A Panel Data Analysis of the Connection Between Employee Remuneration, Productivity and Minimum Wage in Romania

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A Panel Data Analysis of the Connection between Employee Remuneration, Productivity and Minimum Wage in Romania

MARIA DENISA ANTONIE, AMALIA CRISTESCU, NICOLAE CATANICIU National Scientific Research Institute for Labor and Social Protection 6-8 Povernei Str., District 1, Bucharest ROMANIA [email protected], [email protected], [email protected]

Abstract: - In this paper we present the results of a panel data analysis of the impact of productivity and minimum wage upon employee remuneration. We used a fixed effect regression model with Driscoll and Kraay standard errors to account for the possible problem of heteroskedastic and autocorrelated error structure. The main conclusion is that in the studied period the Romanian economy was characterized by a strong correlation between productivity and remuneration, which indicates the economic efficiency.

Key-Words: - productivity, remuneration, econometric model, panel data, fixed effects, robust standard errors

1 Introduction (which is actually the most significant component of the In an economy, and especially in an emerging one like labor cost) on the labor productivity and the minimum Romania, the relationship between productivity and wage. growth potential is important, mainly if the productivity The analysis was conducted over a period of five years level is seen as the third factor of economic growth after (2003-2007), using data for the 29 activities of the labor force and capital. The potential GDP growth Romanian economy. As for the method, we choosed a creates the prerequisites for reducing the existing excess panel data model. demand in the economy and for ensuring real economic Panels are attractive since they contain more information convergence. Secondly, the productivity influences the than single cross-section and allow for an increase inflation and the exchange rate. A low correlation precision in estimation. between wages and productivity creates inflationary pressures by increasing the costs. In order to achieve the competitiveness on the European unique market, 2 Data Romania must focus on the economic growth [5]. Also, The variables used are: employee remuneration (lrem), most of the times, the competitiveness is assessed by the productivity (lprod) and minimum wage (lhminwage). correlation between wages (labor costs) and labor Initial data are annual, for the 29 activities of Romanian productivity. economy. We worked with log data, after we brought Since productivity and wages are both essential them to hourly values. Also, employee remuneration and economic factors, the way they interrelate is a constant minimum wage were deflated by using the CPI with the concern for the economists, as well as for employers and base in 2003. For the productivity, in order to ensure policy-makers. The literature is focused on the comparability, the values were divided to the production connection between these two factors. There are several index with the base in 2003. papers concerning labor productivity and wages in The remuneration per hour was calculated by dividing Romania that use different models and tools. A revised the employee remuneration to the number of hours form of the coefficient of structural changes was used in worked. The employee remuneration is part of the added order to determine the regional/sectoral dissimilarities value and includes the total remuneration, in cash (gross between productivity and wage [8]. Also, a short term wages) or in kind, that an employer pays an employee in forecast of the correlation between the labor productivity exchange for the work performed over a period of time, index and the average gross earnings index in the and the employer’s contribution to social insurance. The Romanian industry was conducted using lag econometric employer’s contribution to social insurance covers the models, ARIMA processes, as well as feed forward state social insurance contribution (including neural networks [1]. contributions to the retiring fund); the contribution to the In the analysis undertaken in this study, we tried to fund for of unemployment benefits payment; the capture the dependence of employee remuneration contribution to the social health insurance fund.

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The productivity per hour was calculated as the ratio function that describes the correlation between labor between production and the working hours performed by costs and the productivity level, and the impact of the the occupied population in the 29 economic activities minimum wage. This made the authors to choose the (the occupied population includes employees and following regression equation: freelance workers). lremit = C+ a*lprodit + b*lhminwageit + uit The minimum wage per hour was calculated as the ratio where lrem is the log of the hourly employee between the national minimum wage and the average remuneration, lprod – the log of the productivity per number of working hours per month (170 hours). hour and lhminwage – the log of the national minimum The sources of our data are the publications of the wage per hour. Romanian National Institute of Statistics (National Accounts, Romanian Statistical Yearbook). 4 Methodology

