Questions and Answers of Econometric

What is meant by a reduced form (regression) equation? What is its use?
What is the meaning of a structural, or behavioral, equation?
What is meant by indirect least squares? When is it used?
What is the nature of the identification problem? Why is it important?
What is the order condition of identification?
Explain the meaning of the following terms: a. Dynamic models b. Distributed lag models c. Autoregressive models
To assess the impact of capacity utilization on inflation, Thomas A. Gittings obtained the following regression for the United States for the period 1971 to 1988: Ŷt = - 30.12 + 0.1408Xt + 0.2360Xt
Table 12-7 gives data on the results of spraying rotenone of different concentrations on the chrysanthemum aphis in ~50 batches. Develop a suitable model to express the probability of death as a
From the regression (12.36), compute the probability of owning a house for each income level shown in Table 12-3.
Based on a sample of 20 couples, Barbara Bund lackson26 obtained the following regression.where P = the probability of restaurant usage, = 1 if went to a restaurant, 0 otherwise Income = the income
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
Table 12.8 (on the textbook's Web site) gives data on the dependent variable, the final grade on the intermediate macroeconomics examination (V), such that V = 1 if the final grade is an A and V = 0
On the textbook's Web site, Table 12-9 contains data on the daily U.S. /EU exchange rate from 2004 to 2008. a. Create a scatter plot of the rates over time. What pattern do you see? b. Now take the
Table 12-10 on the textbook's Web site gives data for 2000 women regarding work (1 = a woman works, 0 = otherwise), age, marital status (1 = married, 0 = otherwise), number of children, and education
Download the data set Benign, which is Table 12-11 on the textbook's Web site. The variable cancer is a dummy variable, where 1 = had breast cancer and 0 = did not have breast cancer.27 Using the
What is wrong with the strategy of determining the number of lagged terms in a distributed lag model sequentially, that is, adding each successive lagged term if the t value of an added lagged term
Although the logit and probit models may be superior to the LPM model, in practice, we should choose the LPM model because of its simplicity per Occam's razor principle. Do you agree with this
What is the connection between co integration and spurious regression?
Table 12-6 (on the textbook's Web site) gives data on personal consumption expenditure (PCE) and personal disposable income (PDI) for the United States for 1970 to 2007; all figures are in billions
Use the data in Problem 12.8, but now consider the following models: In PCEt = A1 + A2In PDIt + ut In PCEt = B1 + B2In PDIt + B3 In PCEt-1 + vt where In = the natural log. a. Interpret these
What is meant by the moments of a PDF? What are the most frequently used moments?
The following table gives the joint PDF of random variables X and Y, whereX = the first-year rate of return (%) expected from investment A, andY = the first-year rate of return (%) expected from
You are told that £(X) = 8 and var (X) = 4. What are the expected values and variances of the following expressions? a. Y = 3X + 2 b. Y = 0.6X - 4 c. Y = X/4 d. Y = aX + b, where a and b are
Consider formulas (B.32) and (B.33). Let X stand for the rate of return on a security, say, IBM, and Y the rate of return on another security, say, General Foods. Let s2X = 16, s2Y = 9, and r = -
Table B-6 gives data on the number of new business incorporations (Y) and the number of business failures (X) for the United States from 1984 to 1995.a. What is the average value of new business
For Problem A. 13, find out the var (X + Y). How would you interpret this variance?
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
Let ER stand for U.K. pound/$ exchange rate (i.e., the number of U.K. pounds per U.S. dollar) and RPR stand for the ratio of the U.S. CPI/U.K. CPI. Is the correlation between ER and RPR expected to
Find the expected value of the following PDF: f(X) = X2 / 9 0 ≤ x ≤ 3
Show that a. E(X2) ≥ [E(X)2] b. cov (X,Y) = E[(X - µX)(Y - µY)] = E(XY) - µXµY where µX = E(X) and µY = E(Y). How would you express these formulas verbally?
Establish Eq. (B.15).
Explain the meaning of a. Expected value b. Variance c. Standard deviation d. Covariance e. Correlation f. Conditional expectation
Establish Eq. (B.17).
According to Chebyshev's inequality, what percentage of any set of data must lie within c standard deviations on either side of the mean value if (a) c = 2.5 and (b) c = 8?
Show that E(X - k)2 = var (X) + [E(X) - k]2. For what value of k will E(X - k)2 be minimum? And what is that value of k?
For the PC / printer sales example discussed in this appendix compute the conditional variance of Y (printers sold) given that X (PCs sold) is 2.
Compute the expected value and variance for the PDF given in Problem A.19. Problem A.19 The PDF of a continuous random variable X is as follows: f(X) = c(4x - 2x2) 0 ≤ x ≤ 2 = 0 otherwise
Why is it important to make the distinction between population moments and sample moments?
