[SOLVED] Econometrics ii homework 4 spring 2025 p0

1. Consider the model
yt = β0 + β1x1t + β2x2t + ut .
Rewrite the model so that the restriction β1 = β2 becomes a single zero restriction that you can test using a t-test. (This should be easy, but it is often useful in practice.)
2. Almost the same question but super relevant for practice): A sample consists of males andfemales. We have a dummy Dm for males and a dummy Df for females. Consider the regression equation
yi = β + βmDim + βfDif + ui .
a) Show explicitly that there is perfect multi-collinearity in this model. So you now drop the constant to get rid of the collinearity and want to estimate
yi = βmDim + βfDif + ui .
b) Explain how you can rewrite the model such that βf = βm becomes a single zero restriction that you can test using a t-test.
3. Computer question (continuation of homework 1, 2, and 3). In Matlab, regress real per capita U.S.
data consumption growth on income growth and the interest rate using the posted dataset.
(This is the what you did in homework 1.)
a) Calculate the t-test for each of the parameters and display the P-values.
b) Test if the coefficient to income growth is identical to the coefficient for the interest rate. (Thetests don’t make much economic sense, but this exercise is about the tools.) Explain how you could use a t-test (how) or an F-test. Verify in Matlab that the P-values are identical for the two alternative tests.
c) Test if the coefficients to income growth and the coefficient to the interest rate are both zero.(This means that you do one test for this.) How does the P-value compare to the ones that you get if you test the coefficients one-by-one using t-tests?
d) Test if (simultaneusly) the coefficients to income growth is equal to the constant and if thecoefficient to the interest rate are equal to the constant. (This is two linear constraints, not economically meaningful, but that is not the goal here.)