Info Efr
200 PART ONE SINGLE-EQUATION REGRESSION MODELS that is, the mean of actual Y values need not be equal to the mean of the estimated Y values the two mean values are identical for the intercept-present model, as can be seen from 3.1.10 . It was noted that, for the zero-intercept model, r2 can be negative, whereas for the conventional model it can never be negative. This condition can be shown as follows. r 1 TSS 1 y2 12 Now for the conventional, or intercept-present, model, Eq. 3.3.6 shows that...
The Logit Model For Ungrouped Or Individual Data
To set the stage, consider the data given in Table 15.7. Letting Y 1 if a student's final grade in an intermediate microeconomics course was A and Y 0 if the final grade was a B or a C, Spector and Mazzeo used grade point average GPA , TUCE, and Personalized System of Instruction PSI as the TABLE 15.7 DATA ON THE EFFECT OF PERSONALIZED SYSTEM OF INSTRUCTION PSI ON COURSE GRADES TABLE 15.7 DATA ON THE EFFECT OF PERSONALIZED SYSTEM OF INSTRUCTION PSI ON COURSE GRADES
E4e4 1 4
where r2 3 is the coefficient of correlation between X2 and X3. 10.21. Using 7.4.12 and 7.4.15 , show that when there is perfect collinearity, the variances of ft and ft are infinite. 10.22. Verify that the standard errors of the sums of the slope coefficients estimated from 10.5.6 and 10.5.7 are, respectively, 0.1549 and 0.1825. See Section 10.5. 10.23. For the k-variable regression model, it can be shown that the variance of the kth k 2,3, , K partial regression coefficient given in 7.5.6 can...
Info Cka
Yt a 01 Xit 02 X2t 03 Yt-i vt Suppose Yt-i 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 estimated Yt from this regression. Then regress Yt a 0i Xu 02 X2t 03 Yt-i vt where Yt-i are estimated from the first-stage regression. a. How does this procedure remove the correlation between Yt-i and vt in the original model b. What are the advantages of the recommended procedure over the...
Info Vca
The preceding equation was based on the assumption that the desired level of employment Et is a function of output, time, and time squared and on the hypothesis that Et Et-1 S E Et-1 , where S, the coefficient of adjustment, lies between 0 and 1. F. P. R. Brechling, The Relationship between Output and Employment in British Manufacturing Industries, Review of Economic Studies, vol. 32, July 1965. Gujarati Basic I III. Topics in Econometrics I 17. Dynamic Econometric I I The McGraw-Hill...
Info Nno
Apply Bartlett's test to the data of Table 11.1 and verify that the hypothesis that population variances of employee compensation are the same in each employment size of the establishment cannot be rejected at the 5 percent level of significance. Note fi, the df for each sample variance, is 9, since ni for each sample i.e., employment class is 10. 11.14. Consider the following regression-through-the origin model You are told that u1 N 0, o2 and u2 N 0, 2o2 and that they are statistically...
Info Boz
Note The figures in parentheses are the estimated standard errors. Note The figures in parentheses are the estimated standard errors. Consumption of good X 1 2 3 4 5 Consumption of good Y 4 3.5 2.8 1.9 0.8 How would you estimate the parameters of this model Apply the preceding model to the data in Table 5.8 and comment on your results. 5.16. Since 1986 the Economist has been publishing the Big Mac Index as a crude, and hilarious, measure of whether international currencies are at their correct...
Info Szy
You are to consider the following model Yi 01 02 X2t 03 X3t 04 X4t 05 06 X6t Ut a. Estimate the preceding regression. b. What are the expected signs of the coefficients of this model c. Are the empirical results in accordance with prior expectations d. Are the estimated partial regression coefficients individually statistically significant at the 5 percent level of significance e. Suppose you first regress Y on X2, X3, and X4 only and then decide to add the variables X5 and X6. How would you...
