Again on trade elasticities: evidence from a selected sample of countries

Although the most prominent recent case is that of China, Germany, Japan and the UK have also manipulated their real exchange rates. Japan and the UK used quantitative easing in order to counter the current recession (Gagnon 2013; Joyce et al. 2011), and, according to the US Treasury, Germany’s low level of investment and high savings rate contributed to the Eurozone crisis, which is characterised by increasing trade troubles for the EU periphery and huge surpluses for Germany.

Indeed, if domestic and foreign goods were perfect substitutes, then one should observe either the goods having a market share of unity, and each country acts as an importer or exporter of a traded good but not both (Goldstein and Khan 1985). Again, the coexistence of trade-flows and domestic production makes the hypothesis of perfect substitutes unrealistic.

As the economic model from which the foreign demand originates is well-known, we omit to present the system of eight equations proposed by Goldstein and Khan (1985). In this we follow Hamori and Yin (2011), Ketenci and Uz (2011), Shigeyuki and Yoichi (2009), Caporale and Chui (1999), Senhadji and Montenegro (1999), Bahmani-Oskooee and Niroomand (1998), Sawyer and Sprinkle (1996) and Thorbecke (2011).

Algieri (2011) reports that the price elasticities of the exports of France, Italy, Japan, the Netherlands, Spain, the UK and the USA are rather small (in the range −0.3/0.8) over the period 1978–2009. Similarly, exports price-elasticity of Eurozone countries is low in Bayoumi et al. (2011) and in Chen et al. (2012) (0.6 and 0.46 respectively). Anaraki (2014) uses a Keynesian model and quarterly data over the 2001–2010 period and finds that a 10 % Euro devaluation against the major currencies (yuan, dollar and yen) would increase the Eurozone’s exports to China by 3.4 %, to the USA by 2.4 % and to Japan by 1.9 %. Ketenci and Uz (2011) looked at the EU bilateral trade flows over 1980–2007 and found an export price-elasticity ranging in the 0.08/0.64 interval. The price elasticity of German exports is 0.6 in Thorbecke and Kato (2012). Thorbecke and Kato (2012) focus on Japanese exports to 17 partners over the period 1988–2009 and find that exports are price inelastic, although a unitary long-run elasticity is found for consumption products. Crane et al. (2007) find that in the 1981–2006 period the price-elasticity is low for Italy (0.7), Japan (0.34) and the USA (0.6). Yao et al. (2013) looked at total Chinese exports from 1992 to 2006 and, even after controlling for an increase in product-variety, they find a short-run price-elasticity of 0.65. Dezeure and Teixeira (2014) argue that in spite of depreciation of the pound, the weak growth of British exports in the 2000 s is due to the virtually zero elasticity between exports and the exchange rate.

Argentina, Australia, Brazil, Canada, Chile, China, Colombia, Costa Rica, Denmark, Egypt, the United Kingdom, Hong-Kong, Indonesia, India, Israel, Japan, Korea, Mexico, Malaysia, Norway, New Zealand, Peru, the Philippines, Singapore, Sweden, Switzerland, Thailand, Turkey, Uruguay, the United States, Venezuela and the Euro area.

According to the Houthakker and Magee (1969), if growth is uniform across country and the relative prices of imports/exports remain constant over time, then an economy will experience a permanent trade deficit, provided that the income elasticity of imports is higher than that of exports. If the asymmetry of income elasticities persists, then long-run trade balance can be assured only by large home currency devaluation. This line of research has received much attention in the past, proving that the asymmetry is robust across time periods, countries and econometric methods (see e.g., Chinn 2004; Crane et al. 2007; Hooper et al. 2000). However, it disappears for services and, thus, might attenuate at national level when countries will trade more in services than in manufacturing (Mann 2002; Wren-Lewis and Driver 1998).

For each country, the real exchange rates is constructed as the trade-weighted average exchange rate of a currency against a basket of currencies after adjusting for inflation differentials with regard to the countries concerned. It is based on the Consumer Price Index (CPI), thus, in formula we have this general expression \( REX_{i,t} = {{CPI_{it} } \mathord{\left/ {\vphantom {{CPI_{it} } {CPI_{RoW,t} }}} \right. \kern-0pt} {CPI_{RoW,t} }} \times E_{it} \), where the nominal exchange rate E _it is the domestic currency price of one unit of foreign currency. For countries with the same currency, i.e. EU countries, the differences in REER collapse to differences in domestic prices.

World income (Y^w) is also non-stationary. This comes from the augmented Dickey–Fuller test (1981). The statistic-test is the tau-test (τ), as tabulated by MacKinnon (2010). The estimated coefficient of Y^w is −3.03 with a p value = 0.12 Furthermore, the evidence of Table 1 overlaps that obtained when performing the ADF-t test for heterogeneous panels as proposed by Im et al. (2003) (results are available upon request). It is also important to emphasize that our panel is composed of a sectional dimension of seven exporters. This issue belongs to the long-dated discussion comparing large to small panel data (Eberhardt 2011). It can be addressed by performing robustness analyses as made in, e.g., Roudet et al. (2007). In our case, the large T dimension should ensure the reliability of panel data results. However, we find that panel data estimations for exports overlap a lot of those obtained from the individual-country study, while they differ from VECM evidence as far as imports are concerned (cfr. Table 5).

