** Must Provide STATA output for full answer credit**

Estimate an aggregate consumption function for the U.S. economy for the period 19452006, testing your equation for serial correlation, and, if appropriate, taking corrective action. We end the sample with 2006 to avoid the (admittedly interesting) complications introduced by the Great Recession).

Step 1: State the Variables and the Expected Signs of the Coefficients

The goal is to model U.S. aggregate consumption as a function of disposable personal income and the real interest rate. The data are from the St. Louis Federal Reserve FRED database and the Economic Report of the President. Descriptions of the variables are in Table 4.1, along with the hypothesized signs for the coefficients, and the dataset is called CONS9.

Table 4.1 Variable Definitions

Variable	Description	Expected Sign
cont	The real personal consumption expenditures in year t, in billions of 2009 dollars	NA
dpit	The real disposable personal income in year t, in billions of 2009 dollars	+
aaat	the real interest rate on Aaa corporate bonds in year t	-
yeart	Year t	NA

Step 2: Estimate the Aggregate Consumption Function

Now estimate the consumption function, using disposable personal income and the real interest rate as the independent variables. If youre using Stata, be sure to tell Stata that this is a time series and that year is the time variable.

Step 3: Examine the Residuals

Generate the residuals from the regression in Step 2 (naming them e) and plot them as a line graph against year_t (year_t should be on the x-axis). Does the plot look entirely random? Explain.

Step 4: Run the Durbin-Watson Test

Conduct a Durbin-Watson test for positive serial correlation.

a. Carefully write the null and alternative hypotheses.

b. Run a Durbin-Watson test for positive serial correlation at the 5-percent level. What are the upper and lower critical values in this case? What can you conclude?

Step 5: Run the Lagrange Multiplier Serial Correlation Test

Lets see if our Durbin-Watson results can be confirmed with the Lagrange Multiplier test.

a. Are the null and alternative hypotheses for the Lagrange Multiplier test the same as for the Durbin-Watson test? Why or why not?

b. Conduct a Lagrange Multiplier test for serial correlation at the 5-percent level. What can you conclude? Explain.

Step 6: Estimate the Model with Generalized Least Squares

a. If you encountered serial correlation in either of the previous steps, re-estimate our aggregate consumption model using Generalized Least Squares.

b. Are the GLS coefficients and t-statistics the same as the OLS coefficients and t-statistics? Explain.

c. After the GLS transformation, does serial correlation still appear to exist? Support your answer.

Step 7: Calculate Newey-West Standard Errors

a. If you ran a GLS model in Step 6, now estimate the aggregate consumption model using the Newey-West method with a lag of 1.

b. After the Newey-West calculation, are the coefficients the same as the OLS coefficients? Explain.

c. Why are the Newey-West t-statistics different from the OLS t-statistics? Which do you prefer? Why?

Go back to Steps 5 though 7

a. Lets consider testing for higher-order serial correlation. Conduct the LMSC test for third-order serial correlation. What do you find? (Describe the null hypothesis and provide the new regression results. Interpret your findings.)

Hint: In this case, we use:

e_t = ₀ + ₁dpi_t + ₂aaa_t + ₃e_t-1 + ₄e_t-2 + ₅e_t-3 + u_t

b. Now estimate Newey-West standard errors with a lag of 3. Interpret your findings.