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introductory econometrics modern

Introductory Econometrics Using Monte Carlo Simulation With Microsoft Excel 1st Edition Humberto Barreto, Frank Howland - Solutions

Use the equations for quantity demanded and quantity supplied to find the reduced-form expressions for Q and P.
Compare the paired XY and residuals bootstraps for this case.Which one do you prefer?Why?
Use the Bootstrap add-in to run a residuals bootstrap of the coefficient on Body-Weight in Model 4. Take a screenshot of your bootstrap results.
The OLS estimated SE for the coefficient on BodyWeight in Model 4 is 0.315.Does your bootstrap SE substantially agree with the OLS estimated SE? Explain the reason for the difference or agreement.
Usethe Bootstrap sheet in PairedXYBootstrap.xls to estimate theSEand sampling distribution of the coefficient on BodyWeight in Model 4. Take a screenshot of your bootstrap results.
Suppose you had an original sample from a 95-percent free shooter in which he or she made all 20 free throws. How would the bootstrap work in this case?
In Section 23.2, the text claims that, “in other words, the bootstrap will do a better job of answering questions that involve the shape of the sampling distribution when its profile is not normal. Suppose, for example, that we wanted to know the chances that a 95-percent free throw shooter will
From the MortDisc.xls workbook, set β3 = 2 and follow the instructions in Section 22.8 to create your own sample and estimate it via NLLS. Report your results.Do you find evidence of discrimination in mortgage lending from your sample?
Open the MortDisc.xls workbook.With a positive level of discrimination, use the MCSim.xla add-in to make sure the model is responding as expected. In other words, track both Loan Denial cells and check to make sure the probability of loan denial rates are correct. Take a picture of your results and
Open the NLLSMCSim.xls workbook. Click the Get a 100 Obs Sample button in the Data sheet and use your sample to estimate the model via OLS and Probit NLLS.Create a graph that compares the predicted probabilities of the two estimation techniques.
Change the probability of dying by Raid to 18 percent. Resample by hitting the F9 key. What kinds of results do you get? Does Raid ever seem to be effective(even though it really is not)?
Repeatedly clicking the Repeat the Experiment button offers convincing evidence that the sample effectiveness of Raid is bouncing. That means it has a sampling distribution.Determine and report its center and spread. Describe your procedure.
Open the Raid.xls workbook and go to the Death By Raid sheet. The initial default parameters were A2 = 18 percent and G2 = 78 percent. Could these parameters have produced the results in Figure 22.2.1?
(Lagged Dependent Variables) In the Example sheet of PartialAdjustment.xls, we have set the initial value of Y as follows:Bearing in mind the equation for the data generating process, Yt = γ0 + γ1Yt−1 + γ2Xt , use algebra to explain why this is an equilibrium value (i.e., a value such that if
In the coal mining example, a regression of the fatality rate on the regulation dummy variable gives the results in Figure 21.11.5, whereas a regression of the fatality rate on the regulation dummy variable and a trend term gives the results in Figure 21.11.6. Explain why the coefficient estimate
(Dummy Variables) In the TimeSeriesDummyVariable.xls file we set up a “short regression” in which we regressed Ice Cream Sales on Price only, ignoring the Coupon dummy variable. Then we performed a Monte Carlo analysis; the average value of the estimated slope coefficient for Price in 1,000
(Creating Predicted Level Using Log-Linear Trend Model) To see why it is necessary to correct for the influence of the error term, make sure the MCSim add-in is installed and available; then open a blank Excel workbook and create 400 cells with the formula =NORMALRANDOM(0,1) in column A. In column
Suppose we are considering two variables to measure trend in a study of U.S.population. The first five values of each variable are in Figure 21.11.1: We ran two regressions,(1) PredictedU.S.Population = a1 + b1Trend1, and(2) PredictedU.S.Population = a2 + b2Trend2, and obtained the results in
If autocorrelation is present, what is wrong with using the conventional estimated SE formula (in cell K27)? How do you know?HINT: Use the MCSim.xla add-in to run a Monte Carlo simulation on cell K27.
