Applied Micro Economics

Question 1

Assumptions OLS

Answer 1

1. Linear in parameters
2. Random sampling
3. No perfect collinearity
4. Zero conditional mean
   (5) homoskedasticy
   (6) normality

Question 2

Linearitity in parameters

Answer 2

In the population model the dependent variable, y, is related to the independent variable, x, and the error, u as

Y=beta0 + beta1x +u

Question 3

No perfect collinearity

Answer 3

In the sample
• none of the independent variables is constant, and
• there are no exact linear relationships among the independent variables

Question 4

Panel data

Answer 4

Several observations in the same unit

Question 5

Exogene variable

Answer 5

No IV needed

Question 6

Endogene variable

Answer 6

IV needed
•related to the parameter
•whether we are able to obtain an estimate of the variable of interest that is in expectation the population parameter

Question 7

Idiosyncratic error term

Answer 7

Time varying component of the error term. Unique for each unit-time observation

Question 8

Error term alpha: unit heterogeneity

Answer 8

• The same for all observations of one unit
• Unique to each unit
• Time invariant component of the error term

Question 9

Estimater panel data

Answer 9

•un biased if both components of the error term are uncorrelated with the variable of interest

Question 10

Inefficiënt estimators

Answer 10

• produce incorrect standard errors
• are error terms correlated across time?
• unlikely that error terms are not correlated: you have to account for that
• efficiency is related to how precisely one can estimate the parameter…thus the standard erros and confidence interval

Question 11

Pooled OLS

Answer 11

•estimation of parameters using OLS on data combining multiple observations of units in the sample
•use if error term is uncorrelated with the variable of interest
• exploits al data variation
• is the Best Linear Unbiased Estimator (BLUE)
- zero conditional mean holds
- no serial correlation/ no autocorrelation
Assumptions:
1. Cov=0 (exogeneity assumption)
2. No serial correlation
3. Other MRL assumptions

Question 12

Fixed effects

Answer 12

• prefer FE unless estimating alpha is relevant
• use if idiosyncratic shock is uncorrelated with the variable of interest and the individual heterogeneity is correlated with the variable of interest.

Assumptions:

1. Cov=0 (strict exogeneity assumption)
2. Other MLR assumptions

Question 13

Least square dummy

Answer 13

• provides estimates for intercept alpha

* computationally burdensome since you need to estimate one additional parameters for each unit

Question 14

First difference FD

Answer 14

•Differentiates alpha out

Assumptions:

1. Cov=0 (strict exogeneity assumption)
2. Other MLR assumptions

Question 15

FE,LSDV & FD challenges

Answer 15

1. Only produce estimates from within variation therefore:
   - not possible to estimate the effect of time-invariant characteristics
   - Lesse efficiënt methods since they use a limited source of variation
2. Measurement error problems are more important
3. Strict exogeneity assumption

• to be unbiased the idiosyncratic shock must be uncorrelated with the variable of interest.
• if Pooled OLS is unbiased than FE/LSDV/FD is also unbiased

Question 16

RE model

Answer 16

• will be more similar to FE model when the individual heterogeneity has a larger share of the variation
• if FE is unbiased it is uncertain if RE will be unbiased
• if theta is 0 it implies that most of the variation is coming from an idiosyncratic shock. So it will look more like a pooled ols model
• use if error term is uncorrelated with the variable of interest

Question 17

CRE correlated random effects

Answer 17

Hypothesis gamma=0

Reject hypothesis:

• at least one component of the time variant averages influences the outcome, therefore it is likely that other unobserved components matter.
• alpha is likely correlated with the variable of interest: so use FE/LSDV/FD

Failure to reject hypothesis:

• likely that no other unobserved time variant components matter
• alpha is likely uncorrelated with the variable of interest: RE is unbiased and more efficient

Question 18

Panel data

Answer 18

Several observations in the same unit

Question 19

Exogene variable

Answer 19

No IV needed

Question 20

Endogene variable

Answer 20

IV needed

Question 21

Idiosyncratic error term

Answer 21

Time varying component of the error term. Unique for each unit-time observation

Question 22

Error term alpha: unit heterogeneity

Answer 22

• The same for all observations of one unit

* Unique to each unit

Question 23

Hausman test

Answer 23

•Compare FE and RE
•significant differences in time varying coefficients imply that time invariant characteristics matter:
-RE is likely to be biased
-FE is more appropriate to account for all time invariant characteristics.
• Non-significant differences in time varying coefficients imply that time invariant characteristics do NOT matter:
- RE liken to be unbiased
- RE is more appropriate since it is also more efficient

Question 24

RE random effects

Answer 24

Assumptions:

1. Cov=0
2. Other MRL assumptions

•more efficient than pooled OLS

Question 25

Attrition

Answer 25

Units drop from the sample:

• loss of follow up
• death
• refusal to remain in the survey

Also possible:
Item non-response; people do not respond to certain questions.

Question 26

Attrition test

Answer 26

Test whether being present is associated with outcomes.

Method:

• unit is available in all waves
• unit is available in the next wave
• number of waves individuals is present

Caution: not all methods can be used with fixed effects.

Question 27

All waves methods

Answer 27

Step1. Create binary indicator if unit is present in all waves
Step2. Run model including indicator as covariant
Step3. -interpret coefficient
-significant correlation implies missing non at random
-discuss how such misgivings could lead to bias

Question 28

Unit is available next wave method

Only method with FE

Answer 28

Step1. Create binary indicator if unit is present in next wave.
Step2. Run model including indicator as covariant
Step3: -interpret coefficient
-significant correlation implies missing non at random
-discuss how such missing could lead to bias

Question 29

Number of waves method

Answer 29

Step1: create continuous indicator for number of waves present
Step2: Run model including indicator as covariant
Step3: -interpret coefficient
-significant correlation implies missing non at random
-discuss how such missings could lead to bias

Question 30

DID main idea

Answer 30

1. -quasi-experimental approach
   
   • compares two groups
   • Assumes that all unobserved time-variant changes are common to both groups and therefore can be differentiated out one group to the other.
2. Complements panel data by accounting for unobserved time-variant changes… but not exclusive to panel data
3. Main idea: we can differentiate out the sources of bias by using two comparable groups where change in the treatment status is the only time-variant difference.

Question 31

DiD assumption

Answer 31

Correlation between e and x (treatment variable of interest) is constant

• trends of control and treatment group are similar in absence of treatment
• stable unit treatment value assumption (SUTVA)