# Advanced Microeconometrics

**Prerequisites (knowledge of topic)**

Required knowledge of statistics and introductory econometric (or equivalent biometrics, technometrics, etc.) which should comprise basic statistics, estimation and testing in multivariate linear regression models, simple calculus (also with vectors and matrices). Knowledge of estimation should include moment, likelihood, and least squares methods.

Some knowledge of inference in non- or generalized linear models is an advantage.

**Hardware**

Laptops.

**Software**

The statistics language **R** should be implemented on the laptops.

**Learning objectives**

The topic is estimation and testing of regression problems typically considered in microeconometrics by the means of (standard) nonparametric methods.

The concept/content is: nonparametric density estimation (univariate, joint, conditional); nonparametric estimation of conditional moments; miscellaneous (model selection, bandwidth choice, conditional distribution); semiparametric estimation of generalized structured models; nonparametric testing.

The approach is teaching half intuition, half (asymptotic) theory.

After a successful completion, the students will know, understand and be able to apply nonparametric methods for data analysis, in particular estimation and regression. Moreover, the mixed approach enables them to broaden and deepen their knowledge in this direction for also applying non- and semiparametric methods in much more complex situations than those outlined in this course.

**Course content**

Nonparametric density estimation (histograms and kernel densities) for uni- and multivariate distributions; Nonparametric regression (with kernels, kNN, series estimators and splines); Miscellaneous of nonparametric regression (model selection, bandwidth selection, practical issues including implementation); Semiparametric estimation of regression functions and probabilities (in particular backfitting and marginal integration for generalized structured models); Nonparametric specification testing (of parametric, semiparametric and structural hypotheses).

**Structure***Day 1: *

Morning session: 1. The basic model for studying variables

(a) From histograms and empirical distribution function to kernel densities;

(b) What means model selection if there is none

Afternoon session: 2. Toward the study of relations of variables

(a) Multivariate/joint densities; (b) Conditional densities*Day 2:*

Morning session: 3. Conditional Moments: regression without model specification.

(a) From conditional distributions to conditional moments; (b) Local vs global fits

Afternoon session: continued ...

(c) Mixtures of global and local fits *Day 3: *

Morning session: 4. Miscellaneous of nonparametric regression

(a) Model selection and its applications;

Afternoon session: continued ...

(b) Conditional c.d.f. (c) Comments on causality *Day 4:*

Morning session: 5. Generalized Structured Models

(a) Basic principles of semiparametrics; (b) Marginal integration; (c) Linear Mixed Models

Afternoon session: continued ...

(d) Backfitting; (e) likelihood related approaches *Day 5:*

Morning session: 6. Validation of economic models

(a) Bootstrap in non- and semiparametrics; (b) Nonparametric tests

Afternoon session: continued ...

(c) Semiparametric tests; (d) Notes on subsampling

**Literature**

**Mandatory**

None.

**Recommendations**

W. Härdle, M. Müller, S. Sperlich, A. Werwatz (2004) Nonparametric and Semiparametric Models,

Springer Series in Statistics, Springer-Verlag, Heidelberg, NY; ISBN: 3-540-20722-8

For R-codes and more visit http://www.marlenemueller.de/nspm.html

Qi Li and Jeffrey Scott Racine (2006) Nonparametric Econometrics: Theory and Practice, Princeton University Press, Princeton; ISBN: 978069112611

D.J. Henderson and C.F. Parmeter (2015) Applied Nonparametric Econometrics, Cambridge University Press, NY, ISBN: 978-0-521-27968-0

**Mandatory readings before course start**

None.

**Examination part**

The examination is 100% conducted in form of a written test (closed book if possible); for content and structure of the test see below.

**Supplementary aids**

None.

**Examination content**

The test will be written, 120 minutes at the end of the course.

It will be 50% a multiple choice test with 4 possible answers (one correct) and another 50% a list of short questions to be answered in text and mathematical formulas. Explicit proofs and calculations are not demanded.

The list of questions in both parts intent to cover all subjects treated, see "Structure" in which the detailed list is given. Students will mainly asked comprehension questions to test both, their understanding and their knowledge of the functioning of nonparametric estimation methods.

**Literature**

None.