Applied Economics Letters, 2006, 13, 1003–1008

Is per capita real GDP stationary in African countries? Evidence from panel SURADF test

Tsangyao Changa,*, Hsu-Ling Changb, Hsiao-Ping Chuc and Chi-Wei Sud aDepartment of Finance, , , bDepartment of Accounting and Information Technology, Ling Tung University, Taichung, Taiwan cDepartment of Business Administration, Ling Tung University, Taichung, Taiwan dDepartment of Finance, , Taichung, Taiwan

This note uses the newly developed panel SURADF tests advanced by Breuer et al. (2001) to investigate the time-series properties of real GDP for 47 African countries for the period 1980 to 2004. While the other Panel-based unit root tests are joint tests of a unit root for all members of the panel and are incapable of determining the mix of I(0) and I(1) series in the panel setting, the Panel SURADF tests a separate unit-root null hypothesis for each individual panel member and, therefore identifies how many and which series in the panel are stationary processes. The empirical results from several panel-based unit root tests indicate that the per capita real GDP for all the countries studied are non-stationary, however, when Breuer et al.’s Panel SURADF tests are conducted, one finds unit root in per capita real GDP only exist in two-third of countries studied. These results have important policy implications for African countries.

I. Introduction making, modelling, testing and forecasting. Studies on this issue are of concern not only to empirical Ever since Nelson and Plosser (1982) published their researchers but also policymakers. seminal work, various studies have been devoted to While numerous studies support a unit root in real investigating the potential non-stationarity of impor- output levels, critics have claimed that the drawing of tant macroeconomic variables. Researchers have such conclusions may be attributed to the lower been especially interested in the time-series properties power of the conventional unit root tests employed. of real output levels. As pointed out by Nelson and More recently, it has been reported that conventional Plosser, the modelling of real output levels as either unit root tests not only fail to consider information a trend stationary or a difference stationary process across regions, thereby leading to less efficient has important implications for macroeconomic policy estimations, but also have lower power when

*Corresponding author. E-mail: [email protected]

Applied Economics Letters ISSN 1350–4851 print/ISSN 1466–4291 online ß 2006 Taylor & Francis 1003 http://www.tandf.co.uk/journals DOI: 10.1080/13504850500425881 1004 T. Chang et al.

