First Stage Regression

Definition

First stage regression is a crucial step in the two-stage least squares (2SLS) estimation process used to address endogeneity in regression models. In this step, the endogenous explanatory variable is regressed on all exogenous variables, including the instruments, to generate predicted values that can then be used in the second stage of the analysis. This process helps isolate the variation in the endogenous variable that is explained by the instruments, making it possible to estimate causal relationships more accurately.

5 Must Know Facts For Your Next Test

1. In first stage regression, the primary goal is to obtain the predicted values of an endogenous variable that are free from bias due to endogeneity.
2. The quality of instruments used in the first stage directly impacts the validity of the 2SLS estimates, as weak instruments can lead to unreliable predictions.
3. The first stage regression output provides important diagnostic information that helps assess the strength and relevance of the chosen instruments.
4. It is essential to check for over-identification in first stage regression, which occurs when there are more instruments than endogenous variables, ensuring that instruments are not invalid.
5. The residuals from the first stage regression should ideally be uncorrelated with the error term in the second stage regression, validating that endogeneity has been addressed.

Review Questions

• How does first stage regression contribute to resolving issues of endogeneity in econometric models?
  • First stage regression helps address endogeneity by isolating the part of an endogenous variable that can be attributed to exogenous factors. By regressing the endogenous variable on all relevant exogenous variables and instruments, this step generates predicted values free from bias due to simultaneous causality or omitted variable bias. These predicted values are then used in the second stage regression to produce unbiased estimates of causal relationships.
• What criteria should be considered when selecting instruments for use in first stage regression?
  • When selecting instruments for first stage regression, it is essential to ensure they are both relevant and valid. Relevance means that the instruments must have a strong correlation with the endogenous variable; weak instruments can lead to inaccurate predictions and biased estimates. Validity requires that the instruments do not correlate with the error term in the second stage, ensuring they serve as legitimate sources of exogenous variation.
• Evaluate how the results from first stage regression can affect interpretations of causal relationships derived from two-stage least squares estimates.
  • The results from first stage regression significantly influence interpretations of causal relationships by determining the reliability of the predicted values used in the second stage. If the instruments are weak or invalid, this can lead to biased estimates and incorrect conclusions about causal effects. Additionally, diagnostic tests from the first stage, such as checking for instrument strength and over-identification, inform researchers about potential issues that could undermine their findings. Therefore, a thorough assessment of first stage results is crucial for ensuring that 2SLS estimates reflect true causal relationships.

Related terms

Endogeneity:

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

Instrumental Variable: A variable used in regression analysis that is correlated with the endogenous explanatory variable but uncorrelated with the error term, serving to provide a source of exogenous variation.

Two-Stage Least Squares (2SLS): A statistical method used to estimate parameters in models with endogenous variables by performing two separate regression analyses.