Rationality of Post Accession Migration

Motivation Framework Empirical Model Results Policy Implications Rationality of Post Accession Migration Katarzyna B. Budnik Conference on European Economic Integration (CEEI) 17th November 2008, Wien Katarzyna B. Budnik Rationality of Post Accession Migration

Outline Motivation Framework Empirical Model Results Policy Implications 1 Motivation 2 Framework 3 Empirical Model 4 Results 5 Policy Implications Katarzyna B. Budnik Rationality of Post Accession Migration

Outline Motivation Framework Empirical Model Results Policy Implications Motivation 1 Motivation 2 Framework 3 Empirical Model 4 Results 5 Policy Implications Katarzyna B. Budnik Rationality of Post Accession Migration

Motivation Framework Empirical Model Results Policy Implications Questions Addressed Motivation Do expected income differences drive migration? Is migration an effective sorting mechanism? Validation of neoclassical description of migration movements Katarzyna B. Budnik Rationality of Post Accession Migration

Motivation Framework Empirical Model Results Policy Implications Rationality of Migration Motivation Assumption of unbiased anticipations of workers Do workers maximize their expected return? Not a test of rationality of migrants/stayers expectations Katarzyna B. Budnik Rationality of Post Accession Migration

Polish Experience Motivation Framework Empirical Model Results Policy Implications Motivation EU enlargement in 2004 was coupled with introduction of open-door policy for migrants from the accession countries by some of the former member countries The policy introduced free movement of labour between countries with sharp income differentials Magnitude and abruptness of changes offers a perfect playground for analysis of drivers of (temporary) migration Micro (Labour Force Survey) data provide information that might be used to derive measures of macro efficiency of migration Katarzyna B. Budnik Rationality of Post Accession Migration

Data Motivation Framework Empirical Model Results Policy Implications Motivation The data on Polish-born workers (working age population) from the labour force survey (LFS) for Poland and the UK covering the period from the first quarter 2004 to the first quarter 2008 The data contain information about labour market activity and (sometimes) wages of a respondent Both surveys are conducted with quarterly frequency and are based on a rotating design (truncation of the sample to unrepeated observations) Katarzyna B. Budnik Rationality of Post Accession Migration

Motivation Framework Empirical Model Results Policy Implications Motivation Intuitive Measures of Rationality Rationality of migration: Do actual migrants earn more than they would at the source labour market? (returns to migration) Do actual migrants earn more abroad than would an observationally identical non-migrant? (selection into migration) Rationality of staying: Do actual stayers earn more than they would at the foreign labour market? (returns to staying) Do actual stayers earn more at home than would an observationally identical migrant? (selection in to staying) Katarzyna B. Budnik Rationality of Post Accession Migration

Outline Motivation Framework Empirical Model Results Policy Implications Test Observed Wage Identification of Returns to Unobservables 1 Motivation 2 Framework 3 Empirical Model 4 Results 5 Policy Implications Katarzyna B. Budnik Rationality of Post Accession Migration

Test of Rationality Motivation Framework Empirical Model Results Policy Implications Test Observed Wage Identification of Returns to Unobservables Assume that expected returns to migration drive migration Construct a model that describes the expected income abroad and at home on the base of individual traits of individuals Assume that workers correctly calculate the expected income Derive measures of rationality of migration and staying Test whether measures calculated for actual migrants and stayers correspond with the assumption of positive gains from migration for migrants and positive gains from staying for stayers (rationality of migration and staying) Katarzyna B. Budnik Rationality of Post Accession Migration

Observed Wage (1) Motivation Framework Empirical Model Results Policy Implications Test Observed Wage Identification of Returns to Unobservables w M (i) = µ M (i) + η M (i) + ɛ M (i) where: M an index of a country M {0, 1} where 0 represents the source country variable and 1 the host country variable w(i) an observed wage rate µ(i) a wage norm η(i) returns to unobserved traits of an individual ɛ(i) random variation in productivity of an individual (E(ɛ(i) = 0)) Katarzyna B. Budnik Rationality of Post Accession Migration

Observed Wage (2) Motivation Framework Empirical Model Results Policy Implications Test Observed Wage Identification of Returns to Unobservables Wage norm Returns to unobserved traits Characteristics of a worker Problem Identification gender education work experience engagement open-mindness creativity Different valuation of skills cross labour markets Regression of wages on observed variables (for those for whom we observe the former)? Katarzyna B. Budnik Rationality of Post Accession Migration

Motivation Framework Empirical Model Results Policy Implications Intuition behind the Procedure Test Observed Wage Identification of Returns to Unobservables Out of two observationally identical workers the one with higher expected return to unobserved traits on the foreign labour market shall migrate and one with higher expected return to unobserved traits on the home labour market shall stay Identify factors that are correlated with migration decision Probability of migration/staying should be correlated with returns to unobserved traits on two labour markets Katarzyna B. Budnik Rationality of Post Accession Migration

Procedure Motivation Framework Empirical Model Results Policy Implications Test Observed Wage Identification of Returns to Unobservables Selection into migration (and staying) modelled jointly with the employment decision with different processes driving the labour market participation on the home and host labour market (trivariate Probit with partial observability) Predictions of the model used in the standard wage regressions run for Polish migrants in the UK and Polish residents (switching reression) Contribution of predicted variables based on the selection model to expected wage rates interpreted as returns to unobservables Katarzyna B. Budnik Rationality of Post Accession Migration

