Chapter 13 - Extra Practice Problems

Group did not adjust to the treatment treatment

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Unformatted text preview: sufficiently before [t = p] that [the treatment group] did not adjust to the treatment € treatment , before control , before before [t=1] – otherwise [ Y –Y will reflect the effect of the treatment; (2) [t = 2] must be sufficiently after [t = p] to allow the treatment's effect to be fully felt; and (3) we must be sure that the same difference [ Y treatment ,before – Y control,before ] would have been observed at [t = 2] if the treatment had not been imposed, that is, [the control group must be good enough] that there is no need to adjust the differences for € € factors other than the treatment that might have caused them to change." € Use a figure similar to the textbook to explain what this reviewer meant. € 4. Consider the simple population regression model where the treatment is the same for the members of the treatment group, and hence X is a binary variable. Explain why the coefficient on X represents the difference between two means. How is the test for the statistical significance of the coefficient on X related to the test for differences in means between two populations, when their variances are different? Write down the null and alternative hypothesis in each case. 5. Present alternative estimators for causal effects using experimental data when data is available for a single period or for two periods. Discuss their advantages and disadvantages. 6. To analyze the effect of a minimum wage increase, a famous study used a quasi-experiment for two adjacent ˆ states: New Jersey and (Eastern) Pennsylvania. A β1diffs− in − diffs was calculated by comparing average employment changes per restaurant between to treatment group (New Jersey) and the control group (Pennsylvania). In addition, the authors provide data on the employment changes between "low wage" restaurants and "high wage" restaurants in New Jersey only. A restaurant was classified as "low wage," if the € starting wage in the first wave of surveys was at the then prevailing minimum wage of $4.25. A "high wage" restaurant was a place with a starting wage close to or above the $5.25 minimum wage after the increase. a. b. Explain why employment changes of the "high wage" and "low wage" restaurants might constitute a quasi-experiment. Which is the treatment group and which the control group? The following information is provided FTE Employment before FTE Employment after Low wage 19.56 20.88 High wage 22.25 20.21 where FTE is "full time equivalent" and the numbers are average employment per restaurant. ˆ Calculate the change in the treatment group, the change in the control group, and finally β1diffs− in − diffs . ˆ diffs− in − diffs to be positive or negative? Since minimum wages represent a price floor, did you expect β 1 c. ˆ The standard error for β1diffs− in − diffs is 1.48. Test whether or not this is statistically significant, given that there are 174 observations....
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