Dual-earner migration in Britain.

Earnings gains, employment, and self-selection

Birgitta Rabe1

Ruhr-University Bochum

Institute for Social and Economic Research, Essex

email: iserg003@essex.ac.uk

26/1/2006

Abstract

This paper examines how spouses in dual-earner couples in Britain weigh each partner’s expected wage growth in the decision to migrate. Previous research suggests that husbands’ job prospects dominate the migration choice irrespective of their relative earnings potential. Based on British panel data this paper employs an endogenous switching model and estimates wage change differentials of migrating vs. staying for husbands and wives corrected for double selectivity of migration and employment. The analysis shows that dual-earner couples put roughly equal weights on each partner’s expected wage gains when deciding to migrate. Moreover, migrant wives’ employment declines temporarily and there are significant selection effects in migration and employment among non-migrants. Keywords: family migration, dual-earner couples, double selection, endogenous switching JEL Classification: J61, D19, C35

1. Introduction

This paper examines the factors influencing whether dual-earner couples migrate. In

particular it investigates the effects of expected wage gains of a husband and a wife on

the decision to migrate. Whether the effects are asymmetric has received much

attention and has important implications for discriminating between the unitary and

collective theory of family migration, but has rarely been explicitly analyzed. In 1 This paper was produced during a research visit to the Institute of Social and Economic Research whose hospitality I gratefully acknowledge. Thanks to John Brice, John Ermisch, Axel Heitmueller, Stephen P. Jenkins, Cheti Nicoletti, Mark Taylor and seminar participants at the University of Essex and the Policy Studies Institute, London, for helpful comments and suggestions.

1

addition, the paper studies the employment and wage consequences of migration for

couples while rigorously modelling selection effects in employment and migration.

The paper makes several contributions. It is one of the first to explicitly

examine the impact of each spouse’s wage differential between origin and destination

on family migration decision-making. The main finding is that spouses weigh each

partner’s expected wage growth roughly equally in the migration decision. Moreover,

it models the double selection into migration and employment of both spouses,

revealing that spouses who choose not to migrate and non-migrating wives who

choose to work possess comparative disadvantages. Furthermore it gives insight into

what happens to the employment of husbands and wives when families move. While

wives experience a temporary 8% reduction in labour force participation after

migration, husbands’ employment remains unaltered.

2. Previous research

Theories of migration generally assume that people relocate because they expect

higher utility in the new location. In most cases individuals are attracted to locations

where they can receive higher wages, and the earnings gains offset the social and

economic costs associated with migration.

Looking at migration of families, the common theoretical assumption is that

spouses seek to maximize joint family income when making the decision to migrate.

In the traditional unitary model of the household the spouses maximize a single utility

function. They are indifferent as to who contributes to joint family income and in

which proportion (Mincer 1978, Sandell 1977). Whenever maximization of family

income makes spouses stay (move) although they could individually receive higher

earnings by moving (staying), these spouses are tied stayers (movers). Mincer (1978)

predicts that greater market earnings power and more continuous labour force

participation potentially yields higher migration returns to husbands than to wives.

Wives are therefore likely to be tied movers who presumably experience reductions in

wages and working hours following the move, thus reinforcing the initial differences

in “earnings power” between the spouses. On the other hand, working wives - in

particular if they contribute a large share to family income and have a stable labour

force attachment - presumably deter family mobility, making husbands likely to be

tied stayers.

2

There is ample empirical evidence supporting the hypotheses proposed by

Mincer and colleagues in the 1970’s. Several papers have shown a reduced migration

in couples with a working wife (e.g. Long 1974; Sandell 1977; Mincer 1978; Juerges

1998; Nivalainen 2004). Here the husband may be a tied stayer who foregoes

potential earnings increases in order to secure the wife’s labour market position.

Married women have been shown to experience a decline in labour market

participation and earnings following a family move, thus classifying them as tied

movers (e.g. Morrison and Lichter 1988; Jacobsen and Levin 1997; Lee and Roseman

1999; Boyle et al. 2001). Research investigating the dynamics of employment and

earnings in the years following a move shows that, after an initial drop, women do

recover their pre-move positions after 1-3 years (Spitze 1984, Maxwell 1988, Lichter

1983). A more recent paper reveals no effect of family migration on wives’ earnings

and a dip in their labour force participation which gradually disappears after 3 years

(LeClere and McLaughlin 1997).

Husbands’ earnings are generally found to increase after migration (e.g.

Sandell 1977; Cooke 2003) while their employment remains unaffected. The effect on

household earnings is less clear. By expectation the household as a whole should

benefit from migration (Sandell 1977; Cooke 2003), but Axelsson and Westerlund

(1998) find no effect, and Jacobsen and Levin (1997) find a negative effect of family

migration on household income.

While these results generally support the unitary family model, there has been

research suggesting that expected earnings gains of husbands are weighted more

heavily than the earnings gains of wives in the family migration decision.

Specifically, several studies show that, contrary to expectation, personal and job

characteristics of the wife which should be indicative of their earnings potential, like

high occupational status, earnings, or job attachment, exert little or no influence on

family migration (e.g. Duncan and Perrucci 1976; Lichter 1982; Shihadeh 1991;

Juerges 1998; Nivalainen 2004; however: Bird and Bird 1985). This research usually

studies how migration probability is influenced by characteristics at origin, not at the

potential destination, and thus does not explicitly analyze the gains from migration.

By contrast, Jacobsen and Levin (2000) explicitly test the coefficients on a measure

of the spouses’ potential earnings gain in a migration equation. This measure is

created by estimating wage equations for each of the 37 locations available to each

household in their sample. They find that migration is positively related to potential

3

household earnings change regardless of who contributes to it. On the other hand,

using spouses’ pre-migration income as a measure of earning potential, Cooke (2003)

finds that post-migration income is correlated with the husband’s earning potential but

not with the wife’s, thus giving evidence of asymmetrical decision-making in favour

of the husband. This literature often concludes that a gender-role model does better in

predicting migration than human capital theory does (e.g. Bielby and Bielby 1992).

Another interpretation of this evolving literature is that it challenges the

unitary family model which underlies the theory of family migration. In recent years

household economics has seen a departure from the unitary family utility function in

favour of collective models of marriage which analyze interactions of spouses with

separate sets of preferences (e.g. Chiappori 1992; Fortin and Lacroix 1997).

