Two-Stage Least Squares (2SLS) Regression Analysis

Two-Stage least squares (2SLS) regression analysis is a statistical technique that is used in the analysis of structural equations. Two-stage least squares (2SLS) regression analysis technique is the extension of the OLS method. Two-stage least squares (2SLS) regression analysis technique is used when the dependent variable’s error terms are correlated with the independent variables. Additionally, two-stage least squares (2SLS) regression analysis is useful when there are feedback loops in the model. In structural equations modeling, we use the maximum likelihood method to estimate the path coefficient. Two-Stage least squares (2SLS) regression analysis is an alternative technique in SEM modeling to estimate the path coefficient. Two-Stage least squares (2SLS) regression analysis technique can also be applied in quasi-experimental studies.

Key concepts and terms in two-stage least squares (2SLS) regression analysis:

Problematic causal variable: In two-stage least squares (2SLS) regression analysis, a problematic causal variable is the dependent or endogenous variable whose error term is correlated with the other dependent variable error term. In two-stage least squares (2SLS) regression analysis, a problematic causal variable is replaced with the substitute variable in the first stage of the two-stage least squares (2SLS) regression analysis.

Instruments: In two-stage least squares (2SLS) regression analysis, an instrument variable is used to create a new variable by replacing the problematic variable.

Stages in two-stage least squares (2SLS) regression analysis: in ordinary least square method, there is a basic assumption that the value of the error terms is independent of predictor variables. When this assumption is broken, two-stage least squares (2SLS) regression analysis helps us to solve this problem. Two-stage least squares (2SLS) regression analysis assumes that there is a secondary predictor that is correlated to the problematic predictor but not with the error term. Given the existence of the instrument variable, two-stage least squares (2SLS) regression analysis uses the following two methods:

1. In the first stage of the two-stage least squares (2SLS) regression analysis, a new variable is created using the instrument variable.
2. In the second stage of the two-stage least squares (2SLS) regression analysis, the model-estimated values from stage one are then used in place of the actual values of the problematic predictors to compute an OLS model for the response of interest.

Assumptions in two-stage least squares (2SLS) regression analysis:

1. In two-stage least squares (2SLS) regression analysis, models should be correctly specified.
2. In two-stage least squares (2SLS) regression analysis, the error variance of all the variables should be equal.
3. In two-stage least squares (2SLS) regression analysis, error terms should be normally distributed.
4. In two-stage least squares (2SLS) regression analysis, it is assumed that the outlier is removed from the data.
5. In two-stage least squares (2SLS) regression analysis, observations should be independents of each other.

Two-Stage Least Squares (2SLS) Regression Analysis and SPSS:

All statistical software does not perform this regression method. In SPSS, to perform Two-Stage Least Squares (2SLS) Regression Analysis, the following steps are involved:

1. Click on the “SPSS” icon from the start menu.
2. Click on the “Open data” icon and select the data.
3. Click on the “analysis” menu and select the “regression” option.
4. Select two-stage least squares (2SLS) regression analysis from the regression option. From the 2SLS regression window, select the dependent, independent and instrumental variable. Click on the “ok” button. The result window will appear in front of us. The result explanation of the two-stage least squares (2SLS) regression analysis is same as the OLS, MLE or WLS method.

Two-Stage Least Squares Regression Analysis Resources

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Kelejian, H. H., & Prucha, I. R. (1998). A generalized spatial two-stage least squares procedure for estimating a spatial autoregressive model with autoregressive disturbances. The Journal of Real Estate Finance and Economics, 17(1), 99-121.

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