A panel data regression differs from a regular time-series 3 Economic description or cross-section regression in that it has a double The economic theory favors the need to link wages with subscript on its variables: labor productivity. From this perspective, the labor ’ yit = a + X it b + uit , i = 1, …, N; t = 1, …, T (1) demand is often described as a decreasing curve of the The i subscript denotes the cross-section dimension and t labor’s marginal productivity. However, in practice, denotes the time-series dimension. Most of the panel there are certain elements that complicate the disclosure data application utilize a one-way error component of the correlation between the wage level and the model for the disturbances, with: uit = αi + εit [2]. productivity level. First, employers are interested in There are several different linear models for panel data. labor costs and not just wages. Second, the employment The fundamental distinction is that between fixed-effects relationship is bilateral between an employer (interested and random-effects models. In the fixed-effects (FE) in labor costs) and employees (interested in wage and model, the αi are permitted to be correlated with the other associated benefits). From a microeconomics regressors xit, while continuing to assume that xit is perspective, such a relationship is characterized by uncorrelated with the idiosyncratic error εit. In the asymmetric information and by incomplete and incorrect random-effects (RE) model, it is assumed that αi is disclosure of both parties’ intentions. This means that purely random, a stronger assumption implying that αi is there are problems in estimating the level of individual uncorrelated with the regressors [4]. labor productivity. From the macroeconomic perspective, the labor supply 4.1 Test for poolability of the data and demand curves are built at the expense of omitting One of the main motivations behind pooling a time the heterogeneous nature of the aggregation elements. series of cross-sections is to widen the database in order Thus, labor demand reflects the marginal productivity to get better and more reliable estimates of the curve of the labor, aggregated at the level of the national parameters of the model. The question is to pool or not economy or of the economic sectors (activities). to pool the data. Technically speaking, the relationship between the labor The simplest poolability test has its null hypothesis the supply and demand should take into account the work OLS model: y = a + b’X + ε and as its alternative the force remuneration. The problem is that this it it it FE model: yit = a + b’Xit +αi + εit [9]. In other words, we remuneration includes a variable component with many test for the presence of individual effects. Formally, we degrees of freedom – the wage (economic activities, write H0: αi = 0, i = 1,…, N. We consider the F statistics administrative units and time) and a semi-variable according to the construction principle: component (or semi-constant), namely the social (ESS - ESS /() N - )1 R U , where ESSR denotes the contributions paid by the employer (to make it more F1-way = ESS /(( -- KNT ))1 simple, we will ignore other minor elements of wage U costs) that are changed from time to time, as a result of residual sum of squares under the null hypothesis, ESSU government decisions, but do not vary in relation to the the residual sum of squares under the alternative. Under type of the economic activity. H0, the statistic F1-way is distributed as F with (N-1, (T - On the other hand, the wage structure is not the same for 1) N - K) degrees of freedom. The two sums of squares all workers, depending on the various fields of activity. evolve as intermediate results from OLS and from FE However, these wages have also mutual factors of estimation. influence, the most important of which being the In Stata, if we run the xtreg command with the fe option, minimum wage. we obtain at the bottom of the output the F-test that all Under these circumstances, it is necessary to identify a αi=0. If we reject the null hypothesis it also means that tradeoff between the motivational base of the behavior

