde{{m}}}_{{t}}$ will also have a unit root.
(b)	The log of the relative price of imports will be assumed to be difference-stationary (we will see that this assumption cannot be rejected statistically for most countries).1/
(c)	${\tilde{{p}}}_{{t}}$ and ${\tilde{{d}}}_{{t}}$ are not cointegrated with cointegrating vector (1 −α).
2.	One of the three variables is trend-stationary (TS)
We have three cases depending on which variable is TS:
(a)	${\tilde{{m}}}_{{t}}$ is TS.	(a)	${\tilde{{p}}}_{{t}}$ and ${\tilde{{d}}}_{{t}}$ are cointegrated with cointegrating vector(1−α).
	The model would yield this case under these three assumptions: ${\tilde{{p}}}_{{t}}$ is DS; assumption (a) in case 1; and ${\tilde{{p}}}_{{t}}$ and ${\tilde{{d}}}_{{t}}$ are cointegrated with cointegrating vector (1 − α).
(b)	${\tilde{{p}}}_{{t}}$ is TS.	(b)	${\tilde{{m}}}_{{t}}$ and ${\tilde{{d}}}_{{t}}$ are cointegrated with cointegrating vector (1−1/β).
(c)	${\tilde{{d}}}_{{t}}$ is TS.	(c)	${\tilde{{m}}}_{{t}}$ and ${\tilde{{p}}}_{{t}}$ are cointegrated with contegrating vector (1−α/β).
	From equations (7) and (15), ${\tilde{{d}}}_{{t}}$ will be TS if δ > r.		In all three cases, if a cointegration relation between these pairs of variables does not exist, attempts to estimate the import demand equation will result in a spurious regression. Hence, to detect this potential spuriousness, a residual-based cointegration tests will be performed on equation (13).
3.	Two of the three variables are TS	This case can be viewed as a rejection of the model, since there is no linear combination of the three variables that yields a stationary process.
4.	All three variables are TS
This is the only case in which classical inference is valid.		The import demand equation (13) becomes a classical regression equation with population coefficients (1 1/β −α/β).

^1/${\tilde{{p}}}_{{t}}$ is either exogenous under a perfectly elastic import supply or is endogenously determined by the interaction of the demand and supply of imports. The supply of imports is not modeled explicitly here.

^2/See Stock and Watson (1988).

View Table

Table 1:

The four possible model specifications

Model Specification		Model predictions and testing strategy
1.	All three variables are difference-stationary (DS)
In the model, the following three assumptions are necessary to achieve DS for all three variables:		Under assumptions (a) − (c), equation (13) implies that ${\tilde{{m}}}_{{t}}$, ${\tilde{{d}}}_{{t}}$, and ${\tilde{{p}}}_{{t}}$ are cointegrated with cointegrating vector (1 1/β −α/β) Furthermore, this cointegrating vector is unique (up to a scale factor) since the import demand equation (13) has three I(1) variables and two common stochastic trends.2/If a cointegration relation between these three variables does note exist, estimation of the import demand equation (13) will result in a spurious regression. Hence, to detect this potential spuriousness, a residual-based cointegration test will be performed on equation (13).
(a)	For ${\tilde{{d}}}_t$ to be DS, we must assume r = δ. Then the Euler equation (7) becomes: $\begin{array}{ccc}{{\lambda }}_{{t}}={{E}}_{{t}}{{\lambda }}_{{t}+1}& & (18)\end{array}$
	Thus, λt can be written as: λt = λt+1 + et, where et is such that Et et = 0. In other words, λt has a unit root and, therefore, ${\tilde{{d}}}_{{t}}$ will also inherit a unit root since ${\tilde{{A}}}_{{t}}$ is stationary. If ${\tilde{{d}}}_{{t}}$ has a unit root, then, from equation (13), ${\tilde{{m}}}_{{t}}$ will also have a unit root.
(b)	The log of the relative price of imports will be assumed to be difference-stationary (we will see that this assumption cannot be rejected statistically for most countries).1/
(c)	${\tilde{{p}}}_{{t}}$ and ${\tilde{{d}}}_{{t}}$ are not cointegrated with cointegrating vector (1 −α).
2.	One of the three variables is trend-stationary (TS)
We have three cases depending on which variable is TS:
(a)	${\tilde{{m}}}_{{t}}$ is TS.	(a)	${\tilde{{p}}}_{{t}}$ and ${\tilde{{d}}}_{{t}}$ are cointegrated with cointegrating vector(1−α).
	The model would yield this case under these three assumptions: ${\tilde{{p}}}_{{t}}$ is DS; assumption (a) in case 1; and ${\tilde{{p}}}_{{t}}$ and ${\tilde{{d}}}_{{t}}$ are cointegrated with cointegrating vector (1 − α).
(b)	${\tilde{{p}}}_{{t}}$ is TS.	(b)	${\tilde{{m}}}_{{t}}$ and ${\tilde{{d}}}_{{t}}$ are cointegrated with cointegrating vector (1−1/β).
(c)	${\tilde{{d}}}_{{t}}$ is TS.	(c)	${\tilde{{m}}}_{{t}}$ and ${\tilde{{p}}}_{{t}}$ are cointegrated with contegrating vector (1−α/β).
	From equations (7) and (15), ${\tilde{{d}}}_{{t}}$ will be TS if δ > r.		In all three cases, if a cointegration relation between these pairs of variables does not exist, attempts to estimate the import demand equation will result in a spurious regression. Hence, to detect this potential spuriousness, a residual-based cointegration tests will be performed on equation (13).
3.	Two of the three variables are TS	This case can be viewed as a rejection of the model, since there is no linear combination of the three variables that yields a stationary process.
4.	All three variables are TS
This is the only case in which classical inference is valid.		The import demand equation (13) becomes a classical regression equation with population coefficients (1 1/β −α/β).

^1/${\tilde{{p}}}_{{t}}$ is either exogenous under a perfectly elastic import supply or is endogenously determined by the interaction of the demand and supply of imports. The supply of imports is not modeled explicitly here.

^2/See Stock and Watson (1988).

Equation (14) will be estimated in a dynamic form (that is, with the lagged dependent variable included as an explanatory variable) which proved to be more successful in the estimation stage.⁸ It is obtained by postulating a partial adjustment process of actual imports toward import demand:⁹

where ${\tilde{m}}_t^a$ and ${\tilde{p}}_t$ and ${\tilde{m}}_t^a$ denote actual and demanded imports, respectively. If ϕ is close to one, it implies that actual imports adjust quickly to import demand. Substituting equation (14) into (16) yields the final import demand equation:

Where θ₀=ϕ c, θ₁=1−ϕ, θ₂=−ϕ(1/β), and θ₂=ϕ(α/β). Note that all the coefficients of the import demand equation can be recovered from equation (17). The discussion above and Table 1 remain valid for equation (17) as long as $\left|{\varphi }\right|<1,$, which is the case for most countries in our sample (see Table 2).¹⁰

Table 2:

Augmented-Dickey-Fuller test for variables entering the import demand equation

Note: Variables are real imports of goods and non-factor services (m), the real exchange rate (p), computed as the ratio of imports deflator to GDP de exports (gdpx). These three variables are tested for the existence of a unit root using the Augmented-Dickey-Fuller (ADF) test. The optimal lag se criterion in the ADF regression is given by k. Critical values are a linear interpolation between the critical values for T=25 and T=50 given in Hamilton 4), where T is the sample size. Significance levels at 1% and 5% are indicated by**and*, respectively.

