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Econometric Analysis of Panel Data

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Title: Econometric Analysis of Panel Data


1
Econometric Analysis of Panel Data
  • William Greene
  • Department of Economics
  • Stern School of Business

2
Econometric Analysis of Panel Data
  • 20. Sample Selection and Attrition

3
Received Sunday, April 27, 2014 I have a paper
regarding strategic alliances between firms, and
their impact on firm risk. While observing how a
firms strategic alliance formation impacts its
risk, I need to correct for two types of
selection biases. The reviews at Journal of
Marketing asked us to correct for the propensity
of firms to enter into alliances, and also the
propensity to select a specific partner, before
we examine how the partnership itself impacts
risk. Our approach involved conducting a probit
of alliance formation propensity, take the
inverse mills and include it in the second
selection equation which is also a probit of
partner selection. Then, we include inverse mills
from the second selection into the main model.
The review team states that this is not correct,
and we need an MLE estimation in order to
correctly model  the set of three equations. The
Associate Editors point is given below. Can you
please provide any guidance on whether this is a
valid criticism of our approach. Is there a
procedure in LIMDEP that can handle this set of
three equations with two selection probit
models? AEs comment Please note that the
procedure of using an inverse mills ratio is only
consistent when the main equation where the ratio
is being used is linear. In non-linear cases
(like the second probit used by the authors),
this is not correct. Please see any standard
econometric treatment like Greene or Wooldridge.
A MLE estimator is needed which will be far from
trivial to specify and estimate given error
correlations between all three equations.
4
Hello Dr. Greene, My name is xxxxxxxxxx and I go
to the University of xxxxxxxx. I see that you
have an errata page on your website of your
econometrics book 7th edition. It seems like you
want to correct all mistakes so I think I have
spotted a possible proofreading error. On page
477 (theorem 13.2) you want to show that theta is
consistent and you say that "But, at the true
parameter values, qn(?0) ?0. So, if (13-7) is
true, then it must follow that qn(?ˆGMM) ??0 as
well because of the identification assumption" I
think in the second line it should be  qn(?ˆGMM)
? 0,  not ?0.
5
I also have a questions about nonlinear GMM -
which is more or less nonlinear IV technique I
suppose. I am running a panel non-linear
regression  (non-linear in the parameters) and I
have L parameters and K exogenous variables with
LgtK. In particular my model looks kind of like
this  Y   b1Xb2 e, and so I am trying to
estimate the extra b2 that don't usually appear
in a regression. From what I am reading, to run
nonlinear GMM I can use the K exogenous variables
to construct the orthogonality conditions but
what should I use for the extra, b2
coefficients? Just some more possible IVs (like
lags) of the exogenous variables? I agree that by
adding more IVs you will get a more efficient
estimation, but isn't it only the case when you
believe the IVs are truly uncorrelated with the
error term? So by adding more "instruments" you
are more or less imposing more and more
restrictive assumptions about the model (which
might not actually be true). I am asking because
I have not found sources comparing nonlinear
GMM/IV to nonlinear least squares.  If there is
no homoscadesticity/serial correlation what is
more efficient/give tighter estimates?
6
(No Transcript)
7
Dueling Selection Biases From two emails, same
day.
  • I am trying to find methods which can deal with
    data that is non-randomised and suffers from
    selection bias.
  • I explain the probability of answering questions
    using, among other independent variables, a
    variable which measures knowledge
    breadth. Knowledge breadth can be constructed
    only for those individuals that fill in a skill
    description in the company intranet. This is
    where the selection bias comes from.

8
The Crucial Element
  • Selection on the unobservables
  • Selection into the sample is based on both
    observables and unobservables
  • All the observables are accounted for
  • Unobservables in the selection rule also appear
    in the model of interest (or are correlated with
    unobservables in the model of interest)
  • Selection Biasthe bias due to not accounting
    for the unobservables that link the equations.

9
A Sample Selection Model
  • Linear model
  • 2 step
  • ML Murphy Topel
  • Binary choice application
  • Other models

10
Canonical Sample Selection Model
11
Applications
  • Labor Supply model
  • ywage-reservation wage
  • dlabor force participation
  • Attrition model Clinical studies of medicines
  • Survival bias in financial data
  • Income studies value of a college application
  • Treatment effects
  • Any survey data in which respondents self select
    to report
  • Etc

12
Estimation of the Selection Model
  • Two step least squares
  • Inefficient
  • Simple exists in current software
  • Simple to understand and widely used
  • Full information maximum likelihood
  • Efficient
  • Simple exists in current software
  • Not so simple to understand widely misunderstood