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the OLS estimates suffer from an omission variables iitiit )'()( bxxyy -+-=- ee iit )( (2) problem and they are biased and inconsistent. The within estimator is the OLS estimator of this model. Because αi has been eliminated, OLS leads to consistent 4.2 The Hausman test estimates of b even if αi is correlated with xit as is the The Hausman principle can be applied to all hypothesis case in the FE model. This result is a great advantage of testing problems, in which two different estimators are panel data. Consistent estimation is possible even with ˆ available, the first of which b is efficient under the null endogenous regressors, provided that xit is correlated hypothesis, however inconsistent under the alternative, only with the time-invariant component of the error, αi, ~ while the other estimator b is consistent under both and not with the time-varying component of the error, εit. hypotheses, possibly without attaining efficiency under Stata fits the model: any hypothesis. Hausman had the intuitive idea to ( iit () iit )'bxxxayyy ( it i +-++-+=+- eee ) (3) construct a test statistic based on q = ˆ − ~ . Because of b b where, for example, = )/1( yNy i is the grand mean of yit. the consistency of both estimators under the null, this This parameterization has the advantage of providing an difference will converge to zero, while it fails to intercept estimate, the average of the individual effects converge under the alternative. Hausman suggested the αi, while yielding the same slope estimate b as that from -1 ~ statistic m = q’(var q) q, where var q = var b − var bˆ the within model. In Stata, the within estimator is follows from the known properties of both estimators computed by using the xtreg command with the fe under the null hypothesis and from uncorrelatedness. option. The default standard errors assume that after 2 The statistic m is distributed as χ under the null controlling for αi, the error εit is independent and hypothesis, with degrees of freedom corresponding to identically distributed (i.i.d). The vce (robust) option the dimension of b. relaxes this assumption and provides cluster-robust In the concrete case of panel models, we know that the standard errors, provided that observations are FE estimator is consistent in the RE model as well as in independent over i and N ® ¥ .[4] the FE model. In the FE model it is even efficient, in the 4.3.2 First-difference estimator (FD) RE model it has good asymptotic properties. By contrast, The first-difference estimator is obtained by performing the RE–GLS estimator cannot be used in the FE model, OLS on the first-differenced variables: while it is efficient by construction in the RE model. The )'()( bxxyy -+-=- ee )( inconsistency of the RE estimator in the FE model iit t-1, tiit -1, tiit -1, First-differencing has eliminated α , so OLS estimation follows from the fact that, as T → ∞, the individual fixed i of this model leads to consistent estimates of b in the FE effects α are not estimated but are viewed as realizations i model. The coefficients of time-invariant regressors are of random variables with mean zero. The violation of the not identified. assumption Eα = 0 for the regression model leads to an The FD estimator is relying on weaker exogeneity inconsistency [9]. assumptions that become important in dynamic panels. In Stata, the Hausman test statistic can be properly For the static FE models, the within estimator is computed based upon the contrast between the RE traditionally favored as it is more efficient estimator if estimator and fixed effects (FE). the ε are i.i.d. [4] it

4.3 Estimators for the fixed-effects model 4.4 Heteroskedasticity Estimators of the parameters b of the FE model must The standard error component given by equation (1) remove the fixed-effects α . i assumes that the regression disturbances are 4.3.1 Within estimator homoskedastic with the same variance across time and The within estimator eliminates the fixed-effect by individuals. This may be a restrictive assumption for mean-differencing. It performs OLS on the mean- panels. When heteroskedasticity is present the standard differenced data. Because all the observations of the errors of the estimates will be biased and we should mean-difference of a time-invariant variable are zero, we compute robust standard errors correcting for the cannot estimate the coefficient on a time-invariant possible presence of heteroskedasticity. variable. Because the within estimator provides a The fixed-effects regression model estimated by xtreg, fe consistent estimate of the FE model, it is often called the invokes the OLS estimator under the classical FE estimator. It is also consistent under the RE model, assumptions that the error process is independently and but alternative estimators are more efficient. identically distributed [3]. Also, the command xtreg, fe The fixed-effects α can be eliminated by subtraction of i estimates this model assuming homoskedasticity. The the corresponding model for individual means most likely deviation from homoskedastic errors in the 'bxy += e leading to the within model or mean- itii context of pooled cross-section time-series data (or panel difference model:

