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About 833 results. 1294 free access solutions
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| m79492 | Use the data in NYSE.RAW to answer these questions.
(i) Estimate the model in equation (12.47) and obtain the squared OLS residuals. Find the average, minimum, and maximum values of u] over the sample.
(ii) Use the squared OLS residuals to estimate the following model of heteroske¬dasticity:
Var(ut|returnt-1 returnt-2 ....) = Var (u1|returnt-1) = (0 + (1 returnt-1 + (2 return 2t-1
Report the estimated coefficients, the reported standard errors, the R-squared, and the adjusted R-squared.
(iii) Sketch the conditional variance as a function of the lagged return-t. For what value of return - 1 is the variance the smallest, and what is the variance?
(iv) For predicting the dynamic variance, does the model in part (ii) produce any negative variance estimates?
(v) Does the model in part (ii) seem to fit better or worse than the ARCH(l) model in Example 12.9? Explain.
(vi) To the ARCH(l) regression in equation (12.51), add the second lag, u2_2. Does this lag seem important? Does the ARCH(2) model fit better than the model in part (ii)? |
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| m79493 | Use the data in OKUN.RAW to answer this question; see also Computer Exercise 11.11.
(i) Estimate the equation pcrgdpt = (0 + (1 (unemt + ut and test the errors for AR(1) serial correlation, without assuming [(unemt;. t = 1, 2, ...} is strictly exogenous. What do you conclude?
(ii) Regress the squared residuals, 2t, on kunem (this is the Breusch-Pagan test for heteroskedasticity in the simple regression case). What do you conclude?
(iii) Obtain the heteroskedasticity-robust standard error for the OLS estimate 1. Is it substantially different from the usual OLS standard error? |
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| m79494 | Use the data in OPENNESS.RAW for this exercise.
(i) Because log(pcinc) is insignificant in both (16.22) and the reduced form for open, drop it from the analysis. Estimate (16.22) by OLS and IV without log(pcinc). Do any important conclusions change?
(ii) Still leaving log(pcinc) out of the analysis, is land or log(land) a better instrument for open?
(iii) Now, return to (16.22). Add the dummy variable oil to the equation and treat it as exogenous. Estimate the equation by IV. Does being an oil producer have a ceteris paribus effect on inflation? |
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| m79495 | Use the data in PHILLIPS.RAW for this exercise, but only through 1996.
(i) In Example 11.5, we assumed that the natural rate of unemployment is constant. An alternative form of the expectations augmented Phillips curve allows the natural rate of unemployment to depend on past levels of unemployment. In the simplest case, the natural rate at time t equals unemt-1.If we assume adaptive expectations, we obtain a Phillips curve where inflation and unemployment are in first differences:
(inf = (0 + (1 (unem + u.
Estimate this model, report the results in the usual form, and discuss the sign, size, and statistical significance of 1.
(ii) Which model fits the data better, (11.19) or the model from part (i)? Explain. |
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| m79496 | Use the data in PHILLIPS.RAW for this exercise.
(i) Estimate an AR(1) model for the unemployment rate. Use this equation to predict the unemployment rate for 2004. Compare this with the actual unemployment rate for 2004. (You can find this information in a recent Economic Report of the President.)
(ii) Add a lag of inflation to the AR(1) model from part (i). Is inft-l statistically significant?
(iii) Use the equation from part (ii) to predict the unemployment rate for 2004. Is the result better or worse than in the model from part (i)?
(iv) Use the method from Section 6.4 to construct a 95% prediction interval for the 2004 unemployment rate. Is the 2004 unemployment rate in the interval? |
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| m79497 | Use the data in PHILLIPS.RAW for this exercise.
(i) In Example 11.5, we estimated an expectations augmented Phillips curve of the form
Δinft = β0 + β1 unemt + et,
where Δinft = inft - inft-1. In estimating this equation by OLS, we assumed that the supply shock, e, was uncorrelated with unem. If this is false, what can be said about the OLS estimator of β1?