Empirical Model Motivation Framework Empirical Model Results Policy Implications Test Observed Wage Identification of Returns to Unobservables E(w M (i)) = α 0 x(i) + ɛ M (i) 1 if M > 0 M(i) = 0 if M < 0 M (i) = πx(i) + e(i) 1 if VM(i) > 0 V M (i) = 0 if VM(i) < 0 V M(i) = β M x(i) + ς M (i) where w M observed only if M = 1 and V 1 = 1 for migrant and M = 0 and V 0 = 1 for stayer Katarzyna B. Budnik Rationality of Post Accession Migration

Outline Motivation Framework Empirical Model Results Policy Implications 1 Motivation 2 Framework 3 Empirical Model 4 Results 5 Policy Implications Katarzyna B. Budnik Rationality of Post Accession Migration

Selection Model Motivation Framework Empirical Model Results Policy Implications Equation Emigration propensity Propensity to work in Poland Propensity to work in the UK Independent Variables gender, family and martial status, age, education, experience gender, family and martial status, education, general job experience, disability duration of stay in the UK Katarzyna B. Budnik Rationality of Post Accession Migration

Motivation Framework Empirical Model Results Policy Implications Wage Regressions Equation Wage rate in Poland Wage rate in the UK Independent Variables gender, education, general job experience, firm-specific experience, disability, hours worked, time dummies, control variable for probability of emigration/staying, control variable for probability of working in the UK/Poland country-specific job experience, countryspecific education, duration of stay in the UK Katarzyna B. Budnik Rationality of Post Accession Migration

Motivation Framework Empirical Model Results Policy Implications Summary of Intermediate Results (1) There is no significant difference in propensity to migrate of Polish men and women, however significant differences persist in their propensity to be employed Propensity to emigrate is the highest in the age of 30-35, increasing before the age and falling thereafter Be married, having children and being disabled reduces propensity to emigrate Having (small) children has negative impact on work propensity of women, the effect is more pronounced for migrant mothers (availability of childcare?) Katarzyna B. Budnik Rationality of Post Accession Migration

Motivation Framework Empirical Model Results Policy Implications Summary of Intermediate Results (2) Those better educated have an edge over less educated in wages and employment chances in Poland but the advantage is absent on the UK labour market General, country-specific and job-specific experience have positive impact on wages Wages of Polish workers were monotonically increasing in the period under consideration and remained stable for Polish immigrants in the UK Katarzyna B. Budnik Rationality of Post Accession Migration

Outline Motivation Framework Empirical Model Results Policy Implications Measures of Rationality of Migration Measures of Rationality of Staying 1 Motivation 2 Framework 3 Empirical Model 4 Results 5 Policy Implications Katarzyna B. Budnik Rationality of Post Accession Migration

Motivation Framework Empirical Model Results Policy Implications Definition of Returns to Migration Measures of Rationality of Migration Measures of Rationality of Staying Returns to Migration: Difference between the expected earnings abroad and at home of an actual emigrant. Takes account of differences in labour market valuation of observable (difference in wage norms between markets) and unobservable characteristics (sorting gains to migration). κ 1 (i) = E(w 1 (i) M(i) = 1) E(w 0 (i) M(i) = 1) = (α 1 α 0 )x(i) + ν 1 (i) Sorting gains to migration: Difference between valuation of unobservable skills abroad and at home of an actual emigrant. ν 1 (i) = E(η 1 (i) M(i) = 1) E(η 0 (i) M(i) = 1) Katarzyna B. Budnik Rationality of Post Accession Migration

Returns to Migration Motivation Framework Empirical Model Results Policy Implications Measures of Rationality of Migration Measures of Rationality of Staying Density 0.5 1 1.5 2 Returns to migration in EUR 1 1.5 2 2.5 ln(wage rate in the UK/Wage rate in Poland) Density 0.5 1 1.5 2 2.5 Real returns to migration 0.5 1 1.5 2 ln(wage rate in the UK/Wage rate in Poland) Katarzyna B. Budnik Rationality of Post Accession Migration

Motivation Framework Empirical Model Results Policy Implications Sorting Gains to Migration Measures of Rationality of Migration Measures of Rationality of Staying Density 0 5 10 15 20 25 Sorting gains into migration in EUR -.1 0.1.2.3 ln(wage rate in the UK/Wage rate in Poland) Density 0 5 10 15 Real sorting gains into migration -.8 -.6 -.4 -.2 ln(wage rate in the UK/Wage rate in Poland) Katarzyna B. Budnik Rationality of Post Accession Migration

Motivation Framework Empirical Model Results Policy Implications Definition of Selection to Migration Measures of Rationality of Migration Measures of Rationality of Staying Selection to Migration: Compares average host labour market valuation of unobservables of actual migrants and stayers. h 1 (i) = E(w 1 (i) M(i) = 1) E(w 1 (i) M(i) = 0) = E(η 1 (i) M(i) = 1) E(η 1 (i) M(i) = 0) Katarzyna B. Budnik Rationality of Post Accession Migration

Motivation Framework Empirical Model Results Policy Implications Selection to Migration Measures of Rationality of Migration Measures of Rationality of Staying Selection into migration in EUR Real selection into migration Density 0 1 2 3 4.5 1 1.5 2 ln(wage rate in the UK/Wage rate in Poland) Density 0 1 2 3 0.5 1 1.5 ln(wage rate in the UK/Wage rate in Poland) Katarzyna B. Budnik Rationality of Post Accession Migration