Table 2:

Augmented-Dickey-Fuller test for variables entering the import demand equation

Country	m	k	P	k	gdpx	k	nobs	Country	m	k	P	k	gdpx	k	nobs
1 ALGERIA	-0.33	1	1.08	2	-1.25	2	34	26 GAMBIA	-1.60	1	-3.06	1	-1.28	1	34
2 ARGENTINA	-3.29	2	-2.04	1	-2.44	1	34	27 GERMANY	-1.87	2	-1.90	1	-1.52	1	34
3 AUSTRALIA	-4.45**	1	-1.71	1	-2.15	1	34	28 GREECE	-2.66	1	-1.19	1	0.20	1	34
4 AUSTRIA	-1.77	1	-1.67	1	-1.50	1	34	29 GUATEMALA	-1.98	1	-0.81	1	-2.25	1	34
5 BELGIUM-LUXEMBOURG	-1.79	1	-0.09	2	-2.08	1	34	30 HAITI	-2.83	1	0.88	1	-1.73	1	34
6 BENIN	-0.56	2	-1.12	2	-0.89	1	34	31 HONDURAS	-2.91	1	-2.62	2	-3.08	2	34
7 BRAZIL	-1.11	1	0.21	1	-2.64	1	34	32 ICELAND	-1.82	1	-0.94	2	-4.38**	3	34
8 BURUNDI	-3.09	1	-2.85	3	-4.46**	1	34	33 INDIA	-2.20	1	-2.16	1	-2.71	1	34
9 CAMEROON	-1.28	1	0.40	1	-1.16	1	29	34 INDONESIA	-1.88	1	-2.31	1	-1.64	1	27
10 CANADA	-2.54	1	0.69	1	-1.45	1	34	35 IRELAND	-2.54	1	0.04	1	-2.20	1	34
11 CENTRAL AFRICAN REPUBLIC	-0.07	2	-3.17	1	-4.86**	1	34	36 ISRAEL	-1.69	1	-1.97	1	-1.71	1	34
12 CHAD	-2.08	1	-1.85	1	-3.34	1	34	37 ITALY	-2.15	1	-0.39	1	-1.10	1	34
13 CHILE	-1.99	1	-2.15	1	-2.07	2	34	38 JAPAN	-2.04	1	-2.09	1	-1.54	1	34
14 CHINA	-1.89	1	-4.33**	1	-2.40	2	34	39 KENYA	-2.02	1	-0.41	1	-1.25	1	34
15 COLOMBIA	-2.17	1	-0.28	1	-1.98	1	34	40 KOREA	-1.48	1	-2.30	1	-3.76*	1	34
16 CONGO	-2.10	2	-2.25	1	-2.55	2	34	41 MADAGASCAR	-2.92	1	-1.77	1	-2.45	1	34
17 COSTA RICA	-1.78	1	-1.04	2	-3.43	1	34	42 MALAWI	-2.46	1	-1.97	1	-2.77	1	34
18 COTE DTVOIRE	-0.25	1	-2.69	1	-2.74	1	34	43 MALAYSIA	-2.01	1	0.27	1	-2.38	1	34
19 DENMARK	-2.11	1	-1.60	1	-1.88	1	34	44 MAURITANIA	-1.53	1	-2.50	2	-2.55	1	34
20 DOMINICAN REPUBLIC	-3.51	1	-1.10	1	-2.94	1	34	45 MAURITIUS	-2.44	2	-2.22	1	-1.99	1	34
21 EGYPT	-1.21	1	-0.83	1	-2.50	2	34	46 MEXICO	-3.47	2	-1.17	1	-1.63	1	34
22 EL SALVADOR	-2.20	2	-1.80	1	-1.40	2	34	47 MOROCCO	-1.67	1	-1.41	1	-1.50	1	34
23 FINLAND	-1.82	1	-1.71	1	-1.40	2	34	48 MYANMAR	-1.69	1	-1.37	2	2.39	1	34
24 FRANCE	-2.03	1	-1.49	1	-1.62	1	34	49 NETHERLANDS	-2.22	1	-1.98	1	-2.23	1	34
25 GABON	-1.03	1	-1.31	1	-2.36	1	34	50 NEW ZEALAND	-3.28	1	-2.37	2	-2.00	1	34
51 NICARAGUA	-3.81*	1	-1.96	1	-2.52	1	34	65 SWEDEN	-2.06	1	-0.73	1	-1.52	1	34
52 NIGERIA	-1.23	2	-2.57	1	-0.58	1	34	66 SWITZERLAND	-1.41	1	-2.74	1	-4.27**	2	34
53 NORWAY	-1.74	1	1.29	1	-2.47	1	34	67 THAILAND	-1.39	1	-1.88	1	-2.00	1	34
54 PAKISTAN	-2.79	1	-2.34	2	-2.50	1	34	68 TOGO	-0.39	1	-3.31	1	-3.62*	1	34
55 PANAMA	-2.26	1	-1.69	1	-1.45	1	34	69 TRINIDAD AND TOBAGO	-2.59	1	0.95	1	-4.35**	1	34
56 PAPUA NEW GUINEA	-2.83	1	-3.63*	3	-1.88	2	33	70 TUNISIA	-1.32	1	-1.55	1	-3.75*	1	33
57 PARAGUAY	-2.45	1	-1.28	1	-1.97	1	34	71 TURKEY	-1.81	1	-1.87	1	-1.40	1	34
58 PERU	-3.78*	2	-1.34	1	-1.65	1	34	72 UNITED KINGDOM	-2.17	1	-3.48	1	-1.59	2	34
59 PHILIPPINES	-3.68*	2	-0.41	1	-1.67	1	34	73 UNITED STATES	-2.34	1	-2.69	1	-0.59	1	34
60 PORTUGAL	-2.31	1	-0.64	1	-0.60	1	34	74 URUGUAY	-1.89	1	-3.72*	1	-2.22	2	34
61 RWANDA	-2.31	1	-1.65	3	-3.55*	1	34	75 YUGOSLAVIA	-1.76	1	0.25	1	-2.62	1	31
62 SOUTH AFRICA	-3.18	1	0.07	1	-0.37	1	34	76 ZAIRE	-2.56	1	-1.72	1	-4.02*	1	30
63 SPAIN	-2.68	1	-1.47	1	-1.51	2	34	77 ZAMBIA	-2.09	1	-2.73	1	-2.27	1	34
64 SUDAN	-1.79	1	-1.97	1	-1.39	1	32

Note: Variables are real imports of goods and non-factor services (m), the real exchange rate (p), computed as the ratio of imports deflator to GDP de exports (gdpx). These three variables are tested for the existence of a unit root using the Augmented-Dickey-Fuller (ADF) test. The optimal lag se criterion in the ADF regression is given by k. Critical values are a linear interpolation between the critical values for T=25 and T=50 given in Hamilton 4), where T is the sample size. Significance levels at 1% and 5% are indicated by**and*, respectively.

View Table

Table 2:

