Tests Flashcards
Test for coefficients
T-test:
- t-test when you test ONE COEFF
- H0: coeff = 0 or a value
F-test
Joint test to test SEVERAL COEFF
- H0: all coefficients are 0.
o Point of test. See if the fit is “much” better with the variables
Tests for normality
Normality: Skewness (S) = 0, kurtosis (K) = 3
• Jarque-Bera:
• Shapiro-Wilk:
o Best in small sample sizes
• Kolmogorov-Smirnov:
Test for heteroskedasticity
- Goldfeld-Quant:
- Breusch-Pagan:
- White:
Test for serial correlation
Durbin-Watson
Breusch-Godfrey:
Test for functional misspecification
• Ramsey RESET test:
Test for multicollinearity
• Variance Inflation Factor (VIF)
o VIF = 1 / (1+R2j)
o If VIF > 10 (or 5) Multicollinearity
Testing for endogeneity (J-test)
• Compare the values of 2SLS with OLS. If they are similar, x is exogenous.
• Regress the original model. Then, use the residuals as the dependent variable and the
instruments as independent variables. If the R2 is high, then the instruments can
explain parts of the error terms. This means that they are no independent and we have
endogeneity. Requires AT LEAST 2 instruments, and this is the J-test
Testing for non-stationarity
- Dickey-Fuller test for unit root
- Augmented Dickey Fuller test (for several lags aka. higher order)
- Dickey Fuller test with time trend
ADF is utilized for a larger and more complicated set of time series models.
Test integration of order
How to identify highly persistent time series?
1. Test series with ADF test: If we reject the null Non-stationary Integrated of
order 0, I(0)
2. If not rejected in ADF, take the first difference and plot the change in xt. Run ADF on
new series, and if we then reject the null, we have I(1)
3. If not rejected in the second ADF, then take difference of difference, check again, and
repeat if not rejected.
Test for cointegration
• Run regular regression and get residuals
• Check if the residuals are stationary by using a ADF-test on the residuals
• If the t-stats are lower than a strict DF-critical (to account for Beta being estimated)
Reject null Series are cointegrated
Test for random effects vs. fixed effects
• Hausman test
o W = (BFE - BRE)2 / (Var(BFE) – Var(BRE)), which is chi-squared distributed
with 1 df
o H0: Strict exogeneity Can use random effects (lower variance more
efficient)
o H1: Strict exogeneity does not hold Cannot use random effects (not
consistent) Use fixed effects
o Large value of w reject null hypothesis
o The test compares the consistency of the two estimators with the relative gains
of efficiency which can be obtained by using random effects instead of fixed
effects
Binary dependent variable tests
• Likelihood ratio test
o Test to choose the “best” model between a model and a “nested model” (some
variables removed). The best model is the one that makes the data most likely,
e.g. that maximizes likelihood. The test compares the fit of two models.
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o LR = s(logL | θ-hatML) – logL(θHO)), which is chi-squared with q (number of
restrictions) df
o H0: θ = θH0 The smaller model is the “best” model
o H1: θ > θH0 Significant improvement in fit with large model Large
model is best
o If there is a significant difference between the θ’s, we reject H0
• Wald test
o Test to find out if independent variables in a model are significant (add
something to the model)
o H0: parameter = 0 Remove variable
o H1: parameter =/ 0 Keep variable
o For large values of N, the Wald test is roughly equivalent to the t-test
o Works for samples from 30 and beyond
o Chi-squared distributed with 1 degree of freedom (df)
• Score test (Lagrange Multiplier test)
o Alternative to Wald test
o Chi-squared distributed with q (number of restrictions) degrees of freedom
o Score given by the gradient of our observation on the distribution function