Motivation Framework Empirical Model Results Policy Implications Results on Rationality of Migration Measures of Rationality of Migration Measures of Rationality of Staying Returns to migration were strongly positive both in nominal and real terms The difference in valuation of unobservable characteristics of migrants (sorting gains to migration) in nominal terms was significantly positive for most of migrants (even though negative if measured in the real terms) Strong support for rationality of migration decision Katarzyna B. Budnik Rationality of Post Accession Migration

Returns to Staying Motivation Framework Empirical Model Results Policy Implications Measures of Rationality of Migration Measures of Rationality of Staying Density 0.2.4.6.8 Returns to staying in EUR -5-4 -3-2 -1 0 ln(wage rate in the UK/Wage rate in Poland) Density 0.2.4.6.8 Real returns to staying -4-3 -2-1 0 1 ln(wage rate in the UK/Wage rate in Poland) Katarzyna B. Budnik Rationality of Post Accession Migration

Motivation Framework Empirical Model Results Policy Implications Sorting Gains to Staying Measures of Rationality of Migration Measures of Rationality of Staying Density 0 5 10 15 Sorting gains into staying in EUR 0.1.2.3.4 ln(wage rate in the UK/Wage rate in Poland) Density 0 2 4 6 8 Real sorting gains into staying.4.6.8 1 1.2 ln(wage rate in the UK/Wage rate in Poland) Katarzyna B. Budnik Rationality of Post Accession Migration

Selection to Staying Motivation Framework Empirical Model Results Policy Implications Measures of Rationality of Migration Measures of Rationality of Staying Density 0 1 2 3 Selection into staying in EUR -2-1 0 1 ln(wage rate in the UK/Wage rate in Poland) Density 0.5 1 1.5 2 2.5 Real selection into staying -2-1 0 1 2 ln(wage rate in the UK/Wage rate in Poland) Katarzyna B. Budnik Rationality of Post Accession Migration

Motivation Framework Empirical Model Results Policy Implications Results on Rationality of Staying Measures of Rationality of Migration Measures of Rationality of Staying Returns to staying were negative for most of the Polish residents However, the sorting gains into staying were positive both in the nominal and the real terms Only negligible fraction of stayers recoded positive selection into staying in nominal terms but around half of them in the real terms Katarzyna B. Budnik Rationality of Post Accession Migration

Outline Motivation Framework Empirical Model Results Policy Implications 1 Motivation 2 Framework 3 Empirical Model 4 Results 5 Policy Implications Katarzyna B. Budnik Rationality of Post Accession Migration

Key Result Motivation Framework Empirical Model Results Policy Implications Why? Positive validation of rationality of migration less clear results on rationality of staying Presence of significant travelling (movement) costs Presence of significant social costs (other evidence) Job status Family situation Welfare policy Age (demography) Networks Katarzyna B. Budnik Rationality of Post Accession Migration

Implications (1) Motivation Framework Empirical Model Results Policy Implications Open-border policy and presence of significant income differences drive migration even though these are not only determinants of the magnitude of migration flows Income differences originate in different valuation of workers skills in a source and a host countries Workers may experience lower returns to their education and job experience abroad which reduces possible gains from moving Additionally, migration propensity is likely to be constrained by social costs of moving Katarzyna B. Budnik Rationality of Post Accession Migration

Implications (2) Motivation Framework Empirical Model Results Policy Implications In macro analysis and forecasting of migration flows the case-specific approach that takes into account demographics, welfare policies, habits, existing networks may deliver more reliable results than assessments referring only to income differentials and distance between host and source labour markets (gravity models) Importance of non-observable traits in triggering or hindering migration Still, neoclassical approach to model migration movements (consistent with mainstream macro models models) seems to be a useful device for analysis of migration Katarzyna B. Budnik Rationality of Post Accession Migration

Rationality of Post Accession Migration Katarzyna B. Budnik November 11, 2008 Abstract After EU enlargement in 2004, thousands of Polish workers moved to the UK. This study evaluates market efficiency in sorting Polish-born workers to locations where they enjoyed the highest returns to their individual skills, exploring Polish and UK labour force survey data to establish whether the Poles that emigrated to the UK did so on rational premises. The expected gains from migration reflect both observable characteristics (e.g. education and labour market experience) and unobservable traits (e.g. motivation). Returns to unobservable skills are identified via the Heckman (1979) self-selection correction procedure. A model of joint selection into migration and employment allows separating returns to unobservable traits that influenced the relocation choice. The results support the rationality of migration from Poland to the UK: those who left gained both in nominal and real terms. Rationality tests are less conclusive about the optimality of staying. Some of those who stayed might have earned more had they migrated. The outcomes suggest that the anticipated wage gains do not fully explain the intensity of migration between Poland and the UK. They underline the importance of also considering non-economic factors, i.e. social costs, in exploring post-accession migration movements. JEL Classification: C34,C35,J61 Keywords: emigration, EU enlargement, rationality, selection bias, partial observability model Preliminary and incomplete. Please, send any suggestions to this paper to kbudnik@sgh.waw.pl. The author would like to thank Bernhard Hammer for research assistance. The author benefited a lot from comments of Philipp Schmidt-Dengler, Christine Zulehner, two anonymous referees and language revision of the text by Ingeborg Schuch. 1