13
Heckmans Model
14
Two Step Estimation
The LAMBDA
15
FIML Estimation
16
Classic Application
  • Mroz, T., Married womens labor supply,
    Econometrica, 1987.
  • N 753
  • N1 428
  • A (my) specification
  • LFPf(age,age2,family income, education, kids)
  • Wageg(experience, exp2, education, city)
  • Two step and FIML estimation

17
Selection Equation
---------------------------------------------
Binomial Probit Model
Dependent variable LFP
Number of observations 753
Log likelihood function -490.8478
---------------------------------------------
----------------------------------------------
------------------ Variable Coefficient
Standard Error b/St.Er.PZgtz Mean of
X -------------------------------------------
--------------------- ---------Index function
for probability Constant -4.15680692
1.40208596 -2.965 .0030 AGE
.18539510 .06596666 2.810 .0049
42.5378486 AGESQ -.00242590
.00077354 -3.136 .0017 1874.54847 FAMINC
.458045D-05 .420642D-05 1.089 .2762
23080.5950 WE .09818228
.02298412 4.272 .0000 12.2868526 KIDS
-.44898674 .13091150 -3.430 .0006
.69588313
18
Heckman Estimator and MLE
19
Extension Treatment Effect
20
Sample Selection
21
Extensions Binary Data
22
Panel Data and Selection
23
Panel Data and Sample Selection Models A
Nonlinear Time Series
  • I. 1990-1992 Fixed and Random Effects
    Extensions
  • II. 1995 and 2005 Model Identification through
    Conditional Mean Assumptions
  • III. 1997-2005 Semiparametric Approaches based
    on Differences and Kernel Weights
  • IV. 2007 Return to Conventional Estimators,
    with Bias Corrections

24
Panel Data Sample Selection Models
25
Zabel Economics Letters
  • Inappropriate to have a mix of FE and RE models
  • Two part solution
  • Treat both effects as fixed
  • Project both effects onto the group means of the
    variables in the equations
  • Resulting model is two random effects equations
  • Use both random effects

26
Selection with Fixed Effects
27
Practical Complications
The bivariate normal integration is actually the
product of two univariate normals, because in the
specification above, vi and wi are assumed to be
uncorrelated. Vella notes, however, given the
computational demands of estimating by maximum
likelihood induced by the requirement to evaluate
multiple integrals, we consider the applicability
of available simple, or two step procedures.
28
Simulation
The first line in the log likelihood is of the
form Ev?d0?() and the second line is of the
form EwEv?()?()/?. Using simulation
instead, the simulated likelihood is
29
Correlated Effects
Suppose that wi and vi are bivariate standard
normal with correlation ?vw. We can project wi
on vi and write wi ?vwvi (1-?vw2)1/2hi where
hi has a standard normal distribution. To allow
the correlation, we now simply substitute this
expression for wi in the simulated (or original)
log likelihood, and add ?vw to the list of
parameters to be estimated. The simulation is
then over still independent normal variates, vi
and hi.
30
Conditional Means
31
A Feasible Estimator
32
Estimation
33
Kyriazidou - Semiparametrics
34
Bias Corrections
  • Val and Vella, 2007 (Working paper)
  • Assume fixed effects
  • Bias corrected probit estimator at the first step
  • Use fixed probit model to set up second step
    Heckman style regression treatment.

35
Postscript
  • What selection process is at work?
  • All of the work examined here (and in the
    literature) assumes the selection operates anew
    in each period
  • An alternative scenario Selection into the
    panel, once, at baseline.
  • Why arent the time invariant components
    correlated? (Greene, 2007, NLOGIT development)
  • Other models
  • All of the work on panel data selection assumes
    the main equation is a linear model.
  • Any others? Discrete choice? Counts?

36
Sample Selection
37
TECHNICAL EFFICIENCY ANALYSIS CORRECTING FOR
BIASES FROM OBSERVED AND UNOBSERVED VARIABLES
AN APPLICATION TO A NATURAL RESOURCE MANAGEMENT
PROJECT Empirical Economics Volume 43, Issue 1
(2012), Pages 55-72
  • Boris Bravo-Ureta
  • University of Connecticut
  • Daniel Solis
  • University of Miami
  • William Greene New York University

38
The MARENA Program in Honduras
  • ? Several programs have been implemented to
    address resource degradation while also
    seeking to improve productivity, managerial
    performance and reduce poverty (and in some
    cases make up for lack of public support).
  • ? One such effort is the Programa Multifase de
    Manejo de Recursos Naturales en Cuencas
    Prioritarias or MARENA in Honduras focusing
    on small scale hillside farmers.

