Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.

ERF Training Workshop Panel Data 1 Raimundo Soro - Catholic University of Chile

182 views

Published on

ERF Training on Advanced Panel Data Techniques Applied to Economic Modelling

29 - 31 October, 2018
Cairo, Egypt

Published in: Government & Nonprofit
  • Be the first to comment

ERF Training Workshop Panel Data 1 Raimundo Soro - Catholic University of Chile

  1. 1. 3 Warnings • Chileans speak very fast. I speak even faster slow me down if I rush or don’t finish sentences • I am very informal. My teaching is informal ask, reply and participate as much as possible. We all learn from this. • I am politically incorrect. Stop me if you feel offended.
  2. 2. ERF Training Workshop Panel Data 1 Raimundo Soto Instituto de Economía, PUC-Chile
  3. 3. MENU • INTRODUCTION • STATIC MODELS FOR CONTINUOUS VARIABLES • STATIC MODELS FOR DISCRETE VARIABLES • DYNAMIC MODELS FOR CONTINUOUS VARIABLES • DYNAMIC MODELS FOR DISCRETE VARIABLES 3
  4. 4. INTRODUCTION • Considerthe followingstatement : – Participationratesfor womeninthelabor marketis 25%(WorldBank,2018) • How do you“read”this information? – Case1:onequarterofthewomenparticipatesinthe labormarketall ofthetime,therestneverdoes – Case2:ineveryinstant,womenhave25%chanceof beinginthelabormarketand75%ofbeingoutof thelabormarket 4
  5. 5. INTRODUCTION • Case1:onequarterof thewomenparticipatesin the labor marketallof thetime, therestneverdoes • Women are heterogeneous • No turnover in the labor market for females • The best predictor of future labor market status is her current status 5
  6. 6. INTRODUCTION • Case2:in everyinstant,womenhave25%chanceof being inthelabor marketand75%of being outof the labor market • Women are homogeneous • Very high turnover in the labor market for females • The best predictor of future labor market status is her expected value: ¼, if being in the labor force is 1 and 0 otherwise 6
  7. 7. INTRODUCTION • Obviouslyitisneithercase1 norcase2exclusively • A betterwaytomodelthe phenomenonisas“the probability of awomenof certaincharacteristicsto participateinthemarketateveryinstantof time” • Forthis weneedpaneldata,i.e.,informationon the statusinthelabormarketofeverywoman“i”andher characteristicsattime“t” 7
  8. 8. INTRODUCTION • Panel Data – Repeated observations of the same individual in time – Repeated cross-sections and synthetic panels 8
  9. 9. INTRODUCTION • Advantages of Panel Data – True but not very relevant: • Increase in the degrees of freedom, improve on estimation precision, inferences and predictions. – True and very relevant: • Better management of heterogeneity and its evolution • Account for unobservable characteristics of the individuals that can potentially bias econometric results 9
  10. 10. INTRODUCTION • Consider the following true model 𝑃𝑖𝑡 = 𝛼𝑖 + 𝛽𝑋𝑖𝑡 + 𝜇𝑖𝑡 • Since 𝛼𝑖 cannot be observed, the estimated model is: 𝑃𝑖𝑡 = 𝛽𝑋𝑖𝑡 + 𝜀𝑖𝑡 • Where 𝜀𝑖𝑡 = 𝛼𝑖 + 𝜇𝑖𝑡 • If 𝑐𝑜𝑣(𝑋𝑖𝑡, 𝛼𝑖) ≠ 0, then 𝑝𝑙𝑖𝑚 𝛽 ≠ 𝛽 and the estimator is inconsistent (biased) 10
  11. 11. INTRODUCTION • Why is 𝛼𝑖 unobserved? – It cannot be truly observed (measured) – There are no data 11
  12. 12. INTRODUCTION • Case when it cannot be observed – Consider the “microeconomic case” of school performance (cross section) 𝑃𝑒𝑟𝑓𝑖 = 𝛼 + 𝛽1 𝑄𝑢𝑎𝑙𝑖 + 𝛽2 𝑆𝑡𝑢𝑑𝑦 +𝛽3 𝑃𝑎𝑟𝐸𝑑𝑖 + 𝜇𝑖 – Missing: natural ability of individuals 𝐴𝐵𝑖 (unobservable) – But 𝐴𝑏𝑖 could correlate with: • Parent’s Education, cov 𝑃𝑎𝑟𝐸𝑑𝑖, 𝐴𝑏𝑖 > 0 • School quality, cov 𝑄𝑢𝑎𝑙𝑖, 𝐴𝑏𝑖 > 0 • Study effort, cov 𝐻𝑜𝑟𝑎𝑠𝑖, 𝐴𝑏𝑖 < 0 12
  13. 13. INTRODUCTION • Case when data are not available – Consider “macroeconomic case” of consumption (time series) – 𝑁𝑡 consumers that consume according to permanent income hypothesis, 𝐶𝑃𝐼𝐻𝑡 = 𝑎0 + 𝑎1 𝑌𝑃𝑡 𝑃𝐼𝐻 + 𝜇 𝑡 where 𝑌𝑃𝑡 𝑃𝐼𝐻 = 𝑘 + 𝜃 𝑁𝑃𝑉(𝐸𝑡 𝑌𝑡+𝑖, 𝑟) and 𝑘 = 𝜃𝐴 𝑡 – 𝑀𝑡 consumers under liquidity constraints, 𝐶𝐿𝑄𝑡 = 𝑐0 + 𝑐1 𝑌𝑡 + 𝜀𝑡 13
  14. 14. INTRODUCTION • Data refers to aggregate consumption, i.e. 𝐶𝑡 = 𝐶𝑃𝐼𝐻𝑡+ 𝐶𝐿𝑄𝑡 • But the number of individuals in each group changes in time (heterogeneity) according to: – Business cycle – Financial sector development – Human capital levels • Hence, there will be selection bias 14
  15. 15. Type of Models • An ignorant estimator (pooled) • Individual effects estimator (fixed effects) • Sample-determined estimator (random effects) • Choice of models: – Hausman-Wu Test – Poolability Test • Practical examples in Stata 15
  16. 16. Consistency • Recall the OLS estimator of model 𝑦 = 𝑥𝛽 + 𝜀: 𝛽 = 𝑥′ 𝑥 −1 𝑥′ 𝑦 = 𝑐𝑜𝑣(𝑥, 𝑦) 𝑣𝑎𝑟(𝑥) • Then 𝛽 = 𝑥′ 𝑥 −1 𝑥′ 𝑥𝛽 + 𝜀 𝛽 = 𝛽 + 𝑥′ 𝑥 −1 𝑥′𝜀 • OLS estimator is consistent (unbiased) iff 𝑝𝑙𝑖𝑚 𝑥′ 𝜀 = 0 16

×