Skills or culture? An analysis of the decision to work by immigrant women in Italy

3.1. How do economists obtain reservation wages?

The aim of this paper is to report an econometric estimate of the immigrants’ reservation wages. In job search theory, the reservation wage is the lowest offered wage that an unemployed individual looking for work is prepared to accept (see Blundell and MaCurdy, 1999) ⁸. Although this is a crucial variable in the neoclassical theory of labor supply, there is still an open discussion on the best way to estimate it. Two prevailing methods are usually available in literature.

The first is based upon surveys in which unemployed respondents are directly asked what their reservation wage is ⁹. This information is widely used in many studies: see, among others, Addison et al. (2004 2010) and, for the Italian case, Sestito and Viviano (2011). The reliability of this information, however, is widely debated. As shown by Burdett and Vishwanath (1988) and Hofler and Murphy (1994), self-reported reservation wages are often biased and they are usually inconsistent with the actual behaviour of a worker. As Addison et al. (2010) point out, this is mainly due to the fact that respondents usually answer by indicating the prevailing wage on the labor market, rather than their true reservation value.

The second method treats reservation wages as unobservables, that must be inferred econometrically by the actual behaviour of a worker. This was pioneered by Heckman (1974) in his contribution on women’s shadow prices in the labor market and was subsequently developed in further studies (see, Kiefer and Neumann, 1979 1981 ; Fishe, 1982 ; Ferber and Green, 1985 ; Duncan, 1992 ; Sharpe and Abdel-Ghany, 1997). The idea is that observed wages for employed individuals are those that succeed in exceeding the individual reservation values. This implies that, by controlling for the selectivity bias, actual market wages contain enough information to infer workers’ reservation wages ¹⁰.

In this paper we adopt the second methodology for two main reasons. The first relates upon the above-mentioned reliability problems of self-reported reservation wages – problems that can be greatly aggravated for migrants, whose understanding of the crucial features of the local labor market is more limited. The second relates to the availability of sufficient observations in the LFS. In Appendix 2 we provide the results for self-reported reservation wages in the Italian LFS. By concentrating on immigrants living in the North, we end up with just under 1,000 individuals, which is one-tenth of our baseline estimation sample.

The methodology we use in this paper is based on the Mohanty’s (2005) extension of the Heckman model with frictional unemployment and feedbacks between labor demand and supply. As will soon be clearer, from a technical point of view, the only difference between this methodology and Heckman’s lies in the first stage, which is bivariate-probit rather than probit estimated. This allows us to take into account a double selectivity bias due to involuntary unemployment or feedback effects between demand and supply ¹¹.

3.2. The estimate of reservation wages: an econometric approach

A woman i decides to participate in the labor market (i.e. to be active) whenever the wage offers she expects to receive are greater than her own reservation wage. In formulas, this implies that she is active whenever ${\mathrm{w}}_{\mathrm{i}}^0{–\mathrm{w}}_{\mathrm{i}}^{\mathrm{r}}{=\mathrm{y}}_{1\mathrm{i}}\ge 0$, where w^o _i is the expected wage offer, w^r _i is her reservation wage and y_1i represents the (normalised) individual preference for labor market participation. Whenever y_1i is greater than zero, individual i participates to the labor market, whenever it is negative she prefers to stay at home. It immediately follows that reservation wages can be obtained as ${\mathrm{w}}_{\mathrm{i}}^{\mathrm{r}}{=\mathrm{w}}_{\mathrm{i}}^0{–\mathrm{y}}_{1\mathrm{i}}$ and can be computed by estimating preferences (y_1i) and wage offers (w^o _i).

Estimates for y_1i and w^o _i are obtained in two steps.

where y_2i represents the (normalised) employers’ preferences over individual i.

As for the supply components, x₁ includes schooling, potential experience, religion dummies and their interaction with marital status, number of children below and above 18 years of age and a set of time dummies. The number of under age children may indicate a greater interest for childcare and housekeeping while the number of children over 18 should have a positive effect on the labor supply since offspring could need financial support from the family of origin. Religion dummies indicate a cultural attitude toward labor, especially when a woman is married. As will be clear later, religion dummies play a fundamental role as identification variables in the empirical strategy.