Regarding the migration of dual-earner couples, a non-cooperative bargaining model

suggests that each spouse’s individual utility maximization may result in location and

employment decisions which are not efficient at the household level (Lundberg and

Pollak 2003). The main argument is that location decisions of dual-earner couples

may affect future bargaining power, for example via the assumption that individual

earnings determine distribution within marriage. In the absence of binding

commitments to prevent exploitation of future bargaining advantage, inefficient

outcomes are plausible and provide an alternative explanation of asymmetrical

decision-making.

Against this background this paper investigates how the prospective earnings

gains of husbands and wives are weighted when making the migration decision. Put

another way, it addresses the question of how the gains and losses resulting from

family migration are distributed between the spouses within individual families. The

analysis is based on the British Household Panel Survey, 1991-2003, which provides

a rich set of information about individual and household characteristics. The panel

nature of the data allows one to identify pre- and post-migration characteristics and to

account for individual heterogeneity. Migration is defined as a move across a Local

Authority District boundary. Unlike most other papers, the focus is on matched

partnerships rather than groups of husbands and wives that are not necessarily

associated to each other. Couples are defined to include legally married or cohabiting

adults of opposite sex, with or without children. These will be referred to as

‘husbands’ and ‘wives’, or ‘families’.

4

I estimate reduced and structural forms of the migration decision function as

well as selectivity-corrected earnings change equations for migrants and non-migrants

(separately for husbands and wives) in an endogenous switching model. The paper

accounts for selectivity both in the migration decision and in each spouse’s labour

force participation by employing a double-selection framework (Heckman 1979;

Tunali 1986). Many previous migration studies have refrained from modelling

selection effects. Those who have modelled them obtained results which suggest that

there is either positive selection into migration or that selection effects cannot be

uncovered (see Greenwood 1997 for a review). Only few papers have studied the

double selection into migration and employment (Vijverberg 1995; McNabb and

Vijverberg 1998).

3. Econometric methods

In line with the standard human capital formulation a family’s decision to migrate is

modelled as a function of, for each spouse, the difference between origin and

destination earnings, and migration costs. For simplicity I aggregate all potential

destinations into one so that migration is treated as a binary choice. A couple will

decide to migrate if the discounted net gain of moving, , is positive. This can be

written as:

cM

0* >−∆+∆≡ cwhc CYYM , (1)

where , are the present values of the expected lifetime earnings differentials

of migrating vs. not migrating for husbands and wives respectively. is the present

value of the couples’ mobility costs which include monetary and non-monetary costs

of moving like gathering information about alternative labour markets, leaving

networks of family and friends, house-price differentials, etc.

hY∆ wY∆

cC

In the empirical specification of this model I take the hourly wage gain of

migrating vs. staying between 1−t and t (around one year in the data) as a predictor

of lifetime earnings change. However, for migrants we only observe the change in

origin to destination wage, and for non-migrants we only observe the wage change in

the origin from one year to another. The alternative expected wage changes are not

observable. Neither are migration costs directly observable. Instead of the actual gain

from migrating we observe a binary random variable which is defined as *cM

5

⎩⎨⎧ ≥

=otherwise 0

0* if 1 cc

MM .

Assuming that migration costs are determined by a vector of exogenous household

and both spouse’s individual characteristics as well as house prices in the origin

locality, Z , and defining 1−−≡ tt www , a structural probit model of family migration

can be described such that:

ccwswmhshmc vZwwwwM ++−+−= ')()(* 321 γγγ , (2)

where the first two terms capture the predicted hourly wage change differential of

migrating vs. staying for husbands and wives respectively. The error

term, , is normally distributed with zero mean and unit variance.

),( sm ),( wh

cv

The predicted hourly wage change differential is obtained by estimating

earnings change equations for migrants and non-migrants respectively, separately for

husbands and wives. These are used to impute earnings changes for the counterfactual

situation, i.e. the change in earnings a migrant (stayer) would have received had he or

she stayed (migrated). Letting X be a vector of human capital and personal variables

that determine log hourly wages and defining 1−−≡ tt XXx and 1−−≡ tt εεε , the log

hourly wage change equations for migrating and non-migrating husbands and wives

respectively which complete the model are:

hmhhmhm xw εβ += 'ln , (3)

hshhshs xw εβ += 'ln , (4)

wmwwmwm xw εβ += 'ln , (5)

wswwsws xw εβ += 'ln . (6)

Taking first differences of the variables over a one year period eliminates any time-

invariant unobserved heterogeneity present in the error term. The wage-change

equations could consistently be estimated by OLS under the assumption

that 0)( 1 =− −ttE εε if wage data for migrants and non-migrants was randomly

selected. However, equations (3)-(6) may be subject to selectivity both in mobility

and labour force participation choice.

Self-selection. The selection into migrants and non-migrants may be non-

random as arguably migrants may differ from stayers in observed and unobserved

characteristics which also affect wages. Some forms of individual heterogeneity like

6

ability may be interpreted as time invariant and are thus eliminated by differencing the

variables in the outcome equation over time. However, there may be a transitory

component of the error term correlated with the migration choice. For example, the

cost-benefit calculation implicit in the migration decision will depend on the current

economic environment which is likely to change over time (Yankow 2003), and

motivation to invest into human capital can change with life-cycle events like having

children or getting married. Not controlling for this will lead to biased estimators.

Furthermore, post-migration wages are only observed for individuals who

participate in the labour market, and they may be a non-random sample of the

population. For example, individuals who have the greatest difficulties in finding new

employment post migration select out of the labour market. One obvious example of

time-varying factors which may influence such difficulties for women and also affect

their wages is family factors.

The equations which model these selection processes are

111 '* uXM c += δ family migration choice (7)

222 '* uMXP cw ++= µδ wife’s labour force participation (8)

333 '* uMXP ch ++= ηδ husband’s labour force participation. (9)

Equation (7) is in essence a reduced form of the structural model described by

equation (2). and are latent variables, *wP *hP 1,2,3)( =bX b are vectors of

explanatory variables assumed to determine mobility and labour force participation

respectively, 'mδ are vectors of unknown coefficients, and ηµ , are scalar unknown

coefficients. By including a migration status indicator variable into the

participation equations of husbands and wives I allow participation to vary according

to the migration choice made. This binary variable captures a level effect of migration

on labour force participation of each spouse.2 The potential endogeneity of migration

choice with respect to the participation equations is discussed below.

