Everyone is consuming way too much news on the only news in town. So I’m going to skip the preliminaries and go straight to documenting what turns out to be a very puzzling phenomenon. We’ve seen that the class gradient of the odds ratios for COVID-19 deaths in Britain were more disconcerting than those associated with race; all the hullabaloo about race gradients notwithstanding. I expected to find something similar in the United States. As it turns out, this is not the case. While the race gradient is embarrassingly large and of the expected sign, the class gradient sports the *wrong sign*. This is an astonishing puzzle. One that we believe deserves some attention.

We don’t have data at the individual level for the United States. What we’re going to do is examine the cross-section of US counties and interrogate the covariates of said death rates. All data below is from Social Explorer. Before we can examine the gradients for class and race, we need a null model. Our null model is straightforward. Death rates per hundred thousand from COVID-19 by county are modeled as a linear function of confirmed cases per hundred thousand, population density, and the percentage of the county’s populace that is over 85 years old (over 65 yields similar results).

We estimate the gradients in three ways. First, we use OLS to estimate the slopes (controlling for the null model when we estimate the race and class gradients). Second, we admit state fixed effects. That is, we allow the intercept to vary by state. Third, we admit state random effects. In this case, the state intercepts are estimated not as fixed parameters but as centered Gaussian random variables with fixed but unknown scale parameters. Random effects are preferable when the error terms are not correlated with the predictors. Since we do not know if this is the case, we keep an open mind. Congruence between the three gradient estimates would suggest that the results are robust to estimation procedure and hence more reliable. Conversely, disagreement between the three estimates would be grounds for skepticism and call for greater care in the interpretation of the gradient estimates.

Let’s get on with it. Table 1 displays the three estimates for the null model. The null model can explain 30 percent of the variation without state fixed effects, and 45 percent of the variation with state fixed effects. We can see that we need to control for interstate variation in order to recover the age gradient. The slope estimates with state fixed effects (column 2) and state random effects (column 3) are comparable. From now on, we shall suppress the estimates for the variables of the null model with the understanding that they are all significant in the models that follow.

Table 1. Null Model. |
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Case rate | 3.48 |
2.90 |
2.95 |

std error | 0.11 | 0.10 | 0.11 |

Density | 0.42 |
0.31 |
0.33 |

std error | 0.04 | 0.04 | 0.04 |

Senior | 0.12 |
1.32 |
1.35 |

std error | 0.33 | 0.34 | 0.34 |

Intercept | Yes | No | Yes |

State FE | No | Yes | No |

State RE | No | No | Yes |

Source: Social Explorer (May 19, 2020), author’s computations. All predictors are standardized to have mean 0 and variance 1. Estimates in bold are significant at the 5 percent level. |

We proxy race by percent of the county population that is black. In Table 2, we proxy class by college graduation rate. We can see that the gradient for race is extremely large and significant. One standard deviation change in percent of the populace that is black increases the death rate by +2.28 per hundred thousand. By comparison, the mean absolute deviation of the death rate is 13.5 and the standard deviation is 23.7. Note that we are controlling for age, population density, and the incidence rate of COVID-19 cases. So this gradient is an indictment of American institutions. Put simply, the implication is that black people are dying at higher rates because American institutions are less responsive to them than those who are categorized as white.

Table 2. Race and Class gradients. |
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Black | 2.46 |
2.28 |
2.28 |

std error | 0.18 | 0.23 | 0.23 |

College | 1.28 |
0.83 |
0.92 |

std error | 0.32 | 0.31 | 0.32 |

Case rate | Yes | Yes | Yes |

Density | Yes | Yes | Yes |

Senior | Yes | Yes | Yes |

Intercept | Yes | No | Yes |

State FE | No | Yes | No |

State RE | No | No | Yes |

Source: Social Explorer (May 19, 2020), author’s computations. All predictors are standardized to have mean 0 and variance 1. Estimates in bold are significant at the 5 percent level. |

Given what we know about race relations in the United States, this is to be expected. What is really surprising is that more educated people are dying at higher rates than less educated people. In other words, the class gradient is the wrong way around!

This is not an artifact of our choice of models or variables. Table 3 replaces college graduation rate by the natural log of median household income. We find an even stronger gradient for median income than for college graduation rate. The gradient of race also turns out to be slightly larger.

Table 3. Race and Class gradients. |
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Black | 2.75 |
2.49 |
2.51 |

std error | 0.20 | 0.24 | 0.24 |

Median income | 1.94 |
1.49 |
1.61 |

std error | 0.37 | 0.39 | 0.39 |

Case rate | Yes | Yes | Yes |

Density | Yes | Yes | Yes |

Senior | Yes | Yes | Yes |

Intercept | Yes | No | Yes |

State FE | No | Yes | No |

State RE | No | No | Yes |

Source: Social Explorer (May 19, 2020), author’s computations. All predictors are standardized to have mean 0 and variance 1. Estimates in bold are significant at the 5 percent level. |

Table 4 uses the natural log of median gross rent as the proxy for class. The gradient estimates are close to those obtained from using median income.

Table 4. Race and Class gradients. |
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Black | 2.46 |
2.29 |
2.29 |

std error | 0.18 | 0.23 | 0.23 |

Rent | 1.82 |
1.16 |
1.31 |

std error | 0.35 | 0.39 | 0.39 |

Case rate | Yes | Yes | Yes |

Density | Yes | Yes | Yes |

Senior | Yes | Yes | Yes |

Intercept | Yes | No | Yes |

State FE | No | Yes | No |

State RE | No | No | Yes |

bold are significant at the 5 percent level. |

We have documented a highly counter-intuitive puzzle. Why is the class gradient of COVID-19 death rates of the wrong sign? One hypothesis is that death rates are elevated in the more globally-connnected parts of the US economy, ie the coastal areas. But we have already controlled for their higher case counts and higher population densities. Moreover, such effects should be absorbed by state fixed and random effects. We can see some of this attenuation. But the class gradients remain robust and continue to sport the wrong sign. This is a profound puzzle.

*Postscript*. Just a very quick note to make three points. First, within-county inequality, as captured by the Gini index, is also a strong predictor of death rates. Second, I should’ve noted that the random effect covariance parameter is also highly significant, as is evident from the confidence intervals for it displayed below. This means that the random effects model is preferable; especially since the results are otherwise congruent and we have no good reason to suspect that the error term is correlated with any of the predictors. Lastly, all the predictors are individually and jointly significant, as attested by likelihood ratio tests. We only display the result of the joint test. The estimates displayed below may be taken as final.

I wonder if there is an effect of who gets tested and who does not so it may be that it was just known at death that they had COVID.

Hi C, so we should expect lower detection rates for deaths due to COVID-19 in more marginal communities? They’re dying at the same or higher rates but the reporting rates are higher in more affluent counties? That would be one way to resolve the puzzle.

I think you control for testing rates by getting the counts of confirmed positive tests (per a 1K) . I bet you that’s what you are seeing: African Americans in general have poor health access or bad quality as well as more likely to have underlying health issues (eg diabetes) but that more Affluent communities – marginalized ones– are just testing more.

Agree on the interpretation of the race gradient too. That’s what I suspect. And it’s more testable that the underreporting theory of the class gradient. How would one test that?

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