39 2.4 Análisis de la oferta

The literature on transition matrices concentrates on the statistical description of mobility. Recent years have instead been characterised by studies focusing on the econometric modelling of individual transitions within the classes of the wage distribution; in other words, these contributions take into account the determinants of the assignment of individuals to the cells of the transition matrix. Attempts in this

1 Individual wage dynamics, persistent inequality and mobility

direction can also be found in the descriptive literature, where they are based on the estimation of mobility indices on sub-samples defined according to workers’ attributes (see, for example, Bigard et al. [1998]). Such an approach presents at least two disadvantages. Firstly, the analysis remains at the aggregate level in that it cannot distinguish between heterogeneity and pure state dependence within aggregate persistence, an important distinction which will be discussed at length in Chapter 4. Secondly, the interpretation of results is not straightforward, in particular

being hard to make ceteris paribus statements in the presence of many explanatory

variables.

Given that the object of the analysis is a probability, the natural route followed by researchers for its econometric modelling is the one of discrete response models. In practice, it is supposed that for each individual the discrete outcome mobile/not- mobile is the realisation of some latent propensity to move, of which only a binary realisation is observable; the resulting dummy indicator is then regressed on the set of personal characteristics by means of discrete response models. Compared to an equation of wage growth rates, such an approach introduces a loss of information by discretising an originally continuous variable, so that no distinction is made between transitions of different length. However, this caveat can be overcome by using discrete response models with more than two feasible outcomes to assess the number of jumps such as ordered probits or count data (see Chapter 4 for an application of the first).

The econometric analysis of transition probabilities is complicated by two potential sources of endogenous selection which are inherent to the structure of the problem. First of all, analysing transitions requires conditioning on lagged wage states and, as long as the assignment of workers to such states is non-random, selecting those starting from a given wage class to estimate the model can bias

1. Individual wage dynamics, persistent inequality and mobility

parameters estimates. Secondly, transitions can be observed only for those who belong to the sample of wage earners at both extremes of the time interval investigated, and the presence of non-random exits from the wage distribution can, again, lead to biased estimates. A first group of studies assumes the exogeneity of both selection processes. This is the case in Smith and Vavrichek [1992], who adopt a logit model to analyse mobility out of US minimum wages for a sample of individuals previously employed at the minimum wage and show that the lack of education is the main factor in determining the ceteris paribus probability of persistence. A linear probability model, in which the dummy dependent variables is treated by OLS, is proposed by Gregory and Elias [1994] to analyse transition probabilities from the bottom quintile of the distribution using NES data: they find that low-pay persistence rises with age. Sloane and Theodossiou [1996] use BHPS data and adopt a multinomial logit model to analyse destination states of workers observed below the third decile of the origin wage distribution, with destinations also including the exit from the data set, in this way avoiding selection on the basis of panel retention. It is shown that low-wage persistence is significantly lower for males, workers in large firms or those participating in re-training programmes. A logit model is utilised by Contini et al. [1998] to model the conditional probability of being below the third decile of the distribution for those starting the transition below the third decile or above the seventh on Italian administrative data (INPS); they show that job mobility and employment in large firms positively influence transitions out of low-pay, while, on the other hand, employment in the service sector and past unemployment episodes favour transitions into low-pay. Guillotin and Hamouche [1998] utilise a count data model to analyse the number of ascending jumps through deciles computed on French administrative data (DADS). They consider the whole origin distribution and include dummies for the origin decile among regressors, thus

1. Individual wage dynamics, persistent inequality and mobility

conditioning on starting states. Their results suggest that human capital accumulation favours ascending mobility and preserve higher wage ranks once reached.

The formal assessment of the potential endogeneity of initial conditions of the wage process and attrition from the wage distribution characterises two recent contributions to the econometric literature on wage mobility. The set-up adopted in these studies is based on multivariate microeconometric models in which selection and transition probabilities are jointly estimated, thus allowing correlation between error terms and tackling endogeneity problems. The framework is basically that of endogenous selection models, in which control is made for the fact that the equation of interest (the mobility equation) can be estimated only if observations satisfy two endogenous sample selection rules (initial conditions and attrition). The work of Bingley et al. [1995] jointly models state probabilities, retention probabilities and mobility across deciles of the wage distribution using a panel of Danish wages: the whole set-up is a trivariate probit. Identification of the model requires exclusion restrictions in the form of variables only entering each of the selection equations and not the mobility equation or the other selection equation; the authors assume that age only affects retention probabilities, while industrial affiliation and the number of children in the household only affect the origin decile. Results from the mobility equation indicate that changes in occupation or industry determine downward mobility; on the other hand, human capital in the form of education and labour market experience is associated with upward movements. The estimated error covariance matrix is characterised by statistically significant elements, signalling the actual endogeneity of the two selectivity processes and justifying the whole framework adopted.

1. Individual wage dynamics, persistent inequality and mobility

The paper of Stewart and Swaffield [1999] is focused on the analysis of low- pay transition probabilities using BHPS data. They use a bivariate probit to model the probability of current low-pay states conditional on lagged states, thus tackling the endogeneity of initial conditions. Their base model considers only wage earners at both extremes of the transition; the control for panel attrition is assessed by extending this model and modifying the binary outcome in the arrival year from “low- pay/high-pay” to “not moved up/high-pay”, where “not moved up” includes low-pay and exits from the wage distribution. The authors pay great attention to the strategy adopted for identification of initial conditions; in particular they reach exact identification using the square of labour market experience (which doesn’t enter the transition equation given its nature of wage change equation) and test the validity of parental background indicators as instruments for initial conditions, concluding in favour of their use. This paper is also characterised by the parallel use of several low-pay thresholds, and it is shown that results are typically robust to changes in the definition of low-pay. The estimated correlation coefficient between state and transition probabilities is statistically significant, thus rejecting the exogeneity of initial conditions; by comparing results from the bivariate probit with those obtained assuming exogenous initial conditions the authors show that in this last case both size and significance of estimates is higher, especially for education. On the other hand, factors such as training, plant size, union coverage and gender retain their significance in affecting low-pay transition after controlling for endogenous initial conditions.

Chapter 2