Quasi-Experimental Studies: Instrumental Variables Approach (Research Paper Sample)

Instrumental Variable
Name
Institution
Instrumental Variable
This paper proposes to use an instrumental variables approach to analyze the effect of tuition amount on math scores. The amount of money spent on tuition (x variable) is expected to be lead to better educational outcomes (y variable). However, that does not confirm causality. One confounding factor of the relationship is family income (u). Higher family income allows the parents to spend more on tuition. Also, studies have proven that family income is positively related to higher educational outcome (Gregg & Blanden, 2004). The instrumental variable proposed is the number of siblings. The reasoning behind this is that since per person consumption is largely a function of family size and disposable income, then the more the siblings the smaller the amount of money available for tuition expenditure per child. However, the number of siblings one has is not expected to affect math scores or total family income. This paper has two main aims. One (already stated) is to use an instrumental variables approach to analyze the effect of tuition amount on math scores. The other one is to test the validity of the instrument by checking whether the instrumental variable proposed satisfies all the assumptions of an instrumental variable.
Relationships and Dataset
Figure1: The relationships
To run the analysis the ECLS dataset that will be used. The variable named X8INCCAT_I captures the values of household income. The tuition amount variable is called P2HOWPAY. For this study, the total number of variables is 1,745. X8MTHETK4 captures the math scores. X8NUMSIB captures the number of siblings in a house.
Endogeinity
Apart from the number of siblings, there is a high likelihood that there exist other variables that affect tuition and math scores too. However, getting data for such variables is not always easy as a particular dataset rarely includes all confounding variables. Using the instrumental variable approach allows one to account for the endogeneity without having to measure the confounding variables. To do that, one tries to move away from just using OLS and to restrict himself/herself to look at just some of the variation seen in tuition fees that is not correlated with the error term.
The linear model between the dependent and independent variables can be represented as:
Math scores = βo+ β1Tuition + ɛ
As per Gauss-Markov condition, the expectation of the error term given the x variable has to be equal to zero. That is:
E[ɛ1│xi] = 0
However, the circumstance does not hold if there are omitted variables that are correlated with the x term, when there are measurement errors in the independent variable, and if there is reverse causality. If the Gauss-Markov condition does not hold the consequence is that the expectation of the OLS estimator no longer equals the true parameter β and hence it is biased. Another problem is that no matter how large the number of elements is the estimated does not move towards the true parameter β. In other words, the estimator is also inconsistent as represented below.