1 Introduction While European integration is a gradual process on all markets, changes in immigration policy still raise strong social unease. Workers from the Central and Eastern European countries (CEECs) that joined the EU in 2004 remain (temporarily) shut out of most old EU countries labour markets, given concerns that the large income disparity might facilitate an unprecedented movement of labour from East to West. The UK, Ireland and Sweden were the only EU countries to introduce an open-door policy right away, followed by Southern-European countries and the Netherlands after some time. Even though Germany and Austria, which had expected to attract the highest share of migrants, retained a closed-door policy, the actual outflow of workers from the CEECs greatly outpaced any earlier calculations (Zaiceva (2006)). Thus, EU enlargement in 2004 constituted a,,natural experiment that encourages testing the hypothesis about the rationality of migration choice 1, i.e. movements 2. evaluating to what extent expected earnings differentials may explain migration The rationality of internal migration has been verified by a few studies, among those Kaun (1970), later Tunali (2000) and quite recently Dostie and Leger (2006). specifically on the rationality of EU post-accession cross-border migration. However, no study to my knowledge focused I assess temporary migration from Poland to the UK to test whether migration, once barriers for cross-country labour force mobility had been removed, improved the welfare of Polish natives by leading to an optimal selection of people staying and people migrating. The underlying data stem from labour force surveys (LFS) conducted in the UK and Poland. Although not originally developed to study migration movements, LFS questionnaires contain relevant information about skills and wages. changes in derived income measures over time 3. Moreover, the survey schedule enables tracking trends and To evaluate the rationality of migrate-or-stay decisions, this study uses two measures of the difference between the income individuals might expect to earn abroad and at home. The first measure refers to the wage gain migrating individuals might anticipate to achieve by migrating or non-migrating workers by staying. Basically, this measure relates the migrate-or-stay decision to the different pricing of workers observed and unobserved skills on different labour markets. The second measure assesses the differences in the valuation of unobserved skills on the two labour markets among observationally identical individuals. The test of rationality based on the latter measure builds on the presumption that rational workers with equal observed characteristics should have chosen the location that allowed them to maximize their income (via higher returns to unobserved skills). The returns to calculated expected wage differences between countries may be easily derived through consistent estimates of wage regressions. To identify the value of unobserved characteristics, I follow the idea of 1 In the article, rationality of migration choice is defined narrowly as importance of the expected earnings differentials in explaining migration movements. 2 The question about the role of disparities in the expected income differentials in triggering migration might also be restated as an examination of the validity of the neoclassical view on labour force movements according to which individuals attempt to maximize their anticipated income. 3 More popular approach used in the migration research is to merge data from Population Censuses that usually include more detailed information about individuals and cover larger subsamples of migrants. Aydemir (2002) referred to data from US and UK Census and analysed it jointly with data from migration survey in Canada. Mishra (2007) and Chiquiar and Hanson (2008) used data from Population Censuses conducted in the United States and Mexico to study migration movements between the two countries and their effects on Mexican economy. Still, no Population Census either in Poland or in the UK was conducted within a period after the EU enlargement in 2004. 2

Tunali (2000), who studied internal migration across Turkish regions. He used the popular Heckman (1979) self-selection scheme, first to arrive at consistent estimates of returns to observable characteristics of workers; and second to establish the expected value of returns to unobservables, which allow ex post assessment of the impact unobserved heterogeneity had on expected income profiles 4. The intuition behind the approach is clear-cut. If earnings depend on observed and unobserved human capital characteristics, assuming unbiased wage anticipations and rational decision-making, individuals should have chosen the option that allows them to reap the highest return on their skills. Two conclusions follow. First, migration propensity assessed ex post should be correlated with returns on the full set of workers skills. Therefore migration propensity might be used as an instrument in the wage regression controlled for observable characteristics with a view to rendering consistent estimates of returns on observables. Second, sustaining the assumption of correlation between observables and unobservables from the first stage of the Heckman procedure, expected differences in returns on unobservables might be approximated effectively by the difference in correction terms of observationally equivalent individuals. As wages are measured only for those employed, it was necessary to deal with the additional problem of non-random selection into employment, and in particular with the interdependence of self-selection into employment and into migration. To alleviate bias problems in wage equation parameter estimates due to both selection mechanisms acting simultaneously, I developed a model of joint selectivity into emigration and employment. The selection model is based on sequential Probit, where the emigrate-or-stay decision is followed by a participation decision 5. Employment decisions on both labour markets are allowed to be dependent on different sets of factors. Tying up the migration decision with an employment decision seemed a natural extension of Tunali s (2000) approach, as unequal employment probabilities in different destinations may impact the emigration decision. The contribution of the present study to the existing literature lies in applying the above set of rationality tests in a systematical manner to temporary international migration 6. In this respect, income disparity would 4 The alternative would have been to adopt a productivity-based approach following Dostie and Leger (2006), who employ data on Canadian physicians and use the fact that they are paid on the fee-for-service base as identification criteria. They approximated unmeasured productivity of physicians by deviation of wage from,,the average wage observed among observationally equal physicians in a region prior movement decision. The data used in this article do not however deliver enough information on past productivity of workers to implement that approach. 5 The selectivity issue constitutes the core problems that are usually addressed in empirical studies of migration movements, particularly those that refer to wage data. The issue of self-selection into migration goes back to the article of Borjas (1987; for immigrant men in the U.S.; Cobb-Clark (1993) delivered corresponding results for women), who showed that the selection on unobservables such as migrants motivation need not be related to the selection on observables. Among recent studies that explicitly addressed the problem, Constant and Massey (2002) estimated wage equations, controlling them for effects of selective outmigration. Their main concern was to check the robustness of earlier estimates of assimilation effects on wages to explicit treatment of selection of return migrants. Rabe (2006) attempted to measure earnings gains of wives and husbands following the decision to migrate to Britain. She studied migration decisions and earnings of couples in Britain in a self-selection framework taking account of double selectivity in mobility and labour participation of wives and husbands. The main difference between the other studies and the approach used in the presented analysis is that the self-selection correction method developed by Heckman is used not only to arrive at unbiased estimates of the wage regressions but also to identify wage effects tied to unobservable characteristics of individuals. 6 The choice of short-term migration (rather that migration) as a subject of the study was tied to predominance of short duration movements across the EU national boarders following its enlargement in 2004. Establishing drivers short-term labour force movements seemed to be therefore a promising avenue for understanding labour market developments after removing immigration restrictions between Poland and the UK. Secondly and partly tied to the former point, data on short-term migrants in the UK of Polish origin were relatively abundant when size of the sample of longer-term migrants was significantly smaller. 3

