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Empirical Economics > Panel Data > Flashcards

Panel Data Flashcards

1
Q

Clustered standard errors are presented for the Pooled OLS results in Table #. Is there a need for clustering? Please motivate your answer.

A

The presence of random effects causes the error term to be autocorrelated. By clustering the standard errors, this has been taken into account.

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2
Q

What may cause the differences between the Pooled OLS and Random Effects results in table #.

A

The differences might be due to the difference in the exogenetiy assumption of each model.

The key assumption of the Random Effects estimator is strict exogeneity [𝐸(𝑢t|𝑋)= 0], while the key assumption of the OLS estimator is contemporaneous exogeneity [𝐸(𝑢t|𝑋t)= 0].

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3
Q

By taking first differences, the individual effect ai…

A

…is removed from the model.

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4
Q

…exogeneity is needed (no lagged dependent variable, no feedback effects) for consistency (unbiasedness) of the first-difference estimator.

A

strict exogeneity

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5
Q

Why would one use a First-Difference (FD) or a Fixed Effects (FE) estimator instead of a Random Effects estimator when estimating the panel equation? Based on the estimation results, was there a need for using a FD or FE estimator?

A

The Random Effects RE model assumes that the individual effect (ai) is uncorrelated with the explanatory variables.

The Fixed Effects FE model/estimator and the FD estimator allow for correlations between the individual effect (ai) and the explanatory variables.

Yes, the effects are (in absolute) more significant when using FE & FD estimators than a RE estimator. However, we do not know for sure and need to test FE vs RE using a Hausman test formally.

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6
Q

Claim: random effects yield significant t- statistics more easily than fixed effects.

A

TRUE

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7
Q

In the Hausman test, If H0 is true then…

A

…both estimators are unbiased (consistent) However, random effects yield smaller standard errors, so that it is preferred to fixed effects.

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8
Q

Why might a simple regression estimate be positive while the first differences and fixed effects estimators negative?

A

They differ because the first difference and fixed effects remove the effect of a fixed part of the estimator, ai, and they are negative because the ai was positively correlated with x.

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9
Q

Stata: how do you use first differences versus fixed effects regressions?

A

A
For first differences just set up for panel data, use “xtreg” and then “d.” in front of every variable. For fixed effects set up for panel data, use “xtreg”, and end with “, fe”

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10
Q

Why might you want to use a lagged version of a variable of interest in a fixed effects model?

A

You would want to include a lagged version in case the effect takes some time to show up.

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11
Q

The fixed effects model is…

A

…a method of estimating panel data equations that works by allowing each cross-sectional unit to have a different intercept.

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11
Q

When comparing estimates from an OLS regression and a fixed effects regression, why might the OLS estimate be positively biased?

A

There may be a correlation between unobserved effects and the explanatory variables in each time period, causing positive omitted variable bias. The fixed effects estimator removes such fixed effects from the error term, removing the bias.

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12
Q

What do the estimators of Fix Effects and First Differences have in common? And what are the consequences of the similarities

A

They allow for correlation between 𝑎, and the explanatory variables E(𝑎,| x1it … xkiT) ≠0

The assumption of strict exogeneity means that the regression equation contains no feedback mechanism and no lag of dependent variables.

The consequence of the similarities is that the parameter estimates of both estimators should be about the same (if the assumption of strict exogeneity is true)

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13
Q

In the Hausman test, If H0 is not rejected then…

A

RE is preferred over FE because RE yields smaller standard errors and corrects for the presence of autocorrelation in the error term.

If the RE estimator’s variance is less than the variance of the within estimator (FE), then RE yields significant t-statistics easier than FE. (therefore smaller s.e)

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14
Q

What can explain the difference between the RE and FX in table..

A

In the RE model, it is assumed that the ai and RHS are uncorrelated whereas in the FE they are allowed to be corrllated.

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15
Q

> reg D.HoursWork DL.HoursWork D.Wage DL.Wage Linear regression, cluster(nr);

Why might the First Difference estimator of the regression result table be inconsistent?

A

The model includes a lagged dependent variable so the strict exogeneity assumption is violated, leading to inconsistent (biased) estimates.

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15
Q

What does it mean that strict exogeneity is needed for consistency (unbiasedness) of the first- difference estimator?

A

no lagged dependent variable

no feedback effects

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16
Q

Claim: In the 1st Diff and Fixes Effects estimator we allow for correlation between the explanatory variable ai and the other explanatory variables x1it ,…xkit .