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data) is likely to be error variances specific to the cross- propose a nonparametric covariance matrix estimator sectional unit. which produces heteroskedasticity consistent standard When the error process is homoskedastic within cross- errors that are robust to very general forms of spatial and sectional units, but its variance differs across units we temporal dependence. have so called groupwise heteroskedasticity. Stata has a long tradition of providing the option to The xttest3 Stata command calculates a modified Wald estimate standard errors that are “robust” to certain statistic for groupwise heteroskedasticity in the residuals violations of the underlying econometric model. The of a fixed-effect regression model. The null hypothesis Stata program xtscc, implemented by Daniel Hoechle, 2 2 specifies that σ i= σ for i = 1,..., Ng, where Ng is the estimates pooled OLS and fixed effects (within) number of cross-sectional units. The resulting test regression models with Driscoll and Kraay standard statistic is distributed Chi-squared under the null errors. The error structure is assumed to be hypothesis of homoskedasticity. heteroskedastic, autocorrelated up to some lag, and possibly correlated between the groups (panels) [7]. 4.5 Serial correlation Because serial correlation in linear panel-data models biases the standard errors and causes the results to be 5 Results less efficient, researchers need to identify serial By analyzing the data about Romania, we can observe correlation in the idiosyncratic error term in a panel-data that, considering the overall economy during 2003-2005, model. While a number of tests for serial correlation in the productivity registered a growth above the increase panel-data models have been proposed, a new test of wages, except for the service and agriculture sectors. discussed by Wooldridge (2002) is very attractive However, it appears that, during 2006-2007, in terms of because it requires relatively few assumptions and is the overall economy, the productivity grew less than the easy to implement [6]. wages (a phenomenon that is caused by the work force Wooldridge’s method uses the residuals from a shortages in certain industries, but also by the low regression in first-differences. Note that first- unemployment rate as a result of work force migration). differencing the data removes the individual-level effect, In terms of industry, which is considered the main the term based on the time-invariant covariates and the tradable sector, we can say that a wage growth above constant, productivity generates, beside the inflationary pressures, yit − yit−1 = (Xit − Xit−1) b1 + εit − εit−1 a deterioration of the external competitiveness of exports Δyit = ΔXitb1 +Δ εit by increasing the unit labor cost. Regarding services, it’s where Δ is the first-difference operator. worth mentioning that productivity was not correlated Wooldridge’s procedure begins by estimating the with the wage increase (which is related to the parameters b1 by regressing Δyit on ΔXit and obtaining manifestation of the Balassa-Samuelson effect), the residuals eˆit . Central to this procedure is especially in public administration. Agriculture has the

Wooldridge’s observation that, if the εit are not serially lowest rate of productivity as it is the least efficient correlated, then Corr (Δεit, Δεit−1) = −0.5. Given this branch of the economy. observation, the procedure regresses the residuals 5.1 The econometric results eˆit from the regression with first-differenced variables on their lags and tests that the coefficient on the lagged We consider a linear regression model with lrem the dependent variable and lprod and lhminwage as residuals is equal to −.5. To account for the within-panel regressors. correlation in the regression of eˆ on eˆ , the VCE is it it-1 First, we explore the data. With the xtsum command we adjusted for clustering at the panel level. Since cluster () obtain the variance decomposition. The variable implies robust, this test is also robust to conditional minimum wage has zero between variance because it is heteroskedasticity. individual-invariant. Also, the within variation for this This test is implemented in Stata by David Drukker regressor is 0.05, meaning that it has little variation over under the name xtserial. The command xtserial performs time. For the productivity, the between variation is 0.71, a Wald test, where the null hypothesis is no first order while the within variation is only 0.17. autocorrelation.

4.6 Driscoll and Kraay estimator

Standard error estimates of commonly applied covariance matrix estimation techniques are biased and hence statistical inference that is based on such standard errors is invalid. Fortunately, Driscoll and Kraay (1998)

ISSN: 1790-2769 137 ISBN: 978-960-474-194-6 RECENT ADVANCES in MATHEMATICS and COMPUTERS in BUSINESS, ECONOMICS, BIOLOGY & CHEMISTRY

