Introductory Econometrics A Modern Approach 3rd Edition Jeffrey M. Wooldridge - Solutions

Unlock a comprehensive understanding of "Introductory Econometrics: A Modern Approach, 3rd Edition" by Jeffrey M. Wooldridge with our expertly crafted solutions. Our online platform offers a complete answers key and detailed solution manual, providing solutions pdfs and solved problems for every chapter. Dive into questions and answers designed to enhance your learning experience, complete with a test bank and chapter solutions that include step-by-step answers. Whether you're using the instructor manual or the textbook itself, our resources are available for free download, ensuring you have everything you need for success in econometrics at your fingertips.

Exercise 3.4 Show that a Spatial Lag modelcan beexpressed as a pure autoregression of the independent variable y with a(non-zero mean) error term which incorporates the (non-stochastic)independent variable. can be
Exercise 3.3 Show that in the Spatial Error model, if the spatial correlation parameter r and the error variance s2e are both known, the ML estimators of β coincide with the GLS estimators. Derive the explicit expression of the GLS solution and of their error variances.
Exercise 3.2 Show that a Spatial Error model yi = b Xi + ui ;
Exercise 3.1 The following map shows the boundaries of the 27 countries that were the members of the European Union in July 2012.Using the procedure illustrated in Section 2.3.2, prepare a .GAL file and build up the row-standardized W matrix with the criterion of adjacency (join the island to the
8. Why do we need to consider the robust versions of the Lagrange Multiplier tests of spatial dependence?
7. Why can we use Moran’s I instead of a Lagrange Multiplier test for spatial dependence obtaining the same inferential conclusions?
6. What is the aim of Ord’s decomposition?
5. How can we define a Cochrane–Orcutt transformation in space? How can this transformation help in the process of model estimation?
4. Why is it necessary within the Feasible GLS to consider a Method of Moments procedure?
3. In what sense is the procedure in section 3.4.3 described as “feasible”?
2. What are the relative advantages and weaknesses of employing a Maximum Likelihood strategy and a Generalized Least Squares strategy in estimating a SARAR model?
1. What is a major limitation of using the Moran’s I statistics in testing the hypothesis of no spatial autocorrelation among the regression residuals? How can this limitation be addressed? What alternative tests are available?
Exercise 2.9 Visit the website http://gis.cancer.gov/tools/seerstat_ bridge/fips_vars/#statefips and download the shapefiles related to the 51 US states. Then, by using the procedure illustrated in section 2.3.3, generate the weight matrix and plot the map of the boundaries of the 51 states.
Exercise 2.8 Using the procedure illustrated in section 2.3.2, generate a weight matrix for the 20 Italian regions and replicate Examples 2.3 and 2.4.
Exercise 2.7 Given the results of Exercise 2.4 re-estimate model 1 of Exercise 1.1 [GVA = f(labor productivity; business birth rate)] and test for the presence of spatial autocorrelation among the residuals. Can we accept the hypothesis of residuals spatial uncorrelation?
Exercise 2.6 On the basis of the results obtained in Exercise 2.5, draw a scatter diagram with the variable GVA on the horizontal axis and the lagged variable L(GVA) on the vertical axis. This graph represents the exploratory tool termed “Moran scatterplot” in the literature (Anselin, 1995).
Exercise 2.5 Given the data shown in Exercise 1.1 and using the results of Exercise 2.4, compute the spatially lagged values of the variable GVA(Gross Value Added) for the 12 UK regions.
Exercise 2.4 Given the 12 UK regions reported in Exercise 1.1, by using the procedure illustrated in section 2.3, create the *.GAL file and derive the weight matrix. Consider Northern Ireland to be adjacent to Scotland and Wales.
