- Monte Carlo experiment: Consider the following model:Yi = ?1 + ?2X2i + ?3X3i + uiYou are told that ?1 = 262, ?2 = ?0.006, ?3 = ?2.4, ?2 = 42, and ui??N(0, 42).Generate 10 sets of 64 observations on
- The following table gives data on the crime rate in 47 states in the United States for 1960. Try to develop a suitable model to explain the crime rate in relation to the 14 socioeconomic variables
- Using the data in the following table, develop a suitable model to explain the behavior of gross real investment in the Greek economy for the period 1960?1995. Look up any textbook on macroeconomics
- As noted in the text, there may be several structural breaks in the U.S. economic time series dataset introduced in Section 21.1. Dummy variables are a good way of incorporating these shifts in the
- With the definitions of the variables given there, consider the following two models to explain Y:Model A: Yt = α1 + α2X3t + α3X4t + α4X6t + utModel B: Yt = β1 + β2X2t + β3X5t + β4X6t +
- The following table gives data on the hourly compensation rate in manufacturing in U.S. dollars, Y (%), and the civilian unemployment rate, X (index, 1992 = 100), forCanada, the United Kingdom, and
- The following table gives data on the hourly compensation rate in manufacturing in U.S. dollars, Y (%), and the civilian unemployment rate, X (index, 1992 = 100), forCanada, the United Kingdom, and
- Consider the following simple macroeconomic model for the U.S. economy, say, for the period 1960?1999. Private consumption function: Private gross investment function: A money demand
- Class Exercise: Consider the following demand-and-supply model for loans of commercial banks to businesses:Demand: Qdt = α1 + α2Rt + α2RDt + α4IPIt + u1tSupply: Qst = β1 + β2Rt + β3RSt +
- From the quarterly data for the period 1950€“1960, F. P. R. Brechling obtained the following demand function for labor for the British economy (the figures in parentheses are standard
- Since R2as a measure of goodness of fit is not particularly well suited for the dichotomous dependent variable models, one suggested alternative is the Ï‡2test described below:where Ni =
- Triangular, or arithmetic, distributed-lag model.€ This model assumes that the stimulus (explanatory variable) exerts its greatest impact in the current time period and then declines by
- Consider Eq. (17.13.4):To obtain the variance of Î²Ì‚i from the variances of aÌ‚i, we use the following formula:a. Using the preceding formula, find the variance of
- Consider the following distributed-lag model:Assume that Î²i can be adequately expressed by the second-degree polynomial as follows:Î²i = a0 + a1i + a2i2How would you estimate
- The inverted V distributed-lag model. Consider the k-period finite distributed-lag modelF. DeLeeuw has proposed the structure for the Î²€™s as in Figure 17.11, where the
- Refer to Exercise 12.15. Since the d value shown there is of little use in detecting (first-order) autocorrelation (why?), how would you test for autocorrelation in this case?
- Consider the following model:Yˆ—i = Î± + Î²0Xt + utwhere Yˆ— = desired, or long-run, business expenditure for new plant and equipment, Xt = sales, and
- Suppose someone convinces you that the relationship between business expenditure for new plant and equipment and sales is as follows:where Yˆ— is desired expenditure and Xˆ—
- Using the data given in Exercise 17.22, determine whether plant expenditure Granger-causes sales or whether sales Granger-cause plant expenditure. Use up to six lags and comment on your results. What
- Assume that sales in Exercise 17.22 has a distributed-lag effect on expenditure on plant and equipment. Fit a suitable Almon lag model to the data.
- Reestimate Eq. (17.13.16) imposing (1) near-end restriction, (2) far-end restriction, and (3) both end restrictions and compare your results given in Eq. (17.13.16). What general conclusion do you
- The following table gives data on private fixed investment in information processing and equipment (Y, in billions of dollars), sales in total manufacturing and trade (X2, in millions of dollars),
- The following table gives data on indexes of real compensation per hour (Y) and output per hour (X2), with both indexes to base 1992 = 100, in the business sector of the U.S. economy for the period
- What is the connection, if any, between Granger causality tests and VAR modeling?
