ERF Training on Advanced Panel Data Techniques Applied to Economic Modelling 29 - 31 October, 2018 Cairo, Egypt

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. ERF Training Workshop
Panel Data 1
Raimundo Soto
Instituto de Economía, PUC-Chile

3. MENU
• INTRODUCTION
• STATIC MODELS FOR CONTINUOUS VARIABLES
• STATIC MODELS FOR DISCRETE VARIABLES
• DYNAMIC MODELS FOR CONTINUOUS VARIABLES
• DYNAMIC MODELS FOR DISCRETE VARIABLES
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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
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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
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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
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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”
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8. INTRODUCTION
• Panel Data
– Repeated observations of the same individual in time
– Repeated cross-sections and synthetic panels
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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
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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)
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11. INTRODUCTION
• Why is 𝛼𝑖 unobserved?
– It cannot be truly observed (measured)
– There are no data
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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
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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
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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
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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
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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
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