L12 - Panel Data Econometrics Flashcards

1
Q

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

A
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2
Q

What are the Linear Unobserved Effects Panel Data Models?

A
  • unobserved heterogeneity latent heterogeneity –> assuming constant over time
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3
Q

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

A
  • Pooled Model
  • Individual and Time Dummies
  • Fixed Effects Model
  • Random Effects Model
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4
Q

What is a Pooled Model?

A
  • 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)
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5
Q

What are the two types of Unobserved Effects models?

A
  • 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
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6
Q

What is the Fixed Effects methods transformation?

A
  • 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
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7
Q

What is the Random Effects model transformation?

A
  • 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
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8
Q

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

A
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9
Q

What is the Generalised Least Squares (GLS) Estimator?

A
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10
Q

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

A
  • 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
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11
Q

What is the difference between a balanced and unbalanced panel?

A
  • 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
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12
Q

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

A
  • 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
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13
Q

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

A
  • 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%
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14
Q

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

A
  • 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
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15
Q

Example of Hausman test to choice between two models?

A
  • 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
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