Augmented-Dickey-Fuller test for variables entering the import demand equation

Country	m	k	P	k	gdpx	k	nobs	Country	m	k	P	k	gdpx	k	nobs
1 ALGERIA	-0.33	1	1.08	2	-1.25	2	34	26 GAMBIA	-1.60	1	-3.06	1	-1.28	1	34
2 ARGENTINA	-3.29	2	-2.04	1	-2.44	1	34	27 GERMANY	-1.87	2	-1.90	1	-1.52	1	34
3 AUSTRALIA	-4.45**	1	-1.71	1	-2.15	1	34	28 GREECE	-2.66	1	-1.19	1	0.20	1	34
4 AUSTRIA	-1.77	1	-1.67	1	-1.50	1	34	29 GUATEMALA	-1.98	1	-0.81	1	-2.25	1	34
5 BELGIUM-LUXEMBOURG	-1.79	1	-0.09	2	-2.08	1	34	30 HAITI	-2.83	1	0.88	1	-1.73	1	34
6 BENIN	-0.56	2	-1.12	2	-0.89	1	34	31 HONDURAS	-2.91	1	-2.62	2	-3.08	2	34
7 BRAZIL	-1.11	1	0.21	1	-2.64	1	34	32 ICELAND	-1.82	1	-0.94	2	-4.38**	3	34
8 BURUNDI	-3.09	1	-2.85	3	-4.46**	1	34	33 INDIA	-2.20	1	-2.16	1	-2.71	1	34
9 CAMEROON	-1.28	1	0.40	1	-1.16	1	29	34 INDONESIA	-1.88	1	-2.31	1	-1.64	1	27
10 CANADA	-2.54	1	0.69	1	-1.45	1	34	35 IRELAND	-2.54	1	0.04	1	-2.20	1	34
11 CENTRAL AFRICAN REPUBLIC	-0.07	2	-3.17	1	-4.86**	1	34	36 ISRAEL	-1.69	1	-1.97	1	-1.71	1	34
12 CHAD	-2.08	1	-1.85	1	-3.34	1	34	37 ITALY	-2.15	1	-0.39	1	-1.10	1	34
13 CHILE	-1.99	1	-2.15	1	-2.07	2	34	38 JAPAN	-2.04	1	-2.09	1	-1.54	1	34
14 CHINA	-1.89	1	-4.33**	1	-2.40	2	34	39 KENYA	-2.02	1	-0.41	1	-1.25	1	34
15 COLOMBIA	-2.17	1	-0.28	1	-1.98	1	34	40 KOREA	-1.48	1	-2.30	1	-3.76*	1	34
16 CONGO	-2.10	2	-2.25	1	-2.55	2	34	41 MADAGASCAR	-2.92	1	-1.77	1	-2.45	1	34
17 COSTA RICA	-1.78	1	-1.04	2	-3.43	1	34	42 MALAWI	-2.46	1	-1.97	1	-2.77	1	34
18 COTE DTVOIRE	-0.25	1	-2.69	1	-2.74	1	34	43 MALAYSIA	-2.01	1	0.27	1	-2.38	1	34
19 DENMARK	-2.11	1	-1.60	1	-1.88	1	34	44 MAURITANIA	-1.53	1	-2.50	2	-2.55	1	34
20 DOMINICAN REPUBLIC	-3.51	1	-1.10	1	-2.94	1	34	45 MAURITIUS	-2.44	2	-2.22	1	-1.99	1	34
21 EGYPT	-1.21	1	-0.83	1	-2.50	2	34	46 MEXICO	-3.47	2	-1.17	1	-1.63	1	34
22 EL SALVADOR	-2.20	2	-1.80	1	-1.40	2	34	47 MOROCCO	-1.67	1	-1.41	1	-1.50	1	34
23 FINLAND	-1.82	1	-1.71	1	-1.40	2	34	48 MYANMAR	-1.69	1	-1.37	2	2.39	1	34
24 FRANCE	-2.03	1	-1.49	1	-1.62	1	34	49 NETHERLANDS	-2.22	1	-1.98	1	-2.23	1	34
25 GABON	-1.03	1	-1.31	1	-2.36	1	34	50 NEW ZEALAND	-3.28	1	-2.37	2	-2.00	1	34
51 NICARAGUA	-3.81*	1	-1.96	1	-2.52	1	34	65 SWEDEN	-2.06	1	-0.73	1	-1.52	1	34
52 NIGERIA	-1.23	2	-2.57	1	-0.58	1	34	66 SWITZERLAND	-1.41	1	-2.74	1	-4.27**	2	34
53 NORWAY	-1.74	1	1.29	1	-2.47	1	34	67 THAILAND	-1.39	1	-1.88	1	-2.00	1	34
54 PAKISTAN	-2.79	1	-2.34	2	-2.50	1	34	68 TOGO	-0.39	1	-3.31	1	-3.62*	1	34
55 PANAMA	-2.26	1	-1.69	1	-1.45	1	34	69 TRINIDAD AND TOBAGO	-2.59	1	0.95	1	-4.35**	1	34
56 PAPUA NEW GUINEA	-2.83	1	-3.63*	3	-1.88	2	33	70 TUNISIA	-1.32	1	-1.55	1	-3.75*	1	33
57 PARAGUAY	-2.45	1	-1.28	1	-1.97	1	34	71 TURKEY	-1.81	1	-1.87	1	-1.40	1	34
58 PERU	-3.78*	2	-1.34	1	-1.65	1	34	72 UNITED KINGDOM	-2.17	1	-3.48	1	-1.59	2	34
59 PHILIPPINES	-3.68*	2	-0.41	1	-1.67	1	34	73 UNITED STATES	-2.34	1	-2.69	1	-0.59	1	34
60 PORTUGAL	-2.31	1	-0.64	1	-0.60	1	34	74 URUGUAY	-1.89	1	-3.72*	1	-2.22	2	34
61 RWANDA	-2.31	1	-1.65	3	-3.55*	1	34	75 YUGOSLAVIA	-1.76	1	0.25	1	-2.62	1	31
62 SOUTH AFRICA	-3.18	1	0.07	1	-0.37	1	34	76 ZAIRE	-2.56	1	-1.72	1	-4.02*	1	30
63 SPAIN	-2.68	1	-1.47	1	-1.51	2	34	77 ZAMBIA	-2.09	1	-2.73	1	-2.27	1	34
64 SUDAN	-1.79	1	-1.97	1	-1.39	1	32

Note: Variables are real imports of goods and non-factor services (m), the real exchange rate (p), computed as the ratio of imports deflator to GDP de exports (gdpx). These three variables are tested for the existence of a unit root using the Augmented-Dickey-Fuller (ADF) test. The optimal lag se criterion in the ADF regression is given by k. Critical values are a linear interpolation between the critical values for T=25 and T=50 given in Hamilton 4), where T is the sample size. Significance levels at 1% and 5% are indicated by**and*, respectively.

III. ESTIMATION RESULTS

The import demand equation (17) will be estimated by both the OLS and the FM estimator. The FM estimator is an optimal single-equation method based on the use of OLS with semiparametric corrections for serial correlation and potential endogeneity of the right-hand variables. The method was developed in Phillips and Hansen (1990) and generalized to include deterministic trends by Hansen (1992a). The FM estimator has the same asymptotic behavior as the full systems maximum likelihood estimators.¹¹

The data comes from the World Bank database BESD. The sample includes 77 countries for which the required data are available for a reasonable time span (the list of countries is given in Table 2). In general, the data are available from 1960 to 1993.¹² The usual problem is of course the choice of the corresponding proxies for the variables in the model, since the model is usually a crude simplification of reality—which is the case here. Data constraints highly restrict this choice. Total imports and exports of goods and services will be used for m_t and x_t in equation (17). The relative price of imports p_t will be computed as the ratio of the import deflator to the GDP deflator.¹³ The activity variable will be computed as the difference between GDP and exports.¹⁴

B. Import demand equations

The results underscore the presence of nonstationarity in the data and the adverse consequences of neglecting it. Table 2 shows that most countries—60 of the 77—fall into the first case of Table 1 (the unit root hypothesis cannot be rejected for all three variables in the import demand equation) and the remaining countries—17 of the 77—into the second case (the unit root hypothesis can be rejected for only one of the three variables). In the first case, the model predicts a cointegrating relationship between the three I(1) variables, and in the second case between the two I(1) variables. No country belongs to either the third or fourth cases.

Table 3 shows both the OLS and FM estimates of the import demand equation. Only countries with the right sign for the price and income elasticities are reported (66 of the 77 countries). The columns of Table 3 labeled x_−1,p and gdpx give, respectively, the coefficient estimates of the lagged dependent variable (log of imports of goods and nonfactor services), the short-term price elasticity (that is, the coefficient of the log of relative price of imports) and the short-term income elasticity (the coefficient of the log of gdpx). The long-run price and income elasticities are defined as the short-run price and income elasticities divided by one minus the coefficient estimate of the lagged dependent variable. They are given by E_p and E_y for the FM estimates.¹⁵ The column labeled ser reports the standard error of the regression. Finally, the column labeled AC gives Durbin’s autocorrelation test. It amounts to estimating an AR(1) process on the estimated residuals of the import equation. Durbin’s test is simply a significance test of the AR(1) coefficient using the usual t-test. For the OLS regressions, AR(1) autocorrelation is detected (at 10 percent or less) for 17 of the 66 countries.