Table 1. Summary statistics of real gross domestic product per capita

Country (US dollar) Mean Std Max. Min. Skewness Kurtosis J-B Algeria 2035.897 381.422 2753.697 1499.143 0.518 1.498 3.469 Angola 497.549 538.762 1189.953 363.506 0.191 1.092 3.944 Benin 300.673 102.918 581.233 178.336 0.779 3.136 2.546 Botswana 2313.439 680.007 3572.989 1272.046 0.212 1.978 1.274 Burkina Faso 256.590 68.339 388.669 178.041 0.614 2.070 2.471 Burundi 175.549 120.816 371.072 23.367 0.164 1.595 2.168 Cameroon 774.224 332.512 1343.355 345.756 0.124 1.566 2.206 Cape Verde 879.951 138.754 1240.351 653.064 1.032 4.033 5.545* Central African Republic 338.491 148.081 680.999 161.469 0.425 2.198 1.424 Chad 195.618 63.145 316.784 112.137 0.479 1.828 2.386 Comoros 411.015 120.596 721.4585 244.951 0.570 2.789 1.402 Congo, Republic of 769.195 299.048 1282.790 415.787 0.550 1.797 2.768 Coˆte d’Ivoire 1201.525 562.539 2729.909 550.948 0.772 3.221 2.532 Djibouti 722.763 182.969 974.7221 502.455 0.054 1.367 2.788 Equatorial Guinea 236.526 182.602 808.950 89.908 1.939 5.941 24.675*** Ethiopia 79.659 43.4106 131.701 28.572 0.045 1.116 3.704 Gabon 4346.859 1662.414 8554.497 2154.364 0.592 2.713 1.545 Gambia, The 486.039 439.192 1635.512 90.918 1.454 3.747 9.387*** Ghana 711.827 734.978 2984.895 271.557 4.497 2.335 33.903*** Guinea 918.228 1142.041 4231.459 137.319 1.832 5.228 19.153*** Guinea-Bissau 180.305 73.212 335.528 81.995 0.297 1.957 1.500 Kenya 333.481 261.302 1034.231 96.826 1.073 3.411 4.968* Lesotho 363.363 236.658 1012.594 110.362 1.352 4.140 8.971*** Madagascar 179.399 243.841 1005.623 15.305 2.069 6.819 33.039*** Malawi 206.078 220.511 772.170 5.524 1.069 3.204 4.807* Mali 231.828 76.581 417.832 134.539 0.635 2.398 2.056 Mauritania 325.860 164.159 662.988 127.336 0.494 2.219 1.652 Mauritius 2451.358 359.508 3539.317 1711.967 0.746 4.888 6.029** Morocco 525.732 113.615 973.546 396.456 2.652 10.922 94.670*** Mozambique 1264.538 2012.412 5814.852 12.0382 1.266 3.009 6.677** Namibia 2635.201 2491.935 10 697.51 559.390 1.972 6.237 27.113*** Niger 234.053 116.218 574.534 105.240 1.039 3.981 5.501* Nigeria 661.764 1100.186 3991.718 21.536 1.989 5.783 24.543*** Rwanda 220.151 144.776 437.481 48.952 0.114 1.343 2.913 Sa˜o Tome´and Prı´ncipe 793.407 965.308 2601.297 7.055 0.767 1.882 3.751 Senegal 563.376 204.657 1065.590 318.445 0.494 2.350 1.456 Seychelles 5260.307 1503.335 7236.928 2959.876 0.359 1.566 2.681 Sierra Leone 242.423 87.477 412.0230 132.253 1.808 4.698 16.619*** South Africa 6462.024 5457.954 21045.53 1389.232 1.456 4.116 10.132*** Sudan 100.571 163.942 687.869 123.579 2.194 7.798 44.031*** Swaziland 1041.070 603.715 2471.466 305.989 1.055 3.409 4.809* Tanzania 886.439 1346.512 3934.956 35.241 1.363 3.267 7.809** Togo 322.239 155.899 751.911 137.682 0.788 3.255 2.654 Tunisia 1615.540 370.336 2944.431 1294.548 2.439 8.624 57.752*** Uganda 314.9610 80.587 546.667 135.638 2.446 7.643 47.379*** Zambia 3943.519 7183.844 677.150 260.170 1.742 4.508 15.011*** Zimbabwe 873.905 983.927 1881.997 497.806 1.149 3.203 5.538* Notes: Std denotes standard deviation and J-B denotes the Jarque–Bera test for normality. ***, **, and * indicate significance at the 0.01, 0.05 and 0.1 levels, respectively. GDP in African countries 1005 compared with near-unit-root but stationary alter- results meanwhile indicate that the per capita real natives. It is not surprising that these factors have GDP datasets for more than half of the 47 African cast considerable doubt on many of the earlier countries are not approximately normal. findings that have been based on a unit root in real output levels. A feasible way for increasing the power when testing unit root is to suggest that panel data have III. Panel Unit Root Methodology and been used. Taylor and Sarno (1998), Breuer et al. Empirical Results (2001), Taylor (2003) and Taylor and Taylor (2004) showed that the recent methodological refinements of Breuer et al.’s seemingly unrelated regressions aug- the Levin-Lin test fail to fully address the ‘all- mented Dickey–Fuller test (SURADF). Breuer et al. or-nothing’ nature of the test. Because they are joint (2001) claimed that, by analogy to simple regression, tests of the null hypothesis, they are not informative when an F-statistic rejects the null that a vector of with regard to the number of series that are stationary coefficients is equal to zero, it does not follow that processes when the null hypothesis is rejected. Breuer each coefficient is nonzero. Similarly, when the unit- et al. (2001) further claimed that, by analogy to root null hypothesis is rejected, it may be erroneous simple regression, when an F-statistic rejects the null to conclude that all series in the panel are stationary. that a vector of coefficients is equal to zero, it does To avoid the problem, Breuer et al. (2001) introduced not follow that each coefficient is nonzero. Similarly, the ‘seemingly unrelated regressions augmented when the unit-root null hypothesis is rejected, it may Dickey–Fuller’ (SURADF) test, which is an augmen- be erroneous to conclude that all series in the panel ted Dickey–Fuller test based on the panel estimation are stationary. method of seemingly unrelated regression (SUR). The This empirical note contributes to this line of system of the ADF equations that is estimated here is: research by determining whether or not the unit root Xk1 process is characteristic of the African real output X1, t ¼ 1 þ 1X1, t1 þ t þ 1, jX1, tj þ "1, t levels. This study, tests the non-stationarity of per j¼1 capita real GDP of 47 African countries by using the t ¼ 1, 2, ..., T panel SURADF unit root tests of Breuer et al. (2001). Xk2 The present paper is the first to our knowledge to X2, t ¼ 2 þ 2X2, t1 þ t þ 2, jX2, tj þ "2, t examine the non-stationary in real output levels for j¼1 African countries. t ¼ 1, 2, ..., T The remainder of this empirical study is organized as follows. Section II presents the data used. XkN Section III first describes the methodology employed, XN, t ¼ N þ NXN, t1 þ t þ N, jXN, tj þ "N, t then discusses the empirical findings and policy j¼1 t ¼ 1, 2, ..., T implications. Section IV concludes. ð1Þ The N null and alternative hypotheses are tested individually:

