Published Apr 29, 2024 Limited Information Maximum Likelihood (LIML) estimation is a statistical method used in econometrics to estimate the parameters of a model when the available information is limited. It is primarily used in the context of structural equation models, particularly when dealing with simultaneous equations models. LIML is valuable because it provides a way to obtain consistent estimates even when the equations in the model are exactly identified or just-identified, where traditional methods like Ordinary Least Squares (OLS) may fail to provide reliable results. Consider an economist studying the supply and demand for a particular commodity. The economist has the following two equations: one for demand and another for supply. Both equations include an error term that is assumed to be correlated between equations, a situation that violates the OLS assumptions. By applying the LIML method, the economist can estimate the parameters of the supply and demand equations taking into account the simultaneous relationship between the two and the endogeneity that arises from the error term correlation. In this scenario, the LIML estimation would help identify how factors such as price, income levels, and production costs affect the supply and demand for the commodity, taking into consideration the structural relationship between these two equations in the model. The significance of LIML estimation in economics and econometrics is vast. It is particularly useful in analyzing systems of equations where simultaneous relationships exist, such as between supply and demand in markets or among variables in macroeconomic models. LIML estimation allows for the accurate estimation of model parameters in the presence of endogeneity and where there may be limited information about the structural model. As such, it enables economists to make more reliable inferences about economic relationships and policies. LIML’s consistency under conditions where other estimators fail makes it indispensable for conducting empirical research with complex economic models. Moreover, it facilitates a better understanding of the structural mechanisms driving observed economic phenomena and allows for the testing of economic theories with empirical data more effectively. LIML estimation differs from OLS in that it is specifically designed to handle the unique challenges of simultaneous equations models, including the presence of endogeneity and the correlation of error terms across equations. OLS, which estimates one equation at a time without considering the simultaneity of the system, can lead to biased and inconsistent estimates in such cases. LIML addresses these issues by considering the system of equations as a whole. LIML estimation is most appropriate in situations where the econometric model involves simultaneous equations with potentially endogenous variables. It is especially valuable when dealing with exactly identified or just-identified models where traditional estimation methods like OLS or Two-Stage Least Squares (2SLS) may not provide consistent estimates. Such situations are common in the fields of macroeconomics, labor economics, and industrial organization, among others. One of the primary challenges with LIML estimation is its computational complexity, especially as the size of the model or the number of instruments increases. Additionally, LIML estimators can have high finite sample variance, making them less precise in small samples. It also requires strong theoretical knowledge to correctly specify the model and identify which variables are endogenous and need instruments. Moreover, finding valid instruments that are correlated with the endogenous regressors but uncorrelated with the error term can be challenging but is crucial for the reliability of LIML estimates.Definition of Limited Information Maximum Likelihood (LIML) Estimation
Example
Why LIML Estimation Matters
Frequently Asked Questions (FAQ)
How does LIML estimation differ from Ordinary Least Squares (OLS)?
When is LIML estimation most appropriate to use?
What are the challenges or limitations associated with LIML estimation?
Economics