Table 3:

Import demand equations

Note: The dependent variable is real imports of goods and non-factor services (m). The explanatory variables are the lagged dependent variable (m.j), the real exchange rate (p) computed as the ratio of imports deflator to gdp deflator, and gdp minus exports (gdpx). The import demand equation is estimated using both OLS and the Phillips-Hansen Fully Modified estimator. The long-run price and income elasticities are given by E_p and E_y, respectively. ${{{E}}_{{p}}}^{{c}}$ and ${{{E}}_{{y}}}^{{c}}$ give the long-run price and income elasticities corrected for bias (see Table 4). For each country, the estimated coefficients and their t-stat (below the coefficient estimates) are provided. The following statistics are also provided: Durbin’s test for autocorrelation (AC), R², standard error of the regression (ser), and the number of observations for each country (nobs). Cointegration between the three variables in the import demand equation is tested using the Phillips-Ouliaris residual test given in column P-O. Finally, the columns labeled E_p=−1 and E_y=l report the two-tailed t-test for unit-price and unit-income elasticities, respectively. The asymptotic critical values for the -Phillips-Ouliaris test at 10%, 5% and 1% are, respectively, −3.84, −4.16 and −4.64. The letters a, b and c indicate significance at 1%, 5% and 10%. Exact critical values (from Table 8) are used to compute the significance level of E_p, E_y, E_p=−1 and E_y=1

Table 3:

