New Semester Started Get 50% OFF Study Help! --h --m --s Claim Now

Question Answers

Textbooks

Find textbooks, questions and answers

Oops, something went wrong!

Change your search query and then try again

Result Not Found

Books FREE
Study Help
Tutors
AI Study Planner NEW
Sell Books

Search
Sign In
Register

study help
business
econometrics

Introduction To Econometrics 2nd Edition G. S. Maddala - Solutions

Estimate the supply equation in the model of the Australian wine industry in Section 9.5 if it is normalized with respect to P...
Consider the model Q=B+B,P. + BY + u demand function supply function Q = a +P + S + u Estimate this model by 2SLS, instrumental variable, and indirect least squares methods using the data in Table 9.2 (transform all variables to logs). Would you get different results using the three methods? How
Examine whether each of the following statements is true (T), false (F), or uncertain (U), and give a short explanation. (a) In a simultaneous equation system, the more the number of exoge- nous variables the better. (b) If the multiple correlations of the reduced-form equations are nearly 1, the
Explain how you would compute R in simultaneous equations estimation methods.
The structure of a model with four endogenous and three exogenous vari- ables is as follows: (1 indicates presence and 0 absence of the variable in the equation)
What is meant by the phrase: "The estimator is invariant to normaliza- tion"? Do any problems arise if an estimator is not invariant to normali- zation? Which of the following estimation methods gives estimators that are invariant to normalization? (a) Indirect least squares. (b) 2SLS. (c)
Consider the model = yay + 8x + 1 By + x + y = where x is exogenous, and the error terms u, and u have mean zero and are serially uncorrelated. (a) Write down the equations expressing the reduced-form coefficients in terms of the structural parameters. (b) Show that if y0, then can be identified.
Consider the three-equation model y Biszty + us yz Bay's + By + 727* + 22X2 + 12 Y's Yes + where y, y, and y, are endogenous, and x,, x2, and x, are exogenous. Dis- cuss the identification of each of the equations of the model, based on the order and rank conditions. Now suppose that you want to
Explain concisely what is meant by "the identification problem" in the context of the linear simultaneous equations model.
Explain the meaning of each of the following terms. (a) Endogenous variables. (b) Exogenous variables.. (c) Structural equations. (d) Reduced-form equations. (e) Order condition for identification. (f) Rank condition for identification. (g) Indirect least squares. (h) Two-stage least squares. (i)
Table 8.7 presents data on bride and bride-groom characteristics and dow- ries for marriages in rural south-central India." The variable definitions follow the table: (a) Estimate an equation explaining the determinants of the dowry. (b) Estimate probit and tobit equations explaining the
Explain how you will formulate a model explaining the following. In each case the sample consists of some observations for which the dependent variable is zero. Suggest a list of explanatory variables in each case. (a) Automobile expenditures (in a year) of a number of families. (b) Hours worked by
Consider a model with a zero-one dependent variable. You have a multiple regression program and a program for the logit and probit models. You have computed the coefficients of the linear probability model and the logit and probit models: (a) How will you transform the coefficients of the three
You are asked to estimate the coefficients in a linear discriminant function. You do not have a computer program for this. All you have is a program for multiple regression analysis. How will you compute the linear discrim- inant function?
The following equation was estimated to explain a short-term interest rate: (Figures in parentheses are standard errors.)
In the model where Yax Ya +tz + Us! Y = = BUX +131 Yx OLX +1821 IN(0, 2), IN(0, o), y IN(0. a), and y, are mutually independent, explain how you will estimatea, , and o.
In the model Y, Bx + x + Boxy + the coefficients are known to be related to a more basic economic param- etera according to the equations B + B = xx B+ B, - Explain how you would estimate a and the variance of .
Explain how you would use dummy variables for generating predictions from a regression model.
What would be your answer to the following queries? (a) My regression program refuses to estimate four seasonal coefficients when I enter the quarterly data including a zero-one dummy for each quarter. What am I supposed to do? (b) I estimated a model with a zero-one dependent variable using the
