Unemployment Hysteresis in Transition Countries: Evidence using Stationarity Panel Tests with Breaks

Unemployment Hysteresis in Transitions Countries: Evidence from using stationarity panel tests with breaks Mariam Camarero Department of Economics Jaume I University Josep Lluís Carrion-i-Silvestrey Anàlisi Quantitativa Regional (AQR) Research Group Department of Econometrics, Statistics and Spanish Economy University of Barcelona Cecilio Tamarit Department of Applied Economics II University of Valencia April 5, 2005 Abstract This paper tests hysteresis e¤ects in unemployment using panel data for Transition Countries covering the period 1992:1-2003:11. The tests exploit the crosssection variations of the series, and additionally, allow for a di¤erent number of endogenous breakpoints in the unemployment series. The critical values are simulated based on our speci…c panel sizes and time periods. The …ndings stress the importance of accounting for exogenous shocks in the series and give support to the natural-rate hypothesis of unemployment for the majority of the countries analyzed. Key words: Hysteresis, panel unit root tests, structural break. JEL classi…cation: C22, C23, J64. M. Camarero and C. Tamarit gratefully acknowledge the …nancial support from Project SEC200203651 (CICYT) and INTECO Research Group 03-151 AVCiT. J. Ll. Carrion-i-Silvestre acknowledges the …nancial support from Project SEJ2004-05052-ECON. yCorresponding author: AQR Research Group. Department of Econometrics, Statistics and Spanish Economy. University of Barcelona. Av. Diagonal, 690. 08034 Barcelona. Tel: +34 934021826; Fax: +34 934021821; e-mail: [email protected] 1 1 Introduction Enlargement is one of the most important challenges in the European Union (EU) agenda. The accession countries included in the enlargement process at present consist of ten Central and Eastern European Countries (CEECs), as well as Cyprus, Malta and Turkey. Since 1989, the process of transition has proceeded at a rapid pace. However, only eight out of the ten CEECs have ful…lled the so-called Copenhagen criteria set up in June 1993, and consequently, Bulgaria and Romania have been excluded from the May 2004 enlargement. Focusing on the evolution of the labor markets, employment fell considerably in the CEECs during the transitional contraction period and continued to decline since then, despite transitory improvements in the economic growth pace from the middle of the nineties. Besides, there was a decrease in participation rates, which fell from the high levels typical of socialist economies. Unemployment exploded in the early transition years having a striking e¤ect on poverty and social exclusion –see [?]. Since 1994, measured unemployment, based on labor market surveys following the ILO methodology1, …rst decreased slightly below 10 per cent but increased again. However, in relative contrast to the overall pace of structural change in the transition countries, labor markets are characterized by very low mobility of workers across labor market strata, occupation and sectors ([?] and [?]). The macroeconomic stabilization measures that these countries had to accomplish in order to meet the requirements for joining the EU, such as budgetary consolidations or in‡ation and exchange rate stabilizations are likely to have caused important shocks to output, prices and unemployment. Thus, unemployment is one of the key variables to facilitate the adjustment process through macroeconomic equilibrium. Moreover, with irrevocably …xed exchange rates, country-speci…c monetary conditions can no longer cush1The de…nition of and measurement of unemployment are neither very precise nor uniform among countries, so that a cross-country comparison of unemployment rates requires some adjustment to transform national measures into a reasonably standardized indicator. The standardized unemployment rates, which are based on labor market surveys, greatly improve comparability among countries. This measure, though, has some limitations as a measure of labor market slack, since it excludes discouraged workers, part-time employment, early retirement, government training and employment schemes and invalidity or disability schemes. 