1. STRUCTURAL MODELS Eva Hromádková, 16.12.2010 Applied Econometrics JEM007, IES Lecture 10

2. Structural modeling Introduction  We want to derive empirical specification from the decision making model  e.g. selection into group (e.g. labor force) by maximizing utility function w.r.t. budget constraint  Decision model explicitly defines endogenous and exogenous variables  Goal = estimate parameters of decision making function

3. Structural modeling Example 1 – Todd and Wolpin (2009)  Todd and Wolpin (2009) – Structural Estimation and Policy Evaluation in Developing Countries  Discrete choice dynamic programming method  Evaluation of different policies To increase school attendance (and reduce child labor) and improve school quality, How do gvt pension programs affect HH labor supply and retirement decisions Fostering small businesses through microfinance Immigration policies and migrant flows

4. Example 1 – Todd and Wolpin (2009) Basic set-up  Latent variable framework:  In each period, agent makes a choice between 2 alternatives – d it – {0,1} Work/education; legal/illegal work  Choice is based on latent variable v it *, reflecting the difference in payoffs from two alternatives  v it * is function of – (1) past choices D, (2) observed characteristics X, and (3) unobservables  v it * (functional form) is unobserved

5. Example 1 – Todd and Wolpin (2009) Structural approach  2 approaches to build econometric model  Reduced form – just identify determinants of choice + run probit  Structural approach: solution of utility maximization Example: Child Labor and schooling (static approach)  Family i chooses whether to send child to work (d it =1) or school (d it =0)  Utility is derived from consumption + school attendance  Utility from school attendance (X – e.g. gender)  HH budget constraint

6. Example 1 – Todd and Wolpin (2009) Structural approach - threshold  2 alternative-specific utilities  Latent variable – difference of two utilities  Ω it - is a space of observables, that consists w and x  We define ε * as threshold – families are indifferent between schooling and working (v=0)  Educ. attainment shock below threshold – child working  Educ. attainment shock above threshold – child at school

7. We do not observe wages for schooled children  + sometimes we do not observe working children  Thus, we need to specify wage function + new latent variable function Example 1 – Todd and Wolpin (2009) Structural approach - problem

8. Example 1 – Todd and Wolpin (2009) Structural approach - estimation Likelihood function for our observations: This corresponds to How to estimate it? Heckman – assumption of joint normality of distribution f( ε,η) For identification – we need at least one excluded variable, i.e. difference between sets x it and z it

9. Example 1 – Todd and Wolpin (2009) Structural approach - identification  Why do we need difference between x it and z it ?  We would like to separate preferences (x it ) from opportunities (z it ) E.g. Are differences between girls’ and boys’ labor outcomes based on social (preferences) or monetary (lower wages) reasons?  Evaluation of policy experiments – e.g. subsidy to schooling, that will affect budget constraint (but not preferences) We can simulate (and distinguish) effect of potential policy without actual implementation

10. Example 1 – Todd and Wolpin (2009) Structural approach - Extensions Dynamic models:  Where h it = Σ τ=1,…, t-1 d it, thus today’s utility is dependent on previous decisions – need for panel data Multinomial choice:  K>2 mutually exclusive alternatives, K-1 latent variables Unobserved heterogeneity:  Agents can be distinguished into a fixed number of types – additional parameters in the utility

11. Example 1 – Todd and Wolpin (2009) Structural approach - Application Duflo, Hanna & Ryan (2008) – India  Randomized field experiment to reduce teacher absenteeism  120 schools: 60 in school, 60 in treatment group  In both groups, checking attendance by photo with class  Basic salary: for 20 days of work – 1000 Rh  Treatment group  +50 Rh for every day over 20  - 50 Rh for every day under 20 (max fine = 500 Rh)  Absenteeism rate: baseline – 65%  Treatment – 79%, control - 58%

12. Example 1 – Todd and Wolpin (2009) Structural approach - Application Duflo, Hanna & Ryan (2008) – India  Structural model:  Choice of teacher – attend / not attend class  Dynamic model – increment of wage corresponding to working today depends on how many days the teacher has worked so far 500 Rh for 1 st day of work, 0 for next 10 days, then for every next day teacher earns 50 Rh Stochastic stream of utility from not working  Evaluation of alternative incentive schemes => different parameterization of payoff function

13. Structural modeling Structural x “atheoretical”  Comprehensive summary: Kaene, M.P. (2010). Structural vs. atheoretic approaches to econometrics. Journal of Econometrics 156, 3-20 + full content of issue Structural models are not very popular because:  Very hard to do  Lot of explicit assumptions (on distributions, functional forms,…)  BUT the same applies for “atheoretical models” – just the assumptions are implicit

14. Structural modeling Structural x “atheoretical Example – Angrist (1990) –Vietnam draft lottery  IV – random lottery number that decides can/cannot be drafted – “perfect”  military service lowered earnings by 15% Problems with interpretation of coefficients:  Existence of always compliers  remember, IV only identifies effect on the subpopulation whose behavior is influenced by the instrument  What is the underlying mechanism (policy relevant) ?  Is the return to military experience lower than that to civilian experience?  Does draft interrupt schooling?  Are there negative psychic / physical effects?