Does autocorrelation have the same effect on the sampling distribution of the percentage of made free throws if μ=0.8? Describe your procedure in answering this question.
What effect does increasing autocorrelation have on the sampling distribution of the percentage of made free throws? Describe your procedure in answering this question.
Click on cell B11 in the Model sheet. The heart of the formula is “B10+IF(C10=1,zeta,-zeta).” Explain how this formula is inducing autocorrelation.
Simply for practice, go ahead and run an FGLS estimation of the model. Describe your procedure in transforming the data and report your results.Open the FreeThrowAutoCorr.xls workbook and use it to answer the questions below. Read the Intro sheet and explore the workbook to get a sense of what is
We actually know that autocorrelation is not really present in these data. Why, then, is it showing up in our tests?
Now run a Durbin–Watson test. Your answer should include clearly stated null and alternative hypotheses, a test statistic, a P-value, and a decision on rejecting or not rejecting the null.
Recall the fable about Galileo (see Chapter 6) in which he estimated the model Predicted Distance = −124.82 + 96.83 × Time(ft) (ft) (ft/s) (s).This is a good example of a model in which the functional form is incorrect. Recall that the true model includes neither an intercept nor a Time term
In addition to the theoretical argument for the semilog functional form presented in Chapter 6, your work in Question 2 on the semilog model is an example of why we routinely take the natural log of the dependent variable (a measure of remuneration)in earnings function regressions.What part of your
Use the OLSRegression.xla add-in to find robust SEs for the linear model. Report your regression results in a nicely formatted table with SEs in parentheses under the parameter estimates.
In answering the previous question, you reject the null for the linear model, but not for the semilog model. Suppose that for the linear model someone asks for a two-tailed test of the claim that education has no effect on wage. They use the results from your answer to Question 1. What is the
We are worried, however, that there is heteroskedasticity. Run a B–P test on each model. Describe your procedure. Your answer should include clearly stated null and alternative hypotheses, a test statistic, a P-value, and a decision on rejecting or not rejecting the null.
Open SemiLogEarnings.xls (in the Chapter 6 folder on the CD-ROM) and proceed to the EducWageData sheet. Use the Regression option in Excel’s Data Analysis add-in to run regressions on the two models. Report your results in a nicely formatted table with SEs in parentheses under the parameter
Consider the case in which Education is included but CompAtWork is omitted in the short regression explaining the log of wages. Using the information in the Data sheet of ComputerUse1997.xls, carefully explain the computation of the difference in coefficient estimates for the sample slope of ln
Set the correlation betweenTraining andTalent (cell B6) in theTrueModel sheet of SkiingOVB.xls equal to 0.9 but make the value of β2 equal to 0. Hit F9 a few times.You should find that the two slope coefficients in cells I3 and O3 are not equal.However, as stated in Section 18.3, omitted-variable
Suppose you obtain a data set that includes a measure of IQ in addition to standard data on wages and education. You run a short regression of wages on education and then a long regression of wages on both education and IQ. How do you think the slope of wage on education will differ between the two
Use the MCSim sheet in the ComputerUse1997.xls data set to demonstrate that the bias of the short regression does not change as the sample size increases. Do this for both the sample slope of ln Wage on Education and for the sample slope on ln Wage on CompAtWork.
Explain why it is important to include control variables like Age and Education in the model of savings behavior discussed in Section 17.1.
