*3.2. Model Estimation*

Panel data models can be static or dynamic. Static panel data models can be estimated using pooled ordinary least squares (OLS), fixed effects (FE), and random effects (RE) models, but these models do not take the problems of heteroscedasticity, serial correlation, and the endogeneity of the explanatory variables into account [61–63]. The pooled OLS model ignores fixed industry and time effects. In FE, these are fixed effects correlated with the inputs, while it is assumed that they do not correlate with inputs in the RE model. In all the models, the time effects are captured by the trend. In the FE model, we estimate the effects in the form of industry intercepts, while, in RE, we estimate the parameters of the distribution of the industry effects which, are assumed to have means of zero and constant variance [63].

To solve the estimation problems related to a static panel formulation, we use the dynamic panel model of difference GMM and system GMM estimators, as proposed by Arellano Bond [64] and Arellano and Bover [65], respectively. The difference GMM and system GMM are dynamic panel estimators designed for large N and small T, many groups/individuals, a few time periods, a linear functional relationship, one left-hand side that is dynamic depending on its own past realization, and for independent variables that are not strictly exogenous [66]. System GMM contains both level and first difference equation parts, it uses instruments in levels for equations in first difference and uses instruments in first difference for equations in levels [61]. After estimating the dynamic panel data models, tests for the serial correlation of the residuals and overidentification were done using Hausman or Sargan tests and the autoregressive AR (2) test, respectively [64,65].

#### **4. The Data**

#### *4.1. Data and Variables*

All data used in this study are taken from the Ethiopian Central Statistical Authority (CSA). The period 2005–2016 is chosen for the study since the latest information on all variables is available only up to 2016. The number of industry groups and the study period were determined by data availability. A two-digit industry sector level is the most disaggregated data level available for this specific case. The number of observations for industry groups (industrial sectors) is 15, where, for every industry group, the relevant variables available are included. Table 1 provides a list of the industry groups. The medium and large manufacturing industries in Ethiopia are categorized into 15 industry groups.



Source: Central Statistical Authority (CSA).

Table 2 gives the list of variables used in this study and their definitions. To define labor productivity, we need information on production and employment. Production, in our case, is defined as the gross value of production by industry group. Employment is defined as the number of employees by industry group. Accordingly, labor productivity is defined as the ratio of production to employment by industry group or per capita employed production, labeled in the literature as labor productivity. Energy is defined as the ratio of the value of energy consumed by the industry groups. Capital is defined as the total value of the fixed assets by industry groups. Table 2 also shows the expected

effects of the variables in the model on labor productivity. Labor productivity is the dependent variable and the explanatory variables are energy use, employment, capital, and trend which are expected to be statistically significant in the empirical estimation. The expected sign for employment is positive as industries in Ethiopia are more labor intensive, so adding more labor is expected to increase production. Similarly, the expected signs of the parameters for energy, capital, and technical change are expected to be positive. It is assumed that energy use and capital will increase labor productivity in the manufacturing industries in Ethiopia. Wages and salaries were included as a proxy for human capital but they were excluded from the estimation due to high collinearity problem. An increase in wages and salaries is expected to positively affect labor productivity and higher wages per capita reflect the laborers' skills and education levels.


**Table 2.** List of variables, expected level of significance, and coefficient signs.
