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# An Example of Ideology Leading to Bad Statistics and Social Injustice

Summary:
My post “Adding a Variable Measured with Error to a Regression Only Partially Controls for that Variable” scolds statistical practitioners for all to often assume that adding a variable to a regression controls for that variable, when almost all such variables are measured with error. The math then shows that adding a variable measured with classical error yields a result between what one would get with a pristine version of the added variable measured without error and omitting that variable entirely. Thus, adding a variable measured with error only partially controls for that variable.But there is something worse

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My post “Adding a Variable Measured with Error to a Regression Only Partially Controls for that Variable” scolds statistical practitioners for all to often assume that adding a variable to a regression controls for that variable, when almost all such variables are measured with error. The math then shows that adding a variable measured with classical error yields a result between what one would get with a pristine version of the added variable measured without error and omitting that variable entirely. Thus, adding a variable measured with error only partially controls for that variable.

But there is something worse than pretending to control for a variable by adding an error-ridden measure of it without adjustment for measurement error: not trying to control for confounding factors at all.

To me, a principle of social justice is that we should do more for people who are worse off, especially when being worse off makes the same amount of resources more effective at helping someone. On average, in our society, being a racial minority puts people at a disadvantage. But it is not true that all Black people are worse off than all White people. In the extreme, other things equal, would you rather be a Black billionaire or a White homeless person?

It is a very interesting question how the overall well-being of Black and White people of equal income compares on average. Racism in all probability still makes it harder on average to be Black even at an equal income. But noticing that an important part of the disadvantage of Blacks is reflected in lower income is surely important.

New York’s current policy on the rationing of scarce COVID-19 treatments provides a useful thought experiment to think about both these statistical and these social justice issues. What I know about this is from John Judis and Ruy Teixeira’s January 7, 2021 Wall Street Journal op-ed “New York’s Race-Based Preferential Covid Treatments.”

Jon and Ruy begin by saying:

New York state recently published guidelines for dispensing potentially life-saving monoclonal antibodies and oral antivirals like Paxlovid to people suffering from mild to moderate symptoms of Covid-19. These treatments are in short supply, and they must be allocated to those most in need.

According to these guidelines, sick people who have tested positive for Covid should be eligible to receive these drugs if they have “a medical condition or other factors that increase their risk for severe illness.” These include standard criteria like age and comorbidities like cancer, diabetes and heart disease—but, startlingly, they also include simply being of “non-white race or Hispanic/Latino ethnicity,” which “should be considered a risk factor, as longstanding systemic health and social inequities have contributed to an increased risk of severe illness and death from COVID-19.”

Using racial data would be appropriate in this context if we didn’t have income to go by. But making race a criterion for scarce health resources without also making income a criterion as seems unfair.

As far as we know, COVID-19 is not a disease like sickle-cell anemia where genetic differences put Blacks at greater danger. Jon and Ruy write:

There isn’t any study we have seen that, controlling for other factors, such as income, education and residence, shows clearly that Americans of Hispanic, African or Asian ancestry are at greater risk for severe Covid-19.

Of course race is correlated with Covid-19 incidence, in a big way. The question is whether that is operating through income and education or needs to be accounted for by a separate causality. Jon and Ruy argue:

It is probable that a good part—perhaps most—of the observed racial disparity in Covid effects is attributable to factors that can be loosely grouped under class: income, education, poverty status, occupation, health-insurance status, housing and so on. The way to test this would have been to collect individual-level data on such variables in addition to race, ethnicity, age and gender. But that has not been done, so only racial disparities, uncontrolled for class factors, have been reported.

As one example of what such studies might find, Kaiser Family Foundation survey data on vaccination rates revealed that black and white college graduates were vaccinated at roughly equal (high) rates, while there was a yawning chasm between these college graduates and their noncollege counterparts of the same race. Clearly then, the observed disparities in vaccination rates between blacks and whites have a lot to do with the higher noncollege proportion among the black population.

Many people in our nation face big difficulties. We should be helping people in trouble.

As a side note, there is a crucial underdiscussed dimension in which we don’t treat poor people very well in this country—and in particular don’t treat poor Black people well: rich people use exclusionary single-family house zoning to keep poor people—and perhaps especially poor black people—out of their neighborhoods and out of their kids’ schools. Poor kids (including poor black kids) on average get a worse education and also lose out on the advice and connections that having at least some rich neighbors could help with. To me, this is one of the best examples of structural racism. It doesn’t make any sense to talk structural racism in general without talking about this elephant in the room (or “elephant in the neighborhood”). I would at least like to have people be put on the spot trying to justify something that has a disparate impact through such an unfair mechanism. I think it would be quite possible for a good reporter to quite appropriately make a lot of people look really bad in this context. And that might lead to some constructive change.

Note that as long as Black people are in an initial condition that leaves them poorer, for whatever reason, anything that is unfair to poor people should count as structural racism because being unfair to poor people is going to slow down any possible convergence in status between Black and White people. And I suspect that there is an interaction making racism disadvantaging poor Blacks as against equally poor Whites stronger than racism disadvantaging rich Blacks as against equally rich Whites.

Miles Kimball is Professor of Economics and Survey Research at the University of Michigan. Politically, Miles is an independent who grew up in an apolitical family. He holds many strong opinions—open to revision in response to cogent arguments—that do not line up neatly with either the Republican or Democratic Party.