*4.2. Cointegration Test*

Cointegration is a powerful way of detecting the presence of long-run relationships or steady-state equilibrium between variables [31]. Different cointegration techniques were developed to determine the long-run relationships between the time series [32–34]. In all these cointegration techniques, the most important restriction is that all the series must be of the same ordered integrations. However, a recently developed cointegration approach, namely the autoregressive-distributed lag (ARDL), also known as the bounds test, eliminates this restriction [35]. The ARDL approach allows the regressors to be stationary in levels (I (0)) or the first-differenced (I (1)). Owing to this convenience, the ARDL method has been used in many empirical works, and it was also used to obtain the long-run relationship among the series in this study. The long-run ARDL equation was specified as follows:

$$\begin{aligned} \ln \exp\_t &= \beta\_0 + \sum\_{i=0}^m \beta\_{1i} \ln \exp\_{t-1-i} + \sum\_{i=0}^n \beta\_{2i} \ln ER\_{t-i} + \sum\_{i=0}^o \beta\_{3i} \ln RDGP\_{t-i} + \sum\_{i=0}^p \beta\_{4i} \ln FDI\_{t-i} \\ \sum\_{i=0}^q \beta\_{5i} \ln FGDP\_{t-i} + \sum\_{i=0}^r \beta\_{6i} \ln Price\_{t-i} + \sum\_{i=0}^r \beta\_{8i} \ln RIR\_{t-i} + \omega DLI\_t(T\_b) + \varepsilon\_t \end{aligned} \tag{1}$$

where exp: represents horticultural exports, FDI: foreign direct investment, ER: real effective exchange rate, RGDP: real GDP of Ethiopia, FGDP: foreign GDP, Price: world average price of fresh fruits and vegetables, DUt: Dummy variable representing the Structural break (*Tb* (break year) = 2005 in this case), and RIR: real interest rate.

The F-test was employed to test co-integration among the variables, where the null hypothesis that the betas were jointly equal to zero (i.e., *β*<sup>1</sup> = *β*<sup>2</sup> = *β*<sup>3</sup> = *β*<sup>4</sup> = *β*<sup>5</sup> = *β*<sup>6</sup> = *β*<sup>7</sup> = *β*<sup>8</sup> = 0) was tested. Reference [32] provided critical *F*-values; one for the lower bound and the other for the upper bound,

for testing whether there was co-integration. If the computed *F*-value was less than the *F*-value for the lower bound, then the null hypothesis cannot be rejected. If the computed *F*-value exceeded the *F*-value for the upper bound, then the null hypothesis of no co-integration was rejected, otherwise the test was inconclusive.

To select the lag values *m*, *n*, *o*, *p*, *q,* and *r* in Equation (1), model selection criteria, such as AIC, SIC, Hannan-Quinn information criteria, Adjusted R-squared were used. The short-run dynamics of the variables was described by employing the Error Correction Model (ECM) [24]. The ECM representation was specified as follows:

<sup>Δ</sup> ln exp <sup>=</sup> *<sup>α</sup>*<sup>0</sup> <sup>+</sup> *<sup>m</sup>* ∑ *i*=0 *<sup>λ</sup>i*<sup>Δ</sup> ln exp*t*−1−*<sup>i</sup>* <sup>+</sup> <sup>0</sup> ∑ *i*=0 *<sup>ϕ</sup>i*<sup>Δ</sup> ln *ERt*−*<sup>i</sup>* <sup>+</sup> *<sup>n</sup>* ∑ *i*=0 *<sup>θ</sup>i*<sup>Δ</sup> ln *RGDPt*−*<sup>i</sup>* <sup>+</sup> *<sup>n</sup>* ∑ *i*=0 *γi*Δ ln *FDIt*−*i*+ *p* ∑ *i*=0 *ψi*Δ ln *FGDPt*−*<sup>i</sup>* + *q* ∑ *i*=0 *ηi*Δ ln *RIRt*−*<sup>i</sup>* + ∑ *∂*Δ Pr*icet*−*i*+*ω*Δ*DUt*(*Tb*) + *λECMt*−<sup>1</sup> + *ε<sup>t</sup>* (2)

The coefficient of the *ECMt*−1, *λ* in Equation (2) shows the speed of adjustment of a parameter, indicating how quickly the series can come back to its long-run equilibrium. The sign of the coefficient must be negative and significant. Diagnostic tests which include serial correlation and heteroscedasticity tests were conducted to ensure the acceptability of the model. In addition, cumulative sum (CUSUM), the cumulative sum of squares (CUSUMQ), and recursive coefficient estimates were also applied to the series to assess stability of the coefficients and this was illustrated using graphics.

## *4.3. Independent Variables Included in the Model and their Expected Signs*

Foreign direct investment (FDI): It was defined as new investment made by foreign investors in horticultural sub-sectors. The results of the reviewed literature show varied results with regards to the impact of FDI on export performance. However, in Ethiopia, the government have given due attention to attract foreign investors into this potential sub-sector. Consequently, the expected sign of FDI in this study was expected to be positive.

ER: the real effective exchange rate was defined as the product of the nominal effective exchange rate and domestic consumer price index divided by the foreign consumer price index. An increase in the real effective exchange rate (depreciation) makes the exports cheap in the international market, thereby increasing the exports of the country. The opposite happens when it increases. Consequently, in this study, the expected sign of the real effective exchange rate was positive.

FGDP: Foreign GDP was defined as the average real GDPs of the major importers of horticultural crops. Diversification of both commodities exported and importing countries were considered by many as an important means of improving export performance in developing economies. Consequently, foreign income was hypothesized to influence horticulture export performance positively.

RIR: Real interest rate was defined as the nominal lending rate adjusted for inflation. The higher the interest rate, the lower the investment in production of horticultural crops and the less will be the volume of exports. Consequently, a negative relationship was expected between horticultural exports and the real interest rate.

RGDP: It was defined as the real GDP of the exporting country which was Ethiopia in this case. The higher the real GDP of the country, the higher will be its export performance. Consequently, real GDP of the exporting country was expected to influence export performance positively.

PRICE: It was the average world price of fresh fruits and vegetables (dollars/kg) sourced from the World Bank and FAO statistics. It was hypothesized to have positive effects on horticultural export performance, since increases in output prices will lead to increased revenues.

BREAK: This was a dummy variable included in the model to capture the impact of the structural break that occurred in 2005. It was expected to have a positive impact on the export performance of the horticultural sub-sectors.
