Suppose that we want to estimate the effect of several variables on annual saving and that we have a panel data set on individuals collected on January 31, 1990, and January 31, 1992. If we include a year dummy for 1992 and use first differencing, can we also include age in the original model? Explain.

No, we cannot include age in the original model as an explanatory variable in the original model

Explanation:

No, we cannot include age in the original model because Each of the person in the panel data set is exactly two years older on January 31, 1992 than that of January 31, 1990 which means that 2=∆i age for all i.

Although the equation we would estimate will be in this form .

∆savingi β⁰+δ¹∆age i +...,

where δ will be the coefficient of the year dummy for 1992 in the original model. In a situation where we have an intercept in the model this means that we cannot include an explanatory variable which is constant across i, and since age tend to change by the same amount for everyone, it means we cannot differentiate the effect of age from that of the aggregate time effects.