Presentation and updating of the model’s coefficients

4Daniel Courgeau’s model is based on the observation that most French data sources track migrants (i.e. persons who have moved between two dates) rather than migrations (changes of place of residence). This underestimates mobility because it fails to record repeat and return migration over a given period. To remedy this problem, the migrants-migrations model converts numbers of migrants recorded over multi-year periods to an annual mobility rate. This model has often been applied to the data from the population census, which takes place every five to nine years. The model is based on the following assumptions (Courgeau, 1973):

• the probability K that a person who has migrated once will do so again in the future is practically independent of the order of the previous migration. However, this probability depends on the spatial level observed, i.e. whether the move was to a new dwelling or a new commune, [1] département or region;
• for the population exposed to the risk of repeat migration, the instantaneous probability of repeat migration, k, is independent of the interval between two migrations, the order of the previous migration and the spatial level of observation;
• among second or higher order migrations during the period in question, a proportion l represents return migrations to the original area.

5

6where P is total population, m is the instantaneous mobility rate and l represents returns to the original area expressed as a proportion of second or higher order migrations.

7To measure the instantaneous migration rate, m, for each period, parameters k and K(1 + l) must be estimated from longitudinal survey data tracking individuals’ lifetime migrations.

8To estimate the instantaneous probability of a new migration, k, complete knowledge of individuals’ lifetime migrations is needed. This coefficient was updated most recently in 1997 using data from the Youth and Careers survey (enquête Jeunes et Carrières) (L’Hospital, 2001). The coefficient obtained was 0.26, compared to 0.18 for the coefficient estimated by Courgeau in 1973. Thanks to more recent life event history data provided by the 2003 Life History survey, [2] we can update coefficient k (Appendix). The instantaneous migration rate, which is close to an annual rate, can be determined by solving the following system (Courgeau, 1986):

9

where m₁ is the proportion of migrants for the entire period and the mean annual mobility rate.

Application to Housing Survey data

10Until now, the migrants-migrations model has been applied to census data (Courgeau, 1978, 1990; Baccaïni et al., 1993; Baccaïni, 2005; L’Hospital, 2001; Courgeau and Lelièvre, 2004). In this study, we apply it to the 2001-2002 Housing Survey to extend the table published by Courgeau and Lelièvre (2004). The proportion of migrants for the entire period m₁ is calculated from answers to the question “Where was M. living on [date of last survey]?”, i.e. for a five-year period. The question covers only the reference persons and their partners because the Housing Surveys do not record information on all household members. The mean annual mobility rate is taken from the Labour Force Surveys of 1999 to 2002. [3] The results are close to those published by Courgeau and Lelièvre in 2004 for migrations to another region or département, but are more divergent for migrations to another commune (Table 1). They are similar to Baccaïni’s last estimates (Baccaïni 2005). [4] Using the value of parameter k calculated for the 40-60 year age group, the mobility rates obtained are still very close to those estimated with a k of 0.25 (for the 40-45 age group). [5] Last, using the median rather than the mean also gives similar results. [6] However, the migrants-migrations model does not provide an accuracy indicator, and this makes comparisons difficult, particularly when updating coefficients using new data sources.

Table 1

Instant migration rates estimated with the migrants-migrations model (per 1,000)

Period Change of Region Département Commune Dwelling 1954-1962 13.3 20.0 48.7 – 1962-1968 15.1 25.1 53.4 – 1968-1975 17.9 29.0 60.5 97.7 1975-1982 16.5 26.5 58.8 94.7 1982-1990 16.2 25.8 55.6 85.6 1990-1999 (a) 16.8 28.7 67.8 122.0 1990-1999 (b) 16.2 27.3 63.5 111.8 1990-1999 (c) 16.0 28.0 65.0 117.0 1997-2001 17.5 30.3 72.8 122.4 1999-2004 19.0 31.0 73.0 120.0 Sources: 1954-1975: Courgeau estimate, 1978, revised (Baccaïni et al., 1993), population census. 1975-1982: Courgeau estimate, 1990, revised (Baccaïni et al., 1993), population census. 1982-1990: Baccaïni et al. estimate (1993), population census. 1990-1999: (a) Courgeau and Lelièvre (2004) estimate, population census; (b) L’Hospital (2001) estimate, persons aged 20 and over, population census; (c) Baccaïni (2005) estimate, persons aged 5 and over, population census. 1997-2001: Donzeau and Pan Ké Shon estimate, reference persons and their partners aged 20 and over, 2001-2002 Housing Survey. 1999-2004: Baccaïni estimate (2005), persons aged 5 and over, 2004 annual census survey.