Info Udi
Source Data on Yare from Citibase and on x2 through x6 are from the U.S. Department of Agriculture. I am indebted to Robert J. Fisher for collecting the data and for the statistical analysis. Note The real prices were obtained by dividing the nominal prices by the Consumer Price Index for food. Source Data on Yare from Citibase and on x2 through x6 are from the U.S. Department of Agriculture. I am indebted to Robert J. Fisher for collecting the data and for the statistical analysis. Note The...
Exercises 1
where yi Y Y and xi X X . In this case, the regression line must pass through the origin. True or false Show your calculations. 6.2. The following regression results were based on monthly data over the period January i978 to December i987 where Y monthly rate of return on Texaco common stock, , and X a. What is the difference between the two regression models b. Given the preceding results, would you retain the intercept term in the first model Why or why not c. How would you interpret the...
Yt f2 Xt u
where Y GDP deflator for domestic goods and X GDP deflator for imports. 198 PART ONE SINGLE-EQUATION REGRESSION MODELS a. How would you choose between the two models a priori b. Fit both models to the data and decide which gives a better fit. c. What other model s might be appropriate for the data 6.16. Refer to the data given in exercise 6.15. The means of Y and X are 1456 and 1760, respectively, and the corresponding standard deviations are 346 and 641. Estimate the following regression where...
Http Fairmodel.econ.yale.edu Rayfair Pdf 1978dat.zip
lie on the horizontal axis. If Y is observed, the observations ni , denoted by dots, will lie in the X-Y plane. It is intuitively clear that if we estimate a regression line based on the n1 observations only, the resulting intercept and slope coefficients are bound to be different than if all the n1 n2 observations were taken into account. How then does one estimate tobit, or censored regression, models, such as 15.11.1 The actual mechanics involves the method of maximum likelihood, which is...
Example 26
Let X1, X2 Xn be a random sample from a distribution with mean m and variance a2. Show that the sample mean X is a consistent estimator of m. From elementary statistics it is known that E X m andvar X a2 n. Since E X m regardless of the sample size, it is unbiased. Moreover, as n increases indefinitely, var X tends toward zero. Hence, X is a consistent estimator of m. The following rules about probability limits are noteworthy. 1. Invariance Slutsky property . If 0 is a consistent estimator of...
Info Dwr
Notes All financial variables are in thousands of dollars. Housing status Rent 1 if rents 0 otherwise Housing status Own 1 if owns 0 otherwise Source Janet A. Fisher, An Analysis of Consumer Good Expenditure, The Review of Economics and Statistics, vol. 64, no. 1, Table 1, 1962, p. 67. Notes All financial variables are in thousands of dollars. Housing status Rent 1 if rents 0 otherwise Housing status Own 1 if owns 0 otherwise Source Janet A. Fisher, An Analysis of Consumer Good Expenditure, The...
Info Jcq
We now describe the various steps in estimating the logit regression 15.6.1 1. For each income level X, compute the probability of owning a house as Pi ni Ni. 2. For each Xi, obtain the logit as24 3. To resolve the problem of heteroscedasticity, transform 15.6.1 as wiLi Pi wi fa wiXi JWM 15.6.6 23As shown in elementary probability theory, Pi, the proportion of successes here, owning a house , follows the binomial distribution with mean equal to true Pi and variance equal to Pi 1 - Pi Ni and as...
Deseasonalization Of Data Using Dummy Variables
FIGURE 9.7 Discontinuous piecewise linear regression. Cathy Schaefer, Price Per Ounce of Cola Beverage as a Function of Place of Purchase, Size of Container, and Branded or Unbranded Product, unpublished term project. CHAPTER NINE DUMMY VARIABLE REGRESSION MODELS 329 Pi 0.0143 - 0.000004DH 0.0090D2i 0.00001D3i Se 0.00001 0.00011 0.00000 t -0.3837 8.3927 5.8125 Note The standard errors are shown only to five decimal places. a. Comment on the way the dummies have been introduced in the model. b....