In a hypothetical data set with 400 adults in the New York metropolitan area, 250 own their homes and 150 do not. Of the home owners, 245 own a car. Of the 150 non-home-owners, only 25 own a car. A researcher runs a regression of expenditures on movie entertainment on the dummy variable OwnHome and
Create your own Monte Carlo study. The workbook MyMonteCarlo.xls contains the functions NormalRandom(), Uniform(), and Expo() in a Visual Basic module.Use this file and these functions to see how well the Whole Model F-Test performs under alternative assumptions about the error terms – that they
In the Setup sheet of the CorrelatedEstimates.xls, set both β1 and β2 to 1 and set the SD of the errors equal to 10. Set the correlation of the X’s to 0.99.Using the Monte Carlo add-in, run a Monte Carlo experiment that approximates the sampling distribution of the sum b1 + b2. Take a picture
In the food stamps example (FDistFoodStamps.xls), check to see whether the SD of the errors (and therefore the variance of the errors) affects the distribution of the F-statistic. Use 10,000 repetitions. The SD of the errors is controlled by cell B7 of the Example sheet.
The Dead sheet in FDistFoodStamps.xls contains data that does not bounce. The data were generated according to the following DGP:Food Purchases = β0 + β1 Number of adults in family+ β2 Number of children in family+ β3 Cash Income+ β4 Value of Food Stamps + ε.a. Test the following null
Use the P Value Calculator add-in (see Section 10.5 for instructions) to conduct a two-tailed test of the claim that the true rate of return for one more year of education (i.e., β1) is 8 percent. Show all of your work. What do you conclude? follows the classical econometric model. We consider two
For the Semilog Model, we want to conduct a two-tailed test of the claim that the true rate of return for one more year of education (i.e., β1) is 8 percent.Why is it not possible to use the reported P-value from Excel’s Data Analysis: Regression output to answer this question? follows the
Trying to convince her son to go to college, mom (who happens to be an econometrician)argues that the rate of return to education is incredibly statistically significant, and this proves that college is worth it. What do you think of this logic? follows the classical econometric model. We consider
For the Linear Model, conduct a two-tailed test of the claim that education has no effect on wage. Your answer should include clearly stated null and alternative hypotheses, a test statistic, a P-value, and a decision on rejecting or not rejecting the null. follows the classical econometric model.
In your work for Question 1, the Data Analysis: Regression output generated 95-percent and 90-percent confidence intervals. Explain why the 90-percent intervals are smaller. follows the classical econometric model. We consider two models:Linear Model: Wagei = β0 + β1 Educationi + εi Semilog
In Chapter 6, we interpreted the coefficients on Education in the two models.For the Linear Model, one more year of education is associated with an additional$1.65 per hour in the wage. The interpretation of the Semi-Log Model is different: each additional year of education is associated with a
Open SemiLogEarningsFn.xls (in the Chapter 6 folder on theCD-ROM)and proceed to theEducWageData sheet. Use the Regression option in Excel’s Data Analysis add-in to run regressions on the two models. Use the Confidence Level option to create a 90-percent confidence interval for the Education
In the MCSim sheet of SEForecast.xls, we chose β0 = 100, β1 =1, andSD(Error) = 50. We then ran two Monte Carlo simulations of forecasts, one with X set to 100 and the second with X set to 200.We graphed the Forecast Errors against Forecasted Y for the first 100 repetitions in both experiments.The
Explain why we do not use the RMSE as the SE of the Forecast Error. Take pictures from the SEForecast.xls workbook to support your argument.
Run a Monte Carlo simulation that compares the performance of the RMSE to the SD of the Residuals using the Mean Squared Error criterion with n = 10.You will have to create a new formula in a cell in the Data sheet of EstimatingSDErrors.xls that computes the squared deviation of each sample’s
In the ExactSEb1 sheet in SEb1OLS.xls, the exact SE in cell F4 is about 0.4. If someone wanted the SE to be cut in half, how could you change the setup to make this so?
What is the difference between the exactSEof the sample slope and the estimated SE of the sample slope?Which one is reported by regression software?
Compare the Monte Carlo results in the previous question with the exact solutions obtained in Question 8. Do you find substantial agreement? Explain.
Run a Monte Carlo simulation of the Missing Last Value estimator. Evaluate the results, commenting on the approximate expected value and SE.