Import demand equations

		OLS estimates						Fully-Modified estimates
		m−1	P	gdpx	AC	ser	R2	m−1	P	gdpx	Ep	Ey	Epc	Eyc	ser	R2	P−O	Ep=−1	Ey=1	nobs
1 ALGERIA		0.81	-0.06	0.16	0.45	0.15	0.92	0.87	-0.01	0.11	-0.08	0.83	-0.07	0.84	0.07	0.91	-3.66	1.73	-0.74	34
		7.71	-0.41	1.73	2.65			16.14	-0.14	2.23	-0.14	3.66 a
2 ARGENTINA		0.42	-0.64	0.80	0.19	0.16	0.80	0.42	-0.68	0.70	-1.17	1.21	-1.07	1.27	0.12	0.80	-5.24 a	-0.85	1.12	34
		3.50	-5.00	4.57	1.01			4.71	-6.96	5.25	-5.99 a	6.38 a
3 AUSTRALIA		0.49	-0.34	0.70	0.25	0.07	0.98	0.82	-0.12	0.21	-0.66	1.19	-0.64	1.22	0.08	0.97	-10.82 a	0.28	0.52	34
		3.93	-1.78	3.81	1.34			5.57	-0.55	0.95	-0.54	3.22 b
4 AUSTRIA		0.76	-0.33	0.48	-0.07	0.04	1.00	0.82	-0.27	0.32	-1.50	1.76	-1.56	1.77	0.03	1.00	-5.55 a	-1.19	2.25	34
		10.02	-2.20	2.64	-0.36			14.11	-2.39	2.23	-3.55 a	5.23 a
5 BELGIUM-LUXEMBOURG		0.95	-0.17	-0.04	-0.09	0.05	0.99	0.96	-0.11	0.00	-2.57	0.10	-2.68	0.10	0.03	0.99	-5.45 a	-1.14	-0.76	34
		57.15	-1.96	-0.59	-0.44			76.91	-1.86	0.09	-1.86 b	0.08
6 BENIN		0.90	-0.54	0.37	0.07	0.14	0.93	0.93	-0.47	0.34	-6.74	4.91	-6.66	4.83	0.08	0.94	-4.77 a	-1.68	1.38	34
		16.68	-1.58	1.04	0.43			29.26	-2.29	1.61	-1.97 b	1.74 b
7 BRAZIL		0.83	-0.30	0.19	0.31	0.12	0.96	0.84	-0.29	0.20	-1.73	1.24	-1.80	1.25	0.07	0.96	-4.35 b	-0.95	1.41	34
		8.17	-2.78	1.64	1.71			12.97	-4.16	2.72	-2.24 c	7.26 a								34
8 BURUNDI		0.63	-0.27	0.55	-0.10	0.11	0.96	0.81	-0.19	0.31	-0.99	1.63	-0.98	1.60	0.07	0.96	-6.10 a	0.01	1.58 c
		5.16	-1.29	3.46	-0.52			10.20	-1.44	2.83	-1.23	4.09 a
9 CAMEROON		-0.01	-0.76	1.02	0.28	0.08	0.96	0.10	-0.69	0.91	-0.77	1.01	-0.80	1.00	0.07	0.96	-3.88 c	1.95	0.24	29
		-0.05	-3.91	5.71	1.40			0.72	-4.23	6.07	-6.53 a	25.24 a
10 CANADA		0.53	-0.57	0.72	0.19	0.05	0.99	0.58	-0.54	0.63	-1.28	1.48	-1.33	1.49	0.03	0.99	-4.11 a	-1.77	5.35 a	34
		4.36	-3.14	3.76	0.90			7.27	-4.78	4.78	-8.00 a	16.56 a
11 CHILE		0.26	-0.09	1.41	0.42	0.11	0.93	0.37	-0.01	1.18	-0.02	1.87	-0.01	1.94	0.12	0.93	-3.79	8.66 a	4.89 a	34
		2.14	-1.29	6.63	2.74			2.95	-0.14	5.21	-0.14	10.47 a
12 CHINA		0.76	-0.19	0.53	0.41	0.19	0.98	0.89	-0.04	0.24	-0.39	2.16	-0.39	2.12	0.17	0.97	-3.78	0.39	1.34	34
		9.73	-1.00	3.15	2.54			10.99	-0.24	1.39	-0.26	2.50 a
13 COLOMBIA		0.32	-0.63	0.76	0.25	0.13	0.93	0.46	-0.44	0.59	-0.80	1.09	-0.78	1.09	0.10	0.92	-3.02	0.59	1.13	34
		1.37	-2.35	3.06	1.03			2.54	-2.09	3.04	-2.38 b	13.38 a
14 CONGO		0.60	-0.42	0.36	0.41	0.15	0.81	0.71	-0.29	0.25	-1.02	0.87	-1.02	0.88	0.11	0.81	-3.43	-0.03	-0.56	34
		4.01	-2.21	2.31	2.33			6.21	-2.02	2.16	-2.27 b	3.82 a
15 COSTA RICA		0.74	-0.55	0.38	0.15	0.08	0.98	0.86	-0.57	0.16	-4.18	1.21	-3.99	1.22	0.07	0.98	-5.08 a	-1.27	0.53	34
		8.01	-5.90	2.48	0.82			10.35	-6.81	1.16	-1.67	3.09 a
16 COTE DTVOIRE		0.67	-0.46	0.32	0.24	0.10	0.95	0.67	-0.34	0.32	-1.04	0.96	-0.96	0.96	0.09	0.96	-3.91 c	-0.08	-0.26	34
		7.58	-2.93	3.55	1.85			8.43	-2.40	3.78	-2.24 b	6.86 a
17 DENMARK		0.48	-0.14	0.89	0.05	0.04	0.99	0.58	-0.14	0.69	-0.34	1.63	-0.33	1.67	0.04	0.99	-5.45 a	3.98 a	4.64 a	34
		5.26	-1.72	4.78	0.29			6.84	-1.93	4.04	-2.05 c	11.98 a
18 DOMINICAN REPUBLIC		0.30	-0.32	0.69	0.16	0.16	0.90	0.51	-0.15	0.43	-0.30	0.86	-0.30	0.85	0.15	0.90	-5.72 a	2.36 o	-0.96	34
		1.89	-1.95	3.90	0.93			3.51	-0.98	2.63	-1.02	5.95 a
19 EL SALVADOR		0.54	-0.49	0.71	0.39	0.10	0.91	0.66	-0.42	0.50	-1.23	1.47	-1.19	1.50	0.10	0.90	-3.75	-0.38	1.79	34
		4.46	-3.39	3.86	2.28			5.66	-3.05	2.74	-2.01 c−	5.65 a
20 FRANCE		0.41	-0.22	1.21	-0.18	0.04	1.00	0.50	-0.20	1.02	-0.40	2.02	-0.42	2.03	0.02	1.00	-6.78 a	6.85 a	23.05 a	34
		4.11	-3.61	5.41	-1.04			7.67	-5.50	6.95	-4.65 a	45.69 a
21 GABON		0.55	-0.27	0.66	0.28	0.15	0.97	0.64	-0.22	0.52	-0.62	1.45	-0.60	1.46	0.12	0.97	-5.23 a	1.60	2.01 c	34
		6.24	-2.16	4.16	1.59			8.69	-2.17	3.98	-2.56 b	6.44 a
22 GAMBIA		0.88	-0.18	0.11	-0.04	0.22	0.71	0.92	-0.13	0.12	-1.57	1.51	-1.49	1.48	0.10	0.70	-5.88 a	-0.48	0.53	34
		8.02	-1.31	1.00	-0.21			18.06	-2.04	2.43	-1.32 c	1.58 b
23 GERMANY		0.49	-0.06	1.43	0.41	0.03	1.00	0.54	-0.10	1.26	-0.21	2.73	-0.20	2.76	0.03	1.00	-3.55	5.11 a	14.10 a	34
		6.12	-0.85	5.77	2.44			7.07	-1.41	5.19	-1.34	22.26 a
24 GREECE		0.79	-0.40	0.33	-0.03	0.07	0.99	0.84	-0.26	0.21	-1.66	1.32	-1.62	1.32	0.05	0.99	-6.59 a	-1.60	1.04	34
		10.57	-3.30	2.29	-0.17			14.13	-2.65	1.73	-4.00 a	4.30 a
25 HAITI		0.37	-0.56	1.72	-0.21	0.15	0.93	0.51	-0.51	1.36	-1.05	2.79	-1.03	2.74	0.11	0.94	-6.40 a	-0.28	4.91 a	34
		2.31	-3.77	3.22	-1.07			4.06	-4.33	3.15	-6.38 a	7.66 a
26 HONDURAS		0.80	-0.14	0.17	0.22	0.09	0.95	0.86	-0.05	0.10	-0.39	0.74	-0.39	0.76	0.06	0.94	-4.24 b	0.74	-0.73	34
		9.62	-0.84	1.58	1.22			14.31	-0.47	1.42	-0.47	2.11
27 ICELAND		0.16	-0.44	0.59	0.34	0.08	0.97	0.20	-0.38	0.57	-0.48	0.71	-0.50	0.70	0.08	0.98	-3.39	2.79 c	-8.85 a	34
		1.11	-3.19	5.48	2.05			1.27	-2.56	4.71	-2.53 b	21.62 a
28 INDIA		0.66	-0.14	0.49	0.14	0.10	0.96	0.79	-0.03	0.28	-0.12	1.33	-0.11	1.33	0.07	0.96	-5.64 a	1.85	1.22	34
		5.04	-1.09	2.94	0.83			8.02	-0.25	2.14	-0.25	4.90 a
29 INDONESIA		0.60	-0.62	0.36	0.44	0.10	0.99	0.67	-0.51	0.32	-1.56	0.98	-1.51	0.98	0.10	0.98	-2.86	-1.66	-0.16	27
		4.22	-2.56	2.21	2.38			4.62	-2.01	1.92	-4.64 a	7.98 a
30 ISRAEL		0.62	-0.10	0.49	0.04	0.08	0.99	0.76	-0.08	0.32	-0.32	1.34	-0.32	1.35	0.07	0.98	-5.27 a	1.28	2.29 c	34
		4.53	-0.86	2.34	0.19			6.42	-0.71	1.81	-0.61	9.02 a
31 ITALY		0.44	-0.21	0.99	0.04	0.05	0.99	0.48	-0.19	0.92	-0.35	1.75	-0.37	1.75	0.04	0.99	-4.86 a	8.15 a	14.29 a	34
		4.35	-3.69	5.04	0.22			6.16	-4.25	6.20	-4.46 a	33.33 a
32 JAPAN		0.65	-0.14	0.38	-0.02	0.06	0.99	0.73	-0.14	0.29	-0.52	1.04	-0.53	1.07	0.05	0.99	-4.93 a	2.01	0.35	34
		6.00	-2.27	2.44	-0.08			9.55	-3.31	2.65	-2.15 c	8.49 a
33 KENYA		0.47	-0.77	0.55	-0.33	0.12	0.75	0.57	-0.71	0.49	-1.66	1.14	-1.82	1.11	0.07	0.74	-6.25 a	-2.41 b	0.84	34
		3.38	-3.61	3.69	-1.54			7.03	-5.68	5.61	-6.09 a	6.90 a
34 KOREA		0.74	-0.17	0.42	0.17	0.13	0.99	0.88	-0.10	0.16	-0.84	1.32	-0.75	1.33	0.11	0.99	-6.60 a	0.10	0.42	34
