Beyond Linearity: Nonlinear Models and Generalized Method of Moments (GMM) Training Course

Introduction

Many real-world phenomena, particularly in economics, finance, and social sciences, do not conform to simple linear relationships, nor do they always meet the stringent assumptions of classical estimation techniques like Ordinary Least Squares (OLS). When dealing with limited dependent variables, complex dynamic relationships, or endogeneity issues in settings where traditional instrumental variables are scarce, researchers require more flexible and robust modeling approaches. Nonlinear models capture intricate data patterns, while the Generalized Method of Moments (GMM) provides a powerful and versatile framework for estimation, especially when faced with heteroscedasticity, autocorrelation, and endogeneity, offering an invaluable alternative to restrictive assumptions.

This intensive training course is meticulously designed to equip participants with a comprehensive and practical understanding of both nonlinear econometric models and the Generalized Method of Moments (GMM). From dissecting the theory behind various non-linear specifications and applying them to diverse data types, to mastering the principles of GMM estimation, identifying appropriate moment conditions, and navigating advanced GMM applications in dynamic panel data, you will gain the expertise to analyze complex empirical problems with greater sophistication. This empowers you to build more accurate and robust models, extract richer insights, and contribute to cutting-edge research and policy analysis.

Target Audience

  • Econometricians and applied economists in academia and industry.
  • Quantitative researchers and financial analysts.
  • Data scientists and statisticians working with complex economic or financial data.
  • Researchers in social sciences and public policy.
  • Graduate students (Master's and PhD) in economics, finance, and statistics.
  • Professionals involved in empirical modeling and forecasting.
  • Anyone seeking to extend their econometric toolkit beyond linear models and basic estimation.

Duration: 10 days

Course Objectives

Upon completion of this training course, participants will be able to:

  • Understand the theoretical foundations and applications of various nonlinear econometric models.
  • Grasp the concepts of limited dependent variables and implement models like Logit, Probit, and Tobit.
  • Analyze the principles and assumptions underlying the Generalized Method of Moments (GMM).
  • Comprehend how to derive and specify appropriate moment conditions for GMM estimation.
  • Evaluate the strengths of GMM in handling endogeneity, heteroscedasticity, and autocorrelation.
  • Develop practical skills in implementing nonlinear models and GMM using statistical software.
  • Navigate advanced GMM applications, particularly in dynamic panel data models (e.g., Arellano-Bond).
  • Formulate a strategic approach for selecting and applying appropriate nonlinear and GMM techniques to real-world data.

Course Content

  1. Introduction to Nonlinear Econometrics
  • Why go beyond linearity? Limitations of linear models
  • Overview of common nonlinear relationships in economics (e.g., diminishing returns, threshold effects)
  • Types of nonlinear models: intrinsic vs. extrinsic nonlinearity
  • Introduction to maximum likelihood estimation (MLE) as a general framework
  • Software considerations for nonlinear estimation
  1. Limited Dependent Variable Models I: Binary Choice
  • The nature of binary outcomes (yes/no, buy/not buy, default/not default)
  • Linear Probability Model (LPM): strengths and weaknesses
  • Logit Model: Functional form, interpretation of coefficients (log-odds), marginal effects
  • Probit Model: Functional form, interpretation, comparison with Logit
  • Estimation and inference for Logit/Probit models
  • Goodness-of-fit measures for binary choice models
  1. Limited Dependent Variable Models II: Ordinal, Count, and Censored
  • Ordinal Logit/Probit: For ordered categorical outcomes
  • Count Data Models: Poisson and Negative Binomial regression for count outcomes (e.g., number of loans, patents)
  • Tobit Model (Censored Regression): For outcomes censored at a specific value (e.g., expenditure with zero values)
  • Heckman Selection Model: Addressing sample selection bias
  • Implementation and interpretation of these models
  1. Introduction to Generalized Method of Moments (GMM)
  • Limitations of OLS, IV, and MLE in certain contexts
  • The intuition behind GMM: matching sample moments to population moments
  • Overview of moment conditions and orthogonality conditions
  • GMM estimator: efficiency and consistency
  • Comparison of GMM with other estimation methods (OLS, MLE, IV)
  1. GMM: Core Principles and Estimation
  • Defining population moment conditions
  • Sample moment conditions and the objective function
  • The weighting matrix in GMM: efficient GMM (Hansen's J-test)
  • One-step vs. two-step GMM estimation
  • Asymptotic properties of GMM estimators (consistency, asymptotic normality)
  1. Specification of Moment Conditions
  • How to choose appropriate instruments or moment conditions
  • Exogeneity of instruments: internal vs. external instruments
  • Time series applications of GMM: using lagged variables as instruments
  • Panel data applications: using internal instruments
  • Over-identification tests (Sargan/Hansen test) for validity of moment conditions
  1. Advanced GMM Applications: Dynamic Panel Data Models
  • The problem of endogeneity and unobserved heterogeneity in dynamic panel models
  • Arellano-Bond GMM (Difference GMM): handling lagged dependent variables as regressors
  • Arellano-Bover/Blundell-Bond GMM (System GMM): improving efficiency with additional moment conditions
  • Assumptions and diagnostic tests for dynamic panel GMM (e.g., AR(1), AR(2) tests)
  • Implementing dynamic panel GMM in statistical software
  1. GMM for Time Series and Financial Econometrics
  • Estimating models with conditional heteroscedasticity (GARCH-in-Mean) using GMM
  • Estimating Euler equations from intertemporal optimization problems
  • Consumption-based asset pricing models using GMM
  • GMM in macroeconomics: estimating DSGE models (conceptual)
  • Challenges and considerations for GMM in time series contexts
  1. Practical Implementation and Software Applications
  • Hands-on exercises using real-world datasets for nonlinear models and GMM
  • Implementing Logit/Probit/Tobit in Python (statsmodels) and R (glm, VGAM, AER)
  • Implementing GMM in Python (statsmodels, linearmodels) and R (gmm, plm)
  • Interpreting output, reporting results, and diagnostic checking for both nonlinear and GMM models
  • Best practices for model selection and robustness checks
  1. Challenges, Extensions, and Future Directions
  • Weak instruments and many instruments problem in GMM
  • Small sample properties of GMM estimators
  • Combining GMM with machine learning techniques
  • Robust GMM estimation for outliers and heavy-tailed distributions
  • Current research frontiers and advanced topics in nonlinear and GMM econometrics.

CERTIFICATION

  • Upon successful completion of this training, participants will be issued with Macskills Training and Development Institute Certificate

TRAINING VENUE

  • Training will be held at Macskills Training Centre. We also tailor make the training upon request at different locations across the world.

AIRPORT PICK UP AND ACCOMMODATION

  • Airport pick up and accommodation is arranged upon request

TERMS OF PAYMENT

Payment should be made to Macskills Development Institute bank account before the start of the training and receipts sent to info@macskillsdevelopment.com

For More Details call: +254-114-087-180

 

 

Beyond Linearity: Nonlinear Models And Generalized Method Of Moments (gmm) Training Course in Kenya
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