39
OVERALL CONCEPTUAL FRAMEWORK
Training Financing
More Production and Productivity
MARENA
Natural, Human Social Capital
More Farm Income
Off-Farm Income
Sustainability
Working HYPOTHESIS if farmers receive private
benefits (higher income) from project activities
(e.g., training, financing) then adoption is
likely to be sustainable and to generate positive
externalities.
40
The MARENA Program
  • ? COMPONENT I Strengthening Strategic
    Management Capabilities among Govt.
    Institutions (central and local)
  • ? COMPONENT II Support to Nat. Res. Management.
    Projects
  • ? Module 1 Promotion and Organization
  • ? Modulo 2 Strengthening Local Institutions
    Organizations
  • ? Module 3 Investment (farm, municipal
    regional)
  • ? COMPONENT III Administration and Supervision

41
Component II - Module 3
  • ? Component II - Module 3 focused on promoting
    investments in sustainable production
    systems with a budget of US 7.6 million
    (Bravo-Ureta, 2009).
  • ? The major activities undertaken with
    beneficiaries training in business
    management and sustainable farming practices and
    the provision of funds to co-finance
    investment activities through local rural savings
    associations (cajas rurales).

42
Conclusions
Rural poverty in Honduras, largely due to policy
driven unsustainable land use gt environmental
degradation, productivity losses, food
insecurity, growing climatic vulnerability
(GEF-IFAD, 2002).
43
Expected Impact Evaluation
44
Methods
  • ? A matched group of beneficiaries and control
    farmers is determined using Propensity Score
    Matching techniques to mitigate biases that
    would stem from selection on observed
    variables.
  • ? In addition, we deal with possible
    self-selection on unobservables arising from
    unobserved variables using a selectivity
    correction model for stochastic frontiers
    introduced by Greene (2010).

45
A Sample Selected SF Model
di 1?'zi hi gt 0, hi N0,12 yi
? ?'xi ?i, ?i N0,??2 (yi,xi)
observed only when di 1. ?i vi - ui ui
?uUi where Ui N0,12 vi ?vVi
where Vi N0,12. (hi,vi) N2(0,1), (1,
??v, ?v2)
46
Simulated logL for the Standard SF Model
This is simply a linear regression with a random
constant term, ai a - su Ui
47
Likelihood For a Sample Selected SF Model
48
Simulated Log Likelihood for a Selectivity
Corrected Stochastic Frontier Model
The simulation is over the inefficiency term.
49
JLMS Estimator of ui
50
Closed Form for the Selection Model
  • ? The selection model can be estimated without
    simulation
  • ? The stochastic frontier model with
    correction for sample selection revisited.
    Lai, Hung-pin. Forthcoming, JPA
  • ? Based on closed skew normal distribution
  • ? Similar to Maddalas 1982 result for the
    linear selection model. See slide 42.
  • ? Not more computationally efficient.
  • ? Statistical properties identical.
  • ? Suggested possibility that simulation chatter
    is an element of inefficiency in the
    maximum simulated likelihood estimator.

51
Closed Form vs. Simulation
Spanish Dairy Farms Selection based on being
farm 1-125. 6 periods
The theory works.
52
Variables Used in the Analysis
Production
Participation
53
Findings from the First Wave
54
A Panel Data Model
  • ? Selection takes place only at the baseline.
  • ? There is no attrition.

55
Simulated Log Likelihood
56
Main Empirical Conclusions from Waves 0 and 1
  • Benefit group is more efficient in both years
  • The gap is wider in the second year
  • Both means increase from year 0 to year 1
  • Both variances decline from year 0 to year 1

57
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58
Attrition
  • In a panel, t1,,T individual I leaves the
    sample at time Ki and does not return.
  • If the determinants of attrition (especially the
    unobservables) are correlated with the variables
    in the equation of interest, then the now
    familiar problem of sample selection arises.

59
Application of a Two Period Model
  • Hemoglobin and Quality of Life in Cancer
    Patients with Anemia,
  • Finkelstein (MIT), Berndt (MIT), Greene (NYU),
    Cremieux (Univ. of Quebec)
  • 1998
  • With Ortho Biotech seeking to change labeling
    of already approved drug erythropoetin.
    r-HuEPO

60
QOL Study
  • Quality of life study
  • i 1, 1200 clinically anemic cancer patients
    undergoing chemotherapy, treated with
    transfusions and/or r-HuEPO
  • t 0 at baseline, 1 at exit. (interperiod survey
    by some patients was not used)
  • yit self administered quality of life survey,
    scale 0,,100
  • xit hemoglobin level, other covariates
  • Treatment effects model (hemoglobin level)
  • Background r-HuEPO treatment to affect Hg level
  • Important statistical issues
  • Unobservable individual effects
  • The placebo effect
  • Attrition sample selection
  • FDA mistrust of community based not clinical
    trial based statistical evidence
  • Objective when to administer treatment for
    maximum marginal benefit

61
Dealing with Attrition
  • The attrition issue Appearance for the second
    interview was low for people with initial low QOL
    (death or depression) or with initial high QOL
    (dont need the treatment). Thus, missing data at
    exit were clearly related to values of the
    dependent variable.
  • Solutions to the attrition problem
  • Heckman selection model (used in the study)
  • ProbPresent at exitcovariates F(z?) (Probit
    model)
  • Additional variable added to difference model ?i
    F(zi?)/F(zi?)
  • The FDA solution fill with zeros. (!)