Explain the meaning of each of the following terms. (a) Seasonal dummy variables. (b) Dummy dependent variables. (c) Linear probability model. (d) Linear discriminant function. (e) Logit model. (f) Probit model. (g) Tobit model. (h) Truncated regression model.
Estimate demand for gasoline on the basis of the data in Table 4.8. Are the wrong signs for Pg a consequence of multicollinearity?
Estimate demand for food functions on the basis of the data in Table 4.9. Discuss if there is a multicollinearity problem and what you are going to do about it.
In a study analyzing the determinants of faculty salaries, the results shown on p. 296 were obtained." The dependent variable is 1969-1970 academic year salary. We have omitted eight more other explanatory variables. (a) Do any of the coefficients have unexpected signs? (b) Is there a
Examine whether the following statements are true or false. Give an expla- nation. (a) In multiple regression, a high correlation in the sample among the re- gressors (multicollinearity) implies that the least squares estimators of the coefficients are biased. (b) Whether or not multicollinearity
Explain the following methods. (a) Ridge regression. (b) Omitted-variable regression. (c) Principle component regression. What are the problems these methods are supposed to solve?
Define the term "multicollinearity." Explain how you would detect its pres- ence in a multiple regression equation you have estimated. What are the consequences of multicollinearity, and what are the solutions?
In the case of data with housing starts in Table 4.10 illustrate the use of fourth-order autocorrelation using the DW test and the LM test.
Apply Sargan's common factor test to check that the significant serial cor- relation is not due to misspecified dynamics.
In each case compare the results with those obtained by using the DW test and Durbin's h-test if there are lagged depen- dent variables in the explanatory variables.
Apply the LM test to test for first-order and second-order serial correlation in errors for the estimation of some multiple regression models with the data sets presented in Chapter
The phrase "since the model contains a lagged dependent variable, the DW statistic is unreliable" is frequently seen in empirical work. (a) What does this phrase mean? (b) Is there some way to get around this problem?
Examine whether the following statements are true or false. Give an expla- nation. (a) Serial correlation in the errors u leads to biased estimates and biased standard errors when the regression equation yx + u is estimated by ordinary least squares. (b) The Durbin-Watson test for serial
I am estimating an equation in which y,..., is also an explanatory variable. I get the following results.
Use the Durbin-Watson test to test for serial correlation in the errors in Exercises 17 and 19 at the end of Chapter
Explain the following. (a) The Durbin-Watson test. (b) Estimation with quasi first differences. (c) The Cochrane-Orcutt procedure. (d) Durbin's h-test. (e) Serial correlation due to misspecified dynamics. (f) Estimation in levels versus first differences.
In discussion of real estate assessment, it is often argued that the higher- priced houses get assessed at a lower proportion of value than the lower- priced houses. To determine whether such inequity exists, the following equations are estimated:
In a study of 27 industrial establishments of varying size, y = the number of supervisors and x = the number of supervised workers. y varies from 30 to 210 and x from 247 to 1650. The results obtained were as follows:
In the linear regression model y = a + x, + u, the errors, are presumed to have a variance depending on a variable z. Explain how you will choose among the following four specifications. var() = var(u,) = z, var(u) = o'z var(u,) = o'z
Explain how you will choose among the following four regression models.
In the model Y = + + you are told that +222 + ~IN(0, ), +12=0771 11-12 = IN(0, 40), and u, and u,, are independent. Explain how you will estimate the parameters as a 2, 4, and o.
Apply the following tests to choose between the linear and log-linear regres- sion models with the data in Tables 4.7 and 5.5. (a) Box-Cox test. (b) BM test. (c) PE test.
Indicate whether each of the following statements is true (T), false (F), or uncertain (U), and give a brief explanation. (a) Heteroskedasticity in the errors leads to biased estimates of the regression coefficients and their standard errors. (b) Deflating income and consumption by the same price