Exercise 2.3 (a) Using the procedure illustrated in section 2.3.1 generate a (rook’s case based) weight matrix for the following regular square lattice grid of dimension 5-by-5 (n = 25).1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25(b) Given the data arranged on the previously
Exercise 2.2 Given the weight matrix derived in Exercise 2.1 and the data shown in the following table, compute the spatially lagged variable of infant mortality rates. Regions RO11- Nord-Vest RO12-Centru R021 - Nord-Est RO22-Sud-Est RO31-Sud-Muntenia RO32- Bucuresti - Ilfov RO41-Sud-Vest Oltenia
Exercise 2.1 The Nomenclature of Units for Territorial Statistics (NUTS)is a geocoded standard for referencing the subdivision of European Union countries for statistical purposes. For each of the Member States, a hierarchy of three NUTS levels is established by Eurostat, level NUTS1 corresponding
5. In Question 5 of Chapter 1 we introduced the Durbin–Watson test statistics [ ]2 2=2 1 =1 = T T t t t t t d Σ e −e − Σ e t=1,…,T. Rewrite the statistics in matrix notation, making use of an appropriate W matrix which properly describes the proximity between temporal units.
4. What is the meaning of the randomization hypothesis used in deriving the sampling distribution of the Moran I test statistics?
3. What is the meaning of row-standardization of a weight matrix? In which case is this operation beneficial?
2. What is the meaning of spatially lagged variable?
1. Why can’t the Durbin–Watson test (available in all econometric software and used to test the hypothesis of no residual autocorrelation)be employed in the case of regressions estimated on spatial data?
Exercise 1.1 The data shown in the table below refer to some regional economic data in the United Kingdom. They report the regional Gross Value Added (GVA) as a percentage of the country total, labor productivity(reported to a country total of 100) and the business birth rate. Country Region GVA
6. Why do we have to use the GLS estimation procedure instead of the OLS procedure when estimating a regression model on data that do not satisfy the hypotheses of homoscedasticity or/and residuals uncorrelation?
5. In time series regression modeling we test autocorrelation in the residuals using the Durbin-Watson test statistics defined byΣ [ − − ] Σ 2 2=2 1 =1 = T T t t t t t d e e e t = 1,…, T. Such a test exploits the natural ordering of the time observations which is evident in the expression
4. In Instrumental Variable (IV) estimation how can we prove that an instrument is relevant?
3. What are the crucial elements to consider if we want to judge the goodness of fit of the empirically observed data to our theoretical model?
2. Suppose we have a variable y = regional consumption, and variable x = regional income, both expressed in thousands of dollars and assume further the regression model y = bx +e. What are the consequences on the OLS estimator of b (say bˆ) of expressing the income in millions of dollars instead?
1. Under what conditions are the OLS estimators equivalent to the ML estimators? Are these conditions likely to be encountered when dealing with regressions on spatial data? What are the implications of such equivalence? What are the implications of the lack of this equivalence?
17. What factors affect manufacturing productivity at the state level? In addition to levels of capital and worker education, you could look at degree of unionization. A panel data analysis would be most convincing here, using two census years (say, 1980 and 1990). Clark (1984) provides an
16. Collect murder rates for a sample of counties (say, from the FBI Uniform Crime Reports) for two years. Make the latter year such that economic and demographic variables are easy to obtain from the County and City Data Book. You can obtain the total number of people on death row plus executions
15. What effect, if any, does success in college athletics have on other aspects of the university (applications, quality of students, quality of nonathletic departments)? McCormick and Tinsley (1987) looked at the effects of athletic success at major colleges on changes in SAT scores of entering
14. You can test whether the market for gambling on sports is efficient. For example, does the spread on football or basketball games contain all usable information for picking against the spread? The data set PNTSPRD.RAW contains information on men’s college basketball games. The outcome
11. What factors affect student performance at public schools? It is fairly easy to get school-level or at least district-level data in most states. Does spending per student matter? Do student-teacher ratios have any effects? It is difficult to estimate ceteris paribus effects because spending is
7. Are blacks discriminated against in the lending market? Hunter and Walker (1996) looked at this question; in fact, we used their data in Computer Exercises C7.8 and C17.2.
