All tests with hypothesis Flashcards
1
Q
Ramsey Reset Test (OLS)
A
- test for functional form misspecification
H0: no omitted variables -> regression well specified in form
HA: omitted variables
2
Q
Breusch Pagan Test (OLS)
A
- 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
3
Q
Sargan J-Test (OLS)
A
- 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
4
Q
Hausmann Test (OLS)
A
- 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)
5
Q
Breusch-Gottfrey Test (OLS)
A
- Checks for serial correlation of residuals. Only works with time series data.
H0: No serial correlation of residual
HA: Serial correlation of residual
6
Q
First Stage F-statistic (IV)
A
- checks for weak instruments
- same as t^2 test –> (Coefficient/SE)^2
- must be > 10. Otherwise weak instruments
7
Q
Hausman Test (IV)
A
- 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
8
Q
IV assumptions
A
- 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.
9
Q
Sargan J Test (IV)
A
- 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
10
Q
Information Criteria (ARDL)
A
- too few lags can decrease forecast accuracy since valuable info may be lost
- too many lags increase estimation uncertainty
11
Q
F-statistic (ARDL)
A
- 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
12
Q
BIC (ARDL)
A
- 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
13
Q
AIC (ARDL)
A
- 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
14
Q
Residual Autocorrelation (ARDL)
A
- 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
15
Q
Breusch-Gottfries (ARDL)
A
- can be used with multiple lags
H0: no serial correlation between residuals
HA: serial correlation between residuals
16
Q
Durbin-Watson (ARDL)
A
- 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
17
Q
Wooldridge Test (Dynamic Panel)
A
H0: no serial correlation
HA: There is serial correlation
–> if we have serial correlation, add more lags
18
Q
Anderson-Hsiao-IV-Estimator
A
- 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”)
19
Q
Arellano-Bond-GMM-Estimator
A
- 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
20
Q
Generalized Methods of Moments (GMM) procedure
A
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).
21
Q
Blundell-Bond-GMM estimator
A
- 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
22
Q
Hansen’s J-statistic
A
- 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.
23
Q
Augmented Dickey Fuller Test
A
- 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
24
Q
Testing for Cointegration
A
1) Expert knowledge and economic theory
2) Graph the series
3) Perform statistical tests for cointegration
25
Q
Univariate test (EG-ADF, DOLS, ARDL/Bounds)
A
- need to make assumption about direction of causality
- require weak exogeneity
26
Q
Engle-Granger test
A
- essentially the same as Dickey-Fuller or Augmented Dickey-Fuller
H0: no cointegration
HA: conintegration
27
Q
Dickey-Fuller-Test
A
H0: Series has a unit root
HA: Series is stationary
28
Q
Johansen Procedure (Multivariate)
A
- 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
