panel data models with heterogeneous marginal effects
DESCRIPTION
NES 20th Anniversary Conference, Dec 13-16, 2012 Panel Data Models with Heterogeneous Marginal Effects (based on the article presented by Kirill Evdokimov at the NES 20th Anniversary Conference). Author: Kirill Evdokimov, Princeton UniversityTRANSCRIPT
Panel Data Models with Heterogeneous Marginal Effects
Kirill Evdokimov
Princeton University
The NES 20th Anniversary ConferenceDecember 14, 2012
Kirill Evdokimov (Princeton U) Nonlinear Panel Data Models 12/14/12 1 / 16
Based on two papers of mine:
“Identification and Estimation of a Nonparametric Panel Data Modelwith Unobserved Heterogeneity”
“Nonparametric Quasi-Differencing with Applications”
Kirill Evdokimov (Princeton U) Nonlinear Panel Data Models 12/14/12 2 / 16
Model
Yit = m (Xit , αi ) + Uit ; i = 1, . . . , n; t = 1, . . . ,T
i - individual, t - time period
Observed: Yit and XitUnobserved: αi - scalar heterogeneity, Uit - idiosyncratic shocks
function m (x , α) is not known
∂m (Xit , αi ) /∂x depends on αi ⇒ heterogeneous marginal effects
will ID m(x , α) and Fαi (α|Xit )distributions of the outcomes, counterfactuals
"what percentage of the treated would be better/worse off?"
Kirill Evdokimov (Princeton U) Nonlinear Panel Data Models 12/14/12 3 / 16
Model
Yit = m (Xit , αi ) + Uit ; i = 1, . . . , n; t = 1, . . . ,T
i - individual, t - time period
Observed: Yit and XitUnobserved: αi - scalar heterogeneity, Uit - idiosyncratic shocks
function m (x , α) is not known
∂m (Xit , αi ) /∂x depends on αi ⇒ heterogeneous marginal effects
will ID m(x , α) and Fαi (α|Xit )distributions of the outcomes, counterfactuals
"what percentage of the treated would be better/worse off?"
Kirill Evdokimov (Princeton U) Nonlinear Panel Data Models 12/14/12 3 / 16
Model
Yit = m (Xit , αi ) + Uit ; i = 1, . . . , n; t = 1, . . . ,T
i - individual, t - time period
Observed: Yit and XitUnobserved: αi - scalar heterogeneity, Uit - idiosyncratic shocks
function m (x , α) is not known
∂m (Xit , αi ) /∂x depends on αi ⇒ heterogeneous marginal effects
will ID m(x , α) and Fαi (α|Xit )distributions of the outcomes, counterfactuals
"what percentage of the treated would be better/worse off?"
Kirill Evdokimov (Princeton U) Nonlinear Panel Data Models 12/14/12 3 / 16
Model
Yit = m (Xit , αi ) + Uit ; i = 1, . . . , n; t = 1, . . . ,T
i - individual, t - time period
Observed: Yit and XitUnobserved: αi - scalar heterogeneity, Uit - idiosyncratic shocks
function m (x , α) is not known
Some assumptions:
E [Uit |Xit ] = 0 and Uit ⊥ αi |Xitno restrictions on Fαi (α|Xit = x) ⇒ fixed effects
no parametric assumptions; T = 2 is suffi cient
Yit must be cont.; also, no lagged dep. variables
Kirill Evdokimov (Princeton U) Nonlinear Panel Data Models 12/14/12 4 / 16
Motivation
Union Wage Premium
Yit = m (Xit , αi ) + Uit
Yit is (log)-wage,
Xit is 1 if member of a union, 0 o/w,
αi is skill and Uit is luck
m(1,αi)−m(0,αi) is union wage premium
When m (Xit , αi ) = Xitβ+ αi , it becomes
m (1, αi )−m (0, αi ) = β = const !
Kirill Evdokimov (Princeton U) Nonlinear Panel Data Models 12/14/12 5 / 16
Motivation
Union Wage Premium
Yit = m (Xit , αi ) + Uit
Yit is (log)-wage,
Xit is 1 if member of a union, 0 o/w,
αi is skill and Uit is luck
m(1,αi)−m(0,αi) is union wage premium may be NOT monotone in αi
When m (Xit , αi ) = Xitβ+ αi , it becomes
m (1, αi )−m (0, αi ) = β = const !