(ii) Suppose that et is unpredictable given all past information E(et|inft-1, unemt-1,....,) = 0. Explain why this makes unemt-1 a good IV candidate for unemt.
(iii) Regress unemt on unemt-1. Are unemt and unemt-1 significantly correlated?
(iv) Estimate the expectations augmented Phillips curve by IV. Report the results in the usual form and compare them with the OLS estimates from Example 11.5. |
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| m79498 | Use the data in PHILLIPS.RAW to answer these questions.
(i) Estimate the models in (18.48) and (18.49) using the data through 1997. Do the parameter estimates change much compared with (18.48) and (18.49)?
(ii) Use the new equations to forecast unem1998: round to two places after the decimal. Which equation produces a better forecast?
(iii) As we discussed in the text, the forecast for unem1998 using (18.49) is 4.90. Compare this with the forecast obtained using the data through 1997. Does using the extra year of data to obtain the parameter estimates produce a better forecast?
(iv) Use the model estimated in (18.48) to obtain a two-step-ahead forecast of unem. That is, forecast unem1998 using equation (18.55) with - 1.572, = .732, and h = 2. Is this better or worse than the one-step-ahead forecast obtained by plugging unem1998 = 4.9 into (18.48)? |
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| m79499 | Use the data in PHILLIPS.RAW to answer these questions.
(i) Using the entire data set, estimate the static Phillips curve equation inft = (0 + (1 unemt + ut by OLS and report the results in the usual form.
(ii) Obtain the OLS residuals from part (i), t, and obtain ( from the regression 1 on 1-t. (It is fine to include an intercept in this regression.) Is there strong evidence of serial correlation?
(iii) Now estimate the static Phillips curve model by iterative Prais-Winsten. Compare the estimate of (1 with that obtained in Table 12.2. Is there much difference in the estimate when the later years are added?
(iv) Rather than using Prais-Winsten, use iterative Cochrane-Orcutt. How similar are the final estimates of (? How similar are the PW and CO estimates of (1? |
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| m79500 | Use the data in PNTSPRD.RAW for this exercise.
(i) The variable sprdcvr is a binary variable equal to one if the Las Vegas point spread for a college basketball game was covered. The expected value of sprdcvr, say p., is the probability that the spread is covered in a randomly selected game. Test H1: ( ( .5 against H1 : ( + .5 at the 10% significance level and discuss your findings. (This is easily done using a t test by regressing sprdcvr on an intercept only.)
(ii) How many games in the sample of 553 were played on a neutral court?
(iii) Estimate the linear probability model
sprdcvr = (0 + (1 favhome + (2 neutral + (3 fav25 + (4 und25 + u
and report the results in the usual form. (Report the usual OLS standard errors and the heteroskedasticity-robust standard errors.) Which variable is most significant, both practically and statistically?
(iv) Explain why, under the null hypothesis H0: (1 = (2 = (3 = (4 = 0, there is no heteoskedasticity in the model.
(v) Use the usual F statistic to test the hypothesis in part (iv). What do you conclude?
(vi) Given the previous analysis, would you say that it is possible to systematically predict whether the Las Vegas spread will be covered using information available prior to the game? |
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| m79501 | Use the data in PNTSPRD.RAW for this exercise.
(i) The variable favwin is a binary variable if the team favored by the Las Vegas point spread wins. A linear probability model to estimate the probability that the favored team wins is
P(favwin = 1 | spread) = β0 + β1spread.
Explain why, if the spread incorporates all relevant information, we expect β0 = .5.
(ii) Estimate the model from part (i) by OLS. Test H0: β0 = .5 against a two-sided alternative. Use both the usual and heteroskedasticity-robust standard errors.
(iii) Is spread statistically significant? What is the estimated probability that the favored team wins when spread = 10?
(iv) Now, estimate a probit model for P( favwin = spread). Interpret and test the null hypothesis that the intercept is zero.
(v) Use the probit model to estimate the probability that the favored team wins when spread = 10. Compare this with the LPM estimate from part (iii).