)( cM

By assumption, a family chooses to migrate if the utility of moving exceeds

that of staying. At the same time, the spouses make participation choices for the wife

and the husband that depend on both spouse’s personal and job-related characteristics

and which may be interdependent. I discuss the empirical specification of the models

2 Several authors have shown that labour force participation choices may differ between migrants and stayers, for example because female migrants might temporarily withdraw from the labour force in order to accommodate increased household needs in the first years following a move.

7

in the next section. The household will choose participation by a spouse in the labour

market if the household’s utility from participation exceeds that of non-participation.

The utilities of the three selection equations are not directly observable; we observe

only a dichotomous variable indicating whether or not an individual migrates and

whether or not the spouses are employed.

A two-step estimation approach in the spirit of Heckman (1979) is adopted to

deal with the self-selection problems. This procedure begins by estimating the

selection equations and constructing sample-selection correction terms based on these

estimates. Then the wage equations (3)-(6) can consistently be estimated by OLS,

including the correction terms as additional regressors. The wives’ wage change

equations for migrants and non-migrants are corrected for selectivity in migration and

the wives’ labour force participation. Likewise, the husbands’ wage change equations

are corrected for non-random selection into migration and husbands’ employment.

If the selection effects specified in equations (7)-(9) are independent, i.e. the

correlations of the error terms, 1221 ],[ ρ=uuCov ; 1331 ],[ ρ=uuCov ; 2332 ],[ ρ=uuCov ,

are all equal to zero, the correction terms can be derived from separate probit models

for migration and participation choices as in the single selection case. The correction

terms for selection into migration then are the inverse Mills ratios, namely:

)()(

11

11

XX

M δδφ

λΦ

= if and 1=cM)(1

)(

11

11

XX

M δδφ

λΦ−

−= if 0=cM (10)

where φ is the standard normal density function and Φ the corresponding standard

normal distribution function. The correction terms for selection into employment are

derived analogously.

As the migration and participation decisions are – by assumption – made

jointly, the selection processes may not be independent, i.e. some or all of the

correlations 231312 , , ρρρ may not be equal to zero even after controlling for

observed heterogeneity. If only one of the pair-wise correlations, say 23ρ , is different

from zero, it is possible to apply a double-selection framework (Tunali 1986; Fishe et

al. 1981; Ham 1982). This assumes a trivariate normal distribution of the error terms

of the outcome equations and, in our example, the two equations modelling the

spouses’ selection into employment. The selection processes are estimated using a

bivariate probit, and augmented selection correction terms are derived for migrants

who are working:

8

),ˆ,ˆ()ˆ()ˆ(

232

2

ρφ

λhw

wP PP

GPΦ

Φ= (wife) and

),ˆ,ˆ()ˆ()ˆ(

232

1

ρφ

λhw

hP PP

GPΦ

Φ= (husband). (11)

The correction terms for working non-migrants are:

),ˆ,ˆ()ˆ()ˆ(

232

2

ρφ

λ−−Φ

−Φ−=

hw

wP PP

GP (wife) and

),ˆ,ˆ()ˆ()ˆ(

232

1

ρφ

λ−−Φ

−Φ−=

hw

hP PP

GP (husband) (12)

where

223

2322

23

231

1

ˆˆˆ ,1

ˆˆˆρ

ρ

ρ

ρ

−

−=

−

−= whhw PP

GPP

G ,

and is the bivariate standard normal distribution function. 2Φ

Selection correction terms accounting for the interdependence among three

selection equations have – to my knowledge – not been derived in the literature. I

therefore adopt an evidence-based procedure as follows. First I estimate the selection

equations (7)-(9) jointly in a trivariate probit model using simulation methods based

on the GHK simulator (Gourieroux and Monfort 1996; Cappellari and Jenkins 2003),

and choosing 94 random draws which is the square root of the sample size. The

resulting model is a recursive, simultaneous equation model because the dependent

variable of equation (7) appears as independent variable in equations (8) and (9).

Identification of the equation system is assured by employing a set of exclusion

restrictions. In particular, each equation includes one exogenous variable assumed to

be relevant only for this equation which is excluded from the other equations. I

describe the variables used in the next section and provide test results for the validity

of these restrictions in the results section. In all estimates I adjust the standard errors

for having repeated observations on some couples.

These estimates yield values for 231312 , , ρρρ and can be seen as a test for

independence of the selection processes. Based on these results I am able to separate

the migration equation from the participation equations because I do not reject the

assumption 01312 == ρρ while I do reject 023 =ρ at 1% level of significance. This

also means that the migration dummy is exogenous in the participation equations.

Thus I continue to estimate a single migration probit and a bivariate probit of

husbands’ and wives’ labour market participation. I derive inverse Mills ratios to

account for selection into migration and augmented correction terms to account for

9

selection into employment as described above, equations (10)-(12). These then enter

into the wage change equations and allow consistent estimation.

The estimated coefficients on the migrants’ and non-migrants’ log hourly

wage change equations are used to predict each spouses’ expected wage change when

migrating and when staying in the original location, separately for husbands and

wives. The coefficients of the migrants’ wage change equations can be interpreted as

a weighted average of prices obtainable for individual and job-related characteristics

in potential destinations. The weights represent the locations actually chosen by

migrants. Conversely, the coefficients on the non-migrants’ equations reflect the

prices obtainable at an average origin, weighted by the origin locations of stayers.

Expected wage changes are derived from predicted using wln

)2ˆˆexp(ln)ˆ( 2εσ+= wwE . Differencing predicted wage changes in origin and

destination yields a wage change differential of migrating vs. staying for each

individual. The final step of the procedure is to estimate the structural version of the

migration probit (equation 3) using these differentials. The coefficients on the wage

change differentials reveal how the potential gains and losses of migration are

weighted between the spouses. In interpreting these coefficients the different expected

working times of husbands and wives have to be taken into account.

