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| m61318 | Verify the result in (20-10). |
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| m61337 | We are interested in the long run multiplier in the model Assume that xt is an autoregressive series, xt = rxt−1 + vt where |r | < 1.
a. What is the long run multiplier in this model?
b. How would you estimate the long-run multiplier in this model?
c. Suppose you that the preceding is the true model but you linearly regress yt only on a constant and the first 5 lags of xt. How does this affect your estimate of the long run multiplier?
d. Same as c. for 4 lags instead of 5.
e. Using the macroeconomic data in Appendix F5.1, let yt be the log of real investment and xt be the log of real output. Carry out the computations suggested and report your findings. Specifically, how does the omission of a lagged value affect estimates of the short-run and long-run multipliers in the unrestricted lag model? |
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| m61338 | We are interested in the ordered probit model. Our data consist of 250 observations, of which the response are Using the preceding data, obtain maximum likelihood estimates of the unknown parameters of the model. |
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| m61343 | We now consider the Tobit model that applies to the full data set.
a. Formulate the log-likelihood for this very simple Tobit model.
b. Reformulate the log-likelihood in terms of θ = 1/σ and γ = μ/σ. Then derive the necessary conditions for maximizing the log-likelihood with respect to θ and γ.
c. Discuss how you would obtain the values of θ and γ to solve the problem in Part b.
d. Compute the maximum likelihood estimates of μ and σ. |
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| m61345 | What are the probability limits of (1/n) LM, where LM is defined in (13-31) under the null hypothesis that σ2 u = 0 and under the alternative that σ2u ≠ 0? |
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| m61363 | What is the covariance matrix, Cov [β, β − b], of the GLS estimator β = (X Ω−1X)−1 X Ω−1 y and the difference between it and the OLS estimator, b =(X X)−1 X y? The result plays a pivotal role in the development of specification tests in Hausman (1978). |
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| m61402 | You might find it useful to read the early sections of Chapter 21 for this exercise.) The extramarital affairs data analyzed in Section 22.3.7 can be reinterpreted in the context of a binary choice model. The dependent variable in the analysis is a count of events. Using these data, first recode the dependent variable 0 for none and 1 for more than zero.Now, first using the binary probit estimator, fit a binary choice model using the same independent variables as in the example discussed in Section 22.3.7. Then using a semiparametric or nonparametric estimator, estimate the same binary choice model. A model for binary choice can be fit for at least two purposes, for estimation of interesting coefficients or for prediction of the dependent variable. Use your estimated models for these two purposes and compare the two models. |
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| m66231 | 2.8. State whether the following models are linear regression models:
a. Yi = B1 + B2(l / Xi)
b. Yi = B1 + B2 In Xi + ui
c. In Yi = B1 + B2 Xi + ui
d. In Yi = B} + B2In Xi + ui
e. Yi = Bi + B2B3Xi + ui
f. Yi = B] + B32 Xi + ui |
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| m66247 | A and B are two events. Can they be mutually exclusive and independent simultaneously? |
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| m66324 | a. Compute the covariances between the S&P 500 index and the CPI and between the three-month Treasury bill rate and the CPI. Are these population or sample covariances?
b. Compute the correlation coefficients between the S&P 500 index and the CPI and between the three-month Treasury bill rate and the CPI. A priori, would you expect these correlation coefficients to be positive or negative? Why?
c. If there is a positive relationship between the CPI and the three-month Treasury bill rate, does that mean inflation, as measured by the CPI, is the cause of higher T bill rates?
For Information: Refer to Table 1-2 given in Problem 1.6. |
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| m66342 | a. Create a standard LIV (linear-in-variables) regression model and note the results.
b. Using the software package of your choice, obtain White s heteroscedasticity-corrected regression results. What are they?
c. Is there a substantial difference between the results obtained in parts (a) and (&)?
For Information: Refer to Table 9-7 on the textbook s Web site. This data set considers R&D expenditure data in relation to sales. |
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| m66365 | a. Establish a 95% confidence interval for the true σ2.
b. Test the hypothesis that the true variance is 8.2.
For Information: Refer to Example C.14 in Appendix C. |
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| m66377 | a. Find the expected value of X.
b. What is the variance and standard deviation of X?
c. What is the coefficient of variation of X?
d. Find the skewness and kurtosis values of X.
For Information: Refer to Problem A.12. |
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| m66468 | a. If B2 = 0, b2 / se(b2) = ...
b. l(B2 = 0,t = b2/ ...
c. r2 lies between ... and ...
d. r lies between ... and ...
e. TSS = RSS +...
f. d.f. (of TSS) = d.f. (of...) + d.f. (of RSS)
g. is called ...
h. ∑y2i = 2(Yi - ...)2
i. ∑y2i = b2(...) |
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| m66480 | a. Interpret the coefficient of the labor input X2. Is it statistically different from 1?
b. Interpret the coefficient of the capital input X3. Is it statistically different from zero? And from 1?
c. What is the interpretation of the intercept value of - 1.6524?
d. Test the hypothesis that B2 = B3= 0.
For Information: Refer to the Cobb-Douglas production function given in regression (5.11). |
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| m66585 | a. Partial regression coefficient
b. Coefficient of multiple determination, R2
c. Perfect collinearity
d. Perfect multicollinearity
e. Individual hypothesis testing
f. Joint hypothesis testing
g. Adjusted R2 |
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| m66609 | a. Plot the data on profits and dividends and visually examine if the two time series are stationary.
b. Apply the unit root test to the two series individually and determine if the two series are stationary.
c. If the profits and dividends series are not stationary and if you regress dividends on profits, would the resulting regression be spurious? Why or why not? How do you decide? Show the necessary calculations.
d. Take the first differences of the two time series and determine if the first difference time series are stationary.
For Information: Refer to the data given in Table 12-2 (found on the textbook s Web site). |
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| m66654 | A random sample of 10 female S.A.T. scores on the math test gave a sample variance of 142. Knowing that the true variance is 102.07, what is the probability of obtaining such a sample value? Which probability distribution will you use to answer this question? What are the assumptions underlying that distribution?
For Information: Refer to Problem A.12. |
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| m66876 | a. The marginal cost (MC) is the change in the TC for a unit change in output; that is, it is the rate of change of the TC with respect to output. (Technically, it is the derivative of the TC with respect to X, the output.) Derive this function from regression (5.32).
b. The average variable cost (AVC) is the total variable cost (TVC) divided by the total output. Derive the AVC function from regression (5.32).
c. The average cost (AC) of production is the TC of production divided by total output. For the function given in regression (5.32), derive the AC function.
d. Plot the various cost curves previously derived and confirm that they resemble the stylized textbook cost curves.
For Information: Refer to the cubic total cost (TC) function given in Eq. (5.32). |
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| m66879 | A three-variable regression gave the following results:
a. What is the sample size?
b. What is the value of the RSS?
c. What are the d.f. of the ESS and RSS?
d. What is R2? And 2?
e. Test the hypothesis that X2 and X3 have zero influence on Y. Which test do you use and why?
f. From the preceding information, can you determine the individual contribution of X2 and X3 toward Y? |
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