perhaps best be expressed in nominal terms. Yet as the cost of living of migrants is likely to be related to the local price level, tests of rationality are run twice, using measures expressed in both nominal and real terms to draw relevant conclusions. Moreover, contrary to earlier works on rationality of migration, the study explicitly deals with double selectivity in migration and employment; it allows to extend a sample of workers whose rationality is being assessed to the non-working population. Finally, the data structure allows to track the evolution of the wage differentials and rationality measures over time. Therefore some conclusions might be derived from the evolution of migration, and some forecast formulated on the intensity of future migration flows. In what follows, the article first describes the wage and selectivity model (section 2) and discusses the measures of wage differences and rationality used (section 3). The next steps are a description of empirical model implementation details (section 4), an overview of the data used (section 5) and an outline of the regression estimates (section 6). The main results are discussed in section 7. Conclusions close the paper. 2 Model Individuals are allowed to move freely between the two labour markets and may remain either employed or non-employed. Distribution of wage offers and employment prospects on the labour markets impact the decision to migrate between the regions. The observed wage on a source country labour market is denoted as w 0 and on a foreign labour market by w 1 (where wage rates are given in logarithms). To facilitate the understanding of the analysis in the empirical section, an observed wage w M for M {0, 1} after Vijverberg (1995) is decomposed into three components: w M (i) = µ M (i) + η M (i) + ɛ M (i) (1) where µ M is interpreted as the,,wage norm or market determined average productivity that depends on a worker s education or particular labour market-relevant job experience. Here, µ M is assumed to be observed both by a worker and an econometrician. η M represents a person-specific productivity factor that summarizes her work attitude or skills that are only imperfectly observed by a worker and employer and unobserved by an econometrician. ɛ M is a random variation in productivity and E(ɛ M ) = 0. Individuals predict the two earnings prospects w 0 and w 1. The tilde indicates the subjective expectations of an individual based on information available when choosing to migrate or not and when taking on a job. If variables describing observed characteristics of a person are summed up in a vector x(i), then: µ M (i) = α M x(i) (2) where α M are vectors of wage equation parameters with some set of non-zero elements. Individuals elicit information about η M on the base of past realizations of η M + ɛ M under additional assumptions that ɛ M = 0 and that they know the correlation between the two η M. The model describes subjective wage expectations of an individual who knows the wage distribution in both countries conditional on a given education or work history but has incomplete information about the worth of her nonmeasurable skills. She derives the latter It could hamper reliability of results derived for long-term migrants. 4

information observing the,,smoothing-out effects that unpredictable events like sickness (contained in ɛ M ) have had on productivity in the past. An important point is the assumption that an individual who knows how much unobservable skills acquired in the past are worth is able to predict the value of her unobservable skills on the other labour market. Hence: E( w M (i)) = α M x(i) + E( η M (i)) = α M x(i) + η M (i) = E(w M (i)) (3) where E is an expectation operator denoting values expected by an econometrician, or: w M (i) = w M (i) + v M (i) (4) and the prediction error fulfills the condition E(v M ) = 0. Unbiasedness of the wage rate predictions, stated in (3), is a strong identifying assumption in the model. A forecast error of an individual originates in a false assessment of the valuation of unobservable skills. If non-employed, a person expects to have shadow income of b 0 at the home labour market and b 1 at the foreign labour market respectively. It is further assumed that shadow income may be decomposed similarly to (1) and (4), and that individuals know the correlation structure between the valuation of person-specific productivity factors across different labour market states and labour markets. The probability of being employed depends on the labour supply decision of a person given the wage prospect w M and the fallback position b M, selection of workers by employers and labour market institutions influencing matching effciency. A worker living in M will decide to work if the difference between w M and b M (denoted by δ M ) is greater than zero, or else withdraw from the labour market. Job creation is observed only if the labour supply condition stated above is fulfilled concurrently with the labour demand condition, which is not explicitly specified. The reduced form employment equation is of the form: V M (i) = { 1 if V M (i) > 0 0 if V M (i) 0 (5) where VM is an index latent variable corresponding with dichotomous outcome of actual employment of an individual V M : VM (i) = β M x(i) + ς M (i) (6) and E(ς M (i)) = 0. Individuals will chose to move abroad when the anticipated gain from migration outweighs a plausible gain from staying. Namely: M = { 1 if M > 0 0 if M 0 (7) and the latent variable M measuring the propensity to emigrate is expected to be proportional to the expected gain from moving: 5

