Questions and Answers of Econometrics

A simplified version of Suits€™s model of the watermelon market is as follows:*WhereP = price(Q/N) = per capita quantity demanded(Y/N) = per capita incomeFt = freight costs(P/W) = price
Consider the following demand-and-supply model for money:Money demand: Mdt = Î²0 + Î²1Yt + Î²2Rt + Î²3Pt + u1tMoney supply: Mst = Î±0 +
The Hausman test discussed in the text can also be conducted in the following way. Consider Eq. (19.4.7):Qt = β0 + β1Pt + β1vt + u2ta. Since Pt and vt have the same coefficients, how would you
State whether each of the following statements is true or false:a. The method of OLS is not applicable to estimate a structural equation in a simultaneous equation model.b. In case an equation is not
Why is it unnecessary to apply the two-stage least-squares method to exactly identified equations?
Consider the following modified Keynesian model of income determination:where C = consumption expenditureI = investment expenditureY = incomeG = government expenditureGt and Ytˆ’1 are
Consider the following results:where WÌ‚t , PÌ‚t , MÌ‚t , and XÌ‚t are percentage changes in earnings, prices, import prices, and labor productivity
Assume that production is characterized by the Cobb€“Douglas production functionQi = AKÎ±i LÎ²iWhereQ = outputK = capital inputL = labor inputA, Î±, and
Consider the following demand-and-supply model for money:WhereM = moneyY = incomeR = rate of interestP = priceAssume that R and P are predetermined.a. Is the demand function identified?b. Is the
Refer to Exercise 18.10. For the two-equation system there obtain the reduced-form equations and estimate their parameters. Estimate the indirect least-squares regression of consumption on income and
Consider the following model:Rt = Î²0 + Î²1Mt + Î²2Yt + u1tYt = Î±0 + Î±1Rt + u2twhere Mt (money supply) is exogenous, Rt is the interest
Suppose we change the model in Exercise 20.8 as follows:Rt = Î²0 + Î²1Mt + Î²2Yt + Î²3Ytˆ’1 + u1tYt = Î±0 + Î±1Rt +
Consider the following model:Rt = Î²0 + Î²1Mt + Î²2Yt + u1tYt = Î±0 + Î±1Rt + Î±2 It + u2twhere the variables are as defined in
Suppose we change the model of Exercise 20.10 as follows:Assume that M is determined exogenously.a. Find out which of the equations are identified.b. Estimate the parameters of the identified
Verify the standard errors reported in Eq. (20.5.3).
Return to the demand-and-supply model given in Eqs. (20.3.1) and (20.3.2).Suppose the supply function is altered as follows:Qt = Î²0 + Î²1Ptˆ’1 + u2twhere
In this exercise we examine data for 534 workers obtained from the Current Population Survey (CPS) for 1985. The data can be found as Table 20.10 on the textbook website. The variables in this table
Explain with a brief reason whether the following statements are true, false, or uncertain:a. All econometric models are essentially dynamic.b. The Koyck model will not make much sense if some of the
Prove Eq. (17.8.3).cov [Yt−1, (ut − λut−1)] = −λσ2 17.8.3
Assume that prices are formed according to the following adaptive expectations hypothesis:where P* is the expected price and P the actual price. Complete the following table, assuming Î³ =
Consider the modelSuppose Ytˆ’1 and vt are correlated. To remove the correlation, suppose we use the following instrumental variable approach: First regress Yt on X1t and X2t and obtain the
a. Evaluate the median lag for λ = 0.2, 0.4, 0.6, 0.8.b. Is there any systematic relationship between the value of λ and the value of the median lag?
a. Prove that for the Koyck model, the mean lag is as shown in Eq. (17.4.10).b. If λ is relatively large, what are its implications?