On the demand side, x₂ contains schooling, years since migration, dummies for country of origin, time, and space ¹². Years since migration are expected to enhance the probability for a worker to be employed since during these years the worker is likely to increase his ability to understand the crucial features of the host country’s labor market and local language; ¹³ country dummies capture the workers’ heterogeneity in terms of the quality of the institutions in their area of origin (for example, educational system, sectoral specialization) while spatial dummies capture time invariant local characteristics that are likely to influence employment levels.

x₁ and x₂ share the schooling variable and time dummies, since education is likely to have an effect on both the demand and supply components and year dummies take into consideration business cycle fluctuations.

The latent variable of interest (ŷ₁) is calculated by taking the predicted values (linear prediction) of equation (1).

where u _i  = ε _i  − c ₁₃ λ _1i  − c ₂₃ λ _2i , ${\lambda }_{1i}=\frac{\phi \left(x_{1i}{b}_1\right)\Phi \left(\frac{x_{2i}{b}_2-\rho x_{1i}{b}_1}{\sqrt{1-{\rho }^2}}\right)}{F\left(x_{1i}{b}_1,x_{2i}{b}_2,\rho \right)}$ and ${\lambda }_{2i}=\frac{\phi \left(x_{2i}{b}_2\right)\Phi \left(\frac{x_{1i}{b}_1-\rho x_{2i}{b}_2}{\sqrt{1-{\rho }^2}}\right)}{F\left(x_{1i}{b}_1,x_{2i}{b}_2,\rho \right)}$. ϕ and Φ represent, respectively, the density and the cumulative function of a univariate standard normal distribution, F denotes the bivariate standard normal distribution, while ρ (rho) is the correlation of the error terms in the bivariate probit. x₃ includes standard variables in migration-augmented mincerian equations: schooling, potential experience and years since migration. The regression includes spatial dummies (D _s ) to take into account spatial differences in wage levels; time dummies (D _t ) to control for business cycle effects. Country of origin dummies (D _c ) control for institutional factors such as educational quality (inserting area dummies deliver very similar results).

Where $\left(\widehat{\text{ln}{w}^m}\right)$ is the predicted value of equation (3). ${\widehat{w}}^o$ represents the expected market wage conditional on the individual characteristics and controlling for the selectivity bias due to participation and hiring decisions ¹⁴.

Reservation wages can now be calculated as ${\widehat{\mathrm{w}}}^{\mathrm{r}}{=\widehat{\mathrm{w}}}^0{-\widehat{\mathrm{y}}}_1$ for all the individuals in the sample.

By comparing all the variables in x₁, x₂ and x₃, the crucial role of religion dummies and their interaction with marital status as identification variables is now apparent. The idea is that religion is a private matter that affects the individual working decisions but should not affect the labor market evaluation (wages) and the hiring decision by a non-discriminating employer. In other words, the worker’s productivity should be influenced by the country of origin’s institutional setting (school quality, sectoral specialization etc.) but not by the migrant’s private attitudes toward religion (which does, however, influence her decision to work). This implies that by inserting country dummies in equations (2) and (3) we estimate a supply effect that is within-country and across religions. This can be done only if we have an imperfect overlap between religions and countries of origin, i.e. when there are different religious creeds within a country. In order to have a suitable sample for this identification we exclude all individuals coming from a country where, according to the ISMU dataset, only one creed is professed. The list of a diversification indicator of religions (Herfindhal index: HI¹⁵) in each country is provided in Appendix 1; the higher HI the less diverse the country; in all the analyses we exclude all countries with a HI equal to one.

A possible challenge to the identification of equations (1), (2) and (3) is the presence of occupations in which foreigners coming from the same nation tend to cluster (Patel and Vella, 2007). This would invalidate the cross-country comparison since reservation wages are driven by cross-nation sector of specialization and the mobility is low. Ideally, this would be solved by inserting sector dummies in equation (3); however, in this case the computation of wage offers for not-employed immigrants would be impossible since predicted values cannot be calculated for unemployed and inactive. It should be noted, however, country dummies in equation (2) and (3) take also into account differentiated search networks and their effects on wages, thus limiting the relevance of these concerns. In a robustness check, we calculate reservation wages for employed individuals by inserting sector dummies with results much in line with the one presented here ¹⁶.

