Econometrics By Example 2nd Edition Damodar Gujarati - Solutions

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Use the data set CONSUMP for this exercise.(i) Estimate a simple regression model relating the growth in real per capita consumption (of nondurables and services) to the growth in real per capita disposable income. Use the change in the logarithms in both cases. Report the results in the usual
Use the data in EZANDERS for this exercise. The data are on monthly unemployment claims in Anderson Township in Indiana, from January 1980 through November 1988. In 1984, an enterprise zone (EZ) was located in Anderson (as well as other cities in Indiana). [See Papke (1994) for details.](i) Regress
In Example 10.4, we wrote the model that explicitly contains the long-run propensity, u0, as gfrt 5 a0 1 u0pet 1 d1 1pet21 2 pet 2 1 d2 1pet22 2 pet 2 1 u, where we omit the other explanatory variables for simplicity. As always with multiple regression analysis, u0 should have a ceteris paribus
In Example 10.4, we saw that our estimates of the individual lag coefficients in a distributed lag model were very imprecise. One way to alleviate the multicollinearity problem is to assume that the dj follow a relatively simple pattern. For concreteness, consider a model with four lags:yt 5 a0 1
When the three event indicators befile6, affile6, and afdec6 are dropped from equation (10.22), we obtain R2 5 .281 and R2 5 .264. Are the event indicators jointly significant at the 10% level?
Suppose yt follows a second order FDL model:yt 5 a0 1 d0zt 1 d1zt21 1 d2zt22 1 ut.Let z pdenote the equilibrium value of zt and let yp be the equilibrium value of yt, such that yp 5 a0 1 d0z p 1 d1z p 1 d2z p.Show that the change in yp, due to a change in z p, equals the long-run propensity times
Let gGDPt denote the annual percentage change in gross domestic product and let intt denote a shortterm interest rate. Suppose that gGDPt is related to interest rates by gGDPt 5 a0 1 d0intt 1 d1intt21 1 ut, where ut is uncorrelated with intt, intt21, and all other past values of interest rates.
Use the data in ECONMATH to answer this question. The population model is score 5 b0 1 b1act 1 u.(i) For how many students is the ACT score missing? What is the fraction of the sample?Define a new variable, actmiss, which equals one if act is missing, and zero otherwise.(ii) Create a new variable,
Use the data in CEOSAL2 to answer this question.(i) Estimate the model lsalary 5 b0 1 b1lsales 1 b2lmktval 1 b3ceoten 1 b4ceoten2 1 u by OLS using all of the observations, where lsalary, lsales, and lmktvale are all natural logarithms. Report the results in the usual form with the usual OLS
Use the data in ELEM94_95 to answer this question. See also Computer Exercise C10 in Chapter 4.(i) Using all of the data, run the regression lavgsal on bs, lenrol, lstaff, and lunch. Report the coefficient on bs along with its usual and heteroskedasticity-robust standard errors. What do you
Use the data in MURDER only for the year 1993 for this question, although you will need to first obtain the lagged murder rate, say mrdrte21.(i) Run the regression of mrdrte on exec, unem. What are the coefficient and t statistic on exec?Does this regression provide any evidence for a deterrent
You need to use two data sets for this exercise, JTRAIN2 and JTRAIN3. The former is the outcome of a job training experiment. The file JTRAIN3 contains observational data, where individuals themselves largely determine whether they participate in job training. The data sets cover the same time
In this exercise, you are to compare OLS and LAD estimates of the effects of 401(k) plan eligibility on net financial assets. The model is nettfa 5 b0 1 b1inc 1 b2inc2 1 b3age 1 b4age2 1 b5male 1 b6e401k 1 u.(i) Use the data in 401KSUBS to estimate the equation by OLS and report the results in the
Use the data in TWOYEAR for this exercise.(i) The variable stotal is a standardized test variable, which can act as a proxy variable for unobserved ability. Find the sample mean and standard deviation of stotal.(ii) Run simple regressions of jc and univ on stotal. Are both college education