		6.14	-0.82	1.62	1.04			9.03	-0.59	0.78	-0.50	1.72 b
35 MADAGASCAR		0.60	-0.26	-0.04	0.12	0.14	0.78	0.79	-0.15	0.11	-0.71	0.52	-0.69	0.52	0.11	0.77	-5.08 a	0.70	-0.50	34
		3.88	-1.46	-0.13	0.62			6.60	-1.13	0.50	-1.73 c	0.53
36 MALAWI		0.35	-0.94	0.68	0.26	0.13	0.78	0.48	-0.86	0.60	-1.65	1.14	-1.63	1.12	0.12	0.77	-4.79 a	-1.59	0.72	34
		2.57	-3.86	4.36	1.46			3.85	-3.85	4.07	-4.06 a	5.86 a
37 MAURITANIA		0.81	-0.45	0.23	-0.13	0.21	0.87	0.91	-0.33	0.26	-3.61	2.83	-3.50	2.83	0.16	0.87	-6.82 a	-0.88	0.81	34
		8.37	-1.03	0.86	-0.77			12.52	-0.99	1.30	-1.22	1.25 c
38 MAURITIUS		1.00	-0.26	0.10	0.51	0.10	0.96	0.96	-0.11	0.09	-2.78	2.25	-2.70	2.25	0.08	0.96	-3.11	-0.34	0.57	34
		15.32	-1.20	0.94	3.35			19.63	-0.65	1.07	-0.53	1.03
39 MEXICO		0.69	-0.37	0.44	0.55	0.16	0.94	0.72	-0.22	0.37	-0.77	1.31	-0.64	1.35	0.10	0.94	-3.19	0.66	2.05 a	34
		5.22	-2.18	2.37	4.50			8.30	-1.98	2.95	-2.15 c	8.57 a
40 MOROCCO		0.73	-0.21	0.33	0.21	0.10	0.96	0.81	-0.15	0.24	-0.78	1.23	-0.78	1.23	0.07	0.96	-4.46 b	0.38	1.11	34
		5.63	-1.41	2.16	1.15			8.38	-1.39	2.05	-1.34	6.02 a
41 MYANMAR		0.81	-0.04	0.08	0.16	0.21	0.63	0.90	-0.06	0.01	-0.57	0.09	-0.60	0.09	0.12	0.61	-4.67 a	0.61	-1.49	34
		7.48	-0.37	0.74	0.80			14.28	-0.97	0.15	-0.83	0.15
42 NEW ZEALAND		0.42	-0.38	1.12	0.14	0.07	0.96	0.60	-0.32	0.84	-0.80	2.11	-0.83	2.08	0.07	0.96	-5.21 a	0.94	5.54 a	34
		3.45	-4.11	4.54	0.72			4.81	-3.54	3.21	-3.72 a	10.55 a
43 NICARAGUA		0.40	-0.15	0.36	0.12	0.18	0.43	0.52	-0.12	0.27	-0.26	0.57	-0.26	0.58	0.10	0.44	-9.37 a	6.28 a	-2.36 c	34
		2.68	-1.47	2.00	0.69			6.26	-2.27	2.77	-2.20 b	3.19 b
44 NIGERIA		0.63	-0.34	0.59	0.55	0.17	0.95	0.67	-0.30	0.60	-0.90	1.81	-0.88	1.81	0.13	0.94	-3.05	0.74	3.39 a	34
		5.27	-2.75	2.50	3.49			7.21	-3.10	3.25	-6.96 a	7.59 a
45 NORWAY		0.76	-0.41	0.16	0.05	0.05	0.98	0.82	-0.39	0.09	-2.22	0.53	-2.31	0.52	0.03	0.98	-5.01 a	-1.47	-1.58	34
		7.09	-1.90	1.28	0.27			11.44	-2.52	1.08	-2.68 b	1.79 c
46 PAKISTAN		0.04	-0.52	0.83	0.27	0.11	0.85	0.15	-0.42	0.70	-0.49	0.82	-0.47	0.83	0.08	0.84	-4.18 b	6.67 a	-2.40	34
		0.26	-4.40	5.27	1.58			1.17	-4.71	5.95	-6.35 a	11.22 a
47 PANAMA		0.49	-0.01	0.46	0.40	0.11	0.93	0.62	-0.06	0.38	-0.16	0.99	-0.16	1.00	0.08	0.91	-3.57	2.06	-0.06	34
		2.60	-0.03	2.34	2.31			4.28	-0.43	2.54	-0.40	9.73 a
48 PAPUA NEW GUINEA		0.65	-0.27	0.79	0.25	0.08	0.96	0.75	-0.27	0.47	-1.08	1.86	-1.10	1.90	0.07	0.96	-9.44 a	-0.16	1.74	33
		8.93	-1.99	3.29	1.28			11.63	-2.25	2.17	-2.11 c	3.77 b
49 PARAGUAY		0.53	-0.16	0.72	0.10	0.20	0.93	0.56	-0.14	0.69	-0.33	1.58	-0.30	1.57	0.11	0.94	-4.56 b	3.76 a	5.78 a	34
		2.98	-1.13	2.60	0.56			5.46	-1.73	4.15	-1.82 b	15.81 a
50 PERU		0.53	-0.32	0.19	0.39	0.11	0.65	0.67	-0.21	0.17	-0.63	0.50	-0.61	0.52	0.11	0.62	-3.99 c	1.02	-2.09	34
		4.63	-3.04	2.15	2.29			5.80	-2.05	1.93	-1.75	2.13 c
51 PHILIPPINES		0.79	-0.36	0.44	0.43	0.09	0.97	0.89	-0.29	0.24	-2.73	2.25	-2.73	2.26	0.09	0.97	-3.14	-0.88	1.79	34
		7.56	-2.22	2.27	2.38			9.02	-1.79	1.31	-1.39	3.22 b
52 PORTUGAL		0.73	-0.38	0.40	0.18	0.10	0.97	0.75	-0.29	0.35	-1.18	1.42	-1.14	1.42	0.07	0.97	-4.24 b	-0.53	2.67 b	34
		6.47	-2.73	2.20	0.96			9.07	-2.86	2.65	-3.51 a	9.00 a
53 RWANDA		0.38	-0.12	0.98	-0.04	0.14	0.96	0.49	-0.04	0.83	-0.07	1.63	-0.08	1.61	0.09	0.96	-6.51 a	4.31 a	7.21 a	34
		2.34	-0.67	3.63	-0.24			4.61	-0.33	4.85	-0.34	18.72 a
54 SOUTH AFRICA		0.50	-0.53	0.33	0.19	0.10	0.87	0.56	-0.44	0.30	-1.00	0.67	-1.04	0.68	0.05	0.87	-5.23 a	-0.02	-5.62 a	34
		3.96	-3.43	3.39	1.10			8.65	-5.63	5.98	-5.58 a	11.45 a
55 SPAIN		0.56	-0.35	0.75	0.46	0.07	0.99	0.64	-0.26	0.61	-0.74	1.70	-0.74	1.71	0.08	0.99	-3.50	0.84	2.47 c	34
		4.94	-3.52	2.80	2.69			4.79	-2.31	1.95	-2.43 b	6.01 a
56 SWEDEN		0.57	-0.06	0.94	-0.00	0.04	0.99	0.67	-0.05	0.71	-0.16	2.13	-0.16	2.18	0.03	0.99	-5.28 a	5.33 a	7.46 a	34
		5.26	-0.77	3.57	-0.02			7.45	-0.95	3.15	-1.00	14.04 a
57 SWITZERLAND		0.87	-0.22	-0.05	0.23	0.06	0.98	0.92	-0.13	0.02	-1.64	0.23	-1.73	0.23	0.05	0.98	-3.97 c	-0.58	-0.32	34
		8.71	-1.22	-0.24	1.32			9.98	-0.76	0.09	-1.50	0.09
58 THAILAND		0.69	-0.51	0.55	0.46	0.11	0.98	0.74	-0.38	0.44	-1.43	1.67	-1.37	1.69	0.08	0.98	-3.62	-0.82	4.13 a	34
		5.30	-2.66	2.69	2.87			7.65	-2.52	2.86	-2.74 b	10.29 a
59 TRINIDAD AND TOBAGO		0.50	-0.49	0.25	0.16	0.12	0.98	0.57	-0.44	0.22	-1.02	0.50	-1.07	0.50	0.10	0.98	-4.88 a	-0.35	-3.12 b	34
		5.00	-5.15	2.52	0.85			6.91	-5.43	2.51	-15.51 a	3.16 b
60 TURKEY		0.86	0.03	0.21	0.18	0.14	0.%	0.93	-0.03	0.13	-0.35	1.78	-0.34	1.80	0.10	0.95	-4.29 b	0.65	1.01	34
		5.68	0.27	0.89	0.93			8.58	-0.32	0.73	-0.35	2.30 b
61 UNITED KINGDOM		0.49	−0.01I	1.23	0.09	0.03	1.00	0.56	-0.03	1.08	-0.07	2.43	-0.07	2.45	0.02	0.99	-5.26 a	9.77 a	17.87 a	34
		6.61	-0.16	6.72	0.50			9.08	-0.71	7.01	-0.70	30.34 a
62 UNITED STATES		0.44	-0.25	1.35	0.19	0.04	1.00	0.56	-0.23	1.09	-0.52	2.45	-0.50	2.51	0.04	1.00	-5.06 a	3.45 a	19.88 a	34
		4.92	-4.80	6.57	1.05			5.99	-4.53	4.94	-3.67 b	33.56 a
63 URUGUAY		0.68	-0.20	1.38	0.22	0.12	0.92	0.77	-0.22	1.24	-0.99	5.48	-0.94	5.54	0.11	0.91	-3.78	0.02	3.23 b	34
		6.93	-1.93	3.94	1.30			8.24	-2.27	3.63	-1.66	3.95 a
64 YUGOSLAVIA		0.69	-0.41	0.35	0.25	0.09	0.94	0.80	-0.33	0.25	-1.67	1.24	-1.65	1.22	0.09	0.94	-3.85 c	-1.11	0.81	31
		6.91	-3.74	2.58	1.24			8.34	-3.16	1.93	-2.76 a	4.21 a
65 ZAIRE		0.92	-0.02	0.11	-0.14	0.18	0.90	0.93	-0.02	0.00	-0.34	0.03	-0.35	0.03	0.10	0.90	-5.60 a	0.94	-0.29	30
		9.48	-0.26	0.33	-0.66			18.10	-0.43	0.01	-0.49	0.01
66 ZAMBIA		0.56	-0.51	0.16	0.06	0.11	0.93	0.62	-0.44	0.13	-1.17	0.34	-1.22	0.34	0.09	0.93	-8.82 a	-1.25	-4.86 a	34
		5.72	-4.56	2.28	0.32			8.35	-5.17	2.31	-8.55 a	2.45 c
	Mean	0.59	-0.32	0.56				0.68	-0.26	0.45	-1.08	1.45	-1.07	1.46
	Median	0.60	-0.31	0.48				0.69	-0.22	0.32	-0.80	1.32	-0.79	1.33
	Stdev	0.21	0.20	0.39				0.19	0.19	0.34	1.08	0.93	1.06	0.93
	Min	-0.01	-0.94	-0.05				0.10	-0.86	0.00	-6.74	0.03	-6.66	0.03
	Max	1.00	0.03	1.72				0.96	-0.01	1.36	-0.02	5.48	-0.01	5.54

