Dynamics of Output Growth and Convergence in the Middle East and North African Countries: Heterogeneous Panel ARDL Approach

Abstract

The present study investigates the convergence process of per-worker output for a panel of 15 countries in the Middle East and North African (MENA) region over the period 1970–2016. Further, the study discusses the dynamic impact of various productive factors (physical capital, human capital and total factor productivity) on per-worker output. In order to estimate the long-run relationship, the paper employs various dynamic panel autoregressive distributed lag (ARDL) models. The econometric approach controls for cointegration, nonstationarity, heterogeneity and cross-sectional dependence in the variables and residuals. The results suggest the presence of cross-sectional dependence and mixed order of integration of the variables. The statistical results of Pedroni and Westerlund cointegration tests indicate that per-worker output, physical capital stock, human capital stock and total factor productivity tend to have a long-run relationship. The four-step methodology adopted in the present study consistently accepts the conditional β-convergence towards steady state of output per worker. Besides, the paper finds a positive impact of physical capital and total factor productivity on long-run economic growth.

Appendices

Appendix 1

This section introduces the concepts of parameter heterogeneity, cross-sectional dependence, non-stationarity and cointegration in the panel framework. Parameter heterogeneity and cross-section dependence allows us to model differences in technology across countries; global shocks having differential impact across the countries and common (unobservable) factors to which individual countries react idiosyncratically.

Parameter Heterogeneity

In the long panel time series data, we can estimate separate regressions for each unit. Hence, the assumption of homogeneity (${\beta }_{i}=\upbeta \forall i=1,\dots ,N$ in Eq. 1, “Model Specification”) becomes implausible in long panels. Formally, heterogeneity is modelled by allowing all the parameters, ${\alpha }_{i} \mathrm{and} {\beta }_{i}$ (in Eq. 1, “Model Specification”) to vary across countries.

Cross-Sectional Dependency Tests

In the long panel, observations from individual countries are more likely than not to be correlated across the panel either by some spatial process or by effects of common factors, formally known as cross-sectional dependence. Presence of cross-section dependence affects inference and leads to biased estimates unless we account for it in our empirical model. This cross-correlation may arise as a result of global shocks (e.g. oil shock, global technological shock, spatial spill overs, world interest rates, and supply chains) and/or local shocks (countries reliant on exports of oil resources, trade networks and business cycles). We use the Pesaran (2004) CD test as a pre-estimation check on the variables or residuals to get an idea whether or not the data is cross-sectionally dependent. It calculates correlation coefficient (${\rho }_{ij}$) between time-series variable of the $i$ individual with the remaining $(j=i+1\dots . N)$ members in the panel. In our case of 15 countries, the test would calculate 15*14 correlations. Pesaran (2004)’s cross-section dependence test statistic is given as

$$CD=\sqrt{\frac{2}{N(N-1)}}\sum_{i=1}^{N-1}\sum_{j=i+1}^{N}\sqrt{{T}_{ij}}\widehat{ {\rho }_{ij}}$$

where N is the number of countries and ${T}_{ij}$ refers to the number of observation used in calculating the pairwise correlation between $i$ and $j=i+1\dots . N$ countries. The null hypothesis of the test assumes cross-section independence and is distributed as asymptotically standard normal. Pesaran (2004)’s CD test is found to be robust to structural break, non-stationarity and parameter heterogeneity.

Unit Root Tests

An important step in the formal analysis of long time series panel data is to determine the order of integration of the variables. Most of the macro-variables, such as per-worker GDP, indeed contain a unit root (Nelson & Plosser, 1982). The literature identifies two strands of panel unit root tests, namely first-generation and second-generation tests. These tests are based on the rationale of Dickey-Fuller and augmented Dickey-Fuller regressions, given by

$$\Delta {y}_{it}={\mu }_{i}+{\beta }_{i}t+\left({\rho }_{i}-1\right){y}_{i,t-1}+\sum_{i=1}^{k}{\pi }_{i}{\Delta y}_{it}+{u}_{it}$$