(vi) Add the variables favhome, fav25, and und25 to the probit model and test joint significance of these variables using the likelihood ratio test. (How many df are in the chi-square distribution?) Interpret this result, focusing on the question of whether the spread incorporates all observable information prior to a game. |
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| m79502 | Use the data in RDCHEM.RAW to further examine the effects of outliers on OLS estimates and to see how LAD is less sensitive to outliers. The model is
rdintens = (0 + (1 sales + (2 sales2 + (3 profmarg + u,
Where you should first change sales to be in billions of dollars to make the estimates easier to interpret.
(i) Estimate the above equation by OLS, both with and without the firm having annual sales of almost $40 billion. Discuss any notable differences in the estimated coefficients.
(ii) Estimate the same equation by LAD, again with and without the largest firm. Discuss any important differences in estimated coefficients.
(iii) Based on your findings in (i) and (ii), would you say OLS or LAD is more resilient to outliers? |
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| m79503 | Use the data in RECID.RAW to estimate the model from Example 17.4 by OLS, using only the 552 uncensored durations. Comment generally on how these estimates compare with those in Table 17.4. |
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| m79504 | Use the data in RENTAL.RAW for this exercise. The data for the years 1980 and 1990 include rental prices and other variables for college towns. The idea is to see whether a stronger presence of students affects rental rates. The unobserved effects model is
Log(rentit) = (0 + (0y90t + (1 log (popit) + (3 (log) (acginc it) pctstuit + ai + uit
Where pop is city population, avginc is average income, and pctstu is student population as a percentage of city population (during the school year).
(i) Estimate the equation by pooled OLS and report the results in standard form.
What do you make of the estimate on the 1990 dummy variable? What do you get for pctstu?
(ii) Are the standard errors you report in part (i) valid? Explain.
(iii) Now, difference the equation and estimate by OLS. Compare your estimate of (pctstu with that from part (ii). Does the relative size of the student population appear to affect rental prices?
(iv) Obtain the heteroskedasticity-robust standard errors for the first-differenced equation in part (iii). Does this change your conclusions? |
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| m79505 | Use the data in RENTAL.RAW for this exercise. The data on rental prices and other variables for college towns are for the years 1980 and 1990. The idea is to see whether a stronger presence of students affects rental rates. The unobserved effects model is
where pop is city population, avginc is average income, and pctstu is student population as a percentage of city population (during the school year).
(i) Estimate the equation by pooled OLS and report the results in standard form. What do you make of the estimate on the 1990 dummy variable? What do you get for pctsu?
(ii) Are the standard errors you report in part (i) valid? Explain.
(iii) Now, difference the equation and estimate by OLS. Compare your estimate of βpctsu whit mat from Part Does the relative size of the student population appear to affect rental prices?
(iv) Estimate the model by fixed effects to verify that you get identical estimates and standard errors to those in part (iii). |
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| m79506 | Use the data in SLEEP75.RAW for this exercise. The equation of interest is
sleep = (0 + (1 totwrk + (2educ + (3 age + (4age2 + (5 yngkid + u.
(i) Estimate this equation separately for men and women and report the results in the usual form. Are there notable differences in the two estimated equations?
(ii) Compute the Chow test for equality of the parameters in the sleep equation for men and women. Use the form of the test that adds male and the interaction terms male-totwrk, male-yngkid and uses the full set of observations. What are the relevant df for the test? Should you reject the null at the 5% level?
(iii) Now, allow for a different intercept for males and females and determine whether the interaction terms involving male are jointly significant.
(iv) Given the results from parts (ii) and (iii), what would be your final model? |
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| m79507 | Use the data in SLEEP75.RAW from Biddle and Hamermesh (1990) to study whether there is a tradeoff between the time spent sleeping per week and the time spent in paid work. We could use either variable as the dependent variable. For concreteness, estimate the model
Sleep = (0 + (1 totwrk + u,
Where sleep is minutes spent sleeping at night per week and totwrk is total minutes worked during the week.
