Theoretical background

As Stated in the previous section, the added w orker effect is a tem porary change in labour supply behaviour. This effect has two com ponents: an increase in the number of hours the wife actually w orks and a change in her willingness to w ork, that is, in her decision to participate in the labour market. L abour dem and restrictions may imply that it is not always possible to change the num ber o f hours and individual w orks (or to change job ), as it was seen in Chapter 2. This w ould not mean that there is no effect o f the husband’s unemployment on the labour supply decisions o f the wife. H er decisions to enter or exit the labour force can be affected. Therefore, we abstract here from the effect on hours o f w ork and w ould concentrate on how the participation decisions vary.

Given the uncertainties concerning the magnitude, timing and frequency o f job offers and the duration o f jobs, labour m arket histories are best described as realisations o f a stochastic process. W ithin this fram ework, flow rates betw een labour m arket states are the object o f study. The theoretical model behind this approach was proposed by B urdett and M ortensen (1978) and applied to the analysis o f the added w orker effect by Lundberg (1981, 1985). It w ould be briefly outlined bellow.

Let a tw o-person household maximise the expected value o f their life-time utility, that is, the discounted sum o f their utility flow in each period. Lets assume the utility flow is a concave function, U{xt, L„ //,) w here x, is the household commodity

consum ption in period t, and Ijt and Imt are the fractions o f time devoted to leisure by the husband and the w ife, respectively.

In principle, lets suppose that there are three possible states for each member o f a couple: unemployment (U ), employment (E) or out o f the labour force (N P). Employment requires to devote to work a fixed fraction o f available time, A,.

Unem ployment requires an extra fraction, 5, < hi, to be spend on job search. Each

em ployed person receives a w age, w,. This w age, jointly with the nonlabour incom e, determines the budget constraint in each period. Job offers only arrive to unemployed individuals and they consist o f a wage drawn from a known distribution that may vary across individuals.

In such a setting the allocation o f time and incom e is com pletely determined by the state occupied. Therefore, the household’s optimal strategy, maximising the utility flow , can be derived by comparing the expected utility associated with occupying alternative states.

Lundberg (1985) show s that given the husband status, the household’s strategy will partly consists o f tw o reservation w age functions depending on the husband’s w age. The first one equates the value o f the w ife’s em ploym ent to the value o f unemployment. The second equates the value o f the wife's em ploym ent to the value o f nonparticipation. Jointly, both w ages determine participation and acceptance decisions for the w ife.

The added worker effect appears when analysing how the husband’s w age alters these tw o reservation w ages. If leisure for both household members are substitutes, it can be shown that the change in the second reservation w age due to a change in the husband’s w age is greater than the change in the first reservation w age, both changes being positive. This means that, an increase in the husband’s w age increases both reservation w ages o f the w ife, making her less likely to participate in the labour force, and should she participate, less likely to accept a job offer. Therefore, a w ife w ould be more likely to search for work and to accept a given w age offer if her husband is unemployed. H ow ever this effect will not be clear when the leisure times o f both

members are not substitutes. Therefore, one reason for not finding any added worker effect could be the existence o f strong complem entarities in leisure.

The main result o f the previous m odel is that both reservation w ages (the value o f unemployment and the value o f nonparticipation) are low er for w ives w hose husbands are not em ployed. Three im plications can then be inferred concerning transition rates:

1.Em ployed w ives are less likely to leave em ploym ent when their husbands are unemployed.

2.W ives non participating are more likely to enter the labour force when their husbands are unem ployed.

3.Unem ployed w ives will find more jobs acceptable and becom e em ployed more rapidly when their husbands are unemployed.

From the previous m odel, a way to take into account joint labour supply decisions for husbands and w iv es in the household is to consider the set o f possible states the household can be in. If each individual o f the household may be in three different states, as it was explained before, the household as a w hole may be in nine different states: husband working - w ife working, husband working - w ife unemployed, husband working - wife non participating and so on. Transitions from and to any o f these nine states (72 in total) can be constructed and compared to analyse the presence o f an added worker effect.

Given the nature o f our data, it is not possible to estimate the com plete m odel so then w e restrict the number o f possible transitions by individual. A s the focus in this chapter is to study the effect o f husband's job status on wives' participation probabilities, w e consider only tw o possible states per individual. The husband may be either working (W ) or not working (N W ) and the wife may be participating (P) or non participating (NP). Table 1 shows the household transition matrix resulting from this specification.

N ext section describes the reduced form transition probabilities and the econom etric m ethodology proposed for their estimation.

Table 4.1: Possible transition intensities. Source State W -P D estination State W -N P N W -P N W -N P W -P ^ W P -N W N p (^

P)

P

P

Notes: First letter indicates husband status (W for working and N W for non working) and the second one w ife status (P for participating and N P for nonparticipating ). The intensities depend on the duration spend on a given status and are conditional on a set o f observable and unobservable variables (Z). P are the parameters o f interest.