Use the algebra of expectations to compute the exact expected value and SE of the Missing Last Value estimator by means of Set 2 of the X’s (see the Q&A sheet for the values of the X’s in Set 2).
In the BivariateSample sheet, create the Missing Last Value estimator. This silly estimator uses the same weights as the OLS slope estimator but makes the weight of the tenth observation equal to 0.Without running a Monte Carlo, can you tell if this estimator is biased? Explain.
From the UnivariateSample sheet, use Excel’s MEDIAN function to compute the sample median of the observed Y values. Use the Monte Carlo simulation add-in to race the Median against the Sample Average. Who wins? Why?
Explore the consequences of changing the error distribution from normal to uniform in the UnivariateSample sheet. (Section 14.6 compares the normal and uniform distributions.) Replace the normalrandom formula in column B with the uniform function.What effect does this have on the sampling
Would you prefer the Odd estimator or the Sample Average estimator? Explain your choice.
Use the Monte Carlo simulation add-in to analyze the sampling distribution of the Odd estimator. Is it biased? What part of the Monte Carlo results did you use to answer this question?
The Odd estimator of the population average gives each odd-numbered observation a weight of 2/n. Apply this estimator in the UnivariateSample sheet.What do the weights in column D look like?
Here is an estimator for the population average that might be applied when you know the data generating process produces only nonnegative numbers.Take each number in the sample, square it, find the average of the squared values, and take its square root. In equation form, the formula for this Weird
Go to the NonZeroMeanTalent sheet. Make sure that the parameter values in cells B2, B3, and B4 are β0 = 100, β1 = −0.5, and β2 = −0.2, respectively. Use the MCSim add-in to verifty that, when the average value of Talent is set to 0 (in cell B7), the estimate of the intercept term b0
Independence between two random variables X and Y means that E(XY) =E(X) · E(Y), the expected value of the product of two random variables, equals the product of their expected values. Suppose that, as assumed in the CEM, an error term ε with mean zero is independent of the variable X. Then the
In the text we claim that we have set things up so that the long-run correlation between the observed variable Training and the unobserved variable Talent is zero.a. Verify this by using the Monte Carlo add-in to find the distribution of the correlation between Training and Talent recorded in cell
Suppose that Training in fact has nothing to do with skiing time, in other words suppose that β1 = 0.What would happen? To answer the question, set β1 = 0 andβ2 = −0.2 in the EstimatingBeta1 sheet. Then go to the Winners sheet and run a Monte Carlo experiment. Explain the results, copying and
In Section 12.4 we proposed a two box model for the data generation process in an example in which Hourly Wages was the dependent variable and educational attainment (as measured by whether the worker had a college degree) was the independent variable. Instead of comparing the sample averages
In Section 5.7 we discussed a regression of Hourly Wages on Education.a. Write down a model for the data regression process that conform to the CEM, and could be used to support this regression.b. What evidence did we present in Section 5.7 that suggests the data do not in fact conform to the CEM?
Would you reject the null hypothesis? Explain.
On the assumption that the null is true, draw a rough sketch of the sampling distribution of the difference of the sample averages. Mark the location of the$3.10 per hour difference we observed in our sample.
Find the SE of the difference of the sample averages. Show your work.
State the null and alternative hypotheses.
Draw a two box model that represents the data generation process.
The difference between the average wage of the Experienced workers and the average wage of the Inexperienced workers is $3.10 per hour. Why can we not conclude that experience raises a person’s wage based on this fact?
Report the average wage for Experienced and Inexperienced workers.
Reconsider the hypothetical Galileo story of Section 6.2. Write down a measurement box model of the data generation process for Galileo’s data on time and distance of a falling object.