6. Do changes in traffic laws affect traffic fatalities? McCarthy (1994) contains an analysis of monthly time series data for the state of California. A set of dummy variables can be used to indicate the months in which certain laws were in effect. The file TRAFFIC2.RAW contains the data used by
5. Do parental consent laws increase the teenage birthrate? You can use state level data for this: either a time series for a given state or, even better, a panel data set of states. Do the same laws reduce abortion rates among teenagers? The Statistical Abstract of the United States contains all
C18.13 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 Exercise 10.11. (i) Using the standard Dickey-Fuller regression, test whether Itotace, has a unit root. Can you reject a unit root at the
C18.12 This exercise also uses the data from VOLAT.RAW. Computer Exercise 18.11 studies the long-run relationship between stock prices and industrial production. Here, you will study the question of Granger causality using the percentage changes. (i) Estimate an AR(3) model for pcip, the percentage
C18.11 Use the data in VOLAT.RAW for this exercise. (i) Confirm that Isp500 = log(sp500) and lip log(ip) appear to contain unit roots. Use Dickey-Fuller tests with four lagged changes and do the tests with and without a linear time trend. (ii) Run a simple regression of Isp500 on lip. Comment on
C18.10 Use the data in INTQRT RAW for this exercise. (i) Using the data from all but the last four years (16 quarters), estimate an AR(1) model for Ar6,. (We use the difference because it appears that r6, has a unit root.) Find the RMSE of the one-step-ahead forecasts for Ar6, using the last 16
C18.9 Use CONSUMP.RAW for this exercise. (i) Let y, be real per capita disposable income. Use the to estimate the model y = a + B + SONI data through 1989 SALE OR and report the results in the usual form. (ii) Use the estimated equation from part (i) to forecast y in 1990. What is the forecast
C18.7 Use the data in BARIUM.RAW for this exercise. (i) Estimate the linear trend model chnimp, = a + t+u,, using the first 119 observations (this excludes the last 12 months of observations for 1988). What is the standard error of the regression? Now, estimate an AR(1) model for chnimp, again
C18.6 Use the data in PHILLIPS.RAW to answer these questions. (i) Estimate the models in (18.48) and (18.49) using the data t ONLARNING 1997. Do the parameter estimates change much compared with (18.48) and (18.49)? (ii) Use the new equations to forecast unem round to two places after the decimal.
C18.5 Use INTQRT.RAW for this exercise. (i) In Example 18.7, we estimated an error correction model for the hold- ing yield on six-month T-bills, where one lag of the holding yield on three-month T-bills is the explanatory variable. We assumed that the cointegration parameter was one in the
C18.2 Use the data in HSEINV.RAW for LRP to those (i) Test for a unit root in log(impc), including a linear time trend and two lags of Alog(invpc.). Use a 5% significance level. (ii) Use the approach from part (i) to test for a unit root in log(price). (iii) Given the outcomes in parts (i) and
C18.1 Use the data in WAGEPRC.RAW for this exercise. Problem 11.5 gave estimates of a finite distributed lag model of gprice on gwage, where 12 lags of gwage are used. (i) Estimate a simple geometric DL model of gprice on gwage. In partic- ular, estimate equation (18.11) by OLS. What are the
18.9 Let {y,) be an I(1) sequence. Suppose that 8, is the one-step-ahead forecast of Ay,+ and let f = + y,, be the one-step-ahead forecast of y,+1. Explain why the fore- cast errors for forecasting Ay,+1 and y,+1 are identical.
18.8 Suppose that PRO y = a +82-1+ u u = pu-1+e, REVIEW ONLYws the model E(e,1,-1) = 0, contains y and z dated at t -1 and earlier. - Show that E(y+1) = (1 - p)a + py, +8z, p8z. (Hint: Write u-1-1a-8-2 and plug this into the second equation; then, plug the result into the first equation and take
18.7 Let gM, be the annual growth in the money supply and let unem, be the unem- ployment rate. Assuming that unem, follows a stable AR(1) process, explain in detail how you would test whether gM Granger causes unem.
