ECON321 Lecture Notes - Lecture 7: Birth Weight, Econometrics, Multicollinearity

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bluesalmon414

17 Oct 2015

School

University of Waterloo

Department

Economics

Course

ECON321

Professor

Amanda Clark

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Introduction to econometrics 321; spring 2013, university of waterloo. Week 5: solution i to omitted variable bias: multiple linear regression model. We can potentially get rid of ovb by adding the omitted variable in the regression. Remark: this solution assumes that we have (or can obtain) data on the variable causing the omitted variable bias. Often this unrealistic and hence we have to use other solutions (see e. g. chapters 10, 12 and 13). Yi = (cid:12)0 + (cid:12)1x1;i + (cid:12)2x2;i + (cid:1) (cid:1) (cid:1) + (cid:12)kxk;i + ui; i = 1; :::; n. Yi = (cid:12)0x0;i + (cid:12)1x1;i + (cid:12)2x2;i + (cid:1) (cid:1) (cid:1) + (cid:12)kxk;i + ui; i = 1; :::; n; where x0;i = 1 for all i = 1; :::; n: the regressor x0;i is thus a constant. Now e (yi jx1;i = x1; :::; xk;i = xn ) = (cid:12)0 + (cid:12)1x1 + (cid:1) (cid:1) (cid:1) + (cid:12)kxk: and therefore.

Related Questions

PROBLEM 1 (This one is designed to give you lots of math practice!)

Consider the following individual utility functions:

Adam Smith: U(x,y) = xy

Jeremy Bentham: U(x,y) = x^ay^b (Cobb-Douglas utility function)

Alfred Marshall: U(x,y) = ln x + ln y

John M. Keynes: U(x,y) = x + y^b (Quasi-linear utility function)

Joan Robinson: U(x,y) = aX + bY (linear; perfect substitutes)

a. Solve for the MRS(XY) for each of the gentlemen (i.e., all but Joan Robinson). Show that Mr. Smith, Mr. Bentham, and Mr. Marshall all have diminishing MRS(XY), but that if a=b=2, their preferences exhibit constant, increasing, and decreasing marginal utility respectively. (Fortunately, diminishing MRS is the condition that guarantees convex indifference curves, so we can solve for their optimal consumption!)

b. What is the general formula for Mrs. Robinsons (constant) MRS?

c. Find demand functions for x and y for Smith, Bentham, Marshall, and Keynes. Assume that each man has income I and that the prices of x and y are p_x and p_y respectively.

d. Now assume that a=1/2, b = 1/4, I = 600, p_x = 10 and p_y = 20. Use these values to find the utility-maximizing quantities of x and y consumed by each man.

e. Find an expression for the share of income Mr. Bentham and Mr. Marshall each devote to the consumption of good x, where this share, s_x, is defined as

(p_x x)/I.

f. Find expressions for the income elasticity of demand for good x for Mr. Bentham and Mr. Marshall. Find expressions for the (own) price elasticity of demand for good y for these two men.

aquamarinescorpion997

Jill buys two goods: X and Y and has the following utility function: U(X,Y) = 2X0.25Y0.75

a. Find the equation for her generalized demand curve for X*(Px,Py,I)

b. Find the equation for her generalized demand curve for Y*(Py,Px,I)

c. Are the above generalized demand functions homogeneous of degree 0? (Show your work)

d. Is X a normal good?

e. Is X a gross substitute or complement to Y?

f. Find the compensated demand curve for Xc(Px, Py, U)

g. Find the compensated demand curve for Yc (Py, Px, U)

h. Are the compensated demand functions homogenous of degree 0 in Px and Py if utility is held constant?

i. Find the expenditure function: E(Px, Py, U)

j. Use Shephardâs Lemma to verify that your compensated demand functions Xc and Yc are correct.

k. Find the indirect utility function: V(Px,Py,I)

AI 16. If the price of X is set at $0.10 per unit, the quantity of the good purchased by this consumer each month will be: B) 2 C)3 D) 4 E) 6 F) 8 G) 10 H) 12 I) 16.5 J) 23.5 K) 63 L) 64 M) 128 N) 129 0) 150 P) 156 Q) 157.5 R) 159.5 S) 160 T) 255 U) 256 V) 256.5 W) 257.5 X) 260 Y)0 Z) none of the above

ECON321 Lecture Notes - Lecture 7: Birth Weight, Econometrics, Multicollinearity

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