Suppose you obtained the data in Figure 11.8.1 from the Measure.xls workbook.Note that the true distance is not revealed. You are told that in the Monte Carlo experiment there were 1,000 repetitions. In each repetition, 25 measurements were taken of the unknown distance. You are asked to give your
In the univariate measurement model described in Measure.xls, the residual is defined as the difference between the individual measurement and the sample average. No matter how many times you make 25 new measurements, in the LiveSample sheet you will notice that the residuals always average to zero
Suppose that the measuring device described in Sections 11.2 to 11.5 was systematically biased – in particular that the measurements on average were 0.5 km too big but all the other assumptions about the box model still held true. How would Figure 11.5.1, which shows the three areas of the
In this book we develop two different languages for describing data generation processes. The first uses the box model metaphor, whereas the second employs formal mathematical symbols. What box model concepts correspond to each of these formal mathematical symbols, statements, and equations?a.
In a new workbook, we drew a standard normal random variable (average 0 and SD 1) in cells A1 and A2 and added them together in cell A3. Then we ran a 1,000-repetition Monte Carlo and got the results in Figure 10.9.1.
Open the Consistency.xls workbook. Is eSampleAverage an unbiased estimator of eAverageBox? If not, is eSampleAverage a consistent estimator of eAverageBox? Describe your procedure.
Return to the Setup sheet and click the Draw a Sample from the Box button. Suppose you did not know the contents of the box. With your sample, test the claim that the average of the box is 3.6. Describe your procedure.
If the DGP changes so that we take 100 draws instead of 25 draws, what happens to the chances of getting an average of 3.6 or more? Describe your procedure.HINT: You can directly change the Setup sheet in BoxModel.xls.
Does Monte Carlo simulation give similar results? Describe your procedure.
What are the exact chances of getting an average of 3.6 or more? Describe your procedure.
Properly configure BoxModel.xls to represent this DGP.What does BoxModel.xls display as the average and SD of the box?
Draw the box model for this DGP.
Use the Record All Selected Cells option and run another 10,000-repetition Monte Carlo. In your 10,000 samples, how many times was the group-level r negative? HINT: Use an IF statement like this: =IF(D3 < 0,1,0), then add the entire column. (Do not forget to hit F9 to calculate the sheet if
How do the average and SD reported by the Monte Carlo simulation relate to the expected value and SE?4B. As the number of repetitions increases, what happens to the expected value and SE?
Open the EcolCorr.xls workbook used (in Chapter 2) and run a Monte Carlo simulation (from the Live sheet) with 10,000 repetitions that tracks both the individual- and group-level correlation coefficients. Take a picture of your results. Copy and paste the picture in yourWord document. Comment on
Change the setup in the Sample sheet of MonteCarlo.xls to simulate a more complicated process. On the very first shot that a player takes, he or she has an 80-percent chance of hitting the free throw. On every subsequent shot, the chances of hitting depend on what happened on the previous attempt.
Change the setup in the Sample sheet of MonteCarlo.xls to simulate the freethrow shooting behavior of Shaquille O’Neal, who shoots 50 percent from the free-throw line. Run a 1,000-repetition Monte Carlo simulation of 100 free throws by O’Neal. Of course he will make fewer free throws on average
a. Add an Education*UNION interaction term to your semilog earnings function.Report your results.5B. Use the regression results to create a graph that compares the predicted wages of Union and Nonunion members as a function of Education.
Create a new dependent variable, ln Wage. Regress ln Wage on UNION and Education. Report your results and interpret the coefficient on UNION.HINT: SeeHowToUseDummyXVariables.doc (in BasicTools\HowTo) onhow to interpret dummy variables in a semilog functional form regression.
RegressWage on UNION and Education. Report your results and interpret the coefficient on UNION.
Compute the average of the UNION dummy variable and interpret the result.
Create the dummy variable UNION, using the CPS variable PEERNLAB. Fill your formula down.
In Figure 7.6.3, the interior of the table and the heights of the bars indicate the value of a variable Z as a function of variables X and Y. Write down the equations for three different planes that could fit the data in Figure 7.6.3.What phenomenon does this example illustrate? Average of

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