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ECON 2560 – Applied Econometrics – Fall 2022 – Final review problems

Instructions:  Complete the problems below in a readable format (word, excel, pdf), showing work for partial credit. Submit via Canvas or email within 2 hours. You may use external resources such as the textbook, notes, internet etc. (On the exam, you will be given point values for guidance on time and effort allocation.) 

1.  In a fixed-effects panel data regression, each of the dependent and independent variables are "time-demeaned", that is, average values across each time period but within each cross-sectional unit are subtracted from original variables. What is the econometric purpose of the time-demeaning (what classical regression assumption is assumed to be violated without the time-demeaning, and how does the time-demeaning fix that problem)?

2.  Squared residuals from a regression of ABT (Abbott Labs) returns on S&P500 returns were regressed against the S&P500 returns and squared S&P500 returns, which produced the following output:

a) Compute a White heteroscedasticity test statistic from this information.

b) What distribution does this test statistic have (type of distribution and degrees of freedom)?

c) What is the approximate 1% critical value for this test?

3.  Using annual data, the following Phillips curve was estimated:

inflhat = 0.32 + 0.92*infl(-1) + 0.08*infl(-2) - 0.033*unemp(-1) + 0.011*chgoil(-1)

               (0.56)  (0.142)           (0.045)             (0.012)                   (0.023)

           n = 55, R^2 = 0.174

where infl is the inflation rate and infl(-1) and infl(-2) are lags of inflation, unemp(-1) is the lagged unemployment rate and chgoil is the lagged change in oil prices (all data entered in percent, e.g. 5.0% = 5.0).

If the past 2 years' inflation rates were 2.1% and 1.9%, last year's unemployment rate was 7.3%, and last year's change in oil prices was 25%, what would the model's forecast for inflation be?

4.  Residuals from a regression of JPM returns on S&P500 returns were regressed against two lags of those residuals and the S&P500 returns, which produced the following output:

a) Compute a Breusch-Godfrey serial correlation test statistic from this information.

b) What distribution does this test statistic have (type of distribution and degrees of freedom)?

c) What is the approximate 10% critical value for this test?

5.  Which of the following statements about two-stage least squares (2SLS) regression is most correct? (? pts)

a) In 2SLS, the first stage is to run regressions of exogenous variables against each other, and the second stage is to run regressions of endogenous variables against each other.

b) Estimating simultaneous equations using OLS leads to biased but consistent parameter estimates.

c) The first stage of 2SLS is Dickey-Fuller tests, and the second stage is a Cointegration test.

d) The first stage of 2SLS is reduced-form regressions, and the second stage replaces endogenous RHS variables with predicted values from the first-stage regressions.

6.  An OLS regression of house prices (in dollars) against house age, age^2, age*area, distance to central business district, area (size of house in square feet), number of rooms, and number of bathrooms produced the following output:

What is the model's estimated impact of age on house price for a house that is 4 years old and has 2500 square feet? Show work for partial credit.

7.  Using the logit model below, what is the estimated probability of failure for a bank that has primary capital to total assets of 18 (percent), 12 (percent) of its loans more than 90 days past due, and net loan charge-offs to total assets of 8 (percent)? (? pts)

8.  A regression of the log of IBM's stock price against the first lag of the log of IBM's stock price produced the results below.

a) Use those results to compute a Dickey-Fuller test statistic for the null hypothesis that the log of IBM's stock price follows a random walk.

b) What is the approximate 5% (one tail) critical value? Do you reject the null hypothesis at a 5% (one tail) significance level?