Limited Information Maximum Likelihood

Definition

Limited Information Maximum Likelihood (LIML) is an estimation technique used in econometrics, particularly when dealing with models that involve instrumental variables. It provides a way to estimate the parameters of a model when the instruments used may not be strong enough to provide reliable estimates, often referred to as weak instruments. By utilizing only the information from the equation of interest, LIML can yield more consistent estimates compared to ordinary least squares, especially in scenarios where the traditional assumptions may not hold true.

5 Must Know Facts For Your Next Test

1. LIML is particularly useful in settings with weak instruments, as it adjusts for the bias that can arise in standard methods like 2SLS.
2. The LIML estimator has desirable properties in large samples, providing consistent estimates even when traditional methods fail due to weak instruments.
3. It focuses on maximizing the likelihood function based only on the parameters of interest, making it more robust under certain conditions.
4. Unlike 2SLS, which uses two stages to deal with endogeneity, LIML can provide parameter estimates directly without needing to compute intermediate values.
5. LIML is sensitive to model specification; incorrect specification can still lead to biased results, similar to other estimation techniques.

Review Questions

• How does Limited Information Maximum Likelihood address issues arising from weak instruments in econometric models?
  • Limited Information Maximum Likelihood (LIML) specifically targets the problems posed by weak instruments by providing a more reliable estimation method when traditional approaches fail. Weak instruments can lead to biased estimates when using ordinary least squares or even two-stage least squares. LIML offers a way to mitigate this issue by focusing solely on the equation of interest and maximizing the likelihood function based on available data. This approach yields consistent estimates even when instruments do not strongly correlate with endogenous variables.
• Compare and contrast Limited Information Maximum Likelihood and Two-Stage Least Squares in terms of their use and effectiveness with weak instruments.
  • Limited Information Maximum Likelihood (LIML) and Two-Stage Least Squares (2SLS) both aim to address endogeneity but differ significantly in their approaches. While 2SLS relies on two separate stages—first predicting endogenous variables using instruments and then regressing on these predicted values—LIML focuses directly on maximizing the likelihood function based on the parameters of interest. In scenarios with weak instruments, LIML often provides more reliable and consistent estimates than 2SLS, making it a preferred choice under such conditions.
• Evaluate the implications of using Limited Information Maximum Likelihood for policy analysis when faced with weak instruments in empirical research.
  • Using Limited Information Maximum Likelihood (LIML) for policy analysis offers significant advantages, especially in empirical research where weak instruments are a concern. LIML's ability to provide consistent estimates helps policymakers make informed decisions based on more reliable data. This method acknowledges the limitations posed by weak correlations and adjusts for potential biases that could skew results. However, researchers must ensure proper model specification, as incorrect specifications can still lead to misleading conclusions. The careful application of LIML enhances the credibility of empirical findings, thus influencing effective policy development.

Related terms

Weak Instruments: Instruments that have a weak correlation with the endogenous explanatory variables in a model, which can lead to biased and inconsistent estimates if not handled properly.

Two-Stage Least Squares (2SLS): An estimation method that addresses endogeneity by first predicting the endogenous variables using instruments and then performing regression on these predicted values.

Endogeneity: A situation in a regression model where an explanatory variable is correlated with the error term, leading to biased and inconsistent estimates.