M (i) = (V 1 (i) δ 1 (i) + b 1 (i)) (V 0 (i) δ 0 (i) + b 0 (i)) (8) Here, the propensity to emigrate is described as a combination of anticipated shadow incomes and expected labour market-specific surpluses over shadow wage ( δ M ). Further, I assume that the reduced form of (8) may be expressed as: M (i) = πx(i) + e(i) (9) The reduced form equation ignores non-linearity of the model present in (8)and assumes that the shadow value of migration may be linearized without loss of generality. The advantage of the above specification is that it keeps the selectivity model simple and at the same time enables a relatively detailed treatment of the limited transferability of skills and education between countries, as vector x may contain separate variables measuring country and foreign education or job experience. Tracking back the mechanism of the model, it follows that employment decisions are generally taken jointly with the location decision. This in turn implies that (5) and (6) have to be estimated jointly with the equation on the propensity to live in one of two countries (7) and (8). Wages are observed only when workers have joined the labour market and are employed. Therefore: E(w 0 (i)) = α 0 x(i) + E(η 0 (i) + ɛ 0 (i) M(i) = 0, V 0 (i) = 1) = α 0 x(i) + E(η 0 (i) M(i) = 0, V 0 (i) = 1) α 0 x(i) (10) E(w 1 (i)) = α 1 x(i) + E(η 1 (i) + ɛ 1 (i) M(i) = 1, V 1 (i) = 1) = α 1 x(i) + E(η 1 (i) M(i) = 1, V 1 (i) = 1) α 1 x(i) (11) If the above equalities would hold, then it would be possible to derive potential wages of individuals based on the actual distribution of wages in each of the two countries and a set of individual characteristics. In fact, unobservable characteristics of individuals are likely to impact not only measured wages but also the probability that wages are actually observed (propensity of a person to be employed). Therefore, the selfselectivity problem may emerge. To obtain information on wages on each of the labour markets that apply to all individuals the migration selection model has to be specified, and the self-selection mechanism has to controlled for to deliver consistent estimates of wage equation parameters. 3 Earnings Differentials and Rationality Measures In this section a range of measures is developed that illustrate the expected change in income following the migrate-or-stay decision of a worker. Importantly, formulas for the anticipated earnings differential or gain are derived for all population of workers even though only earnings of employed are actually observed. 6

3.1 Earnings Differentials The income differential in favour of migrants z 1 is defined as an income expected abroad compared to an income anticipated at the home labour market. It may be expressed as: z 1 (i) = E(w 1 (i) M(i) = 1) E(w 0 (i) M(i) = 0) = (α 1 α 0 )x(i) + E(η 1 (i) M(i) = 1) E(η 0 (i) M(i) = 0) (12) Similarly, earnings differentials expressing a foregone option for a person that did not migrate z 0 are defined as: z 0 (i) = E(w 1 (i) M(i) = 0) E(w 0 (i) M(i) = 1) = (α 1 α 0 )x(i) + E(η 1 (i) M(i) = 0) E(η 0 M(i) = 1) (13) Significant differences in α M across countries are likely to introduce selection in observables (contained in vector x), which should result in different wages for emigrants and stayers. The second component of wage differentials corresponds with the different valuation of individuals unobserved characteristics. Earnings differentials for employed individuals (for whom wages are observed) closely correspond with a traditional Blinder and Oaxaca (1973) decomposition of the average wage rate observed in two subpopulations. In this case the Blinder and Oaxaca scheme is useful for distinguishing between an effect of different distribution of observed and unobserved characteristics of migrants and different returns to the same characteristics on two labour markets on the observed wage differentials. Averaging variables values for stayers and migrants (or alternatively, averaging z 1 across individuals) and ignoring non-random selection to reporting wages and employment: w 1 w 0 = α 1 x 1 + E(η 1 M = 1) (α 0 x + E(η 0 M = 0)) = α 1 ( x 1 x 0 ) + (α 1 α 0 ) x 0 + E(η 1 M = 1) E(η 0 M(i)) (14) where α 1 ( x 1 x 0 ) is part of the wage gap between migrants and stayers that may be explained by differences in their average characteristics ( x 1 is the vector of average characteristics of migrants and x 0 of stayers). (α 1 α 0 ) x 0 is a fraction of the wage gap that may be explained by different returns to characteristics across labour markets and E(η 1 M(i) = 1) E(η 0 M(i) = 0) is the average selection into migration effect on wages. 3.2 Rationality Measures Following Tunali (2000) I refer to a set of measures that allow for evaluation of rationality of migration where rationality is understood as earnings-enhancing behaviour of migrating individuals. Here, the framework used by Tunali is extended to allow for non-employment outcome that is partly the result of self-selectivity. It provides an opportunity to evaluate the rationality of labour force movements between countries for those in and, which is a novel feature of this study, for those out of jobs. 7

