Panel Data

Question 1

What is panel data?

Answer 1

Also called longitudinal data, are data for multiple entities in which each entity is observed at two or more periods.

Balanced & Unbalanced.

Pooled OLS: If individual effect does not exist. Does not take time-specific effects and variation across entities into account. If theres no cross-sectional or time specific effect, Pooled OLS can be used

Fixed Effects: 1) Control for unobserved variables that vary across entities but not over time, and 2) time specific effects that don’t vary across entities.

Can control for biases that control across entities, but not over time. For example, if you are analyzing Norwegian exports to the EU region, this variable can control for the French price sensitivity, which might be different to Polands.

You can also control for time specific effects. From the last example, if there EU issues a law, this will affect all of the buyers (not vary across entities).

Random Effects:
That entities have variables that individually varies over individual time. individual disturbance

Fixed: the different regressions have different intercept

Random: have individual disturbance

Question 2

What are the assumptions?

Answer 2

Same as OLS with some small adjustments

1.Error term must have a conditional mean of zero WITH ALL OBSERVATIONS OF THE VARIABLE X: so there shall be no past, present, future interactions between x and u. a - good profit one year does not mean anything the next year?

2. I.I.D ACROSS ENTITES: this one is not the same as in a regular OLS.
   - observations within an entity can correlate, X - autocorrelation allowed
   - Autocorr: a firms income one week can affect the income the next week. BUT, Firm A’s income cannot affect firm B’s
3. large outliers unlikely
4. no perfect multicorr

Question 3

How can the fixed regression be done?

Answer 3

1. Binary regression
2. Entity demeanded
3. First diff specification

Entity demeaned the way to go

Question 4

How can you do entity demeandet regression in R

Answer 4

Use plm-package with the “within” function. Next use “coeftest” and its function “vcovGC”. This will extract the heteroskedasticy and handle the autocorrelation.

Question 5

Why are panel data useful?

Answer 5

With panel data you can control for factors that:

(1) vary across entities but do not vary over time,
(2) could cause omitted variable bias if they are omitted,
(3) are unobserved or unmeasured – and therefore cannot be included in the regression using multiple regression.

The key idea: if an omitted variable does not change over time, then any changes in y over time cannot be caused by the omitted variable

Question 6

Describe the differences and equalities in the regressions if you have a entity fixed regression

Answer 6

The intercept is unique for each entity, but the slope is the same for all.
Recall that shifts in the intercept can be represented using binary regressors

Question 7

What is Time Fixed Effects regression?

Answer 7

An omitted variable might vary over time but not across states. This can for example be safer cars or changes in national laws. These produce intercepts that change over time. We use S to find the combined effect of variables with changes over time that are same for each entity.

Question 8

Why do we use clustered standard error?

Answer 8

The usual OLS standard errors will in general be wrong, because they assume that the error term is not autocorrelated. The solution for this is to use clustered standard errors. We allow for autocorrelation WITHIN entities. Are also robust for heteroskedasticy within and across entities.

Question 9

what is the main advantage of panel data

Answer 9

we are able to allow for certain forms of unobserved individual heterogeneity that is constant over time which cannot be done with cross-sectional or time-series

Question 10

do you need cluster robust standard errors for pooled OLS

Answer 10

yes, standard errors don’t take the serial correlation of vit into account will be wrong,
need cluster rob se unless σσ^2=0 (2nd σ subscript)

Question 11

what is heterogeneity

Answer 11

the quality or state of being diverse in character or content

Question 12

In panel data, is omitted variables a problem?

Answer 12

No, assuming the ommited variable does not change over time, the change in Y must be caused by the observed factors

Question 13

What is a fixed effects model?

Answer 13

A regression performed on panel data to test the effect of being in state i. The model can be either entity demeaned, time demeaned or both. All regressions will have the same slope, but different intersections.

Question 14

Pick Fixed Effects versus Pooled OLS

Answer 14

F-test or Wald Test

When H0 is rejected

Question 15

Pooled OLS vs Random Effects

Answer 15

Breusch-Pagan LM test

LM = Linear Model

Question 16

Pooled OLS

Answer 16

If theres no cross-sectional or time specific effect, Pooled OLS can be used

Question 17

Standard Errors

Answer 17

• Standard errors are found under the assumption that there is no autocorrelation or heterosced
• so the given standard error cannot be used
• that is why we use Clustered Standard Errors. They allow for heterosked and multicorr WITHIN an entity, but not across.
• multicorr and heterosked does not affect coefficient value, only standard error
• clustered: allows for heterosked and autocorr

Question 18

What is Pooled OLS

Answer 18

• no individual effects

- no time specific effects or variation across entities

Question 19

What is the difference in the assumptions?

Answer 19

1. Error term must have mean of zero FOR ALL OBSERVATIONS OF THE VARIABLE X. past, present and future
2. I.I.D ACCROS Entitites:
   - observations within an entity can autocorr, but not corr across entities

(3. large outliers unlikely
4. no perfect multicorr)

Question 20

Fixed effect panel data model regression will look like:

Answer 20

The different regressions will have different intercepts. The variable that controls for omitted biases and Time Fixed Effects will be the same across the panel

Question 21

Random effect model looks like:

Answer 21

All regressions have individual disturbance which make them individual

Question 22

SER is found under the assumption that _______.

That is why we use ______

Answer 22

tandard errors are found under the assumption that there is no autocorrelation or heterosced

• so the given standard error cannot be used
• that is why we use Clustered Standard Errors. They allow for heterosked and multicorr WITHIN an entity, but not across.