Labor Productivity and Okun s law: An empirical application to Italian regional panel data

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1 Labor Productivity and Okun s law: An empirical application to Italian regional panel data Giovanni Busetta, Dario Corso Abstract Okun s law, named for its proposer, Arthur Okun, was first applied during the 1960s in the USA to describe the relationship between economic growth and unemployment fluctuations. Several attempts were later made to test the empirical applicability of the relationship to different countries and historical periods. Heterogeneous results were generally found in estimating Okun s coefficient, depending on the sample and context analysed. The main goal of this paper is to analyze the relevance of Okun s law to Italian regions. We perform a panel analysis to estimate the influence of asymmetry and local market differences on Okun s relationship. Moreover, observing particularly low values of participation rate in labor markets in southern areas, we propose other indicators to estimate Okun s coefficient which are more compatible with a delayed development area. Keywords: Okun s law; Asymmetry; Italian regions; Employment; Unemployment. JEL classification: C23; C26; D32; E24; E32; J64. Introduction Okun s law postulates an inverse relationship between changes in the unemployment rate and real gross domestic product (henceforth GDP) growth rate 1. Applied to the US economy, it was found that the link between the two variables could be quantified with a ratio of 1 to 3 for the US economy 2. Following Okun s original estimate, attempts were made to verify the empirical robustness strength of the law in different space-time contexts 3, highlighting the role of some economic and social components. Most recently, several studies have tried to analyze the relationship between unemployment and real GDP growth rate, focusing on the incidence of asymmetric components. The meaning of this asymmetry should be sought in a different response of the unemployment rate to real GDP growth rate variations, depending on whether the economy is in a phase of expansion or recession. The authors wish to thank Vincenzo Fazio and Alberto Zazzaro for their advice and a group of anonymous referees for their invaluable suggestions. Busetta Giovanni, Università degli studi di Messina, Dipartimento di Economia, Statistica, Matematica e Sociologia "Vilfredo Pareto",Via T. Cannizzaro 278, Messina, Italy gbusetta@unime.it Dario Corso, Università degli studi di Palermo, Dipartimento di Scienze Economiche, Aziendali e Finanziarie, Viale delle Scienze, ed. 2, Palermo, Italy, dario.corso@unipa.it. 1 This relation comes from the studies originally conducted by Okun on the post-war U.S. economy and which led to the drafting of a text measuring the nature and intensity of the link between the two variables (Okun 1962). 2 The logic behind Okun s intuition is that the maximum level of wealth that an economic system can produce is obtained with full employment, and it corresponds to strictly frictional unemployment rates. 3 The main analyses confirming the validity of Okun s law for the Unites States are the following: Smith 1975, Gordon 1984, Evans 1989, Prachowny 1993 and Weber A second group of analyses tested Okun s law in different countries in order to estimate potential differences in the intensity of the relationship (Knoester 1986, Kaufman 1988, Moosa 1997). In both cases the law was essentially confirmed, despite fairly large differences in the values of the estimated coefficients amongst countries. 1

2 Lee (2000) conducted his analysis on 16 nations belonging to the OECD (Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Italy, Japan, Holland, Norway, Sweden, Switzerland, Britain and the USA). He considered data for the period , showing considerable differences in terms of the value and significance of the estimated coefficients for different nations. According to the author, the reason for such differences in the coefficients should be sought in the degree of labor market flexibility as well as in the level of legal guarantees for workers 4. Virén (2001) examined the 20 countries belonging to the OECD for the period , concluding that real GDP growth rate has a more significant effect on the unemployment rate when the latter is low and real GDP is high. According to the author, implications of asymmetry in the relation are more relevant for those countries belonging to the European Monetary Union, and this is because these countries differ from one another considerably in terms of their economic cycle. Other analyses (Mayes and Virén 2002) find that one of the main reasons for such asymmetry has to be sought in the way the labor market operates. Rapid downward trends in the economy can have an incremental rather than proportional effect on the unemployment rate, and this is also due to the fact that demand and supply do not necessarily meet