# Advanced econometrics: Semi-parametric and simulations

### Objective

This course is made of two parts: the first part shows (high-dimensional) semiparametric econometric models, their applications and theoretical properties, the second part of the course will show how to estimate these models.

Part I. Often economic models provide only a set of moment restrictions, instead of a likelihood function, that identify the parameter of interest. One of the classical tool to estimate the economic model by exploiting moment restrictions is the Generalized Method of Moments (GMM). Classic examples are the consumption based asset pricing model or the instrumental variable regression model. After recalling the GMM estimation method and its properties, we will consider models characterized by many moment restrictions. These are models in high-dimension that require extensions of the GMM to be estimated.

Part II. Many econometric models are highly nonlinear. For usual inference techniques, the criterion functions have often no analytical expression. It is the case if this criterion is based on a probability density function (MLE) or moments (GMM) that are based on high dimension integrals that combine the information from the sample and the vector of parameters to be estimated. In practice, the estimation of such models using conventional techniques is quite difficult. However, econometricians have proposed fast and accurate smooth probabilities simulators and have developed methods that allows to estimate economic models from which it is easy to simulate data.

Simulation based estimation techniques can be used in a variety of empirical applications and to investigate important economic issues like educational and occupation choices, household choices, labor market dynamics, dynamic stochastic general equilibrium models, dynamic discrete choice models, duration models, stochastic volatility models, structural Markov decision processes, discretely-sampled diffusion, consumer level models of vehicle choice, models with peer interactions in smoking behavior (among many others).

At the end of this course students should be able to use estimation techniques at the frontier of econometrics to study many economic issues and to adapt these estimation techniques to models that are similar to the ones considered in the course.  Students should be able to use these estimation methods in order to practice applied econometrics to study a wide range of economic problems.

Evaluation: students have to do a project to validate the exam. They have to work in groups. We will provide a list of papers/ topics among which students have to choose. Then, each group should briefly explain the theoretical method and apply the methodology to real or simulated data.

### Planning

Part I

(1) Reminder of the Generalized Method of Moments (GMM)

(2) Instrumental variable regression models: the problem of weak instruments

(3) High-dimensional moment condition models: many instruments asymptotic

(4) High-dimensional moment condition models: regularized GMM

Part II

(1) Simulation / Simulated Maximum Likelihood Estimation (SMLE)

(2) Simulated Method of Moments (SMME)

(3) Indirect Inference

(4) Some Applications

(5) EM Algorithm / Simulated EM Algorithm / importance Sampling

(6) Dynamic Discrete Choice Models: MLE and SMME

(7) Dynamic Discrete Choice Models: Generalized Indirect Inference

(8) Nonparametric Simulated Maximum Likelihood Estimation Method

### References

Belloni A., Chernozhukov V., Chetverikov D., Hansen C. and K. Kato (2018). “High-dimensional econometrics and regularized GMM”, preprint.

Bruins M.,  J.A. Duffy, M.P. Keane, A.A. Smith (2018), “Generalized Indirect Inference For Discrete Choice Models”, Journal of Econometrics, 205, 177-203.

Carrasco M., J.-P. Florens, “Simulation-Based Method of Moments and Efficiency”, Journal of Business & Economic Statistics, vol. 20, n°4, 482-492.

Eisenhauer P., J.J. Heckman, S. Mosso (2015), “Estimation of Dynamic Discrete Choice Models by Maximum Likelihood And The Simulated Method Of Moments”, International Economic Review, vol. 56 n°2, 331-357.

Fermanian J.D., B. Salanié (2004), « A Nonparametric Simulated Maximum Likelihood Estimation Method”, Econometric Theory, vol. 20, n°4, 701-734.

Gelman A. (1995), “Method of Moments Using Monte Carlo Simulation”, Journal of Computational and Graphical Statistics, vol 4, n°1, 36-54.

Gouriéroux Ch., A. Monfort (1991), “Simulation Based Inference in Models with Heterogeneity”, Annals of Economics and Statistics, 20/21, 69-107.

Hansen C., Hausman J. and W. Newey (2008), “Estimation with Many Instrumental Variables”, Journal of Business & Economic Statistics, Vol. 26, 398-422.

Keane M. (2009), “Simulated Maximum Likelihood Estimation Based on First-Order Conditions”, International Economic Review, vol. 9, n°2, 627-675.

Kristensen D., Y. Shin (2012), “Estimation Of Dynamic Models With Nonparametric Simulated Maximum Likelihiood”, Journal of Econometrics, 167, 76-94.

Laroque G, B. Salanié (1993), “Simulation-Based Estimation of Models with Lagged Latent Variables”, Journal of Applied Econometrics, vol. 8, S119-S133.

McFadden D., P.A. Ruud (1994), “Estimation by Simulation”, The Review of Economic Studies”, vol. 76, n°4, 591-608.

Nakajima R. (2007), “Measuring Peer Effects on Youth Smoking Behaviour”, The Review of Economic Studies, vol. 74, n°3, 897-935.

Nielsen S.F. (2000), “On Simulated EM Algorithm”, Journal of Econometrics, 96, 267-292.

Stern S. (1997), “Simulation-Based Estimation”, Journal of Economic Literature, 65, N°4, 2006-2039.