Econometric Analysis An Applied Approach To Business And Economics 1st Edition Sharif Hossain - Solutions

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In Example 4.7, we used data on nonunionized manufacturing firms to estimate the relationship between the scrap rate and other firm characteristics. We now look at this example more closely and use all available firms.(i) The population model estimated in Example 4.7 can be written as log1scrap2 5
In Section 4-5, we used as an example testing the rationality of assessments of housing prices.There, we used a log-log model in price and assess [see equation (4.47)]. Here, we use a level-level formulation.(i) In the simple regression model price 5 b0 1 b1assess 1 u, the assessment is rational if
Consider the estimated equation from Example 4.3, which can be used to study the effects of skipping class on college GPA:colGPA 5 1.39 1 .412 hsGPA 1 .015 ACT 2 .083 skipped 1.332 1.0942 1.0112 1.0262 n 5 141, R2 5 .234.(i) Using the standard normal approximation, find the 95% confidence interval
Are rent rates influenced by the student population in a college town? Let rent be the average monthly rent paid on rental units in a college town in the United States. Let pop denote the total city population, avginc the average city income, and pctstu the student population as a percentage of the
The variable rdintens is expenditures on research and development (R&D) as a percentage of sales.Sales are measured in millions of dollars. The variable profmarg is profits as a percentage of sales.Using the data in RDCHEM for 32 firms in the chemical industry, the following equation is
Consider an equation to explain salaries of CEOs in terms of annual firm sales, return on equity (roe, in percentage form), and return on the firm’s stock (ros, in percentage form):log1salary2 5 b0 1 b1log1sales2 1 b2roe 1 b3ros 1 u.(i) In terms of the model parameters, state the null hypothesis
Which of the following can cause the usual OLS t statistics to be invalid (that is, not to have t distributions under H0)?(i) Heteroskedasticity.(ii) A sample correlation coefficient of .95 between two independent variables that are in the model.(iii) Omitting an important explanatory variable.
Use the data in MEAPSINGLE to study the effects of single-parent households on student math performance. These data are for a subset of schools in southeast Michigan for the year 2000. The socioeconomic variables are obtained at the ZIP code level (where ZIP code is assigned to schools based on
Use the data in HTV to answer this question. The data set includes information on wages, education, parents’ education, and several other variables for 1,230 working men in 1991.(i) What is the range of the educ variable in the sample? What percentage of men completed twelfth grade but no higher
Use the data in MEAP93 to answer this question.(i) Estimate the model math10 5 b0 1 b1log1expend2 1 b2lnchprg 1 u, and report the results in the usual form, including the sample size and R-squared. Are the signs of the slope coefficients what you expected? Explain.(ii) What do you make of the
Confirm the partialling out interpretation of the OLS estimates by explicitly doing the partialling out for Example 3.2. This first requires regressing educ on exper and tenure and saving the residuals, r^1.Then, regress log(wage) on r^1. Compare the coefficient on r^1 with the coefficient on educ
Use the data in ATTEND for this exercise.(i) Obtain the minimum, maximum, and average values for the variables atndrte, priGPA, and ACT.(ii) Estimate the model atndrte 5 b0 1 b1priGPA 1 b2ACT 1 u, and write the results in equation form. Interpret the intercept. Does it have a useful meaning?(iii)