in every sector of economic activity and in every local labor market. In his original work of 1962, Okun highlighted the capability of the labor market s structural changes to invalidate the estimated relation. In particular, according to the author, there are three variables which can affect the above relation: the level of participation in the labor market, working hours per worker and the labor productivity. Another possible explanation for these differences consists in the overestimation of the coefficient resulting from the choice of a bivariate model. The omission of relevant variables, such as labor productivity and individual working hours, could have a different influence on the estimation of the coefficient, depending on the features of the various countries. Some authors (Juhn, Murphy and Topel 1991, Weiner 1993) sought the determinants of the loss in the intensity of the estimated coefficient, detected by many analyses. The majority of the analyses concerning OECD countries found these determinants in: (1) increasing participation of women in the labor market, (2) slowdown in productivity and wages and (3) the reorganization process of some companies. Balakrishnan and Michelacci (2001) included parameters in their unemployment dynamic estimation that were capable of recognizing shocks on the unemployment rate, depending on labor force fluctuations. This is because identical unemployment rates can result from different levels of the labor force (Layard, Nickell and Jackman 1991). Villaverde and Maza (2007) worked specifically on estimating the differences between regions in the same country. In particular, they worked on Spanish regions over the period finding lower coefficients than those originally estimated by Okun. Giannini, Lanzarotti and Seghelini (1995) also focused on regional differences In their detailed analysis of the Italian dynamic, the authors found that real GDP growth rates only contribute to explaining unemployment fluctuations in the short and medium term, with long-run dynamics being unaffected. Lanzafame (2009) concentrated on investigating the possible influence of endogeneity in determining the real GDP growth rate changes. In order to do so, annual data regarding Italian regions over the period were analyzed, highlighting strong indicators of non-linearity in the relation originally estimated by Okun. In particular, results emerging from the analysis quantified the anti-cyclical effect of unemployment in real GDP contraction phases and the procyclical effect in expansion ones. 4 The coefficients estimated in the analysis are significantly higher for the reduction rather than the increase in unemployment rate in Finland, Japan and the United States. The contrary happens in countries like Canada, France and the Netherlands. The highest values have been registered by countries like the United States and Canada, whereas lower values of the coefficients are found in European countries and Japan, due to the greater severity of their own labor market. In particular, coefficients referring to Italy registered much lower values than the other countries analyzed. 2

3 The main goal of our analysis is to verify the applicability of Okun s law in Italy at the regional level, considering, at the same time, the effects of a possible asymmetric component and of area dynamics. In order to investigate the strength of this relation in Italy, we used a regional dataset for the period In order not to overestimate Okun s coefficient, we decided to abandon a bivariate model in favor of a multivariate one. Consequently, several indicators concerning the main features of the labor market have been inserted as explanatory variables for the analysis. Our estimation is based on the hypothesis that the differences between Italian regions involve some of those aspects that Okun considered to be responsible for modifying his empirical relation. In order to register the possible impact of these regional differences, in addition to the traditional regressors, we included in our analysis variables such as time flexibility and labor productivity. To do so, we calculated Okun s law coefficient, considering the impact of possible asymmetric and/or area components. Furthermore, the analysis is repeated using Annual Working Units 5 (from now on AWUs) and the employment rate as dependent variables, because they are usually less sensitive to changes in the participation rate in the labor market. The remainder of the paper proceeds as follows. In section 1 the data used in the empirical analysis are described as well as the applied methodology. In section 2 we present the main empirical results. Section 3 provides the conclusions to the paper. 