Applied Economics Cost-Benefit Analysis Problems
Meta-analysis is the use of statistical methods to synthesize the results from multiple, related empirical studies with the objective of drawing general conclusions. For this assignment, you will be applying recent meta-analysis techniques (not covered in the lecture notes) to synthesize the estimates of the value of mortality risk reductions. Specifically, you will be use the estimates of the Value of a Statistical Life (VSL) from 25 studies to draw general conclusions about the best estimate of the VSL and how to best model it.
Each of the 25 "primary studies" contains an estimate of a common metric: the VSL. This common metric is often referred to as the "effect size." Let n represent a sample of studies containing estimated effect sizes, indexed by i=1,...,n. For this exercise, we will assume that the n estimates are independent of each other. The true effect size in the population is denoted by β and the estimate reported in the ith primary study is denoted by Yi. The true effect size may or may not vary across the population. Each estimate of the effect size for a primary study is accompanied by the standard error of that estimate. Since the standard errors of all the estimates are different, the data are, by definition, heteroskedastic. Meta-analysis techniques assume that more precise estimates should be given greater weight in the analysis and this can be accomplished by weighting the estimates or by the use of weighted-least squares in a meta-regression.
There are several possible objectives of a meta-analysis: (1) estimate an average effect size in the sample, its confidence interval, and generalize about the distribution of effects in the population; (2) explain the variation in the sample of effects using a meta-regression model, without regard to possible selection bias in the sample; (3) estimate a meta-regression model that adjusts for sample selection bias.
A spreadsheet entitled "VSL data.xls" has been posted on Blackboard containing two tabs. The first tab is a data dictionary describing the variables. The second is a set of 25 estimates of the VSL in 2009 dollars, the standard error of these estimates, and additional data characterizing the data used for each estimate. You will conduct a meta-analysis of the VSL using this data.
You will need a spreadsheet program (e.g., Microsoft Excel) and a statistical software package (e.g., Stata) to complete this assignment. Please let us know immediately if you do not have access to these programs.
1. Calculate the number of observations, minimum, maximum, unweighted mean, variance, standard deviation, standard error, and the 95th percent confidence interval of the estimated VSL from the sample of 25 primary studies.
2. Calculate the fixed-effects weighted mean, variance, standard deviation, and the 95th percent confidence interval of the estimated VSL from the sample of 25 primary studies.
3. Calculate the Cochran's Q-statistic for the sample of 25 primary studies using the fixed-effects weighted mean you calculated in part 2 and determine if the fixed-effects model is appropriate?
4. Calculate the I2 statistic for the sample of 25 primary studies using the Q-statistic calculated in part 3 and determine if the fixed-effects model is appropriate?
5. Calculate C, τ2, the random-effects weighted mean, the study error variance, the random effects standard error, and the random effects 95th percent confidence interval for the estimated VSL from the sample of 25 primary studies. Report those values here.
6. Run an OLS regression with robust standard errors on the sample of 25 primary studies with the VSL as the dependent variable.
7. Run a weighted regression on the sample of 25 primary studies with the VSL as the dependent variable and weights equal to 1 over the variance. The independent variables should be the natural log of income, the dummy variable for studies with white workers only, the dummy variable for North America studies, the data year, a precision variable equal to one over the standard error, and a constant. Report the results of that regression here, including the adjusted R-squared value.
8. Using the results from the fixed-effects meta-regression in part 7, make an estimate of τ2.
9. Run a random-effects weighted regression on the sample of 25 primary studies with the VSL as the dependent variable and weights equal to [1/(si2 +τ2)].
10. Interpret your results from parts 1-9 in a few paragraphs. Imagine that you are presenting your results to a decision maker. Assume that she is a reasonably intelligent individual who understands what the VSL is and has a limited exposure to statistical results. She understands what a coefficient and R-squared is and she knows what statistical significance means.
Attachment:- Assignment Files.rar