18.6 Using the monthly data in VOLAT.RAW, the following model pcip 1.54.344 pcip+.074 pcip-2+.073 pcip (.56) (.042) (.045) (.042) n = 554, R = .174, R2 = .168, where pcip is the percentage change in monthly industrial production, at an annualized rate, and pcsp is the percentage change in the
8.5 Suppose the process {(x,y,): t = 0,1,2,...} satisfies the equations OR and y = x, + u where E(u) =E(v,|,-1) == Ax = yAx,-1 + v, 0,1,contains information on x and y dated at time t-1 and earlier, 0, and y < 1 [so that x,, and therefore y,, is I(1)]. Show that these two equations imply an error
18.4 Consider the error correction model in equation (18.37). Show that if you add another lag of the error correction term, y-2-Bx,-2, the equation suffers from perfect (Hint: Show that y-2-BX-2 is a perfect linear function of y-1 - Bx,-1, Ax,-1, and Ay,-1-) 1
18.3 Suppose that (y,) and (z,) are I(1) series, but y, z, is I(0) for some 0. Show that for any 8 B. y, - Sz, must be I(1).
18.2 An interesting economic model that leads to an econometric model with a lagged dependent variable relates y, to the expected value of x,, say, x, where the expectation is based on all observed information at time - 1:A natural assumption on {u} is that E(u,,-1) = 0, where I,- denotes all
18.1 Consider equation (18.15) with k = 2. Using the IV approach to estimating the Y and p, what would you use as instruments for y,-1?
C17.11 Use the data in CPS91.RAW for this exercise. These data are for married women, where we also have information on each husband's income and demographics. (i) What fraction of the women report being in the labor force? (ii) Using only the data for working women-you have no choice- estimate the
C17.9 Use the data in APPLE.RAW for this exercise. These are telephone survey data attempting to elicit the demand for a (fictional) "ecologically friendly" apple. Each family was (randomly) presented with a set of prices for regular apples and the eco-labeled apples. They were asked how many
C17.8 The file JTRAIN2.RAW contains data on a job training experiment for a group of men. Men could enter the program starting in January 1976 through about mid-1977. The program ended in December 1977. The idea is to test whether participation in the job training program had an effect on
C17.7 Use the MROZ.RAW data for this exercise. EVIE Using the 428 women who were in the workforce, estimate the return to education by OLS including exper, exper, nwifeinc, age, kidsl16, and kidsge as explanatory variables. Report your estimate on educ and its standard error. (ii) Now, estimate the
C17.6 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 com- pare with those in Table 17.4.
C17.5 Refer to Table 13.1 in Chapter 13. There, we used the data in FERTILI.RAW to estimate a linear model for kids, the number of children ever born to a woman. (i) Estimate a Poisson regression model for kids, using the same vari- ables in Table 13.1. Interpret the coefficient on y82. (ii) What
C17.4 In Example 9.1, we added the quadratic terms pcnv, ptimes and inc86 to a linear model for narr86. (i) Use the data in CRIME1.RAW to add these same terms to the Pois- son regression in Example 17.3. (ii) Compute the estimate of o given by 2 (1 19 Is there evidence of overdispersion? How should
C17.3 Use the data in FRINGE.RAW for this exercise. (i) For what percentage of the workers in the sample is pension equal to zero? What is the range of pension for workers with nonzero pension benefits? Why is a Tobit model appropriate for modeling pension? (ii) Estimate a Tobit model explaining
C17.2 Use the data in LOANAPP.RAW for this exercise; see also Computer Exercise C7.8. (i) Estimate a probit model of approve on white. Find the estimated probability of loan approval for both whites and nonwhites. How do these compare with the linear probability estimates? (ii) Now, add the
