3.1 Data Sources and Variables
This study used annual panel data of Ethiopia’s coffee export and its 71 trade partners over the period of 2005–2015. The panel data has better efficiency than other data types and offer more variability, more degree of freedom and reduce the multicollinearity among explanatory variables, improve the reliability of the regression results [
4]. The study comprised the following variables based on gravity model theory as [
6,
14,
24].
First, Ethiopia’s Coffee Export (ECE) refers to the annual USD value of Ethiopian coffee exported to each selected 71 countries, included as a dependent variable. The data was extracted from the National Bank of Ethiopia database. The selected countries were consistent Ethiopian coffee importer (ECI) that are importing Ethiopia’s coffee at least once in a year throughout the periods of the study, and are listed in Appendix-A.
Second, Real Exchange Rate (RER) measures the international competitiveness of goods produced domestically. To facilitate computation of the average real exchange rate, the study applied the IMF definition of the real exchange rate: real exchange rate as the price of domestic currency against foreign currency, i.e. RER = E.P*/P. Where E is the bilateral nominal exchange rate, P* is the foreign price index of the major Ethiopian exports and P is the Ethiopia consumer price index. Third, the Gross Domestic Product (GDP): Annual USD values of GDP (in Billions) were extracted from the IMF, IFS database. Fourth, the Distance (DIS) is a time-invariant variable. Data on the distance between Ethiopia and its ECI were collected based on the geographic distance between Addis Ababa and capital cities of the selected ECI countries. The data was measured in kilometers’ (km) and the data was obtained from
www.distancefromto.net/.
Fifth, the Population (POP) is the total populations (in millions) of Ethiopia and selected ECI countries were obtained from WB, WDI database. It is used to measure the influence Ethiopia’s and that of ECI degree of self-sufficiency and absorption effect. Sixth, Openness to trade (OPEN) implies an economy’s openness to the flow of goods and services from around the world. It is computed as the total trade (the sum of exports and imports) of a country with the world economy divided by its real GDP. These data were obtained from IMF, IFS database. Seventh, Institutional Quality (IQ) as the world governance indicator (WGI) project estimates the institutional quality of a particular country in terms of six parameters: rule of law, political stability, and absence of violence or terrorism, voice and accountability, government effectiveness, regulatory quality and control of corruption. The rank out of 100% is given for each component. The average value or principally the geometric mean of the six components as a proxy for Ethiopia’s institutional quality. These parameters were obtained from the WGI website.
3.2 Model Specification
The study adopted and used the econometric specification of the dynamic panel gravity model described on [
6,
14,
24]. It specified as follows:
$$ \begin{aligned} {\text{lnECE}}_{{\rm ijt}} = &\upbeta_{ 0} + \sum\limits_{{{\text{l}} = 1}}^{\text{p}} {\updelta_{{\rm l}} {\text{lnECE}}_{{{\text{ij,t}} - {\text{l}}}} } +\upbeta_{ 2} {\text{lnGDP}}_{{\rm it}} +\upbeta_{ 3} {\text{lnGDP}}_{{\rm jt}} +\upbeta_{ 4} {\text{lnPOP}}_{{\rm it}} +\upbeta_{ 5} {\text{lnPOP}}_{{\rm jt}} \\ & +\upbeta_{ 6} {\text{lnWDIS}}_{{\rm ijt}} +\upbeta_{ 7} {\text{lnRER}}_{{\rm ijt}} +\upbeta_{ 8} {\text{lnOPEN}}_{{\rm it}} +\upbeta_{ 9} {\text{lnOPEN}}_{{\rm jt}} +\upbeta_{ 1 0} {\text{lnIQ}}_{{\rm it}} +\upalpha_{{\rm i}} +\upvarepsilon_{{\rm ijt}} \\ \end{aligned} $$
(3.1)
where ECE
ijt is the USD value of coffee export from country i (Ethiopia) to j, its ECI countries at time t, GDP
it is gross domestic product of country i in year t and GDP
jt is gross domestic product of country j in year t that indicate economic size, POP
it is the population size of country i at time t and POP
jt is the population size of country j at time t and, WDIS
ijt is weighted distance between country i and country j at time t. Since physical distance (DIS
ij) is a fixed variable overtime, RER
ijt is real exchange rate at time t, IQ
it is institutional quality of Ethiopia’s at time t, OPEN
it is openness to trade country i at time t, OPEN
jt is openness to trade country j at time t, and the unobservable error term is consists of the country specific unobserved error term, α
i, and idiosyncratic disturbance term, ε
ijt. This is assumed to follow a one-way error component model.