4. Data

The analysis uses the 13 currently available waves of the British Household Panel

Survey (BHPS), spanning 1991 to 2003. The BHPS is a nationally representative

sample of about 5,500 households recruited in 1991, containing approximately 10,000

adults who are interviewed each successive year. Data are collected on a broad range

of socio-economic characteristics at both the individual and the household level. The

use of panel data allows identification of both the pre- and post-migration situation.

From the BHPS I extract an estimation subsample. Following common

practice I restrict the analysis to couples, married or cohabiting, who remain intact and

living together at the same address over a two-year period.3 I choose couples where

3 Restricting the sample to include only couples who remained intact over a two-year period potentially introduces selection bias in the analysis because it could be differences in migration preferences that lead to couple dissolution. Indeed, in our dataset mobility is higher among recently separated individuals than among intact couples. However, divorced and separated persons are shown to have higher migration propensities compared with other individuals as a result of partnership break-up. With causality running in both directions it is difficult to disentangle the effects (Mincer 1978).

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both spouses were in employment at 1−t , i.e. prior to a possible move and are aged

between 20 and 58 inclusive. The focus on dual-earners allows examination of wage

changes for both partners. The age band concentrates the analysis on a group most

likely to migrate for work-related reasons. Migration by individuals approaching

retirement age may reflect retirement location decisions. The inclusion of younger

individuals would potentially confound education-related moves with migration.

Same-sex couples, individuals who ever worked in the armed forces, and employed

individuals reporting zero working time in the previous week were dropped from the

dataset. Finally the bottom and top 0.3% of the hourly wage distribution were deleted

in order to eliminate extreme outliers. The resulting sample is an unbalanced panel

which includes all couples, for whom information is available at two consecutive

interviews, allowing the same couple to enter the sample several times. After

removing observations with missing data for any of the variables used in the analysis,

the sample comprises 8,557 observations with 1,838 unique couples.

Migration is defined in this paper as a change in a family’s address in the

period between two interviews which also involved crossing the boundaries of one of

Britain’s 278 local authority districts (Böheim and Taylor 2005). Any local move

within the boundaries of a local authority is thus considered to be residential mobility.

This definition identifies 196 migrating couples in the dataset. While the BHPS

attempts to follow all movers who remain in private households in Britain, attrition

rates are higher among individuals who move house than among those who remain in

the same residence (Buck 2000). However, in most cases it is possible to identify the

destination area and thus the migrant status of individuals who do not remain in the

sample. I have analysed non-response among dual-earner couples whose pre-attrition

characteristics were identical to the restrictions imposed on my estimating subsample.

Attrition is very low in this group (below 2% both among non-migrants and

migrants). Therefore I do not expect it to influence the results.

The dependent variable in the wage change equations is the change in the log

of usual real hourly gross earnings from 1−t to t in January 2000 prices. Hourly

wages were derived from usual monthly wages using hours worked and assuming that

paid overtime hours were associated with a 50% wage premium. Wages were

modelled as a function of changes in time-variant personal and job-related

characteristics. In particular, changes in occupational status (5 binary variables),

working time, hours of paid overtime, type of job contract (temporary/permanent),

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sector (public/private), occupational pension, and union membership are included in

the wage change equations. As there is a close link between the returns to migration

and job mobility I also include a dummy indicating whether an individual has changed

jobs between two interviews in the wage change equations of migrants and non-

migrants. It would be desirable to further distinguish layoffs, quits and transfers

among job changes (Bartel 1979). However, information on this is collected

retrospectively in the BHPS and is known to suffer from problems of recall error and

ex-post rationalisation (Böheim and Taylor 2005). A variable for the change in job

tenure measures the time between two interviews for individuals who don’t change

job, and time elapsed between starting a new job and the next interview for job

changers. The wage change equations also contain correction terms for the selection

into migration vs. non-migration and for the selection into labour market participation.

Each equation also includes year-of-interview indicator variables.

The three equations modelling the selection effects are specified as follows.

The migration equation includes all personal and job-related variables of both spouses

which are relevant for the wage change equations. These are included to capture the

economic opportunities that individuals face in the labour market. In particular, they

model risk of job-loss (e.g. via information on fixed-term job contracts), labour

market attachment (e.g. job tenure), and job offer arrival rates. In addition I include

personal and household characteristics which act as proxies for the direct and indirect

costs of moving. Older individuals are expected to be less mobile than younger ones,

either because they reap the benefits of migration for a shorter period or because they

are more attached to their current location. Thus I include the husband’s age as well as

the age difference between husband and wife in the migration probit. A binary

variable coding whether each partner has received a higher qualification (degree,

teaching qualification or other higher qualification/other qualification) is assumed to

proxy their ability to perform effective job search. The size of the household is an

indicator of the direct costs of moving and of the network attached to any family. I

distinguish between the number of children under age five and over age five in the

household. Families with pre-school children are often found to migrate in search for

better environments for their children while the presence of school-children usually

deters relocation because of the difficulties involved in changing schools. I also

include a variable which indicates whether any of the pre-school children were newly

born between . Binary variables indicating outright home ownership vs. tt and 1−

12

mortgaged home ownership vs. rental accommodation approximate the costs of

relocation. Finally, because legally married spouses may attach a higher cost to

partnership dissolution and would therefore be more likely to migrate together than

those merely cohabiting, I include this variable in the migration equation. All of these

variables are measured at , i.e. the time when the migration decision is assumed

to be made.

1−t

The husbands’ and wives’ labour force participation equations each include

the same variables as the migration equation, i.e. personal and job-related variables of

both spouses. As the labour force participation of spouses is by assumption

interdependent, a husband’s job prospects may influence the wife’s participation

decision and vice versa. The job-related characteristics are measured at time ,

assuming that characteristics of each partner’s job determine the likelihood of labour

force participation for each spouse. The personal characteristics refer to time .

Labour force participation will depend on the partners’ ages, education, and marital

status – being married generally decreasing the labour force attachment of women and

increasing it for men. Likewise, the existence of children is expected to reduce a

woman’s involvement in market work, especially if the children are young, while it

will tend to increase a man’s labour market activity. Owning a home outright and

having more non-labour household income should reduce the dependence of the

family on earned wages and thus participation in the labour market.