2 ion di¤erences in cyclical positions nor help them to adjust to asymmetric shocks. Within a prospective enlarged euro area, if required, real exchange rate changes will have to be achieved by real wage changes directly, rather than indirectly via changes in the nominal exchange rate. The large rates of structural unemployment and the high regional concentration of unemployment suggest that labor market ‡exibility is not currently up to this requirement and, therefore, more geographic mobility would be needed (and expected). In the prospect of euro-area membership, the ful…llment of the Maastricht criteria will imply in‡ation rates in line with the 2% European Central Bank rate. Due to the real adjustment process involved, further employment destruction may be expected. In order to implement EU level policy measures to address the social problems associated, knowledge about the structural rate of unemployment and its shifting nature may be crucial for policy makers ([?]). From a theoretical point of view, we can distinguish two main hypotheses relating unemployment and shocks. The …rst one, the so-called “natural”rate of unemployment or NAIRU. The concept of structural or “natural” rate of unemployment was …rst introduced by [?] and [?]. According to this approach, in the long-run the structural rate of unemployment is reached and hence there is no long-term trade-o¤ between in‡ation and unemployment. However, in the short-term the Phillips Curve exists. From a statistical point of view, unemployment would be characterized as a mean reverting process, which means that the unemployment rate tends to revert to its equilibrium in the long run. According to the structuralist school the natural rate is endogenous and a¤ected by market forces like any other economic variable (Pissarides, 1990, Layard et al., 1991) giving rise to autonomous movements of the natural rate due to changes either in real macroeconomic variables as real interest rates (Blanchard, 1999), rate of productivity growth (Pissarides, 1990), oil prices (Oswald, 1999) and stock prices (Phelps, 1999) or in the institutional framework such as the generosity of the unemployment-bene…t welfare system, other forms of nonwage income, the family network, and the (consumption) tax wedge. The structuralist view would be in line with the existence of structural breaks of the steady-state path of a stochastic stationary process while hysteresis or persistence 3 would be consistent with unit-root or near-unit root, processes, respectively. From a theoretical point of view, the slow adjustment process to that equilibrium is modelled by introducing real-wage rigidity through, for example, e¢ ciency-wage or union behaviour models. The second one, also known as the “hysteresis”hypothesis, states that shocks have permanent e¤ects on the level of unemployment due to labour market rigidities as introduced by insider-outsider interactions (Blanchard and Summers, 1986) or human-capital e¤ects (Layard et al., 1991), and, therefore, the level of unemployment can be characterized as a non-stationary process. It is worth to note that there is a crucial di¤erence between the concepts of “hysteresis”and “persistence”. Persistence implies a slow speed of adjustment towards the long run equilibrium level, and therefore, is a special case of the natural rate of unemployment hypothesis, as the series show mean reversion after all. From an econometric point of view it can be characterized by a near unit root process. If this is the case, macroeconomic policy would have long lasting but not permanent effects while, conversely, if hysteresis applies, the e¤ects on unemployment are permanent. Sometimes the existence of persistence might be hiding changes in the level of the natural rate. This possibility has been pointed out by the structuralist view of the natural rate of unemployment (Phelps, 1994). There is an extensive empirical literature on this hypothesis using time series, with mixed and sometimes counterintuitive results. The results of these studies applied to