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EC 303: Empirical Economic Analysis
Due Wednesday October 6, 11:59 pm. 1 Theoretical Problems Problem 1 (10 points). Suppose X ⇠ Binomial(n, ✓). Recall that in the lecture we derived E[X] and V [X] by using the fact that X is a sum of independent Bernoulli random variables. (Check lecture 5 slides). Show same results by applying moment generating function of X directly. Problem 2 (10 points). What is Analogy principle? How do you use it in estimating ✓ where X ⇠ Binomial(n, ✓) (check lecture 5 slides). Now, suppose we want to estimate p success probability where X ⇠ Bernoulli(p). How would you estimate p by using Analogy principle? What kind of sample (or data) do you need? Explain your estimation procedure. Problem 3 (10 points). Explain the di↵erences between Binomial, Negative Binomial, and Hypergeo- metric distributions. What kind of questions can you answer with these models? Try to come up with an interesting application (in economics or other sciences) for each of these 3 models. Problem 4 (10 points). Work on the problems from the textbook chapter 2: 4, 8, 14, 18, 26, 28, 46, 50, 52, 58, 70, 72, 78, 80. A subset of these questions will be graded. Problem 5 (10 points). Work on the problems from the textbook Chapter 3: 12, 14, 16, 22, 28, 34, 36, 38, 40, 44, 46, 56(a), 64, 70, 88, 90. A subset of these questions will be graded. 2 Empirical Problems Problem 2.1: Working with real data set. For this problem, you first need to download a data set that includes GDP per capita by countries in year 2020. As a reference you may use World Bank website. Feel free to use any other website, data bank or repository that you are more familiar with. You need to submit a Stata do file to get a full credit for this problem. When your code is run by the grader (your TA), it should work with no error. a. (5 points) What does each row/observation in your data set represent? b. (5 points) Explain your choice of GDP per capita measurement? In logs, in dollars, in 1000 dollars etc. c. (5 points) Provide summary statistics for your variable: min, max, mean, median, percentiles, standard deviation. Interpret your results. Are there any outliers? d. (5 points) Prepare a frequency table for income levels. You can construct income levels such as 0-10K, 10-20K, .. and so on. What are relative frequecies of each income bracket? e. (5 points) Draw a histogram for income levels. Make your labels and titles visually appealing. 1 Problem 2.2: Simulation. For this simulation exercise, refer to example 2.30 in the textbook. The goal here is to simulate incidences of a rare disease and test results with synthetic data. You need to generate a random sample that is consistent with the data generating process given in the example 2.30. You need to submit a Stata do file to get a full credit for this problem. When your code is run by the grader (your TA), it should work with no error. a. (5 points) Set number of observations in your data set to 100000. Since only 1 in 1000 adults is a✏icted with the disease, randomly assign 100 observations to the a✏icted group. b. (5 points) Out of a✏icted 100 observations, randomly assign 99 of them to the tested positive group and remaining 1 to the tested negative group. c. (5 points) For 99900 non a✏icted observations, randomly assign 2 percent of them to the tested positive and remaining observations to the tested negative group. d. (5 points) How many observations are tested positive? Out of those tested positive, how many of them are a✏icted? e. (5 points) Did your simulation produce the results you expected? Explain.