Identifying the MPC-Liquidity Gradient in High-Quality Data

We estimate the gradient of the Marginal Propensity to Consume (MPC) with respect to liquidity using a new estimator designed for administrative data with negligible measurement error in income. We derive a state-dependent consumption pass-through equation from the canonical buffer-stock model, and show that the pass-through coefficient of this equation can be used to construct tight bounds on the MPC conditional on the relevant state. We recover latent permanent and transitory income shocks with a Kalman smoother and use them as regressors in an empirical representation of the consumption equation. The Kalman-shock estimator identifies the theoretical pass-through coefficient under the assumption of negligible measurement error in income, and attains the minimum variance within the class of estimators that are linear in household income histories, including the canonical GMM estimator by Blundell et al (2008) and recent refinements thereof. Applying the method to Swedish administrative tax registers, we show that consumption responses to transitory shocks have a sharp negative and convex gradient with respect to cash-on-hand; the associated annual MPC falls from 0.7 in the lowest cash-on-hand decile to 0.3 in the top decile. The permanent-shock pass-through is close to one across the cash-on-hand distribution. These patterns are not visible when using traditional, less efficient, estimators.