1−t

t

The three equations modelling the selection process are, in a first step,

estimated simultaneously. Identification of the equation system is assured by a set of

exclusion restrictions, i.e. including an exogenous variable in each equation which is

not included in or relevant for any other equation. In particular, the migration equation

includes a time-varying measure of local house prices in the origin location, assuming

that families seek to move away from high house prices.4 For the spouses’

participation equations we make use of information on the employment status of each

individual’s parents. We assume that a woman will be influenced in her choice of

employment status by the status her mother chose when she was a youth. Arguably a

mother serves as a role model in terms of female labour market participation for her

daughter. Likewise we assume a man to be influenced by his father’s past 4 A price index was constructed using historical data provided by Halifax Housing Research on average annual house prices at UK posttown level from 1991-2003. These data were aggregated to Local Authority District (LAD) level, and the annual index in any LAD is the log of average house prices in that LAD divided by the national average.

13

employment status, particularly with respect to the choice between employment and

self-employment. We use a binary variable indicating whether an individual’s mother

(father) was an employee when she (he) was aged 14 to identify the wife’s

(husband’s) labour force participation equation.

5. Empirical results

Table 1 presents descriptive evidence on migration, wages, and labour market

participation over the period 1991-2003 for the analysis sample. About 9% of the

couples in the sample migrate some time over the 13 year period, which are 2.2% of

the couple-year observations. These migration rates are well below those found in the

BHPS for a sample of married and single men (15% and 3.9% over a 12 year period

according to Böheim and Taylor 2005), confirming the hypothesis of reduced

migration among dual-earner families. Migration is concentrated among couples with

pre-migration wages well above the average: hourly wages of migrating husbands

were 17%, and those of migrating wives 21% higher than those of their non-migrant

counterparts prior to migration. The table also shows that wage increases over a one-

year period are greater for migrants than non-migrants. Interestingly, on average both

migrating and non-migrating working women have wage increases that exceed those

of their husbands by about one percentage point. Hours normally worked per week are

slightly higher among migrants before they move and increase post-migration

particularly among employed women. However, participation in the labour market

declines more among migrants than non-migrants. While this difference is moderate

among men (1 percentage point), the participation rate of migrating wives is 11.9

percentage points lower than that of non-migrating wives. Finally, the table shows

that, as expected, job change is more prevalent for migrants than non-migrants. In

summary, these descriptive results indicate that couples migrate to get better paid jobs

of husbands and wives, but that migrating wives may stop working following a move.

Obviously we can only confirm these conjectures by controlling for individual and

couple heterogeneity which I do next.

The first step in the estimation procedure is to estimate the three selection

equations by multivariate probit in order to explore the error term correlations. The

upper panel of table 2 presents Wald test results for instrument validity and hence the

identification of the model. The hypothesis that the coefficients on the instruments

14

equal zero can be rejected at conventional levels of significance, both separately and

jointly. The lower panel of table 2 displays the estimates for the error term

correlations. It shows that there is no statistically significant correlation of the

unobservables of the migration equation with the two participation equations. Thus I

can reject endogeneity of the migration dummy in the participation equations. This

allows me to estimate a single migration probit and to derive the selection correction

terms from the results. The labour force participation of husbands and wives are,

however, clearly interdependent even after the influence of the observed factors is

accounted for. This interdependence must be taken into account when constructing the

selection correction terms. Augmented correction terms are derived from a bivariate

probit model of labour market participation by husbands and wives.

Table 3 shows the estimates. The migration probit confirms most of the

standard expectations about mobility choices. The presence of school-age children

and house ownership inhibit migration. Migration propensity also declines with age of

husband and wife, while high house prices raise this propensity. Marital status and

education do not seem to influence migration probabilities. The results pertaining to

the characteristics of the spouses’ job in 1−t are noteworthy, however. Unlike for

husbands, wives’ job characteristics at origin such as occupational status, type of job

contract, etc. (not displayed separately) play no role in the joint migration decision.

The Wald test does not reject the hypothesis that the coefficients on these variables

are jointly equal to zero for the wife. These estimates thus prima facie replicate the

findings cited in the literature review that it is the husbands’ job that drives the

migration choice.5 The estimates of the structural model containing the estimated

wage change differentials between origin and destination, presented below, will imply

that this conclusion should be revised.

Characteristics of the job in origin are clearly important in determining wives’

employment. In particular, public sector employees, skilled manual workers,

permanent contract and occupational pension holders as well as individuals working

many hours have a high probability of post-migration employment. New mothers are

5 The wife’s job characteristics might be unimportant in the migration decision if couples with dissimilar work attachment select into migration. I have tested this proposition by including relational variables comparing the spouses’ education and occupational status instead of separate variables for husbands and wives characteristics in the migration equation. The results rather suggest that couples with similar traits migrate together. This may suggest that collinearity of husbands and wives’ characteristics, which is likely to appear in the presence of assortative mating, may inflate standard errors. However, collinearity diagnostics do not support this.

15

less likely to work while mothers of school-age children have an increased likelihood

of employment. Having a mortgage rather than renting increases female participation

while higher levels of non-labour household income decrease it. Most important,

wives who migrate have lower employment rates at the interview following migration

than those who do not. Evaluated at the means of the other variables, a migrating wife

has a 7.6 percentage point (or 8%) lower probability of employment than a non-

migrating wife controlling for her personal, household, and job-related characteristics.

This reduction is lower than that found in several other studies predominantly based

on US data (e.g. LeClere and McLaughlin 1997: 13% (US); Boyle et al. 2001: 42.5%

(UK), 40.7% (US); Lee and Roseman 1999: around 10-15 percentage points (US)).

Probit estimates based on data for those 7,285 wives also interviewed in the following

year ) reveal that migration no longer has a negative impact on their

employment probability. The coefficient on the migration dummy is not significantly

different from zero at 1+t (not shown). Thus the decline in wives’ employment

probability is temporary and, in line with the findings in other papers, they recover

after a

1( +t

bout one year.

Also in accordance with past research, migrant husbands do not experience a

reduction in employment, compared with non-migrant husbands. The presence of

school-age children and being married enhance employment propensities, whereas

age and non-labour household income inhibit it. Moreover, husbands’ labour market

participation is directly linked to their wives’ past job characteristics. Finally, those

who worked in the private sector or in temporary job contracts at have lower

employment rates, while higher levels of paid overtime and occupational pension

coverage increase employment probability at t.