The subscript i on ${\mu }_{i}$, ${\beta }_{i}$ and ${\rho }_{i}$ makes it explicit that the time-series properties of the panel vary across the individual countries. The lag structure corrects for serial correlation in the errors. We use Maddala and Wu (1999) and Pesaran (2007) panel unit root tests. Maddala and Wu (1999) is an example of first-generation panel unit root test and assumes cross-section independence in data, whereas Pesaran (2007) is a second-generation test and allows for the presence of cross-section dependence. These tests run augmented Dickey-Fuller regressions one by one for each N countries to obtain an estimate of ${(\rho }_{i}-1)$. They, however, use different procedures for summarising that information into a single panel test statistic.¹³ Both of the tests examine the null hypothesis of nonstationary in all panel member series. The alternative hypothesis is stationarity in at least some country series (heterogeneity in autoregressive coefficients of the Dickey-Fuller regressions) and is more appropriate than the homogeneous alternative (stationarity in all the country series). If the variables are found to be nonstationary, then cointegration test (Engle & Granger, 1987) can be applied to test the long-run relationship between the variables. Engle and Granger test the time series properties of the residuals obtained from a regression of nonstationary variables using the (augmented) Dickey-Fuller test. The null hypothesis assumes that the residuals are nonstationary. Rejection of null indicates that the residuals are stationary, and the variable series are cointegrated.

Panel Cointegration Tests

After using panel unit root tests to determine the order of integration of the variables, panel cointegration tests are used to examine the tendency of convergence in output and its sources among a cross-section of MENA countries over time. Cointegration means the existence of a long-run relationship in the data. Panel cointegration testing can be divided into first- and second-generation procedures, where the former assumes cross-section independence, and the later relax that assumption. The residual-based tests by Kao (1999) and Pedroni (2004) are examples of first-generation residual-based cointegration tests, where the former assumes homogenous cointegration¹⁴ and the latter assumes heterogeneous cointegration. Westerlund (2007) is an example of second-generation error correction test that allows for heterogeneous cointegration as well. Pedroni (2004)’s cointegration test is based on residuals estimated from the possible cointegrating equation between nonstationary variables y and x (Eq. 1, “Model Specification”) under the null hypothesis of no cointegration:

$${\widehat{\varepsilon }}_{it}= \rho {\widehat{\varepsilon }}_{i,t-1}+{\upsilon }_{it}$$

Pedroni (2004) computes seven cointegration statistics with null of no cointegration in a heterogeneous mixed (I(0) and I(1) variables) panel framework.¹⁵ These tests can be divided into two groups on the basis of cointegrating residuals, ${\widehat{\varepsilon }}_{it}$. The first group includes four ‘panel statistic’ cointegration tests based on pooling along within dimension (pooling the AR coefficients across different countries of the panel for the unit-root test on the residuals). The second group, ‘group-mean statistic’ includes three tests based on pooling the ‘between’ dimension (averaging the AR coefficients for each member of the panel for the unit-root test on the residuals).

Westerlund (2007) proposed error correction-based cointegration test that corrects for cross-section dependence¹⁶ in the data. The approach involves the following error correction model of Eq. 1, “Model Specification”:

$$\Delta \left({y}_{it}\right)={\pi }_{i}+{\Psi }_{i}\left({y}_{i,t-1}- {{\beta }_{i}}^{\prime}{X}_{i, t-1}\right)+ {{\gamma }_{i}}^{\prime}\Delta {X}_{i, t}+{\mu }_{it}$$

(3)

where ${\Psi }_{i}$ is referred to as error (equilibrium) correction coefficient or speed of convergence. It indicates how fast the system returns to long-run equilibrium following a shock in the system. Westerlund (2007) developed four test statistics based on the assumption that ${\Psi }_{i}=0$. Two of these tests are group mean cointegration statistic (Gt and Ga) that investigates cointegration in atleast one unit, ${\Psi }_{i}<0 \mathrm{for at least one} i$. The other two tests are the panel cointegration statistics (Pt and Pa) that investigate cointegration for the entire panel, ${\Psi }_{i}<0 \mathrm {for all} i$. Westerlund test allows bootstrapping procedure in which cointegration tests can be repeated multiple times, which is meaningful in the presence of cross-section dependence.

