Testing Private Information Models with Asset Accumulation

The complete insurance hypothesis is soundly rejected by the data (e.g. Attanasio and Davis, 1996). On the other hand, the permanent income model assumes that the only mechanism available to the agents to smooth consumption is personal savings (self insurance). Those are clearly two extreme characterizations of the economy faced by the consumers. The evidence on the PIH is mixed. On the one hand some authors (see Attanasio 2000) argue that the so-called excess sensitivity of consumption to predicted changes in income can be explained away by non-separability between leisure and consumption and demographic effects. On the other, some authors (Campbell and Deaton, 1989) point out that consumption also seems to be ‘excessively smooth’ to be consistent with the PIH: that is consumption does not seem to react ‘enough’ to permanent innovation to income. In this paper, we show how a model with imperfect risk sharing because of moral hazard can reconcile these facts. In particular, consumption will not exhibit excess sensitivity but, because of the additional insurance provided to consumers relative to a Bewley economy, gives rise to ‘excess smoothness’ in the spirit of Campbell and Deaton. We compare two dynamic models of asymmetric information with asset accumulation, which virtually exhaust the existing literature in dynamic contracting: We consider the hidden income (adverse selection) model and the action moral hazard framework. When asset accumulation is fully observable the two models have essentially the same prediction on income and consumption data. When the agent has secrete access to the credit market Allen (1985) and Cole and Kocherlakota (2001) (ACK) show that in the adverse selection model the optimal allocation of consumption coincides with the one the agents would get by insuring themselves through borrowing and lending. Abraham and Pavoni (2004) (AP) in contrast show that in the action moral hazard model the efficient allocation of consumption generically differs from self insurance. In fact, in is also important to notice that AP show that, in its general formulation, the action moral hazard model actually nests the ACK model of adverse selection. Our empirical strategy exploits this marked discrepancy between the two allocations to disentangle the nature of the information asymmetry existing in the economy. Because of incentive compatibility on saving decisions, both in ACK and AP the time series of individual consumption satisfies the usual Euler equation. This in particular implies that, in both models conditional on past consumption, present consumption should not react to predictable changes in (permanent) income. In other terms it should not display excess sensitivity (Flavin, 1991). This characteristic of individual consumption is a key distinguishing features of these models with respect to models of asymmetric information with perfectly monitored assets (Ligon, 1998). It is also well known that in the Quadratic utility version of the self-insurance/ACK model consumption moves one to one with permanent income. Hence, it should fully react to unexpected shocks on permanent income. In terms of Campbell and Deaton (1989), consumption should not display excess smoothness either. This later aspect of consumption and income time series is the key leverage for our test, since in the model proposed by AP consumption is partially insensitive to permanent income shocks due to the presence of some degree of risk sharing. To perform the empirical test we use data from the UK Family Expenditure Survey, two main reasons. First, the fact that we are addressing questions which are essentially dynamic in nature it is important to have a long time series. Second, in contrast to panel data available to the US for example, the UK Family Expenditure Survey contains detailed individual information both on income and consumption. The evidence is in favor of the AP model: individual consumption seems to not display excess sensitivity but it does have some degree of excess smoothness.