Explain the following tests for homoskedasticity. (a) Ramsey's test. (b) Goldfeld and Quandt's test. (c) Glejser's test. (d) Breusch and Pagan's test. Illustrate each of these tests with the data in Tables 4.7 and 5.5.
Define the terms "heteroskedasticity" and "homoskedasticity." Explain the effects of heteroskedasticity on the estimates of the parameters and their variances in a normal regression model.
The demand for Ceylonese tea in the United States is given by the equa- tion log Q=B + , log Pc + B log P, + B, log P, + , log Y + u where Q = imports of Ceylon tea in the United States Pe price of Ceylon tea P, price of Indian tea - - Pg price of Brazilian coffee Y = disposable income
In a study of investment plans and realizations in U.K. manufacturing industries since 1955, the following results were obtained:
In a study on determinants of children born in the Philippines," the fol- lowing results were obtained:
A study on unemployment in the British interwar period produced the following regression equation (data are given in Table 4.11):
In the model y = Bx + Btz + B3x3 + 1 the coefficients are known to be related to a more basic economic param- etera according to the equations Assuming that the x's are nonrandom and that u, IN(0, 2), find the best unbiased linear estimator of a and the variance of a.
Explain how you will estimate a linear regression equation which is piece- wise linear with a joint (or knot) at x = x if (a) x, is known. (b) x is unknown.
Instead of estimating the coefficients , and B from the model y= a + x + Btz + u it is decided to use ordinary least squares on the following regression equation: y = a + Bxj + Bx + v where x is the residual from a regression of x, and x, and v is the distur- bance term. (a) Show that the resulting
Given the following estimated regression equations C, const. +0.92Y, C, const. +0.84C1 C-- const. +0.78Y, Y, const. +0.55C, calculate the regression estimates of , and for C, B+B,Y,+BC,- + 1,
A student obtains the following results in several different regression problems. In which cases could you be certain that an error has been committed? Explain. (a) R123 0.89, R 1234 0.86 (b) R0.86, R1234 -0.82 (c) 20.23, 0.13, R = 0.70 (d) Same as part (c) but r = 0
What would be your answer to the following queries regarding multiple regression analysis? (a) I am trying to find out why people go bankrupt. I have gathered data from a sample of people filing bankruptcy petitions. Will these data enable me to find answers to my question?
Suppose that the least squares regression of Y on X, X2,.... yields coefficient estimates b,j = 1, 2,..., k) none of which exceed their re- spective standard errors. However, the F-ratio for the equation rejects, at the 0.05 level the hypothesis thatb, (a) Is this possible? b = (b) What do you
The model was estimated by ordinary least squares from 26 observations. The results were 9=2+ 3.5x,-0.7x + 2.0x (191 (15 I-ratios are in parentheses and R2 -0.982. The same model was estimated with the restriction , = B. Estimates were: 9, 1.5+ 3(x+x) - 0.6x (24) R = 0.876 (a) Test the significance
A researcher tried two specifications of a regression equation. y= a + x + 11 ya+B'x+y'z + u' Explain under what circumstances the following will be true. (A "hat" over a parameter denotes its estimate.) (a) -. (b) Ifa, anda, are the estimated residuals from the two equations (c) is statistically
Suppose that you are given two sets of samples with the following infor- mation:(a) Estimate a linear regression equation for each sample separately and for the pooled sample. (b) State the assumptions under which estimation of the pooled regres- sion is valid. (c) Explain how you will test the
The following estimated equation was obtained by ordinary least squares regression using quarterly data for 1960 to 1979 inclusive (7 = 80).
Indicate whether each of the following statements is true (T), false (F), or uncertain (U), and give a brief explanation or proof. (a) Suppose that the coefficient of a variable in a regression equation is significantly different from zero at the 20% level. If we drop this variable from the
The following regression equation is estimated as a production function. log Q 1.37 +0.632 log K + 0.452 log L 0257) 01219) R-0.98 cov(b.b) -0.044. The sample size is 40. Test the following hy- potheses at the 5% level of significance. (a) bkb. (b) There are constant returns to scale.