3.3. Cross-country differences and robustness

After computing the reservation wages, we test whether they systematically differ across groups of nationalities. We calculate the percentage differences between each group and a reference cluster. Our first choice would have been native women. However since the ISMU dataset only concentrates on immigrants, we chose the CEEC (Central and Eastern European Countries) group. The choice of CEEC as a benchmark relies on the fact that they share similar institutions with the host country and are generally seen as a reference group in the assimilation patterns in most countries ¹⁷. We focus on the differences between the CEEC group and two nationalities that display the lowest activity and employment rates: NENAC and Central Asia. If the reservation wages for those groups were higher, the observed low labor market participation would be interpreted as voluntary: the value NENAC and Central Asian women attach to their time spent at home is so high that they are not attracted by the local labor market. Conversely, if their reservation wages were comparable or lower to that of our reference group, their inactive status would be interpreted as involuntary: their reservation values are not particularly high but they remain unemployed because the arrival rate of job offers is quite low.

We further check the robustness of these estimates along four lines.

The first check is based on Italian migration law according to which it is necessary to have a job in order to obtain a visa. As an exception to this rule, immigrants can enter Italy to join their family and obtain a visa based on family reunification. For those cases, migrants’ true shadow values should be revealed since they do not need to work to obtain a residence permit. We check this issue by restricting the analysis to those women who migrated to Italy with a family reunification visa. This information is available for all years except for 2004: migrants entering the country for with a family reunification visa amount to 2,408.

The previous scheme obviously implies that the immigrants have a good knowledge of the Italian migration laws. We can generalise it by focussing on migrants with a blood relative already residing in the country at migration time. Again, for those individuals their shadow values could be higher, since they can rely on the family's financial support while looking for work. We check this issue by restricting the analysis to women who entered the country when a next of kin was already residing here. This leaves us with 1,753 individuals.

The third check is based on the analysis of the irregular migrants. Undocumented aliens have very weak bargaining power with respect to their employers as they cannot join a union and must work off the books. This implies that wage offers are usually quite low (Accetturo and Infante, 2010) and, therefore, they may be quite close to the reservation wages. Moreover, illegal aliens’ incentives to work are particularly strong since their only chance of being regularised under one of the recurrent amnesties is strictly linked to evidence that they are employed on Italian soil. In other words, they are more likely to accept the jobs they are offered. In the ISMU dataset, irregular women are surveyed each year and they amount to 1,303 individuals.

The fourth check is based on the relationship between religions and countries. As we said before, we already discard all the observations coming from one-religion countries. However, in some countries a religion could prevail but not be the only one (for example, Islam in Arab countries or Roman Catholicism in Central and South America); this implies that from the employer’s point of view religions and countries of origin are quite indistinguishable thus invalidating our identification structure. We cope with this problem by restricting our analysis to a group of countries that can be considered truly multi-religious. This is done by discarding all observations coming from countries whose HI based on religions exceeds 0.75: this leaves us with 8,305 individuals.

4.1. Baseline sample

The first part of this section is devoted to the results of the baseline sample. This group is constituted by all the regular women of working age interviewed in the 2001-2005 waves.

In the second step, we estimate a classical wage equation for all working individuals and we take into account the possible selection bias by plugging the computed λ₁ and λ₂ into the equation. Results are displayed in column [3]. All variables have the expected sign and are significant. The highly significant coefficients of λ₁ and λ₂ imply that selection is at work. The use of estimated values of columns [1] and [3] allows us to compute reservation wages.

Estimates show that while the share of active and working population is substantially low for the NENAC and Central Asia group, their reservation wages are statistically smaller than those computed for the CEEC group. This suggests that low participation should not be attributed to a cultural attitude that raises the economic value of the time spent at home, but, rather, to a skill mismatch between local labor market requirements and immigrants’ abilities.

We further split the computed reservation wages across educational levels and years since migration.

4.2. Robustness

So far we have obtained the interesting result that the low employment/activity rates registered for certain groups are not associated with higher reservation wages.

In this section we present four robustness checks by restricting the analysis to: (i) women benefitting from a visa based on family reunification, (ii) immigrants with a blood relative at the time of migration to the host country, (iii) undocumented immigrants, and (iv) immigrants coming from truly multi-religious countries.

Endnotes

¹ The literature on the assimilation of migrants is actually huge. Past and more relevant contributions are Chiswick (1978), Borjas (1985), and Friedberg (2000). For Italy, see Brandolini et al. (2005) and Accetturo and Infante (2010).

² The result is opposite to that found by Niesing et al. (1994). By analysing the high unemployment rates of ethnic minorities in the Netherlands, they conclude many national groups suffer from a “discrimination in employment possibilities” due to employer choices.

