## Simultaneous Equations Models

Consider the following two equation model y Yy + Pn*i + P21X2 + P31X3 + si y2 Y2yi + P12X1 + P22X2 + P32X3 + 62. (a) Verify that as stated, neither equation is identified. (b) Establish whether or not the following restrictions are sufficient to identify (or partially identify) the model (i) p21 p32 0, (8) CT12 0, P21 P22 P31 P32 0, (9) CT12 0, P11 P21 P22 P31 P32 0. Since nothing is excluded from either equation and there are no other restrictions, neither equation passes the order condition...

## Probability and Distribution Theory

How many different 5 card poker hands can be dealt from a deck of 52 cards There are I 5 I 2,598,960 possible hands. 2. Compute the probability of being dealt 4 of a kind in a poker hand. There are 48(13) possible hands containing 4 of a kind and any of the remaining 48 cards. Thus, given the answer to the previous problem, the probability of being dealt one of these hands is 48(13) 2598960 .00024, or less than one chance in 4000. 3. Suppose a lottery ticket costs 1 per play. The game is played...

## Models for Panel Data

The following is a panel of data on investment (y) and profit (x) for n 3 firms over 7 10 periods. i 1 i 2 i 3 (a) Pool the data and compute the least squares regression coefficients of the model yit a+ P'x,j + sii. (b) Estimate the fixed effects model of (13-2), then test the hypothesis that the constant term is the same for all three firms. (c) Estimate the random effects model of (13-18), then carry out the Lagrange multiplier test of the hypothesis that the classical model without the...

## Estimation Frameworks in Econometrics

Compare the fully parametric and semiparametric approaches to estimation of a discrete choice model such as the multinomial logit model discussed in Chapter 21. What are the benefits and costs of the semiparametric approach A fully parametric model estimator provides consistent, efficient, and comparatively precise results. The semiparametric model estimator, by comparison, is relatively less precise in general terms. But, the payoff to this imprecision is that the semiparametric formulation...

## Functional Form and Structural Change

In Solow's classic 1957 study of technical change in the U.S. Economy, he suggests the following aggregate production function q t A t f k t where q t is aggregate output per manhour, k t is the aggregate capital labor ratio, and A t is the technology index. Solow considered four static models, q A a plnk, q A a - p k, ln q A a plnk, ln q A a - p k. He also estimated a dynamic model, q t A t - q t-1 A t-1 a pk. b Solow's data for the years 1909 to 1949 are listed in Table A8.1 Op. cit., page...

## Finite Sample Properties of the Least Squares Estimator

Suppose you have two independent unbiased estimators of the same parameter, 8, say 9iand 8 2, with different variances, v1 and v2. What linear combination, 8 c181 c2 8 2 is the minimum variance unbiased estimator of 8 Consider the optimization problem of minimizing the variance of the weighted estimator. If the estimate is to be unbiased, it must be of the form c181 c2 82 where c1 and c2 sum to 1. Thus, c2 1 - c1. The function to minimize is Min L c12v1 1 - c1 2v2. The necessary condition is...

## Inference and Prediction

A multiple regression of y on a constant, x1, and x2 produces the results below y 4 ,4xi .9x2, R 8 60, e' e 520, n 29, X'X The estimated covariance matrix for the least squares estimates is the test may be based on t .4 .9 - 1 .410 .256 - 2 .051 1 2 .399. This is smaller than the critical value of 2.056, so we would not reject the hypothesis. 2. . Using the results in Exercise 1, test the hypothesis that the slope on x1 is zero by running the restricted regression and comparing the two sums...