In the multiple regression equation y= a + Bx + Bxy + Bx, +11 = Explain how you will test the joint hypothesis B, , and , = 1.
In a multiple regression equation, show how you can obtain the partial 's given the r-ratios for the different coefficients.
Define the following terms. (a) Standard error of the regression. (b) R and R. (c) Partial (d) Tests for stability. (e) Degrees of freedom. (f) Linear functions of parameters. (g) Nested and nonnested hypotheses. (h) Analysis of variance.
Given data on y and x explain how you will estimate the parameters in the following equations by using the ordinary least squares method. Spec- ify the assumptions you make about the errors. (a) yare (b) y=ae
Consider the regression model y, u, ax, +11, IN(0, 1) i = 1, 2,....T
(Stochastic regressors) In the linear regression model y= a + x,+u, Suppose that x, IN(0, 1). What is the (asymptotic) distribution of the least squares estimator ? Just state the result. Proof not required.
A local night entertainment establishment in a small college town is trying to decide whether they should increase their weekly advertising expen- ditures on the campus radio station. The last six weeks of data on monthly revenue (y) and radio advertising expenditures (x) are given in the accom-
In Exercise 9 we considered the relationship between grade-point average (GPA) and weekly hours spent in the campus pub. Suppose that a fresh- man economics student has been spending 15 hours a week in the Orange and Brew during the first two weeks of class. Calculate a 90% confidence interval for
A small grocery store notices that the price it charges for oranges varies greatly throughout the year. In the off-season the price was as high as 60 cents per orange, and during the peak season they had special sales where the price was as low as 10 cents, 20 cents, and 30 cents per orange. Below
Suppose you are attempting to build a model that explains aggregate sav- ings behavior as a function of the level of interest rates. Would you rather sample during a period of fluctuating interest rates or a period of stable interest rates? Explain.
Since the variance of the regression coefficient varies inversely with the variance of x, it is often suggested that we should drop all the observa- tions in the middle range of x and use only the extreme observations on x in the calculation of . Is this a desirable procedure?
Two variables y and x are believed to be related by the following stochas- tic equation: y = a + x + u where u is the usual random disturbance with zero mean and constant variance o. To check this relationship one researcher takes a sample size of 8 and estimates with OLS. A second researcher takes
At a large state university seven undergraduate students who are majoring in economics were randomly selected from the population and surveyed. Two of the survey questions asked were: (1) What was your grade-point average (GPA) in the preceding term? (2) What was the average number of hours spent
Given data on y and x explain what functional form you will use and how you will estimate the parameters if (a) y is a proportion and lies between 0 and 1. (b) x > 0 and x assumes very large values relative to y. (c) You are interested in estimating a constant elasticity of demand function.
Let , be the residuals in the least squares fit of y, against x, (i = 1, 2, ... n). Derive the following results: and x,A,- 0
The following are data on y x quit rate per 100 employees in manufacturing unemployment rate The data are for the United States and cover the period 1960-1972.
In the regression model y, a + x, +, if the sample mean of x of x is zero, show the cov(, B) = 0, where and are the least squares esti- mators of a and B.
Show that the simple regression line of y against x coincides with the simple regression line of x against y if and only if 1 (where r is the sample correlation coefficient between x and y).
The following data present experience and salary structure of University of Michigan economists in 1983-1984. The variables are y salary (thousands of dollars) x years of experience (defined as years since receiving Ph.D.)
A store manager selling TV sets observes the following sales on 10 differ- ent days. Calculate the regression of y on x where y x number of TV sets sold number of sales representatives Present all the items mentioned in Exercise 1.
Comment briefly on the meaning of each of the following. (a) Estimated coefficient. (b) Standard error. (c) 1-statistic. (d) R-squared. (e) Sum of squared residuals. (f) Standard error of the regression. (g) Best linear unbiased estimator.