1. Data and methodology 1.1. Dataset representation The objective of this analysis is to test the strength of Okun s law for Italian regions over the period The data are from the Central Institute of Statistics (ISTAT). In particular, data on real GDP concern the regional economic accounts and are expressed at constant prices (year 1995). Data concerning employment, unemployment, and the labor force are from the ISTAT labor force survey 6. All of the variables are expressed in terms of annual data and they are expressed in thousands 7. With regard to population, for the period , we looked at the intra-census reconstruction of the resident population. Data on the whole population were used to calculate the employment rate 8. Lastly, employment and unemployment rates were calculated as an annual average on the basis of the aggregates mentioned above. The sample used for the ISTAT labor forces survey comes from the municipal register office and guarantees comparability with the values regarding the resident population. Data on the value-added and on the AWU 9 come from the 5 AWUs have the advantage of being calculated in terms of full-time equivalent worker, whereas in calculating employment and unemployment rates an individual only needs to work one hour per week to be considered employed. 6 Data referring to the labor market for the period are taken from a time-series reconstruction made by ISTAT. Data regarding the year 2004 come from the new continuous survey on the labor force. Such an approach fully guarantees the comparability of data. 7 The use of annual data for Italian regions is due to the lack of data with a higher temporal frequency. Such an option is in line with the one chosen amongst others by Knoester (1986), Paldman (1987) and Moosa (1997), who used annual data to estimate Okun s law in heterogeneous area contexts. Annual data on regional profit and loss are provided by ISTAT. Such an approach guarantees comparability amongst different geographical realities. 8 Data for 2002 and 2003 come from a survey on the local residential population per sex, date of birth and marital status which ISTAT has conducted since 1992 at Municipal registry offices in Italy. Finally, data related to 2004 come directly from the population data quoted in continuous research on the labor force. 9 These measures estimate the contribution of the labor factor to the value added produced by the country. They are calculated by transforming employment into full-time units and ensure comparability within different productive sectors (ISTAT, Glossary on the National Accounting of the national profit and loss accounts, various years). 3

4 area dataset of national accounting. Many macroeconomic time series contain unit roots dominated by stochastic trends (Nelson and Plosser 1982). As a non-stationary regressor invalidates many standard empirical results, we carried out some unit root tests to check stationarity of the time series data. Once the presence of a unit root was established in all time series considered 10, as in Lee (2000) and in Silvapulle, Moosa and Silvapulle (2004), we proceeded to consider a linear transformation of all the variables 11. More specifically, in line with previous research on this subject (Okun 1962, Mankiw 1994, Moosa 1999, Lee 2000, Silvapulle, Moosa and Silvapulle 2004), we calculated the real GDP growth rate in log first differences. On the one hand, the use of first differences linear transformation eliminates the presence of unit roots from the time series. On the other hand, a logarithm is useful to linearize the relation between real GDP growth trends and labor market variables. The results of the unit root tests carried out are shown below (Tab.1). Each of the tests to be presented below is based on a specific hypothesis. Tests of Levin, Lin and Chu (2002), the Breitung test (2000), ADF chi-square, Fisher PP chi-square (Maddala and Wu 1999, Choi 2001) and Statistic W by Im, Persaran and Shin (2003) are based on the null hypothesis of the presence of a unit root, whereas the Hadri Z Stat test (1999) is based on the null hypothesis of its absence 12. TAB.1. Tests of the unit-root hypothesis Real GDP (log-difference) Unemployment rate (first difference) Employment rate (first difference) AWU (first difference ) Labor productivity (first difference) Time flexibility (first difference) Method Stat. Prob.* Stat. Prob.* Stat. Prob.* Stat. Prob.* Stat. Prob.* Stat. Prob.* Null hypothesis of presence of a unit root Test of Levin, Lin and Chu T Stat of Breitung W Stat of Im, Pesaran and Shin ADF Chi squared of Fisher PP - Chisquared of Fisher Null hypothesis of presence of a unit root Null hypothesis of absence of a unit root Hadri Z Stat Test *Probabilities for Fisher tests are computed using an asymptotic Chi-square distribution. All other tests assume asymptotic normality. Tests results show that all variables are stationary. As underlined by authors such as Mankiw 10 The results of the first tests are not quoted in order not to make the text too heavy. However, they are available upon request. 11 This procedure has become common practice in papers that deal with estimating the relationship between GDP and unemployment rate in a panel context (Freeman 2001). 