A

TRUE

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16
Q

Claim: contemporaneous exogeneity is sufficient enoight to prove consistency of the first-difference estimator bhat (fdif)

A

FALSE

contemporaneous exogeneity is too weak to prove consistency of the first-difference estimator.

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17
Q

Claim: Pooled OLS allows for correlation between the individual-specific effects ai and the RHS variables XkiT.

A

FALSE!

Pooled OLS is an estimator for a zero correlation between ai and the explanatory variables.

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18
Q

Which estimator models assume that the individual specific effect ai and the explanatory variables are uncorreleted?

A

Random Effects

Pooled OLS

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19
Q

Claim: In the Pooled OLS uit is uncorrelated with all of the explanatory variables and
ai.

A

TRUE

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20
Q

Claim: In pooled OLS there is always autocorrelation.

A

TRUE

21
Q

State the steps for the Pooled OLS estomarion precedure.

A
  • We started with the pooled OLS estimator.
  • Next, we checked for autocorrelation, using the Breusch
    Godfrey test.
  • The parameter on the lagged residual was statistically
    different from zero (t-value), there is AC as expected.
  • We re-estimated the model with the pooled OLS estimator,
    using clustered standard errors.
22
Q

Outline the First DIfference estimation procedure.

A
  • We started with the first-difference estimator bhat(fdif)
  • Next, we check for autocorrelation, using the Breusch Godfrey test.
  • The parameter on the lagged residual was statistically different from zero (t-value).
  • We re-estimated the model with the first-difference estimator, using clustered standard errors.
23
Q

Which panel data estimator methods allow for correlation between the ai and explanatory variables?

A
  1. First differences
  2. LSDV procedure
  3. FE Within estimation
24
Q

Claim: The FE and LSVD methods produce identical estimates for β.

A

True

25
Q

In the FE, the b.hat and ai are consistent if …

A

… we have many time observations T and many individuals (Large T and N)

26
Q

Is strict exogeneity needed in the FE method? What does that exclude?

A

Yes, strict exogeneity excludes lagged dependent variables and feedback effects.

27
Q

Claim: Contemporaneous exogeneity is too weak to prove the consistency of the fixed effects estimator.

A

True

We need strict exogeneity for the FE estimator to be consistent.

28
Q

Stata: xtreg y x, fe

What does the fe subcommand do?

A

subcommand fe tells Stata to apply the FE estimator

29
Q

Under the assumption of strict exogeneity, with estimation method yields a smaller SE between FE and First Diff. What does that mean?

A

Fixed-effect estimator gives smaller standard errors if there is strict exogeneity.

That means this estimator is more efficient.

29
Q

First-difference estimator is preferred over the Fixed Effects if…

A

…there is a unit root in the error terms ie follows a random walk.

29
Q

What do Fixed effects and First differences have in common? And what are the consequences of the similarities

A
  1. They allow for correlation between ai and the explanatory variables xi1,…xiT: E(ai | x1it,…, xkiT ) ≠ 0
  2. They assume strict exogeneity (which means that the regression equation contains no feedback mechanism and there is no lag of the dependent variable)

The consequence of the similarities is that the parameter estimates of both estimators should be about the same (if the assumption of strict exogeneity is true)

30
Q

Between FE and First Difference, which of the two estimation procedures is preferable?

A

It depends on the behaviour of the error term uit.

If it is a white noise error term, use Fixed Effects (within) estimation procedure.

If it follows a random walk ( uit = uit −1 + eit ), use the first-difference b.hat (fdif) .

31
Q

Which estimator methods assume that the individual specific effects ai and the explanatory variables are uncorrelated?

A
  1. Pooled OLS
  2. Random Effects
32
Q

Claim: Both random effects and pooled OLS allow for the inclusion of time-invariant individual variables (e.g. gender in a wage equation)

A

True

33
Q

Stata: The following commands refer to…

xtreg y x, fe
est store fixed
xtreg y x, re
Hausman fixed, force

A

… Hausman test

34
Q

If you run a Breush - Godfrey test and -0.5 is not in the [95% Conf. Inter.] that mean that we are testing..

A

wether we prefer the first-difference estimator above the fixed-effects estimator.

If -0.5 is not in [95% Conf. Inter.] : 1st Diff, not FE

35
Q

If there is heteroskedasticity Robust S.E. helps to obtain …

A

… unbiased s.e.

36
Q

How do estimators of fix effects and first differences differ, and what are the consequences of those differences?

