Please, Do Not Comment on This Post Unless You Understand the Following Terms

  • Population mean
  • Sample mean
  • Population standard deviation
  • Sample standard deviation
  • Standard error
  • Administrative data
  • Survey data
  • Point estimate
  • Confidence interval
  • Sampling bias
  • Reporting bias

Now, let’s begin. Here is a graph of estimates of cumulative fatalities in Puerto Rico over time.


Figure 1: Estimates from Santos-Lozada and Jeffrey Howard (Nov. 2017) for September and October (calculated as difference of midpoint estimates), and Nashant Kishore et al. (May 2018) for December 2017 (blue triangles), and Roberto Rivera and Wolfgang Rolke (Feb. 2018) (red square), and calculated excess deaths using average deaths for 2015 and 2016 compared to 2017 and 2018 using administrative data released 6/1 (black square), and Santos-Lozada estimate based on administrative data released 6/1 (large dark blue triangle), end-of-month figures, all on log scale. + indicate upper and lower bounds for 95% confidence intervals. Orange + denotes Steven Kopits 5/31 estimate for range of excess deaths through September 2018. Cumulative figure for Santos-Lozada and Howard October figure author’s calculations based on reported monthly figures. [Figure revised 6/3]
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Estimates of Excess Fatalities in Puerto Rico, Post-Maria

Given some criticisms of the Harvard School of Public Health led study, published in the New England Journal of Medicine, I thought it useful to compare point estimates and 95% confidence intervals of several extant studies, placed in a time context.


Figure 1: Estimates from Santos-Lozada and Jeffrey Howard (Nov. 2017) for September and October, and Nashant Kishore et al. (May 2018) for December 2017 (blue triangles), and Roberto Rivera and Wolfgang Rolke (Feb. 2018) (red square), end-of-month figures, all on log scale. + indicate upper and lower bounds for 95% confidence intervals. Cumulative figure for October author’s calculations based on reported monthly figures.

The growth rate of cumulative excess fatalities is in the range of 70% per month.

Steven Kopits has characterized the study published in the New England Journal of Medicine as “garbage”, noting that it uses survey data. He has instead relied on Demographic Registry Data in his assessment. He places cumulative excess deaths at 200-400. Interestingly, Rivera and Rolke (2018) also used Demographic Registry Data and concluded that 822 excess deaths occurred from September 20 through October 31 alone, with 95% CI (605, 1039). Extrapolating linearly through end-December (time span conforming to the NEJM article) would imply 2603 excess deaths, well within the 95% confidence interval of 793-8498.

It should be also remarked upon that the Santos-Lozada and Howard study uses actual statistics for baseline from Puerto Rico Vital Statistics System, and cited numbers processed through Puerto Rico Department of Health for September (extrapolated for October). Hence, this estimate is also not survey based.

Hence, we have two sets of non-survey based estimates that as of October exceed Mr. Kopits’ upper bound of 400.

What Will Policy Uncertainty Be Tomorrow?

Below is reported Economic Policy Uncertainty through 5/31/2018, reflecting newspaper accounts through 5/30.


Figure 1: US Economic Policy Uncertainty index (blue) and centered 7-day moving average (bold red). Source: policyuncertainty.com accessed 31 May 2018, and author’s calculations.

As of 2PM EST, Dow down 1%, VIX up 6.69%.

All that is old is new again

Tonight:

Nearly century and a half ago, political cartoonist Tomas Nast presents a “harsh commentary on the hypocrisy of these new Americans and their willingness to oppress others who are in the same circumstances in which they found themselves 30 years earlier. The once oppressed have now become the oppressors.”:

“Throwing Down the Ladder by Which They Rose,” by Thomas Nast, 23 July 1870. Source

For more, see this.

Heckuva Job, Donny! Puerto Rico Edition

From New England Journal of Medicine, results of a study led by researchers at Harvard T.H. Chan School of Public Health and Beth Israel Deaconess Medical Center:


Figure 4. Estimates of Excess Deaths and Reported Causes of Death.
Panel A shows a comparison of estimates of excess deaths from official reports, press (New York Times)8 and academic (Santos–Lozada and Howard)9 reports, and from our survey. Panel B shows deaths according to the month of death and the age at death as reported in our survey, categorized according to the cause of death reported by the household member. Two persons who died of similar causes at the same age are represented by dots that are superimposed in December; thus, the 37 points shown represent 38 deaths after the hurricane.
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