12 If you identify ρi as the coefficient on which you define the presence of unit root, where i = 1,2,,N represents the number of time-series analysis observed over time t = 1,2,,T i, se ρ i <1, then you will find weak-sense stationarity. Otherwise if ρ i =1 there is a unit root. Regarding the elements of the tests there are two assumptions on the basis of the tests pertaining to the ρ i parameter. Levin, Lin and Chu s tests, Breitung and the Hadri Z Stat test assume that the presence of the parameters is common amongst all the observed cross-sections, hence that ρ i=ρ. Instead, ADF Chi-square, PP Fisher Chi-square and Im Statistics W, Pesaran and Shin assume that ρ i. varies across all cross-sections. In Levin, Lim and Chu s tests the null hypothesis is H 0: ρ=0 whereas the alternative one is H A: ρ < 0. In the Breitung t statistics the null hypothesis is H 0: ρ i=1 versus each i. In Im W statistics, Pesaran and Shin the null hypothesis is H 0: ρ i=0 versus each i whereas the alternative hypothesis are H A: ρ i = 0 versus i =1,2,, N 1 and H A: ρ i < 0 versus i = N+1, N+2,, N. The ADF Fisher Chi-square and PP Fisher Chi-square assume as a null hypothesis that H 0: ρ i=0 versus each i whereas the alternative hypothesis is H A: ρ i=0 versus i =1,2,, N 1 and H A: ρ i < 0 versus i = N+1, N+2,...,N. In the Hadri Z Stat test the null hypothesis is H 0: ρ=0, whereas the alternative one is H A: ρ < 0 (Levin, Lin and Chu 2002, Breitung 2000, Hadri 1999, Maddala and Wu 1999, Choi 2001, Im, Pesaran and Shin 2003 and Hadri 1999). 4

5 (1994) and Lee (2000), the first-difference model represents a very efficient instrument to make the series stationary, especially when dealing with data containing unit roots, as in the case observed by Okun. Furthermore, using first differences in the regression model eliminates the risk of multicollinearity between variables. Variables moving in the same direction over time are one of the main reasons of multicollinearity, and the process of First Difference linear transformation represents a way to minimize such dependence. Therefore, there is no reason to think that variables highly related in levels, should maintain this status of relation, if considered in their first differences (Guajarati et al., 2003) Methodology The main idea of this paper is that the considerable differences between Italian regions in terms of unemployment rates are related to differences in the participation rates in the labor market. For this reason, the reduction in the significance of the relation could be due to changes in the degree of participation in the labor market, taking place within expansion and recession phases of the economic cycle. Furthermore, we will use a balanced annual data panel based on data from 20 Italian regions in order to investigate geographical differences. The choice of using panel data comes from three sets of considerations. First of all, through the utilization of panel methodology we could obtain an increase in the degree of freedom with a consequent improvement in the efficiency of the estimator. Such a procedure is particularly useful in Italy because it overcomes the lack of time series of a certain length, comparable with each other. Secondly, as Freeman (2001) has highlighted, the utilization of panel data allows the reduction of the collinearity problem 13, thanks to the additional variability of the regressors. Lastly, as stressed by Baltagi and Griffin (1995), panel estimators produce fewer forecasting errors (compared to the estimates of individual time series) even in those cases where the hypothesis of slope homogeneity for the various cross-sections is rejected 14. The model presented in (1) is the original statement for the estimation of Okun s law: u it =β 0 +β 1 y it +ε it (1) where u it is the unemployment rate for the region i at time t and y it is the real GDP growth rate for the region i at time t, represents the difference term and ε is a white noise disturbance term. Starting from this formulation and considering the results emerging from previous studies, we implemented the original model with some additional components. The first aspect to be considered is the possible existence of asymmetric effects in the relation between real GDP and unemployment rate. As we highlighted in the previous section, the intensity of Okun s coefficients can be quite different, depending on the phase of the economic cycle 15. Following most of the previous literature, we controlled for asymmetry splitting the explanatory 13 «The additional degree of freedom available in pooled data can produce more efficient estimates, and additional variability in the regressor can mitigate the collinearity problems that often plague macroeconomic data», (Freeman 2001, page 512). 14 According to the authors, the distortion in estimating the parameters caused by the heterogeneity of the slope is broadly offset by the reduction in the variance. 15 Courtney (1991) and Palley (1993) are the first authors who took into consideration the possible presence of an asymmetric relation between GDP and the unemployment rate. From those initial contributions, many authors have included estimators of such asymmetry in analyzing economic systems belonging to the G-7 (Moosa 1997, Lee 2000), OECD countries (Virén 2001), and the ten most industrialized economic systems (Paldman 1987, Freeman 2001). 5

