Question: Simple versus Multiple Regression Coefficients. This is based on Baltagi (1987b). Consider the multiple regression Yi = + 2X2i + 3X3i + ui i

Simple versus Multiple Regression Coefficients. This is based on Baltagi (1987b). Consider the multiple regression Yi = α + β2X2i + β3X3i + ui i = 1, 2, . . . , n along with the following auxiliary regressions:

X2i = a +bX3i + ν2i X3i = c + dX2i + ν3i In section 4.3, we showed that β2, the OLS estimate of β2 can be interpreted as a simple regression of Y on the OLS residuals ν2. A similar interpretation can be given to β3. Kennedy (1981, p. 416)

claims that β2 is not necessarily the same asδ2, theOLS estimate of δ2 obtained from the regression Y on ν2, ν3 and a constant, Yi = γ +δ2ν2i +δ3ν3i +wi. Prove this claim by finding a relationship between the β’s and theδ’s.

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