(about insurance for HW) estimating moral hazard using difference-in-differences/ consumption smoothing and crowd out.
1. Consumption Smoothing and Crowd Out
(a) Suppose we were to find that giving individuals an additional dollar of social insurance has no effect on their consumption drop when faced with an unemployment shock. What does this imply about the level of crowd out? Explain (1-2 sentences)
(b) In the standard framework, what would that mean for the welfare gain from providing individuals with more generous social insurance? Explain, with reference to the optimal social insurance formula from class.
(c) Explain briefly the empirical strategy Gruber (1997) uses to estimate crowd out and what he finds (3-4 sentences)
2. Estimating Moral Hazard using Differences-in-Differences
The following questions will require you to use the dataset available in the Assignments folder called “Assignment3.xls.” You will only need to use basic Excel commands (calculating averages, basic graphing) for the questions below; we will not be doing any regressions or tests of statistical significance.
This dataset contains observations on unemployment durations for two states, New York and New Jersey, in 3 years (1985, 1990, 1995). So the variable Dur_NY_1995 gives unemployment durations observed in New York in 1995, etc. Please note that these numbers were generated for the purposes of the assignment question and do not reflect actual unemployment durations in these states in these years.
Let’s suppose that New York enacted a more generous UI system between 1990 and 1995 and we want to test whether that increased average unemployment durations.
(a)Suppose we did a simple pre-post comparison using just the data from New York, looking at the years closest to when the program was enacted. Our simple difference estimator would be: D = Dur_NY_1995 – Dur_NY_1990. Please calculate this estimator and express what the results are telling us if we took it as a causal estimate (“The estimate implies that the program increased average unemployment durations by XX weeks.”)
(b)What is the identifying assumption needed in order for the estimate in (a) to be a valid causal estimate of the program?
(c)Now suppose that we take New Jersey as a control group. Write down the difference-in-difference estimator in terms of the variables we would use (as shown in part (a)).
(d)Please calculate this estimator from the data and express what the results are telling us (again, in the form shown in part (a)).
(e)What is identifying assumption needed in order for the estimate in (d) to be a valid causal estimate?
(f)Suppose that we only had data for New York and New Jersey in 1990 and 1995. Can we test the identifying assumption in (d)? Why or why not? (1-2 sentences)
(g)Note that we in fact have data for 1985 as well, and both 1985 and 1990 are prior to when the New York program was enacted. This means we can construct a “placebo difference-in-difference” estimator by comparing changes in New York and New Jersey between 1985 and 1990. Write down this estimator in terms of the variables we would use.
(h)Given that there were no social insurance changes between 1985 and 1990, what would we expect this estimator to be if New Jersey is a “good” control group for New York?
(i)Please calculate the actual estimator from the data and explain the results (1-2 sentences). (j)[10 points] Please create a graph of average unemployment durations in New York and New Jersey over time and explain what this graph suggests about the validity of our differences-in-differences estimat
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