Question

(3) Suppose that you run a regression of wage on a set of independent variables: age, years of education, experience, and a dummy variable married. There are 100 observations, i.e., n=100. You want to test whether all the coefficient and intercept estimates in the equation for married and unmarried are equal to each other. i.e.,

Married: wage = β0 + β1*age + β2*educ + β3*exper + uUnmarried: wage = α0 + α1*age + α2*educ + α3*exper + v

(a) Write down the null hypothesis and alternative hypothesis.
(b) Write down the formula to calculate the Chow statistic. You don’t need to compute a numerical value. Just provide the formula.
(b) Suppose the critical value is 2.5. When will the null hypothesis get rejected?

(4) Provide the steps of implementing a hypothesis test.
(5) What is the formula for variance estimator in White(1980) to deal with heteroskedasticity?

Answer 1

a)

Null Hypothesis:

H₀: Pooled model is correct ie there is no significant improvement in fit from running two regressions.

Alternate Hypothesis:

H_a: Pooled model is not correct ie there is significant improvement in fit from running two regressions.

b)

RSS_A is defined as the RSS using only subsample of Married

RSS_B is defined as the RSS using only subsample of Unmarried

RSS_P is defined as the RSS using the entire(pooled) sample

The Chow test is an F test with the following F-statistic:

F = {(RSS_P – RSS_A – RSS_{B ­­­­­­­­})/k}/ {(RSS_A + RSS_B)/(n-2k)}

where k is the number of parameters in pooled model

c)

If our F value is greater than critical value, then we reject the null hypothesis ie if out F value is greater than 2.5, we will reject the null hypothesis.

4)

The steps of a hypothesis test are:

• Specify the Null Hypothesis.
• Specify the Alternative Hypothesis.
• Set the Significance Level (alpha)
• Calculate the Test Statistic and Corresponding P-Value.
• Draw a Conclusion.

5)

Steps of testing heteroskedasticity are:

• Estimate model using OLS:

• Obtain the predicted Y values after estimating our model.
• Estimate the model using OLS:

• Retain the R-squared value from this regression:
• Calculate the F-statistic or the chi-squared statistic:

The degrees of freedom for the F-test are equal to 2 in the numerator and n – 3 in the denominator. The degrees of freedom for the chi-squared test are 2. If the test statistics is significant, then we have evidence of heteroskedasticity. If not, we fail to reject the null hypothesis of homoskedasticity.