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Testing economic convergence in non-stationary panel

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Abstract

This paper emphasizes the role of Panel Analysis of Nonstationarity in the Idiosyncratic and Common components (PANIC) in purging effects of cross-country correlation and structural instability from the convergence equation. In doing so, we run some simulations to show that, in addition to controlling correlations, PANIC handles the presence of a single structural change naturally and then solves the problems of low power that it generates. Applications are also conducted using a sample of 20 OECD member countries and 20 countries in Sub-Saharan Africa.

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Notes

  1. Equation (1) is an implication of the neoclassical growth model. This prediction can be written: \(\frac{1}{T}\ln \left( {{{y}_{i,T}}}/{{{y}_{i,0}}}\; \right) =\kappa -T^{-1}\left( 1-{{e}^{-\theta T}} \right) \ln \left( {{y}_{i,0}} \right) +\varphi {{\Xi }_{i}}+{{\xi }_{i}}\) where we use \(\beta \) to denote \(-T^{-1}\left( 1-{{e}^{-\theta T}} \right) \), and keep only essential details. Interpret the right hand side of (1) as the long-run per capita GDP growth rate and \(\theta \) as the rate of convergence. So, \( \theta \) is the proportionate change in growth rate caused by change in initial per capita GDP. Thus, poor and rich economies appear to be converging towards each other at a uniform rate of \(\theta \) per year. Using \(-T^{-1}\left( 1-{{e}^{-\theta T}} \right) \,\,\Rightarrow \,\,\left( 1+\beta T \right) ={{e}^{-\theta T}}\), we can retrieve the convergence speed \(\theta =-{{T}^{-1}}\ln \left( 1+\beta T \right) \).

  2. This equation shows the link between the cross-section and panel specifications. \( \lambda \) is a convergence parameter that we will define in the next section.

  3. Notice that \( P_a \) and \( P_b \) converge to normal laws if the kernel functions and truncation parameter q satisfy the kernel conditions defined in Moon and Perron (2004). Moon and Perron use a Quadratic-Spectral kernel-type function: \(\omega ({{q}_{i}},j)=\frac{25}{12{{\pi }^{2}}{{w}^{2}}}\left[ \frac{\sin (6\pi w/5)}{6\pi w/5}-\cos \left( \frac{6\pi w}{5} \right) \right] \) with \(w=\frac{j}{{{q}_{i}}}\). \(q_i\) is the optimal truncation parameter of unit i . It is defined as \({{q}_{i}}=1.3221{{\left( {4\hat{\psi }_{i,1}^{2}{{T}_{i}}}/{{{\left( 1-{{{\hat{\psi }}}_{i,1}} \right) }^{4}}}\; \right) }^{1/5}}\) with \({{\hat{\psi }}_{i,1}}\) the estimator of the first order autocorrelation of \({{\hat{\varepsilon }}_{it}}\).

  4. Program realized by the authors. We thank Christophe Hurlin, Serena Ng and Pierre Perron for making available the additional codes used to develop programs of both experiments.

  5. In the application of the PANIC procedure, we have nevertheless retained the model (10) for this group of countries.

  6. Please notice that the pooled statistic of the idiosyncratic component \(P_{\hat{e},\textit{Choi}}^c\) is standardized from the standardization procedure of Choi (2001).

  7. In this work, we call the third generation of tests those which take into account both the economic interdependence and structural change.

  8. Following Evans and Karras (1996) we take for granted that \( \lambda \ge 1 \).

  9. The data used by Gaulier et al. (1999) are from the Summers and Heston database.

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Authors and Affiliations

  1. Department of Economics and Management, University of Ziguinchor, BP 523, Ziguinchor, Senegal

    Abdou-Aziz Niang

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  1. Abdou-Aziz Niang
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Correspondence to Abdou-Aziz Niang.

Appendix

Appendix

See Tables 6, 7, 8 and 9.

Table 6 Average number of estimated factors in the simulations
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Table 7 Structural change tests
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Table 8 Cross-section dependence (CD) test
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Table 9 Individual CADF tests
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Niang, AA. Testing economic convergence in non-stationary panel. Stat Methods Appl 26, 135–156 (2017). https://doi.org/10.1007/s10260-016-0361-z

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