Instant migration rates estimated with the migrants-migrations model (per 1,000)

11The coverage of mobility studies can vary, often depending on constraints inherent to the data sources. Under the new census system, data from annual census surveys are aggregated over five years, which means that only persons aged 5 and over can be taken into account (Pan Ké Shon, 2007). The Housing Surveys only cover reference persons and their partners, whose mobility is known, and cannot be used to estimate mobility for the total population. However, the difference between mobility rates of the total population and those of household reference persons and their partners can be calculated from the Labour Force Surveys. [7] In 2003, the mobility of individuals aged 15 and over was 0.1 percentage points lower than that of the total population. Reference persons and their partners aged 15 and over had a mobility rate 0.5 points higher than that of the total population in the same age group.
By its nature, the migrants-migrations model can only be used to estimate mean annual mobility for the whole of the period covered by the source used, with no possibility of detecting any trend changes or mobility peaks within the period. Yet based on data from the Labour Force Surveys, the variation observed between 1990 and 1999 is around 3 points.

Towards an alternative model?

12In an article published in 2005, Debrand and Taffin suggested an alternative measure of residential mobility using the Housing Surveys for the period 1984-2001, based on answers to the question about the dwelling occupied at the time of the previous survey (four or five years earlier depending on the survey concerned). They calculated the proportion of persons who had moved by comparing the number of households that had done so with the total number of households at the time of the survey. They then estimated annual rates using the following formula:

13

14where T is the annual rate,

15T_n is the rate calculated for n months,

16(1 – T_n) is the probability of not moving for n/12 years, and

17(1 – T) is the mean probability of not moving in the course of the year.

18This method is based on the implicit assumption that migration behaviour is uniform across the population, i.e. that an identical probability of migration applies to all individuals regardless of their migration history. But in fact, mobility changes over the life course and while some people are highly mobile, others are far less so. If one assumes that migration behaviour is identical between individuals, the movements of highly mobile people will not be fully captured and the migration rate will be underestimated.

19As shown in Figure 1, Debrand and Taffin’s estimates are close to the results obtained by Courgeau between 1984 and 1988 but markedly lower than more recent estimates. Unfortunately, this new method does not provide an accuracy indicator either.

Figure 1

Estimates of annual mobility since 1968 from population censuses (PC) and Housing Surveys (HS)

Estimates of annual mobility since 1968 from population censuses (PC) and Housing Surveys (HS)

Semi-direct estimates from Housing Surveys, 1973-2006

21Initiated in 1955, the French National Housing Survey is conducted by INSEE every four or five years. Coverage varies from year to year, ranging between 23,500 and 45,000 households living in metropolitan France, [8] representing 65,000 to 135,000 individuals. The survey concerns trends in housing supply, housing conditions, rents, home loans, etc., and includes information on individual and household characteristics. These data make it particularly suitable for mobility research. The eight most recent Housing Surveys, conducted in 1973, 1978, 1984, 1988, 1992, 1996, 2001 and 2006, can be used to track the past mobility of household reference persons. The question “In which year did the reference person move into this dwelling?” has been asked regularly since 1973. Taking those who moved in the year of the survey itself as a proportion of the total sample gives the year’s percentage of migrants. Over such a short period, this rate is close to a migration rate since it is rare for people to change residence more than once in the same year (Courgeau, 1973). For the 2006 survey, the data collection protocol was changed. The survey was extended to the French overseas départements and was run in six waves spread over the last ten months of the year.

22With this method, the mobility rate is not measured over the whole year: only migrations occurring before the survey date are recorded. This is the main difficulty to be overcome when using this method to estimate annual mobility. Up until 2001, Housing Survey interviews generally took place in the last quarter of the year. October surveys thus covered mobility, if any, over nine to ten months, depending on whether the interview took place early or late in the month. Without information on the exact date of each interview, we have to apply an average mid-month interview date, and possible migrations in the remaining 2.5 months of the year go unrecorded. Likewise, there is a 1.5 month deficit of potential migrations for respondents interviewed in November, while in December interviews are mainly held in the first two weeks of the month because of the festive season, so there is a 0.75 month deficit. Unless corrections are made for these incomplete observation periods, migration will be considerably underestimated. [9]

23One correction method involves adjusting the data to account for the months not covered by the survey question. In 1973, for example, interviews were held on average after 10.42 months. [10] Before correction the 1973 residential mobility rate is 8.93%. The adjusted rate is obtained as follows:

24

25An identical procedure is used for the first seven surveys. In 2006, the data were gathered in six waves, and respondents were asked about their moves over a retrospective period that ranged from 2.5 months for those interviewed in March to 11.25 months for those interviewed in December. The mobility rate prior to correction was 5.31%, so the correction was larger for this survey:

26

27The proportion of unobserved migrations [11] varies from 3.5% to 13.2% for the old-formula Housing Surveys, with a peak of 37.5% for the 1978 survey. For the continuous Housing Surveys it is 41.9%. This makes the results for 2006 uncertain, as they are for 1977.