Predicting A Bond Rating
Based on a pooled time series and cross-sectional data of 200 Aa high-quality and Baa medium-quality bonds over the period 1961-1966, Joseph Cappelleri estimated the following bond rating prediction model.10 Yi fa fa X2 X3I fa fas Xsi u, where Y, 1 if the bond rating is Aa Moody's rating 0 if the bond rating is Baa Moody's rating X2 debt capitalization ratio, a measure of leverage dollar value of long-term debt _ dollar value of total capitalization X3 profit rate dollar value of net total...
Info Wos
MULTICOLLINEARITY WHAT HAPPENS IF THE REGRESSORS ARE CORRELATED There is no pair of words that is more misused both in econometrics texts and in the applied literature than the pair multi-collinearity problem. That many of our explanatory variables are highly collinear is a fact of life. And it is completely clear that there are experimental designs X'X i.e., data matrix which would be much preferred to the designs the natural experiment has provided us i.e., the sample at hand . But a...
Y Jjx
FIGURE 17.6 The gradual adjustment of the ------L 26This is adapted from Figure 7.4 from Rudiger Dornbusch and Stanley Fischer, Macroeconomics, 3d ed., McGraw-Hill, New York, 1984, p. 216. Models Autoregressive and Distributed-Lag Models CHAPTER SEVENTEEN DYNAMIC ECONOMETRIC MODELS 675 desired stock of capital each period. Thus, in the first period it moves to Y2, with investment equal to Y2 - Y1 , which in turn is equal to half of Y -Y1 . In each subsequent period it closes half the gap...
Info Kmy
FIGURE 12.12 Hypothetical regression 12.13. Based on the Durbin-Watson d statistic, how would you distinguish pure autocorrelation from specification bias the us are in fact serially independent. What would happen in this situation if, assuming that ut p ut-i et, we use the generalized difference regression Yt - p Yt-i Pi i - p Pi Xt - pPi Xt_i et Discuss in particular the properties of the disturbance term et. 496 PART TWO RELAXING THE ASSUMPTIONS OF THE CLASSICAL MODEL 12.15. In a study of...
Consequences Of Model Specification Errors
Whatever the sources of specification errors, what are the consequences To keep the discussion simple, we will answer this question in the context of the three-variable model and consider in this section the first two types of specification errors discussed earlier, namely, 1 underfitting a model, that is, omitting relevant variables, and 2 overfitting a model, that is, including unnecessary variables. Our discussion here can be easily generalized to more than two regressors, but with tedious...
Intrinsically Linear And Intrinsically Nonlinear Regression Models
When we started our discussion of linear regression models in Chapter 2, we stated that our concern in this book is basically with models that are linear in the parameters they may or may not be linear in the variables. If you refer to Table 2.3, you will see that a model that is linear in the parameters as well as the variables is a linear regression model and so is a model that is linear in the parameters but nonlinear in the variables. On the other hand, if a model is nonlinear in the...
The Logit Model
We will continue with our home ownership example to explain the basic ideas underlying the logit model. Recall that in explaining home ownership in relation to income, the LPM was Pi E Y 1 Xi P1 fa Xi 15.5.1 where X is income and Y 1 means the family owns a house. But now consider the following representation of home ownership For ease of exposition, we write 15.5.2 as Equation 15.5.3 represents what is known as the cumulative logistic distribution function.15 It is easy to verify that as Zi...
p n2k2
where n total number of observations, d Durbin-Watson d, and k number of coefficients including the intercept to be estimated. Show that for large n, this estimate of p is equal to the one obtained by the simpler formula 1 d 2 . 12.7. Estimating p The Hildreth-Lu scanning or search procedure. Since in the first-order autoregressive scheme p is expected to lie between 1 and 1, Hildreth and Lu suggest a systematic scanning or search procedure to locate it. They recommend selecting p between 1 and...
