Recent changes to the system of Higher Education (HE) funding in the UK that require graduates to contribute more to the cost of their HE than previously, brought to the forefront of the policy debate just how much graduates earn over their working lifetimes. Various estimates of average graduate earnings were cited, and of earnings of hypothetical graduates, though they were all too often politically expedient, clouding as they did the range of uncertainty about lifetime earnings. This policy debate formed the main motivation behind this paper, and indeed the ultimate application of the methodology set out in this paper is to estimate the distribution of lifetime earnings of graduates and non-graduates in the UK. Our methodology that underlies the construction of lifetime earnings uses statistical distributions characterised by copulas to model the dynamics of earnings. With the exception of Bonhomme and Robin (2005), this approach is new to the literature on modelling earnings dynamics.
In this paper we illustrate both the usefulness of copulas as a statistical technique for modelling dependence in earnings across the lifecycle, as well as contrast it with more traditional approaches for modelling earnings dynamics that appear in the literature. Our model can be estimated using a two-period panel on earnings, in contrast to more traditional approaches which generally require a panel of at least three periods for identification. We show that this is not at the expense of any of the richness inherent in such models, by illustrating how our method captures the same features of the dynamics of earnings that show up in traditional linear models. We then go on to apply our method to the estimation of lifetime earnings distributions in the UK for four groups characterised by education and gender.
Our paper makes a number of contributions. First, the methodology employed can be implemented with a two-period panel, which has potential value for researchers constrained by the length of panel data available. Even though this less stringent data requirement is gained by not explicitly incorporating unobserved heterogeneity, we show that the non-linear dependence structures between variables that our model embodies, captures dynamics that are normally captured by a fixed effect in more traditional auto regressive moving average (ARMA) models. A second contribution of the paper is thus to illustrate similarities and differences between copula models and ARMA models in modelling earnings. These contributions are distinct from Bonhomme and Robin (2005). Third, we add to the literature on lifetime earnings differentials between graduates and non-graduates, by applying our method to constructing lifetime earnings distributions for these groups separately. To our knowledge, this is the first empirical paper to characterise distributions of lifetime earnings in the UK. Finally, this is the first paper to provide evidence on how the auto correlation of earnings varies across the lifetime earnings distribution, over the lifecycle and between observable groups of individuals in the UK.
There is a vast literature on modelling earnings dynamics, with increasingly rich models, as seen in recent contributions that incorporate extensive heterogeneity and persistence in the first two moments of the distribution, such as Alvarez, Browning and Ejrnaes (2002), Heathcote, Storesletten and Violante (2004), and Pistaferri and Meghir (2004). Most models require panels of at least three periods for identification, lending this literature a notable US flavour due to the availability of the Panel Study of Income Dynamics. However, a practical concern is that researchers are often restricted to panels of length two, and in this paper we look at how far models that require no more than two periods for identification go towards capturing the features of earnings that can be modelled in more ”traditional” linear models.
We address this using the fourteen-wave British Household Panel Survey (BHPS). We first use these data to illustrate the methodology, showing how it can be implemented using two periods of earnings data. Our starting assumption is that earnings follow a first-order Markov process, so that all of the dependence between earnings can be captured by two adjacent observations. In order to show that the use of two periods of data is not at the expense of important features of earnings distributions captured by traditional models, we contrast our methodology with traditional approaches that appear in the literature. We do this by comparing the copula estimates with the estimates obtained from a traditional model implemented using the full panel component of the BHPS data. We show that our method is sufficiently rich to incorporate the effects of heterogeneity that usually stem from fixed effects, despite not modelling it explicitly. Intuitively, the flexibility comes from relaxing the assumption of linearity which allows earlier labour market realisations to be relatively more important in determining the shape of lifetime earnings. We also argue that even a very rich Gaussian model of earnings is not able to capture certain features of the data that our copula model can.
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