The first measure of rationality refers to a comparison of ex ante optimal and non-optimal choices. If an individual opted to migrate, the measure expresses the difference between the expected income abroad as compared with expected income at home. The returns to migration κ 1 for employed individuals may be therefore defined as: κ 1 (i) = E(w 1 (i) M(i) = 1) E(w 0 (i) M(i) = 1) = (α 1 α 0 )x(i) + ν 1 (i) (15) and returns to staying κ 0 as: κ 0 (i) = E(w 0 (i) M(i) = 0) E(w 1 (i) M(i) = 0) = (α 0 α 1 )x(i) + ν 0 (i) (16) Correspondingly, the left-hand expressions in (15) - (16) can be separated as sorting gains to migration and staying (ν 1 and ν 0 ): ν 1 (i) = E(η 1 (i) M(i) = 1) E(η 0 (i) M(i) = 1) (17) ν 0 (i) = E(η 0 (i) M(i) = 0) E(η 0 (i) M(i) = 0) (18) Rationality implies that the average mover anticipated higher earnings at the destination than the average stayer and vice versa. That interpretation of rationality delivers another measure of rationality, namely the selection of migrants h 1 : h 1 (i) = E(w 1 (i) M(i) = 1) E(w 1 (i) M(i) = 0) = E(η 1 (i) M(i) = 1) E(η 1 (i) M(i) = 0) (19) and a similarly defined selection of stayers h 0 : h 0 (i) = E(w 0 (i) M(i) = 0) E(w 0 (i) M(i) = 1) = E(η 0 (i) M(i) = 0) E(η 0 (i) M(i) = 1) (20) 4 Model Implementation The selectivity model described by equations (5), (6), (7) and (9) could be estimated jointly with (11) and (12). However, using Maximum Likelihood methods could prove tedious. We refer instead to Heckmans 8

(1979) two-step selection procedure. The two step selection method was extended by Behrman et al. (1980) and by Tunali (1986) to double selectivity. Here I adjust the method to the specific structure of the model, when employment outcomes are observed only on one of the two labour markets. The population in the model is defined as Polish-born residents of Poland and the UK. The first Probit equation, corresponding with (7) and (9), represents the selection of Polish natives into two labour markets. Further equations represent process governing employment decisions where factors influencing employment propensity in two countries can be heterogenous: M(i) = { 1 if M > 0 0 if M 0 (21) M (i) = πx(i) + e(i) (22) { 1 if V V M (i) = M (i) > 0 0 if VM (i) 0 (23) V M (i) = β M x(i) + ς M (i) (24) V 1 is observed only if M = 1 and V 0 only if M = 0. There are four mutually exclusive options represented by the set of above equations: employment in Poland, non-employment in Poland, employment in the UK and non-employment in the UK. Further, it is assumed that the country M wage rate random terms ɛ M, ς M and a random variation in the emigration propensity e are jointly normally distributed with the two covariance matrices: σ 2 ɛ M σ ɛm e σ ɛm ς M σ 2 e σ eςm σ 2 ς (25) for M {0, 1}. The assumption of normal distribution of errors, similarly to the assumption of unbiasedness of workers anticipations, constitutes an identifying postulate for the empirical model. Importantly, correlation coefficient between ς 0 and ς 1 remains unidentified in the model due to inability to jointly observe V 0 and V 1. In the estimation process, diagonal elements of matrices are normalized to 1. The corresponding correlation coefficients between ς M and e are denoted by by ρ 0 = σ eς0 /σe 2 and ρ 1 = σ eς1 /σe. 2 Based on the selection mechanism described by (21)-(25) the inverse Mills ratios are derived to control wage regressions (and non-wage income regressions) estimated in the next step of the procedure. Assuming that ρ 0 = ρ 1 = 0the inverse Mills ratio for emigration decision would have a form: λ M=1 (i) = φ(πx(i))/φ(πx(i)) (26) and for the staying decision respectively: λ M=0 (i) = φ(πx(i))/φ( πx(i)) (27) 9

φ is the univariate standard normal density function and Φ the univariate cumulative standard normal distribution function. Selection terms into employment would in turn take a form: λ VM =1(i) = φ(β M x(i))/φ(β M x(i)) (28) The wage regressions for residents of the UK is controlled for (26) and (28) for M = 1 when the wage regression for residents of Poland for (27) and (28) for M = 0. Namely: E(w 1 (i)) = α 1 x(i) + ϕ 1,1 λ M=1 (i) + ϕ 1,0 λ V1=1(i) (29) E(w 0 (i)) = α 0 x(i) + ϕ 0,1 λ M=0 (i) + ϕ 0,0 λ V0=1(i) (30) where given independent selection mechanisms ϕ 1,M = σ ɛ1 and ϕ 0,M = σ ɛ0 for M {0, 1}. For non zero correlation between the two selection mechanisms, into emigration and employment, relations (26)-(28)are replaced by (see Appendix A): in the wage regression for migrants, and: ( πx(i) ρ1 β 1 x(i) ) λ 1,1 = φ(β 1 x(i))φ (1 ρ 2 F (πx(i), β 1 x(i), ρ 1 ) 1 1 )1/2 (31) ( β1 x(i) ρ 1 πx(i) ) λ 1,0 = (φ(πx(i))φ (1 ρ 2 F (πx(i), β 1 x(i), ρ 1 ) 1 1 )1/2 (32) ( λ 0,1 = φ(β 0 x(i))φ πx(i) ρ 0β 0 x(i) ) (1 ρ 2 F ( πx(i), β 0 x(i), ρ 0 ) 1 0 )1/2 (33) ( β0 x(i) ρ 0 πx(i) ) λ 0,0 = (φ(πx(i))φ (1 ρ 2 F ( πx(i), β 0 x(i), ρ 0 ) 1 0 )1/2 (34) where F is a bivariate cumulative standard normal distribution function. However, selection terms in (31) - (34) do not allow for a straightforward interpretation of effects on wages of self-selection into emigration (corresponding with λ I ) and into employment (corresponding with λ VI ). Let χ 1,1, χ 1,0, χ 0,1 and χ 0,0 be parameters of the wage equations defined as below: E(w 1 (i)) = α 1 x(i) + χ 1,1 λ 1,1 (i) + χ 1,0 λ 1,0 (i) (35) E(w 0 (i)) = α 0 x(i) + χ 0,1 λ 0,1 (i) + χ 0,0 λ 0,0 (i) (36) then estimated regressions (35) and (36)may be rewritten like in (29) and (30) with with λ M=1 = λ 1,1 +ρ 1 λ 1,0, λ M=0 = λ 0,1 + ρ 0 λ 0,0, λ V1=1 = λ 1,0 (i) + ρ 1 λ 1,1 and λ V0=1 = λ 0,0 + ρ 0 λ 0,1. The parameters ϕ are functions of correlation coefficients ρ 1 and ρ 0 and selection regressions parameters. They might be derived based on wage regression estimates as: ϕ 1,1 = χ 1,1 ρ 1 χ 1,0 1 ρ 2 1 (37) 10