(i) Report your results in equation form along with the number of observations and R2. What does the intercept in this equation mean?
(ii) If totwrk increases by 2 hours, by how much is sleep estimated to fall? Do you find this to be a large effect? |
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| m79508 | Use the data in SMOKE.RAW for this exercise.
(i) The variable cigs is the number of cigarettes smoked per day. How many people in the sample do not smoke at all? What fraction of people claim to smoke 20 cigarettes a day? Why do you think there is a pileup of people at 20 cigarettes?
(ii) Given your answers to part (i), does cigs seem a good candidate for having a conditional Poisson distribution?
(iii) Estimate a Poisson regression model for cigs, including log(cigpric), log(income), white, educ, age, and age2 as explanatory variables. What are the estimated price and income elasticities?
(iv) Using the maximum likelihood standard errors, are the price and income variables statistically significant at the 5% level?
(v) Obtain the estimate of σ2 described after equation (17.35). What is ? How should you adjust the standard errors from part (iv)?
(vi) Using the adjusted standard errors from part (v), are the price and income elasticities now statistically different from zero? Explain.
(vii) Are the education and age variables significant using the more robust standard errors? How do you interpret the coefficient on educ?
(viii) Obtain the fitted values, t from the Poisson regression model. Find the minimum and maximum values and discuss how well the exponential model predicts heavy cigarette smoking.
(ix) Using the fitted values from part (viii), obtain the squared correlation coefficient between y. and yt.
(x) Estimate a linear model for cigs by OLS, usi |
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| m79509 | Use the data in TRAFFIC2.RAW for this exercise. Computer Exercise C10.11 previously asked for an analysis of these data.
(i) Compute the first order autocorrelation coefficient for the variable prcfat. Are you concerned that prcfat contains a unit root? Do the same for the unemployment rate.
(ii) Estimate a multiple regression model relating the first difference of prcfat, (prcfat, to the same variables in part (vi) of Computer Exercise CI0.11, except you should first difference the unemployment rate, too. Then, include a linear time trend, monthly dummy variables, the weekend variable, and the two policy variables; do not difference these. Do you find any interesting results?
(iii) Comment on the following statement: "We should always first difference any time series we suspect of having a unit root before doing multiple regression because it is the safe strategy and should give results similar to using the levels." [In answering this, you may want to do the regression from part (vi) of Computer Exercise C 10.11, if you have not already.] |
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| m79510 | Use the data in TRAFFIC2.RAW for this exercise.
(i) Run an OLS regression of prcfat on a linear time trend, monthly dummy variables, and the variables wkends, unem, spdlaw, and beltlaw. Test the errors for AR(1) serial correlation using the regression in equation (12.14). Does it make sense to use the test that assumes strict exogeneity of the regressors?
(ii) Obtain serial correlation- and heteroskedasticity-robust standard errors for the coefficients on spdlaw and beltlaw, using four lags in the Newey-West estimator. How does this affect the statistical significance of the two policy variables?
(iii) Now, estimate the model using iterative Prais-Winsten and compare the estimates with the OLS estimates. Are there important changes in the policy variable coefficients or their statistical significance? |
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| m79511 | Use the data in TRAFFIC2.RAW for this exercise. These monthly data, on traffic accidents in California over the years 1981 to 1989, were used in Computer ExerciseC10.11.
(i) Using the standard Dickey-Fuller regression, test whether Itotacct, has a unit root. Can you reject a unit root at the 2.5% level?
(ii) Now, add two lagged changes to the test from part (i) and compute the augmented Dickey-Fuller test. What do you conclude?
(iii) Add a linear time trend to the ADF regression from part (ii). Now what happens?
(iv) Given the findings from parts (i) through (iii), what would you say is the best characterization of Itotacct. an I( 1) process or an 1(0) process about a linear time trend?
(v) Test the percentage of fatalities, prcfatt, for a unit root, using two lags in an ADF regression. In this case, does it matter whether you include a linear time trend? |
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