Specification error (Functional form)

Specification error (Functional form) - Econ107 Applied...

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Econ107 Applied Econometrics 5 Speci fi cation: Choosing Independent and Depen- dent Variables (Studenmund, Chapters 6, 7) Before we estimate an equation, we have to specify it. Specifying an econometric equation consists of three parts: choosing the correct independent variables, choosing the correct functional form, choosing the correct form of the stochastic error term. A speci fi cation error results when one of these choices is made incorrectly. We study fi rst choosing the independent variables and then choosing the correct functional form. The last choice will be studied in later topics. 1
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5.1 Speci fi cation: Choosing the Independent Variables We fi rst deal with the choice of independent variables. Misspeci fi cation of independent variables may be due to omitted (relevant) variables, redundant variables (including irrelevant variables). An example of wage equation Huge attention in labor economics has focused on the estimation of wage equation to characterize the payo ff of schooling/education. For simplicity, we consider the following linear regression model: ln W i = β 0 + β 1 S i + β 2 T i + ε i , (1) where W i is the wage rate of worker i, 2
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S i is the years of schooling (formal education) of worker i, T i is the e ff ective years of on-the-job training of work i. The idea is that we have two forms of human capital: general human capital obtained through formal education and speci fi c human capital obtained through vocational education, apprenticeship programmes, etc. Both may increase wages (i.e., β 1 > 0 and β 2 > 0), but usually not at the same rate (i.e., β 1 6 = β 2 ). 3
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