Using the formula for the mean lag given in Eq. (17.4.9), verify the mean lag of 10.959 quarters reported in the illustration of the following table. Coeff. Coeff. Coeff. It| 3.249 3.783 |t|
Supposewhere M = demand for real cash balances, Y* = expected real income, and R* = expected interest rate. Assume that expectations are formulated as follows:where Î³1 and Î³2
If you estimate Eq. (17.7.2) by OLS, can you derive estimates of the original parameters? What problems do you foresee? (For details, see Roger N. Waud.)
Consider the following model:Yt = Î± + Î²Xt + utAssume that ut follows the Markov first-order autoregressive scheme given in Chapter 12, namely,ut = put-1 +
Use the investment data given in the following table.a. Estimate the Grunfeld investment function for each company individually.b. Now pool the data for all the companies and estimate the Grunfeld
Refer to the data in the following table.a. Let Y = eggs produced (in millions) and X = price of eggs (cents per dozen). Estimate the model for the years 1990 and 1991 separately.b. Pool the
Refer to the airline example discussed in the text. Instead of the linear model given in Eq. (16.4.2), estimate a log€“linear regression model and compare your results with those given in
Based on the Michigan Income Dynamics Study, Hausman attempted to estimate a wage, or earnings, model using a sample of 629 high school graduates, who were followed for a period of six years, thus
For the investment data given in the following table, which model would you choose€”FEM or REM? Why? C-1 C-1 F-1 Observation E-1 Observation GE US 1935 1935 209.9 1362.4 53.8 33.1 1170.6
Refer to the data on eggs produced and their prices given in the following table. Which model may be appropriate here, FEM or ECM? Why? State Y1 Y2 X1 X2 State Y, Y2 X1 X2 92.7 66.0 AL 2,206 2,186
How would you extend model (16.4.2) to allow for a time error component? Write down the model explicitly.
When are panel data regression models inappropriate? Give examples.
Is there a difference between LSDV, within-estimator, and first-difference models?
What is meant by an error components model (ECM)? How does it differ from FEM? When is ECM appropriate? And when is FEM appropriate?
What is meant by a fixed effects model (FEM)? Since panel data have both time and space dimensions, how does FEM allow for both dimensions?
What are the special features of (a) cross-section data, (b) time series data, and (c) panel data?
Download the data set Benign, which is Table 15.29, from the textbook website. The variable cancer is a dummy variable, where 1 = had breast cancer and 0 = did not have breast cancer.* Using the
For the smokers example discussed in the text (see Section 15.10) download the data from the textbook website in Table 15.28. See if the product of education and income (i.e., the interaction effect)
Table 15.27 on the textbook website gives data for 2,000 women regarding work (1 = a woman works, 0 = otherwise), age, marital status (1 = married, 0 = otherwise), number of children, and education
Monte Carlo study. As an aid to understanding the probit model, William Becker and Donald Waldman assumed the following:E(Y | X) = ˆ’1 + 3XThen, letting Yi = ˆ’1 + 3X +
To find out who has a bank account (checking, savings, etc.) and who doesn€™t, John Caskey and Andrew Peterson estimated a probit model for the years 1977 and 1989, using data on U.S.
To study the effectiveness of a price discount coupon on a six-pack of a soft drink, Douglas Montgomery and Elizabeth Peck collected the data shown in the following table. A sample of 5,500 consumers
Thirteen applicants to a graduate program had quantitative and verbal scores on the GRE as listed in the following table. Six students were admitted to the program.a. Use the LPM to predict the
The following table gives data on the results of spraying rotenone of different concentrations on the chrysanthemum aphis in batches of approximately fifty. Develop a suitable model to express the
In the probit model given in the following table the disturbance ui has this variance:where fi is the standard normal density function evaluated at Fˆ’1(Pi).a. Given the preceding variance
In an important study of college graduation rates of all high school matriculants and Black-only matriculants, Bowen and Bok obtained the results in the following table, based on the logit model.*a.
From the household budget survey of 1980 of the Dutch Central Bureau of Statistics, J. S. Cramer obtained the following logit model based on a sample of 2,820 households. (The results given here are
Compare and comment on the OLS and WLS regressions in Eqs. (15.7.3) and (15.7.1).