6 variable into its negative and positive components 16. In this way, we calculated a different coefficient for each of the two partitions. Therefore, the model can be rewritten as follows: u it =β 0 +β 1 + I it + y it +β 1 I it y it +ε it (2) where I it represents the Heaviside step function (see Lee 2000), so that: I I = + i t = i t s s s s e y e y e y i t e y i t 0 < 0 < 0 0 i t i t The indicator I it + assumes value 1 for positive variations of real GDP and value 0 for negative ones, whereas I it - is specular to the previous. Using the Heaviside step function we separately measured the effects of positive and negative variations of the real GDP growth rate on the corresponding variations in the unemployment rate. The second aspect that we considered concerns the possibility of non-homogeneous behavior of the relation at local level. In order to consider this second aspect, we included fixed regional effects in the analysis using territorial dummies. To avoid endogeneity problems, a Two-Stage Least Square (from now on 2SLS) instrumental variables procedure is applied to the model. This method consists in two stages of analysis: in the first, the explanatory variables have to be regressed on the instrumental variables obtaining first stage predicted values. Afterwards, the first stage predicted values have to be regressed on the dependent variable. In order to detect the most efficient labor market indicator to be related to real GDP growth rate, we carried out three different estimations modifying both the dependent and explanatory variables group. Values used in the analyses as dependent variables are the employment rate, unemployment rate, and the AWU. Variables used as regressors are the real GDP growth rate logarithm, labor productivity 17 and time flexibility 18. In particular, while labor productivity is calculated as the valueadded to AWU ratio, time flexibility is calculated as the AWU to workers ratio. In all the following 16 In terms of this methodology, Palley (1993) was the first to suggest a dynamic model where unemployment is independently linked to positive and negative variations of real GDP growth rate. Empirical results in this paper point to a deeper reaction of the US unemployment rate to negative rather than to positive variations in the GDP growth rate. 17 As Okun already highlighted in his first contribution (1962), the labor productivity factor is one of the parameters which can highly influence variations in the empirical relationship that he found. 18 Time flexibility index indicates the degree of overtime currently used. Therefore, if for instance its value increases without a corresponding increase in the denominator, this means that the total number of working hours has increased without a corresponding increase in the number of workers. 6

7 analyses the variables considered are taken in first differences and the above-mentioned regressors, taken at time t-1, are used as instrument. The need to estimate the impact of variations in GDP growth rates on unemployment rates, and the relation between AWU and employment rate has led to different specifications of the model. In particular, in the first specification, the unemployment rate was regressed on the real GDP growth rate, on labor productivity and on time flexibility. In the second the AWU has been regressed on the real GDP growth rate, on the labor productivity and on the employment rate. In the third specification the employment rate has been regressed on the real GDP growth rate, on the labor productivity and on the time flexibility. In all these three cases, the logarithm variations of the real GDP growth rate were divided into their positive and negative components. 2. Empirical results In this section we present the empirical results of the estimations obtained using models presented in section 1.2. All the analyses use the real GDP growth rate as regressors, expressed in logarithms, and the most common aggregates of labor market performance, all considered in first differences. Furthermore, the regressors used, taken in levels at time t-1, were included in the analysis as instrumental variables. All the subsequent analyses pass the usual Durbin-Watson and Sargan test, supporting the appropriateness of instruments and the consequent absence of correlation with the error term. Our study started analyzing the traditional Okun s law relationship and the results of this initial analysis are shown in Tab. A.1 