First Stage Regression

Definition

First stage regression is a crucial step in the two-stage least squares (2SLS) method used to address endogeneity in regression models. In this stage, the endogenous variable is regressed on the instrumental variables to isolate the variation that is uncorrelated with the error term. This process helps to obtain consistent estimates for the coefficients in the second stage of 2SLS.

5 Must Know Facts For Your Next Test

1. In the first stage regression, the focus is on predicting the endogenous variable using one or more instrumental variables that are assumed to be exogenous.
2. The purpose of this regression is to provide a fitted value of the endogenous variable, which is then used in the second stage to estimate the main model of interest.
3. The validity of the first stage regression heavily relies on the strength of the instruments; weak instruments can lead to poor estimation results.
4. After running the first stage regression, it's essential to check for relevance and validity of the instruments by looking at their correlation with the endogenous variable.
5. The results from the first stage help ensure that any biases introduced by endogeneity are minimized in the second stage of 2SLS.

Review Questions

• How does first stage regression help in addressing endogeneity issues in regression analysis?
  • First stage regression helps tackle endogeneity by using instrumental variables to isolate variations in the endogenous variable that are not correlated with the error term. By regressing the endogenous variable on these instruments, we obtain fitted values that represent only exogenous variation. This step is crucial for producing consistent estimates in the second stage of 2SLS, where we substitute these fitted values into our main equation.
• Discuss how weak instruments can affect the results of first stage regression and subsequent analysis.
  • Weak instruments can significantly compromise the reliability of first stage regression results by failing to explain enough variation in the endogenous variable. When instruments lack strength, it leads to biased estimates and inflated standard errors, which can misguide conclusions drawn from subsequent analyses. This issue underscores the importance of conducting tests for instrument strength before relying on first stage regression results for further estimation in 2SLS.
• Evaluate how first stage regression contributes to robust causal inference in econometric modeling.
  • First stage regression enhances robust causal inference by ensuring that estimates derived from models are not distorted by endogeneity. By identifying and utilizing valid instrumental variables during this initial step, researchers can effectively purge any bias caused by unobserved confounding factors linked with both dependent and independent variables. Consequently, this systematic approach allows for more reliable interpretations of causal relationships and strengthens overall conclusions drawn from econometric models.

Related terms

Endogeneity:

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

Instrumental Variable (IV): A variable that is used in regression analysis to provide a source of variation that can help identify causal relationships when endogeneity is present.

Two-Stage Least Squares (2SLS):

An estimation technique used when dealing with endogeneity, involving two stages: first, estimating the endogenous variable using instrumental variables, and second, substituting this estimate into the original equation.