Kirill Evdokimov (Princeton U) Nonlinear Panel Data Models 12/14/12 5 / 16
Motivation (Yit = m (Xit , αi) + Uit)
Life Cycle Models of Consumption and Labor SupplyHeckman and MaCurdy (1980), MaCurdy (1981). Under theassumptions of these papers and ρ = r :
Cit = C (Wit ,λi )︸ ︷︷ ︸unknown fn.
+ Uit︸︷︷︸meas .err .
Cit and Wit - (log) consumption and hourly wageλi - Lagrange multiplier
Parametric specification of utility ⇒ additively separable λiInstead note that:
C (w ,λ) is unknownC (w ,λ) is strictly increasing in λ(unobserved) λi is likely to be correlated with Witcan handle this nonparametrically
Kirill Evdokimov (Princeton U) Nonlinear Panel Data Models 12/14/12 6 / 16
Motivation (Yit = m (Xit , αi) + Uit)
Life Cycle Models of Consumption and Labor SupplyHeckman and MaCurdy (1980), MaCurdy (1981). Under theassumptions of these papers and ρ = r :
Cit = C (Wit ,λi )︸ ︷︷ ︸unknown fn.
+ Uit︸︷︷︸meas .err .
Cit and Wit - (log) consumption and hourly wageλi - Lagrange multiplier
Parametric specification of utility ⇒ additively separable λiInstead note that:
C (w ,λ) is unknownC (w ,λ) is strictly increasing in λ(unobserved) λi is likely to be correlated with Witcan handle this nonparametrically
Kirill Evdokimov (Princeton U) Nonlinear Panel Data Models 12/14/12 6 / 16
Motivation (Yit = m (Xit , αi) + Uit)
Life Cycle Models of Consumption and Labor SupplyHeckman and MaCurdy (1980), MaCurdy (1981). Under theassumptions of these papers and ρ = r :
Cit = C (Wit ,λi )︸ ︷︷ ︸unknown fn.
+ Uit︸︷︷︸meas .err .
Cit and Wit - (log) consumption and hourly wageλi - Lagrange multiplier
Parametric specification of utility ⇒ additively separable λiInstead note that:
C (w ,λ) is unknownC (w ,λ) is strictly increasing in λ(unobserved) λi is likely to be correlated with Witcan handle this nonparametrically
Kirill Evdokimov (Princeton U) Nonlinear Panel Data Models 12/14/12 6 / 16
Motivation (Yit = m (Xit , αi) + Uit)
Life Cycle Models of Consumption and Labor SupplyHeckman and MaCurdy (1980), MaCurdy (1981). Under theassumptions of these papers and ρ = r :
Cit = C (Wit ,λi )︸ ︷︷ ︸unknown fn.
+ Uit︸︷︷︸meas .err .
Cit and Wit - (log) consumption and hourly wageλi - Lagrange multiplier
Parametric specification of utility ⇒ additively separable λiInstead note that:
C (w ,λ) is unknownC (w ,λ) is strictly increasing in λ(unobserved) λi is likely to be correlated with Witcan handle this nonparametrically
Kirill Evdokimov (Princeton U) Nonlinear Panel Data Models 12/14/12 6 / 16
Identification, Yit = m (Xit , αi) + Uit
1 Subpopulation Xi1 = Xi2 = x : thenm(Xi1, αi ) = m(Xi2, αi ) = m(x , αi )
Yi1 = m(x , αi ) + Ui1Yi2 = m(x , αi ) + Ui2
Yi1 − Yi2 = Ui1 − Ui2 =⇒ Obtain distr L (Uit |Xit = x)2 Deconvolve: Yit = m(Xit , αi )+Uit , αi ⊥Uit given Xit = x , thus
L (Yit |Xit = x)︸ ︷︷ ︸from data
= L (m (x , αi ) |Xit = x) ∗L (Uit |Xit = x)︸ ︷︷ ︸from step 1