In what follows we report the Johansen test, country-by-country. The cointegration rank is 1 for Italy (p value 0.25), Japan (p value 0.38), France (p value 0.78), China (p value 0.07), UK (p value 0.61), Germany (p value 0.88), USA (p value 0.38).

The starting point to calculate Z_a and Z_t statistics is to estimate the first-order serial correlation coefficient, \( \hat{\rho }^{ * } \) of OLS residuals. The difference between Z_a and Z_t consists in the fact that Z_t consider also a transformation of the long-run variance \( \hat{s}^{2} \) of OLS residuals (in formulas: \( Z_{a} \left( \tau \right) = n\left( {\hat{\rho }_{\tau }^{*} - 1} \right) \) and \( Z_{t} \left( \tau \right) = {{\left( {\hat{\rho }_{\tau }^{*} - 1} \right)} \mathord{\left/ {\vphantom {{\left( {\hat{\rho }_{\tau }^{*} - 1} \right)} {\hat{s}}}} \right. \kern-0pt} {\hat{s}}} \). The \( ADF\left( \tau \right) \) statistic is calculated by regressing OLS residuals (in first-differences) against their lags and the lagged first-differences. The statistics ADF, Z_a and Z_t are calculated across all estimated values of the regime shifts \( \tau \in {\rm T} \). Then, the GH test is performed by taking the smallest values of each statistics, as they constitute evidence against the null hypothesis. The test-statistics become \( Z_{a} = \inf_{{\tau \in {\rm T}}} \;Z_{a} \left( \tau \right) \), \( Z_{t} = \inf_{{\tau \in {\rm T}}} \;Z_{t} \left( \tau \right) \) and \( ADF = \inf_{{\tau \in {\rm T}}} \;ADF\left( \tau \right) \).

In the econometric estimations of exports model we control for these breaks in the co-integration vectors of France, China and the UK. To this end, we augment the regressions by allowing for differences in slopes after 2008. However, results do not change. This is likely because the value of the calculated statistics is slightly smaller than the critical value (Table 2), suggesting that the breaks that the GH tests reveal are not strong enough to induce any structural change in the co-integration vectors.

They are basically the traditional pooled estimators (fixed and random effects estimators), where the intercepts differ across groups while the other coefficients and error variances are constrained to be the same (Pesaran et al. 1996).

Both MG and PMG offer a good compromise between consistency and efficiency. The PMG is useful if countries share the determinants of steady-state, whereas the short-run adjustment are related to country characteristics. In other words, the PMG predicts a common long-run equilibrium relationship and short-run dynamics of each country. In brief, MG always yields consistent estimates, whilst PMG results are consistent and efficient only if the hypothesis of common long-run elasticity is empirically accepted (Pesaran et al. 1996, 1999).

The PMG estimator is quite appealing when studying small sets of arguably ‘similar’ countries rather than heterogeneous panels (Eberhardt 2011). The requirements for the validity of both these methods are such that: (1) there is a long-run relationship among the variables of interest and, (2) the dynamic specification be augmented such that the regressors are exogenous and the residuals are serially uncorrelated. Finally, this analytical framework does not control for cross-country common factor effects. This issue is left for future work.

The MG offers the opportunity to obtain only one short-run and long-run elasticity simply by averaging the estimations of each individual country.

For PMG we accept the null hypothesis of unitary elasticity (the test-statistic is 1.58 with p value of 0.21), while for MG estimations we reject the null hypothesis as the test-statistic is 8.50 (p value = 0.0035).

For PMG the test-statistic is 0.66 (p value = 0.42), while for MG it is 0.22 (p value = 0.64).

From the exports side, it becomes important to verify which is the best performing model between MG and PMG. To this end we ran an LR test. The two models are nested in each other: the PMG is the restricted model, while the MG is without restrictions. The long-run elasticities are common across countries under the H₀ hypothesis, while the alternative is that they differ from one country to another (as assumed by the MG estimator). According to LR results, we reject the null hypothesis: the LR yields a χ ²(12) = 44.0 with a p value = 0. This means that the assumption that countries share the same equilibrium is unrealistic and not supported by data. On the contrary, we find that each country converges to its own long-run equilibrium. Based on this, our discussion then focuses only on the price and income elasticities estimated through the MG method (Tables 4, 8), while the PMG evidence is reported in the Appendix Table 7.

Income is even more important in the short-run. Indeed, if a positive shock of 1 % in world income occurred, then exports would increase, in the short-run, by 6.94 % in Japan, 4.06 % in Italy, 3.9 % in the UK, about 3 % in China, France and Germany and by 2.6 % in the USA. Furthermore, the short-run analysis reinforces the low sensitivity of exports to prices, as a significant relationship between exports and REX has been estimated only for Italy (−0.33), France (−0.25), UK (−0.23) and USA (−0.19) (Appendix Tables 7, 8).

As for REX, for each reporting country the nominal effective exchange rate it is weighted through by the respective trade shares of each partner (cf. footnote 7). Data needed to calculate the relative import/export prices are from OECD. The relative price is the ratio between two index prices (1995 = 100), that is, the home index consumer price of each trader and the foreign index consumer price. As there are no index prices for the all trade-partners, the foreign prices are those calculated by OECD for all members. Here, the assumption is that OECDs, as a whole, is a good proxy of world market, both from import and export sides of every country in the sample.