OECD almost uniformly fail to reject unit roots in the unemployment rates (with the exception of the US). The overwhelming evidence in favour of hysteresis was probably due to lack of power of the tests, pointing to the importance of either expanding the time span (and then allowing for discontinuities in the deterministic components as in Arestis and Mariscal (1999) and Papell et al. (2000)), or increasing the amount of information through panel data. More recently, there is a new generation of empirical papers using tests for unit roots in panels of countries trying to increase the power of the tests thanks to the increase of cross-section information, such as Song and Wu (1997, 1998) which strongly reject a unit root in the unemployment rate for US states using Levin and Lin 4 test, and León-Ledesma (2002) which is able to reject hysteresis for the US but not for the EU using the IPS tests. The presence of structural breaks has been also taken into account in panel data (Strazicich et al. (2001), and Murray and Papell (2000)) However, the number of empirical studies is still very scarce for Transition countries. Exceptions are the papers by León-Ledesma and McAdam (2004) and Camarero, Carrion-i-Silvestre and Tamarit (2005), that reject the hysteresis hypothesis using univariate methods. In this paper we contribute to the empirical literature in several respects. First, we apply both panel unit root and stationarity tests; in particular, those proposed by Im, Pesaran and Shin (1997, 2003)2and Maddala and Wu (1999) for the null of unit root, and Hadri (2000) tests for the null of stationarity. Second, we use two versions of each of these tests: the …rst one, imposing cross-section independence and, the second one, allowing for dependence and computing critical values by boostrap techniques. Third, we apply a new panel stationarity test incorporating multiple structural changes endogenously determined as proposed by Carrion-i-Silvestre et al. (2005), also accounting for crosscorrelation in the residuals. Accounting for these two features (structural breaks and dependence) provide important power gains compared to the time series equivalent tests. The remainder of the paper is organized as follows. Section 2 brie‡y describes the tests used in the paper, and the econometric results. Finally, in section 3 we report the main results and conclusions. 2 Empirical results The main limitation for the analysis is the short span of the statistical information available for these new EU countries. The standard sources of statistical information such as the OECD, AMECO and EUROSTAT databases just o¤er a short sample of unemployment rates for these countries. In this Section we analyze the order of integration of the unemployment rates for all the CEECs countries acceding to the EU in May 2004. Due to the particularities of this group of countries, we have a constraint concerning the time span available for any economic variable. Thus, we have decided to use monthly data, 2IPS hereafter. 5 in order to increase the number of observations3. The monthly harmonized unemployment rates have been taken from EUROSTAT (Euroindicators) for the period 1998:12 to 2003:11. Then, we have applied backwards the growth rates of the monthly unemployment rates drawn from [?] to extend the database4that, at best, covers from 1991:1 to 2003:115.These harmonized unemployment rates are depicted in Figure 1. 2.1 Panel unit root and stationarity tests. No breaks case Thus, in order to test for hysteresis in the unemployment rate the empirical results presented in this section are organised in two groups. First, we test the null hypothesis of unit root using the t-bar (t)and LM-bar (LM )statistics in Im, Pesaran and Shin (1997, 2003), and the MW statistic in Maddala and Wu (1999) panel unit root tests, as well as the Hadri (2000) stationarity test.6Since these statistics are now well known, we address readers to the respective papers. Second, we apply the Carrion-i-Silvestre et al. (2005) test allowing for structural changes endogenously determined in a panel context, which improves largely the power of the time series