62
An Early Attrition Model
63
Methods of Estimating the Attrition Model
  • Heckman style selection model
  • Two step maximum likelihood
  • Full information maximum likelihood
  • Two step method of moments estimators
  • Weighting schemes that account for the survivor
    bias

64
Selection Model
65
Maximum Likelihood
66
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67
A Model of Attrition
  • Nijman and Verbeek, Journal of Applied
    Econometrics, 1992
  • Consumption survey (Holland, 1984 1986)
  • Exogenous selection for participation (rotating
    panel)
  • Voluntary participation (missing not at random
    attrition)

68
Attrition Model
69
Selection Equation
70
Estimation Using One Wave
  • Use any single wave as a cross section with
    observed lagged values.
  • Advantage Familiar sample selection model
  • Disadvantages
  • Loss of efficiency
  • One can no longer distinguish between state
    dependence and unobserved heterogeneity.

71
One Wave Model
72
Maximum Likelihood Estimation
  • See Zabels model in slides 20 and 23.
  • Because numerical integration is required in one
    or two dimensions for every individual in the
    sample at each iteration of a high dimensional
    numerical optimization problem, this is, though
    feasible, not computationally attractive.
  • The dimensionality of the optimization is
    irrelevant
  • This is much easier in 2015 than it was in 1992
    (especially with simulation) The authors did the
    computations with Hermite quadrature.

73
Testing for Selection?
  • Maximum Likelihood Results
  • Covariances were highly insignificant.
  • LR statistic0.46.
  • Two step results produced the same conclusion
    based on a Hausman test
  • ML Estimation results looked like the two step
    results.

74
A Dynamic Ordered Probit Model
75
Random Effects Dynamic Ordered Probit Model
76
A Study of Health Status in the Presence of
Attrition
  • THE DYNAMICS OF HEALTH IN THE BRITISH HOUSEHOLD
    PANEL SURVEY,
  • Contoyannis, P., Jones, A., N. Rice
  • Journal of Applied Econometrics, 19, 2004,
  • pp. 473-503.
  • Self assessed health
  • British Household Panel Survey (BHPS)
  • 1991 1998 8 waves
  • About 5,000 households

77
Attrition
78
Testing for Attrition Bias
Three dummy variables added to full model with
unbalanced panel suggest presence of attrition
effects.
79
Attrition Model with IP Weights
Assumes (1) Prob(attritionall data)
Prob(attritionselected variables)
(ignorability) (2) Attrition is
an absorbing state. No reentry.
Obviously not true for the GSOEP data
above. Can deal with point (2) by isolating a
subsample of those present at wave 1 and the
monotonically shrinking subsample as the waves
progress.
80
Probability Weighting Estimators
  • A Patch for Attrition
  • (1) Fit a participation probit equation for each
    wave.
  • (2) Compute p(i,t) predictions of participation
    for each individual in each period.
  • Special assumptions needed to make this work
  • Ignore common effects and fit a weighted pooled
    log likelihood Si St dit/p(i,t)logLPit.

81
Inverse Probability Weighting
82
Spatial Autocorrelation in a Sample Selection
Model
Flores-Lagunes, A. and Schnier, K., Sample
selection and Spatial Dependence, Journal of
Applied Econometrics, 27, 2, 2012, pp. 173-204.
  • Alaska Department of Fish and Game.
  • Pacific cod fishing eastern Bering Sea grid of
    locations
  • Observation catch per unit effort in grid
    square
  • Data reported only if 4 similar vessels fish in
    the region
  • 1997 sample 320 observations with 207 reported
    full data

83
Spatial Autocorrelation in a Sample Selection
Model
Flores-Lagunes, A. and Schnier, K., Sample
selection and Spatial Dependence, Journal of
Applied Econometrics, 27, 2, 2012, pp. 173-204.
  • LHS is catch per unit effort CPUE
  • Site characteristics MaxDepth, MinDepth, Biomass
  • Fleet characteristics
  • Catcher vessel (CV 0/1)
  • Hook and line (HAL 0/1)
  • Nonpelagic trawl gear (NPT 0/1)
  • Large (at least 125 feet) (Large 0/1)

84
Spatial Autocorrelation in a Sample Selection
Model
85
Spatial Autocorrelation in a Sample Selection
Model
86
Spatial Weights
87
Two Step Estimation
?
?
88
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