When are
we born?

All 62,187,024 births in the United States from 2000 to 2014.

The data are just .

The same 5,479 daily counts, without regard to date.

Variance explained

The four components

Daily births decomposed into four sources of variation.

Long term trend

Births rose during the economic expansion of the mid 2000s and fell during and after the Great Recession (2007 to 2009).

Season

Each line represents one year. Births peak in September, approximately 38 weeks after the winter holidays…

Day of week

Each line represents one year. Births are most frequent on Tuesday and least frequent on Sunday.

Day of year

Effect of each calendar date on weekday births after adjustment for day of week and season.

Holidays

Births by calendar date

All 366 dates

Births on each calendar date relative to the mean daily births of the same year. The Day of year panel shows the same dates after adjustment for day of week and season.

The data

Daily birth counts for 5,479 consecutive days, January 1, 2000, through December 31, 2014.

DateDayBirthsModel expectedvs year mean

Calendar fine print

There are only 14 distinct calendars, one for each day of the week a year can start on, in common and leap years. From 1901 to 2099, where every fourth year is a leap year, they repeat in the same order every 28 years. In each cycle the common year calendars are used three times each and the leap year calendars once each, and every date falls on each day of the week exactly four times. The pattern breaks at century years, which are leap years only when divisible by 400, so 1900 and 2100 have no February 29 while 2000 does. The 15 years from 2000 to 2014 cover only part of a cycle and use 11 of the 14 calendars, so dates other than February 29 fell on a weekend unequal numbers of times (3, 4 or 5). Since fewer births occur on weekends, each extra weekend lowers a date's average by about 2%, so raw counts by date depend partly on the arbitrary start and end of the series rather than on the date itself. This is one reason a model is needed. It separates the effect of a date from the day of the week it happened to fall on.

The model

log births(t) =
  trend(t)Trend is a smooth curve with a time scale of about eight months. + season(t)Season is a smooth annual curve that drifts slowly over the period. + week(t)Week gives each day of the week its own level, which drifts over about two years. + date(t) + ε(t)What the model leaves over. On a typical day, actual births differ from the model by about .

All components are estimated together, in a simplified version of the model in BDA3 section 21.2.

Residuals

Observed births minus the model's expected births, as a percentage of expected, for each of the 5,479 days.

all daysnormal density with the same SDdates with repeated digits

Dates with repeated digits

Each date compared with the model, and its rank among all 5,479 days by absolute size of residual.

DateDayvs modelRank

Worked example

The week of June 6, 2006

Births above or below the model on each day.