# Econometrics B (ØkB)

### Course content

Econometrics B gives a detailed account of principles for estimation and inference based on the most conventional methods for estimation of both linear and non-linear parametric models, such as non-linear least squares, maximum likelihood estimation (MLE) and generalized method of moments (GMM) with application to cross-sectional data and panel data. These methods are used to estimate a microeonometric models for panel and cross-sectional data covered in the course. The course provides both the theoretical foundations of these estimation methods, as well as the practical tools to implement them in an imperative programming language such as MATLAB and Python.

The course will be developed along the following four axes:

1) Linear unobserved effects panel data models

• Estimation with strictly exogenous regressors
• (Random Effects, Fixed Effects, First Differences)
• GMM estimation of dynamic panel data models with sequentially exogenous regressors

2) Estimation Methods and numerical tools for non-linear parametric models

• M-Estimators (WNLS, NLS, LAD, MLE, etc.) and two-step m-estimators
• Generalized Method of Moments (GMM)
• Simulation-based estimation methods
• Numerical optimization (e.g., Nelder-Mead, Newton-Raphson, BHH algorithms)

3) Discrete Choice Models

• Binary response models for cross-sectional and panel data
• Multinomial choice models (e.g. Logit, Nested Logit, Probit, Mixed Logit models)
• Structural models that combine discrete and continuous choices.
• Structural models for discrete demand in oligopolistic markets

4)  Traditional non-and semi-parametric methods and introduction machine learning methods

• Kernel and series regression
• Regularized linear regression
• Regression trees and forests
• Deep learning and neural nets

The course will provide the student with a statistical toolbox that can be used for the estimation of a wide range of reduced form and structural microeonomtric models. As an integral part of the course, students will learn how to carry out, present, and discuss an empirical analysis on their own.

Education

BSc Programme in Computer Science and Economics

Learning outcome

After completing the course the student is expected to be able to:

Knowledge:

• Understand the central assumptions in linear panel data model with unobserved effects; including how these assumptions are tested and how potential violation affect identification and estimation of parameters.
• Understand the specification, identification and estimation issues that arise in static and dynamic binary response model for panel data models with and without unobserved effects (e.g. scale and level normalization, state dependence, initial conditions, endogeneity, neglected heterogeneity).
• Understand the specification, identification and estimation issues that arise in multinomial discrete choice models and their implied predictions (substitution patterns,
• Understand the principle of M-estimation in terms of estimation and inference, as well as key examples of M-estimators such as maximum likelihood and non-linear least squares.
• Understand the properties of simulation based estimators (consistency, asymptotic normality, rates of convergence and smoothness) and how they can be applied in the context of discrete choice models.
• Understand how the most common numerical optimizers and solution algorithm work in an estimation context.
• Understand the differences in goals, methods and settings between the machine learning methods and the traditional econometrics and statistics methods.

Skills:

• Identify the characteristic properties of a given economic cross-sectional or panel data set, suggest and construct an appropriate econometric model and select a suitable estimation approach.
• Derive estimators of the statistical model’s parameters using the principles of M-estimation and estimate and interpret the parameters. This may involve deriving the sample objective function (such as the likelihood function), the gradient and the information matrix and implement the estimation method numerically using optimization methods.
• Construct misspecification tests, analyze to what extent an econometric model is congruent with the data, formulate economic questions as hypotheses on the parameters of the statistical model and test these hypotheses.
• Use an imperative programing language such as Python or MATLAB to implement the mathematical representation of the econometric models and estimation methods covered in the course. This involves computing parameter estimates that are typically not available in closed form as well as computation of partial effects, elasticities, standard errors, test statistics, and simulation of counterfactual predictions based on the estimated model.
• Present a statistical model and empirical results in a clear and concise way in a focused paper. This includes using statistic and econometric terms in a correct way, giving statistically sound and economically relevant interpretations of statistical results, and presenting results in a way so that they can be reproduced by others.

Competencies:

When faced with a new dataset and a given economic problem, students should be able to:

• Assess which estimator is best suited to address the problem.
• Develop arguments supporting an identification strategy.
• Program the estimator and estimate the parameters of the model.
• Test specification and economic hypotheses in their model.
• Report and interpret the results (marginal effects, elasticities, counterfactual simulations)
• Assess the identification strategies in existing research papers as well as in their own analyses.
• Read and critically evaluate research papers containing applied econometric cross-section and panel data analyses.

The acquired skills in microeconometric theory and practice provide a strong background that enable students to do empirical analyses at a level suitable for the bachelor thesis, but also relevant for answering empirical economic questions that could be encountered in a government agency or in the private sector.

The course is a combination of lectures and exercise classes. There will be 3x2 hours of lectures og 3x2 hours of exercise classes per week in 7 weeks.

The lectures cover the theory and the intuition behind the estimators, methods and econometric models. The exercise classes allow students to put into practice the theory through exercises, and also to obtain hands-on coding experience by implementing the estimators on real datasets using an imprerative programming language such as MATLAB.

Students are expected to prepare the exercises before coming to the exercise classes.

During the semester three mandatory take-home assignments covering the major topics of the course must be handed in and not later than the given deadline.

At least 2 of out of 3 assignments will have to be handed in to an online peer assessment platform, where students will give peer feedback on each other’s assignments. At the end of the semester, an improved version (based on the peer feedback received) of one of the assignments will have to be resubmitted and approved by the teacher (pass/fail). The final assignment to be resubmitted will be selected at random. The assignments can be written in groups of three students maximum.

See Absalon

Prerequisites equivalente to the courses PoP, MatIntro, Grundlæggende Statistik og Sandsynlighedsregning (GSS), Økonometri A (ØkA) and Numeriske Metoder (NuMe).

Written
Oral
Individual
Collective
Continuous feedback during the course of the semester
Peer feedback (Students give each other feedback)
ECTS
7,5 ECTS
Type of assessment
Written assignment, During the course
The final exam is a term paper where students independetly undertake an empirical analysis on data provided.
Aid
All aids allowed
Marking scale
Censorship form
External censorship
##### Criteria for exam assessment

Students are assessed on the extent to which they master the learning outcome for the course.

To receive the top grade, the student must be able to demonstrate in an excellent manner that he or she has acquired and can make use of the knowledge, skills and competencies listed in the learning outcomes.

Single subject courses (day)

• Category
• Hours
• Lectures
• 42
• Class Instruction
• 42
• Preparation
• 84
• Project work
• 38
• English
• 206