1−t

The estimates were used to derive the selection correction terms for time-

variant individual heterogeneity described by equations (10)-(12). These are used as

regressors in the log wage change equations in order to derive consistent estimates.

Table 4 displays the results. Wage changes were estimated for individuals employed

in . The estimates of the migrants’ wage change equations are based on relatively

small samples and thus have low levels of significance. The coefficients are quite

consistent across the four groups. Most notably, wage changes are negatively

associated with work hours and paid overtime, indicating that extended hours are not

rewarded with proportional pay rises. Jobs covered with occupational pension

t

16

schemes have a wage premium attached to them, and becoming a union member also

helps. Changing to a fixed-term contract has a negative effect on year-to-year wage

changes, especially for migrants. On the other hand, migrant wives are rewarded more

than non-migrants for taking on a new job. The coefficients on the occupational status

binary variables are a bit surprising. In contrast to non-migrants, wages are lower for

both migrating husbands and wives if they move into some of the higher status groups

compared to the reference group (partly and unskilled occupations). On average,

migrants improve their occupational status more than non-migrants, but there is no

wage premium associated with this.

The estimates also reveal statistically significant selection bias for non-

migrants. The signs on the coefficients on Mλ indicate that non-migrants had

unobserved characteristics which deter both migration and wage growth. Moreover,

non-migrant wives who chose to work receive lower wages than the female

population at large, as the negative coefficient on WPλ indicates. In contrast, non-

migrant husbands who chose employment possess comparative advantage at it, but

with a smaller effect on wage changes than the selection into non-migration. The

coefficients for migrants are not statistically significant, giving no evidence of

selection bias for them.

The coefficients on the wage change equations reflect the average price of

each individual and job characteristic in a hypothetical origin and destination

respectively. In order to explore the counterfactual wage changes I define the potential

destination for each non-migrant as the average of the locations chosen by migrants,

the hypothetical origin as the average of the locations chosen by non-migrants. Using

these estimates, wage changes were imputed for each husband and wife for the

counterfactual situation, i.e. the wage change a non-migrant would have received

when migrating and vice versa. The coefficients on the selection-correction terms

were included when imputing the counterfactuals. This implicitly assumes that the

unobserved (time-variant) differences between individuals captured in the selectivity

terms are equally useful in origin and destination. Deriving expected wage changes

from the log wage equations and differencing between origin and destination wage

change yields a wage change differential for each employed individual. Individuals

not employed in t will, by assumption, also evaluate lifetime earnings changes in

their decision to migrate which are approximated by the immediate expected returns.

17

For these individuals I derive a wage change differential by assuming their personal

and job characteristics in t to be equal to the average among the group of migrants and

non-migrants respectively. Any migration-related withdrawal from the labour market,

often associated for women with accommodating family needs post migration, is

interpreted as being temporary – indeed no effect of migration on participation choice

remains in . As there is no methodology available for deriving counterfactual

withdrawal information for stayers, the costs related to women’s temporary non-

participation will be picked up in the error terms of the structural migration probit.

1+t

Table 5 describes the distribution of predicted wage gains of migrating versus

staying by forming groups based on whether or not the husband, wife, and the couple

as a whole gain in terms of wage changes by moving. Column I gives counts of

migrants and non-migrants who could as a couple achieve a positive wage change by

migrating for different combinations among the spouses. Column II counts couples

who would fare worse in terms of joint income change by migrating. Below the

counts are, in parentheses, average estimated hourly wage change differentials in each

category, first for husbands and then for wives. Looking first at migrants, column I

shows that in 195 migrating couples (99.5% of migrants) both spouses gain a

considerable wage change by migrating: husbands gain an average of 48 pence per

hour in year 2000 prices, wives gain an average of 34 pence. Migration thus seems to

be a rational choice for these families. Only one couple migrates with a positive

family return to migration but minor losses for the wife. According to our estimates

there is thus only one case of a wife possibly being a tied mover. In the entire sample

we observe no migration with a negative family return.

Turning now to non-migrants, the first row in column I shows that 4,016

couple-observations (47% of observations) do not migrate although they would

apparently experience wage gains individually and as a couple by doing so. Compared

to the migrants in this category, however, their average expected gains are modest,

amounting to 16 pence for husbands and 12 pence for wives per hour worked. As the

figures do not include the unknown mobility costs, it is well possible that these

couples would in total not fare better by migrating. Likewise, it may well be that the

2,377 observations (28%) of couples seen not to be moving in spite of a predicted

family wage gain, would not benefit after taking mobility costs into consideration.

However it is possible that some husbands in the group are tied stayers who would

have fared better individually by moving net of migration costs. Likewise, the 606

18

observations listed in the row below could include wives who are tied stayers. Non-

migrants in column II have nothing to gain as a family from migration. While for 432

observations listed in the bottom row the decision was probably unambiguous, the

two middle rows may include a number of husbands and a few wives who are tied

stayers.

The comparison between migrants’ and non-migrants’ expected wage gains is

consistent with expectations. Although we cannot observe the earnings gain threshold

after which migration becomes profitable individually or as a family, the estimates

show that couples who expect higher wage gains migrate. Migrants’ expected wage

gains do not vary by distance moved, although information on this is only available up

to year 2002.

The last step in the estimation procedure is to estimate a structural migration

probit containing the predicted wage change differentials of husbands and wives.

Table 6 displays two different sets of results. Column (1) measures the hourly

expected wage change differentials in January 2000 pounds. Column (2) takes the

spouses’ log wage change differentials as independent variables. Bootstrapping was

used to derive confidence intervals in order to infer significance levels for the two-

stage procedure (1000 iterations). If the bias-corrected confidence interval did not

include zero, the effect was taken to be significant at the level indicated by the size of

the confidence interval.

The coefficients on the spouses wage change differentials are quite similar

between husbands and wives. The wives’ and husbands’ predicted wage change

differentials are weighed 41% to 59% in the family migration decision in specification

(1). Specification (2) yields a relationship of 46% to 54% in favour of the husband.

Considering that women work fewer hours than men, however, and that the wage

differentials refer to changes in hourly wages, it seems that both spouses wage gains

are roughly equally important. In answer to the main question driving this paper I

conclude that both spouses in dual-earner couples weigh their respective wage gains

about equally in the migration decision. Thus I reject earlier findings that it is the

husband’s job alone that motivates dual-earner migration. I discuss the implications of

these findings in the conclusion.