test used in Papell et al. (2000). Additionally, this test allows for multiple number and type of breaks and accounts for cross-correlation in the residuals, solving the main drawbacks in panel studies above mentioned. Before presenting these results we should introduce some comments on the deterministic speci…cations that are used along the paper. We should bear in mind that the rejection of hysteresis establishes that the unemployment rate evolves in a stationary way around the natural rate. Thus, the deterministic speci…cation when testing both for the unit root hypothesis or for the stationarity hypothesis is the one given by a constant term. Although looking at the pictures of the variables in Figure 1 in the Appendix one could 3However, we are aware of the limitations of proceeding this way, since the increase of the frequency does not imply an increase of the long-run information. 4We thank Miguel León-Ledesma for kindly providing us the data. 5Speci…cally, for the Czech Republic the data spans from 1991:1 to 2003:10, Estonia (1995:5, 2003:11), Hungary (1991:3, 2003:11), Latvia (1994:1, 2003:11), Lithuania (1994:1, 2003:11), Malta (1997:3, 2003:10), Poland (1991:1, 2003:11), Slovakia (1991:1, 2003:11) and Slovenia (1992:1, 2003:11). 6When computing the panel stationarity test in Hadri (2000) we have estimated the long-run variance using the procedure in Sul, Phillips and Choi (2003), which reduces size distortions when stochastic processes are close to non-stationarity. Further details are given below and in Carrion-i-Silvestre and Sansó (2005). 6 decide to include a time trend in most of them, this speci…cation would mask the fact that the unemployment rate might be experiencing a long transition between shifting natural rates.7This is pointed out in Papell et al. (2000) where it is mentioned that while a nonzero trend for unemployment does not make sense asymptotically, a slowly increasing natural rate could be represented by trend stationarity process in small samples. Let us …rst focus on results without structural breaks. The results of the panel data unit root and stationarity tests applied to the unemployment rate are reported in Panel A of Table 1. Assuming that the individuals are cross-section independent, all the tests mainly point to the presence of hysteresis in unemployment for the set of CEECs countries that has been analysed. Thus, the unit root hypothesis cannot be rejected by neither the IPS nor the MW tests. In addition, the test in Hadri (2000) strongly rejects the null hypothesis of stationarity. This conclusion is reached irrespectively of the deterministic speci…cation. The assumption of cross-section independence is rarely found in practice, especially in a globalised economy where the shocks overpass the borders. However, these countries are in a process of opening-up. This is of special interest in our study, due to the inclusion in the panel data set of twelve EU countries, which in part are ruled by common governmental institutions. These facts question the validity of this assumption. In order to account for cross-section dependence, we have followed two approaches. Firstly, the independence assumption can be relaxed to allow for time-varying aggregate e¤ects in the data. These e¤ects can be removed by subtracting the cross-section mean from the data –see O’Connell (1997), and Levin, Lin and Chu (2002). The results that are obtained after removing the cross-section mean are reported in Panel B in Table 1. The main drawback of this approach is that it assumes that the e¤ect of the crosssection dependence is the same for all individuals. In order to account for more general situations we have decided to compute the bootstrap distribution of the tests. This is the second approach that is followed here. The details of the bootstrap are given 7This is especially true in the case of France, New Zealand, Spain, Norway and Japan. 