Consider a labour market with a labour supply function L³= Bo + BiWi+ 5labour demand fuction Ld = Yo+ed and a market equilibrium condition I³ = Lº. Inaddition E[] = E[¹] = 0 and Cov(es, ed) = 0.a) Show that Cov(W₁, &$) f-0.b) Show that the OLS estimator of B₁ is inconsistent.and ak

In this problem, we are presented with a labor market model consisting of a labor supply function, a…

Answered: Consider a labour market with a labour…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Consider the linear regression model (with deterministic regressors) y = Bi + P2x, + €,, G - (0,0) i.i.d., i = 1.,n. Let ô = (,. BY be the OLS estimator of B = (B. P2) and (x,-x) be another estimator of B. True False Elyı] = Ely.) The estimator , is biased as EIA,) = B (x, - x1) The estimator , is an efficient estimator of Pi as only two observations are needed for its calculation. The estimator B, is a linear estimator of Pi .
Suppose a logistic regression model is fitted for the probability of car ownership for residents of a certain city in Oman (Y=1 if a resident owns a car, Y=0 if a resident does not own a car). Suppose the explanatory variables used are x1=no. of years a resident spent in schooling and x2 is gender of the resident of the city (x2=1 for a male and x2=0 for a female resident) a) Interpret el and e82 b) if BO= -1.6, B1=0.4 and B2=3, estimate the probability of a resident in the city owning a car.
9
Consider a labour market with a labour supply function Is i = Bo + B₁W₁ +8² and a labour demand fuction Id = Yo + ed and a market equilibrium condition I = Ld. In i addition E[¹] = E[ed]= 0 and Cov(es, ed=0. eq) a) Show that Cov(Wi, &) f-0. b) Show that the OLS estimator of B₁ is inconsistent.
The functions i)= e **2f,(x) = e*-3 %3D are O A. Insufficient information to conclude None of them O B. O C. Neither linearly dependent or independent OD. Linearly independent O E. Linearly dependent
Assume that a population of patients contains 30% of individuals who suffer from a certain fatal syndrome Z, which simultaneously makes it uncomfortable for them to take a life-prolonging drug X. Let Z = 1 and Z = 0 represent, respectively, the presence and absence of the syndrome, Y = 1 and Y = 0 represent death and survival, respectively, and X = 1 and X = 0 represent taking and not taking the drug. Assume that patients not carrying the syndrome, Z = 0, die with probability 0.5 if they take the drug and with probability 0.5 if they do not. Patients carrying the syndrome, Z = 1, on the other hand, die with probability 0.7 if they do not take the drug and with probability 0.3 if they do take the drug. Further, patients having the syndrome are more likely to avoid the drug, with probabilities p(X = 1|Z=0) = 0.9 and P(X = 1|Z = 1) = 0.6 . Based on this model, compute the joint distributions and for all values of x, y, and z. Present the following joint distributions in tables. [Hint:…
7. For simple linear regression, we assume that Y = Bo + BIX +e, where e - N(0,0?) and X is fixed (not random). We collect n i.i.d, training sample (x),y1)....(XYn)). Prove that the (Bo.B1) estimated through minimizing RSS equals to the one through maximizing likelihood.
Suppose you would like to test the hypothesis that one year of attending a university is worth one years of attending a two-year school (junior college), in terms of effect on wages, using the following econometric model: Y = Bo + B₁X₁ + B2X2 + B3X3 + U where Y = monthly wage in dollars X₁ = number of years attending a two-year college X₂ = number of years at a four-year college X3 = months in the workforce. u = error term The relevant null hypothesis in this case would be Hỏ: B₁-B₂. Equivalently, by creating a new parameter that is a linear combination of ß₁ and B2, this null can be stated as Ho:-
Consider a model with an interaction term between being female and being married. The dependent variable is the log of the hourly wage: log(wage) = 0.151 - 0.038 female + 0.1 married - 0.301 female* married + 0.079 educ + 0.027 exper+0.029 tenure (0.072) (0.056) (0.055) (0.007) (0.005) (0.007) n = 536, R2 = 0.461 Numbers in parantheses are standard errors of coefficients. Given the estimation result and the observation number fill in the blanks below which aim at discussing the statistical significance of variables. The test statistic of the interaction term is The critical value at 1% significance level is Then the interaction term statistically significant at 1% significance level. (Hint: to fill the blank make a choice between "is" and "is not".)
Consider randomly selecting n segments of pipe and determining the corrosion loss (mm) in the wall thickness for each one. Denote these corrosion losses by Y₁' Yn. The article "A Probabilistic Model for a Gas Explosion Due to Leakages in the Grey Cast Iron Gas Mains"+ proposes a linear corrosion model: Y; = t;R, where t; is the age of the pipe and R, the corrosion rate, is exponentially distributed with parameter 1. Obtain the maximum likelihood estimator of the exponential parameter (the resulting mle appears in the cited article). [Hint: If c> 0 and X has an exponential distribution, so does cX.] O Â = O Â = O λ = * * O n Srit) i = 1 n j = 1 Σ i = 1 n n i = 1 n LY i = 1 n 0 1 = L (rt) 2 i = 1 | = 1 n n Y; | = 1
Consider the Keynesian consumption function Yt = B₁ + B₂x2t + &t where yt is per capita consumption, and x2+ is per capita income. The coefficient ₂ is interpreted causally as the marginal propensity to consume, and we expect 0

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