All tests with hypothesis

Question 1

Ramsey Reset Test (OLS)

Answer 1

• test for functional form misspecification
  H0: no omitted variables -> regression well specified in form
  HA: omitted variables

Question 2

Breusch Pagan Test (OLS)

Answer 2

• 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

Question 3

Sargan J-Test (OLS)

Answer 3

• 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

Question 4

Hausmann Test (OLS)

Answer 4

• 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)

Question 5

Breusch-Gottfrey Test (OLS)

Answer 5

• Checks for serial correlation of residuals. Only works with time series data.
  H0: No serial correlation of residual
  HA: Serial correlation of residual

Question 6

First Stage F-statistic (IV)

Answer 6

• checks for weak instruments
• same as t^2 test –> (Coefficient/SE)^2
• must be > 10. Otherwise weak instruments

Question 7

Hausman Test (IV)

Answer 7

• 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

Question 8

IV assumptions

Answer 8

1. 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.

Question 9

Sargan J Test (IV)

Answer 9

• 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

Question 10

Information Criteria (ARDL)

Answer 10

• too few lags can decrease forecast accuracy since valuable info may be lost
• too many lags increase estimation uncertainty

Question 11

F-statistic (ARDL)

Answer 11

• 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

Question 12

BIC (ARDL)

Answer 12

• 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

Question 13

AIC (ARDL)

Answer 13

• 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

Question 14

Residual Autocorrelation (ARDL)

Answer 14

• 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

Question 15

Breusch-Gottfries (ARDL)

Answer 15

• can be used with multiple lags
  H0: no serial correlation between residuals
  HA: serial correlation between residuals

Question 16

Durbin-Watson (ARDL)

Answer 16

• 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

Question 17

Wooldridge Test (Dynamic Panel)

Answer 17

H0: no serial correlation
HA: There is serial correlation
–> if we have serial correlation, add more lags

Question 18

Anderson-Hsiao-IV-Estimator

Answer 18

• 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”)

Question 19

Arellano-Bond-GMM-Estimator

Answer 19

• 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

Question 20

Generalized Methods of Moments (GMM) procedure

Answer 20

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).

Question 21

Blundell-Bond-GMM estimator

Answer 21

• 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

Question 22

Hansen’s J-statistic

Answer 22

• 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.

Question 23

Augmented Dickey Fuller Test

Answer 23

• 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

Question 24

Testing for Cointegration

Answer 24

1) Expert knowledge and economic theory
2) Graph the series
3) Perform statistical tests for cointegration

Question 25

Univariate test (EG-ADF, DOLS, ARDL/Bounds)

Answer 25

• need to make assumption about direction of causality

- require weak exogeneity

Question 26

Engle-Granger test

Answer 26

• essentially the same as Dickey-Fuller or Augmented Dickey-Fuller
  H0: no cointegration
  HA: conintegration

Question 27

Dickey-Fuller-Test

Answer 27

H0: Series has a unit root
HA: Series is stationary

Question 28

Johansen Procedure (Multivariate)

Answer 28

• 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