Use the data in LOANAPP for this exercise.(i) How many observations have obrat . 40, that is, other debt obligations more than 40% of total income?(ii) Reestimate the model in part (iii) of Computer Exercise C8, excluding observations with obrat . 40. What happens to the estimate and t statistic on
Use the data in RDCHEM to further examine the effects of outliers on OLS estimates and to see how LAD is less sensitive to outliers. The model is rdintens 5 b0 1 b1sales 1 b2sales2 1 b3profmarg 1 u, where you should first change sales to be in billions of dollars to make the estimates easier to
Use the data for the year 1990 in INFMRT for this exercise.(i) Reestimate equation (9.43), but now include a dummy variable for the observation on the District of Columbia (called DC). Interpret the coefficient on DC and comment on its size and significance.(ii) Compare the estimates and standard
Use the data from JTRAIN for this exercise.(i) Consider the simple regression model log1scrap2 5 b0 1 b1grant 1 u, where scrap is the firm scrap rate and grant is a dummy variable indicating whether a firm received a job training grant. Can you think of some reasons why the unobserved factors in u
Use the data set WAGE2 for this exercise.(i) Use the variable KWW (the “knowledge of the world of work” test score) as a proxy for ability in place of IQ in Example 9.3. What is the estimated return to education in this case?(ii) Now, use IQ and KWW together as proxy variables. What happens to
This exercise shows that in a simple regression model, adding a dummy variable for missing data on the explanatory variable produces a consistent estimator of the slope coefficient if the “missingness”is unrelated to both the unobservable and observable factors affecting y. Let m be a variable
The point of this exercise is to show that tests for functional form cannot be relied on as a general test for omitted variables. Suppose that, conditional on the explanatory variables x1 and x2, a linear model relating y to x1 and x2 satisfies the Gauss-Markov assumptions:y 5 b0 1 b1x1 1 b2x2 1 u
Consider the simple regression model with classical measurement error, y 5 b0 1 b1xp 1 u, where we have m measures on xp. Write these as zh 5 xp 1 eh, h 5 1, p , m. Assume that xp is uncorrelated with u, e1, p , em, that the measurement errors are pairwise uncorrelated, and have the same variance,
In the model (9.17), show that OLS consistently estimates a and b if ai is uncorrelated with xi and bi is uncorrelated with xi and x2 i , which are weaker assumptions than (9.19). [Hint: Write the equation as in (9.18) and recall from Chapter 5 that sufficient for consistency of OLS for the
The following equation explains weekly hours of television viewing by a child in terms of the child’s age, mother’s education, father’s education, and number of siblings:tvhoursp 5 b0 1 b1age 1 b2age2 1 b3motheduc 1 b4fatheduc 1 b5sibs 1 u.We are worried that tvhoursp is measured with error
17.5 Table 17.11 on the companion website gives data for 50 US states and Washington, DC for the years 1985–2000 on the following variables:18 beer sales: per capita beer sales in the state income: in dollars beer tax: state’s tax rate on beer Note: Each state has a federal numerical code,
17.4 In their article, Maddala et al. considered the demand for residential electricity and natural gas in 49 states in the USA for the period 1970–1990; Hawaii was not included in the analysis.17 Th ey collected data on several variables; these data can be found in Table 17.10 on the companion
17.3 To fi nd out why productivity has declined and the role of public investment in productivity growth, Alicia Munnell studied productivity data in the 48 continental states of the USA for 17 years from 1970 to 1986, for a total of 816 observations.16 Th e dependent variable is GSP (gross state
17.2 Expand the LSDV model by including the time dummies and comment on the results.
17.1 Table 17.8 gives the LSDV estimates of the charity example. If you examine the raw data given in Table 17.1, can you spot some pattern regarding individuals that have signifi cant intercepts? For example, are married taxpayers likely to contribute more than single taxpayers?