II. Data 1 1 H0: 1 ¼ 0; HA: 1 < 0 2 2 This empirical study uses annual per capita real GDP H0: 2 ¼ 0; HA: 2 < 0 for 47 African countries over the 1980 to 2004 period. ... The source of the data is the World Economic Outlook N N H : N ¼ 0; H : N < 0 Database, and summary statistics are provided in 0 A Table 1. The per capita real GDP datasets indicate that with test statistics computed from the SUR estimates South Africa and Sudan have the highest and lowest of system 1. As Breuer et al. (2001) showed the average per capita incomes of US$6462.024 imposition of an identical lag structure across panel and US$100.571, respectively. The Jarque–Bera test members could bias test statistics, the lag structures 1006 T. Chang et al.

Table 2. Panel unit root test results

Critical value

Method Statistics P-value 1% 5% 10% Levin, Lin & Chu 11.18 0.2142 14.89 14.24 13.96 IPS ’t 0.7367 0.7694 9.282 6.536 5.396 ’LM 0.2282 0.4097 4.064 2.487 1.549 MW-Fisher Chi-square 80.945 0.8291 125.671 156.893 176.406 Hardi (homo) 9.346* 4.529e-21 15.018 10.019 7.629 Hardi (het) 7.068* 7.836e-013 9.933 7.111 5.731

Notes: ***, **, and * indicate significance at the 0.01, 0.05 and 0.1 levels, respectively. Critical values are based on Monte Carlo Simulations using 10 000 replications.