7 in Maddala and Wu (1999) with 2,000 replications for the bootstrap. Panel C in Table 1 reports the percentiles of interest of the bootstrap distribution. Let us …rst focus on the results based on cross-section demeaning. Thus, except for the t-bar IPS statistic the null hypothesis of unit root cannot be rejected at the 5% level of signi…cance, while stationarity is strongly rejected using the panel KPSS statistic. When we compare the statistics with the boostrap distribution we conclude that, except for the panel KPSS statistic that speci…es a time trend, evidence points to non-stationarity. In all, the results support the hysteresis hypothesis in unemployment rates, a conclusion that is robust to the presence of cross-section dependence. In general, this conclusion is also in accordance with the previous results in the literature. However, it should be noted that evidence of stationarity is only found when the time trend is used with panel KPSS statistic. As pointed above, this deterministic speci…cation can be masking the presence of structural breaks that might be shifting the natural rate. This fact is not surprising as the natural rate depends on the fundamentals of the economies and these fundamentals change in accordance to the technological progress. Moreover, this contradiction between the unit root and stationarity tests can be thought to be an indicator of the presence of structural breaks –see Cheung and Chinn (1997). 2.2 Panel stationarity tests allowing for structural breaks endogenously determined In order to account for this feature we proceed to compute the extension of the Hadri (2000) test for stationarity in panel data with multiple structural changes under the null hypothesis, which is proposed in Carrion-i-Silvestre et al. (2005). This framework allows for heterogeneity in several respects: multiple structural changes, multiple structural changes positioned at di¤erent unknown dates, and a di¤erent number of breaks for each individual. The details of this technique are described in the Appendix. In order to detect the breaks, Carrion-i-Silvestre et al. (2005) suggest applying the 8 procedure …rst proposed in Bai and Perron (1998). This consists of specifying a maximum number of breaks (mmax), estimating their position for each mimmax,i=f1; :::; Ng; testing for the signi…cance of the breaks and, then, obtaining their optimum number and position for each series. First, to estimate the dates of the breaks, they choose the argument that minimizes the sequence of individual SSR, as in Bai and Perron (1998). Some trimming would be necessary, that is commonly speci…ed as Ti b2[0:15T; 0:85T]:Once the dates for the possible breaks have been estimated, then the number of optimal structural breaks should be selected for each i(that is, the optimal mi). Bai and Perron (2001) compare two alternative procedures: information criteria (such as the Bayesian information criterion (BIC) and the modi…ed Schwarz information criterion (LWZ) of Liu, Wu and Zidek (1997)) and the sequential computation of structural breaks, using pseudo F-type test statistics. They recommend using the LWZ criterion when the model includes trending regressors, whereas for non-trending ones the sequential procedure has better performance. The results of the computation of the LM()test allowing for up to mmax = 5 breaks, with the deterministic speci…cation given by Model 1, are reported in Table 2. The number of breaks has been selected using the sequential procedure in Bai and Perron (1998). Panel A in Table 2 o¤ers the individual information, i.e. the individual KPSS test, number of breaks and their position. In general, at least one structural break was detected by the sequential procedure in all the countries considered and, in six cases, we found up to four breaks. This …nding may suggest that the analysis conducted in the previous Section would be wrong if these structural breaks were relevant for the analysis of the stochastic properties of the series. 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Evidence from panel unit root tests with structural change”, manuscript, University of North Texas. 