16.8 Table 16.1323 on the companion website gives the following macroeconomic data for the USA for the quarterly period 1960-1Q to 2012-1Q, for a total of 209 quarters: Infl ation: annualized quarterly percentage change in the GDP defl ator Unemployment rate: the civilian unemployment rate;
16.7 Refer to the 3-month and 6-month Treasury Bills example discussed in the text. Suppose you also want to include the Federal Funds Rate (FFR) in the model. Obtain the data on FFR for comparable time period and estimate a VAR model for the three variables. You can obtain the data from the
16.5 Develop a suitable ARIMA model to forecast the labor force participation rate for females and males separately. What considerations would you take into account in developing such a model? Show the necessary calculations and explain the various diagnostic tests you use in your analysis. 16.6
16.4 Suppose you want to forecast employment at the national level. Collect quarterly employment data and develop a suitable forecasting model using ARIMA methodology. To take into account seasonal variation, employment data are often presented in seasonally adjusted form. In developing your
16.2 Refer to the IBM stock price ARIMA model discussed in the text. Using the data provided, try to come up with an alternative model and compare your results with those given in the text. Which model do you prefer, and why? 16.3 Replicate your model used in the preceding exercise using more
16.1 Estimate regression (16.1) using the logs of the variables and compare the results with those obtained in Table 16.2. How would you decide which is a better model?
14.4 Refer to Table 13.10 in Exercise 13.9. (a) Is the dividend time series stationary? How do you fi nd that out? (b) Is the corporate profi ts time series stationary? Explain the tests you use. (c) Are the two time series cointegrated? Show your analysis.
14.3 Suppose you have data on real GDP for Mexico and the USA. A priori, would you expect the two time series to be cointegrated? Why? What does trade theory have to say about the relationship between the two? Table 14.11 on the companion website gives quarterly data on real GDP for Mexico and the
14.1 Consider the relationship between PCE and PDI discussed in the text. (a) Regress PCE on an intercept and trend and obtain the residuals from this regression. Call it S1. (b) Regress PDI on an intercept and trend and obtain residuals from this regression. Call it S2. (c) Now regress S1 on S2.
13.10 Table 13.11 on the companion website gives seasonally adjusted monthly data on US unemployment rate from January 1, 1948 to June 1, 2013. Th ese data are from the US Bureau of Labor Statistics. (a) Plot the unemployment rate chronologically. (b) What pattern or patterns do you observe in the
13.9 Table 13.10 on the companion website gives quarterly data on key macro-economic variables for the US from fi rst quarter of 1947 to the fourth quarter 2007. Th ese data are also from the US Department of Commerce and the Economic Report of the President. Th e variables are: DPI = real
13.8 Table 13.9 on the companion website gives comparatively recent daily data on the US dollar and euro exchange rate (EX), defi ned as dollars per unit of euro, for the period February 3, 2012 to June 16, 2013. Th ese data are from the US Department of Commerce and the Economic Report of the
13.7 If a time series is stationary, does it mean that it is a white noise series? In the chapter on autocorrelation, we considered the Markov fi rst-order autoregressive scheme, such as: u u t t 1 t where ut is the error term in the regression model,  is the coeffi cient of autocorrelation,
13.6 Repeat 13.5 for the Consumer Price Index (CPI) for the USA.
13.5 Would you expect quarterly US real GDP series to be stationary? Why or why not? Obtain data on the quarterly US GDP from the website of the Federal Reserve Bank of St Louis to support your claim.
13.3 For the IBM stock price series estimate model (13.7) and comment of the results. 1 3.4 Suppose in Eq. (13.7) B3 = 0. What is the interpretation of the resulting model?
13.2 Verify Eqs. (13.17) and (13.18).
13.1 Verify Eqs. (13.13) and (13.14).
12.6 Table 12.813 on the companion website gives information on 316 students. Th e response variable is days absent during the school year (daysabs), math standardized tests score (mathnce), language standardized tests score (langnce), and gender (female = 1). Assuming daysabs follow the Poisson
12.5 In a geriatric study of the frequency of falls, Neter et al. obtained data on 100 individuals 65 years of age and older on the following variables:12 Y = number of falls suff ered by an individual X2 = gender (male = 1, female = 0) X3 = a balance index X4 = a strength index Z = an intervention
12.4 Th e productivity of a scholar is often judged by the number of articles he or she publishes in scholarly journals. Th is productivity may be aff ected by factors, such as sex, marital status, number of young children, prestige of the graduate program and the number of articles published by
12.2 Refer to the data in Table 11.7 on the companion website. Th e data refer to Ray Fair’s analysis of extramarital aff airs. Since there are many observations with zero extramarital aff airs, these data can also be used to see if a Poisson and or Negative Binomial Regression Model fi t the
11.4 Refer to Exercise 8.7 on direct marketing of a fi nancial product. In that exercise, we used the data to develop a logit model of customer response for investment in a new investment product. Use the same data to develop a Tobit model of the amount of money invested in the new product, knowing
11.1 Include the Faminc-squared variable in both the censored and truncated regression models discussed in the chapter and compare and comment on the results.
