Assessing individual skill influence on housework time of Italian women: an endogenous-switching approach

Abstract

Using Italian data from the Time Use Survey (Istat) on the time devoted by Italian women to housework tasks, in this study we analyze how much individual ability of a woman employed in the market influences her housework time. To this aim we estimate a two-regime Endogenous-Switching model for both employed and not employed women. As a novelty, a ML estimation of this model provides also the point-estimation of the across-regime correlation parameter, that allows us to evaluate the individual skill effect on the time devoted to housework tasks by a woman and to calculate the probability of choosing one of the two regimes, corrected for the endogeneity of the choice. The estimation framework allows us to identify the role of individual skills of the Italian women in household decision-making.

Synthesis of indicators applying the Mazziotta-Pareto Index (MPI)

A brief description of the MPI index is here reported (see Mazziotta and Pareto 2016), jointly with the indicators (categorical variables drawn from the Istat–Time Use survey) synthesized as different dimensions of the measured phenomena.

The MPI is a composite index for summarizing a set of indicators. It is based on a non-linear function which, starting from the arithmetic mean, introduces a penalty for the units with unbalanced values of the indicators.

Given the matrix ${\textbf{X}} = \{x_{ij}\}$ with $i= 1,2,\ldots ,n$ rows (statistical units) and $j= 1,2,\ldots ,m$ columns (indicators), we calculate the standardized matrix ${\textbf{Z}}= \{z_{ij}\}$ as follows:

$$\begin{aligned} z_{ij} = 100 \pm \frac{{\textbf{X}} - {\textbf{M}}_{X_j}}{{\textbf{S}}_{X_j}} \, 10 \end{aligned}$$

where ${\textbf{M}}_{X_j}$ and ${\textbf{S}}_{X_j}$ are, respectively, the mean and standard deviation of the indicator j and the sign ± is the ‘polarity’ of the indicator j, i.e., the sign of the relation between the indicator j and the phenomenon to be measured (that is $+$ if the individual indicator represents a dimension considered positive and − if it represents a dimension considered negative).

Denoting with ${\textbf{M}}_{z_i}$ and ${\textbf{S}}_{z_i}$, respectively, the mean and standard deviation of the standardized values of the unit i, the generalized form of MPI is given by:

$$\begin{aligned} MPI_i = {\textbf{M}}_{z_i} \pm {\textbf{S}}_{z_i} \frac{{\textbf{M}}_{z_i}}{{\textbf{S}}_{z_i}} = {\textbf{M}}_{z_i} \pm {\textbf{S}}_{z_i} \, cv_{z_i} \end{aligned}$$

where $cv_{z_i}$ is the coefficient of variation for the unit i. The MPI may be decomposed in two parts: mean level, given by ${\textbf{M}}_{z_i}$, and penalty, given by ${\textbf{S}}_{z_i} \, cv_{z_i}$. The penalty is a function of the indicators’ variability in relation to the mean value, and its function is to reward the units that, mean being equal, have a greater balance among the indicators. The sign ± depends on the kind of phenomenon to be measured. Increasing values of the index correspond to positive variations of the phenomenon (e.g., socio-economic development). In this case, $MPI_i = {\textbf{M}}_{z_i} - {\textbf{S}}_{z_i} \, cv_{z_i}$. On the contrary, if the composite index is ‘decreasing’ or ‘negative’, i.e., increasing values of the index correspond to negative variations of the phenomenon (e.g., poverty), then $MPI_i = {\textbf{M}}_{z_i} + {\textbf{S}}_{z_i} \, cv_{z_i}$ is used. In any cases, an unbalance among indicators will have a negative effect (penalty) on the value of the index.

In this analysis, we adopt the MPI index in order to obtain a composite measure of two phenomena: (1) the personality trait known as Conscientiousness, and (2) a gender-role attitude of the woman. In both cases we use as indicators the answers of the subjects to some specific questions of the Istat – Time Use questionnaire.

• (1) Conscientiousness ($MPI\_conscient$) - four questions:

  • i. How is important that the house is always tidy and clean (four ordered responses: “not at all”, “little”, “enough”, “a lot”);

  • ii. If it is a priority caring and assisting children (response: yes or no),

  • iii. If it is a priority caring and assisting elderly and sick family members (response: yes or no);

  • iv. If it is a priority looking after home (response: yes or no).

• (2) Gender-role attitude ($MPI\_g$)- reported level of agreement with the following five statements measuring each one a dimension of the gender-role attitude of the woman (to each statement, one of four ordered responses: “not at all”, “little”, “enough”, “a lot”):

  • i. It is better for the family that the man devotes himself mainly to economic needs and the woman to take care of the house;

  • ii. If both spouses / partners work full-time, the man must carry out the same amount of housework as the woman (washing, ironing, tidying up, cooking, etc.);

  • iii. If both parents work and the child gets sick, the parents have to take shifts to stay at home and take care of the child;

  • iv. Men perform household activities just as well as women;

  • v. Fathers know how to take care of young children just as well as mothers.

We have reversed the polarity of the answer to the statement i) to make the corresponding response consistent with the other dimensions of the analyzed phenomenon.