Full Information Maximum Likelihood

Background

The Full Information Maximum Likelihood (FIML) estimation method plays a pivotal role in econometrics, particularly when dealing with complex nonlinear simultaneous equations models. The general objective of FIML is to maximize a likelihood function while taking into account the structural constraints inherent in the model.

Historical Context

The development of FIML dates back to advances in statistical theory and econometrics that emphasized the need for efficient estimation techniques for complex models. Over the years, FIML has established itself as a cornerstone in the field of econometric estimation, largely due to its efficiency and comprehensive approach.

Definitions and Concepts

Full Information Maximum Likelihood (FIML): A method of estimation for nonlinear simultaneous equations models based on the maximization of a likelihood function while adhering to the model’s structural constraints. FIML considers all information available in the system and estimates all equations and unknown parameters simultaneously.

Major Analytical Frameworks

Classical Economics

While traditional classical economics did not emphasize statistical methods like FIML explicitly, the grounding principles of consistency and efficiency in estimation are relevant across frameworks.

Neoclassical Economics

FIML fits well within neoclassical economics, which often seeks to model economic phenomena with rigorous mathematical precision, including the estimation of complex systems of equations.

Keynesian Economics

In Keynesian models, particularly those emphasizing macroeconomic fluctuations and multipliers, FIML can provide efficient and consistent parameter estimates that are crucial for policy simulations and forecasting.

Marxian Economics

Marxian economists might utilize FIML to estimate parameters in complex, nonlinear models reflecting the interactions between different economic classes and dynamics.

Institutional Economics

For institutional economists focusing on the interplay of economic agents within institutional contexts, FIML provides a robust estimation framework that can handle complex systems with multiple equations.

Behavioral Economics

Behavioral economists can use FIML to estimate models that incorporate psychological factors and heuristics, ensuring that the parameter estimates are efficient and account for the system’s complexity.

Post-Keynesian Economics

This school can benefit from FIML’s comprehensive approach to estimating systems of equations that capture the nuanced relationships in post-Keynesian thought.

Austrian Economics

While Austrian economists may focus less on formal econometric techniques, those who do work with complex dynamic models may find FIML useful for its efficiency and comprehensive nature.

Development Economics

FIML can be particularly useful in development economics for estimating models that take into account numerous interacting factors affecting economic development.

Monetarism

Monetarists can use FIML to estimate complex models relating to monetary policy’s impacts on economic variables, ensuring robustness and efficiency.

Comparative Analysis

FIML vs. Limited Information Maximum Likelihood (LIML):

FIML considers the full set of information by estimating all the equations in the system simultaneously, leading to asymptotically efficient estimations under normal error distributions.
LIML focuses on a subset of equations and may be preferable in some circumstances where less computational complexity is desired, albeit often at the cost of some efficiency.

Case Studies

Examples of FIML applications can be found in various fields such as:

Macroeconomic policy simulations
Structural equations modeling in social sciences
Dynamic stochastic general equilibrium (DSGE) models

Suggested Books for Further Studies

“Econometric Analysis” by William Greene
“Econometric Methods” by Jack Johnston and John DiNardo
“Modelling Economic Systems and Economies” by Miroslav V. Kárný and Bohumír Pauše for insights into holistic estimation techniques in economic modeling.

Limited Information Maximum Likelihood (LIML): An estimation approach that uses a subset of available information, focusing on specific equations within the model, which may be less computationally complex than FIML.
Maximum Likelihood Estimation (MLE): A method of estimating the parameters of a statistical model by maximizing a likelihood function, so the observed data is most probable under the assumed model.
Simultaneous Equations Model (SEM): A statistical model comprising multiple interrelated equations estimated together to capture complex economic relationships.