L12 - Panel Data Econometrics

Question 1

How do we represent Panel Data models as a linear equation?

Answer 1

Question 2

What are the Linear Unobserved Effects Panel Data Models?

Answer 2

• unobserved heterogeneity latent heterogeneity –> assuming constant over time

Question 3

What are the different types of Panel Data we will be looking at?

Answer 3

• Pooled Model
• Individual and Time Dummies
• Fixed Effects Model
• Random Effects Model

Question 4

What is a Pooled Model?

Answer 4

• if there is no correlation between unobserved effects and our explanatory variable –> you can just run OLS
  
  • Observations for the same cross-sectional unit will be correlated with each other (similar for individuals than across them)

Question 5

What are the two types of Unobserved Effects models?

Answer 5

• Most common panel econometric technique that is used in the world –> always be unobserved effects
• If unobserved heteroexogenity is not correlated with the explanatory variables ==> use random effects model
  
  • If it is –> used fixed effect model

Question 6

What is the Fixed Effects methods transformation?

Answer 6

• Takes the value of the dependent variable for each individual and averages them over time and subtracts that from each value of y
  
  • Average individual y over total period
• Same transformation with the error term
• What happens to the unobserved variables?
  
  • As they are constant over time, their average is constant and thus is cancelled out when you do the subtraction of the time averaged dependent variable
• PROBLEM:
  
  • If variables do not vary across time e.g. gender –> they will end up being dropped out of the model

Question 7

What is the Random Effects model transformation?

Answer 7

• If they are uncorrelated with the explanatory variable you can just put the unobserved heterogeneity in the error term
• This will cause the error terms for an individual to be correlated across time

Question 8

What is the variance-covariance matrix for the Random effects model?

Answer 8

Question 9

What is the Generalised Least Squares (GLS) Estimator?

Answer 9

Question 10

How do you decide whether you use a Fixed effects or Random effects model?

Answer 10

• If they arent correlated with the regressors –> used random effects model as it is more efficient
• Null: no correlated between unobserved values and the explanatory variable
  
  • If critical value > Chi-squared statistics
    
    • Or P-Value is less than 0.05
    • Reject the Null –> conclude that betas across different models are differemt and there is correlation between the variables

Question 11

What is the difference between a balanced and unbalanced panel?

Answer 11

• balanced
  
  • Have data for all individuals for every time period
• unbalanced
  
  • Have data for all individuals but may be incomplete e.g. one firm’s data may span the whole 14 year data set whereas another may only span 7 years

Question 12

What do you have to do in Stata when dealing with panel data?

Answer 12

• Let it know you are dealing with panel data!
  
  • Otherwise, it will treat each cross-sectional unit as if they are unrelated
• STATA COMMAND FOR THIS DATA SET:
• tsset firm fyear, yearly
  
  • panel variable: firm (unbalanced)
  • time variable: fyear, 1998 to 2014, but with gaps
  • delta: 1 year

Question 13

What can we conclude from the Random Effects model Stata output?

Answer 13

• We assume there is no correlation between the unobserved effects and the explanatory variables as part of this model
  
  • But they are contained in the error term, so we are actually causing correlation in the error terms of the same cross-sectional unit across time –> that why we use GLS estimator rather than OLS
• Wald test is the same as the F-test
  
  • null hypothesis that all the individuals are jointly statistically insignificant
• R-squared can be interpreted as normal for these model
  
  • ​6.52% of the variation in the data is explained by the four explanatory variables
• sigma_u –> standard deviation with groups
  
  • Sigma_e –> standard deviation overall
  • rho –> proportion of variance of the error term due to intraclass correlation of error terms
• RESULTS:
  
  • can interpret the direction of effects
  • data isn’t logged so we are looking at unit changes
    
    • So if employment increased by 1000 employees Return-on-Asset would increase by 0.000345 unit
  • IF DATA WAS LOG-LOG –> UNLIKE linear models, the panel data interpretation changes
    
    • Don’t need to time anything by 100 for a percentage
    • So if employment increased by 1%, Return-on-Asset would increase by 0.000345%
  • LOG-UNIT (dependent is only logged)
    
    • Coefficients now need to be multiplied by 100
      
      • So if employment increased by 1000, Return-on-Asset would increase by 0.0345%
  • UNIT-LOG (only explanatory is logged ([percentage change on unit changed)
    
    • Coefficients need to be divided by 100
      
      • So if employment increased by 1%, Return-on-Asset would increase by 0.00000345%

Question 14

What can we conclude from the Fixed Effects model Stata output?

Answer 14

• Very similar interpretation to the random effects
  
  • one thing to note is the difference in beta between the random and fixed models
    
    • If the coefficients are similar –> there is an indication that there is no correlation between the unobserved effects and the explanatory variables
    • If they differ largely there is an indication of correlation –> and only the fixed effect will produce reliable estimates
      
      • How close do they need to be aligned? If they are wildly different its obvious if they are close they use Hausman test to establish if they are
• Fixed Effect uses a F-test (same as Wald really) –> in this case jointly statistically significant

Question 15

Example of Hausman test to choice between two models?

Answer 15

• Hausman test looks at the statistically significant coefficient between the two models and groups them
  
  • And test if the difference between them is statistically significant
  • Null: is the difference between the coefficient is not systematic
  • If is it not rejected, it is concluded that the difference between the coefficient is very similar –> we can conclude there is not a correlation between the explanatory variables and the unobserved effects
    
    • Meaning both models produces consistent estimates
    • But as the random effect model is more efficient, it should be chosen
  • If the null is rejected, the correlation exist and only the fixed effect model will produce consistent estimates