Are Women Happier When Their Spouse is Teleworker?

Abstract

This study explores the household production allocation and happiness of women when their spouse is teleworker using data from the British Household Panel Survey over the years 1991–2009. The study aims to answer whether the women spend additional time on housework and are happier when they or their partner is teleworker. Also, we explore whether are happier when they share the household–domestic production with their partners. Fixed effects estimates take place, and we consider a Bayesian Network framework and a directed acyclic graph for causal inference. The results show that women are more likely to state that the household allocation, such as cooking, cleaning, ironing and childcare is shared when their partner teleworks. Shopping is an exception which can be regarded as an outdoor activity while one partner may be mainly responsible for this chore. In addition, women are happier when they or their spouse is teleworker, and they report higher levels of happiness when the household production allocation is a shared process. This may indicate men teleworkers may contribute extra to the household production releasing a burden for the partners and improving their well-being.

Appendix

The graphical structure G = (V, E) of a BN is a directed acyclic graph DAG where V denotes the vertex or node set and E represents the edge set as V _i  → V _j The notation P ^G _i is used to denote the parent set of V_i in G. p ^j _i is used to denote the j-th configuration of the parents of V _i : P _i  ∈ {p ¹ _i , …, p ^qi _i }. Based on that the definition of BN is:

Definition 1

(Bayesian Network) (Pearl 2000; Neapolitan 2003): A Bayesian network model M over a set of variables V = {X ₁ , …, X _N } is a pair (Γ, θ), where G(V) is a DAG over V and θ is a set of conditional probabilities: θ = {θ _ijk : ∀ (ijk)} such that (θ _ijk  = X_i = x ^k _i |P_i = p ^j _i ).

Definition 2

(One-step ahead conditional independence non-causality) X does not strongly cause Y one-step ahead given a set of covariates Z and Y does not cause X given a set of covariates K if (8)–(9) hold.

$$Y_{i,t} \,\bot\, X_{i,t - 1} |Z_{i,t}$$

(8)

$$X_{i,t} \,\bot\, Y_{i,t - 1} |K_{i,t}$$

(9)

Y _i,t ⊆ Z _i,t ⊆ Ω _i,t and X _i,t ⊆ K _i,t ⊆ Ω _i,t . and Ω is the set of all covariates included in sets K and Z, for individual i and time t. The symbol ⊥ is used to express independence.

Definition 3

(Conditional independence non-causality) The conditional independence X is conditional independent from Y in the edge set E iff Y _i,t ⊥ X _i,t |Ω _i,t

The independence assumptions discussed above and are represented by the graph imply that parameters need to be estimated because the probability distribution for each variable depends only on the node’s parents as it is shown in relations (4)–(5) in the methodology section. Using the factorisation Eq. (5) it allows the network factorisation in such a way that it considers each node and its parents in isolation from the rest of the model variables. Otherwise, without employing this factorisation, far more parameters would be required to be estimated and therefore to specify the causal-effect relationships by a fully connected network and “unfactorable” model. Thus, employing factorisation model (5) the very complex models can be estimated avoiding the combinatorial explosion problem.

Definition 4

(d-separation) (Pearl 1988; Spirtes et al. 2000; Neapolitan 2003): Let G = (V, E) be a DAG, A ⊆ V, X and Y be distinct nodes in V—A, and h be a chain between X and Y. Then h is blocked if one of the following cases holds:

• There is a node S ∈ A on the chain h and the edges incident to S on h meet tail-to-tail at S.

• There is a node S such that S and all of S’s descendants are not in A on the chain h and the edges incident to A on h met head-to-head at S.

The d-separation condition is especially important and useful in constructing a BN because it controls possible confounds as in the form of S described here. Graphically, d-separation usually exhibits two main cases: firstly X → S → Y and secondly X ← S → Y. The intuition behind this graphical representation is that X and Y are independent from each other conditioned on S. In the first case X causes Y through S, while in the second case X and Y have a common cause S. In addition, given the edge X → S it is said that the tail of the edge is at X, while the head of the edge is at S. It is also: So let us consider a general directed graph in which X, Y and S are arbitrary non-intersecting sets of nodes and whose union may be smaller than the complete set nodes in the graph. To ascertain whether a particular conditional independence statement X ⊥ Y|S is implied the possible paths from any node in X to any node in Y are considered. Any such path is blocked if it includes a node such that either the arrows on the path meet either head-to-tail or tail-to-tail at the node, and the node is in S, such as the relations X → S → Y and X ← S → Y or the arrows meet head-to-head at the node, and neither the node, nor any of its descendants, is in S. If all paths are blocked, X is d-separated from Y given S, and the joint distribution over all of the variables in the graph will then satisfy X ⊥ Y|S.

Estimating the effect of a factor of interest X on the outcome of interest Y a back-door path is an undirected path between X and Y with an arrow into X and these paths create confounding, by providing an indirect non causal channel along which information can flow. Thus, a set of conditioning variables or controls Z satisfies the backdoor-criterion when Z blocks every back-door between X and Y and also no node in Z is a descendant of X or both descendent of X and ancestor of Y because it will block the causal path between X and Y. Thus, if set Z satisfies the back-door criterion then it will be:

$$\Pr (Y|do(X = x)) = \sum\limits_{z} {\Pr (Y|X = x,Z = z)\Pr (Z = z)}$$

(10)

All the items on the right hand of (10) are observational conditional probabilities and not counterfactuals. Based on (5) in the methodology section and the back-door criterion, for example the causal effect of C to D in the Fig. 2 is a regression of C and its parents (A and B) on D. In this case the back-door criterion is met since A and B block every back-door between C and D and they are not descendant of C. However, Fig. 2 is a very simple case, where DAG derived in the empirical results section is more complicated. In the case where a variable or set of variables S are descendants of C and block every path from C to D, then the causal effect may be totally blocked off. In this case it is said that there is over-control bias, since the descendants of C are effects and not confounders or causes of C. In that case the front-door criterion (Pearl 2000; Spirtes et al. 2000; Neapolitan 2003) is applied.

Definition 5

(Partial correlation) For i ≠ j ∈ 1, …, p, k ∈ X _r , let ρ _i,j|k be the partial correlation between X _i and X _j given X _r and X _r denotes the rest of the variables.

Based on this definition we have that X _i ⊥⊥ X _j |X _r  ⇔ ρ _i,j|k . A test for conditional independence is therefore a test for partial correlation between the variables and the partial correlations can be estimated, via regression analysis. Next a test for the conditional independence is presented.

$$Z(i \cdot j|k) = \frac{1}{2}\frac{{(1 + \hat{\rho }_{i,j|k} )}}{{(1 - \hat{\rho }_{i,j|k} )}}$$

(11)

Then it will be:

$$\sqrt {n - |k| - 3} |Z(i\,\cdot\,j|k)|N(0,1)$$

(12)

The test for independence is based on the PC algorithm (Spirtes et al. 2000) at significance level α. Kalisch and Buhlmann (2007) show that the choice of α is not too important. However, a significance level α = 0.05 is used. The pseudo-code of the PC algorithm is presented in Box 1.

Box 1 PC algorithm