(Stata16): Two-way Error Component Models

‪@CrunchEconometrix‬ simplifies the understanding of error component models using an approach that beginners can grasp. It further shows the estimation, interpretation, and poolability test of the one-way error component model and two-way error component model. The sub-topics are as follows: (1) Understanding Error Component Models; (2) One-way Error Component Model (Common Intercept, Slope coefficients constant but intercept varies over entities, Slope coefficients constant but intercept varies over time); and (3) Two-way Error Component Model (Common Intercept, Slope coefficients constant but intercept varies over entities, Slope coefficients constant but intercept varies over time).
What are error component models? They are used in pooled (panel) data analysis. Panel data or longitudinal data (the older terminology) refer to a data set containing observations on multiple phenomena over multiple time periods. Thus, it has two dimensions: spatial (cross-sectional) and temporal (time series). In general, we can have two types of panels: micro and macro panels. Micro panel: Surveys (usually a large) with sample of countries, households or firms or industries over (usually a short) period of time. Macro panel: Consists of (usually a large) number of countries or regions over (usually a large) number of years. Again, depending upon whether the panels include missing values or not, we can have two varieties: balanced and unbalanced panel. Balanced panel does not have any missing values, whereas the unbalanced have missing values. There are two more models, depending upon the relative size of space and time, short and long panels. Short panel: number of time periods (T) is less than the number of cross-section units (N) and Long panel: number of time periods (T) is longer than the number of cross-section units (N).
The main advantage of panel data comes from its solution to the difficulties involved in interpreting the regression coefficients in the framework of a cross-section only or time series only regression. The question here is, how do we account for the cross-section and time heterogeneity in a panel model? This is done by using a two-way error component assumption for the disturbances error term that is further divided into (1) unobservable individual heterogeneity, (2) unobservable time heterogeneity and (3) remaining random error term. Now depending upon the assumptions about these error components, whether they are fixed or random, we have two types of panel data models, fixed effects and random effects. If we assume that the heterogeneities are fixed parameters to be estimated and the random error term is identically and independently distributed with zero mean and a constant variance, then equation we have a two-way fixed effects error component model or simply a fixed effects model or least squares dummy variable (LSDV) model and a two-way random effects error component model or simply a random effects model, if otherwise.
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References and Readings: Asteriou and Hall (2016) Applied Econometrics, 3ed; Wooldridge, J. M. (1995). Econometric Analysis of Cross Section and Panel Data. London, England: The MIT Press, Cambridge, Massachusetts; Baltagi, B.H. (1995) Econometric Analysis of Panel Data. New York, NY: John Wiley and Sons; Hsiao, C. (1986) Analysis of Panel Data, Econometric Society Monographs No. 11. Cambridge, United Kingdom: Cambridge University Press; Adeleye, N., Eboagu, C. (2019). “Evaluation of ICT Development and Economic Growth in Africa”, NETNOMICS: Economic Research and Electronic Networking, 20(1), 31-53, DOI: 10.1007/s11066-019-09131-6 dx.doi.org/10.1... Adeleye, N., Osabuohien, E., Bowale, E. (2017) “The Role of Institutions in the Finance-Inequality Nexus in Sub-Saharan Africa”, Journal of Contextual Economics, 137(2017), 173 - 192, Duncker & Humblot, Berlin ….and several journal articles.
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