10.4 Class project: Th e World Values Survey (WVS) periodically carries surveys on various economic, social, and political aspects of several countries.18 For example, the 1995–1997 Survey asks the following question: Do you think that what the government is doing for people in poverty is about
10.3 Table 10.8 on the companion website17 gives data, obtained from Compustat, on credit rating for 92 US fi rms in 2005. Th e credit scores range from 1 (lowest) to 7 (highest). Th e data also gives information on fi rm characteristics, such as book leverage, earnings before interest and taxes,
10.2 Table 10.7 (available on the companion website) gives data on a random sample of 40 adults about their mental health, classifi ed as well, mild symptom formation, moderate symptom formation, and impaired in relation to two factors, socio-economic status (SES) and an index of life events (a
10.1 In the illustrative example (warmth category), the assumptions of the proportional odds model is not tenable. As an alternative, estimate a multinomial logit model (MLM) using the same data. Interpret the model and compare it with the proportional odds model.
9.3 In a study of the use of contraceptives, Germán Rodríguez of Princeton University obtained the results in Table 9.10 based on a multinomial logit model.17 (a) How would you interpret these results? (b) A priori, what is the expected sign of the age-squared variable? Are the results in accord
9.2 Refer to Table 9.9 on the companion website.16 Entering high school students make a choices between taking a general program, a vocational program, or an academic program. Th eir choice might be modeled using their writing score and their social economic status. Th e outcome variable is prog,
9.1 From the General Social Survey (1991) conducted by NORC at the University of Chicago, a sample of 633 workers was classifi ed into three occupational categories, coded as follows: Occup = 1, if a worker’s occupation is laborer, operative or craft, Occup = 2, if occupation is clerical, sales
8.9 President Clinton’s Impeachment Trial: On January 7, 1999, Th e US House of Representatives impeached President Clinton on two counts, called Article 1 and Article 2. Article 1 was perjury to grand jury and Article 2 was obstruction of justice. By law, it is the duty of the US Senate to
8.8 To fi nd out if adolescents (ages 15 and 16) ever had sexual intercourse (yeso), Morgan and Teachman studied a sample of 342 adolescents from the National Survey of Children, 134 white males, 149 white females, 23 black males and 36 black females and obtained the following results from a
8.7 Direct marketing for fi nancial products (DMF) Table 8.1321 on the companion website gives data on the response of customers of a commercial bank to direct marketing campaign for a new fi nancial product. Th e variables are as follows: Response =1 if customer invests in the new product, 0
8.6 Table 8.12 on the companion website provides data on heart attack within 48 hours of myocardial infarction onset.20 Th is is a large data set consisting of 4,483 observations. Th e variables used in the analysis are as follows: death = 1, if within 48 hours of myocardial infarction onset, 0
8.5 Table 8.11 on the companion website gives hypothetical data on admission to graduate school.19 Th e variables are defi ned as follows: Admit = 1 if admitted to graduate school, 0 otherwise GRE = graduate record examination score GPA = grade point average Rank of the graduating school, 1, 2, 3,
8.4 Divide the smoker data into 20 groups. For each group compute pi , the probability of smoking. For each group compute the average values of the regressors and estimate the grouped logit model using these average values. Compare your results with the ML estimates of smoker logit discussed in
8.1 To study the eff ectiveness of price discount on a six-pack of soft drink, a sample of 5,500 consumers was randomly assigned to 11 discount categories as shown in Table 8.9.16(a) Treating the redemption rate as the dependent variable and price discount as the regressor, see whether the logit
7.11 Th e data in Table 7.22 are an extract from the well-known study of Mauldin and Berelson.42 Th e variables are setting (an index of social setting), eff ort (an index of family planning eff ort), and change (the percentage decline in the crude birth rate) between 1965 and 1975 for 20 countries
7.10 For the ARDL(1,1) model, the long-run multiplier is given in Eq. (7.27). Suppose for the illustrative example you estimate the following simple regression model: PCEt = C1 + C2 DPIt + ut Estimate this regression and show that C2 is equal to the long-run multiplier given in Eq. (7.27). Can you
7.9 Consider the following simultaneous equation model: Y A AY A X u 1 1 22 3 1 1 t t tt (1) Y B BY B X u 2 1 21 3 2 2 t t tt (2) In this model the Ys are the endogenous variables and the Xs are the exogenous variables and the us are stochastic error terms. (a) Obtain the reduced form