28A second correction method is based on applying monthly mobility rates. The Housing Surveys since 1984 give the month of the move to the current dwelling. Wide month-to-month variations in mobility emerge: migration peaks in July and September, and dips from February to May (Donzeau and Pan Ké Shon, 2009). Under this method, a correction coefficient is attributed to each month according to the mobility rates observed in that month over the three or four years preceding the survey, to keep as close as possible to observed migration patterns. For the 1973 and 1978 Housing Surveys which do not give this information, the corrections available from the 1984 survey onwards are used.
All in all, the two proportional correction methods give similar results when the data are collected at the end of the year, and only limited correction is required. Whichever method is used, the correction rate is very high for the 1978 Housing Survey: since the data were gathered in the second quarter of that year, neither correction method seems truly satisfactory. However, with the shift to continuous data collection in 2006, the months when changes of residence take place must be taken into account. We have therefore adopted the second correction method.
The confidence intervals accompanying the mobility curves give an indication of the precision of estimates but do not take account of possible evaluation bias. Comparing results based on the Housing Surveys and on the Labour Force Surveys provides a means to identify potential biases, if they are not the same for the two surveys.

Direct estimates from the Labour Force Surveys 1973-2006

29Initiated in 1950, the Labour Force Survey serves to assess unemployment, describe the situation of the unemployed and changes in the employment situation (Goux, 2003). Each year it provides a wealth of information on labour force participation by occupation, sex, age, hours worked, and on insecure employment. Until 2002, 75,000 dwellings, representing between 130,000 and over 150,000 individuals, were surveyed in March. Since 2003, the Labour Force Survey data have been gathered continuously, over a six-week period each quarter, from a sample of about 38,000 households in metropolitan France representing about 70,000 respondents and 15,000 children under 15. The rotating sample is gradually renewed, with 1/6 leaving and being replaced each quarter, so that households are interviewed for six consecutive quarters. To understand changes in labour force participation, part of the questionnaire is devoted to the individual’s situation one year previously (more precisely in March of the previous year, for the annual surveys up to 2002). From the questions asked, the person’s mobility over the previous year can be identified, and an annual mobility indicator can be calculated.

30The Labour Force Survey data series can be used to make new estimates for comparison with the semi-direct estimates from the Housing Surveys. The question included in the Labour Force Surveys between 1990 and 2002 was “Where was M. living in March last year?”; the formulation used since 2003 is “Where were you living a year ago?”. Annual residential mobility can be measured from the responses with no correction needed. [12] However, this annual measurement covers three months of year n and nine months of year n – 1. The mobility rate is therefore attributed to year n – 1. The Labour Force Surveys prior to 1990 give only changes of commune, département and region; they cannot be used to check the overall mobility rate calculated from the Housing Surveys. For comparability, the scope is first restricted to household reference persons, then extended to the entire population aged 15 and over.
Note that the mobility estimates based on the Housing Surveys concern the year of the survey itself, symbolized by dots in Figure 2. The lines joining two dots are shown simply for easier reading, since there are no estimates for the three or four years between surveys. The Labour Force Surveys provide annual information. For the years in which Housing Surveys are conducted, estimates coincide with those of the Labour Force Surveys: at a minimum, the confidence intervals of the two surveys overlap, which means the estimates are robust. The only exception is 2006, with a gap of 0.6 points between the confidence intervals, probably because of the high proportion of unobserved migrations in that year’s Housing Survey.

Figure 2

Estimate of annual mobility rates (migrants) from Housing Surveys (HS) and Labour Force Surveys (LFS)

Estimate of annual mobility rates (migrants) from Housing Surveys (HS) and Labour Force Surveys (LFS)

31The mobility of household reference persons is greater than for the population as a whole because reference persons are often working-age men, who are more mobile than other categories. Nonetheless, the two populations’ mobility levels follow parallel trends.