Part 20: Selection [1/66] Econometric Analysis of Panel Data William Greene Department of Economics Stern School of Business

Part 20: Selection [2/66] Econometric Analysis of Panel Data 20. Sample Selection and Attrition

Part 20: Selection [3/66] Received Sunday, April 27, 2014 I have a paper regarding strategic alliances between firms, and their impact on firm risk. While observing how a firm’s 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 Editor’s 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? AE’s 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.”

Part 20: Selection [4/66] 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, q n (θ 0 ) →0. So, if (13-7) is true, then it must follow that q n (θˆGMM) →θ 0 as well because of the identification assumption" I think in the second line it should be q n (θˆGMM) → 0, not θ 0.

Part 20: Selection [5/66] 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 L>K. In particular my model looks kind of like this: Y = b 1 *X^b 2 + e, and so I am trying to estimate the extra b 2 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, b 2 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?

Part 20: Selection [6/66]

Part 20: Selection [7/66] Dueling Selection Biases – From two s, same day. data that is non-randomised and suffers from selection bias  “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.

Part 20: Selection [8/66] 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 Bias”=the bias due to not accounting for the unobservables that link the equations.

Part 20: Selection [9/66] A Sample Selection Model  Linear model  2 step  ML – Murphy & Topel  Binary choice application  Other models

Part 20: Selection [10/66] Canonical Sample Selection Model

Part 20: Selection [11/66] Applications  Labor Supply model: y*=wage-reservation wage d=labor 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…

Part 20: Selection [12/66] 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

Part 20: Selection [13/66] Heckman’s Model

Part 20: Selection [14/66] Two Step Estimation The “LAMBDA”

Part 20: Selection [15/66] FIML Estimation

Part 20: Selection [16/66] Classic Application  Mroz, T., Married women’s labor supply, Econometrica, N =753 N 1 = 428  A (my) specification LFP=f(age,age 2,family income, education, kids) Wage=g(experience, exp 2, education, city)  Two step and FIML estimation

Part 20: Selection [17/66] Selection Equation | Binomial Probit Model | | Dependent variable LFP | | Number of observations 753 | | Log likelihood function | |Variable| Coefficient | Standard Error |b/St.Er.|P[|Z|>z]| Mean of X| Index function for probability Constant| AGE | AGESQ | FAMINC | D D WE | KIDS |

Part 20: Selection [18/66] Heckman Estimator and MLE

Part 20: Selection [19/66] Extension – Treatment Effect

Part 20: Selection [20/66] Sample Selection

Part 20: Selection [21/66] Extensions – Binary Data

Part 20: Selection [22/66] Panel Data and Selection

Part 20: Selection [23/66] Panel Data and Sample Selection Models: A Nonlinear Time Series I : Fixed and Random Effects Extensions II and 2005: Model Identification through Conditional Mean Assumptions III : Semiparametric Approaches based on Differences and Kernel Weights IV. 2007: Return to Conventional Estimators, with Bias Corrections

Part 20: Selection [24/66] Panel Data Sample Selection Models

Part 20: Selection [25/66] 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

Part 20: Selection [26/66] Selection with Fixed Effects

Part 20: Selection [27/66] Practical Complications The bivariate normal integration is actually the product of two univariate normals, because in the specification above, v i and w i 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.”

Part 20: Selection [28/66] Simulation The first line in the log likelihood is of the form E v [  d=0  (…)] and the second line is of the form E w [E v [  (…)  (…)/  ]]. Using simulation instead, the simulated likelihood is

Part 20: Selection [29/66] Correlated Effects Suppose that w i and v i are bivariate standard normal with correlation  vw. We can project w i on v i and write w i =  vw v i + (1-  vw 2 ) 1/2 h i where h i 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, v i and h i.

Part 20: Selection [30/66] Conditional Means

Part 20: Selection [31/66] A Feasible Estimator

Part 20: Selection [32/66] Estimation

Part 20: Selection [33/66] Kyriazidou - Semiparametrics

Part 20: Selection [34/66] 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.

Part 20: Selection [35/66] 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 aren’t 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?

Part 20: Selection [36/66] Sample Selection

Part 20: Selection [37/66] 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 Boris Bravo-Ureta University of Connecticut Daniel Solis University of Miami William Greene New York University

Part 20: Selection [38/66] 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.

Part 20: Selection [39/66] OVERALL CONCEPTUAL FRAMEWORK 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. More Production and Productivity More Farm Income Sustainability Off-Farm Income MARENA Training & Financing Natural, Human & Social Capital

Part 20: Selection [40/66]  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 The MARENA Program

Part 20: Selection [41/66]  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). Component II - Module 3

Part 20: Selection [42/66] Rural poverty in Honduras, largely due to policy driven unsustainable land use => environmental degradation, productivity losses, food insecurity, growing climatic vulnerability (GEF-IFAD, 2002). Conclusions

Part 20: Selection [43/66] Expected Impact Evaluation

Part 20: Selection [44/66] 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).