,
where "∗" means "convolution" and "L" means "probability Law".Then obtain L (m (x , αi ) |Xit = x) by deconvolution
3 Use L (m (x , αi ) |Xit = x), eg. quantiles Qm(x ,αi )|Xit (q|x) [fornonparametric between- or within- variation] more
Kirill Evdokimov (Princeton U) Nonlinear Panel Data Models 12/14/12 7 / 16
Identification, Yit = m (Xit , αi) + Uit
1 Subpopulation Xi1 = Xi2 = x : thenm(Xi1, αi ) = m(Xi2, αi ) = m(x , αi )
Yi1 = m(x , αi ) + Ui1Yi2 = m(x , αi ) + Ui2
Yi1 − Yi2 = Ui1 − Ui2 =⇒ Obtain distr L (Uit |Xit = x)2 Deconvolve: Yit = m(Xit , αi )+Uit , αi ⊥Uit given Xit = x , thus
L (Yit |Xit = x)︸ ︷︷ ︸from data
= L (m (x , αi ) |Xit = x) ∗L (Uit |Xit = x)︸ ︷︷ ︸from step 1
,
where "∗" means "convolution" and "L" means "probability Law".Then obtain L (m (x , αi ) |Xit = x) by deconvolution
3 Use L (m (x , αi ) |Xit = x), eg. quantiles Qm(x ,αi )|Xit (q|x) [fornonparametric between- or within- variation] more
Kirill Evdokimov (Princeton U) Nonlinear Panel Data Models 12/14/12 7 / 16
Identification, Yit = m (Xit , αi) + Uit
1 Subpopulation Xi1 = Xi2 = x : thenm(Xi1, αi ) = m(Xi2, αi ) = m(x , αi )
Yi1 = m(x , αi ) + Ui1Yi2 = m(x , αi ) + Ui2
Yi1 − Yi2 = Ui1 − Ui2 =⇒ Obtain distr L (Uit |Xit = x)2 Deconvolve: Yit = m(Xit , αi )+Uit , αi ⊥Uit given Xit = x , thus
L (Yit |Xit = x)︸ ︷︷ ︸from data
= L (m (x , αi ) |Xit = x) ∗L (Uit |Xit = x)︸ ︷︷ ︸from step 1
,
where "∗" means "convolution" and "L" means "probability Law".Then obtain L (m (x , αi ) |Xit = x) by deconvolution
3 Use L (m (x , αi ) |Xit = x), eg. quantiles Qm(x ,αi )|Xit (q|x) [fornonparametric between- or within- variation] more
Kirill Evdokimov (Princeton U) Nonlinear Panel Data Models 12/14/12 7 / 16
Identification, Yit = m (Xit , αi) + Uit
1 Subpopulation Xi1 = Xi2 = x : thenm(Xi1, αi ) = m(Xi2, αi ) = m(x , αi )
Yi1 = m(x , αi ) + Ui1Yi2 = m(x , αi ) + Ui2
Yi1 − Yi2 = Ui1 − Ui2 =⇒ Obtain distr L (Uit |Xit = x)2 Deconvolve: Yit = m(Xit , αi )+Uit , αi ⊥Uit given Xit = x , thus
L (Yit |Xit = x)︸ ︷︷ ︸from data
= L (m (x , αi ) |Xit = x) ∗L (Uit |Xit = x)︸ ︷︷ ︸from step 1
,
where "∗" means "convolution" and "L" means "probability Law".Then obtain L (m (x , αi ) |Xit = x) by deconvolution
3 Use L (m (x , αi ) |Xit = x), eg. quantiles Qm(x ,αi )|Xit (q|x) [fornonparametric between- or within- variation] more
Kirill Evdokimov (Princeton U) Nonlinear Panel Data Models 12/14/12 7 / 16
Identification, Yit = m (Xit , αi) + Uit
1 Subpopulation Xi1 = Xi2 = x : thenm(Xi1, αi ) = m(Xi2, αi ) = m(x , αi )
Yi1 = m(x , αi ) + Ui1Yi2 = m(x , αi ) + Ui2
Yi1 − Yi2 = Ui1 − Ui2 =⇒ Obtain distr L (Uit |Xit = x)2 Deconvolve: Yit = m(Xit , αi )+Uit , αi ⊥Uit given Xit = x , thus
L (Yit |Xit = x)︸ ︷︷ ︸from data
= L (m (x , αi ) |Xit = x) ∗L (Uit |Xit = x)︸ ︷︷ ︸from step 1
,
where "∗" means "convolution" and "L" means "probability Law".Then obtain L (m (x , αi ) |Xit = x) by deconvolution
