The methodology used to provide an ex-ante evaluation of the hypothetical in-work benefit reforms consists of combining a national tax-benefit calculator with a behavioral model of labor supply using data from the Survey on Household Income and Wealth (SHIW). In what follows, we describe the key ingredients of this evaluation tool.

### 4.1 Tax-benefit calculator and survey data

The tax-benefit calculator used in this study is EconLav, an Italian microsimulation model that covers social security contributions, taxes and public transfers. EconLav is applied to a subsample of married couples from the 2008 wave of the SHIW to approximate the budget sets of each sample unit under both the baseline tax-benefit schedule in the year of data collection and the hypothetical schedules resulting from our in-work benefit reforms. Our working sample consists of 1,926 married couples in which the husband and the wife are both aged between 20 and 65 years, and neither of them is disabled, retired, in education, nor engaged in self-employment activities. We also trimmed 1% of outliers from the observed hourly wage distribution of each spouse. Descriptive statistics on the key variables are presented in the Additional file 1.

### 4.2 Behavioral model of labor supply

For the behavioral model of labor supply, we extend to married couples the multi-sectoral discrete choice model for single decision makers developed by Dagsvik and Strøm (2006). Like other models based on a discrete choice approach, labor supply is treated as the outcome of agents’ choices from a finite set of job opportunities. Thus, utility maximization is performed by finding the best alternative in this finite set, and it becomes simple handling nonlinear and nonconvex budget sets while also accounting for other important issues faced in the estimation of labor supply models (e.g. flexible specifications of preferences, observed and unobserved heterogeneity, unobserved wages, and quantity constraints on the choice set).

The multi-sectoral framework of Dagsvik and Strøm (2006) extends the standard setup for this class of models by accommodating the separation of jobs in different sectors. Within this framework, each job is characterized by fixed hours of work, a sector-specific hourly wage, and other nonpecuniary and unobservable job attributes. Thus, the hourly wage of each agent can vary across jobs of different sectors, and the set of available jobs is allowed to be individual-specific to capture quantity constraints that are determined by market equilibrium conditions and negotiations between unions and employers within each sector.

Our generalization of this framework to married couples is presented in Appendix A: A multi-sector model of labor supply for married couples. A key assumption of this model is that it relies on a unitary approach where husband and wife maximize a common household utility function. As argued by Chiappori and Donni (2009); Vermeulen (2002); and Bargain et al. (2010), the income pooling assumption made in this approach is not exempt from criticisms, and it has been rejected in some empirical studies. A more attractive approach would be a collective model where the two spouses are involved in an intra-household bargaining process to maximize their own preferences (see, for example, Vermeulen 2006 and Francesconi et al. 2009). Earlier studies by Beninger et al. (2006); Beninger et al. (2007); Beninger and Laisney (2002); and Chiuri and Longobardi (2002), among others, suggest that imposing a unitary framework when the data-generating process is a collective framework may lead to downward biased estimates of labor supply responses for wives and upward biased estimates of labor supply responses for husbands. In this paper, we shall not follow this more general approach because full estimation of a collective and multi-sectoral labor supply model with taxes like ours has not been achieved yet.

In the empirical analysis, we focus on a two-sector model that distinguishes between jobs in the public and private sectors to capture the non-negligible differences existing in the labor market conditions and the hourly wage structures of these two sectors in the Italian economy (see, for example, Giordano et al. 2011). The predetermined choice set of each agent includes non-participation plus 6 job opportunities for each sector, yielding 169 job combinations for each couple. In modeling quantity constraints on the choice set, we assume that the number of sector-specific jobs available for each spouse depends on education and regional unemployment rates. Further, we assume that their hours of work distributions are uniform apart from two peaks at full-time jobs with 35 and 40 weekly hours of work, respectively, and one peak at part-time jobs with 20−30 weekly hours of work.

The hourly wage of each agent is allowed to vary among jobs in the public and private sectors but not across jobs within the same sector. This amounts to assuming that hourly wages are independent from hours of work. Since sector-specific hourly wages of the two spouses can never be observed jointly, we estimate a system of four hourly wage equations in an early stage. As described in Appendix B: Estimation of sector-specific hourly wage equations of husbands and wives, this estimation stage is based on a three-step control function procedure that simultaneously accounts for sector-specific selection effects, endogeneity of experience, and correlations among hourly wages of the husband and the wife.

In addition to the bias correction terms that control for selection in each equation of the system and the reduced form residuals that control for endogeneity of experience, the covariates in the hourly wage equations include a third-order polynomial in experience, two indicators for education attainment, gender-specific regional unemployment rates, and two indicators for living in the center and the south of Italy. Identification of the hourly wage equations is attained through a set of exclusion restrictions: second-order polynomials in age and non-labor income, number of children, and indicators for children aged less than 3 years and occupational status of the parents. In other words, we assume that this set of variables help explain the reduced form equation for experience and the selection equations for the choice of the sector, but not the sector-specific hourly wages of the two spouses. Hourly wage predictions also incorporate prediction errors drawn from a multivariate normal distribution with zero means and a variance-covariance matrixequal to the estimates resulting from our three-step procedure.

The utility function includes a systematic component, which takes the form of a quadratic polynomial expansion in disposable household income, leisure of the husband and leisure of the wife, and a random taste-shifter which is identically and independently distributed across households, sectors and jobs according to an extreme value distribution.

Preference variation across couples is taken into account by modeling the marginal utility of each spouse’s leisure in terms of a second-order polynomial in age, number of children, an indicator for children aged less than 3 years, and a random error for unobserved heterogeneity in preferences. The random errors for unobserved heterogeneity in the preferences of husbands and wives are assumed to be mutually independent, independent of prediction errors in the hourly wages, and normally distributed with mean zero and constant variance.

Due to the distributional assumption on the random taste-shifter, the reduced form of the model is equivalent to a multinomial mixed logit model with 169 alternatives and six random errors, two of which account for unobserved heterogeneity in preferences of the two spouses, and four account for prediction errors in their sector-specific hourly wages. Model parameters are estimated via simulated maximum likelihood (SML) to integrate out of the likelihood these unobservable random errors. Provided that the number of draws used in SML goes to infinity faster than the square root of the number of observations, the resulting estimator is known to asymptotically equivalent to the exact maximum likelihood estimator (Hajivassiliou and Ruud 1994).

### 4.3 Labor supply predictions

The SML estimates of our model can be used to predict potential adjustments in labor supply due to changes in the tax-benefit system. In our analysis, these predictions are computed through the procedure of Creedy and Duncan (2002). For each couple, we first draw up to 750 realizations from the extreme value distribution and the estimated asymptotic distribution of the parameter estimates, such that under the baseline tax-benefit system, the observed alternative in the choice set has the highest utility. This gives us one set of draws of the random taste-shifter and the parameters estimates which rationalizesthe observed labor supply choices of the two spouses under the baseline tax-benefit system. Only for couples where none of the 750 realizations yields maximum utility at the observed alternative, labor supply of the two spouses is considered to be invariant. Through repeated applications of this process, we construct 250 sets of draws for all random components of the model, and for each of them we predict labor supply choices of the two spouses under a reform scenario to obtain 250 predictions of labor supply transitions. Finally, we average over the sample and report the mean and the fifth and ninety-fifth percentiles of the distribution of transitions. These percentiles are the bounds of a two sided confidence interval of about 90 percent.