Std. Fixed-effects (within) regression Number of obs = 145 Variable Mean Min Max Observations Dev. Group variable: id Number of groups = 29

overall 15 8.3956 1 29 N = 145 R-sq: within = 0.7030 Obs per group: min = 5 id between 8.5147 1 29 n = 29 between = 0.4051 avg = 5.0 within 0 15 15 T = 5 overall = 0.4350 max = 5

overall 5 1.4191 3 7 N = 145 F (2,114) = 134.93 t between 0 5 5 n = 29 corr(u_i, Xb) = -0.6220 Prob > F = 0.0000 within 1.4191 3 7 T = 5 lrem Coef. Std. Err. t P>|t| [95% Conf. Interval] overall 2.0461 0.4508 0.6183 3.7664 N = 145 lprod 0.738687 0.0743988 9.93 0.000 0.59130 0.88607 lrem between 0.4020 0.9826 2.7344 n = 29 lhminwage 1.599968 0.2441675 6.55 0.000 1.11627 2.08366 within 0.2147 1.5678 3.1096 T = 5 _cons -1.161318 0.2242018 -5.18 0.000 -1.60546 -0.71717 overall 3.4339 0.7235 1.5387 5.2768 N = 145 sigma_u 0.41191234 sigma_e 0.13151224 lprod between 0.7135 2.1351 4.5373 n = 29 rho 0.90749465 (fraction of variance due to u_i) within 0.1689 2.8092 4.1735 T = 5 F test that all u_i=0: F(28, 114) = 28.69 Prob > F = 0.0000 overall 0.4193 0.0515 0.3857 0.5209 N = 145 Fig 3. Fixed-effect (within) regression lhmin~e between 0 0.4193 0.4193 n = 29 The estimated standard deviation of αi (sigma_u) is 0.41, within 0.0515 0.3857 0.5209 T = 5 Fig 1. Variance decomposition much bigger than the standard deviation of εit (sigma_e) which is 0.13, suggesting that the individual-specific A starting point for estimating the model is a pooled OLS component of the error is much more important than the regression. But we must know if pooling the data is the idiosyncratic error. solution in our case. So, a poolability test is needed. The standard error component model assumes that the The results obtained in Stata with the command xtreg, fe regression disturbances are homoskedastic. tells us to reject the null hypothesis that all α are zero. i After the xtreg, fe regression we can perform a modified This also means that the OLS estimator is biased and Wald test for groupwise heteroskedasticity in the fixed inconsistent and we accept the presence of the individual effect model, implemented in Stata by Christopher Baum, effects. using the xttest3 command. The results (P < 0.05) Next, we run a Hausman test to decide whether we have a indicate that we must reject the null hypothesis of random-effects model or a fixed-effects one. homoskedasticity. . hausman f r We also need to test for serial correlation which is very ---- Coefficients ---- likely to appear in an individual-effects model. We do so (b) (B) (b-B) sqrt(diag(V_b-V_B)) with the Stata command xtserial, implemented by David f r Difference S.E. Drukker. xtserial is a test for serial correlation in the lprod 0.7387 0.5708 0.1679 0.4707 idiosyncratic errors of a linear panel-data model. The lhminwage 1.6000 1.8696 -0.2697 0.4855 probability obtained for our model is 0.0093. This b = consistent under Ho and Ha; obtained from xtreg indicates that the errors are autocorrelated. B = inconsistent under Ha, efficient under Ho; obtained from xtreg We are now facing two problems with our model: Test: Ho: difference in coefficients not systematic heteroskedasticity and serial correlation. Assuming chi2(2) = (b-B)'[(V_b-V_B)^(-1)](b-B) homoskedastic disturbances when heteroskedasticity is = 12.72 present or ignoring correlation in the estimation of panel Prob>chi2 = 0.0017 models can lead to biased statistical results. To ensure (V_b-V_B is not positive definite) validity of the statistical results, most recent studies Fig 2. The Hausman test which include a regression on panel data therefore adjust

The probability is 0.0017, less than 0.05, so we reject the the standard errors of the coefficient estimates for null hypothesis that individual effect are random and that possible dependence in the residuals [7]. RE provides consistent estimates. The xtscc, fe performs fixed-effects (within) regression Concluding that we have a fixed-effects model, we with Driscoll and Kraay standard errors. The error continue with the estimation of our model using the structure is assumed to be heteroskedastic, autocorrelated within estimator, the most commonly used with this type up to some lag and possibly correlated between the of models. groups. The author of this Stata command is Daniel . xtreg lrem lprod lhminwage, fe Hoechle. . xtscc lrem lprod lhminwage, fe