and A.2 of the Appendix. The analyses were carried out using the first differences unemployment rate as dependent variables. Log real GDP growth rate, labor productivity and time flexibility are used as regressors. As we have already mentioned all the variables are considered in first differences. Two significant relations are revealed by this first analysis: a negative one between the unemployment rate and real GDP growth rate and a positive one between the unemployment rate and time flexibility. The coefficient intensity of the relation with the real GDP growth rate is The R 2 value is 0.21, meaning that 21% of the whole variability of the phenomenon is captured by the three variables included in the analysis. The relation described seems to be quite consistent with the overall macroeconomic framework. The inverse relation between the real GDP growth rate and unemployment rate shows that decreases (increases) in real GDP are associated to increases (decreases) in the unemployment rates. This result is consistent with those obtained in the other analyses on Italian dynamics, both those focusing on Italy itself (Giannini, Lanzarotti and Seghelini 1995, and Lanzafame 2009) and in the context of other countries (Paldman 1987, Moosa 1997, Lee 2000, Leon-Ledesma and Thirlwall 2002, Dritsaki and Dritsakis 2009). In all these cases the relation found is negative and R 2 values are very similar to each other. On the contrary, the estimated coefficient for Italy varies considerably, depending on the different analyses. Given that the employment growth rate is not necessarily linked to output increases because it can be caused either by an increase in part-time or full-time workers, we decided to distinguish between increases in the number of working people and marginal increases in part-time employment, using AWUs to measure the employment growth rate. The first column in Tab. 2 shows the results of the analysis carried out using the AWU as a dependent variable. To analyze the impact of the real GDP growth rate on AWUs, labor productivity and employment rate were introduced as regressors of the analysis. The estimation presented revealed several interesting results. The first aspect to be pointed out is the positive and significant relation between the real GDP growth rate and AWU. The second aspect is the negative and significant 7

8 relation between labor productivity and AWU 19. The new pattern of variables managed to capture more than 87% of the variability of the AWU growth rate, considerably higher compared to about 21%, captured by the analysis considering the unemployment rate. The second analysis displayed in Tab. 2 was carried out using the employment rate as a dependent variable and adding time flexibility to the set of regressors of the previous analysis. The statistical significance associated to Okun s coefficient appears to be higher, in this case, compared with both the analyses carried out using the unemployment rate and the AWU. In particular, on the one hand, a positive relation emerged upon analyzing the link between the real GDP growth rate and employment rate. On the other hand, the relationships between the employment rate and labor productivity and the employment rate and time flexibility appear to be both negative. In this case the intensity of coefficients is quite low, which is in line with the findings of Gallegati and Stanca (1998). On analyzing time flexibility, quite a deeply negative relation between increases in workers (whether full-time or part-time) and the use of overtime is detected. As well as the previous analysis, the associated R 2 amounts to more than 87%, much higher than that obtained upon analyzing the unemployment rate. TAB. 2. Okun s law relationship measured on AWU and the employment rate Instrumental variables Real GDP (-1); labor productivity (-1); Real GDP (-1); labor productivity (-1); employment rate (-1). time flexibility (-1). AWU Employment rate Constant [ ] [1.501] Real GDP ** [9.7506] **[5.007] Labor productivity ** [ ] **[-4.612] Time flexibility **[-4.174] Employment rate [1.0257] Cross-section fixed effect Abruzzo Basilicata Calabria E-05 Campania Emilia Romagna Friuli Venezia Giulia Lazio Liguria Lombardia Marche Molise Piemonte Puglia Sardegna Sicilia Trentino Alto Adige Toscana Umbria Valle d Aosta Veneto Stat Number of observations R The results of the analyses point out that an increase in the AWU to population ratio produces a significant positive impact on the real GDP growth rate. At the same time such an increase leads to a reduction in labor productivity. Some authors (Gallegati and Stanca 1998) have found the same dynamics in Italy and have clarified that employment reaches its maximum positive correlation to the real GDP growth rate with three-month temporal lags. On the contrary, labor productivity reaches its maximum correlation to the real GDP growth rate with no temporal lags. 8

