Question

In: Economics

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?”

Expert Solution

1.

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

2.

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 2 years ago

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