E471: Econometric Theory and Practice I Spring 2020Assignment 2Due: Thursday, February 27, 2020, 1:00 pmInstructions:• Please upload an electronic copy of your answers to Canvas combining all results inone pdf/word file. If there is any handwritten part, please scan it and include it withthe rest of the answers.• Please also upload your code to Canvas before the due time. The code accounts for50% of the points of the empirical questions.• You are allowed to collaborate in groups, but required to write up answers and codeindependently. Direct copying will be treated as cheating. Please write the names ofyour collaborators at the beginning of your work, if any.Questions:1. This question is a sequel to Question 1 in Assignment 1. Reall that you downloadedthe file Assignment1Data.csv, which contains three series: CITCRP, MARKET, andRKFREE with data from January 1978 to December 1987.Recall the regressionrc,i − rf,i = β0 + β1(rm,i − rf,i) + �i. (1)The capital asset pricing model (CAPM) suggests that β0 should be zero. Using the Rchunks from our lectures, extend your program to:(a) compute a p-value for the null hypothesis H0 : β0 = 0;(b) and to construct 90%, 95%, and 99% confidence intervals for β0 and β1.2. Suppose that E[U|X] = 0, E[X2] = µXX, and V[U|X] = σ2. We used the following tworesults in our derivations for the OLS estimator:(a) Show that E[UX] = 0.(b) Show that V[UX] = E[U2X2] = σ2µXX3. Consider the following regression modelYi = βXi + Ui, β = 1, E[X2i ] = 14, V(Ui|Xi) = 1and the sample size is n = 100. We are interested in testing the null hypothesis thatβ = βH versus the alternative that β 6= βH using a t-statistic of the formt = βˆ − βHσˆβˆ.(a) What is the correct critical value to guarantee that the hypothesis test has a type-Ierror of 5%?(b) Define the type-II error of a hypothesis test.(c) Suppose an econometrician tests the “false” hypothesis that β = βH = 1.2 (the“truth” is that β = 1). What is the type-II error associated with this test?(d) Repeat the calculation for βH = 1.6, βH = 1.8, and βH = 2.(e) What is the power of a test?(f) True or False: The t-test has less power against alternative hypotheseis that arefar away from the null hypothesis. Hint: use your previous results to answer thisquestion.Page 24. You are working for a life insurance company and are preparing for a briefing of theboard. Your economic intuition tells you that the best predictor of life insurance holdingsis income. You gather the relevant data (family life insurance and family income, bothin thousands of dollars) and want to analyze it, running a regressionlifeinsi = β0 + β1incomei + uiThe data set is provided in the file Assignment2Data.csv.(a) Estimate the above regression model. What is your point estimate for β1? What isthe interpretation of that estimate?(b) Provide a 95% confidence interval for the coefficient on income.(c) One of the managers suggests that the industry rule of thumb is that people buy fivedollars life insurance for each additional dollar of their income. Another managerdisagrees and says it could be more or less. You want to examine the difference ofopinion.What null and alternative hypotheses would you use here to discriminate betweenthese hypotheses? Test the hypothesis, using a 5% type I error and interpret theresults.(d) Calculate a p-value for the test in (c).(e) The company wants to offer life insurance to low income households. The chairmanasks you how much life insurance would a household with an income of 20,000dollars buy. Calcul代写E471留学生作业、代做Econometric Theory作业、代做R编程设计作业、代写R语言作业 代做R语言编程ate a point prediction.(f) Explain why it is better to consider an interval prediction rather than a pointprediction.(g) Calculate 90%, 95%, and 99% prediction intervals for the life insurance holding ofa family that earns 20,000 dollars.Page 35. The goal is to replicate Table 2 of Acemoglu, Johnson, and Robinson (AER, 2001). Youcan find the article athttp://www.aeaweb.org/articles.php?doi=10.1257/aer.91.5.1369and the data athttp://economics.mit.edu/faculty/acemoglu/data/ajr2001Download the zip file for the replication of Table 2, and extract the file maketable2.dtainto your work directory. The data set is provided in STATA format which can be readby R (see below).(a) Load the data using the following R chunk.wholeworld = foreign::read.dta(maketable2.dta)head(wholeworld)## shortnam africa lat_abst avexpr logpgp95 other asia## 1 AFG 0 0.3667 NA NA 0 1## 2 AGO 1 0.1367 5.364 7.771 0 0## 3 ARE 0 0.2667 7.182 9.804 0 1## 4 ARG 0 0.3778 6.386 9.133 0 0## 5 ARM 0 0.4444 NA 7.682 0 1## 6 AUS 0 0.3000 9.318 9.898 1 0## loghjypl baseco## 1 NA NA## 2 -3.4112 1## 3 NA NA## 4 -0.8723 1## 5 NA NA## 6 -0.1708 1(b) How many observations are in the “whole world” sample? What does “NA” mean?(c) What is the “base sample” considered in the paper? (you have to read the text,e.g., section II.A., to answer this question!) The following R chunk generates thebase sample:basesample = wholeworld[is.na(wholeworld[,9])==FALSE,]; # delete NAhead(basesample)## shortnam africa lat_abst avexpr logpgp95 other asia## 2 AGO 1 0.1367 5.364 7.771 0 0## 4 ARG 0 0.3778 6.386 9.133 0 0## 6 AUS 0 0.3000 9.318 9.898 1 0## 12 BFA 1 0.1444 4.455 6.846 0 0## 13 BGD 0 0.2667 5.136 6.877 0 1## 16 BHS 0 0.2683 7.500 9.285 0 0## loghjypl baseco## 2 -3.4112 1## 4 -0.8723 1## 6 -0.1708 1## 12 -3.5405 1## 13 -2.0636 1Page 4## 16 NA 1(d) For the whole world sample and the base sample generate a scatter plot of log percapita GDP (y-axis) versus expropriation risk (x-axis).(e) Here is some R chunk for the estimation of specification (1) in Table 2.olsspec1 summary(olsspec1)#### Call:## lm(formula = wholeworld$logpgp95 ~ wholeworld$avexpr)#### Residuals:## Min 1Q Median 3Q Max## -1.902 -0.316 0.138 0.422 1.441#### Coefficients:## Estimate Std. Error t value Pr(>|t|)## (Intercept) 4.6261 0.3006 15.4 ## wholeworld$avexpr 0.5319 0.0406 13.1 ## ---## Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1#### Residual standard error: 0.718 on 109 degrees of freedom## (52 observations deleted due to missingness)## Multiple R-squared: 0.611, Adjusted R-squared: 0.608## F-statistic: 171 on 1 and 109 DF, p-value: How many observations are used in this regression: fewer than in the whole worldsample? Why? Does the number of observations used in your estimation match thenumber of observations reported in the paper?(f) Now write a chunk of R code that estimates specification (2) in Table 2. Do youget the same point estimate? Do you get the same standard error estimate?(g) Follow lecture slides and compute White’s heteroskedasticity consistent standarderrors. Are they bigger or smaller than those under homoskedastic assumption?(h) Now replicate the estimation results for specifications (3) - (8). Report point estimates,standard error estimates, R2, and number of coefficients up to four significantdigits (the paper only reports two significant digits).Page 5转自：http://www.6daixie.com/contents/18/4934.html
