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Econometrics (Hetrosckdasticity- Common in cross-sectional data (Tests…
Econometrics
Multicolliniarity
Symptoms
High SE of estimators
Large confidence interval
t ratio of one or more coefficient Insignificant
High R Square
High VIF
Unstable coefficient on addition of new variables
adding new correlated variables complicates the problem
Remedy
Do Nothing
Drop a redundant variable-Use theory based decision
Transformation of variables
First difference form
Ratio transformation
Increase sample size, if at all possible
Combine correlated variable - Index
Empirical restriction
Theoretical restriction
Hetrosckdasticity- Common in cross-sectional data
Reasons
Error learning Model
Scale variable
Improvement in data collection technique
Presence of Outliers
Specification error
Symtoms
In-efficient OLS estimators, though still unbiased and consistent
Underestimates the variance of estimators
Higher values of t and F statistics
Tests
Park Test
Estimates the equation(*) with OLS and obtain residuals
Regress the natural log of squared residuals on the natural log of a possible proportionality factor
If coefficient of lnZ is significantly different from zero then heteroscedastic
Glejser Test
Useful for large sample
Spearman's rank correlation test
Rank Ui and Xi and arrange in ascending or descending order
Calculate t value
Calculate the spearman's rank correlation coefficient
Goldfeld Quandt test
Compute F value = RSS2/RSS1
White's Test
Compute LM stat = nR2
If LN-stat>X2 critical, reject the null
Breusch-pagan test
Judgement call for which explanatory variable to select unlike white's test
Engle's ARCH
Compute LM stat = (n-p)R2
Remedy
Devide the equation by variance of the error term
Divide the equation by Zi
Divide by Xi
Double log transformation
Use robust standard errors
Auto correlation- Time series data
Reasons
Cyclicity
Specification bias
Lags in data
Data manipulation
Non-stationarity
Symptoms
Coefficient are NO more BLUE
Use GLS and not OLS
Underestimate the variance of error and coefficient
Overestimate Rsquared
t and F stat is no more valid
Tests
Graphical method- Residual against Time
The Runs Test
DW - Durbin Watson Test
Drawbacks
Inconclusive result
Not applicable when lagged sependent variable is used
Can't take higher order autocorrelation
Bruesch Godfrey Test
Lagrange Multiplir test that resilve the drawbacks of DW test
Compute LM statistics = (n-p)R2
Durbin's h test
Remedy
First difference transformation- When Ro is known
Use First difference when d < R2
Generalised transformation
Newey-west method
When ro is Unknown
Cochrane- Orcutt iterative process