9 Durbin-Watson Stat Sargan test (d.f. 1.3) 0 [7.815] 0 [7.815] In brackets the T Stat value and Sargan test critical value for a distribution at χ 2 for 95%; ** Estimate at 0.01; * Estimate at Results produced by our estimation are quite similar to those obtained by Moosa (1997), Lee (2000) and Lanzafame (2009). The positive relation between time flexibility and the unemployment rate (Tab. A.1 of the Appendix) shows that the two aggregates tend to move parallel to each other. As a consequence, a greater use of overtime is preferred than hiring new workers to satisfy a greater demand for labor. As an effect of a labor supply surplus, we could register an increase in the unemployment rate. On the basis of the evidence from previous research discussed in the last section, we wanted to test the potential presence of asymmetric effects 20 in the relationships that had just been analyzed. TAB. 3. Results of Okun s law relationship measured on AWU and employment rate, considering asymmetry Instrumental variables Real GDP positive asymmetry (-1); real GDP negative asymmetry (-1); labor productivity (-1); employment rate (-1). Real GDP positive asymmetry (-1); real GDP negative asymmetry (-1); labor productivity (-1); time flexibility (-1). AWU Employment rate Constant [ ] [ ] Real GDP positive asymmetry ** [ ] ** [ ] Real GDP negative asymmetry [ ] [ ] Labor productivity ** [ ] ** [ ] Time flexibility ** [ ] Employment rate [ ] Cross-section fixed effects Abruzzo Basilicata Calabria E-05 Campania Emilia Romagna Friuli Venezia Giulia Lazio Liguria Lombardia Marche Molise Piemonte Puglia Sardegna Sicilia Trentino Alto Adige Toscana Umbria Valle d Aosta Veneto Stat Number of observations R The risk of ignoring asymmetry when it is relevant could lead to rejecting the null hypothesis of a long-term relationship between the real GDP growth rate and unemployment rate, whereas it actually exists. This error could produce erroneous policy interventions (Silvapulle, Moosa and Silvapulle 2004). In particular, not only could it lead to an incorrect model specification resulting in erroneous forecasts, but it could also produce incorrect inferences on the statistics test (Virén 2001). 9

10 Durbin-Watson Stat Sargan test (d.f.l.3) 0 [9.488] 0 [9.488] In brackets the T Stat value and Sargan test critical value for a distribution at χ 2 for 95%; ** Estimate at 0.01; * Estimate at The first column of Tab. 3 presents the analysis carried out using the AWU as a dependent variable. The estimations display a positive and statistical significant relation to the real GDP growth rate only when positive asymmetry is considered. Moreover, the analysis shows a negative and statistical significant relation to the labor productivity. Basically, the estimations in Tab. 2 are confirmed by the analyses on the AWU. The only difference is that Okun s law, in this case, maintains statistical significance only when positive variations of the real GDP growth rate are considered. Also the relation with AWU is only significant when GDP variations are positive, meaning that, when real GDP grows, the number of AWUs grows too. Also in this case the inverse relation with labor productivity has to be seen in terms of the viscosity linking the real GDP growth rate and increases in productivity (Gallegati and Stanca, 1998). The second column in Tab. 3 contains the analysis including asymmetry and using the employment rate as dependent variable. In this case, as in the previous one, the relation with the real GDP growth rate is only significant for its positive component variations with a positive coefficient. The relationships between the employment rate and labor productivity, and that between the employment rate and time flexibility are also significant. In both cases the coefficient is negative. In particular, the relationship is statistically significant only when positive variations in the employment rate are associated with increases in real GDP growth rates. However, such increases will affect labor productivity negatively and will especially impact adversely on time flexibility. Consequently, time flexibility, is negatively affected by increases in the employment rate. In this case, just like in the previous one, the set of variables used explains nearly 87% of employment rate variability. Once again the analysis passes all the usual tests and the Sargan test. As displayed in Tab. A.2 of the Appendix, the estimation results reveal that, splitting the real GDP growth rate into its negative and positive components, the relation with the employment rate is confirmed in the case of positive variations. Hence, this result only confirms a statistically significant relation between the real GDP growth rate and unemployment rate only when real GDP is growing. On the contrary, a certain degree of rigidity seems to appear during a recession. Basically, labor market rigidities, in terms of welfare protection to workers from downsizing during economic crises, seem to limit excessive increases in unemployment rates. The direct relation between unemployment rates and time flexibility confirms the results of Tab. A.1 of the Appendix with an R 2 value around 20%. 