17 Table 1: IPS and Maddala and Wu (MW) panel unit root tests Panel A: Assuming cross-section independence Panel B: Removing cross-section mean Constant Time trend Constant Time trend Test p-val Test p-val Test p-val Test p-val t0.826 0.796 0.044 0.518 -1.775 0.037 -0.906 0.182 LM -1.448 0.926 -0.213 0.585 1.406 0.079 1.078 0.140 MW 22.829 0.975 30.018 0.819 47.872 0.131 50.376 0.086 Hadri (Hom.) 47.742 0.000 5.399 0.000 24.940 0.000 6.586 0.000 Hadri (Het.) 47.767 0.000 5.424 0.000 22.158 0.000 7.489 0.000 Panel C: Bootstrap distribution (allowing for cross-section dependence) Constant 1% 2.5% 5% 10% 90% 95% 97.5% 99% t-4.035 -3.397 -2.860 -2.264 2.481 3.479 4.452 5.737 LM -2.991 -2.464 -2.024 -1.464 2.744 3.483 4.092 4.893 MW 9.645 13.406 16.921 22.096 63.065 69.929 77.858 85.841 Hadri (Hom.) -3.236 -3.030 -2.814 -2.510 4.838 7.247 9.104 11.246 Hadri (Het.) -2.840 -2.576 -2.377 -2.109 4.877 7.184 8.997 10.904 Time trend 1% 2.5% 5% 10% 90% 95% 97.5% 99% t-4.708 -4.108 -3.636 -3.065 1.539 2.405 3.276 4.285 LM -3.014 -2.296 -1.719 -1.090 3.272 3.879 4.399 5.064 MW 18.256 22.952 27.221 32.504 78.465 86.399 94.495 102.581 Hadri (Hom.) -2.240 -1.875 -1.535 -1.008 4.866 5.964 7.204 8.557 Hadri (Het.) -1.384 -1.075 -0.714 -0.259 5.266 6.206 7.517 9.058 18 Table 2: Panel KPSS tests and individual test. Sample 1956-2001 (T=46) Panel A: Individual information Individual tests miTi b;1Ti b;2Ti b;3Ti b;410% 5% Australia 0.029 4 1974 1981 1989 1995 0.081 0.101 Austria 0.052 2 1961 1981 0.123 0.147 Belgium 0.035 4 1974 1980 1986 1992 0.083 0.104 Canada 0.115 3 1974 1981 1995 0.094 0.114 Denmark 0.036 3 1961 1974 1995 0.102 0.125 Finland 0.023 2 1975 1991 0.107 0.128 France 0.032 3 1974 1980 1991 0.087 0.106 Germany 0.032 4 1961 1974 1981 1992 0.061 0.071 Ireland 0.049 3 1974 1982 1995 0.091 0.110 Italy 0.216 3 1961 1974 1982 0.091 0.110 Japan 0.067 3 1974 1981 1995 0.094 0.114 Netherlands 0.049 4 1973 1980 1988 1995 0.076 0.094 Norway 0.037 4 1971 1981 1988 1995 0.068 0.082 New Zealand 0.340 3 1980 1988 1994 0.124 0.159 Spain 0.129 2 1974 1980 0.123 0.149 Sweden 0.086 1 1991 0.227 0.297 Switzerland 0.056 3 1961 1982 1991 0.099 0.123 United Kingdom 0.049 4 1974 1980 1987 1995 0.081 0.102 USA 0.089 3 1974 1986 1995 0.089 0.108 Panel Stationarity tests (Assuming cross-section independence) Test p-val Homogeneous -0.385 0.650 Heterogeneous 3.216 0.001 Panel B: Removing cross-section mean Test p-val Homogeneous -0.977 0.836 Heterogeneous 1.766 0.039 Panel C: Bootstrap distribution (allowing for cross-section dependence) 1% 2.5% 5% 10% 90% 95% 97.5% 99% Homogeneous 0.885 1.171 1.464 1.950 5.811 6.642 7.331 8.291 Heterogeneous 2.055 2.488 2.833 3.245 8.134 9.268 10.200 11.543 19 Table 3: Structural breaks. Comparison of the di¤erent methods Bai-Perron n breaks León-Led/McAdam León-Led/McAdam in Camarero et al. (2005) 1 break (trend model) Markow Switching Czech Rep. 1996:07 1992:07 1997-98 1998:07 1998:04 Estonia 1997:05 1998:10 Multiple changes 1999:03 2000:05 (1995, 1996, 1999...) 2001:10 Hungary 2000:03 1992:11 Multiple changes Latvia 1996:01 1998:04 1998 1998:09 2000 2000:08 2002:06 Lithuania 1995:05 1997:01 1998-1999 1999:11 2002:01 Malta 1992:11 1999:07 2001:11 Poland 1992:11 1996:03 1996:08 2000:01 Slovakia n=1: 1998:12 1992:11 1998 n=2: 1993:01 n=2: 1999:02 Slovenia 1993:09 1999:06 1994 2000:04 1996 2000 20 Table 4: Dates of the breaks. Political and institutional events. Breaks and main events Countries 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 Czech Rep. 1996:07 1998:07 Havel lost power Post-transition recession Restructuring Estonia 1997:05 1999:03 2001:10 Russian crisis!Current account de…cit Hungary 2000:03 Early reform ERM-2 Stabilization Plan (1995) Employment recovery Latvia 1996:01 1998:09 2000:08 2002:06 Tiny open economy Exposed to external shocks Russian crisis! Lithuania 1995:05 1999:11 2002:01 Exchange Russian crisis!New peg rate peg Faster privatization Fiscal discipline Malta 1998:02 1999:07 2001:11 Tiny open economy September 11th Exposed to external shocks Tourism Poland 1992:11 1996:08 2000:01 Shock therapy for transition Monetary tightening Russian recession (#GDP) Slovakia 1993:01 1999:02 Splits from 1998 elections Czech Rep. Slovenia 1993:09 2000:04 1991: splits from Yugoslavia 21 A Carrion-i-Silvestre, del Barrio and López (2005) panel stationarity tests with