- Consider the data on log DPI (personal disposable income) introduced in Section 21.1 (see the book’s website for the actual data). Suppose you want to fit a suitable ARIMA model to these data.
- Repeat Exercise 22.11 for the LDNIDENDS.In exercise 22.11Consider the data on log DPI (personal disposable income) introduced in Section 21.1 (see the book’s website for the actual data). Suppose
- In Section 13.9 you were introduced to the Schwarz Information criterion (SIC) to determine lag length. How would you use this criterion to determine the appropriate lag length in a VAR model?
- Using the data on LPCE and LDPI introduced in Section 21.1 (see the book’s website for the actual data), develop a bivariate VAR model for the period 1970–I to 2006–IV. Use this model to
- Consider the Koyck (or, for that matter, the adaptive expectations) model given in Eq. (17.4.7), namely,Suppose in the original model ut follows the first-order autoregressive scheme ut ˆ’
- The article by Subhayu Bandyopadhyay and Howard J. Wall, “The Determinants of Aid in the Post-Cold War Era,” Review, Federal Reserve Bank of St. Louis, November/December 2007, vol. 89, number 6,
- In studying the farm demand for tractors, Griliches used the following model:where T* = desired stock of tractorsX1 = relative price of tractorsX2 = interest rateUsing the stock adjustment model, he
- Consider the lag patterns in the following figure. What degree polynomials would you fit to the lag structures and why? Bi i i Lag Lag Bi х х х х Time Time
- Whenever the lagged dependent variable appears as an explanatory variable, the R2 is usually much higher than when it is not included. What are the reasons for this observation?
- Whenever the lagged dependent variable appears as an explanatory variable, the R2 is usually much higher than when it is not included. What are the reasons for this observation?
- Refer to the VAR regression results given in the following table. From the various F tests reported in the three regressions given there, what can you say about the nature of causality in the three
- Continuing with Exercise 20.20, can you guess why the authors chose to express the three variables in the model in percentage change form rather than using the levels of these variables?
- Using the Canadian data given in the following table, find out if M1 and R are stationary random variables. If not, are they cointegrated? Show the necessary calculations. Observation M1 GDP
- Continue with the data given in Table 17.5. Now consider the following simple model of money demand in Canada:ln M1t = β1 + β2 lnGDPt + β3 ln Rt + uta. How would you interpret the parameters of
- Refer to the ARCH(2) model given in Eq. (22.11.4). Using the same data we estimated the following ARCH(1) model:How would you choose between the two models? Show the necessary calculations.
- Table 22.7 gives data on three-month (TB3M) and six-month (TB6M) Treasury bill rates from January 1, 1982, to March 2008, for a total of 315 monthly observations. The data can be found on the
- Since the number of lags to be introduced in a VAR model can be a subjective question, how does one decide how many lags to introduce in a concrete application?
- If the primary object is forecasting, VAR will do the job.” Critically evaluate this statement.
- In what sense is VAR atheoretic?
- What are the differences between Box–Jenkins and VAR approaches to economic forecasting?
- What happens if Box–Jenkins techniques are applied to time series that are nonstationary?
- Outline the major steps involved in the application of the Box–Jenkins approach to forecasting.
- What are the major differences between simultaneous-equation and Box–Jenkins approaches to economic forecasting?
- What are the major methods of economic forecasting?
- The following regressions are based on the CPI data for the United States for the period 1960 2007, for a total of 48 annual observations:1.2.3.WhereRSS = residual sum of squares.a. Examining the
- From the data for the period 1971€“I to 1988€“IV for Canada, the following regression results were obtained:1.2.3.where M1 = M1 money supply, GDP = gross domestic product, both
- 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