C17.1 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) = B + Bspread. Explain why, if the
17.7 Suppose you are hired by a university to study the factors that determine whether tudents admitted to the university actually come to the university. You are given a large random sample of students who were admitted the previous year. You have information on whether each student chose to
17.6 Consider a family saving function for population of all families in the United States: sav=Bo+Binc+Bhhsize + Beduc + age + u, where hhsize is household size, educ is years of education of the household head, and age is age of the household head. Assume that E(ulinc,hhsize,educ,age) = 0. (i)
17.5 (Requires calculus) Let patents be the number of patents applied for by a firm dur- ing a given year. Assume that the conditional expectation of patents given sales and RD is E(patents sales,RD) = exp[B + Blog(sales) + BRD + BRD], where sales is annual firm sales and RD is total spending on
17.4 Let mvp, be the marginal value product for worker i, which is the price of a firm's good multiplied by the marginal product of the worker. Assume that log(mvp) B+Bx + ... + Bxk + ui wage=max(mvp,,minwage), where the explanatory variables include education, experience, and so on, and minwage,
17.3 (Requires calculus) (i) Suppose in the Tobit model that x = log(z), and this is the only place appears in x. Show that OR REVIE JE(yly > 0,x) (B/z){1-(x/o)[x/ + (x/o)]}, (17.52) where , is the coefficient on log(z). (ii) If x = z, and x2 = 2, show that JE(yly > 0,x) = ( + 2z){1-(xlo)[xlo +
17.2 Let grad be a dummy variable for whether a student-athlete at a large university graduates in five years. Let hsGPA and SAT be high school grade point average and SAT score, respectively. Let study be the number of hours spent per week in an organized study hall. Suppose that, using data on
17.1 (i) For a binary response y, let y be the proportion of ones in the sample (which is equal to the sample average of the y;). Let a be the percent correctly predicted for the outcome y = 0 and let be the percent correctly predicted for the out- come y = 1. If p is the overall percent correctly
C16.10 Use the entire panel data set in AIRFARE.RAW for this exercise. The demand equation in a simultaneous equations unobserved effects model is log(passen,)=0+alog(fare) +a+uil where we absorb the distance variables into a (i) Estimate the demand function using fixed effects, being sure to
C16.9 For this exercise, use the data in AIRFARE.RAW, but only for the year 1997. (i) A simple demand function for airline seats on routes in the United States is log(passen)= a log(fare) + Blog(dist) + B 12[log(dist)] + u, where passen is average passengers per day, fare is average airfare, and
C16.8 Use the data set in FISH.RAW, which comes from Graddy (1995), to do this exer- cise. The data set is also used in Computer Exercise C12.9. Now, we will use it to esti- mate a demand function for fish. (i) Assume that the demand equation can be written, in equilibrium for each time period, as
C16.7 Refer to Example 13.9 and the data in CRIME4.RAW. (i) Suppose that, after differencing to remove the unobserved effect, you think Alog(polpc) is simultaneously determined with Alog(crmrte); in particular, increases in crime are associated with increases in police officers. How does this help
C16.6 Use the data in CEMENT.RAW for this exercise. (i) A static (inverse) supply function for the monthly growth in cement price (gprc) as a function of growth in quantity (gcem) is gprc, agcem,+Bo+Bigprcpet + Bfeb, + ... + Bdec, + u where gprcpet (growth in the price of petroleum) is assumed to
C16.5 Use the Economic Report of the President (2005 or later) to update the data in CONSUMP.RAW, at least through 2003. Reestimate equation (16.35). Do any important conclusions change?