7.7 In the cancer data we have 43 observations for each type of cancer, giving a total of 172 observations for all the cancer types. Suppose you now estimate the following regression model: C B B Cig B Lung B Kidney B Leukemia u i ii i i 12 3 4 5 i where C = number of deaths from cancer, Cig =
7.6 Continue with Exercise 7.5. Are there any outliers in the cancer data? If there are, identify them. How would you handle the outliers?
7.5 Use the data given in Table 7.21 on the companion website to fi nd out the impact of cigarette smoking on bladder, kidney, and leukemia cancers. Specify the functional form you use and present your results. How would you fi nd out if the impact of smoking depends on the type of cancer? What may
6.5 Table 6.10 on the companion website presents data for the USA for the years 1973–2011 on the following variables: Hstart: New housing starts , monthly data at seasonally annual rate (thousands) UN: seasonally adjusted civilian unemployment rate (%) M2: Seasonally adjusted M2 money supply
6.4 Re-run the regression in Table 6.7 using ln INC(–1) as a regressor in place of LC(–1), and compare the results with those in Table 6.7. What diff erence, if any, do you see? What may be logic behind this substitution? Explain.
6.1 Instead of estimating model (6.1), suppose you estimate the following linear model: C A A DPI A W A R u t t tt 12 3 4 t (1) (a) Compare the results of this linear model with those shown in Table 6.2. (b) What is the interpretation of the various coeffi cients in this model? What is the
5.6 Table 5.10 on the companion website gives data for 106 countries on the following variables:21 GDPGR = Growth rate of income per worker for a country averaged over 1960-1985 GDP60vsUS = Natural log of a country’s per capita income in 1960 relative to that of the USA for 1960 NONEQINV =
5.5 Refer to Table 5.5. Assume that the error variance is related to the square of income instead of to the square of ABORTIONF. Transform the original abortion rate function replacing ABORTIONF by income and compare your results with those given in Table 5.5. A priori, would you expect a diff
5.2 Refer to the hours worked regression model given in Table 4.5. Use log of hours worked as the regressand and fi nd out if the resulting model suff ers from heteroscedasticity. Show the diagnostic tests you use. How would you resolve the problem of heteroscedasticity, if it is present in the
4.11 Th e Longley Data; 14 well-known data originally collected to assess the computational accuracy of least-squares estimates in several computer programs. Th ey have been used to illustrate several econometric problems, such as (severe) multicollinearity, outliers (discussed in Chapter 7), and
4.10 For the k-variable regression model, it can be shown that the variance of the kth (k = 2, 3, …, K) partial regression coeffi cient given in Eq. (4.10) can also be written as: 2 2 2 2 1 1 var( ) 1 y k k k R b n k R V § · ¨ ¸ ¨ ¸ V © ¹ where 2 Vy = variance of Y, 2 Vk = variance
4.9 Table 4.12 on the companion website gives data on 20 patients on their blood pressure (bp), age (in years), weight (in kg), bsa (body surface area, square meters), dur (duration of hypertension, in years), basal pulse (pulse, beats per minute), and stress index (stress). (a) Estimate a linear
4.8 Refer to Exercise 4.6. First regress Y on X3 and obtain the residuals from this regression, say e1i . Th en regress X2 on X3 and obtain the residuals from this regression, say e2i . Now regress e1i on e2i . Th is regression will give the partial regression coeffi cient given in Eq. (4.2). What
4.7 Th e following data describe the manpower needs for operating a US Navy bachelor offi cers’ quarters, consisting of 25 establishments. Th e variables are described below and the data are given in Table 4.11, 12 which can be found on the companion website: Y: Monthly manhours needed to operate
4.6 Consider the sets of data given in the following two tables:Th e only diff erence between the two tables is that the third and fourth values of X3 are interchanged. (a) Regress Y on X2 and X3 in both tables, obtaining the usual OLS output. (b) What diff erence do you observe in the two
4.4 In the three-variable model, Y and regressors X2 and X3, we can compute three partial correlation coeffi cients. For example, the partial correlation between Y and X2, holding X3 constant, denoted as r12.3, is as follows: r r rr r r 12 3 12 13 23 13 2 23 2 1 1 . ( )( ) where the subscripts 1,
4.3 Continuing with Exercise 4.1, fi nd out the partial correlation coeffi cients for the variables included in Table 4.5, using Stata or any other software you have. Based on the partial correlations, which variables seem to be highly correlated?