The weekly cash inflows (x) and outflows (y) of a business firm are random variables. The following data give values of x and y for 30 weeks. Assume that x and y are normally distributed.(a) Obtain unbiased estimates of the means and variances of x, y, and x -y. Also obtain 95% confidence intervals
If p has a uniform distribution in the range (0, 1) show that -2 log, p has ax-distribution with degrees of freedom 2. If there are k independent tests, each with a p-value, then A = -2 log p, has a x distribution with d.f. 2k. This statistic can be used for an overall rejection or acceptance of
If p has a uniform distribution in the range (0, 1) show that -2 log, p has ax-distribution with degrees of freedom 2. If there are k independent tests.
A stockbroker who wants to compare mean returns and risk (measured by variance) of two stocks and gets the following results: First stock 1,31 x=0.45 5 = 0.60 Second stock My-31 x=0.35 5 = 0.40 Are there any significant differences in the mean returns and risks? (As- sume that daily price changes
A local merchant owns two grocery stores at opposite ends of town. He wants to determine if the variability in business is the same at both loca- tions. Two independent random samples yield n, 16 days 3 = $200 n = 16 days 8 = $300 (a) Is there enough evidence that the two stores have different
An examination of sample items from a shipment showed that 51% of the items were good and 49% were defective. The company president asked the statistician, "What is the probability that over half the items are good?" The statistician replied that the question cannot be answered from the data. Is
In each of the following cases, set up the null hypothesis and the alterna- tive: Explain how you will proceed testing the hypothesis. (a) A biscuit manufacturer is packaging 16-oz. packages. The production manager feels that something is wrong with the packaging and that the packages contain too
Define type I error, type II error, and power of a test. What is the relation-ship between type I error and the confidence coefficient in a confidence interval?
Examine whether the following statements are true or false. If false, cor- rect the statement. (a) With small samples and large o, quite large differences may not be statistically significant but may be real and of great practical signifi- cance. (b) The conclusions from the data cannot be
Examine whether the following statements are true or false. Explain your answer briefly. (a) The null hypothesis says that the effect is zero. (b) The alternative hypothesis says that nothing is going on besides chance variation. (c) A hypothesis test tells you whether or not you have a useful
Explain, using the estimators for in Exercise 20, the difference between lim E, AE, and plim. Give some examples of how they differ.
Suppose that is an estimator of a derived from a sample of size 7. We are given that E(&) a + 2/7 and var() 4a/T + a/T (a) Examine whether as an estimator ofa, is (1) unbiased, (2) consis- tent, (3) asymptotically unbiased, and (4) asymptotically efficient. (b) What is the asymptotic variance of a?
In exercise 20 consider the point estimators of o:Which of these estimators are (a) Unbiased? (b) Consistent? Is the assumption of normality needed to answer this question? For what purposes is the normality assumption needed?
Let x, xx, be a sample of size n from a normal distribution N(, o). Consider the following point estimators of :
Given that ye' is normal with mean 2 and variance 4, find the mean and variance of x.
(Reading the N, 1, x, F tables) (a) Given that X-N(2, 9), 18. (Reading the N, 1, x, F tables) (a) Given that X-N(2, 9), find P(2 < x < 3). (b) If X I find x, and x, such that Note that in the last case, we have several sets of x, and x,. Find three sets. (c) If X-x, find x, and x, such that PX x)
Suppose that you replace every observation x by y 3x + 7 and the mean by 37. What happens to the I-value you use?

Showing 400 - 500 of 4105

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Last

Step by Step Answers

Services

Sitemap
Fun
Definitions
Become Tutor
Used Textbooks
Study Help Categories
Recent Questions
Expert Questions
Campus Wear
Sell Your Books

Company Info

Security
Copyrights
Privacy Policy
Terms & Conditions
SolutionInn Fee
Scholarship
Online Quiz
Give Feedback, Get Rewards

Get In Touch

About Us
Contact Us
Career
Jobs
FAQ
Student Discount
Campus Ambassador

Secure Payment

Download Our App

© 2026 SolutionInn. All Rights Reserved