Part 20: Selection [45/66] A Sample Selected SF Model d i = 1[  ′z i + h i > 0], h i ~ N[0,1 2 ] y i =  +  ′x i +  i,  i ~ N[0,   2 ] (y i,x i ) observed only when d i = 1.  i = v i - u i u i =  u |U i | where U i ~ N[0,1 2 ] v i =  v V i where V i ~ N[0,1 2 ]. (h i,v i ) ~ N 2 [(0,1), (1,  v,  v 2 )]

Part 20: Selection [46/66] Simulated logL for the Standard SF Model This is simply a linear regression with a random constant term, α i = α - σ u |U i |

Part 20: Selection [47/66] Likelihood For a Sample Selected SF Model

Part 20: Selection [48/66] Simulated Log Likelihood for a Selectivity Corrected Stochastic Frontier Model The simulation is over the inefficiency term.

Part 20: Selection [49/66] JLMS Estimator of u i

Part 20: Selection [50/66] 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 Maddala’s 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.

Part 20: Selection [51/66] Spanish Dairy Farms: Selection based on being farm # periods The theory works. Closed Form vs. Simulation

Part 20: Selection [52/66] Variables Used in the Analysis Production Participation

Part 20: Selection [53/66] Findings from the First Wave

Part 20: Selection [54/66] A Panel Data Model Selection takes place only at the baseline. There is no attrition.

Part 20: Selection [55/66] Simulated Log Likelihood

Part 20: Selection [56/66]  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 Main Empirical Conclusions from Waves 0 and 1

Part 20: Selection [57/66]

Part 20: Selection [58/66] Attrition  In a panel, t=1,…,T individual I leaves the sample at time K i 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.

Part 20: Selection [59/66] 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

Part 20: Selection [60/66] QOL Study  Quality of life study i = 1,… 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)  y it = self administered quality of life survey, scale = 0,…,100  x it = 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

Part 20: Selection [61/66] 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 (don’t 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)  Prob[Present at exit|covariates] = Φ(z’θ) (Probit model)  Additional variable added to difference model i = Φ(z i ’θ)/Φ(z i ’θ) The FDA solution: fill with zeros. (!)

Part 20: Selection [62/66] An Early Attrition Model

Part 20: Selection [63/66] 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”

Part 20: Selection [64/66] Selection Model

Part 20: Selection [65/66] Maximum Likelihood

Part 20: Selection [66/66]

Part 20: Selection [67/66] 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)

Part 20: Selection [68/66] Attrition Model

Part 20: Selection [69/66] Selection Equation

Part 20: Selection [70/66] 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.”

Part 20: Selection [71/66] One Wave Model

Part 20: Selection [72/66] Maximum Likelihood Estimation  See Zabel’s 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.

Part 20: Selection [73/66] Testing for Selection?  Maximum Likelihood Results  Covariances were highly insignificant.  LR statistic=0.46.  Two step results produced the same conclusion based on a Hausman test  ML Estimation results looked like the two step results.

Part 20: Selection [74/66] A Dynamic Ordered Probit Model

Part 20: Selection [75/66] Random Effects Dynamic Ordered Probit Model

Part 20: Selection [76/66] 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  Self assessed health  British Household Panel Survey (BHPS) 1991 – 1998 = 8 waves About 5,000 households

Part 20: Selection [77/66] Attrition

Part 20: Selection [78/66] Testing for Attrition Bias Three dummy variables added to full model with unbalanced panel suggest presence of attrition effects.

Part 20: Selection [79/66] Attrition Model with IP Weights Assumes (1) Prob(attrition|all data) = Prob(attrition|selected 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.

Part 20: Selection [80/66] 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: Σ i Σ t [d it /p(i,t)]logLP it.

Part 20: Selection [81/66] Inverse Probability Weighting

Part 20: Selection [82/66] Spatial Autocorrelation in a Sample Selection Model  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 Flores-Lagunes, A. and Schnier, K., “Sample selection and Spatial Dependence,” Journal of Applied Econometrics, 27, 2, 2012, pp

Part 20: Selection [83/66] Spatial Autocorrelation in a Sample Selection Model 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) Flores-Lagunes, A. and Schnier, K., “Sample selection and Spatial Dependence,” Journal of Applied Econometrics, 27, 2, 2012, pp

Part 20: Selection [84/66] Spatial Autocorrelation in a Sample Selection Model

Part 20: Selection [85/66] Spatial Autocorrelation in a Sample Selection Model

Part 20: Selection [86/66] Spatial Weights

Part 20: Selection [87/66] Two Step Estimation  

Part 20: Selection [88/66]