Fill in the gaps in the manner of (a) below. a. The expected value or mean is a measure of central tendency. b. The variance is a measure of... c. The covariance is a measure of... d. The correlation
Explain whether the following statements are true or false. Give reasons. a. Although the expected value of an r.v. can be positive or negative, its variance is always positive. b. The coefficient of
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:
The following table gives the anticipated 1-year rates of return from a certain investment and their probabilities.ANTICIPATED 1 -YEAR RATE OF RETURNFROM A CERTAIN INVESTMENTa. What is the expected
It can be shown that the sum of the first n positive numbers is:Use the preceding formula to evaluate a. b. c.
It can be proved that the sum of squares of the first n positive numbers is:Using this formula, obtain a. b. c. d.
An r.v. X has the following PDFa. What is the value of b? Why? b. Find the P(X ‰¤ 2); prob(X ‰¤ 3); prob(2 ‰¤ X ‰¤ 3).
The following table gives the joint probability distribution, f(X, Y), of two random variables X and Y.a. Find the marginal (i.e., unconditional) distributions of X and Y, namely, f(X) and f(Y).b.
Of 100 people, 50 are Democrats, 40 are Republicans, and 10 are Independents. The percentages of the people in these three categories who read The Wall Street Journal are known to be 30, 60, and 40
Based on a random sample of 500 married women, the following table gives the joint PMF of their work status in relation to the presence or absence of children in the household.10CHILDREN AND WORK
The following table gives the joint probability of X and Y, where X represents a person's poverty status (below or above the poverty line as defined by the U.S. government), and Y represents the
The following table gives joint probabilities relating cell phone usage to stopping properly at intersections.a. Compute the probability of failing to stop at an intersection, given the driver was on
The PDF of a continuous random variable X is as follows: f(X) = c(4x - 2x2) 0 ≤ x ≤ 2 = 0 otherwise a. For this to be a proper density function, what must be the value of c? b. Find P(l < x <
A and B are two events. Can they be mutually exclusive and independent simultaneously?
Consider the following joint PDF: f(x, y) = 12 / 5 x(2 - x - y); 0 < x < 1; 0 < y < 1 = 0 otherwise a. Find P(x > 0.5) and P(y < 0.5) b. What is the conditional density of X given that Y = y, where 0
Four economists have predicted the following rates of growth of GDP (%) for the next quarter: E1 = below 2%, E2 = 2 or greater than 2% but below 4%, E3 = 4 or greater than 4% but less than 6%, and E4
By the conditional probability formula, we have 1. P(A | B) = P(AB) / P(B) and 2. P(B | A) = P(AB) / P(A) → P(AB) = P(B | A) P(A) where → means "implies." If you substitute for P(AB) from the
What do the following stand for?a.b. c. d. e. f. g. h.
Express the following in the X notation: a. x1 + x2 + x3 + x4 + x5 b. x1 + 2x2 + 3x3 + 4x4 + 5x5 c. (x21 + y21) + (x22 + y22) + ... + (x2k + y2k)
Explain the meaning of a. Degrees of freedom. b. Sampling distribution of an estimator. c. Standard error.
Profits (X) in an industry consisting of 100 firms are normally distributed with a mean value of $1.5 million and a standard deviation (s.d.) of $120,000. Calculate a. P(X < $1 million) b. P($800,000
In Problem C.10, if 10 percent of the firms are to exceed a certain profit, what is that profit? Problem C.10 Profits (X) in an industry consisting of 100 firms are normally distributed with a mean
The grade-point average in an econometrics examination was normally distributed with a mean of 75. In a sample of 10 percent of students it was found that the grade-point average was greater than 80.
The amount of toothpaste in a tube is normally distributed with a mean of 6.5 ounces and an s.d. of 0.8 ounces. The cost of producing each tube is 50 cents. If in a quality control examination a tube
If X ~ N(10, 3) and Y ~ N(15, 8), and if X and Y are independent, what is the probability distribution of a. X + Y b. X - Y c. 3X d. 4X + 5y
Continue with Problem C.14, but now assume that X and y are positively correlated with a correlation coefficient of 0.6. Problem C.14 If X ~ N(10, 3) and Y ~ N(15, 8), and if X and Y are independent,
Let X and y represent the rates of return (in percent) on two stocks. You are told that X ~ N(15, 25) and Y ~ N(8,4), and that the correlation coefficient between the two rates of return is - 0.4.
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
The 10 economic forecasters of a random sample were asked to forecast the rate of growth of the real gross national product (GNP) for the coming year. Suppose the probability distribution of the
When a sample of 10 cereal boxes of a well-known brand was reweighed, it gave the following weights (in ounces):a. What is the sample mean? And the sample variance? b. If the true mean weight per box
Consider a random variable (r.v.) X ~ N (8, 16). State whether the following statements are true or false: a. The probability of obtaining an X value of greater than 12 is about 0.16. b. The
The same microeconomics examination was given to students at two different universities. The results were as follows: 1 = 75, S21 = 9.0, n1 = 50 2 = 70, S22 = 7.2, n2 = 40 where the 's denote the
Using Eq. (C.16), compare the values of X2(10) with F10, 10, and F10, 60. What general conclusions do you draw?
