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I have an explanatory variable, 'social class' which I am trying assess the effect on a child's test score. Social class is a 6 fold categorical that breaks down based upon the parent's occupation - professional, manergerial, unskilled etc.

Because of the endogeneity of social class, and unobserved factors that impact upon the allocation of households into social class, I wish to instrument for social class using a dummy variable which takes the value 1 if the family are on a medical card (this is given to low ses households in ireland for free healthcare), and 0 otherwise.

Is this okay to do? The estimates I'm getting are quite different to the OLS estimates, which has me worried.

Thanks in advance.

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2 Answers 2

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This instrument seems like it would fail on both the exogeneity and the relevance criteria. One reason to do IV is that there is something unobservable, like motivation, that is correlated with SES. Your instrument needs to move around social class (relevance) without altering motivation (exogeneity). Proxies tend to make bad instruments: by definition, they are correlated with unobservables. The card is arguably a proxy for low SES. On the relevance front, you just can't predict a categorical variable that takes on six values with a binary one, so it mechanically irrelevant/weak for the high SES categories.

OLS and IV estimate different treatment effects, so even if there was no endogeneity to worry about, you should see different estimates if students' SES has a variable effect on scores. When instruments are weak and there is endogeneity, the bias of IV can more substantial than OLS.

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    $\begingroup$ The conventional abreviation for socioeconomic status is SES, SS as an abreviation has a rather tainted history and is thus best avoided. $\endgroup$ Nov 13, 2014 at 15:25
  • $\begingroup$ Thanks so much for your reply. I understand that the card is a proxy for low SES, but surely not a proxy for whether the parent is a professional, or unskilled. As such, there are surely unobservables that affect whether the parent is a professional/unskilled but which also affect the child's test scores? (parent's motivation, etc). The medical card is something that you only have if you'e in a low paying/no job situation, but having it itself doesnt affect the child's outcome? $\endgroup$
    – StephenB
    Nov 13, 2014 at 16:48
  • $\begingroup$ That's exactly the problem. Your proposed instrument is irrelevant for some of the categories whose effect you are interested in. On the second point, one could argue that if unobserved motivation is a shared trait within families (either because it is heritable or environmentally transmitted), it will be negatively correlated with scores and might contribute to low SES and poor employment outcomes for the parents and cards. There are at least two possible channels. A low income might make it harder for parents to invest in their children. The low income could be an outcome of poor motivation. $\endgroup$
    – dimitriy
    Nov 13, 2014 at 18:38
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(Notwithstanding the basic observation made by @DimitriyV.Masterov about the unsuitability of predicting a 6-values categorical variable with a binary one).

Finding candidate instruments and choosing among them, is one of the fine arts of statistics and econometrics. A very fine art. Although some hard quantitative procedures have been devised in order to assess the choices made, the fact remains that the non-quantitative, verbal and logical argument that supports the choice retains its central and critical importance in order for an instrument choice to have chances to be accepted as valid.

For your particular case, this means that prior to searching for instruments, you must first lay out what are the factors that affect a child's test score, by name and not by the general tag "unobserved factors".

After you name these factors and develop an argument as to why they do affect a child's test score, and so as to why they are thought of as "included in the error term" of your regression specification, then you have to separate those for which you have data available, and those that you do not.

For the factors on which data are available, probably you should include them in the regression specification as controls.

For those remaining factors that are either unobservable, or for which data are not available to you, you have to point out which among them is correlated with SES and why (logical argument again). Denote this subset by $W$.

Then, you have to think what observable and available variable(s) is correlated with SES but uncorrelated with $W$ -and you have to lay down (again) a convincing argument about this difficult to find "correlation / non-correlation" combination.

So, to the specific question "Is this ok to do?", with "this" representing the whole approach as described by you in the question, the answer is a -multidimensional- "No".

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  • $\begingroup$ Thank you again to both you and @Dimitriy, you've both given incredibly detailed answers and I'm extremely grateful. I have another idea, and since it's become clear to me that my understanding of IV approaches is clearly lacking (me thinking of IVs as proxies somehow), I had another idea that I thought I'd pass by you guys - see what you thought. Please let me know if I'm overstepping the bound here. I'll post it in the next comment to give some room! Again feel free to tell me to go ask elsewhere if I'm taking liberties - but I'm at a loss here. $\endgroup$
    – StephenB
    Nov 14, 2014 at 10:22
  • $\begingroup$ @StephenB It would perhaps be better to post this other idea of yours as a new question, rather than as a comment here. $\endgroup$ Nov 14, 2014 at 10:31
  • $\begingroup$ Actually scratch that. I understand IV properly now after an evening of thinking about it. I don't think I can plausibly instrument for SES as there's nothing available to me that would exogenously alter socioeconomic status that aren't correlated with the error term. The idea I was going to tell ye about was using the weekly cost of childcare to instrument for SES, as if it's more expensive the parent's are likely to have to change jobs, but it could also affect other things - i'm at a loss to be honest. Thanks for all the help. $\endgroup$
    – StephenB
    Nov 14, 2014 at 11:22

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