income shares reflect output elasticities is likely to be violated for capital goods especially in the case of foreign direct investment, where monopoly suppliers of capital goods may earn a return in excess of the marginal product of capital. Expanding on this, and drawing on Sard’s (1997) explanation, a point to note is that the income shares can be affected by differences in the structure of production, government taxes, regulations and incentives and the market structure governing the different industries within the broad sectors of manufacturing and services.
5 Remuneration is composed of 3 components, namely, wages and salaries, employer’s contribution to central provident fund/pension funds and other benefits like medical benefits, cost of food, accommodation and benefits in kind. Allowances given to unpaid family workers were also included.
3.84 at 5% level of significance, the null hypothesis stated above cannot be rejected. This along with the earlier evidence of constant returns to scale implies that the Cobb- Douglas functional form is appropriate for the present data for the manufacturing sector.
The Random and Fixed Effects Model
With panel data, questions are often raised on the existence of cross-sectional heterogeneity and autocorrelation in the sample. While autocorrelation can be easily corrected for by autoregression techniques in Ordinary Least Square (OLS) regression, cross-sectional heterogeneity can be a problem. In this case, the cross-sectional heterogeneity refers to the individual industry effects as they produce different output and may even operate differently, although they belong to the same broad sector. There are two common methods of estimation to take into account the individual industry effects using panel data: the fixed effects (FE) and random effects (RE) models
When the individual effects are constant over time t, but specific to the individual cross- sectional industry i, it constitutes the FE model with constant-slope, variable intercept framework. When the individual effects are allowed to vary over time t, besides being specific to the individual cross-sectional industry i, it is the RE model. Mundlak (1978) argues that one should always treat the individual effects as random.
Consider the FE model below:
Yjt = c*oi + X'itOt + uit
and Ooi = 0(o + £,
uit = £. + vit where i = 1,...n
t = 1,... T
ult is a composed error term that combines the time-invariant individual industry effects £i t and the statistical disturbance term vit, which is assumed to be normally distributed and uncorrelated with e, and X'u ‘s in the model.
Unlike the RE model, in the FE model, the time-invariant regressors are eliminated in the ‘within’ transformation and if dummies are used to represent different industries, it is costly in terms of degrees of freedom lost. And the variability of the data within each
industry through time is being utilised; not the variance in the data across industries at any given point in time. Since the magnitude of the variance in a data set is typically between, rather than within industries, this procedure has the disadvantage of greatly reducing the variance of the regressors, creating two problems. First, the reduction in the variance of the regressors tends to exacerbate any multicollinearity problems. Second, it lowers the signal-to-noise ratio for any given set of measurement errors, causing the estimates to bias towards zero.
However, the RE model is not without its limitations. Unlike the FE model, this procedure utilises variations in the data both between industries at a given point in time as well as within each industry through time. Thus, instead of working conditionally on the industry effects £j t we take their stochastic nature explicitly into account. The underlying assumption is that the individual effects are uncorrelated with the other regressors (that is, £j and X ' j t ’s are not correlated). But this is not necessarily true and if such a correlation exists, it would lead to inconsistent and biased estimates. Hence, the FE model, which includes the industry-specific effects as regressors rather than neglecting them to the error terms, overcomes this problem.6
The possibility of such a correlation existing between the regressors and the error terms is due to the following reason. While £j is unobservable from the estimation, its permanency would lead us to expect industries to observe £j and to take its level into account when choosing the explanatory variables, XVs. It is possible, of course, that industries also observe vit, the period-specific shocks. It is customary in the literature to assume that the X ' j t ’s at time t are chosen before vit is observed by the industry (or that the industry never observes vit), making the X'lt ’s at time t independent of this component of the error term. If this assumption is violated, then the FE estimators will join the RE estimators in being inconsistent.
It becomes necessary, therefore, to choose the method that best fits the sample and the purpose of the analysis. One way to proceed is to rely on the statistical properties of the sample, in which case we would apply the RE model for random samples and the FE model otherwise. There also exists the Hausman’s chi-square test to test the RE model
against the FE model. Mundlak (1978:70), however, argues that the decision to use either model is both arbitrary and misleading, and it is up to the user to decide on the type of inference required. Also, the possibility of correlation between the industry effects and the regressors in the model cannot be ruled out. When there is no such correlation and the model is properly specified, both approximation methods yield consistent estimates of the parameters. Given the above arguments, the FE model was chosen over the RE model.
The Fixed Effects Model
A common formulation of the model assumes that differences across industries can be captured in the differences in the constant term. The V s , which are unknown fixed parameters, are estimated using dummies representing each industry. However, a and ß, the ‘within’ estimators, are assumed to be constant across industries. For the purpose of analysis, the model can be written as:
Log Yjt = Z A,j + ß Log Ljt + oc Log Kjt + 8 T + Ujt
j = i
where i = 1,...N (no. of industries) t = 1,....20 (no. of years)
j = 1,...s (no. of dummies representing industry codes) Y = value added output
L = number of workers K = capital used
T = time trend
X = industry dummy
The above model is usually referred to as the least squares dummy variable model and the advantage of this model is that standard errors for all parameter estimators can be obtained, which allows for statistical testing.
Eight dummies were used to group industries according to their 2-digit industry codes to
n
better capture the industry-specific effects. The model was then estimated over the period of 1975-94. Since no constant was included in the estimations, the number of dummies used is equal to the number of grouped industries. As in the earlier estimation,
7 Using separate dummies for each 3-digit industry in the manufacturing sector did not provide