3 Use L (m (x , αi ) |Xit = x), eg. quantiles Qm(x ,αi )|Xit (q|x) [fornonparametric between- or within- variation] more
Kirill Evdokimov (Princeton U) Nonlinear Panel Data Models 12/14/12 7 / 16
Identification, Yit = m (Xit , αi) + Uit
1 Subpopulation Xi1 = Xi2 = x : thenm(Xi1, αi ) = m(Xi2, αi ) = m(x , αi )
Yi1 = m(x , αi ) + Ui1Yi2 = m(x , αi ) + Ui2
Yi1 − Yi2 = Ui1 − Ui2 =⇒ Obtain distr L (Uit |Xit = x)2 Deconvolve: Yit = m(Xit , αi )+Uit , αi ⊥Uit given Xit = x , thus
L (Yit |Xit = x)︸ ︷︷ ︸from data
= L (m (x , αi ) |Xit = x) ∗L (Uit |Xit = x)︸ ︷︷ ︸from step 1
,
where "∗" means "convolution" and "L" means "probability Law".Then obtain L (m (x , αi ) |Xit = x) by deconvolution
3 Use L (m (x , αi ) |Xit = x), eg. quantiles Qm(x ,αi )|Xit (q|x) [fornonparametric between- or within- variation] more
Kirill Evdokimov (Princeton U) Nonlinear Panel Data Models 12/14/12 7 / 16
Identification, Yit = m (Xit , αi) + Uit
1 Subpopulation Xi1 = Xi2 = x : thenm(Xi1, αi ) = m(Xi2, αi ) = m(x , αi )
Yi1 = m(x , αi ) + Ui1Yi2 = m(x , αi ) + Ui2
Yi1 − Yi2 = Ui1 − Ui2 =⇒ Obtain distr L (Uit |Xit = x)2 Deconvolve: Yit = m(Xit , αi )+Uit , αi ⊥Uit given Xit = x , thus
L (Yit |Xit = x)︸ ︷︷ ︸from data
= L (m (x , αi ) |Xit = x) ∗L (Uit |Xit = x)︸ ︷︷ ︸from step 1
,
where "∗" means "convolution" and "L" means "probability Law".Then obtain L (m (x , αi ) |Xit = x) by deconvolution
3 Use L (m (x , αi ) |Xit = x), eg. quantiles Qm(x ,αi )|Xit (q|x) [fornonparametric between- or within- variation] more
Kirill Evdokimov (Princeton U) Nonlinear Panel Data Models 12/14/12 7 / 16
Identification, Yit = m (Xit , αi) + Uit
1 Subpopulation Xi1 = Xi2 = x : thenm(Xi1, αi ) = m(Xi2, αi ) = m(x , αi )
Yi1 = m(x , αi ) + Ui1Yi2 = m(x , αi ) + Ui2
Yi1 − Yi2 = Ui1 − Ui2 =⇒ Obtain distr L (Uit |Xit = x)2 Deconvolve: Yit = m(Xit , αi )+Uit , αi ⊥Uit given Xit = x , thus
L (Yit |Xit = x)︸ ︷︷ ︸from data
= L (m (x , αi ) |Xit = x) ∗L (Uit |Xit = x)︸ ︷︷ ︸from step 1
,
where "∗" means "convolution" and "L" means "probability Law".Then obtain L (m (x , αi ) |Xit = x) by deconvolution
3 Use L (m (x , αi ) |Xit = x), eg. quantiles Qm(x ,αi )|Xit (q|x) [fornonparametric between- or within- variation] more
Kirill Evdokimov (Princeton U) Nonlinear Panel Data Models 12/14/12 7 / 16
Identification, Yit = m (Xit , αi) + Uit
1 Subpopulation Xi1 = Xi2 = x : thenm(Xi1, αi ) = m(Xi2, αi ) = m(x , αi )
Yi1 = m(x , αi ) + Ui1Yi2 = m(x , αi ) + Ui2
Yi1 − Yi2 = Ui1 − Ui2 =⇒ Obtain distr L (Uit |Xit = x)2 Deconvolve: Yit = m(Xit , αi )+Uit , αi ⊥Uit given Xit = x , thus
L (Yit |Xit = x)︸ ︷︷ ︸from data
= L (m (x , αi ) |Xit = x) ∗L (Uit |Xit = x)︸ ︷︷ ︸from step 1
,
where "∗" means "convolution" and "L" means "probability Law".Then obtain L (m (x , αi ) |Xit = x) by deconvolution
3 Use L (m (x , αi ) |Xit = x), eg. quantiles Qm(x ,αi )|Xit (q|x) [fornonparametric between- or within- variation] more