³ See Accetturo and Infante (2010) for a detailed description of the aggregation centres.

⁴ As usual in this literature, we assigned zero years of schooling when the individual does not have any formal education, 8 years for a compulsory school leaving certificate, 13 years for high school and 17 for at least a university degree.

⁵ To be clear, we split the immigrants in three groups as regards employment status. The first comprises the inactive population, i.e. those who stated they were housewives or students. The second group is made up of the self-reported unemployed. The third is composed of all employed persons. The “active” group includes both unemployed and employed individuals.

⁶ A similar finding is reported by Amuedo-Dorantes and de la Rica (2006) for Spain, according to which African women suffer the lowest occupational attainment, with respect to other immigration groups (in particular if taken into account the years since migration), while Central and South Americans, along with immigrants within EU15, show high level of assimilation.

⁷ LFS data are representative for immigration from 2006 on.

⁸ In a static framework, with quasi-convex utility functions, the reservation wage is equal to the marginal rate of substitution between leisure and consumption.

⁹ For example, the Italian labor Force Survey asks unemployed workers “What is the lowest net monthly wage you would be willing to accept?”

¹⁰ An important advance on this topic is the estimation of structural search models by using the panel structure of many LFSs. This method cannot be used in this paper because the ISMU dataset is compiled on the basis of pooled cross-sections.

¹¹ Mohanty (2005), in turn, generalises the procedure to cases with multiple selection bias following the approach in Meng and Schmidt (1985). Recently Baffoe-Bonnie (2009) uses a similar framework to study wage differentials.

¹² Spatial dummies include one dummy for each of local labor markets in the partitions of Lombardy.

¹³ As one referee pointed out, Years in Italy would also enhance the probability of being willing to work. In a robustness check (available upon request) we inserted this variable in x₁ with results much in line with the baseline specification.

¹⁴ Expected wages are also computed for unemployed and inactive individuals. Predicted values are computed without the country of origin dummies coefficients. In this way, we net out the effects of wage level differentials on the computed reservation wages. However, results do not change when we insert country of origin dummies in the predicted values calculations.

¹⁵ HI for country c is calculated as follows: $H{I}_c={\displaystyle \sum _{r\in R}{\left(\frac{P_{\mathit{\text{rc}}}}{P_c}\right)}^2}$ where R is the set of religions, P _rc is the number of immigrants of religion r coming from country c and P _c is the number of people coming from country c. When in country c there is only one religion, HI is equal to one.

¹⁶ As a referee points out, another challenge to the identification is the possible discrimination according to religion by employers. A simple way to show that this is not likely the case is to run eq. (2) for active women by adding also religion dummies and their interaction with the marital status (linear probability model). The adj. R-squared passes from 0.081 to 0.084, with an increase by 3.7 per cent. The same regression without country dummies generates a drop of the adj. R-squared to 0.06 (from 0.084). As a comparison, we evaluate the importance of religion dummies in eq. (1). Dropping those variables generates a fall in the adj. R-squared from 0.265 to 0.159 (almost 40 per cent). This implies that while religion dummies (and their interactions) little add to the total explained variance of the hiring decisions by firms (4 per cent), they fundamentally contribute to the total variance of the labor supply decision (40 per cent). We also made an additional check. The presence of federal and multi-religious countries (like India) may also possibly create a confounding factor. If religious minorities concentrates in a few states, they are likely to influence the schooling system. This implies that we may have the case in which individuals coming from the same country have a different human capital due to heterogeneous educational system. This heterogeneity may be observed by the employer but not by the econometrician, thus creating a confounding factor in the estimates. In order to cope with this problem, we exclude from the baseline sample (made by multi-religious countries) all the federal states, with results much in line with the baseline. All these results are available upon request.

¹⁷ Another option would have been to merge ISMU data with the LFS. We have decided not to go in this direction because of the great differences between the two surveys in terms of data collection and reference population.

¹⁸ This is due to the fact that the dependent variables in the biprobit are highly correlated since they only differ in the values they assume for unemployed individuals. This may generate a collinearity problem between λ₁ and λ₂ in the estimate of the wage equation. A possible way to circumvent this problem is to treat equations (1) and (2) in a sequential way by estimating an Heckprob model. The results, not shown here to save space but available upon request, are in line with those presented in the text.

¹⁹ We define “city” the local labor market of the three most important towns of Lombardy: Milan, Brescia and Bergamo.

