106 Econometric Theory and Applications

1. Estimate the following equation by OLS using ordinary least squares:

01tttpq=++ββε

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where and . ln()ttpP= ln(Q)ttq=

2. What is your estimate of the elasticity of demand? Your estimate is positive, so it looks like something is wrong. In the following questions, we will try to figure out what is wrong.

3. First, the value of a dollar changed a lot from 1926 to 2014. We should really use real prices rather than nominal prices. Run the regression:

, 01tttrq=++ββε

where is the real price. ln()ln(CPI)tttrP=−

4. Compute a 95% confidence interval for β1.

5. Test for autocorrelation in the errors of your regression in (3). What are the implications of your test result for interpreting your results in (3) and (4)?

6. Use the Newey-West correction to fix the regression in (3). Try using up to 12 lags in the correction.

7. Plot the log real price (rt) over time. What is the long run trend in prices?

8. It is possible that prices are being driven by some trends unrelated to quantity. Re-estimate your regression model in (3) with the year as an additional right-hand-side variable.

9. Now, let’s consider changing the model by adding the lags of price and quantity.

012131tttttrqrq−−=++++ββββε

Test for autocorrelation.

10. Using the discussion on slides 21 and 23 from Ch 9, interpret the results from your regression in (9). What is the long-run elasticity of demand? Interpret the error correction model.

11. We are interpreting our regression parameters as inverse elasticities of demand. What precisely are we assuming about how corn production is determined?

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