for each equation are selected based on the approach for most of the provinces studied. Chang et al. adopted by Perron (1989). (forthcoming) also found stationary results in real The major difference between the SURADF outputs for more than half of the 25 Chinese and other panel unit tests derives from the provinces in their study, using more powerful non- formulation of the null hypothesis. While the linear (logistic) unit root tests. The results are also others are joint tests of a unit root for all inconsistent with those of Fleissig and Strauss (1999) members of the panel, the SURADF tests a who found per capita real GDP for OECD countries separate unit-root null hypothesis for each indi- to be trend stationary, using three different panel- vidual panel member and, therefore, identifies how based unit root tests. The results, nevertheless, are many and which of the series in the panel are consistent with those of Cheung and Chinn (1996), stationary processes. Cheung and Westermann (2002) and Rapach (2002), which support the notion of non-stationarity in real Empirical results GDP for various panels of OECD countries. A major policy implication of the present study For comparison, several panel-based unit root tests is that a stabilization policy may have some are first applied to examine the null of a unit root in permanent effects on the output level of most of the the per capita real GDP. Critical values based on African countries studied here. However, it needs to Monte Carlo Simulations using 10 000 replications be asked exactly what are the most effective policies? for each test are reported in Table 2. The results in To answer this question, the underlying reasons Table 2 clearly indicate that the Levin–Lin–Chu first need to be identified, but as this is beyond the (Levin et al., 2002), Im–Pesaran–Shin (Im et al., 2003) scope of this paper, it will be investigated in a future and MW (Maddala and Wu, 1999) tests all fail to study. reject the null of non-stationary per capita real GDP for all 47 countries. The Hardi (2001) test also yields the same results. Table 3 presents Breuer et al.’s (2001) Panel SURADF test results, which indicates a unit root in IV. Conclusions real output levels holds true for only two-third countries studied here. The estimated 1%, 5% and This empirical note employed Breuer et al.’s (2001) 10% critical values, obtained from simulations based Panel SURADF unit tests to assess the non- on 25 observations for each series and 10 000 stationarity properties of per capita real GDP from replications using the lag and covariance structure 47 African countries over the 1980 to 2004 period. from the panel of per capita real GDP data series for Breuer et al.’s (2001) Panel SURADF tests indicate each of the 47 panel members are also reported a unit root in real output levels is supported for only in Table 3. two-third of countries studied here. It is worth noting that the results here are not Finally, as far as major policies are concerned, consistent with those of Smyth (2003) which, based the study implies that a fiscal and/or monetary on the datasets for 24 Chinese provinces using the stabilization policy would possibly permanently different panel-based unit root tests of Im–Pesaran– affect the real output levels of most African countries Shin, support the stationarity in per capita real GDP under study. GDP in African countries 1007

Table 3. SURADF tests and critical values

Critical values

Country panel label SURADF 1% 5% 10% Algeria 1.8461 3.7424 3.1654 2.8518 Angola 0.6857 3.3845 2.8299 2.5464 Benin 3.5299* 4.3042 3.7042 3.4036 Botswana 1.6604 3.6443 2.9947 2.7027 Burkina Faso 4.0323** 4.2948 3.7580 3.4334 Burundi 1.9519 3.3665 2.8301 2.5358 Cameroon 1.8657 4.2056 3.6128 3.3232 Cape Verde 3.4042** 3.8999 3.2416 2.8688 Central African Republic 2.8179 4.6870 4.1690 3.8726 Chad 2.2012 4.6775 4.0888 3.7684 Comoros 1.9117 4.8224 4.2767 3.9813 Congo, Republic of 2.0541 4.7639 4.1940 3.8872 Coˆte d’Ivoire 2.9018 4.9451 4.3846 4.0711 Djibouti 2.0624 3.4994 2.8699 2.5405 Equatorial Guinea 1.0717 3.6473 3.0978 2.8209 Ethiopia 0.0200 3.4933 2.9272 2.6533 Gabon 1.1738 3.8301 3.2692 2.9783 Gambia, The 1.2036 3.5285 2.9336 2.6302 Ghana 6.6624*** 3.6026 3.0164 2.7181 Guinea 3.4050*** 3.3998 2.8415 2.5348 Guinea-Bissau 1.7496 3.9097 3.3479 3.0286 Kenya 1.6358 3.4237 2.8507 2.5666 Lesotho 2.1219 3.4997 2.9461 2.6594 Madagascar 2.4090 3.5623 3.0188 2.7174 Malawi 0.1609 3.6636 3.1193 2.8255 Mali 2.6453 4.0729 3.5184 3.2036 Mauritania 0.5715 3.3307 2.8093 2.5197 Mauritius 2.7641 3.7035 3.1127 2.7894 Morocco 4.0072*** 3.7102 3.1325 2.8056 Mozambique 2.9274 4.4626 3.4626 3.1333 Namibia 2.2826 3.7698 3.1888 2.9067 Niger 3.6408* 4.2530 3.6429 3.3267 Nigeria 3.0406** 3.3631 2.8096 2.5246 Rwanda 0.2970 3.6220 3.0619 2.7454 Sa˜o Tome´and Prı´ncipe 1.1928 3.6613 3.0377 2.7356 Senegal 3.2870* 4.1724 3.5259 3.2291 Seychelles 1.0098 3.7099 3.1451 2.8470 Sierra Leone 3.3452** 3.7141 3.0935 2.7923 South Africa 3.9199** 4.2426 3.6426 3.3370 Sudan 1.0049 3.4259 2.8184 2.5209 Swaziland 2.9027 4.3046 3.7321 3.4147 Tanzania 3.1673** 3.5979 3.0109 2.6791 Togo 2.0279 3.7865 3.1541 2.8323 Tunisia 6.0770*** 3.6718 3.1245 2.8126 Uganda 3.7725*** 3.4116 2.8225 2.5172 Zambia 1.8739 3.3014 2.7687 2.4635 Zimbabwe 3.1141** 3.5127 2.9228 2.6352 Notes: ***, **, and * indicate significance at the 0.01, 0.05 and 0.1 levels, respectively. Critical values are calculated by Monte Carlo simulation with 10 000 draws, tailored to the present sample size. (For details of this simulation, see Breuer et al., 2001). Bold text indicates statistical significance.