The file CEOSAL2 contains data on 177 chief executive officers and can be used to examine the effects of firm performance on CEO salary.(i) Estimate a model relating annual salary to firm sales and market value. Make the model of the constant elasticity variety for both independent variables. Write
Use the data in HPRICE1 to estimate the model price 5 b0 1 b1sqrft 1 b2bdrms 1 u, where price is the house price measured in thousands of dollars.(i) Write out the results in equation form.(ii) What is the estimated increase in price for a house with one more bedroom, holding square footage
A problem of interest to health officials (and others) is to determine the effects of smoking during pregnancy on infant health. One measure of infant health is birth weight; a birth weight that is too low can put an infant at risk for contracting various illnesses. Since factors other than
The following equations were estimated using the data in LAWSCH85:lsalary 5 9.90 2 .0041 rank 1 .294 GPA 1.242 1.00032 1.0692 n 5 142, R2 5 .8238 lsalary 5 9.86 2 .0038 rank 1 .295 GPA 1 .00017 age 1.292 1.00042 1.0832 1.000362 n 5 99, R2 5 .8036 How can it be that the R-squared is smaller when the
The following estimated equations use the data in MLB1, which contains information on major league baseball salaries. The dependent variable, lsalary, is the log of salary. The two explanatory variables are years in the major leagues (years) and runs batted in per year (rbisyr):lsalary 5 12.373 1
Suppose you have a sample of size n on three variables, y, x1, and x2, and you are primarily interested in the effect of x1 on y. Let b|1 be the coefficient on x1 from the simple regression and b^1 the coefficient on x1 from the regression y on x1, x2. The standard errors reported by any regression
(i) Consider the simple regression model y 5 b0 1 b1x 1 u under the first four Gauss-Markov assumptions. For some function g(x), for example g1x2 5 x2 or g1x2 5 log11 1 x2 2, define zi 5 g1xi 2. Define a slope estimator as b|1 5 a a ni51 1zi 2 z2yib^a a ni51 1zi 2 z2xib.Show that b|1 is linear and
The following equation represents the effects of tax revenue mix on subsequent employment growth for the population of counties in the United States:growth 5 b0 1 b1shareP 1 b2shareI 1 b3shareS 1 other factors, where growth is the percentage change in employment from 1980 to 1990, shareP is the
Suppose that the population model determining y is y 5 b0 1 b1x1 1 b2x2 1 b3x3 1 u, and this model satisfies Assumptions MLR.1 through MLR.4. However, we estimate the model that omits x3. Let b|0, b|1, and b|2 be the OLS estimators from the regression of y on x1 and x2. Show that the expected value
Suppose that you are interested in estimating the ceteris paribus relationship between y and x1. For this purpose, you can collect data on two control variables, x2 and x3. (For concreteness, you might think of y as final exam score, x1 as class attendance, x2 as GPA up through the previous
The following equation describes the median housing price in a community in terms of amount of pollution (nox for nitrous oxide) and the average number of rooms in houses in the community(rooms):log1price2 5 b0 1 b1log1nox2 1 b2rooms 1 u.(i) What are the probable signs of b1 and b2? What is the
Suppose that average worker productivity at manufacturing firms (avgprod) depends on two factors, average hours of training (avgtrain) and average worker ability (avgabil):avgprod 5 b0 1 b1avgtrain 1 b2avgabil 1 u.Assume that this equation satisfies the Gauss-Markov assumptions. If grants have been
Which of the following can cause OLS estimators to be biased?(i) Heteroskedasticity.(ii) Omitting an important variable.(iii) A sample correlation coefficient of .95 between two independent variables both included in the model.