In line with most migration studies I also find that home owners and older

individuals are less likely to migrate. The same is true for families with pre-school

and school-age children. The influence of non-labour household income and house

19

prices on family migration is not consistent across specifications. The other factors

hypothesized to influence migration behaviour – marital status and possessing a

higher education which was thought to proxy the ability to perform effective job

search – did not turn out to be statistically significant, however.

In order to test the robustness of results to model specification I carried out

several sensitivity checks. In particular, I tested the effect of using different exclusion

restrictions (information about self-employment status of parents or whether parents

were working at all, different measures of house price differentials) on the weights

attached to each spouse’s wage gain. The weights remained much the same as those

presented here, although in most cases alternative instruments did not identify the

model. In some of these specifications the migration equation was not independent of

the participation equations, which is not surprising in a non-identified model. Further

tests included checking whether the inclusion of imputed wages changed results,

controlling for labour market interruption between dates of interview in the wage

equations, checking the influence of health status on wages and mobility and the role

of care responsibilities outside the household on migration choice. In most cases these

variables were insignificant, and they had little effect on the final results while

reducing sample size due to missing values. Confining the structural probit analysis to

legally married, and thus perhaps more ‘traditional’, couples did not change results

either.

6. Conclusion

This paper provides evidence that dual-earner couples weigh the expected wage

change differentials of husband and wife about equally when deciding whether or not

to migrate. In contrast to much previous research, the results of this paper clearly

reject the assertion that couples make migration decisions asymmetrically in favour of

the husband’s job prospects for the group of dual earners. In fact, the analysis of

couples’ expected wage change differentials has shown that while there may be a

substantial number of husbands who are tied stayers, there is but one case of a wife

possibly acting as a tied mover in the subsample of the BHPS (1991-2003) used for

the estimates.

Previous papers suggesting that decision-making is husband-centred have

often relied on estimates from migration equations where the wife’s personal and job

20

characteristics in origin proxy expected wage gains. Like many of these papers I do

not find the characteristics of the wife’s job in origin to significantly influence the

family migration decision in a reduced form probit equation. However, the wife’s

expected wage change differential, obtained in a switching regression model and

corrected for the double selection into migration and employment, is highly relevant

in a structural form of the migration equation. This suggests that characteristics of the

job in origin may not capture the opportunities that women face in destination when

migrating. Put another way, migrating women have realized higher wage gains than

could have been expected from their jobs at 1−t . This highlights the value of using

panel data on origin and destination characteristics in migration analysis to uncover

these opportunities.

The employment effects of migration found in this paper are less pronounced

than those reported in other papers: In the first year after migration wives’

employment was reduced temporarily by 8% after other factors have been accounted

for, and husbands’ employment was unaltered by migration. In the following year no

migration effect on female employment remained. There is evidence of significant

selection effects among non-migrants. Non-migrants have unobserved characteristics

which deter both migration and wage growth. Moreover, non-migrant wives who

chose to work possess comparative disadvantage at it, while in contrast non-migrant

husbands experience higher wage growth than the population at large. This

emphasises the importance of modelling self-selection not only into migration but also

into employment when analyzing the wage effects of migration. In this paper I

demonstrate how double selection - which is fairly involved when analyzed in a

family context - can be accounted for by following an evidence-based procedure.

What can be learnt from this paper in terms of family decision-making?

Regrettably the results do not allow us to discriminate between the traditional unitary

model and a bargaining model of the family. Symmetry between husband and wife

could equally support the unitary model which assumes equal weights on the partners’

wage gains as it could a bargaining model of the family in which both partners have

equal bargaining power. In fact the assumption of equal bargaining power does not

seem unlikely in dual-earner couples that according to this analysis have similar

educational and occupational backgrounds. A natural research agenda would be to

further test this issue in differing frameworks, for example by explicitly modelling

21

several destinations available to a couple rather than aggregating these options into

one destination.

22

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24

Table 1: Migration, Wages, and Labour Market Participation, BHPS 1991-2003

Non-migrants Migrants Observations 8,557 196 (2.2%)Couples 1,823 175 (8.8%) husbands wives husbands wives Mean hourly wage (£) 1−t 8.7 6.3 10.2 7.6Mean hourly wage t (£) 9.4 6.9 11.5 8.7Mean wage increase to t 1−t 8.0% 9.5% 12.7% 14.5%Mean weekly working hours 1−t 40 29 41 32Change in working hours to t 1−t 0% 0.2% 0.2% 1.2%Participation rate t 95.5% 92.0% 94.4% 80.1%Job changers to t 1−t 19.7% 20.5% 42.7% 45.2%Notes: Gross monthly wages in January 2000 prices. All values for time t refer to individuals employed in t only. Migration is defined as a move across Local Authority District boundaries.

Table 2: Selection model: tests for identification and instrument validity, and estimated correlations of error terms, BHPS 1991-2003

Instrument Equation d.f. 2χ p-value House price index t-1 M 1 3.78 0.052 Mother employee when respondent aged 14 wP 1 4.67 0.031 Father employee when respondent aged 14 hP 1 4.23 0.040 All instruments jointly 3 12.29 0.007 Correlations of error terms variable coefficient t-value Migration, participation wife 12ρ -0.249 (0.83) Migration, participation husband 13ρ -0.423 (1.35) Participation wife, participation husband 23ρ 0.152 (3.10)**Notes: ** significant at 1%. Estimated using GHK simulator (94 draws) and heteroskedasticity-robust standard errors. Top panel displays Wald test that the coefficient estimate for an instrument is zero in the listed equation. Bottom panel displays estimated correlations of error terms. A full set of results is available on request.

