Endogeneity problem with 3 variables in one model, how to solve?

[Ruben Dadema]

Dear all,

I am struggling with a question concerning Endogeneity between multiple variables for my thesis, and can't seem to figure out a possible solution. I am performing panel data analysis using 3 variables:

• Immigration
• Economic growth
• Welfare state provisions (expenditure)

In the following model with an interaction term between welfare state provisions and immigration: Economic growth = Immigration + Immigration*welfare state provisons + welfare state provisions

My research question is: How do welfare state provisions affect the relation between immigration and economic growth?

To answer this question, I included the interaction term between welfare state provisions and immigration to measure how welfare state provisions change the relation between immigration and economic growth. However, the relation between immigration and economic growth becomes an endogeneity problem since immigration can cause economic growth, and economic growth can also cause immigration. Moreover, Economic growth can also lead to welfare state provisions, and welfare state provisions can lead to economic growth.

This means that both immigration and welfare state provisions face an endogeneity problem with economic growth in this model. I noticed that the endogeneity problem between immigration and economic growth could be solved with a two staged least squares model, if I'm correct, but I do not know how to solve the endogeneity between the other explanatory variable and economic growth.

To summarize: In the model: Y = X + X*W + W
Y can cause X, while X can cause Y. At the same time, W can cause Y and Y can cause W. Thus, there are two endogeneity problems. How to account for this in the model if we want to measure the causal relation between X and Y, while measuring how W affects the relation between X and Y?

Any help is very much appreciated, as I might have to pursuit another research question if there is no solution.

[Phil Bromiley]

Welcome to Stata list. You will increase your chances of useful answer by following the FAQ on asking questions-provide Stata code in code delimiters, readable Stata output, and sample data using dataex.

ivreg and user written ivreg2 will allow you to have more than one endogenous variable in the statement. Generally, you need to calculate the interaction and included in the list of endogenous variables. However, you do need good instruments for this to work.

Inherently, if these 3 variables are all you have and you want to allow for simultaneity, you can't do it. You need exogenous variables to act as instruments for the variables included to identify the model. In essence, you seem to have 3 equations so instead of ivreg you probably want reg3 or sem.

[Ruben Dadema]

Thank you Phil for your useful answer. I will be using two instrumental variables which are yet to be calculated. Additionally, I'll create the instrumental variable of the interaction term by multiplying the instrumental variable of the endogenous variable W and the endogenous variable X. Then, I plan to estimate the model using: -ivregress 2sls y (X W*X W =z5 z6 z7)- Where X, X*W and W represent the endogenous variables with X*W being an interaction term, and z5, z6 z7 being the instrumental variables of X, W*X and W respectively, where the z6 is created by simply multiplying z5 and z7. Not sure if this works yet, as I'll need to create the instrumental variables first using a different model. However, I wondered if this approach makes sense / would work.I'll look more into the provision of the relevant state code in code delimiters, output and sample data shortly!

Your input is greatly appreciated, thank you for the useful answer you provided