4.1 For the hours example discussed in the chapter, try to obtain the correlation matrix for the variables included in Table 4.5. Eviews, Stata, and several other programs can compute the correlations with comparative ease. Find out which variables are highly correlated.
3.18 Table 3.22 on the companion website gives data on a sample of 528 workers from the 1985 Current Survey of Population, US Department of Labor, on the following variables: Ed = education in years Region = region of residence = 1 if South, 0 otherwise Nwnhisp = non-white, non-Hispanic = 1, 0
3.17 Determinants of price per ounce of cola. Cathy Schafer, a student of mine, estimated the following regression from cross-section data of 77 observations.19 P B BD BD BD u i i i ii 0 11 22 33 where Pi = price per ounce of cola D1i = 001 if discount store, = 010 if chain store, = 100 if
3.16 Table 3.21 on the companion website gives data on body temperature (degrees Fahrenheit), heart rate (beats per minute), and gender (1 = male, 2 = female) for 130 people.18 (a) Regress body temperature on heart rate and gender, providing the usual regression output. (b) How would you interpret
3.15 Pricing of diamond stones: Th e price of a diamond stone depends on the four Cs: caratage, color, clarity and cut. Table 3.20 on the companion website gives the following data on 308 diamonds sold in Singapore:16 carat =weight of diamond stones in carat units color = color of diamond classifi
3.14 Estimate the eff ects of ban and sugar_sweet_cap on diabetes using the data in Table 3.19, which can be found on the companion website,15 where diabetes = diabetes prevalence in country ban = 1 if some type of ban on genetically modifi ed goods is present, 0 otherwise sugar_sweet_cap =
3.12 Refer to the fashion sales example discussed in the text. Reestimate Eq. (3.10) by adding the trend variable, taking values of 1, 2, and so on. Compare your results with those given in Table 3.11. What do these results suggest?
3.9 Regress Sales, RPDI, and CONF individually on an intercept and the three dummies and obtain residuals from these regressions, say S1, S2, S3. Now regress S1 on S2 and S3 (no intercept term in this regression)14 and show that slope coeffi cients of S2 and S3 are precisely the same as those of
3.6 Suppose instead of coding dummies as 1 and 0, you code them as –1 and +1. How would you interpret the regression results using this coding?
3.5 Suppose you want to consider the geographic region in which the wage earner resides. Suppose we divide US states into four groups: east, south, west, and north. How would you extend the models given in Tables 3.1 and 3.5?
3.4 Besides the variables included in the wage regression in Tables 3.1 and 3.5, what other variables would you include?
2.9 Consider the following model without any regressors. Yi = B1 + ui How would you obtain an estimate of B1? What is the meaning of the estimated value? Does it make any sense?
2.8 Verify Eqs. (2.37), (2.38) and (2.39). Hint: Minimize: 2 2 2 ( ) ¦ ¦ u Y BX i i

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Econometrics By Example 2nd Edition Damodar Gujarati - Solutions

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