Mastering Metrics CH1 PDF

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Mastering Metrics, Chapter 1, Summary

-Randomizing is not the same as ‘holding all else equal’, but it has the same effect. -Methods :

-Random assignment -RD designs -Regression -Diff-in-Diff -IV

These five are ‘furious five of economic research’

- Example one : Health Insurance Treatment: private health insurance Outcomes: Health level (scale from poor to excellent) Now we have a treatment and a control group. A good control group reveals the fate of the treatment group when they were not treated. Just taking the difference in health of treated and non-treated gives a comparison of a different group of people. Insured people tend to be better educated, wealthier etc. These factors might be related to health as well. Without health-insurance: Y0i With health-insurance: Y1i Causal effect is then: Y1i – Y0i Lack of comparability leads to selection bias. This is not something that is fixed by comparing multiple people. It carries over groups. Dummy Di is created to condition on the treated and untreated. Takes value 1 if person i is treated. Difference in group means only gives Avgn [Yi|Di=1] – Avgn [Yi|Di=0] While we want to know Avgn [Y1i – Y0i] When we randomize the people who get insurance, we get rid of the selection bias Sample needs to be large enough When there is random assignment: E[Y0i|Di=1] = E[Y0i|Di=0] This means that if no one is treated, the expected value of the treatment group and control group is the same A difference larger than two times the standard error is seen as significant

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Example Two : The Oregon Trail

75.000 applicants for the lottery for OHP insurance 30.000 of those were randomly selected for the OHP coverage. (45.000 in the control group) The whole experiment showed that is an effect on financial health, but only a very small effect on

physical health

Appendix Difference in random sampling and random assignment is small, but is present E[Y] is a parameter, because it does not vary, it’s fixed Avg[Y] is a sample statistic, because it depends on n and on who ends up in the sample unbiasedness: E[ῩD] = E[Yi] which means that deviations of the sample statistic should not be systematically up or down from the parameter Population variance: V(Yi) = E[(Yi– E[Yi])2] Because it is squared, we use a standard deviation for simplicity V = σ2 V(ῩD) = σ2 Y/n which means that the sampling variance decreases in sample size As n approaches infinity, sampling variance disappears A standard error is different from a standard deviation as a standard error measures the variability in an estimate due to random sampling SE(ῩD) = σY/√n...