and: ϕ 1,0 = χ 1,0 ρ 1 χ 1,1 1 ρ 2 1 (38) and: ϕ 1,1 = χ 0,1 ρ 0 χ 0,0 1 ρ 2 0 ϕ 1,0 = χ 0,0 ρ 0 χ 0,1 1 ρ 2 0 (39) (40) Tests of rationality were conducted based on model parameter estimates as well as derived predictions. Appendix B summarizes the formula used to derive measures of,,wage gaps needed to test the incomemaximizing behaviour of Polish-born workers. Separate Probit regressions were specified to alleviate biases in wage regressions originating in non-reporting of wages by some of individuals. It was assumed that non-reporting is however not correlated with employment or migration decisions that allowed us to derive separate Mills ratios. 5 Data 5.1 LFS Data The Polish Labour Force Survey (LFS) is a quarterly survey based on a rotating scheme, i.e. selected households are interviewed twice, with an annual break, for two consecutive quarters. The UK LFS is a rotating quarterly survey of households and individuals, with respondents staying in the sample for five consecutive quarters. Unlike the Polish LFS, the UK survey covers not only residents living in individual households but also students living in residence halls and people living in National Health Services accommodation. 5.2 Sample The sample spans the period from Q1 2004 to Q1 2008 and is restricted to working-age individuals (i.e. over 15 years and under 60 (women) or 65 (men) years of age). Because the main focus of the paper is the rationality of short-term migration, the sample of Polish migrants in the UK is truncated to those who stay abroad for less than three years. The original sample contained repeated observations on individuals across successive periods, which would have violated the i.i.d. assumption. Multiple observations were dropped from the sample, taking into account that in the UK LFS wages are reported in the first and the fifth wave only. The UK LFS sample was restricted to individuals interviewed either in the first wave, or in the fifth wave if the corresponding observation for the first wave was missing. The Polish LFS sample was similarly restricted to observations from the first and third wave, to mimic the annual break between the first and fifth wave in the UK scheme. The sample used in the empirical section covers over 172 000 working age Polish natives, of which less than 1500 were British residents (constituting under 1% of the total sample). Regressions on the propensity to report wages and wage regressions were carried out only for a subsample of employed workers. 11

5.3 Variable Definitions and Comparability Merging two sets of LFS data required setting common definitions for variables used in the later analysis (see table 1 for a detailed description). In this respect, classifying the education level and allocating responses accordingly proved to be the biggest challenge. More than 60% of Polish residents in the UK reported education levels other than the categories used in the Polish survey (higher education or more, post-secondary education or secondary vocational education, secondary education, vocational education, primary education or less 7 ). These classification problems may reflect national differences in education systems. For persons who reported,,other education, an imputation procedure was run using data on Polish migrants to the UK from the Polish household survey. The Polish household survey is conducted concurrently with the LFS survey and covers both actual residents of households and former residents since emigrated but still affiliated with the household. This survey provides a crude set of emigrants characteristics, such as age and education level. A main advantage of using the sample is lack of redundancy of information with the data used in the further analysis. On the assumption that those reporting,,other education were in one of the three,,middle education groups, i.e post-secondary or secondary vocational education, secondary education and vocational education, the data from the Polish household survey were used to run multivariate Probit regressions where the dependent variable took different values for persons in the three different education groups. Regressions were run on respondents age and gender as well as on the year of the survey variables, accounting for interaction between them. The estimated regression was next used to predict the odds with which those who reported,,other education were in one of the three educational groups that replaces values for individuals dummy variables representing different level of education. The imputation procedure may have introduced a bias into the final results. Moreover it does not deal with a plausible misclassification of the education level of workers for whom an ISCED 97 education level was reported. Therefore to check the robustness of the results (on regression estimates as well as on the evaluation of rationality of migration) alternative specifications of regressions were introduced with an education level approximated by years in education. 5.4 Data Description Tables 2a and 2b summarize basic statistics of variables used in the migration-employment selection model and wage regressions (selection into reporting model). Migrants tended to be younger than stayers (mean age of 28 years versus over 38 years). There were marginally more migrant men than women. There were significantly less disabled persons among migrants (less than 2% as compared to around 10% of subpopulation of stayers). Migrants were also less frequently married or less frequently reported having dependent children. The UK migrants were on average better qualified. The differences in the education level among migrants and stayers were however not monotonous. There were fewer workers with primary or vocational education but also with higher education in the UK than in Poland. Migrants had most often secondary or postsecondary education (including secondary vocational education). There were significant differences in the employment rates between the regions. In the UK the employment 7 Qualifications earned in the UK based on ISCED 97 categorization were aligned with the above categories. 12