How to evaluate time invariant independent variables in regression?

04 April 2018 4 7K Report

Hi!

My and my thesis partner have encountered some problem with our regression and would really appreciate some help / guidance.

We are evaluating a property tax reform and have downloaded tax data for the entire population affected by the reform. In our data set, the population is divided into different groups depending on income-level (discrete variable from 1-26), geographical region (discrete variable from 1-21), age-groups (discrete variable from 1-3) and gender (dummy variable). The tax data is collected yearly for some years before and some years after the reform.

We would like to use a regression model in order to see whether some of these variables (for example income-level) have had a significant effect on the change in tax payments due to the reform. Our problem is to find a proper regression model.

One thought we've had is to use our data as a panel data set. Then it is a short panel data set since N = 3 276 and T = 17. The problem we got then is that our discrete variables that we want to evaluate are time-invariant, which makes the fixed effects model difficult to use. In the same time we think that the unobserved component is correlated with our regressors, which makes the fixed effect more proper to use.

If someone has thoughts on what regression model to use for our data it would help us a lot. Also suggestions for good literature or papers that covers the same kinds of data set that we have would really help us.

Thanks!

Eliud Moyi

You have a short panel (T=17, N=3276) and your interest is evaluating time-invariant variables. You also suspect that the error term is correlated with the explanatory variables (endogeneity). The most appropriate model to use will be system GMM. It is suited to the kind of data that you have and also accommodates endogeneity bias.

A good starting point is Roodman's paper

Hamit Can

https://www.researchgate.net/post/Is_there_a_way_to_estimate_coefficient_of_time_invariant_dummies_in_a_fixed_effect_model

https://pdfs.semanticscholar.org/3056/7f21ab0f3b95a68377ee0a6d7146831a0c91.pdf

https://pdfs.semanticscholar.org/presentation/6961/1f03a4cca2c554785cdfa1f8adbcc62fa7ac.pdf

Christian Dreger

One main problem is this exercise is to avoid multicollinearity. It would occur in the fixed effects model, if one regressor is the same for all panel members (as the fixed effects will add to the unit vector). This is not the case in your data, since income, region, age and gender all vary across the individuals. Furthermore, your potential tax variable is not time invariant. I suppose you work with a dummy equal to 0 before and equal to 1 after the reform. So, after all, your model is assessable, at least in principle.

However, you should take other caveats into account, such as endogeneity of regressors, probably anticipation effects due to an early announcement of the tax reform etc

Bakr Al-Gamrh

Try to use the Hausman test and see what is the proper regression for your data. if you ended up that you must use fixed-effect, then you i think GMM is suitable for your data

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