### 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}{\u2013\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}{\u2013\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.

In the first step we consider both the participation decision and the hiring process in the labor market. Woman *i* is employed only if she decides to participate in the labor market (Participate_{i} =1) and is hired by an employer (Employed_{i} = 1). Formally,

\mathit{\text{Participat}}{e}_{i}=\{\begin{array}{l}1\phantom{\rule{0.75em}{0ex}}\mathrm{\text{if}}\phantom{\rule{0.25em}{0ex}}{y}_{1i}\ge 0\\ 0\phantom{\rule{0.75em}{0ex}}\mathrm{\text{if}}\phantom{\rule{0.25em}{0ex}}{y}_{1i}<0\end{array}

and

\mathit{\text{Employe}}{d}_{i}=\{\begin{array}{l}1\phantom{\rule{0.75em}{0ex}}\mathrm{\text{if}}\phantom{\rule{0.25em}{0ex}}{y}_{2i}\ge 0\\ 0\phantom{\rule{0.75em}{0ex}}\mathrm{\text{if}}\phantom{\rule{0.25em}{0ex}}{y}_{2i}<0\end{array}

where y_{2i} represents the (normalised) employers’ preferences over individual *i*.

The aim of the first step is to compute the latent variables y_{1} and y_{2} by estimating the following two equations:

{\mathrm{y}}_{1}{=\mathrm{x}}_{1}{\mathrm{b}}_{1}{+\mathrm{e}}_{1}

(1)

{\mathrm{y}}_{2}{=\mathrm{x}}_{2}{\mathrm{b}}_{2}{+\mathrm{e}}_{2}

(2)

by a bivariate probit with partial observability. The choice of the bivariate probit is particularly useful since it allows us to treat demand and supply components simultaneously. As mentioned above, this allows us to take into account the existence of feedbacks between the decision to participate and the expected labor market outcome. Operationally, x_{1} contains a set of variables aimed at capturing the economic and cultural determinants for the labor supply, while x_{2} includes all the possible personal characteristics which are likely to influence the employer’s willingness to hire an individual.

As for the supply components, x_{1} 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, x_{2} 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.

x_{1} and x_{2} 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 (ŷ_{1}) is calculated by taking the predicted values (linear prediction) of equation (1).

In the second step, we compute expected wage offers. We estimate the following wage equation using a correction for a double selectivity bias (Tunali, 1986):

\text{ln}{w}_{i}^{m}=\alpha +{b}_{3}{x}_{3}+{c}_{13}{\lambda}_{1i}+{c}_{23}{\lambda}_{2i}+{D}_{s}+{D}_{t}+{D}_{c}+{u}_{i}

(3)

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. x_{3} 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).

Expected wage offers are computed as follows:

{\widehat{w}}^{0}=\text{exp}\left(\widehat{\text{ln}{w}^{m}}\right)

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 x_{1}, x_{2} and x_{3}, 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: HI^{15}) 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.