1. Suppose we have the regression y i = β 0 + β 1 ⋅ x...

1. Suppose we have the regression

y i = β 0 + β 1 ⋅ x i + ϵ i

Measurement error in

I. y will cause the ols estimates to be bias

II. x will cause attenuation bias in the estimate of β 1

III. y will cause the standard error of β 1to shrink

IV. x may cause the estimate of β 1to be statistically insignificant

A. II and IV only

B. II and III only

C. I, III, and IV only

D. I and II only

2. Eddie comes back to you and says “I ran regression about charitable giving. My regression is

gift_i = β₀ + β₁*income_i + e _i

I found a large, (positive, negative)____, and statistically significant estimate for β₁! But my friend who is taking econometrics says that since I (included, omitted)____ age from the regression and age and income are (positively, negatively) ___correlated, I can’t say higher income is associated with greater income. Is that right?”

Solutions

Expert Solution

Measurement error in y causes error variace to go up. However, the OLS estimates are still unbiased and consistent as the error is consumed in the population error term. So, Statement I is not true

A measurement error in x (independent variable) will have a downward bias in beta. The OLS estimated may no longer be unbiased. So, Statement II is correct

Measurement error in y causes the error variance or the standard error to inflate. So, Statement III is incorrect

A measurement error in x (independent variable) may increase the standard errors of the estimate and make them statistically insignificant. The inflated t - vales will give the impression that the variable can be dropped from the model. So, Statement IV. is correct

Hence, option A. is correct

Income is positively related with charitable giving. Higher income implies higher gift.

Variable age is not present in the model. So, it seems that Eddie has omitted a variable.

Age and Income are usually positively correlated as income increases as the person becomes older due to factors such as job promotion, salary hikes etc.

So, the correct fillups are:

I found a large positive and statistically significant estimate for β1! But my friend who is taking econometrics says that since I omitted age from the regression and age and income are positively correlated, I can’t say higher income is associated with greater income.

**if you liked the answer, then please upvote. Would be motivating for me. Thanks

Rahul Sunny answered 1 year ago

Next > < Previous

Related Solutions

Let X and Y be random variables. Suppose P(X = 0, Y = 0) = .1,...

Let X and Y be random variables. Suppose P(X = 0, Y = 0) = .1, P(X = 1, Y = 0) = .3, P(X = 2, Y = 0) = .2 P(X = 0, Y = 1) = .2, P(X = 1, Y = 1) = .2, P(X = 2, Y = 1) = 0. a. Determine E(X) and E(Y ). b. Find Cov(X, Y ) c. Find Cov(2X + 3Y, Y ).

Suppose X and Y have joint probability density function f(x,y) = 6(x-y) when 0<y<x<1 and f(x,y)...

Suppose X and Y have joint probability density function f(x,y) = 6(x-y) when 0<y<x<1 and f(x,y) = 0 otherwise. (a) Indicate with a sketch the sample space in the x-y plane (b) Find the marginal density of X, fX(x) (c) Show that fX(x) is properly normalized, i.e., that it integrates to 1 on the sample space of X (d) Find the marginal density of Y, fY(y) (e) Show that fY(y) is properly normalized, i.e., that it integrates to 1 on...

let the continuous random variables X and Y have the joint pdf: f(x,y)=6x , 0<x<y<1 i)...

let the continuous random variables X and Y have the joint pdf: f(x,y)=6x , 0<x<y<1 i) find the marginal pdf of X and Y respectively, ii) the conditional pdf of Y given x, that is fY|X(y|x), iii) E(Y|x) and Corr(X,Y).

1- The regression of X on Y is not the same as the regression of Y...

1- The regression of X on Y is not the same as the regression of Y on X. Why is this? Select one: a. Because the regression minimises the residuals of y, not the residuals of x. b. Because unlike correlation, regression assumes X causes Y. c. Because one goes through (mean x, mean y) whereas the other goes through (mean y, mean x). d. Because the F test divides MSy by MSx, not the other way round. 2- Using...

Let X and Y have joint pdf f(x,y)=k(x+y), for 0<=x<=1 and 0<=y<=1. a) Find k. b)...

Let X and Y have joint pdf f(x,y)=k(x+y), for 0<=x<=1 and 0<=y<=1. a) Find k. b) Find the joint cumulative density function of (X,Y) c) Find the marginal pdf of X and Y. d) Find Pr[Y<X2] and Pr[X+Y>0.5]

Question 3 Suppose that X and Y have the following joint probability distribution: f(x,y) x 0...

Question 3 Suppose that X and Y have the following joint probability distribution: f(x,y) x 0 1 2 y 0 0.12 0.08 0.06 1 0.04 0.19 0.12 2 0.04 0.05 0.3 Find the followings: E(Y)= Var(X)= Cov(X,Y)= Correlation(X,Y)=

1. Prove by contraction that L = {0^x 1^y 0^x+y | x >= 1 and...

1. Prove by contraction that L = {0^x 1^y 0^x+y | x >= 1 and y >=1} is not Regular. Must use the Pumping Lemma. [ HINT: Describe the language in English first. Use example 3 from the lecture notes ] a) Choose one S from L where S is longer than N (Describe S in terms of N and M) S = **??** b) List all places v can be in S: (i.e. all possible...

We got for x > 0 given a differential equation y’ = 1-y/x, with start value...

We got for x > 0 given a differential equation y’ = 1-y/x, with start value y(2)= 2 Find the Taylor polynomial of first and second degree for y(x) at x =2. Show that y(x) =x/2 +2/x solves the given equation.

f(x,y)=3(x+y) 0<x+y<1, 0<x<1, 0<y<1 (a) E(xy|x)=? (b) Cov(x,y)=? (c) x and y is independent? thank you!

1 Let f(x, y) = 4xy, 0 < x < 1, 0 < y < 1,...

1 Let f(x, y) = 4xy, 0 < x < 1, 0 < y < 1, zero elsewhere, be the joint probability density function(pdf) of X and Y . Find P(0 < X < 1/2 , 1/4 < Y < 1) , P(X = Y ), and P(X < Y ). Notice that P(X = Y ) would be the volume under the surface f(x, y) = 4xy and above the line segment 0 < x = y < 1...

Subjects