XLSTAT: Two-Stage Least Squares Regression (2SLS) in Excel

 

Dataset for Example

The data from Kmenta’s food demand-and-supply example include five variables: food consumption per head (FCH), the ratio of food prices to general price (RFP), disposable income (DI), the ratio of preceding year price (RPP), and the year (1922–1941). FCH and RFP are endogenous, while DI, RPP, and Year are exogenous.

To assess how food consumption varies with RFP and DI, we use the two-stage least squares method, treating DI, RPP, and Year as instrumental variables.

 

Setting Up

• Open XLSTAT.

• Click on the Modeling data menu and select the Two-stage least squares feature.

• After clicking the button, the dialog box opens.

In the General tab:

• Specify FCH as the dependent variable, RFP and DI as explanatory variables, and DI, RPP, and Year as instrumental variables.

• Since the column headers were selected, keep the Variable labels option enabled.

In the Options tab:

• Set the tolerance, the level of confidence intervals and the option to include or not the constant in the model.

• Here we choose to leave the default values.

• Click on the OK button to launch the computations.

• The results are displayed on a new Excel sheet.

 

Interpreting the Results

First, variable statistics are shown. Then, the model’s goodness-of-fit table appears. The R² value indicates the proportion of the dependent variable's variability explained by the model—closer to 1 means a better fit.

The analysis of variance table helps assess if the explanatory variables add significant value to the model. It tests the null hypothesis (H₀) that they do not; rejecting H₀ confirms their relevance over using just the mean.

Fisher's F test shows a p-value below 0.0001, indicating less than a 0.01% risk in rejecting the null hypothesis. Thus, the explanatory variables significantly improve the model. The next table provides model details (coefficients, standard deviations), useful for prediction or population comparisons.

The table and graphs display standardized residuals, which should follow a normal distribution. Ideally, 95% should fall within the interval [-1.96, 1.96]. The histogram helps visually identify any outliers beyond this range.

All residuals fall within the [-1.96, 1.96] interval, indicating no outliers.