Question

When you estimate the first-differenced model, you notice that the model has almost no explanatory power. R^2 is nearly zero and none of the estimated coefficients are statistically significant. Is this consistent with economic theory? Why or why not?

Answer 1

First difference model is obtained when there is serial autocorrelation between peroiods, i.e Y value of two consecutive periods is autocorrelated. Now, we have to understand that serial correlation does not impact estimates i.e. does not make them biased. The standard errors of the OLS estimates become biased leading to unreliable hypothesis testing. Thus, the estimated coefficients after the first differencing are the appropriate estimates which give true explanatory power of the model. It is consistent with economic or econometric theory. This just means that without first differencing the standard errors were highly biased thus gave inappropriate estimates and cosequently  inappropriate explanatory power.