Kirill Evdokimov (Princeton U) Nonlinear Panel Data Models 12/14/12 7 / 16
Identification, Yit = m (Xit , αi) + Uit
1 Subpopulation Xi1 = Xi2 = x : thenm(Xi1, αi ) = m(Xi2, αi ) = m(x , αi )
Yi1 = m(x , αi ) + Ui1Yi2 = m(x , αi ) + Ui2
Yi1 − Yi2 = Ui1 − Ui2 =⇒ Obtain distr L (Uit |Xit = x)2 Deconvolve: Yit = m(Xit , αi )+Uit , αi ⊥Uit given Xit = x , thus
L (Yit |Xit = x)︸ ︷︷ ︸from data
= L (m (x , αi ) |Xit = x) ∗L (Uit |Xit = x)︸ ︷︷ ︸from step 1
,
where "∗" means "convolution" and "L" means "probability Law".Then obtain L (m (x , αi ) |Xit = x) by deconvolution
3 Use L (m (x , αi ) |Xit = x), eg. quantiles Qm(x ,αi )|Xit (q|x) [fornonparametric between- or within- variation] more
Kirill Evdokimov (Princeton U) Nonlinear Panel Data Models 12/14/12 7 / 16
Identification, Yit = m (Xit , αi) + Uit
1 Subpopulation Xi1 = Xi2 = x : thenm(Xi1, αi ) = m(Xi2, αi ) = m(x , αi )
Yi1 = m(x , αi ) + Ui1Yi2 = m(x , αi ) + Ui2
Yi1 − Yi2 = Ui1 − Ui2 =⇒ Obtain distr L (Uit |Xit = x)2 Deconvolve: Yit = m(Xit , αi )+Uit , αi ⊥Uit given Xit = x , thus
L (Yit |Xit = x)︸ ︷︷ ︸from data
= L (m (x , αi ) |Xit = x) ∗L (Uit |Xit = x)︸ ︷︷ ︸from step 1
,
where "∗" means "convolution" and "L" means "probability Law".Then obtain L (m (x , αi ) |Xit = x) by deconvolution
3 Use L (m (x , αi ) |Xit = x), eg. quantiles Qm(x ,αi )|Xit (q|x) [fornonparametric between- or within- variation] more
Kirill Evdokimov (Princeton U) Nonlinear Panel Data Models 12/14/12 7 / 16
More things in the paper
Time Effects: Yit = m (Xit , αi ) + ηt (Xit ) + Uit , η1 (x) ≡ 0Dynamic models, e.g., Yit = m (Xit , αi ) + Uit , Uit = ρUit−1 + εit
Measurement error in covariates
Multivariate unobserved heterogeneity
Yit = m(Xit , β
′iWit
)+ Uit
Estimation - conditional deconvolution
Simple. No optimization. Just run many kernel regressions andcompute a one-dimensional integral
Rates of convergence
Kirill Evdokimov (Princeton U) Nonlinear Panel Data Models 12/14/12 8 / 16
Empirical Illustration - Union Wage Premium
Data: Current Population Survey (CPS), T = 2matchingmigrationmeasurement errorlimited set of variables1987/1988, n = 17, 756 (replicating Card, 1996)
Most related papers: Card (1996) and Lemieux (1998)
Union Wage Premium
Yit = m (Xit , αi ) + Uit
Yit is (log)-wage,
Xit is 1 if member of a union, 0 o/w,
αi is skill and Uit is luck.
∆(α) = m (1, α)−m (0, α) is the union wage premium.Kirill Evdokimov (Princeton U) Nonlinear Panel Data Models 12/14/12 9 / 16
Empirical Illustration - Union Wage Premium
Data: Current Population Survey (CPS), T = 2matchingmigrationmeasurement errorlimited set of variables1987/1988, n = 17, 756 (replicating Card, 1996)
Most related papers: Card (1996) and Lemieux (1998)
Union Wage Premium
Yit = m (Xit , αi ) + Uit
Yit is (log)-wage,
Xit is 1 if member of a union, 0 o/w,
αi is skill and Uit is luck.
