2.5.1 Dynamic panel model
The key modelling technique which is employed in this chapter is the regression using panel data methods. There are several bene…ts from using panel data. According to Baltagi (2013), such technique allows us to:
1. Control for individual heterogeneity;
2. Use more data, obtain more variability, reduce collinearity among the variables
of interest and increase the number of degrees of freedom;
3. Better study the dynamic behaviour of the variables and the relation between
them;
4. Identify and measure e¤ects that are not detectable in pure cross-section or
time-series data;
5. Construct and test more complicated models than those allowed by employing
purely cross-section or time-series data.
Some panel datasets, especially those employing individuals or …rms, usually su¤er from missing data. This is more common some combination of cross-sectional unit and time period(s) (Wooldridge, 2006). In this dataset, information is missing for some of the sample …rms in certain years. As a result, the panel is unbalanced. The unbalanced panel structure has the bene…t of partially mitigating potential selection and survival bias problems (Carpenter and Guariglia, 2008).
Literature on employment commonly uses dynamic panel data models (Arellano and Bover, 1995; Blundell and Bond, 1998). The rationale for estimating the model in a dy- namic panel data setting can be attributed to the lagged value of the dependent variable and the lagged values of the explanatory variables (Gujarati and Porter, 2009). Con- sequently, the models which are de…ned in sub-section 2.5 include lagged values of the explanatory variables, as well as, the time path of the dependent variable employment in relation to its past value. Next it is discussed the estimation method implemented in this chapter.
2.5.2 Estimation methodology
In this chapter all the equations are estimated using the system GMM estimator by Arel-
lano and Bover (1995) and Blundell and Bond (1998).28 The speci…cation model which is
de…ned in sub-section 2.4.1 makes the simple OLS estimator upwards biased and inconsis- tent since the lagged level of employment is correlated with the error term (Verbeek, 2012). The within-groups estimator is also not appropriate due to inconsistency and downward 28All the regressions are performed in Stata using the command xtabond2 developed by Roodman
bias (Nickell and Nicolitsas, 1999). More importantly, the employment model may su¤er from endogeneity. Firm-speci…c variables are likely to be in‡uenced by employment, wage, productivity shocks and the lagged dependent variable is automatically endogeneous due to the presence of the lagged error in the equation (Nickell and Nicolitsas, 1999). For this reason, the most appropriate techique for the abovementioned speci…cation is the GMM estimator.
The implementation of the GMM estimator provides a number of advantages. Firstly, it controls for the endogeneity of the regressors. Secondly, it accounts for unobserved ef- fects and the inclusion of the lagged dependent variable as regressors. The …rst-di¤erence GMM estimator of Arellano and Bond (1991) uses the …rst-di¤erences of the explanatory variables to remove the unobserved …rm-speci…c e¤ects, time-invariant, industry-speci…c and country-speci…c e¤ects. The …rst-di¤erence GMM estimator requires that the regres- sors are used as instruments (i.e. using deep lags of the explanatory variables). The aim is to control for simultaneity bias of the explanatory variables and the correlation be- tween the lag dependent variable and the error term. However, as it is noted by Blundell and Bond (1998), this estimator can create considerable bias. It can su¤er from a weak instrument problem if the the lag dependent variable follows a random walk. In a sce- nario that the time dimension of the sample is small , the …rst-di¤erence GMM estimator performs poorly since lagged levels of the variables are weak instruments for subsequent …rst-di¤erences.
The system GMM estimator is a more e¢ cient estimator. It combines in a system the equation in the …rst-di¤erences with an equation in levels. It makes use of the lagged levels of the regressors as instruments in the di¤erenced equation, and the lagged di¤erences of the regressors as instruments in the levels equation. One of the advantages of the system GMM is that it reduces the potential bias and inaccuracy associated with the use of the …rst-di¤erence GMM estimator. It improves e¢ ciency and a signi…cant reduction in …nite sample bias comparing with the simple …rst-di¤erence GMM approach (Blundell and Bond, 1998).
In the employment models of Chapter 2 …rm-speci…c variables, including interest bur- den may su¤er from some endogeneity issues since they are likely to be in‡uenced by employment wages and demand shocks (i.e. sales growth). To avoid the bias which is associated with this endogeneity problem, Chapter 2 follows Nickell and Nicolitsas (1999) and takes deeper lags of the explanatory variables as instruments in the equations in …rst- di¤erences and in levels. In other words, the use of deeper lags of interest burden may overcome for the possibility of simultaneity bias.
The consistency of the system GMM estimator depends on two di¤erent criteria. First, the Sargan test (also known as J test), which is a test for overidentifying restrictions. Under the null of instrument validity, it is asymptotically distributed as a chi-square with
degrees of freedom equal to the number of instruments less the number of parameters. Second, the GMM estimator can only be appropriate if there is no serial correlation in the
…rst-di¤erenced residuals. In the presence of serial correlation of ordern in the di¤erenced
residuals, the instrument set of the equation in the …rst-di¤erences should be restricted
to lags n+1 and deeper (Roodman, 2009). To check for the existence of nth-order serial
correlation in the di¤erenced of the residuals the m(n) test is implemented. The m(n) test
is asymptotically distributed as a standard normal under the null of no serial correlation
of the di¤erenced residuals. In Chapter 2 it is reported the …rst-(m1) order and the fourth
order-(m4) test for serial correlation of the di¤erenced residuals in the tables. At the
same time it is used four (and deeper) lags of the regressors as instruments. The use of deeper lags is a common procedure in the literature. This enables the research to improve
the speci…cation tests of the models (Chen and Guariglia, 2013; Guariglia et al., 2012).29
Country, industry, time dummies and time dummies interacted with industry dummies are also included in the instrument matrix.
Finally, it should be noted that the system GMM estimator is sometimes weak when it is used on large samples. Blundell et al. (2001) demonstrate using Monte Carlo experiments that this test tends to over-reject the null hypothesis of valid instruments for the system GMM, especially for large samples. Chen and Guariglia (2013) con…rm this …nding using a large panel of Chinese …rms.