Background
Limited Information Maximum Likelihood (LIML) estimation is a method employed in econometrics for estimating a single equation within a linear simultaneous equations model. This technique is particularly regarded for its efficiency when the errors in the system are normally distributed.
Historical Context
The concept of LIML estimation has roots in the development of statistical methods in the mid-20th century. During this period, economists and statisticians were in search of robust estimation techniques that could handle models where multiple equations interact with each other, an issue prevalent in economic modelling.
Definitions and Concepts
LIML estimation focuses on maximizing the likelihood function subject to the structural constraints imposed by the simultaneous equations model. This method contrasts with Full Information Maximum Likelihood (FIML) estimation, which considers the full system of equations simultaneously.
Major Analytical Frameworks
Classical Economics
Classical models often did not require simultaneous equations frameworks. Hence, LIML estimation is not prominently featured in classical economic analysis.
Neoclassical Economics
In neoclassical economics, especially in applications involving comprehensive models like general equilibrium models, LIML can be beneficial for estimating parameters of interest from limited equations within the broader system.
Keynesian Economic
Keynesian models often include simultaneous equations to represent macroeconomic interactions (e.g., IS-LM models). LIML estimation is pertinent when focusing on specific parts of such systems under the assumption that errors follow a normal distribution.
Marxian Economics
Marxian economic models, primarily qualitative and historical-materialist by nature, do not typically apply LIML estimation.
Institutional Economics
Institutional economics, with its focus on rules, enforcement mechanisms, and their effects on economic outcomes, may occasionally use LIML in empirical research to model relationships constrained by institutional frameworks.
Behavioral Economics
As behavioral economics emphasizes the psychological underpinnings of economic decisions, LIML might be applied in empirical work assessing specific behavioral relationships within broader simultaneous systems.
Post-Keynesian Economics
Post-Keynesian models, focusing on dynamics and the non-neutrality of money, can find LIML estimation useful for part of their analytical toolkit, particularly in estimating parts of dynamic systems.
Austrian Economics
Given the Austrian School’s emphasis on qualitative methodology and aversion to formal econometric techniques, LIML estimation is not widely used in Austrian economic models.
Development Economics
In development economics, models often entail simultaneous interaction between numerous economic variables. LIML can help estimate specific policy impacts within such frameworks, assuming error normality.
Monetarism
Monetarist models may incorporate simultaneous equation techniques, making LIML potentially relevant when focusing on singular aspects of large policy models.
Comparative Analysis
LIML estimation holds distinct advantages in environments with normally distributed errors and is often more efficient than alternative single equation estimators like Two-Stage Least Squares (2SLS). However, its applicability necessitates careful consideration of model constraints and error characteristics.
Case Studies
Case studies for LIML application often entail complex econometric models where single-equation precision is paramount. Real-world examples span empirical investigations in macroeconomics and policy simulations, evaluating individual market or policy shocks within intricate systems.
Suggested Books for Further Studies
- “Econometric Analysis” by William H. Greene
- “Econometric Models and Economic Forecasts” by Robert Pindyck and Daniel Rubinfeld
- “Advanced Econometrics” by Takeshi Amemiya
Related Terms with Definitions
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Simultaneous Equations Model: An econometric model encompassing multiple interdependent equations where endogenous variables in one are explanatory variables in others.
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Full Information Maximum Likelihood (FIML): A maximum likelihood estimation method which considers the entire system of equations in a simultaneous equations model.
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Two-Stage Least Squares (2SLS): A method to address endogeneity in simultaneous equation models by first predicting the endogenous variables using instrumental variables then estimating the equations.
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Identification: The condition in econometrics ensuring that unique values of parameters can be derived from the model’s exact statistical specification.
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Instrumental Variables (IV): Variables used in regression analysis to correct for endogeneity biases, acting as replacements for endogenous explanatory variables.