Several studies used the weighted distance to wipe-out the time-invariant nature of the variable distance instead of absolute distance to measure the distance between trading partners in order to get intuitive computations of the model [
14,
24].They used exporter’s GDP as a weight variable. Since, transportation cost is the expenditure of the exporter. Mathematically, weighted distance is calculated as: WDIS
ijt = (DIS
ij* GDP
it)/
\( \sum {\text{GDP}} \)it. Where WDIS
ijt is the relative (weighted) distance between trading partners, DIS
ij is the physical geographical distance, GDP
it is the gross domestic product of country i (Ethiopia) at time t and that
\( \sum {\text{GDP}} \)it is the sum of all GDPs of Ethiopia over the study period.
The national incomes of the countries are proxies by their GDP. GDP is a measure of the size of a country’s economy, so countries with higher GDP are assumed to trade more than countries with lower GDP. The import demand for foreign countries is determined by their income. The higher income of the importing country implies greater demand for imports and thus for Ethiopia’s coffee exports. Hence, the coefficients of GDPs are expected to be positive. The variable GDP for Ethiopia and ECIs was considered in real terms at constant USD prices with 2010 as the base year to account for inflation using the deflator, GDP deflator.
The coefficient of the population is used to measure the influence Ethiopia’s and that of ECI degree of self-sufficiency and absorption effect. Ethiopia with large population size is expected to produce and export more due to economies of scale resulting from cheap labor. Conversely, it can also export less due to higher domestic absorption effect of larger population size. Thus, the coefficient of Ethiopia’s population can be positive or negative. On other direction, ECI’s with large population size is indicative of the potentially larger market size and is expected to import more. So, the coefficient of the ECI population is expected to be positive.
The weighted distance is indicative of the degree of trade resistance or the ability to stay in the trade process with the given transportation cost between the trade partners. The higher the distance, the higher the transportation costs and hence the coefficient is expected to have a negative sign.
The coefficient of the bilateral real exchange rate is incorporated as a measure for the relative price of foreign goods in terms of domestic goods. The bilateral real exchange rate is a measure of the international competitiveness of domestically produced goods. The real depreciation in the real exchange rate means that it takes fewer units of foreign currency to buy one unit of domestic currency. This makes domestic goods relatively cheaper, leading to an increase in exports due to higher foreign demand. While the appreciation in the real exchange rate in an economy is associated with loses in competitiveness because more units of foreign currency are required to buy one unit of domestic currency. This raises the price of exported goods and lowers that of imported goods, leading to an increase in imports due to higher domestic demand. Thus, the coefficient of the real exchange rate is expected to be negative.
Openness to trades is a measure of the ability of countries to exchange freely as a buyer or seller in the international market place. It is also a degree to which government hampers the free flow of foreign goods and services has a direct bearing on the ability of individuals to pursue their economic goals and maximize their productivity and well-being. Trade barriers emerge in the form of regulatory barriers. This determines in general economic efficiency and growth. As a result, the more open an economy is, as indicated by high trade freedom, the more it is expected to trade with other economies. Thus, it is expected that the coefficient will be positive.
Index values computed from the six measures of institutional quality was used in the study. A country with better quality institutions is expected to trade more than a country with poor quality institutions because institutions increase trade by reducing transaction costs. Hence, the sign of this variable is expected to be positive.