From data for 54 standard metropolitan statistical areas (SMSA), Demaris estimated the following logit model to explain high murder rate versus low murder rate:**ln Ôi = 1.1387 + 0.0014Pi +
In the probit regression given in the following table show that the intercept is equal to ˆ’Î¼x/Ïƒxand the slope is equal to 1/Ïƒx, where
Estimate the probabilities of owning a house at the various income levels underlying the regression (15.7.1). Plot them against income and comment on the resulting relationship.
In studying the purchase of durable goods Y (Y = 1 if purchased, Y = 0 if no purchase) as a function of several variables for a total of 762 households, Janet A. Fisherˆ—obtained the
For the home ownership data given in Table 15.1, the maximum likelihood estimates of the logit model are as follows:Comment on these results, bearing in mind that all values of income above 16
Refer to the data given in the following table. If YÌ‚iis negative, assume it to be equal to 0.01 and if it is greater than 1, assume it to be equal to 0.99. Recalculate the weights wiand
The following table gives data on real GDP, labor, and capital for Mexico for the period 1955€“1974. See if the multiplicative Cobb€“Douglas production function given in Eq.
Show that Î²ˆ—2of Eq. (11.3.8) can also be expressed asand var (Î²ˆ—2) given in Eq. (11.3.9) can also be expressed aswhere yˆ—i = Yi €“
Evaluate the following statement made by Henry Theil:Given the present state of the art, the most sensible procedure is to interpret confidence coefficients and significance limits liberally when
Commenting on the econometric methodology practiced in the 1950s and early 1960s, Blaug stated:. . . much of it [i.e., empirical research] is like playing tennis with the net down:instead of
According to Blaug, “There is no logic of proof but there is logic of disproof.” What does he mean by this?
Refer to the St. Louis model discussed in the text. Keeping in mind the problems associated with the nested F test, critically evaluate the results presented in regression (13.8.4).
Suppose the true model isYi = β1 + β2Xi + βX2i + β3X3i + uiBut you estimateYi = α1 + α2Xi + viIf you use observations of Y at X = −3, −2, −1, 0, 1, 2, 3, and estimate the “incorrect”
To see if the variable X2i belongs in the model Yi = β1 + β2Xi + ui , Ramsey’s RESET test would estimate the linear model, obtaining the estimated Yi values from this model [i.e., Ŷi = β̂1 +
Use the data for the demand for chicken given in Exercise 7.19. Suppose you are told that the true demand function isln Yt = β1 + β2 ln X2t + β3 ln X3t + β6 ln X6t + ut ……………… (1)but
Continue with Exercise 13.21. Strictly for pedagogical purposes, assume that model (2) is the true demand function.a. If we now estimate model (1), what type of specification error is committed in
Monte Carlo experiment.* Ten individuals had weekly permanent income as follows:$200, 220, 240, 260, 280, 300, 320, 340, 380, and 400. Permanent consumption (Y∗i) was related to permanent income
Continue with Exercise 13.25. Using the J test, how would you decide between the two models?Data from 13.25Refer to Exercise 8.26. With the definitions of the variables given there, consider the
Refer to Exercise 7.19, which is concerned with the demand for chicken in the United States. There you were given five models.a. What is the difference between model 1 and model 2? If model 2 is
Refer to the following table, which gives data on personal savings (Y) and personal disposable income (X) for the period 1970€“2005. Now consider the following models:How would you choose
Use the data in Exercise 13.28.To familiarize yourself with recursive least squares, estimate the savings functions for 1970€“1981, 1970€“1985, 1970€“1990, and
The data in the following table gives U.S. population, in millions of persons, for the period 1970€“2007. Fit the growth models given in Exercise 14.7 and decide which model gives a better
Continue with Exercise 13.29, but now use the updated data in Table 8.10.a. Suppose you estimate the savings function for 1970–1981. Using the parameters thus estimated and the personal disposable
Omission of a variable in the K-variable regression model. Refer to Eq. (13.3.3), which shows the bias in omitting the variable X3 from the model Yi = β1+β2X2i + β3X3i + ui . This can be
What is meant by intrinsically linear and intrinsically nonlinear regression models?