A

They differ on the assumption about the error term uit:

In Fixed effects, the error term uit is independent over time and across individuals

In the First difference, uit is assumed that follows a random walk.

The consequence is that, under strict exogeneity, FE gives smaller standard errors thus FE is more efficient than the first difference. However, the first differences will be preferred if there is a unit root in the error terms.

37
Q

In a Hausman test if Chisquare > Critical Value then…

A

… then reject Ho, FE is preferred

38
Q

In case RE is preferred ( Hausman test if Chi2 - stat < Chi2 - critical ), explain why it is chosen over FE. Refer to the variance of the estimators.

A

Random Effects are preferred over Fixed Effects because

  1. It yields smaller Standard Errors and,
  2. Corrects for the presence of autocorrelation in the error term.

If the RE estimator’s variance is less than the variance of the within estimator (FE), then RE yields significant t-statistics easier than FE. (therefore smaller s.e)

39
Q

The model of Table 1 is estimated with a Random Effects estimator.

Which model assumption is relaxed if we would use a First- Difference estimator for the model given?

A

We allow for correlation of the individual specific effects ai and the explanatory variables when using the First- Difference estimator.

40
Q

The model of Table 1 is estimated with a Random Effects estimator.

Which model assumption is relaxed if we would use a Fixed Effects estimator for the model given?

A

We allow for correlation of the individual specific effects ai and the explanatory variables when using the Fixed effects (or First- Difference) estimator.

41
Q

In the context of the model estimated in Table 1. Which model assumption is tested with the Breusch-Godfrey test. Why is it important to conduct this test? What would be the consequence for the Breusch-Godfrey test if the assumption of strict exogeneity does not hold?

A

The Breusch - Godfrey test is conducted to test for autocorrelation in the error term.

It is important to conduct its test because if AC is present, then it affects the SE of the estimates.

This test can be conducted under both strict and contemporaneous exogeneity (unlike Durbin - Watson)

42
Q

In the context of the model estimated in Table 1. Which model assumption is tested with the Hausman test? Why is it important to conduct this test? What would be the consequence of the Hausman test if the assumption of strict exogeneity does not hold?

A

The Hausman test, tests if the unobserved/time-constant individual-specific effects are correlated with the explanatory variables.

If so, one needs to use a Fixed Effects estimator instead of the Random Effects estimator used for Table 1 (relates to importance).

If strict exogeneity does not hold, the Hausman test is invalid.

43
Q

Claim: We can conduct a Hausman test under contemoraneus exogenetiy.

A

False:

Strict exogeneity is needed for the Hausman test to be valid.

44
Q

In the FD method, the interpretation of the coefficients remains…

A

…in levels.

45
Q

Claim: Both RE and FE require strict exogeneity of the ai

A

False,

Only RE

46
Q

A Breusch-Pagan test for heteroskedasticity has been carried out. The p-value for this test is equal to 0.006. What do you conclude and what does it imply for the estimation results of Table 1

A

The null-hypothesis of homoscedasticity is rejected at a 1% level of significance (p-value is < 0.01). The slope coefficients are still unbiased/consistent but the standard errors need to be corrected for heteroscedasticity. This has been not been done (robust option, for instance). Hence, in the RE case the standard errors may be incorrect.

47
Q

The random effects model assumes that the firm specific effect (ai) is … with the explanatory variables

A

uncorrelated

48
Q

Claim: The fixed effects model/estimator allows for correlations between the firm specific effect (ai) and the explanatory variables.

A

True

49
Q

Claim: If we reject Ho in a Hausman test RE is inconsistent (biased estimates) and we proceed with Fixed Effects FE

A

True

50
Q

Suppose that there are feedback effects from firms’ investments on Y growth. Suppose also that the feedback effect is as such that X1 in the current period only affects Y in the next period.
What is the econometric problem of such a feedback effect when estimating the model of Table 3 with Least Squares? How would you solve this problem?

A

The econometric problem is that Y is correlated with the differenced error term (uit-uit-1).

Least Squares is no longer a consistent estimator (contemporaneous exogeneity does not hold, in the FD-model; or strict exogeneity does not hold in level & FD model)

That is, one could use lagged dependent variables as instruments.

51
Q

Suppose that you rejecy the H0 in a Breush - Pagan test what do you conclude concerning the estimates?

A

This means that the standard errors are incorrect and need to be adjusted. The adjustment is using robust standard errors

Empirical Economics (4 decks)

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