Approximately 65% of live births linked to prenatal screening records, yielding 2 057 433 singleton births. Table I compares live births from the screened gestations with all births in the test years. The groups appear similar although the screened group had a lower proportion of older women and a higher proportion of privately insured women. These differences probably result from older women being referred directly for amniocentesis rather than for the blood screening test, and uninsured women less frequently obtaining prenatal care and therefore less likely receiving any screening.
Step 1 above, using Box-Jenkins routines to decompose mass layoff UI claims into statistically expected and residual components, yielded the values plotted in . The following Box-Jenkins model best fits the UI series.
Expected and observed values of California mass layoff UI claims for 79 months starting May 2001 (first 6 months lost to modeling).
is the number of mass layoff UI claims in month t. 3
is the difference operator indicating that Y
at month t was subtracted from Y
at month t + 3 to remove strong quarterly autocorrelation (i.e., high or low values at month t followed by similarly high or low values 3 months later). ϕB3
is an autoregressive parameter indicating that a quarterly ‘memory’ remained in the series even after difference at 3 months. The estimated value of ϕ (i.e., .57; SE = 0.0998) suggested that this memory decreased geometrically by about 50% with the passage of each quarter.
Steps 2 and 3, regressing the median male hCG scores in the 71 conception cohorts on the nine covariates and adjusting residuals for autocorrelation, yielded the expected values shown in . The covariates model in shows the coefficients estimated in this adjustment and their standard errors. also shows that we detected and modeled autocorrelation in which high or low median levels of hCG among males repeated, adjusting for covariates, with similar, but smaller, high or low values 16 months later. This pattern implies that we could not predict hCG for cohorts conceived before September 2002. Our final test, therefore, used 55 cohorts conceived from September 2002 through March 2007.
Observed and expected gestational hCG in 55 monthly cohorts of male infants conceived in California starting May 2001 (16 months lost to modeling).
Comparison of study sample to all California births, 2002–2007
Step 4, adding the unexpected mass layoff UI claims derived in step 1 to the model resulting from step 3, yielded the results shown in . Consistent with our argument, the cohorts of male infants conceived 8 months prior to unexpectedly high levels of claims exhibited higher median hCG levels than expected from history and from the specified covariates. shows a scatter plot and regression line for male cohort hCG, adjusted for covariates and autocorrelation, and unexpected mass layoff claims in the 8th month of gestation.
Coefficients from covariates-only and full model predicting median gestational hCG among male infants for 71 monthly California conception cohorts starting May 2001
Scatter plot and regression line of adjusted median gestational hCG (IU/L) in monthly cohorts of male births over residuals of mass layoffs (1000s) in California for 55 months beginning September 2002.
We conducted several additional tests to estimate the robustness of our findings. First, we transformed the dependent variable to natural logarithms to determine whether variability in variation could have induced our results. The findings did not change. In a related test, we applied the routines that detect and control outliers in the dependent variable (Chang et al. 1988
). We detected no outliers. We also used the routines that iteratively ‘pare’ statistically nonsignificant (P
> 0.05; 2-tailed test) covariates from the final model (Liu and Hudak 1992
). This routine left only median female hCG, mean maternal weight, and mean gestational age at blood draw among covariates in the final estimation but mass layoff UI claims remained significantly and positively related to median male hCG scores.
We also tested our hypothesis with three other configurations of our dependent variable. First, we estimated an equation with the male hCG deficit (i.e., median male hCG subtracted from median female hCG) as the dependent variable. This specification reflects the argument that the endemic difference in gestational hCG will shrink when stressors on the population induce selection against less fit fetuses. The coefficient for mass layoff UI claims remained significantly and, consistent with theory, inversely related to the males hCG deficit. Second, we used the ratio of male to female median hCG (i.e., the hCG sex ratio) as the dependent variable. The coefficient for mass layoff UI claims, consistent with the other results, again remained significantly >0. Third, we estimated an equation using only data for males (i.e., male median hCG as the dependent variable, female scores not among covariates). Because excluding median female hCG scores from the test leaves confounders shared by both sexes uncontrolled, we detected and controlled ‘level shifts,’ induced by changes over time in assay methods, in the residuals (Alwan and Roberts 1988
). The results also supported our argument in that increasing mass layoff UI claims predicted higher median male hCG scores.
Our argument assumes that the previously reported association between labor market contraction and the secondary sex ratio would appear in our test population using mass layoffs, adjusted for autocorrelation, in the 8th month of gestation as the independent variable. To test this assumption, we followed the steps described above for our main test. We specified the number of males in each cohort as the dependent variable and included, as covariates, the number of females as well as three characteristics of the cohorts (i.e., mean maternal age, percent non-Hispanic white, and percent African American) that prior literature suggests could confound the association between the economy and the sex ratio. Results showed that, as expected from earlier research, the sex ratio of survivors of the conception cohorts declined as the number of mass layoffs increased above levels expected from autocorrelation.
While the results shown in allow us to reject the null hypothesis, they convey little about the strength of association. We, therefore, made additional calculations to determine whether the discovered effect could actually change the ranking of conception cohorts on male hCG levels. First, we converted our continuous mass layoffs variable to a binary exposure. We followed the convention for creating such exposure variables by using a simple median split of months in which mass layoffs exceeded their expected values (i.e., had positively signed residuals from the Box-Jenkins model). We assigned a score of 1 to the 14 months with residual mass layoffs (in 1000s) above the median (i.e., 5.7909) and scored the remaining 57 months 0. Second, we estimated an equation with all the covariates shown in and the binary exposure variable for the 8th month of gestation (i.e., mass layoffs announced in the 6th month of gestation). Results showed that male median hCG rose by .1985 IU/L in the exposed cohorts. Third, we estimated the implications of this finding for two intuitively informative unexposed conception cohorts. First, the lowest of the 71 median male hCG scores was 19.1200 IU/L and came, as expected, from an unexposed cohort. Our findings imply that exposing this cohort to stressful levels of mass layoff announcements would cull enough less fit male fetuses to raise its score to 19.3185 IU/L (i.e., 19.1200 + 0.1985). This increase means that the effect we estimated has sufficient strength to move the cohort from rank 71 (i.e., lowest) to 64th among all cohorts. Second, the cohort, also unexposed, at the median (i.e., 19.900) of all cohorts would rise from 36th to 19th (i.e., 20.0985) if exposed to these announcements.