In this chapter we discussed several functional forms an empirical model can assume, even within the confines of the linear-in-parameter regression models. The choice of a particular functional form may be comparatively easy in the two-variable case, because we can plot the variables and get some rough idea about the appropriate model. The choice becomes much harder when we consider the multiple regression model involving more than one regressor, as we will discover when we discuss this topic in the next two chapters. There is no denying that a great deal of skill and experience are required in choosing an appropriate model for empirical estimation. But some guidelines can be offered:
1. The underlying theory (e.g., the Phillips curve) may suggest a particular functional form.
2. It is good practice to find out the rate of change (i.e., the slope) of the regressand with respect to the regressor as well as to find out the elasticity of the regressand with respect to the regressor. For the various models considered in this chapter, we provide the necessary formulas for the slope and elasticity coefficients of the various models in Table 6.6. The knowledge of these formulas will help us to compare the various models.
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