Note: The dependent variable is real imports of goods and non-factor services (m). The explanatory variables are the lagged dependent variable (m.j), the real exchange rate (p) computed as the ratio of imports deflator to gdp deflator, and gdp minus exports (gdpx). The import demand equation is estimated using both OLS and the Phillips-Hansen Fully Modified estimator. The long-run price and income elasticities are given by E_p and E_y, respectively. ${{{E}}_{{p}}}^{{c}}$ and ${{{E}}_{{y}}}^{{c}}$ give the long-run price and income elasticities corrected for bias (see Table 4). For each country, the estimated coefficients and their t-stat (below the coefficient estimates) are provided. The following statistics are also provided: Durbin’s test for autocorrelation (AC), R², standard error of the regression (ser), and the number of observations for each country (nobs). Cointegration between the three variables in the import demand equation is tested using the Phillips-Ouliaris residual test given in column P-O. Finally, the columns labeled E_p=−1 and E_y=l report the two-tailed t-test for unit-price and unit-income elasticities, respectively. The asymptotic critical values for the -Phillips-Ouliaris test at 10%, 5% and 1% are, respectively, −3.84, −4.16 and −4.64. The letters a, b and c indicate significance at 1%, 5% and 10%. Exact critical values (from Table 8) are used to compute the significance level of E_p, E_y, E_p=−1 and E_y=1

