All tests with hypothesis Flashcards
Ramsey Reset Test (OLS)
- test for functional form misspecification
H0: no omitted variables -> regression well specified in form
HA: omitted variables
Breusch Pagan Test (OLS)
- Usually tests for heteroscedasticity. For Pooled OLS check poolability. Not possible to pool if Standard Errors are hetero.
H0: No heteroscedasticity / No variance of fixed effects
HA: There is Heteroscedasticity / variance of fixed effects
Sargan J-Test (OLS)
- Checks for correlation between error term and independent variable. In this context, checks whether to use Random Effects
H0: No correlation between error term and independent variable
HA: Correlation between error term and independent variable
Hausmann Test (OLS)
- Checks wether RE & FE generate similar results
H0: FE & RE are not different
HA: FE & RE are different - if not different than use RE because RE is more efficient
- if different use First Difference (FD) or Fixed Effects (FE)
Breusch-Gottfrey Test (OLS)
- Checks for serial correlation of residuals. Only works with time series data.
H0: No serial correlation of residual
HA: Serial correlation of residual
First Stage F-statistic (IV)
- checks for weak instruments
- same as t^2 test –> (Coefficient/SE)^2
- must be > 10. Otherwise weak instruments
Hausman Test (IV)
- checks endogeneity condition and what method to use
H0: no endogeneity problem
HA: endogeneity problem - if fail to reject H0, use POLS as it is more efficient
- if reject H0, use IV since POLS can’t be used with endogeneity
IV assumptions
- Instrument z is correlated with endogenous variable x
2. = exclusion restriction = Instrument z affects dependent variable y only through x. So z does not cause y.
Sargan J Test (IV)
- Checks correlation between error term and independent variable.
- Checks whether IV is valid.
- Can only be used in case of overidentification
H0: no correlation between error term and independent variable
HA: correlation between error term and independent variable - if fail to reject H0, all IV’s are valid
- if reject H0, we have at least one invalid IV -> need expert judgement to tell which one
- an invalid instrument is correlated with the residual
Information Criteria (ARDL)
- too few lags can decrease forecast accuracy since valuable info may be lost
- too many lags increase estimation uncertainty
F-statistic (ARDL)
- checks whether coefficient of a variable is significant at 5% and drops it if not
- coefficient/SE –> if larger than 1.96 = all fine
- Drawback:
- -> Cumbersome with many lags
- -> in 5% of cases, will come up with model thats too large
- Bottom line: works well for small models, but in general can produce models that are too large
BIC (ARDL)
- same as AIC: attempts to find balance between overfitting & undercutting lags in our model
- difference to AIC: higher penalty term for the number of parameters
- usually yields models with less lags
AIC (ARDL)
- if you are concerned that BIC might yield a model with too few lags, AIC provides reasonable alternative since penalty term for a number of parameters is lower
- widely used in practice
Residual Autocorrelation (ARDL)
- If errors are correlated over time, they are said to suffer from serial correlation or autocorrelation. This is only a problem in time series data, as under cross-sectional data, the random sampling ensures uncorrelated errors.
- Breusch-Godfrey or Durbin-Watson
- Breusch Godfrey is better than Durbin-Watson
Breusch-Gottfries (ARDL)
- can be used with multiple lags
H0: no serial correlation between residuals
HA: serial correlation between residuals
Durbin-Watson (ARDL)
- provides similar results as Breusch-Gottfries test but can’t be used with multiple lags
- -> value always between 0&4. If below 2, evidence of positive serial correlation.
- -> substantially more than 2, evidence of negative serial correlation
- -> inconclusive region: 1.75 - 2.25
- -> not valid with lagged dependent variable
- complicated in real life -> not really used
Wooldridge Test (Dynamic Panel)
H0: no serial correlation
HA: There is serial correlation
–> if we have serial correlation, add more lags
Anderson-Hsiao-IV-Estimator
- circumvent endogeneity
- uses an older time period as an IV
- Reasoning: uses Yt-2 to estimate Yt-1 –> Yt-2 definitely related to Yt-2 but its sensible to assume that Yt-2 is not related to ut-1
- not the most robust estimator (“notoriously weak and inefficient”)
Arellano-Bond-GMM-Estimator
- appropriate in small T, large N panels
- linear functional relationship
- One left-hand variable that is dynamic, depending on its own past realizations
- Right-hand variables that are not strictly exogenous: correlated with past and possibly current realizations of the error
- Fixed individual effects, implying unobserved heterogeneity
- Heteroskedasticity and autocorrelation within individual units’ errors, but not across them
Generalized Methods of Moments (GMM) procedure
A model that is specified as a system of equations, one per time period, where the instruments applicable to each equation differ (for instance, in later time periods, additional lagged values of the instruments are available).
Blundell-Bond-GMM estimator
- The BB system estimator involves a set of additional restrictions on the initial conditions of the process generating y and improves on the limitations of the AB estimator.
- Combines Anderson-Hsiao & Arellano-Bond –> more efficient
Hansen’s J-statistic
- tests for validity of instruments
- used when there is heteroskedasticity
- same interpretation as Sargan-J res
H0: No overidentification / instruments are valid
HA: At least one instrument is not valid, but the test does not specify which one.
Augmented Dickey Fuller Test
- tests for NS -> has a problem if coefficient of Yt-1 is 1
H0: has a unit root –> not stationary
HA: no unit root but a deterministic time trend - note: different critical values for this test since distribution isn’t standardized
Testing for Cointegration
1) Expert knowledge and economic theory
2) Graph the series
3) Perform statistical tests for cointegration
Univariate test (EG-ADF, DOLS, ARDL/Bounds)
- need to make assumption about direction of causality
- require weak exogeneity
Engle-Granger test
- essentially the same as Dickey-Fuller or Augmented Dickey-Fuller
H0: no cointegration
HA: conintegration
Dickey-Fuller-Test
H0: Series has a unit root
HA: Series is stationary
Johansen Procedure (Multivariate)
- tests for number of cointegrating relationships
H0: no cointegration
HA: there is more than k con integrating relationships - k is the number of non-stationary variables included in the model