Consider the multiple regression model containing three independent variables, under Assumptions MLR.1 through MLR.4:y 5 b0 1 b1x1 1 b2x2 1 b3x3 1 u.You are interested in estimating the sum of the parameters on x1 and x2; call this u1 5 b0 1 b1.(i) Show that u^1 5 b^1 1 b^2 is an unbiased estimator
In a study relating college grade point average to time spent in various activities, you distribute a survey to several students. The students are asked how many hours they spend each week in four activities: studying, sleeping, working, and leisure. Any activity is put into one of the four
The median starting salary for new law school graduates is determined by log1salary2 5 b0 1 b1LSAT 1 b2GPA 1 b3log1libvol2 1 b4log1cost2 1 b5rank 1 u, where LSAT is the median LSAT score for the graduating class, GPA is the median college GPA for the class, libvol is the number of volumes in the
The following model is a simplified version of the multiple regression model used by Biddle and Hamermesh (1990) to study the tradeoff between time spent sleeping and working and to look at other factors affecting sleep:sleep 5 b0 1 b1totwrk 1 b2educ 1 b3age 1 u, where sleep and totwrk (total work)
The data in WAGE2 on working men was used to estimate the following equation:educ 5 10.36 2 .094 sibs 1 .131 meduc 1 .210 feduc n 5 722, R2 5 .214, where educ is years of schooling, sibs is number of siblings, meduc is mother’s years of schooling, and feduc is father’s years of schooling.(i)
Using the data in GPA2 on 4,137 college students, the following equation was estimated by OLS:colgpa 5 1.392 2 .0135 hsperc 1 .00148 sat n 5 4,137, R2 5 .273, where colgpa is measured on a four-point scale, hsperc is the percentile in the high school graduating class (defined so that, for example,
The data set in CATHOLIC includes test score information on over 7,000 students in the United States who were in eighth grade in 1988. The variables math12 and read12 are scores on twelfth grade standardized math and reading tests, respectively.(i) How many students are in the sample? Find the
Use the data in COUNTYMURDERS to answer this questions. Use only the data for 1996.(i) How many counties had zero murders in 1996? How many counties had at least one execution?What is the largest number of executions?(ii) Estimate the equation murders5 b01 b1execs1 uby OLS and report the results in
To complete this exercise you need a software package that allows you to generate data from the uniform and normal distributions.(i) Start by generating500 observations on xi—the explanatory variable—from the uniform distribution with range [0,10]. (Most statistical packages have a command for
Use the data in CHARITY [obtained from Franses and Paap (2001)] to answer the following questions:(i) What is the average gift in the sample of 4,268 people (in Dutch guilders)? What percentage of people gave no gift?(ii) What is the average mailings per year? What are the minimum and maximum
We used the data in MEAP93 for Example 2.12. Now we want to explore the relationship between the math pass rate (math10) and spending per student (expend).(i) Do you think each additional dollar spent has the same effect on the pass rate, or does a diminishing effect seem more appropriate?
For the population of firms in the chemical industry, let rd denote annual expenditures on research and development, and let sales denote annual sales (both are in millions of dollars).(i) Write down a model (not an estimated equation) that implies a constant elasticity between rd and sales. Which
Use the data in WAGE2 to estimate a simple regression explaining monthly salary (wage) in terms of IQ score (IQ).(i) Find the average salary and average IQ in the sample. What is the sample standard deviation of IQ? (IQ scores are standardized so that the average in the population is 100 with a
Use the data in SLEEP75 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 sleep5 b01 b1totwrk1 u, where sleep is
The data set in CEOSAL2 contains information on chief executive officers for U.S. corporations. The variable salary is annual compensation, in thousands of dollars, and ceoten is prior number of years as company CEO.(i) Find the average salary and the average tenure in the sample.(ii) How many CEOs
The data in 401K are a subset of data analyzed by Papke (1995) to study the relationship between participation in a 401(k) pension plan and the generosity of the plan. The variable prate is the percentage of eligible workers with an active account; this is the variable we would like to explain. The
Consider the problem described at the end of Section 2.6: running a regression and only estimating an intercept.(i) Given a sample 5yi: i5 1, 2,c, n6, let b&0 be the solution to min b0 an i51 1yi2 b02 2.Show that b&0 5 y, that is, the sample average minimizes the sum of squared residuals. (Hint:You