multiple breaks These authors specify the following DGP under the null hypothesis of stationarity: yi;t =i+ mi X k=1 i;kDUi;k;t +it+ mi X k=1 i;kDT  i;k;t +"i;t (1) with DUi;k;t = 1 for t > Ti b;k and 0 elsewhere, DT i;t;k =tTi b;k for t > Ti b;k and 0 elsewhere, where f"i;tgare assumed to be independent across i–this assumption will be addressed below. This model includes the following elements: (i) Individual e¤ects, that are in fact individual structural break e¤ects (or shifts in the mean caused by the structural breaks), (ii) temporal e¤ects if i6= 0 and (iii) temporal structural break e¤ects if i;k 6= 0 (when there are shifts in the individual structural time trend). This speci…cation encompasses Model 1 in Perron and Vogelsang (1992) when i= i;k = 0 and Model C in Perron (1989), that Carrion-i-Silvestre et al. (2005) call Model 2, when i6=i;k 6= 0:This speci…cation has very convenient characteristics: (i) The structural breaks may have di¤erent e¤ects on each individual time series (these e¤ects are measured by i;k and i;k), (ii) these breaks can be located at di¤erent dates, because they do not impose the restriction Ti b;k =Tb;k;8i=f1; :::; Ng, and (iii) the individuals may have di¤erent numbers of structural breaks, so that mi6=mj;8i6=j; fi; jg=f1; :::; Tg: The test is formulated as in Hadri (2000), i.e., the average of the individual KPSS statistic. The general expression takes the form: LM() = N1 N X i=1 ^!2T2 T X t=1 S2 i;t!(2) where Si;t =Pt j=1 ^"i;j denotes the partial sum process obtained form the OLS residuals of equation (1), and ^!2=N1PN i=1 ^!2 i, where ^!2 iis a consistent estimate of the long-run variance of "i;t. The procedure that is applied to estimate !2 iis extremely important. 22 Thus, Caner and Kilian (2001) show that stationarity tests such as the KPSS statistic su¤ers from severe size distortion when the stochastic process is near to non-stationarity. Carrion-i-Silvestre and Sansó (2005) have shown that this size distortion can be reduced if the long-run variance is properly estimated. In this regard, Carrion-i-Silvestre and Sansó (2005) compare di¤erent ways to estimate !2 iand suggest using the procedure described in Sul, Phillips and Choi (2003), which is also used in Carrion-i-Silvestre et al. (2005). In brief, their proposal bases on the application of a prewithened Heteroskedasticity and Autocorrelation Consistent (HAC) variance estimate, which in the …rst stage implies estimating an AR model for the residuals of (1): ^"i;t =#1^"i;t1+: : : +#p^"i;tp+ i;t;(3) and obtaining the long-run variance of the estimated residuals in (3), which is denoted as ~2 i, through the application of a HAC estimator –for instance, Bartlett or Quadratic Spectral window–to control for the presence of heteroskedasticity. In the second stage the estimated long-run variance is recolored: ^!i=~2 i ~ #(1)2; where ~ #(1) denotes the autoregressive polynomial ~ #(L) = 1~ #1L: : : ~ #pLpevaluated at one. In order to avoid the inconsistency of the test statistic, Sul, Phillips and Choi (2003) suggest using the following boundary condition rule to obtain the long-run variance estimate: ^!i= min (T~2 i;~2 i ~ #(1)2): The application of this rule ensures that the long-run variance estimate is bounded above by T~2 i. In all computations the order of the AR model in (3) is chosen by the BIC information criterion specifying 5 lags as the maximum, and ~2 i is obtained using the Quadratic spectral window as depicted in Sul, Phillips and Choi (2003). Note that we do not require to assume homogeneity of the long-run variance across 23 individuals, so that the expression (2) can include separate estimates for the long-run variance of each individual. The parameter denotes the dependence of the test on the dates of the break. The vector i= (i1; :::; i;mi)0= (Ti b;1=T; :::; Ti b;mi=T)0indicates the relative positions of the dates of the breaks on the time period T: Finally, the normalized test statistic converges to a standard Normal distribution and turns out (according to Carrion-i-Silvestre et al. (2005) Monte Carlo results) to be more suited for panels with larger Tcompared to N: 24