Tests Of Nonnested Hypotheses
32Andrew Harvey, The Econometric Analysis of Time Series, 2d ed., The MIT Press, Cambridge, Mass., 1990, Chap. 5. the regressand must be the same. Besides these criteria, there are other criteria that are also used. These include Akaike's information criterion AIC , Schwarz's information criterion SIC , and Mallows's Cp criterion. We discuss these criteria in Section 13.9. Most modern statistical software packages have one or more of these criteria built into their regression routines. In the...
Consequences Of Using Ols In The Presence Of Autocorrelation
As in the case of heteroscedasticity, in the presence of autocorrelation the OLS estimators are still linear unbiased as well as consistent and asymptotically normally distributed, but they are no longer efficient i.e., minimum variance . What then happens to our usual hypothesis testing procedures if we continue to use the OLS estimators Again, as in the case of het-eroscedasticity, we distinguish two cases. For pedagogical purposes we still continue to work with the two-variable model,...
Vol Hp Mpg Sp Wt
cubic feet of cab space engine horsepower average miles per gallon top speed, miles per hour vehicle weight, hundreds of pounds car observation number Names of cars not disclosed . Environmental Protection Agency, 1991, Report EPA AA CTAB 91-02. 434 PART TWO RELAXING THE ASSUMPTIONS OF THE CLASSICAL MODEL a. Consider the following model MPGi 1 2SP 3HP 4WT u Estimate the parameters of this model and interpret the results. Do they make economic sense b. Would you expect the error variance in the...
The Significance Of The Stochastic Disturbance Term
As noted in Section 2.4, the disturbance term ui is a surrogate for all those variables that are omitted from the model but that collectively affect Y. The obvious question is Why not introduce these variables into the model explicitly Stated otherwise, why not develop a multiple regression model with as many variables as possible The reasons are many. 1. Vagueness of theory The theory, if any, determining the behavior of Y may be, and often is, incomplete. We might know for certain that weekly...
Relaxing The Assumptions Of The Classical Model
In Part I we considered at length the classical normal linear regression model and showed how it can be used to handle the twin problems of statistical inference, namely, estimation and hypothesis testing, as well as the problem of prediction. But recall that this model is based on several simplifying assumptions, which are as follows. Assumption 1. The regression model is linear in the parameters. Assumption 2. The values of the regressors, the X's, are fixed in repeated sampling. Assumption...
The Cubic Cost Function Revisited
Recall the cubic total cost function estimated in Section 7.10, which for convenience is reproduced below Y 141.7667 63.4777X, - 12.9615X2 0.9396X,3 se 6.3753 4.7786 0.9857 0.0591 7.10.6 where Y is total cost and X is output, and where the figures in parentheses are the estimated standard errors. Suppose we want to test the hypothesis that the coefficients of the X2 and X3 terms in the cubic cost function are the same, that is, ft ft or ft - ft 0. In the regression 7.10.6 we have all the...
Info Iui
Based on these data, estimate the following regressions Yi ai a2 X2i uii Yi M A3 X3i u2i Yi Pi amp X2i 3 X3i ui Note Estimate only the coefficients and not the standard errors. a. Is a2 f 2 Why or why not What important conclusion do you draw from this exercise 7.2. From the following data estimate the partial regression coefficients, their standard errors, and the adjusted and unadjusted R2 values Y 367.693 X2 402.760 X3 8.0 J2 Yi - Yo2 66042 .269 X2i - XX2 2 84855 .096 x3i - XX3 2 280.000 J2...
Info Wyk
Notes GDP gross domestic product billions M2 M2 money supply. CPI Consumer Price Index 1982-1984 100 . LTRATE long-term interest rate 30-year Treasury bond . TBRATE three-month Treasury bill rate per annum . Source Economic Report of the President, 2000, Tables B-1, B-58, B-67, B-71. Notes GDP gross domestic product billions M2 M2 money supply. CPI Consumer Price Index 1982-1984 100 . LTRATE long-term interest rate 30-year Treasury bond . TBRATE three-month Treasury bill rate per annum . Source...