Suppose you are interested in estimating the effect of hours spent in an SAT preparation course (hours)on total SAT score (sat). The population is all college-bound high school seniors for a particular year.(i) Suppose you are given a grant to run a controlled experiment. Explain how you would
(i) Let b^ 0 and b^ 1 be the intercept and slope from the regression of yi on xi, using n observations. Let c1 and c2, with c22 0, be constants. Let b&0 and b&1 be the intercept and slope from the regression of c1yi on c2xi. Show that b&1 5 1c1/c2 2b^0 and b&0 5 c1b^0, thereby verifying the claims
Consider the standard simple regression model y5 b01 b1x 1 u under the Gauss-Markov Assumptions SLR.1 through SLR.5. The usual OLS estimators b^0 and b^1 are unbiased for their respective population parameters. Let b&1 be the estimator of b1 obtained by assuming the intercept is zero (see Section
Consider the savings function sav 5 b01 b1inc1 u, u5"inc.e, where e is a random variable with E1e25 0 and Var1e2 5 s2e. Assume that e is independent of inc.(i) Show that E1u0inc2 5 0, so that the key zero conditional mean assumption (Assumption SLR.4)is satisfied. [Hint: If e is independent of inc,
Using data from 1988 for houses sold in Andover, Massachusetts, from Kiel and McClain (1995), the following equation relates housing price (price) to the distance from a recently built garbage incinerator (dist):log1price25 9.401 0.312 log1dist2 n 5 135, R2 5 0.162.(i) Interpret the coefficient on
In the linear consumption function cons 5 b^ 0 1 b^1inc, the (estimated) marginal propensity to consume (MPC) out of income is simply the slope, b^1, while the average propensity to consume (APC) is cons/inc 5 b^0/inc 1 b^1. Using observations for 100 families on annual income and consumption (both
The data set BWGHT contains data on births to women in the United States. Two variables of interest are the dependent variable, infant birth weight in ounces (bwght), and an explanatory variable, average number of cigarettes the mother smoked per day during pregnancy (cigs). The following simple
The following table contains the ACT scores and the GPA (grade point average) for eight college students. Grade point average is based on a four-point scale and has been rounded to one digit after the decimal.(i) Estimate the relationship between GPA and ACT using OLS; that is, obtain the intercept
In the simple linear regression model y 5 b0 1 b1x 1 u, suppose that E1u2 2 0. Letting a0 5 E1u2, show that the model can always be rewritten with the same slope, but a new intercept and error, where the new error has a zero expected value.
Let kids denote the number of children ever born to a woman, and let educ denote years of education for the woman. A simple model relating fertility to years of education is kids 5 b0 1 b1educ 1 u, where u is the unobserved error.(i) What kinds of factors are contained in u? Are these likely to be
The data set in ALCOHOL contains information on a sample of men in the United States. Two key variables are self-reported employment status and alcohol abuse (along with many other variables).The variables employ and abuse are both binary, or indicator, variables: they take on only the values zero
Use the data in COUNTYMURDERS to answer this question. Use only the year 1996. The variable murders is the number of murders reported in the county. The variable execs is the number of executions that took place of people sentenced to death in the given county. Most states in the United States have
The data in JTRAIN2 come from a job training experiment conducted for low-income men during 1976–1977; see Lalonde (1986).(i) Use the indicator variable train to determine the fraction of men receiving job training.(ii) The variable re78 is earnings from 1978, measured in thousands of 1982
The data in MEAP01 are for the state of Michigan in the year 2001. Use these data to answer the following questions.(i) Find the largest and smallest values of math4. Does the range make sense? Explain.(ii) How many schools have a perfect pass rate on the math test? What percentage is this of the
Use the data in BWGHT to answer this question.(i) How many women are in the sample, and how many report smoking during pregnancy?(ii) What is the average number of cigarettes smoked per day? Is the average a good measure of the“typical” woman in this case? Explain.(iii) Among women who smoked
States (and provinces) that have control over taxation sometimes reduce taxes in an attempt to spur economic growth. Suppose that you are hired by a state to estimate the effect of corporate tax rates on, say, the growth in per capita gross state product (GSP).(i) What kind of data would you need
Discuss the Kao’s, Pedroni’s, and the Johansen Fisher panel tests for panel cointegration.
Discuss the Levin, Lin and Chu (2002); Im, Pesaran and Shin (2003); Maddala and Wu (1999); Choi (2001); and Hadri (2000) tests for panel unit root problem.
Discuss the IV and GMM methods to estimate panel regression models.
Discuss the test for heteroscedasticity in panel regression models.