View Table

Table 3:

Import demand equations

		OLS estimates						Fully-Modified estimates
		m−1	P	gdpx	AC	ser	R2	m−1	P	gdpx	Ep	Ey	Epc	Eyc	ser	R2	P−O	Ep=−1	Ey=1	nobs
1 ALGERIA		0.81	-0.06	0.16	0.45	0.15	0.92	0.87	-0.01	0.11	-0.08	0.83	-0.07	0.84	0.07	0.91	-3.66	1.73	-0.74	34
		7.71	-0.41	1.73	2.65			16.14	-0.14	2.23	-0.14	3.66 a
2 ARGENTINA		0.42	-0.64	0.80	0.19	0.16	0.80	0.42	-0.68	0.70	-1.17	1.21	-1.07	1.27	0.12	0.80	-5.24 a	-0.85	1.12	34
		3.50	-5.00	4.57	1.01			4.71	-6.96	5.25	-5.99 a	6.38 a
3 AUSTRALIA		0.49	-0.34	0.70	0.25	0.07	0.98	0.82	-0.12	0.21	-0.66	1.19	-0.64	1.22	0.08	0.97	-10.82 a	0.28	0.52	34
		3.93	-1.78	3.81	1.34			5.57	-0.55	0.95	-0.54	3.22 b
4 AUSTRIA		0.76	-0.33	0.48	-0.07	0.04	1.00	0.82	-0.27	0.32	-1.50	1.76	-1.56	1.77	0.03	1.00	-5.55 a	-1.19	2.25	34
		10.02	-2.20	2.64	-0.36			14.11	-2.39	2.23	-3.55 a	5.23 a
5 BELGIUM-LUXEMBOURG		0.95	-0.17	-0.04	-0.09	0.05	0.99	0.96	-0.11	0.00	-2.57	0.10	-2.68	0.10	0.03	0.99	-5.45 a	-1.14	-0.76	34
		57.15	-1.96	-0.59	-0.44			76.91	-1.86	0.09	-1.86 b	0.08
6 BENIN		0.90	-0.54	0.37	0.07	0.14	0.93	0.93	-0.47	0.34	-6.74	4.91	-6.66	4.83	0.08	0.94	-4.77 a	-1.68	1.38	34
		16.68	-1.58	1.04	0.43			29.26	-2.29	1.61	-1.97 b	1.74 b
7 BRAZIL		0.83	-0.30	0.19	0.31	0.12	0.96	0.84	-0.29	0.20	-1.73	1.24	-1.80	1.25	0.07	0.96	-4.35 b	-0.95	1.41	34
		8.17	-2.78	1.64	1.71			12.97	-4.16	2.72	-2.24 c	7.26 a								34
8 BURUNDI		0.63	-0.27	0.55	-0.10	0.11	0.96	0.81	-0.19	0.31	-0.99	1.63	-0.98	1.60	0.07	0.96	-6.10 a	0.01	1.58 c
		5.16	-1.29	3.46	-0.52			10.20	-1.44	2.83	-1.23	4.09 a
9 CAMEROON		-0.01	-0.76	1.02	0.28	0.08	0.96	0.10	-0.69	0.91	-0.77	1.01	-0.80	1.00	0.07	0.96	-3.88 c	1.95	0.24	29
		-0.05	-3.91	5.71	1.40			0.72	-4.23	6.07	-6.53 a	25.24 a
10 CANADA		0.53	-0.57	0.72	0.19	0.05	0.99	0.58	-0.54	0.63	-1.28	1.48	-1.33	1.49	0.03	0.99	-4.11 a	-1.77	5.35 a	34
		4.36	-3.14	3.76	0.90			7.27	-4.78	4.78	-8.00 a	16.56 a
11 CHILE		0.26	-0.09	1.41	0.42	0.11	0.93	0.37	-0.01	1.18	-0.02	1.87	-0.01	1.94	0.12	0.93	-3.79	8.66 a	4.89 a	34
		2.14	-1.29	6.63	2.74			2.95	-0.14	5.21	-0.14	10.47 a
12 CHINA		0.76	-0.19	0.53	0.41	0.19	0.98	0.89	-0.04	0.24	-0.39	2.16	-0.39	2.12	0.17	0.97	-3.78	0.39	1.34	34
		9.73	-1.00	3.15	2.54			10.99	-0.24	1.39	-0.26	2.50 a
13 COLOMBIA		0.32	-0.63	0.76	0.25	0.13	0.93	0.46	-0.44	0.59	-0.80	1.09	-0.78	1.09	0.10	0.92	-3.02	0.59	1.13	34
		1.37	-2.35	3.06	1.03			2.54	-2.09	3.04	-2.38 b	13.38 a
14 CONGO		0.60	-0.42	0.36	0.41	0.15	0.81	0.71	-0.29	0.25	-1.02	0.87	-1.02	0.88	0.11	0.81	-3.43	-0.03	-0.56	34
		4.01	-2.21	2.31	2.33			6.21	-2.02	2.16	-2.27 b	3.82 a
15 COSTA RICA		0.74	-0.55	0.38	0.15	0.08	0.98	0.86	-0.57	0.16	-4.18	1.21	-3.99	1.22	0.07	0.98	-5.08 a	-1.27	0.53	34
		8.01	-5.90	2.48	0.82			10.35	-6.81	1.16	-1.67	3.09 a
16 COTE DTVOIRE		0.67	-0.46	0.32	0.24	0.10	0.95	0.67	-0.34	0.32	-1.04	0.96	-0.96	0.96	0.09	0.96	-3.91 c	-0.08	-0.26	34
		7.58	-2.93	3.55	1.85			8.43	-2.40	3.78	-2.24 b	6.86 a
17 DENMARK		0.48	-0.14	0.89	0.05	0.04	0.99	0.58	-0.14	0.69	-0.34	1.63	-0.33	1.67	0.04	0.99	-5.45 a	3.98 a	4.64 a	34
		5.26	-1.72	4.78	0.29			6.84	-1.93	4.04	-2.05 c	11.98 a
18 DOMINICAN REPUBLIC		0.30	-0.32	0.69	0.16	0.16	0.90	0.51	-0.15	0.43	-0.30	0.86	-0.30	0.85	0.15	0.90	-5.72 a	2.36 o	-0.96	34
		1.89	-1.95	3.90	0.93			3.51	-0.98	2.63	-1.02	5.95 a
19 EL SALVADOR		0.54	-0.49	0.71	0.39	0.10	0.91	0.66	-0.42	0.50	-1.23	1.47	-1.19	1.50	0.10	0.90	-3.75	-0.38	1.79	34
		4.46	-3.39	3.86	2.28			5.66	-3.05	2.74	-2.01 c−	5.65 a
20 FRANCE		0.41	-0.22	1.21	-0.18	0.04	1.00	0.50	-0.20	1.02	-0.40	2.02	-0.42	2.03	0.02	1.00	-6.78 a	6.85 a	23.05 a	34
		4.11	-3.61	5.41	-1.04			7.67	-5.50	6.95	-4.65 a	45.69 a
21 GABON		0.55	-0.27	0.66	0.28	0.15	0.97	0.64	-0.22	0.52	-0.62	1.45	-0.60	1.46	0.12	0.97	-5.23 a	1.60	2.01 c	34
		6.24	-2.16	4.16	1.59			8.69	-2.17	3.98	-2.56 b	6.44 a
22 GAMBIA		0.88	-0.18	0.11	-0.04	0.22	0.71	0.92	-0.13	0.12	-1.57	1.51	-1.49	1.48	0.10	0.70	-5.88 a	-0.48	0.53	34
		8.02	-1.31	1.00	-0.21			18.06	-2.04	2.43	-1.32 c	1.58 b
23 GERMANY		0.49	-0.06	1.43	0.41	0.03	1.00	0.54	-0.10	1.26	-0.21	2.73	-0.20	2.76	0.03	1.00	-3.55	5.11 a	14.10 a	34
		6.12	-0.85	5.77	2.44			7.07	-1.41	5.19	-1.34	22.26 a
24 GREECE		0.79	-0.40	0.33	-0.03	0.07	0.99	0.84	-0.26	0.21	-1.66	1.32	-1.62	1.32	0.05	0.99	-6.59 a	-1.60	1.04	34
		10.57	-3.30	2.29	-0.17			14.13	-2.65	1.73	-4.00 a	4.30 a
25 HAITI		0.37	-0.56	1.72	-0.21	0.15	0.93	0.51	-0.51	1.36	-1.05	2.79	-1.03	2.74	0.11	0.94	-6.40 a	-0.28	4.91 a	34
		2.31	-3.77	3.22	-1.07			4.06	-4.33	3.15	-6.38 a	7.66 a
26 HONDURAS		0.80	-0.14	0.17	0.22	0.09	0.95	0.86	-0.05	0.10	-0.39	0.74	-0.39	0.76	0.06	0.94	-4.24 b	0.74	-0.73	34
		9.62	-0.84	1.58	1.22			14.31	-0.47	1.42	-0.47	2.11
27 ICELAND		0.16	-0.44	0.59	0.34	0.08	0.97	0.20	-0.38	0.57	-0.48	0.71	-0.50	0.70	0.08	0.98	-3.39	2.79 c	-8.85 a	34
		1.11	-3.19	5.48	2.05			1.27	-2.56	4.71	-2.53 b	21.62 a
28 INDIA		0.66	-0.14	0.49	0.14	0.10	0.96	0.79	-0.03	0.28	-0.12	1.33	-0.11	1.33	0.07	0.96	-5.64 a	1.85	1.22	34
		5.04	-1.09	2.94	0.83			8.02	-0.25	2.14	-0.25	4.90 a
29 INDONESIA		0.60	-0.62	0.36	0.44	0.10	0.99	0.67	-0.51	0.32	-1.56	0.98	-1.51	0.98	0.10	0.98	-2.86	-1.66	-0.16	27
		4.22	-2.56	2.21	2.38			4.62	-2.01	1.92	-4.64 a	7.98 a
30 ISRAEL		0.62	-0.10	0.49	0.04	0.08	0.99	0.76	-0.08	0.32	-0.32	1.34	-0.32	1.35	0.07	0.98	-5.27 a	1.28	2.29 c	34
		4.53	-0.86	2.34	0.19			6.42	-0.71	1.81	-0.61	9.02 a
31 ITALY		0.44	-0.21	0.99	0.04	0.05	0.99	0.48	-0.19	0.92	-0.35	1.75	-0.37	1.75	0.04	0.99	-4.86 a	8.15 a	14.29 a	34
		4.35	-3.69	5.04	0.22			6.16	-4.25	6.20	-4.46 a	33.33 a
32 JAPAN		0.65	-0.14	0.38	-0.02	0.06	0.99	0.73	-0.14	0.29	-0.52	1.04	-0.53	1.07	0.05	0.99	-4.93 a	2.01	0.35	34
		6.00	-2.27	2.44	-0.08			9.55	-3.31	2.65	-2.15 c	8.49 a
33 KENYA		0.47	-0.77	0.55	-0.33	0.12	0.75	0.57	-0.71	0.49	-1.66	1.14	-1.82	1.11	0.07	0.74	-6.25 a	-2.41 b	0.84	34
		3.38	-3.61	3.69	-1.54			7.03	-5.68	5.61	-6.09 a	6.90 a
34 KOREA		0.74	-0.17	0.42	0.17	0.13	0.99	0.88	-0.10	0.16	-0.84	1.32	-0.75	1.33	0.11	0.99	-6.60 a	0.10	0.42	34
		6.14	-0.82	1.62	1.04			9.03	-0.59	0.78	-0.50	1.72 b
35 MADAGASCAR		0.60	-0.26	-0.04	0.12	0.14	0.78	0.79	-0.15	0.11	-0.71	0.52	-0.69	0.52	0.11	0.77	-5.08 a	0.70	-0.50	34
		3.88	-1.46	-0.13	0.62			6.60	-1.13	0.50	-1.73 c	0.53
36 MALAWI		0.35	-0.94	0.68	0.26	0.13	0.78	0.48	-0.86	0.60	-1.65	1.14	-1.63	1.12	0.12	0.77	-4.79 a	-1.59	0.72	34
		2.57	-3.86	4.36	1.46			3.85	-3.85	4.07	-4.06 a	5.86 a
37 MAURITANIA		0.81	-0.45	0.23	-0.13	0.21	0.87	0.91	-0.33	0.26	-3.61	2.83	-3.50	2.83	0.16	0.87	-6.82 a	-0.88	0.81	34
		8.37	-1.03	0.86	-0.77			12.52	-0.99	1.30	-1.22	1.25 c
38 MAURITIUS		1.00	-0.26	0.10	0.51	0.10	0.96	0.96	-0.11	0.09	-2.78	2.25	-2.70	2.25	0.08	0.96	-3.11	-0.34	0.57	34
		15.32	-1.20	0.94	3.35			19.63	-0.65	1.07	-0.53	1.03
39 MEXICO		0.69	-0.37	0.44	0.55	0.16	0.94	0.72	-0.22	0.37