Appendix 2

The panel ARDL model (p, q) of the long-run relationship between variables is given by (Pesaran 1999, 2004): (B-1)

$$\Delta lny_{it}=\beta_ilny_{i,t-1}+\theta{X^T}_{i,t}+{\textstyle\sum_{j=1}^{p_i-1}}\xi_{ij}\Delta y_{i,t-1}+{\textstyle\sum_{j=0}^{q_i-1}}\psi_{ij}\Delta{X^T}_{i,t}+\alpha_i+\varepsilon_{i,t}$$

where $X$ is a vector of explanatory variables, ${\upxi }_{\mathrm{ij}}$ and ${\uppsi }_{\mathrm{ij}}$ are the country-specific short-term coefficients. ${\alpha }_{i}$ captures country-specific effects and ${\varepsilon }_{i,t}$ is an error term. The value of ${\beta }_{i}<0$ shows the existence of long-run relationship between the variables. Three different panel ARDL estimators can be used to estimate model B-1, namely mean group (MG), pooled mean group (PMG) and dynamic fixed effect (DFE). Panel ARDL estimators provide estimates for both short- and long-run coefficients as well as an estimate of country-specific equilibrium correction term towards their own steady-state level of income. Based on Pesaran et al. (1999), re-parameterisation of the above model in error correction form is specified as follows:

$$\Delta ln{y}_{it}= {\lambda }_{it}\left({y}_{i,t-1}-{{\theta }_{t}X}_{it-1}\right)+ \sum_{j=1}^{{p}_{i}-1}{\xi }_{ij}\Delta {y}_{i,t-j}+\sum_{j=0}^{{q}_{i}-1}{{\psi }_{ij}}^{^{\prime}}\Delta {\mathrm{X}}_{i,t-j}+ {\alpha }_{i}+{\varepsilon }_{i,t}$$

where ${\lambda }_{it}$ is the error correction coefficient and is expected to be negative. ${\theta }_{t}$ is the vector of long-run coefficients. ${\xi }_{ij}$ and ${\psi }_{ij}$ are the short-run dynamic coefficient. The error correction coefficient measures the speed of short-run adjustment towards long-run equilibrium following an exogenous shock. The long-run or cointegration relationship between GDP and its regressors is inferred from the negative and statistically significant error correction term. This result can also be interpreted as evidence of β-convergence (Martín-Mayoral & Sastre, 2017; Wane, 2004).

Although MG and PMG estimators allow for heterogeneity in the slope coefficients, they may provide misleading results if the common factors are correlated across the countries. A method of allowing for the presence of common factors is based on Pesaran (2006) known as common correlated effects. This method uses cross-sectional averages of the dependent and independent variables computed from the entire panel to account for the presence of unobserved common factors:

$$\Delta ln{y}_{it}= {\lambda }_{it}\left({y}_{i,t-1}-{{\theta }_{t}X}_{it-1}\right)+ \sum_{j=1}^{{p}_{i}-1}{\xi }_{ij}\Delta {y}_{i,t-j}+\sum_{j=0}^{{q}_{i}-1}{{\psi }_{ij}}^{^{\prime}}\Delta {\mathrm{X}}_{i,t-j}+ {\alpha }_{i}+{d}_{t}^{^{\prime}}\stackrel{-}{{Z}_{t}}+{\varepsilon }_{i,t}$$

where $\stackrel{-}{{Z}_{t}}=(\stackrel{-}{{y}_{t}}, \stackrel{-}{{X}_{t}}$), with $\stackrel{-}{{y}_{t}}$ and $\stackrel{-}{{X}_{t}}$ are the cross-country averages of the dependent and independent regressors. (See Table 9).

Appendix 3

Table 7 First-generation panel unit root test without trend

Table 8 First-generation panel unit root test with trend

Table 9 Hausman test on the MG and PMG models

Table 10 Country-specific parameters and speed of conditional convergence