Flashcards in Panel Deck (16)

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1

## 2 assumptions for short T

###
yi, Xi independent over i

parameters in B are common to all i

2

## 2 assumptions for short T

###
yi, Xi independent over i

parameters in B are common to all i

3

## What does predetermined mean?

###
E(xitvit)=0

do not rule out correlations with past v

4

##
Pooled OLS

Consistent?

Efficient?

###
just stack all observations and treat them the same so then just to ols

require x predetermined, uncorrelated with individual effects in the errors to be consistent

Error serially correlated due to individual effects so use cluster-robust standard errors for inference, causes inefficiency

5

##
Within Groups (or fixed effects)

Assumption for consistency in short-T

Can it work with lagged dependent variable ie yit-1?

Alternative method of getting same estimator

Degrees of freedom

###
transform variables by subtracting their mean over time ie sum in t / T

Strict exogeneity: E(xitvis)=0 for all s, t past present and future. If this satisfied, consistency does not require vit to be serially uncorrelated

Does not work with yit-1 as an explanatory variable as necessarily correlated with vit-1

If believe serially correlated errors then report cluster-robust std errors

Can also get same estimator by doing least squares dummy variables (adding dummies for each i=1,...,N)

Hence degrees of freedom=NT-K-N (=N(T-1)-N)

6

##
FDOLS

Condition required for consistency

When would classical standard errors be appropriate

###
First differenced OLS

Lose one equation by doing it (ie 1 t)

E(DxitDvit)=0 where D is 1st diff operator. Ie rules out feedback from vi,t-1 to xit but not from longer lags

if Dvit=white noise (ie vit random walk). Vit serially uncorrelated would lead Dvit to be serially correlated so use cluster-robust

7

##
Most efficient estimator if ni endogenous but vit iid?

if vit is a random walk?

###
WG

FDOLS

Both from Gauss-Markov theorem

8

## When are FDOLS and WG the same?

### T=2

9

## If one explanatory variable in xit is a step function, not good for which type of estimator?

###
FDOLS

As could lead to lots of Dxit=0

10

## Long T consistency condition for WG

### E(xitvit)=0 ie only need predetermined

11

## Long T consistency condition for WG

###
Exactly the same as short T:

E(DxitDvit)=0 so not as good as WG in this case

12

## Are FDOLS or WG efficient if ni is uncorrelated with explanatory variables

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No

lose information by differencing away

13

##
Between groups estimator

Consistency requirements

Efficient

###
regress the time mean of y on the time mean of x (still have variation from different i) Leaves the ni term

error term contains ni and all vi1, vi2,... so requires uncorrelated individual effects and strictly exogenous covariates

Not efficient

14

##
Random effects GLS estimator

when to use

Efficient?

How can it be computed using ols on a transformed model?

###
Compute omega matrix which is E(uu') (NTxNT) which is a diagonal matrix with E(uiui') (TxT) on the diagonal. E(ui,ui')=variance of ni not on the diagonals and the sum of the variances of ni and vit on the diagonal.

Then Bgls=(X'omega^-1X)^-1X'omega^-1y

use when both ni and vit exogenous (but still can have serial correlation as uit=ni+vit), very restrictive assumptions

Yes is efficient under these circumstances

transformed variables yit*=yit-(1-theta) x time mean yi

theta=variance of vit/(variance of vit+Tvariance of ni)

15

## Feasible GLS

### Obtain estimates for the variances of n and v from the WG and between groups estimators and then do Random effects GLS

16