Chile's Population (2012 Census)

The preliminary results of the 2012 Chilean census were recently covered in an Economist article: "Chile's economic statistics".

“Casengate”, as it has become known, is not the only recent statistical anomaly in Chile. Preliminary findings from this year’s census found only 16.6m Chileans. That was surprising since the projection by the National Statistics Institute (INE) from the previous census in 2002 was 17.4m. The new number seemed to confirm worries that this year’s census was poorly conducted. But it allowed Felipe Larraín, the finance minister, to point out wryly that the country’s income per head, at purchasing power parity, is around $19,000—a handy upward leap from $17,222 last year.

This lead to an response by one of Chile's leading economist, Dr. Klaus Schmidt-Hebbel from the Catholic University of Chile:

Furthermore, the 2012 census showed that Chile’s population fell well below the joint UN and government projection, and not, as you said, only below the projection provided by the National Statistics Institute. You infer that “the new number seems to confirm that this year’s census was poorly conducted.” In other words, you are saying that if reality differs from a projection based on ten-year- old data then reality must be wrong. Nor did you mention that the 2012 census was taken over a three-month period in order to survey a larger proportion of Chile’s population, whereas previous censuses were taken on one day. As a result the 2012 census had the largest coverage in Chilean history: 98.34% of households.

Let's look at the data. The following is an extract from the aforementioned preliminary results, which coincides with the 16.6 million mentioned by the Economist:

Looking at the INE's vital statistics report from 2010, the numbers are as follows (especially note the footnote 1: "the census omission in 1960, 70 y 82 was 4,3%, 6,6% y 1,5%, census 1992 1,1% and for the census 2002 3,8%"). Unfortunately, it is not entirely clear whether the data for the census years is before or after correction for census omission.

The 2010 vital statistics shows a strange anomaly with regard to the population growth which turns negative for the census years and then considerably above trend for the subsequent years (this assumes that omission have been incorporated in the above data set).

Unfortunately, the INE has a third data set, namely it's population projection based in the 2001 census. This looks as follows:

This leads to the following three (four) series of population data, which have been disseminated by the INE.

I started writing this post believing that the the difference between the preliminary census results and the population projection and vital statistics could be pretty much explained by an omission rate in line with the previous census. Now, I'm struggling to understand what is going on.

Demographic projections are pretty stable. In Chile's case it would mean the projection was more than 800'000 higher than the census results (or approximately 5%), almost 100'000 on an annual basis. Of the following possible explanations, I only view the last one as plausible:

• birth's are over-reported by 100'000 birth a year (approx. 150'000 instead of 250'000)
• death are under-reported by 100'000 birth a year (approx. 200'000 instead of 100'000)
• net emigration is 100'000 a year
• census omission rate continues do be in the order of 5%