Regression Part-9 Model Specification

Question 1

What is model specification bias?

Answer 1

CLRM assumption that model must be correctly specified

Question 2

What are the attributes of a good model?

Answer 2

1. Parsimony (few variables good)
2. Identifiability (estimated parameters have unique values)
3. Goodness of Fit (using evaluation criteria)
4. Theoretically sound
5. Exogenous regressors (X uncorrelated with error)
6. Data coherency (residuals must be white noise)

Question 3

What are types of model specification errors?

Answer 3

1. Omission of a relevant variable(s).
2. Inclusion of unnecessary variable(s).
3. Implementing a wrong functional form.
4. Errors of measurement

Question 4

What is underfitting?

Answer 4

If we omit a variable

Question 5

What is overfiiting?

Answer 5

If we include irrelevant variable

Question 6

What is the difference between model specification and model misspecification?

Answer 6

Model specification error - we have a true model in mind
Model misspecification - we don’t know the true model

Question 7

What leads to errors in measurement?

Answer 7

Using proxies in the implemented model

Question 8

What are the consequences of Omitted Variable bias?

Answer 8

1. If X3 is correlated with X2 then missepcified model coeffs are inconsistent and biased; The alpha2 overestimates the beta2
2. Var(alpha2) > var(beta2) (overestimated)
3. The intercept may be underestimated
4. Standard errors increase; R squared decrease

Question 9

What are the consequences of Irrelevant Variable inclusion bias?

Answer 9

1. the ols estimators are unbiased and consistent; LUE not Best
2. Var of new model more than true model;
3. var(alpha2)/var(beta2) = 1/(1-r23squared) or the VIF

Question 10

What is the consequence of the two bias?

Answer 10

Underfitting
Overfitting
Coefficients of the variables -
- Biased and inconsistent
- Unbiased and consistent
Error variance
- Incorrectly estimated
- Correctly estimated
Hypothesis testing proc.
- Might be invalid
- Still valid
Variances of coefficients
-Inefficient
-Inefficient (larger

Question 11

What is the consequence of incorrect functional form?

Answer 11

incorrect or illogical values of estimated coefficients

Question 12

What is the reasons of errors in measurement bias ?

Answer 12

nonresponse errors, reporting errors, and computing errors

Question 13

What is the consequence of errors in measurement bias on Y?

Answer 13

1. The OLS estimators are unbiased.
2. The variances are unbiased.
3. The estimated variances of the estimators are larger than true model

Question 14

What is the consequence of errors in measurement bias on X?

Answer 14

1. The OLS estimators are biased.
2. They are also inconsistent; that is, they remain biased even if the sample size increases indefinitely.

Question 15

What is remedy of error in measurement bias?

Answer 15

1. use instrumental or proxy variables.
2. the data are measured as accurately as possible; avoid errors of recording, rounding, or omission

Question 16

How to detect Unnecessary variables specification errors?

Answer 16

We can use the 𝐹 and 𝑡 tests to assess the statistical significance of variables or we can also use the Partial 𝐹 test for assessing the significance of a subset of variables (anova of (new model, old model)

Question 17

How to detect Omitted variables specification errors?

Answer 17

Informal - residual plot - if pattern then omission
Formal - Ramsey’s RESET (Regression Specification Error Test)

Question 18

What are the steps in Ramseys RESET?

Answer 18

1. Obtain predicted values of Y
2. Rerun model with predY squared, and cubed
3. Find out F value
4. If F significant then misspecified model

It is a test of misspecification only says if there is but not where

Question 19

What is the Mckinnon White Davidson test

Answer 19

This test is used to choose between the linear and log-linear regression models.
To see if one specification is better than the other, we can use the MWD test.
𝐻0: linear model 𝑌 is a linear function of 𝑋s
𝐻1: Log-Linear model: ln 𝑌 is a linear function of 𝑋s or a log of the 𝑋

Question 20

What Steps in MWD test?

Answer 20

1. Estimate the linear model and obtain the estimated 𝑌 values
2. Estimate the log-linear model and obtain the estimated ln 𝑌 values
3. Obtain 𝑍1𝑖 = ln 𝑌𝑖 − ln𝑌𝑖
4. Regress 𝑌 on the 𝑋s and 𝑍1𝑖.
   Reject 𝐻0 if the coefficient of 𝑍1𝑖 is statistically significant by the usual 𝑡-test.
5. Obtain 𝑍2𝑖 = exp(lnYi) - Yi
6. Regress ln 𝑌 on the 𝑋s or logs of 𝑋s and 𝑍2𝑖
   Reject 𝐻1 if the coefficient of 𝑍2 in the preceding equation is statistically significant.
   The idea behind the MWD test is that if the linear model is in fact the correct model, the constructed variable 𝑍1𝑖 should not be significant. The same comment applies to the alternative hypothesis 𝐻1

Question 21

What is the order of harsher penalties imposed by model selection criterias?

Answer 21

r squared< adj r squared< AIC< SIC