²⁰ Reported figures are quite similar to those in Table 2 since the regular aliens constitute almost 90 per cent of the ISMU sample.

²¹ This result is confirmed by Constant and Zimmermann (2005).

²² The extension to other regions provides very similar results since immigrants in Italy mostly settle in the North.

Appendix 1. National groups and countries of origin

(Herfindhal index of religions in parenthesis)

Central and Eastern European Countries: Bulgaria (0.42), Czech Rep. (0.46), Estonia (0.33), Latvia (0.38), Lithuania (0.36), Poland (0.66), Romania (0.43), Slovakia (0.62), Slovenia (0.34), Hungary (0.56), Albania (0.30), Belarus (0.70), Bosnia-Herzegovina (0.34), Croatia (0.33), Serbia-Montenegro (0.34), Macedonia (0.31), Moldova (0.68), Russia (0.46), Turkey (0.68), Ukraine (0.59).

Central and Southern America: Argentina (0.54), Bahamas (0.55), Barbados (1), Belize (1), Bolivia (0.88), Brazil (0.67), Chile (1), Colombia (0.77), Costa Rica (0.55), Cuba (0.40), Dominica (0.78), Dominican Rep. (0.72), Ecuador (0.77), El Salvador (0.58), Jamaica (0.37), Guatemala (1), Haiti (1), Honduras (0.72), Mexico (0.94), Nicaragua (1), Panama (0.50), Paraguay (0.83), Peru (0.70), Santa Lucia (1), Trinidad and Tobago (1), Uruguay (0.73), Venezuela (0.58).

Near East and North Africa: Algeria (0.92), Egypt (0.72), Libya (0.76), Morocco (0.81), Tunisia (0.98), Saudi Arabia (1), UAE (1), Jordan (0.53), Bahrain (1), Iran (0.76), Iraq (0.50), Kuwait (1), Lebanon (0.61), Palestine (0.34), Syria (0.66), Yemen (0.25).

Sub-Saharan Africa: Angola (0.41), Benin (0.30), Botswana (1), Burkina Faso (0.44), Burundi (0.45), Cameroon (0.46), Capo Verde (0.73), Central African Rep. (1), Chad, Comores, Congo (0.37), Congo (Dem. Rep.) (0.57), Côte d’Ivoire (0.47), Eritrea (0.31), Ethiopia (0.36), Gabon (0.33), Gambia (0.58), Ghana (0.38), Djibouti (1), Guinea (0.51), Guinea Bissau (0.52), Equatorial Guinea (0.26), Kenya (0.26), Lesotho (0.26), Liberia (0.25), Madagascar (0.52), Malawi (1), Mali (0.88), Mauritania (0.32), Mauritius (0.29), Mozambique (0.59), Namibia (1), Niger (0.36), Nigeria (0.38), Rwanda (0.43), Sao Tome e Principe (1), Seychelles (0.28), Senegal (0.60), Sierra Leone (0.44), Somalia (0.43), South Africa (1), Sudan (1), Tanzania (0.55), Togo (0.38), Uganda (0.72), Zambia (0.59), Zimbabwe (0.50).

East Asia: Cambodia (0.30), China (0.30), North Korea (0.26), South Korea (0.37), Philippines (0.69), Indonesia (0.27), Laos (0.33), Malaysia (0.62), Myanmar (0.50), Singapore (1), Sri Lanka (0.31), Taiwan (1), Thailand (0.53), Vietnam (1).

Central Asia: Afghanistan (0.5), Armenia (1), Azerbaijan (0.55), Bangladesh (0.68), Georgia (1), India (0.25), Kazakhstan (0.36), Kyrgyzstan (1), Nepal (1), Pakistan (0.74), Uzbekistan (0.55).

Appendix 2. A comparison with the self-reported reservation wages in the Italian Labour Force Survey

In this Appendix, we compare our estimates for reservation wages on ISMU data with those provided in the Labour Force Survey (LFS). We use on the 2006-08 waves of LFS, as previous ones do not provide information on the citizenship of foreign workers. Moreover, in order to provide a comparable result we concentrate on unemployed females in the 15-64 age bracket residing in the North of the country, ²² where Lombardy is located. We provide here the answer to the question “What is the lowest net monthly wage you would be willing to accept?” Results (Table 5) show that the magnitude for reservation wages is quite similar across national groups. Moreover, cross-national differences in LFS basically mirror those in our estimates.