1. Kakhramon Yusupov
June 15th, 2017
1:30pm – 3:00pm
Session 3
MODEL DIAGNOSTICS AND SPECIFICATION

2. Multicollinearity: reasons
Data collection process
Constraints on model or in the population being sampled.
Model specification
An over-determined models

3. Perfect v.s less than perfect
Perfect multicollinearity is the case when two ore more independent
variables Can create perfect linear relationship.
Perfect multicollinearity is the case when two ore more independent
variables Can create less than perfect linear relationship.

4. Practical consequences
The OLS is BLUE but large variances and covariances making process estimation difficult.
Large variances cause large confidence intervals and accepting or rejecting hypothesis are biased.
T statistics are biased
Although t-stats are low, R-square might be very high.
The sensitivity of estimators and variances are very high to small changes in dataset.

5. Ha: Not all slope coefficients are simultaneously zero
Due to low t-stats we can not reject our
Null Hypothesis
Ha: Not all slope coefficients are simultaneously zero
Due to high R square the F-value will be very high and rejection of Ho will be easy

6. Detection Multicollinearity is a question of degree.
It is a feature of sample but not population.
How to detect :
High R square but low t-stats.
High correlation coefficients among the independent variables.
Auxiliary regression
High VIF
Eigenvalue and condition index.***

7. Auxiliary regression Ho: The Xi variable is not collinear
Run regression where one X is dependent and other X’s are independent and
Obtain R square
Df num = k-2
Df denom = n-k+1
k- is the number of explanatory variables including intercept.
n- is sample size.
If F stat is higher than F critical then Xi variable is collinear
Rule of thumb: if R square of auxiliary regression is higher than over R square then it might be troublesome.

8. What to do ? Do nothing. Combining cross section and time series
Transformation of variables (differencing, ratio transformation)
Additional data observations.

9. Assumption:
Homoscedasticity or equal variance of ui X Y
f(u)

10. Reasons: Error learning models;
Higher variability in independent variable might increase higher variability in dependent variable.
Spatial Correlation.
Data collecting biases.
Existence of extreme observations (outliers)
Incorrect specification of Model
Skewness in the distribution

11. OLS Estimation: Hetroscedasticity
If variance of residuals is constant then
Our equation collapses to original variance
Formula.

12. Consequences: The regression coefficients are unbiased
The usual formula for coefficient variances is wrong
The OLS estimation is BLU but not efficient.
t-test and F test are not valid.

13. Method of Generalized Least Squares

14. Method of Generalized Least Squares

15. Hetroscedasticity: Detection.
Graphical Method
Park test
White’s general Hetroscedasticity test
Breush-Pagan-Godfrey Test

16. Park test If coefficient beta is statistically different from zero,
Is not known and we use
If coefficient beta is statistically different from zero,
it indicates that Hetroscedasticity is present.

17. Goldfeld-Quandt Test
Order your sample from lowest to highest. Omit your central
your central observation and divide your sample into two samples.
2. Run two regressions for two samples and obtain RSS1 and RSS2.
RSS1 represents RSS from small X sample.
3. Each RSS has following degrees of freedom
Calculate
Follows F distribution with df of num and denom equal to

18. Breush-Pagan-Godfrey Test
If you reject your Null hypothesis then there is
Hetroscedasticity. .

19. Breush-Pagan-Godfrey Test
Step1. Estimate original regression model and get
residuals .
Step2. Obtain
Step3. Construct
Step4. Estimate the following regression model.
Step5. Obtain
m- is number of parameters of Step 4 regression

20. White’s general Heteroscedasticity test
Step1. Estimate original regression model and get
residuals .
Step2. Estimate
If you reject your Null hypothesis then there is
Hetroscedasticity. .

21. Remedial Measures Weighted Least squares
White’s Hetroscedasticity consistent variance and standard errors.
Transformations according to Hetroscedasticity pattern.

22. Heteroscedasticity robust inference
LM test score
and assume that
Regress each element of X2 onto all elements of X1 and collect residual in r matrix
Then form u*R
Then run regression 1 on ur

23. Autocorrelation reasons:
Inertia.
Specification Bias: Omitted relevant variables.
Specification bias: Incorrect functional form.
Cobweb phenomenon.
Lags
Data manipulation.
Data Transformation.
Non-stationary

24. Consequences: The regression coefficients are unbiased
The usual formula for coefficient variances is wrong
The OLS estimation is BLU but not efficient.
t-test and F test are not valid.

25. Detection.
DW test: (the regression model includes intercept, there is no lagged dependent variable, the explanatory variables, the X’s are non-stochastic, residuals follow AR(1) process, residuals are normally distributed)

26. Detection: Breusch-Godfrey
There is no kth order serial correlation
Test Statistic
Where n- number of observations, p-number of residual lag variables.

27. Remedial Measures
GLS
Newey-West Autocorrelation consistent variance and standard errors.
Including lagged dependent variable.
Transformations according to Autocorrelation pattern.

28. Generalized Least Square
If the value of rho is known
If the value of rho is not known

29. Cochrane-Orcutt procedure :
First estimate original regression and obtain residuals
After runing AR(1) regression obtain the value of Rho and run GLS regression
Using GLS coefficients obtain new residuals and obtain new value of Rho
Continue the process until you get convergence in coefficients.

30. Representation

31. Endogeneity
1. Omission of relevant variables

32. What to do ?
If omitted variable does not relate to other included independent variables then OLS estimator still BLUE
Proxy variables
Use other methods other than OLS