3. Conclusions In the present analysis we verified Okun s relationship with regard to the Italian regions over the period Increasing attention has recently been paid to the famous Okun s rule of thumb, as we have observed in Italy a progressive reduction in the unemployment rate without a respective increase of employment rate. All the most recent studies on the subject confirm that Okun s law is still considered valid. Nevertheless, as each national economic system has different peculiarities, the rule of thumb shows different intensity, depending on country-specific peculiarities. In particular, the lack of intensity in the above relation has been shown to be partially caused by differences in the rigidity of the labor market of each individual economy. Countries with a less regulated labor market, especially in terms of social protection and a social 10

11 security cushion, tend to record a higher indicator of Okun s coefficient robustness. However, as the author has already mentioned in his original work and as has emerged from several studies, there are some factors, connected with labor market flexibility and productivity, which are able to affect the significance of the estimates and the intensity of the coefficient. Other analyses (see for instance Freeman 2001) attribute low values of the coefficient to the weak cyclicity of unemployment. In particular, in Italy the unemployment rate appears to be a structural phenomenon, which makes it less sensitive to the cyclical fluctuations of the real GDP growth rate. The objective of this analysis was to verify whether changes in the employment rate and AWU compared to the unemployment rate, were more connected with real GDP growth rate variations in terms of the proportion of variability explained. Both the estimations results confirm this thesis, showing R 2 values close to 87%. Moreover, we wanted to test the existence of asymmetric components in Okun s law for Italy at the regional level. The analysis showed a very strong presence of positive asymmetry in the estimated relation. Hence, phases of increase in real GDP growth rate have a greater influence on the labor market than phases of decrease. As we already clarified in describing the methodology, direct observation of phenomena and the main results of the estimations lead us to believe that the employment rate and AWU may provide a better understanding of the link between real GDP and labor market indicators, especially compared to the unemployment rate. Therefore, the influence of this indicator on variations in the labor force participation rate makes unemployment rate less sensitive to variations in real GDP. To conclude, Okun s law still seems to hold for Italian data at the regional level. Moreover, in contexts in which levels of frictional unemployment are almost reached, it seems that both the employment rate and the AWU lead to more robust results, as they are unaffected by dynamics that may influence the level of participation in the labor market. 11

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15 Appendix TAB. A.1. Results of Okun s law relationship measured on the unemployment rate, considering asymmetry Instrumental variables Real GDP (-1); labor productivity (-1); Time flexibility (-1) Unemployment Rate Constant [0.3993] Real GDP *[0.0301] Labor productivity [0.1457] Time flexibility * [0.0438] Employment rate Cross-section fixed effects Abruzzo Basilicata Calabria Campania Emilia Romagna -1.14E-05 Friuli Venezia Giulia Lazio Liguria Lombardia Marche Molise Piemonte Puglia Sardegna Sicilia Trentino Alto Adige Toscana Umbria Valle d Aosta Veneto Stat Number of observations 220 R Durbin-Watson Stat Sargan test (g.d.l.3) 0 [7.815] In brackets the T Stat value and Sargan test critical value for a distribution at χ 2 for 95%; ** Estimate at 0.01; * Estimate at

16 TAB. A.2. Test output of the relationship between unemployment rate, real GDP asymmetric effects, labor productivity and time flexibility Instrumental variables Real GDP positive asymmetry (-1); Real GDP negative asymmetry (-1); labor productivity (-1); Time flexibility(- 1) Unemployment rate Constant [0.5563] Real GDP positive asymmetry *[ ] Real GDP negative asymmetry [0.7478] Labor productivity [1.4652] Time flexibility * [2.0152] Employment rate Cross-Section fixed effects Abruzzo Basilicata Calabria Campania Emilia Romagna -1.37E-05 Friuli Venezia Giulia Lazio Liguria Lombardia Marche Molise Piemonte Puglia Sardegna Sicilia Trentino Alto Adige Toscana Umbria Valle d Aosta Veneto Stat Number of observations 220 R Durbin-Watson Stat Sargan test (g.d.l.3) 0 [9.488] In brackets the T Stat value and Sargan test critical value for a distribution at χ 2 for 95%; ** Estimate at 0.01; * Estimate at