Econometrics

You are welcome to work in teams, but please: (1) turn in your own write up (i.e. in your own words) and computer code, (2) acknowledge with whom you worked at the top of your assignment. Please print out your code and attach it to your answers.Please submit a physical copy in class unless extenuating circumstances prevent your attendance.

Some questions may have multiple possible answers. Justify your claims for full credit.

1. In this question you will explore a fundamental question in economics: why are some countries rich but others are poor? One popular theory is that richer countries have better political and social institutions. One particular type of institution is property rights. Our hypothesis: countries that provide stronger protections for property rights had more economic growth in the past and thus are richer today.

First, download the dataset institutions.Rda from Carmen under the third homework, and open it in RStudio. This dataset provides data at the country level. The variables we are interested in are:

• loggdp: (natural) log of GDP in 1995
• risk: a measure of protection for property rights, higher values means more protection for property rights.
• logmort0: (natural) log of the mortality rate of the original European settlers of the country.
  1. Estimate the regression equation in R. Report the coefficient estimate for  as well as the standard error. Is the variable significant at any of the conventional levels? Interpret the coefficient estimate for  (Hint: you should specifically interpret the estimate bearing in mind that we have a logged dependent variable. You may refer to changes in the treatment variable as changes in the “risk score”).
  2. One problem with the estimate in part a is omitted variable bias: there may be many factors that are correlated with property rights and GDP growth, including natural resources. To try to solve these problems, economists Acemogulu, Johnson, and Robinson proposed using the initial mortality rates of European settlers as an instrument for property rights. The argument is that European colonizers were more likely to develop “good” institutions in countries with more hospitable climates (which would foster lower mortality rates). In worse areas, Europeans were more likely to simply strip their colonies of their natural resources. “logmort0” is the instrument we will use for “risk”.

What conditions does this instrument need to satisfy? Do you find them plausible (explain why or why not)?

1. Write a regression equation for the first stage.
2. Estimate the first stage equation in R. Report the first stage coefficient estimate and the standard error. Is the result significant? What does this say about the plausibility of the conditions from part b?
3. Write a regression equation for the reduced form.
4. Estimate the reduced form equation in R. Report the reduced form coefficient estimate and the standard error. Is the result significant?
5. Using your answers for parts d and f, calculate the IV estimate for .
6. Now calculate the 2SLS estimate of the effect of “risk” on “loggdp”. You may either do this in one step using the function “ivreg” (which will require you to download the “AER” package in RStudio), or you may do the two steps manually. Report the 2SLS coefficient estimate.
7. How does your answer in part h compare to your answer in part g? Is this result typical for IV and 2SLS estimates?
8. Now suppose we also had data on the democracy index for each country, and we wished to include both the log mortality rate and democracy index variables as instruments in the 2SLS estimation of the effect of “risk” on “loggdp”. How would we do this? Be specific, referencing both stages of the 2SLS estimation. You may either describe the process in words, or write out an equation for each stage (but make sure to carefully define the variables you use).