ISSN: 1790-2769 138 ISBN: 978-960-474-194-6 RECENT ADVANCES in MATHEMATICS and COMPUTERS in BUSINESS, ECONOMICS, BIOLOGY & CHEMISTRY

Regression with Driscoll-Kraay standard errors Number of obs = 145 [2] Badi H. Baltagi, Econometric Analysis of Panel Data,

Method: Fixed-effects regression Number of groups = 29 John Wiley & Sons Ltd, 2008 [3] Christopher F. Baum, Residual diagnostics for cross- Group variable (i): id F( 2, 28) = 6753.19 section time series regression models, The Stata maximum lag: 2 Prob > F = 0.0000 Journal, Vol. 1, No. 1, pp. 101–104, 2001 within R-squared = 0.7030 [4] A. Colin Cameron, P.K. Trivedi, Microeconometrics

Drisc/Kraay Using Stata, Stata Press, 2009 [5] Amalia Cristescu, Alexandra Adam, Romania looking lrem Coef. Std. Err. t P>|t| [95% Conf. Interval] for competence on the European unique market - lprod 0.738687 0.117369 6.29 0.000 0.49827 0.97911 Romania in the European Union. The Quality of lhminwage 1.599968 0.403669 3.96 0.000 0.77308 2.42685 Integration. Growth. Competence. Employment, _cons -1.161318 0.220523 -5.27 0.000 -1.61304 -0.709597 Theoretical and Applied Economics, pp.370-373, Fig 4. Fixed-effect (within) regression with Driscoll and 2007. Kraay standard errors [6] David M. Drukker, Testing for serial correlation in

The resulted econometric model is: linear panel-data models, The Stata Journal, Vol. 3, lrem = -1,1613 + 0,7386 lprod + 1,5999 lhminwage No. 2, pp. 168–177, 2003 There is a significant correlation between the level of the [7] Daniel Hoechle, Robust Standard Errors for Panel employee remuneration and that of the labor Regressions with Cross-Sectional Dependence, The productivity. The value of the corresponding coefficient Stata Journal, Vol. 7, No. 3, pp. 281-312, 2007 (0.7386) reveals the conformation to the condition of [8] Z. Goschin, A.R. Danciu, M. Gruiescu, The economic efficiency. connection between labour productivity and wage in The estimated coefficient of the minimum wage reveals Romania. Territorial and sectoral approaches, its impact on remuneration. However, the high value of available online at this coefficient, compared with that of the labor http://steconomice.uoradea.ro/anale/volume/2008/v2- productivity, is caused by the taking-over of a part of economy-and-business-administration/029.pdf the constant. Also, the within estimator is relatively [9] Robert M. Kunst, Econometric Methods for Panel imprecise for time-varying regressors that vary little over Data – Part II, 2009, available online at time, like the minimum wage. http://homepage.univie.ac.at/robert.kunst/panels2e.pdf [10] Hun Myoung Park, Linear Regression Models for Panel Data Using SAS, Stata, LIMDEP, and SPSS, 2009, Working Paper, The University Information 6 Conclusions Technology Services (UITS) Center for Statistical and In this paper, we have investigated the impact of labor Mathematical Computing, Indiana University, productivity and minimum wages on the remuneration. http://www.indiana.edu/~statmath/stat/all/panel To explain this connection, we used a fixed-effects regression model. The main subject of interest was the way productivity growth is correlated with the increase of wages. The model that we estimated showed that an increase with 1% of the productivity induces an increase of 0.74% of the remuneration. The minimum wage affects to some point the correlation between employee remuneration and productivity because it is an exogenous variable that determines the economic agents to revise their salary budgets. The value of the constant should be interpreted subject to the semi-variable component of the wage remuneration (the social contribution does not vary depending on economic activities).

References: [1] M.E. Andreica, N. Cătăniciu, M.I. Andreica, Econometric and Neural Network Analysis of the Labor Productivity and Average Gross Earnings Indices in the Romanian Industry, Proceedings of the 10th WSEAS Int. Conf. MCBE 2009, pp.106-111

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