25

Table 3: Migration and participation probits, BHPS 1991-2003

Univariate Probit Bivariate Probit Migration LFP wives LFP husbands Migrant -0.483 (4.16)** -0.100 (0.64) Married -0.022 (0.27) -0.105 (1.48) 0.249 (3.27)**New baby -0.021 (0.11) -1.593 (16.09)** 0.182 (1.22) Number children < 5 -0.084 (0.94) -0.013 (0.20) 0.100 (1.26) Number children ≥ 5 -0.111 (2.71)** 0.164 (5.39)** 0.089 (2.55)**Home owner outright -0.537 (3.12)** 0.147 (1.35) -0.034 (0.30) Home owner mortg. -0.560 (6.72)** 0.188 (2.53)** 0.014 (0.16) Non-labour household-income

0.026 (1.15) -0.144 (8.57)** -0.166 (8.43)**

High education wife 0.008 (0.09) 0.021 (0.37) -0.043 (0.67) High education husb. -0.058 (0.76) -0.063 (1.22) 0.038 (0.66) Age husband -0.025 (5.69)** 0.0063 (1.79) -0.013 (3.48)**Age husband-wife 0.018 (2.01)* 0.0084 (1.41) 0.0010 (0.15) House price index 0.235 (2.29)* Mother employee 0.102 (2.16)* Father employee 0.131 (2.03)* Constant -1.473 (4.50)** 1.590 (6.06)** 2.739 (9.18)**Further variables: 2χ p-value 2χ p-value 2χ p-value Husband’s job characteristics (11)

1−t40.21

0.000 6.20

0.860

105.77

0.000

Wife’s job characteristics (11)

1−t12.93

0.298 123.28

0.000

23.90

0.013

Year indicators (11) 9.61 0.566 23.61 0.015 22.50 0.021 ρ 0.123 (2.59)** Log likelihood -831.49 -3422.59 Observations 8,753 8,753 Notes: * significant at 5%, ** significant at 1%. Absolute value of heteroskedasticity-robust t statistics in parentheses. All regressors in migration equation measured at time . Regressors in participation equations measured at time t except job characteristics which are measured at

1−t1−t . Reference categories for indicator

variables are non-migrant, cohabiting, renter, no high education wife/husband, mother/father self-employed or not working. Job characteristics at refer to 11 variables included in wage change equations (table 4) except new job indicator and

1−t

s'λ . 11 year indicator variables included.

26

Table 4: Selectivity-corrected wage change equations, BHPS 1991-2003

Non-migrants Migrants

Husbands Wives Husbands Wives

Constant -0.016 (0.82) 0.013 (0.53) 0.323 (1.90) -0.192 (0.69)Professional

0.065 (3.93)** 0.095 (3.09)** -0.153 (1.15) -0.130 (0.96)Manager/technician 0.056 (3.74)** 0.113 (5.49)** 0.0072 (0.06) -0.056 (0.46)Skilled non-manual 0.040 (2.62)** 0.062 (2.91)** 0.079 (0.50) 0.033 (0.30) Skilled manual 0.019 (1.79) 0.038 (2.27)* -0.083 (0.83) -0.214 (1.03) Working hours -0.014 (17.14)** -0.011 (10.87)** -0.017 (4.51)** -0.013 (3.14)**Paid overtime hours -0.018 (22.14)** -0.037 (24.81)** -0.012 (2.18)* -0.042 (4.85)**Job tenure 0.055 (3.20)** 0.064 (3.17)** -0.037 (0.50) 0.162 (1.17) Fixed-term contract -0.026 (1.05) -0.0047 (0.25) -0.234 (2.47)* -0.233 (1.79)Private sector -0.014 (0.62) -0.0035 (0.20) -0.042 (0.73) -0.0043 (0.04)Occupational pension

0.059 (4.75)** 0.053 (3.82)** -0.036 (0.42) 0.073 (1.17)

Union member 0.032 (2.74)** 0.042 (3.12)** -0.076 (1.26) 0.033 (0.40) New job 0.064 (5.52)** 0.074 (5.49)** 0.045 (0.87) 0.125 (1.70)

Mλ 0.241 (6.21)** 0.137 (3.02)** 0.043 (1.05) 0.006 (0.07)

wPλ -0.043 (2.68)** -0.016 (0.11)

hPλ 0.076

(2.59)** 0.014 (0.06) Observations 8,172 7,873 185 157

2R 0.23 0.25 0.32 0.37 Notes: * significant at 5%, ** significant at 1%. Absolute value of heteroskedasticity-robust t statistics in parentheses. Dependent variable is log of hourly gross wage in January 2000 prices. Independent variables except s'λ and new job indicator measured as change from 1−t to t. Reference categories are partly and unskilled occupation, permanent contract, and public sector. Year indicator variables included.

27

Table 5: Husbands’ and wives’ predicted wage change differentials and mobility

I: 0>∆+∆ wh ww II: 0≤∆+∆ wh ww migrants non-migrants migrants non-migrants

0 ,0 >∆>∆ wh ww 195 4,016 n/a n/a (0.48; 0.34) (0.16; 0.12)

0 ,0 ≤∆>∆ wh ww 1 2,377 0 768 (0.31;-001) (0.20; -0.06) (0.07, -0.13)

0 ,0 >∆≤∆ wh ww 0 606 0 358 (-0.04; 0.16) (-0.08; 0.03)

0 ,0 ≤∆≤∆ wh ww n/a n/a 0 432 (-0.07; -0.06) Notes: are the estimated hourly wage change differentials of migrating vs. not migrating of husbands and wives respectively in January 2000 pounds. The table displays the number of couples in each category. In parentheses are the average wage change differentials for husbands (left) and wives (right).

wh ww ∆∆ ,

Table 6: Structural migration probit, BHPS 1991-2003

(1) (2) Wage change differential wife 4.889 ** 14.281 ** Wage change differential husband 7.108 ** 16.945 ** Married -0.003 -0.468 New baby -0.490 -0.754 Number children < 5 -0.214 -0.633 * Number children ≥5 -0.275 ** -0.762 ** Home owner outright -0.997 ** -3.513 ** Home owner mortgage -0.507 * -1.817 ** High education wife 0.163 -0.056 High education husband 0.174 0.397 Age husband -0.035 ** -0.112 ** Age (husband-wife) 0.045 ** 0.103 ** House price index 0.422 * 0.528 Non-labour household income 0.063 0.233 ** Constant -2.369 ** -3.853 ** Log likelihood -239.53 -35.30 Observations 8,753 8,753 Notes: * significant at 5%, ** significant at 1%. Model (1) measures wage change differentials in pounds, model (2) in natural logs of pounds. All variables except wage change differentials measured at time 1−t . Bootstrapping (1000 replications, sampling couples) was used to derive confidence intervals. Significance of the effects was inferred if the bias-corrected confidence interval failed to include zero.

28