Nonparametric Estimation of the Diamond-Dybvig Banking Model

I propose a nonparametric structural estimator for the distribution of liquidity needs in a version of the Diamond and Dybvig (1983) model when only the aggregate level of withdrawals is observed. The model is an extension of Peck and Shell (2003) with a continuum of depositors. I show how the characterization of the optimal contract proposed in Sultanum (2014) can be used to estimate the distribution of aggregate liquidity needs. The method builds on the literature of estimation of auctions. More precisely, it uses the indirect approach proposed by Guerre et al. (2000). Guerre et al. (2000) use the differential equation associated with the first-order condition for the optimal bid to recover the unobserved distribution of agents' valuations from the distribution of bids in an auction. The method I propose uses the differential equation associated with the first-order condition for an optimal bank contract to recover the unobserved distribution of liquidity needs from the observed distribution of total bank withdrawals. I use a numerical simulation to illustrate the estimation procedure