Given X ~ N(µX,σ2X), prove that ~ N(µX, σ2X / n).
Prove thathas zero mean and unit variance. Note that this is true whether Z is normal or not.
Continue with Question C.2 Consider a random variable (r.v.) X ~ N (8, 16). State whether the following statements are true or false: a. What is the probability distribution of the sample mean
Consider an r.v. that follows the t distribution. a. For 20 degrees of freedom (d.f.), what is the probability that the t value will be greater than 1.325? b. What is the probability that the t value
For a sufficiently large d.f., the chi-square distribution can be approximated by the standard normal distribution as: Z = √2x2 - √2k - 1 ~ N (0, 1). Let k = 50. a. Use the chi-square table to
Give examples where the chi-square and F probability distributions can be used.
What is the distinction between each of the following pairs of terms? a. Point estimator and interval estimator. b. Null and alternative hypotheses. c. Type I and type II errors. d. Confidence
Continuing with problem D.9, based on a random sample of 1000 members, suppose that you find the sample mean income, to be $900. a. Given that µ = $1000, what is the probability of obtaining such a
The number of peanuts contained in a jar follows the normal distribution with mean µ and variance σ2. Quality control inspections over several periods show that 5 percent of the jars contain less
The following random sample was obtained from a normal population with mean µ and variance = 2. 8, 9, 6, 13, 11, 8, 12, 5, 4, 14 a. Test: µ = 5 against µ ≠ 5 b. Test: µ = 5 against µ > 5 use
Based on a random sample of 10 values from a normal population with mean µ and standard deviation σ, you calculated that = 8 and the sample standard deviation = 4. Estimate a 95% confidence
You are told that X ~ N (µX = 8, σ2x = 36). Based on a sample of 25 observations, you found that = 7.5. a. What is the sampling distribution of ? b. What is the probability of obtaining an = 7.5
Compute the p values in the following cases: a. t ≥ 1.72, d.f. = 24 b. Z ≥ 2.9 c. F ≥ 2.59, d.f. = 3 and 20, respectively d. x2 ≥ = 19, d.f. = 30 If you cannot get an exact answer from the
In an application involving 30 d.f. you obtained a t statistic of 0.68. Since this t value is not statistically significant even at the 10% level of significance, you can safely accept the relevant
Let X ~ N([µX,Ïƒ2X). A random sample of three observations was obtained from this population. Consider the following estimators of µX:a. Is 1 an unbiased estimator of µX?
Suppose a random sample of 10 firms gave a mean profit of $900,000 and a (sample) standard deviation of $100,000. a. Establish a 95% confidence interval for the true mean profit in the industry. b.
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.
What is the meaning of a. Statistical inference. b. Sampling distribution. c. Acceptance region. d. Test statistic. e. Critical value of a test. f. Level of significance. g. The p value.
Sixteen cars are first driven with a standard fuel and then with Petro coal, a gasoline with a methanol additive. The results of the nitrous oxide emissions (NOx) test are as follows:a. How would you
Show that the estimator given in Eq. (D.14) is biased.
Explain carefully the meaning of a. An unbiased estimator. b. A minimum variance estimator. c. A best, or efficient, estimator. d. A linear estimator. e. A best linear unbiased estimator (BLUE).
State whether the following statements are true, false, or uncertain. Justify your answers.a. An estimator of a parameter is a random variable, but the parameter is non-random, or fixed.b. An
Suppose in an example with 40 d.f. that you obtained a t value of 1.35. Since its p value is somewhere between a 5 and 10 percent level of significance (one-tailed), it is not statistically very
Find the critical Z values in the following cases: a. α = 0.05 (two-tailed test) b. α = 0.05 (one-tailed test) c. α = 0.01 (two-tailed test) d. α = 0.02 (one-tailed test)
Find the critical t values in the following cases: a. n = 4, α = 0.05 (two-tailed test) b. n = 4, α = 0.05 (one-tailed test) c. n = 14, α = 0.01 (two-tailed test) d. n = 14, α = 0.01 (one-tailed
Assume that the per capita income of residents in a country is normally distributed with mean µ = $1000 and variance σ2 = 10,000 ($ squared). a. What is the probability that the per capita income
Suppose that you are asked to conduct a study to determine whether smaller class sizes lead to improved student performance of fourth graders. (i) If you could conduct any experiment you want, what
A justification for job training programs is that they improve worker productivity. Suppose that you are asked to evaluate whether more job training makes workers more productive. However, rather
Suppose at your university you are asked to find the relationship between weekly hours spent studying (study) and weekly hours spent working (work). Does it make sense to characterize the problem as

Showing 400 - 500 of 833