ECON 306 – Homework 3 The following two problems will require a lot of calculations in STATA (or however you opt toexecute the calculations). It will generate many pages of output. Here is how your shouldorganize it. The first pages should contain your answers to all the questions, along withshowing any key algebraic equations or explanations you need to use along the way. Afterthat, include a printout of the output from the regressions you executed in support of youranswers. Highlight any numbers in this output that you used in the first section. (To save paper,you may print this section double-side and/or with 2-up format.) Last, include a copy of the DOfile that contains the commands you asked STATA to execute. Be sure you organize these in away that will be clear to the reader.1. (52 points total, 4 points each part) With this assignment you will find a STATA data filecalled boston.dta. For reference, the variables in this file are:nox = nitric oxides concentration (parts per 10 million)rm = average number of rooms per dwellingage = proportion of owner-occupied units built prior to 1940dis = weighted distances to five Boston employment centersptratio = pupil-teacher ratio by townlstat = percent lower status of populationmedv = median value of owner-occupied homes (in thousands of dollars)Open this dataset within STATA (only STATA can open it). Before you begin answeringthe following, itâs not a bad idea to ask STATA to summarize the data using the commandsummarize. You should also start a log file to store your results.a.) Run the following regression: MEDV 0 1 * RMb.) Hypothesize the sign of the bias, if any, resulting from excluding age from theregression. Explain your reasoning. (There is no wrong answer as long as you makea sensible story.)c.) Use the data to verify (or not) your claim from b). Break down the bias into itspieces.d.) Now, run the regression:MEDV 0 1 * NOX 2 * RM 3 * AGE 4 * DIS 5 * PTRATIO 6 * LSTATe.) At a level of ?=.05, for which, if any, values of ?i, would you reject the nullhypothesis that ?i=0? f.) What is the predicted medv with nox=0.5, rm=4, age=60, dis=3, ptratio=20,and lstat=10?g.) Redo (f) but with nox=0.6. What is the difference in predicted medv between thesetwo communities? Compare this with the coefficient of nox.h.) Ceteris Peribus, compared to (f), what is the impact of reducing the pupil-teacherratio to 18?i.) What percentage of the variation in medv is explained by the six X-variables?Now change the measurement of nox. Use the âgenâ command:gen noxppm=nox/10and then use this in place of nox in the regression commandregress medv noxppm rm age dis ptratio lstatj.) Compare the coefficient, standard error, and t-ratio for noxppm to that of nox.Interpret the difference between this model and the previous.k.) Also compare the and remaining coefficients. Interpret the difference between this model and the original regression model.Now change the variable age to newagegen newage=100-ageand then use this in place of age in the original regression command. That is,execute:regress medv nox rm newage dis ptratio lstatl.) Compare the coefficient, standard error, and t-ratio for newage to that of age.Interpret the difference between this model and the previous.m.) Also compare the and remaining coefficients. Interpret the difference between this model and the original regression model. 2. (48 points total. 5 points each part, +3 for free.) For the following problem, use theSTATA dataset called crime.dta. This data set was compiled by Christopher Cornwelland William Trumbull to study factors that influence crime rates. The data set containsobservations for 90 counties in North Carolina for 1981. The definitions of the variablesrepresented in the data set are_crmrte=crime rateprbarr=probability of arrestprbconv=probability of convictionprbpris=probability of a prison sentenceavgsen=average sentence in dayspolpc=number of police per capitadensity=population densitypctmin=percent minoritypctymle=percent young maleswmfg=average weekly wage in manufacturingwcon=average weekly wage in constructionwtuc=average weekly wage in transportation,utilities,and communicationswtrd=average weekly wage in wholesale and retail tradewfir=average weekly wage in finance,insurance,and real estatewser=average weekly wage in serviceswfed=average weekly wage in federal governmentwsta=average weekly wage in state governmentwloc=average weekly wage in local governmentAccording to the economic model of crime rates, lower crime rates are associated withbetter labor markets (higher wages), more police presence and tougher sentences, andlower population density. We will use this data set to examine these hypotheses. Use asignificance level of ?=.05 for all hypothesis tests.a.)b.)c.)d.) Run a regression of crmrte on all of the other variables. Call this Model 1.Do any t-statistics indicate a variable is not statistically significant? Which?Interpret the F-statistic STATA has calculated for Model 1.Test the hypothesis that the coefficients on wfed and wsta are equal to each other.Use the t-test method described in the lectures. What transformation do you need todo here? Be specific.e.) Test the hypothesis that the coefficients on wfed, wsta and wloc are all equal toeach other. Do this by writing down the formula for the relevant F-statistic.Calculate it (by running the appropriate restricted regression) and test the hypothesis.Report these results. This restricted version of the regression will be called Model 2. f.) Return to Model 1. Now test the hypothesis that pctmin and pctymle both equalzero. Do this by writing down the formula for the relevant F-statistic. Calculate it(by running the appropriate restricted regression) and test the hypothesis. Reportthese results. This restricted version of the regression will be called Model 3.The model could potentially be simplified by replacing all the wage variables with anaverage. Specifically, let us definewmfg wcon wtuc wtrd wfir wser wfed wsta wloc9Generate this variable.avgwage g.) Return to Model 1 and run using avgwage in place of the individual wage variables.Check the validity of this restriction. As before, do this by writing down the formulafor the relevant F-statistic. Calculate it (by running the appropriate restrictedregression) and test the hypothesis. Report these results. This restricted version of theregression will be called Model 4.h.) Letâs focus our attention on the coefficient for the variable polpc. How does thevalue of this coefficient change â as well as its statistical significance âas we movefrom model to model? To answer this, write down a table containing the results forthis coefficient for each of the four models. In this table, include the coefficientvalues, the values of the t-statistic (for a hypothesis that the coefficient=0,) andwhether youâd reject the hypothesis.i.) What do your results in the last question imply about the relationship between thenumber of police and the crime rate. Are you confident in these results based on thework you have done? Why or why not?
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