Questions and Answers of Econometrics

To show that two variables, each with deterministic trend, can lead to spurious regression, Charemza et al. obtained the following regression based on 30 observations:Ŷt = 5.92 + 0.030Xtt = (9.9)
From the U.K. private sector housing starts (X) for the period 1948 to 1984, Terence Mills obtained the following regression results:The 5 percent critical Ï„ value is ˆ’2.95 and
Continue with the previous exercise. How would you test the first-difference regression for stationarity? In the present example, what would you expect a priori and why? Show all the calculations.
Instead of regressing LDIVIDENDS on LCP in level form, suppose you regress the first difference of LDIVIDENDS on the first difference of LCP. Would you include the intercept in this regression? Why
Take the first differences of the time series given in the U.S. economic time series data posted on the book’s website and plot them. Also obtain a correlogram of each time series up to 36 lags.
Consider the dividends and profits time series given in the U.S. economic time series data posted on the book’s website. Since dividends depend on profits, consider the following simple
Continue with Exercise 21.17. How would you decide if the ADF test is more appropriate than the DF test?
For each of the time series of Exercise 21.16, use the DF test to find out if these series contain a unit root. If a unit root exists, how would you characterize such a time series?
Using the U.S. economic time series data posted on the book’s website, obtain sample correlograms up to 36 lags for the time series LPCE, LDPI, LCP(profits), and LDIVIDENDS. What general pattern do
What is the error correction mechanism (ECM)? What is its relationship with cointegration?
What is a random walk (model)?
What is meant by a trend-stationary process (TSP) and a difference-stationary process (DSP)?
What is the difference between a deterministic trend and a stochastic trend?
What is spurious regression?
What is the difference, if any, between tests of unit roots and tests of cointegration?
What is the meaning of cointegration?
What are Engle–Granger (EG) and augmented EG tests?
What are Dickey–Fuller (DF) and augmented DF tests?
If a time series is I(3), how many times would you have to difference it to make it stationary?
What is the meaning of a unit root?
What is meant by an integrated time series?
What is meant by weak stationarity?
In a test of Granger causality, Christopher Sims exploits the fact that the future cannot cause the present.* To decide whether a variable Y causes a variable X, Sims suggests estimating the
Table 17.13 gives some macroeconomic data for the Greek economy for the years 1960€“1995. Consider the following consumption function:Where PCt* = real desired private consumption
Develop a simultaneous-equation model for the supply of and demand for dentists in the United States. Specify the endogenous and exogenous variables in the model.
Develop a simple model of the demand for and supply of money in the United States and compare your model with those developed by K. Brunner and A. H. Meltzer* and R. Tiegen.
a. For the demand-and-supply model of Example 18.1, obtain the expression for the probability limit of α̂1.b. Under what conditions will this probability limit be equal to the true α1?
For the IS-LM model discussed in the text, find the level of interest rate and income that is simultaneously compatible with the goods and money market equilibrium.
To study the relationship between inflation and yield on common stock, Bruno Oudet€¡ used the following model:where L = real per capita monetary baseY = real per capita incomeI = the
In their article, €œA Model of the Distribution of Branded Personal Products in Jamaica,€™€™* John U. Farley and Harold J. Levitt developed the following model (the
To study the relationship between advertising expenditure and sales of cigarettes, Frank Bass used the following model:WhereY1 = logarithm of sales of filter cigarettes (number of cigarettes) divided
G. Menges developed the following econometric model for the West German economy:where Y = national incomeI = net capital formationC = personal consumptionQ = profitsP = cost of living indexR =
L. E. Gallaway and P. E. Smith developed a simple model for the United States economy, which is as follows:Y = gross national productC = personal consumption expenditureI = gross private domestic
The following table gives you data on Y (gross domestic product), I (gross private domestic investment), and C (personal consumption expenditure) for the United States for the period
Using the data given in Exercise 18.10, regress gross domestic investment I on GDP and save the results for further examination in a later chapter.
Consider the macroeconomics identityC + I = Y ( = GDP)As before, assume thatCt = β0 + β1Yt + utand, following the accelerator model of macroeconomics, letIt = α0 + α1(Yt − Yt−1) + vtwhere u
Supply and demand for gas. Table 18.3, found on the textbook website, gives data on some of the variables that determine demand for and supply of gasoline in the U.S. from January 1978 to August
Show that the two definitions of the order condition of identification (see Section 19.3) are equivalent.
Deduce the structural coefficients from the reduced-form coefficients given in Eqs. (19.2.25) and (19.2.27).
Obtain the reduced form of the following models and determine in each case whether the structural equations are unidentified, just identified, or over identified:a. Chap. 18, Example 18.2.b. Chap.
In the model (19.2.22) of the text it was shown that the supply equation was over identified. What restrictions, if any, on the structural parameters will make this equation just identified? Justify
From the modelthe following reduced-form equations are obtained:a. Are the structural equations identified?b. What happens to identification if it is known a priori that Î³11 = 0? Y1 = B10
Refer to Exercise 19.6. The estimated reduced-form equations are as follows:Y1t = 4 + 3X1t + 8X2tY2t = 2 + 6X1t + 10X2ta. Obtain the values of the structural parameters.b. How would you test the null
The modelproduces the following reduced-form equations:Y1t = 4 + 8X1tY2t = 2 + 12X1ta. Which structural coefficients, if any, can be estimated from the reduced-form coefficients? Demonstrate your
Determine whether the structural equations of the model given in Exercise 18.8 are identified.
Refer to Exercise 18.7 and find out which structural equations can be identified.
The following table is a model in five equations with five endogenous variables Y and four exogenous variables X:Determine the identifiability of each equation with the aid of the order and rank
Consider the following extended Keynesian model of income determination:WhereC = consumption expenditureY = incomeI = investmentT = taxesG = government expenditureu€™s = the disturbance
Refer to the data given in the following table of Chapter 18. Using these data, estimate the reduced-form regressions (19.1.2) and (19.1.4). Can you estimate Î²0and Î²1? Show
Suppose we propose yet another definition of the order condition of identifiability:K ≥ m + k − 1which states that the number of predetermined variables in the system can be no less than the
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

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