Since the error term in the Cobb–Douglas production function can be entered multiplicatively or additively, how would you decide between the two?
What is the difference between OLS and nonlinear least-squares (NLLS) estimation?
The relationship between pressure and temperature in saturated steam can be expressed as:*where Y = pressure and t = temperature. Using the method of nonlinear least squares (NLLS), obtain the normal
State whether the following statements are true or false.a. Statistical inference in NLLS regression cannot be made on the basis of the usual t, F, and χ2 tests even if the error term is assumed to
How would you linearize the CES production function discussed in the chapter? Show the necessary steps.
Models that describe the behavior of a variable over time are called growth models. Such models are used in a variety of fields, such as economics, biology, botany, ecology, and demography. Growth
The true model isY*i = Î²1 + Î²X*i + ui
Critically evaluate the following view expressed by Leamer:My interest in metastatistics [i.e., theory of inference actually drawn from data] stems from my observations of economists at work. The
Refer to Table 8.11, which gives data on personal savings (Y) and personal disposable income (X) for the period 1970â€“2005. Now consider the following models: Model A: Yt = Î±1 + Î±2Xt
Monte Carlo experiment.* Ten individuals had weekly permanent income as follows: $200, 220, 240, 260, 280, 300, 320, 340, 380, and 400. Permanent consumption (Y∗i) was related to permanent income
Continue with Exercise 13.21. Strictly for pedagogical purposes, assume that model (2) is the true demand function.a. If we now estimate model (1), what type of specification error is committed in
Use the data for the demand for chicken given in Exercise 7.19. Suppose you are told that the true demand function isln Yt = β1 + β2 ln X2t + β3 ln X3t + β6 ln X6t + ut
State with reason whether the following statements are true or false.†a. An observation can be influential but not an outlier.b. An observation can be an outlier but not influential.c. An
Refer to the St. Louis model discussed in the text. Keeping in mind the problems associated with the nested F test, critically evaluate the results presented in regression (13.8.4).
According to Blaug, “There is no logic of proof but there is logic of disproof.” What does he mean by this?
Evaluate the following statement made by Henry Theil:*Given the present state of the art, the most sensible procedure is to interpret confidence coefficients and significance limits liberally when
Refer to the demand function for chicken estimated in Eq. (8.6.23). Considering the attributes of a good model discussed in Section 13.1, could you say that this demand function is “correctly”
Suppose that the true model isYi = β1 Xi + ui ……………… (1)but instead of fitting this regression through the origin you routinely fit the usual intercept present model:Yi = α0 + α1Xi +
Continue with Exercise 13.2 but assume that it is model (2) that is the truth. Discuss the consequences of fitting the mis-specified model (1).In exercise 13.2Suppose that the true model isYi = β1
Suppose that the “true” model isYi = β1 + β2X2i + uibut we add an “irrelevant” variable X3 to the model (irrelevant in the sense that the true β3 coefficient attached to the variable X3 is
Consider the following “true” (Cobb–Douglas) production function:ln Yi = α0 + α1 ln L1i + α2 ln L2i + α3 ln Ki + uiwhereY = outputL1 = production laborL2 = nonproduction laborK = capitalBut
Refer to Eqs. (13.3.4) and (13.3.5). As you can see, Î±Ì‚2, although biased, has a smaller variance than Î²Ì‚2, which is unbiased. How would you decide
Show that β estimated from either Eq. (13.5.1) or Eq. (13.5.3) provides an unbiased estimate of true β.
Following Friedman€™s permanent income hypothesis, we may writeYˆ—i = Î± + Î²Xˆ—iwhere Yˆ—i = €œpermanent€

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