Instrumenting a Variable with Interaction using feols

In recent years, there has been a significant interest in using multivariate generalized additive models for non-linear modeling and analysis. These models can capture complex interactions between variables while accounting for the non-linearity of individual effects. One popular software package for estimating these models is feols, which stands for “Generalized Additive Models with interaction.” In this article, we will explore how to use feols to instrument a variable with interaction.

Introduction

feols is an R package that extends the capabilities of generalized additive models (GAMs) by incorporating interaction terms. This allows researchers to model complex relationships between variables in a non-linear and flexible way. In this article, we will focus on using feols to instrument a variable with interaction.

Instrumenting a variable involves creating a new variable that captures the relationship between the original variable and an external variable (often referred to as the “instrument”). The goal of instrumental variable analysis is to identify the causal effect of the original variable on the outcome variable while controlling for the effects of the instrument.

Setting up the Problem

Suppose we want to run y~i(group, x) and instrument x with z. This means we want to estimate the interaction between x and some other variable (group) on the outcome y, while using z as our instrument. In R, this can be achieved using feols.

Using feols for Instrumenting a Variable

The basic syntax for using feols to instrument a variable is:

feols(y~i(group,x)|0|x~z, df)

In this code:

• y is the outcome variable.
• group, x, and z are our variables of interest.
• i(group, x) specifies that we want to model the interaction between group and x.
• 0 indicates that we do not include an intercept term in the model.
• | is used to separate different parts of the model specification.
• x~z specifies that we want to instrument x with z.

However, as you mentioned in your question, this does not seem to produce the desired output.

Alternative Syntax

One alternative syntax for using feols to instrument a variable is:

feols(y~i(group,x)|0|x~z, df)

In this code:

• y is the outcome variable.
• group, x, and z are our variables of interest.
• i(group, x) specifies that we want to model the interaction between group and x.
• 0 indicates that we do not include an intercept term in the model.
• | is used to separate different parts of the model specification.
• x~z specifies that we want to instrument x with z.

However, as you mentioned in your question, this also does not seem to produce the desired output.

Alternative Approach

Another approach to use feols for instrumental variable analysis is by using a different syntax:

feols(y~0|i(group,x|z), df)

In this code:

• y is the outcome variable.
• group, x, and z are our variables of interest.
• i(group, x|z) specifies that we want to model the interaction between group and x while using z as an instrument.

This approach may produce the desired output, but it requires some adjustments in your model specification.

Estimating Instrumental Variables

Once you have specified your feols model, you can use R’s built-in functions to estimate instrumental variables. The main function used for this purpose is feols().

To estimate a feols model, you need to call the feols() function with the following arguments:

feols(y~0|i(group,x|z), df)

In this code:

• y is the outcome variable.
• group, x, and z are our variables of interest.
• i(group, x|z) specifies that we want to model the interaction between group and x while using z as an instrument.

After running this function, R will output a table containing the estimated coefficients for each variable in your model.

Implications of Instrumenting a Variable

Instrumenting a variable can have significant implications for our understanding of causal relationships. By controlling for the effects of the instrument, we can isolate the effect of the original variable on the outcome variable.

However, it is essential to note that instrumental variables may not always be perfectly correlated with the original variable. If the instrument is weakly correlated or has omitted variables, the estimates obtained using feols may be biased.

Conclusion

In conclusion, feols provides a flexible way to model complex relationships between variables while accounting for non-linearity and interaction effects. By using the correct syntax and adjusting our model specification accordingly, we can use feols to instrument a variable with interaction.

Instrumental variable analysis can provide valuable insights into causal relationships and should be used judiciously in research settings.

Additional Resources

If you would like to learn more about instrumental variables and how they are used in practice, I recommend checking out the following resources:

• R Manual: feols documentation.
• R Journal: articles on instrumental variable analysis and generalized additive models.
• Textbooks: books on generalized additive models, instrumental variables, and causal inference.

Acknowledgments

I would like to thank you for providing me with a great question. This article is the result of my efforts to provide clear explanations and examples of how to use feols for instrumental variable analysis.

By following this guide, you should be able to instrument a variable using feols.

Last modified on 2025-01-24