Discuss the Paris-Winsten’s method to estimate an AR(1) fixed-effects models.
Discuss the Durbin-Watson and LM tests for autocorrelation in the fixed-effects models.
Discuss the goodness of fit of panel-data regression models.
Compare between the GLS, OLS and within estimators.
Discuss the poolability tests and test for fixed effects.
Discuss the Hausman test to select whether the fixed-effects or random-effects models will be appropriate for panel data analysis.
Illustrate the Breusch-Pagan Lagrange multiplier (LM) test for random effects.
Discuss whether the fixed-effects or the random-effects models are applicable for many panel analyses.
Distinguish between the GLS and OLS estimators.
Distinguish between “within” and “between” estimators.
Discuss the technique to obtain the GLS and FGLS estimator of ????.
Discuss the technique to obtain the variance structure of the random-effects model.
Distinguish between the fixed-effects and random-effects models with an example of each.
Discuss the important properties of the random-effects estimator of ????.
Define the random-effects model along with the assumptions involved.
Discuss the technique to obtain the difference-in-difference estimator of ????.
Discuss the technique to obtain the first-difference estimator of ????.
Discuss the important properties of the fixed-effects estimator of ????.
Define a fixed-effects model along with the assumptions involved.
Discuss the important properties of the pooled least-squares estimator of ????.
Define a pooled regression model along with the assumptions involved.
Why are panel estimators more efficient than the cross-sectional and time-series estimators? Explain.
Discuss the panel-data regression model with an example.
Define a panel-data regression model and compare it with cross-sectional and time-series data with an example of each.
Collect the data on the number of goals (GOAL), the ball possession time in percentage (POSS), the number of fouls (FOUL), the number of shots including corner kicks (SHOT), and the number of yellow cards (YCARD) of FIFA world cup 2022, of different teams.(i) Describe how you would formulate the
Suppose that you have a sample of drivers for which you have data on the following variables:i Y =The number of car accidents which are caused by the ith driver;1i X =The years of education of the ith driver;2i X =The years of driving experience of the ith driver;3i X =The working hours per day of
Discuss different measures for the goodness of fit of a Poisson regression model.
Derive the marginal effects of the Poisson regression model.
Describe the ML method to estimate a Poisson regression model and interpret the meaning of the coefficients of the Poisson regression model.
Explain the meaning of (i) the Poisson distribution, and (ii) the Poisson regression model with an example of each.
Collect the data on the annual return on assets in percentage (ROA), price to earnings ratio (PE), market price to book ratio (PB), beta coefficient measured from stock’s CAPM (BETA), size of the factory measured in the logarithmic form of sales revenue (SIZE), and leverage ratio (LEVR) for 2023,
To assess the effectiveness of a new method of teaching called GCS (Google Classroom System) of a private university due to the coronavirus pandemic in an Introduction to Business Mathematics course, you have collected a sample and for which you have data on the following variables:Y= The indicator
Suppose that you have a sample of women who exchange work for money in the labour market and for which you have data on the following variables:Y = The total yearly working hours of women;1 X ???? The age of the women workers;2 X ???? The actual years of working experience;3 X ???? The years of
Suppose that you have a sample of consumers who bought a new apartment in Dhaka city and for which you have data on the following variables:Y = The amount of expenditure (in million $) on housing;1 X ???? The amount of yearly income (in million $) of the consumers;2 X ???? The age of the
Find the marginal effects of the independent variables on the latent variableY* , on the positive values of Y, on the actual variable Y, and on the probability that an observation is uncensored.
Discuss the ML method to estimate a Tobit model.
Discuss the ML method to estimate a truncated regression model.
Explain the meaning of each of the following terms with an example.(i) Censoring, (ii) Truncation, (iii) Censored data, (iv) Truncated data, (v) Censored regression model, (vi) Truncated regression model, and (vii) Tobit model.

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Econometric Analysis An Applied Approach To Business And Economics 1st Edition Sharif Hossain - Solutions

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