∆(α) = m (1, α)−m (0, α) is the union wage premium.Kirill Evdokimov (Princeton U) Nonlinear Panel Data Models 12/14/12 9 / 16
Empirical Illustration - Union Wage Premium
Data: Current Population Survey (CPS), T = 2matchingmigrationmeasurement errorlimited set of variables1987/1988, n = 17, 756 (replicating Card, 1996)
Most related papers: Card (1996) and Lemieux (1998)
Union Wage Premium
Yit = m (Xit , αi ) + Uit
Yit is (log)-wage,
Xit is 1 if member of a union, 0 o/w,
αi is skill and Uit is luck.
∆(α) = m (1, α)−m (0, α) is the union wage premium.Kirill Evdokimov (Princeton U) Nonlinear Panel Data Models 12/14/12 9 / 16
Empirical Illustration - Union Wage Premium
Data: Current Population Survey (CPS), T = 2matchingmigrationmeasurement errorlimited set of variables1987/1988, n = 17, 756 (replicating Card, 1996)
Most related papers: Card (1996) and Lemieux (1998)
Union Wage Premium
Yit = m (Xit , αi ) + Uit
Yit is (log)-wage,
Xit is 1 if member of a union, 0 o/w,
αi is skill and Uit is luck.
∆(α) = m (1, α)−m (0, α) is the union wage premium.Kirill Evdokimov (Princeton U) Nonlinear Panel Data Models 12/14/12 9 / 16
Empirical Illustration - Union Wage Premium
∆ (Qαi (0.25)) = 7.0%, ∆ (Qαi (0.5)) = 3.2%, ∆ (Qαi (0.75)) = 0.7%Kirill Evdokimov (Princeton U) Nonlinear Panel Data Models 12/14/12 10 / 16
Empirical Illustration - Union Wage Premium
∆ (Qαi (0.25)) = 7.0%, ∆ (Qαi (0.5)) = 3.2%, ∆ (Qαi (0.75)) = 0.7%Kirill Evdokimov (Princeton U) Nonlinear Panel Data Models 12/14/12 11 / 16
Empirical Illustration - Propensity Score
Also interested in P (Xit = 1|αi = a). Examples:
Kirill Evdokimov (Princeton U) Nonlinear Panel Data Models 12/14/12 12 / 16
Empirical Illustration - Propensity Score
Kirill Evdokimov (Princeton U) Nonlinear Panel Data Models 12/14/12 13 / 16
Alternative Model, Quasi-Differencing
We had
Yit = m (Xit , αi ) + Uit (1)
Identification is based on the NP first-differencing
Now consider
Yit = gt (Xit , αi + Uit ) (2)
Identification is based on the NP quasi-differencing
Applications:
Nonparametric panel (transformation) models
Duration model with multiple spells/states
A class of static games of incomplete information (e.g., Common ValueAuctions, Cournout with common demand parameter)
Also:
Yit = gt (Xit , βiWit + Uit ) (2′)
Kirill Evdokimov (Princeton U) Nonlinear Panel Data Models 12/14/12 14 / 16
Related Literature (incomplete list)
Linear and Semiparametric models:Chamberlain(1984,1992), Horowitz & Markatou (1996),Wooldridge(1997), Blundell, Griffi th, and Windmeijer (2002), Graham andPowell(2008), Graham, Hahn, and Powell (2009), Bonhomme(2010),Honore and Tamer (2006)
Nonparametric Panel Models:Altonji and Matzkin (2005), Arellano and Bonhomme (2011a,gb), Besterand Hansen (2007, 2009), Chernozhukov, Fernandez-Val, Hahn, andNewey (2009), Cunha, Heckman, and Schennach (2010), Hoderlein andWhite (2009), Hu and Shum (2009)
Transformation and Multiple Spell Duration Models:
Abbring and Ridder (2003, 2010), Abrevaya (1999), van den Berg (2001),Flinn and Heckman (1982,1983), Honoré (1993), Horowitz and Lee(2004), Lee (2008), Khan and Tamer (2009), Ridder (1990), and a list ofempirical applications
Kirill Evdokimov (Princeton U) Nonlinear Panel Data Models 12/14/12 15 / 16
Summary
Generalization of first-differencing and quasi-differencing approachesto nonlinear panel data models. Nonparametric identification
Allow identification of distributional, policy, and counterfactual effects
Are useful in a range of applied models
Estimation:
First-Differencing: a simple estimation procedure
Quasi-Differencing: sieve estimation
More details in the papers
Kirill Evdokimov (Princeton U) Nonlinear Panel Data Models 12/14/12 16 / 16