International Migration Flow Table Estimation

International migration flow data is a messy topic. No single pair of countries defines migration in the same way. Even if the did they most likely measure if differently. This causes some big headaches to anyone who wants to create any inference about migration levels, directions, policy implications or the cause and consequences of people’s movements at a cross national level. During my Ph.D. I worked on methods for estimating comparable international migration flows across multiple European countries.

I identified two fundamental data problems: inconsistency (countries with conflicting reports on the number of people moving between them) of and incompleteness (countries not providing any data). I applied both mathematical and statistical methods to create comparable set of international migration flow estimates. For more details see my Ph.D. dissertation (which is online, see the link below). It contains most of the R/S-Plus code to conduct the estimation in the Appendix. Note, there is also a published paper based on my Ph.D. (abstract and links here). I created a TeX template for the University of Southampton School of Social Sciences here.

Publication Details:

Abel, G. J. (2009). International Migration Flow Table Estimation. University of Southampton, Division of Social Statistics, Doctoral Thesis.

Combining census and registration data to estimate detailed elderly migration flows in England and Wales

During my MS.c. I worked on methods for combining internal migration data in England and Wales. Migration data is often represented in square tables of origin-destination flows. These are of particular interest to analysing migration patterns when they are disaggregated by age, sex and some other variable such as illness, ethnicity or economic status. In England and Wales the data within these detailed flow table are typically missing in non-census years. However, row and column (origin and destination) totals are regularly provided from the NHS patient registers (see the first two columns of the hypothetical data situation below). I worked on a method to estimate the detailed missing flow data to sum to the provided totals in non-census years (see the third column of the hypothetical data situation below). This method is particularly useful for estimating migration flow tables disaggregated by detailed characteristics of migrants (such as illness, ethnicity or economic status) that are only provided by the ONS for census years.

Hypothetical Example of Data Set Situation (where migrant origins are labelled on the vertical axis and destinations on the horizontal axis).

Auxiliary Data (e.g. 2001 Census)						Primary Data (e.g. 2004 NHSCR Data)						Detailed Estimates for 2004 Based on Methodology
Without Limiting Long Term Illness												Without Limiting Long Term Illness
	N	M	S										N	M	S
N	80	20	50	150								N	88	56	40	183
M	50	100	50	200		Illness details unavailable						M	29	145	21	195
S	10	30	110	150			N	M	S			S	7	52	54	113
	140	150	210	500		N				260			124	252	115	491
With Limiting Long Term Illness						M				320		With Limiting Long Term Illness
	N	M	S			S				170			N	M	S
N	30	10	20	60			200	370	180	750		N	33	28	16	77
M	40	50	70	160								M	23	73	29	125
S	30	10	40	80								S	20	17	20	57
	100	70	130	300									76	118	65	259

The estimated values maintain some properties (various cross product ratios) of the Census data whilst updating marginal totals to more current data. For more details see my MS.c. dissertation (which I have put online here). The appendix contains the R/S-Plus code to conduct the estimation. There is also a published paper based on my MS.c. that uses a slightly modified R code.

Publication Details:

Raymer J., Abel G.J. and Smith P.W.F. (2007). Combining census and registration data to estimate detailed elderly migration flows in England and Wales. Journal of the Royal Statistical Society Series A (Statistics in Society) 170 (4) 891–908.

A log-linear model is developed to estimate detailed elderly migration flows by combining data from the 2001 UK census and National Health Services patient register. After showing that the census and National Health Service migration flows can be reasonably combined, elderly migration flows between groupings of local authority districts by age, sex and health status for the 2000–2001 and 2003–2004 periods are estimated and then analysed to show how the patterns have changed. By combining registration data with census data, we can provide recent estimates of detailed elderly migration flows, which can be used for improvements in social planning or policy.