Lecture 7 model specifications (1)

1 MODEL SPECIFICATIONS Dr Tu Thuy Anh Faculty of International Economics ThiN ga nH an g co m ThiNganHang com Problems  Model misspecification  Omitting relevant variables  Including irrelevant var[.]

an g co m nH MODEL SPECIFICATIONS Th iN ga Dr Tu Thuy Anh Faculty of International Economics ThiNganHang.com an g co m Problems  Model misspecification:  Omitting relevant variables  Including irrelevant variables nH  Function specification: Ramsey test Th iN ga  Structural change: the Chow test ThiNganHang.com OMISSION OF A RELEVANT VARIABLE an g co m Consequences of Variable Misspecification True Model  b3 X ga Yˆ  b1  b2 X nH Yˆ  b1  b2 X Th iN Fitted Model Y  1   X  u Y  1   X   X  u To keep the analysis simple, we will assume that there are only two possibilities Either Y depends only on X2, or it depends on both X2 and X3 ThiNganHang.com OMISSION OF A RELEVANT VARIABLE an g co m Consequences of Variable Misspecification True Model  b3 X ga Yˆ  b1  b2 X nH Correct specification, ˆ Y  b1  b2 X no problems Correct specification, no problems iN Fitted Model Y  1   X  u Y  1   X   X  u Th If Y depends only on X2, and we fit a simple regression model, we will not encounter any problems, assuming of course that the regression model assumptions are valid Likewise we will not encounter any problems if Y depends on ThiNganHang.com both X2 and X3 and we fit the multiple regression OMISSION OF A RELEVANT VARIABLE an g co m Consequences of Variable Misspecification True Model Yˆ  b1  b2 X ga  b3 X nH Yˆ  b1  b2 X Correct specification, no problems Coefficients are biased (in general) Standard errors are invalid Correct specification, no problems Th iN Fitted Model Y  1   X  u Y  1   X   X  u In this sequence we will examine the consequences of fitting a simple regression when the true model is multiple The omission of a relevant ThiNganHang.com explanatory variable causes the regression coefficients to be biased and the standard errors to be invalid  ... VARIABLE an g co m Consequences of Variable Misspecification True Model  b3 X ga Yˆ  b1  b2 X nH Yˆ  b1  b2 X Th iN Fitted Model Y  1   X  u Y  1   X   X  u To keep the analysis... Variable Misspecification True Model  b3 X ga Yˆ  b1  b2 X nH Correct specification, ˆ Y  b1  b2 X no problems Correct specification, no problems iN Fitted Model Y  1   X  u Y  1 ... If Y depends only on X2, and we fit a simple regression model, we will not encounter any problems, assuming of course that the regression model assumptions are valid Likewise we will not encounter