3.4 Specification Tests
3.4.1 Test for Validity of Instrument Sets
Sargan [
18] and Hansen [
9] shown test for the assumption about the absence of any (asymptotic) correlation between the instrumental variables and the disturbances. In addition to the former assumption, the choice of “good” instruments lies in the potency of the correlation between the endogenous regressors and the instruments. Indeed, Blundell and Bond [
5], show that a small correlation results in erratic parameter estimates. Moreover, Baltagi [
4] showed that there is a significant amount of the deleterious effects of weak instruments. Sargan (Hansen) over identification restriction (OIR) test, which is given by:
$$ {\text{m}} = \Delta \widehat{{\text{u}}^{\prime}}{\text{Z}}\left[ {\sum\limits_{{{\text{i}} = 1}}^{\text{N}} {{\text{Z}}^{\prime }_{{\rm i}} } \left( {\Delta {\hat{\text{u}}}_{{\rm i}} } \right)\left( {\Delta {\hat{\text{u}}}_{{\rm i}} } \right)^{\prime } {\text{Z}}_{{\rm i}} } \right]^{ - 1} {\text{Z}}^{\prime} \left( {\Delta {\hat{\text{u}}}} \right)\sim\upchi_{{_{{{\text{L}} - {\text{K}}}} }}^{ 2} $$
where L refers to the number of columns of Z and
\( \Delta \hat{u} \) denotes the residuals from a two-step estimation.
Under the assumption of no serial correlation in \( \upvarepsilon_{{\rm it}} \), \( \Delta\upvarepsilon_{{\rm it}} \) follow an MA(1) process and, the series yi,t-2, yi,t-3, …, yi,t-T are valid instruments for estimating this model. However, if \( \upvarepsilon_{{\rm it}} ' {\text{s}} \) are serially correlated, this series no longer constitutes a valid instrument set. This implies that one can test H0 or \( \varepsilon_{it} \) is serially uncorrelated against H1 by comparing the difference between Sargan and Hansen statistics corresponding to two instrument sets: Z0 contains the instruments defined by the series yi,t-2, yi,t-3, …, yi,t-T and Z1 is an instrument set not dependent on the assumption of \( \varepsilon_{it} \) not being serially correlated. Indeed, to increase the test’s power, one might be more specific for H1 and test H0 against H1 with the latter hypothesizing, denote the difference between the two Sargan and Hansen statistics by DQsh. Under the null this is distributed as \( \upchi_{{{\text{p}}_{ 0} - {\text{p}}_{ 1} }}^{ 2} \) where P0 and P1 are the number of instruments in Z0 and Z1, respectively.
3.4.2 Test for the Absence of Serial Correlation in ε
The existence of serial correlation in
\( \varepsilon_{it} \) will typically overthrow the use of lagged values and first differences of the endogenous variable as instruments. So, it is crucial to test for such serial correlation. Arellano and Bond [
2] proposed, that is made based on result of the model estimated in first differences.
Let
\( \Delta{\hat{\upvarepsilon}}\) be the vector of residuals from the model in first differences,
\( \Delta{\hat{\upvarepsilon}}_{ - 2} \), its second lag value, and
\(\Delta{\hat{\upvarepsilon}}^{*} \) the reduction of the vector
\(\Delta{\hat{\upvarepsilon}} \) allowing computation of the product
\(\Delta{\hat{\upvarepsilon}}_{ - 2}\Delta{\hat{\upvarepsilon}}^{*} \). This test provides a measure of the importance of serial correlation of order 2 once the model is written in first differences. If they
\( \upvarepsilon_{{\rm it}} ' {\text{s}} \) are serially uncorrelated given by
\( \Delta\upvarepsilon_{{\rm it}} =\upvarepsilon_{{\rm it}} -\upvarepsilon_{{{\text{i,t}} - 1}} \) follow an MA (1) process and thus, are not correlated at order 2. On the contrary, if
\( \Delta \varepsilon_{it} \) appears to be correlated of order two, one can infer that the disturbances
\( \varepsilon_{it} \) exhibit some serial correlation. The test statistics is given by:
$$ {\text{m}}_{ 2} = \Delta{\hat{\upvarepsilon}}^{'}_{ - 2}\Delta{\hat{\upvarepsilon}}^{*} /{\upxi^{ 1 / 2}} $$
The test is one-sided as it will exhibit positive serial correlation. As test statistic, \( {\text{m}}_{ 2} \) show that, under the null of no serial correlation in \( \Delta\upvarepsilon_{{\rm it}} \) at order 2. One rejects H0 of no serial correlation.