C16.4 Use the data in CONSUMP.RAW for this exercise. (i) In Example 16.7, use the method from Section 15.5 to test the single overidentifying restriction in estimating (16.35). What do you conclude? (ii) Campbell and Mankiw (1990) use second lags of all variables as IVs because of potential data
C16.3 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
C16.2 Use MROZ.RAW for this exercise. (i) Reestimate the labor supply function in Example 16.5, using log(hours) as the dependent variable. Compare the estimated elasticity (which is now constant) to the estimate obtained from equation (16.24 average hours worked. SS OF (ii) In the labor supply
C16.1 Use SMOKE.RAW for this exercise. (i) A model to estimate the effects of smoking on annual income (perhaps through lost work days due to illness, or productivity effects) is log(income) = Bo+ cigs + Beduc + age + age + u, where cigs is number of cigarettes smoked per day, on average. How do
16.8 How big is the effect of per-student school expenditures on local housing values? Let HPRICE be the median housing price in a school district and let EXPEND be per-student expenditures. Using panel data for the years 1992, 1994, and 1996, we postulate the model IHPRICE = 0, + BIEXPEND +
16.7 For a large university, you are asked to estimate the demand for tickets to women's basketball games. You can collect time series data over 10 seasons, for a total of about 150 observations. One possible model is IATTEND, B+BIPRICE, + BWINPERC, + BRIVAL, + BWEEKEND, + st + up OR REVI FC where
16.6 Consider a linear probability model for whether employers offer a pension plan based on the percentage of workers belonging to a union, as well as other factors: pension = Bo+Bpercunion + Bavgage + Bavgeduc + B*percmale + Bpercmarr + u. SAR CLAS (i) Why might percunion be jointly determined
16.5 A simple model to determine the effectiveness of condom usage on reducing sex- ually transmitted diseases among sexually active high school students is EV infrate = Bo+B,conuse + Bpercmale + Bavgine + city + u, where infrate is the percentage of sexually active students who have contracted
16.4 Suppose that annual earnings and alcohol consumption are determined by the SEM log(earnings) Bo+ Balcohol + Beduc + u cohol yo+y,log(earnings) + y2educ + y3log(price) + u, where price is a local price index for alcohol, which includes state and local taxes. Assume that educ and price are
16.3 In Problem 3.3 of Chapter 3, we estimated an equation to test for a tradeoff between minutes per week spent sleeping (sleep) and minutes per week spent working (totwrk) for a random sample of individuals. We also included education and age in the equation. Because sleep and totwrk are jointly
16.2 Let com denote per capita consumption of corn in bushels, at the county level, let price be the price per bushel of com, let income denote per capita county income, and let rainfall be inches of rainfall during the last corn-growing season. The following simultaneous equa- tions model imposes
16.1 Write a two-equation system in "supply and demand form," that is, with the same variable y (typically, "quantity") appearing on the left-hand side: + y =a2y2 B222 +2. (i) If a = 0 or a = 0, explain why a reduced form exists for y. (Remember, a reduced form expresses y, as a linear function of
C15.10 Use the data in HTV.RAW for this exercise. (i) Run a simple OLS regression of log(wage) on educ. Without control- ling for other factors, what is the 95% confidence interval for the return to another year of education? (ii) The variable ctuit, in thousands of dollars, is the change in
C15.9 The purpose of this exercise is to compare the estimates and standard errors obtained by correctly using 2SLS with those obtained using inappropriate procedures. Use the data file WAGE2.RAW. (i) Use a 2SLS routine to the equation log(wage) = B+Beduc + Bexper + Btenure + B black + u, where
C15.8 Use the data in 401KSUBS.RAW for this exercise. The equation of interest is a linear probability model: pira 0 1p401k 2inc 3inc2 4age 5age2 u. The goal is to test whether there is a tradeoff between participating in a 401(k) plan and having an individual retirement account
C15.7 Use the data in PHILLIPS.RAW for this exercise. (i) In Example 11.5, we estimated an expectations augmented Phillips curve of the form inft 0 1unemt et , where inft inft inft1. In estimating this equation by OLS, we assumed that the supply shock, et , was uncorrelated with
C15.6 Use the data in MURDER.RAW for this exercise. The variable mrdrte is the murder rate, that is, the number of murders per 100,000 people. The variable exec is the total number of prisoners executed for the current and prior two years; unem is the state unemployment rate. (i) How many states

Showing 1700 - 1800 of 4105

First
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
Last

Introductory Econometrics A Modern Approach 3rd Edition Jeffrey M. Wooldridge - Solutions

Step by Step Answers