Acknowledgements would not have been done in the first place. The authors are grateful to Professor Myles S. The authors also thank an anonymous referee and Wallace and Dr Carrion-i-Silvestre who kindly the editor Professor Mark Taylor for their several provided the RATS and GAUSS program codes, helpful comments, suggestions and time spent in respectively. Without their contributions, this paper reading this paper. These all make this paper more 1008 T. Chang et al. valuable and readable. Any errors that remain are Levin, A., Lin, C. F. and Chu, C.-S. (2002) Unit root in our own. panel data: asymptotic and finite-sample properties, Journal of Econometrics, 108, 1–24. Maddala, G. S. and Wu, S. (1999) A comparative study of unit root tests with panel data and a new simple test, References Oxford Bulletin of Economics & Statistics, 61, 631–52. Breuer, J. B., McNown, R. and Wallace, M. S. (2001) Nelson, C. and Plosser, C. (1982) Trends and random walks Misleading inferences from panel unit-root tests with in macroeconomic time Series, Journal of Monetary an illustration from purchasing power parity, Review Economics, 10, 139–62. of International Economics, 9, 482–93. Perron, P. (1989) The great crash, the oil price shock Chang, T., Ho, Y.-H. and Caudill, S. B. (forthcoming) Is and the unit root hypothesis, Econometrica, 57, per capita real GDP stationary in China? More 1361–401. powerful nonlinear (logistic) unit root tests, Applied Rapach, D. E. (2002) Are real GDP levels nonstationary? Financial Economics Letters. Evidence from panel data tests, Southern Economic Cheung, Y. W. and Chinn, D. (1996) Deterministic, Journal, 68, 473–95. stochastic and segmented trends in aggregate output: Smyth, R. (2003) Is there a unit root in per capita real a cross-country analysis, Oxford Economic Papers, 48, GDP? Panel data evidence from Chinese provinces, 134–62. Asian Profile, 31, 289–94. Cheung, Y. W. and Westermann, F. (2002) Output Taylor, A. M. and Taylor, M. P. (2004) The purchasing dynamics of the G7 countries – stochastic trends and power parity debate, Journal of Economic Perspectives, cyclical movements, Applied Economics, 34, 2239–47. 18, 135–58. Fleissig, A. R. and Strauss, J. (1999) Is OECD real per Taylor, M. and Sarno, L. (1998) The behavior of real capita GDP trend or difference stationary? Evidence exchanges during the post-Bretton Woods period, from panel unit root test, Journal of Macroeconomics, Journal of International Economics, 46, 281–312. 21, 673–90. Taylor, M. P. (2003) Purchasing power parity, Review of Hardi, K. (2001) Testing for stationarity in heterogeneous International Economics, 11, 436–52. panel data, Econometrics Journal, 3, 148–61. Zellner, A. (1962) An efficient method of estimating Im, K. S., Pesaran, M. H. and Shin, Y. (2003) Testing for seemingly unrelated regressions and tests for aggrega- unit roots in heterogeneous panels, Journal of tion bias, Journal of the American Statistical Econometrics, 115, 53–74. Association, 57, 348–68.