This paper catalogues formulas that are useful for estimating dynamic linear economic models. We describe algorithms for computing equilibria of an economic model and for recursively computing a Gaussian likelihood function and its gradient with respect to parameters. We apply these methods to several example economies.

This paper catalogues formulas that are useful for estimating dynamic linear economic models. We describe algorithms for computing equilibria of an economic model and for recursively computing a Gaussian likelihood function and its gradient with respect to parameters. We display an application to Rosen, Murphy, and Scheinkman's (1994) model of cattle cycles.

This paper constructs a model with two structural equations: the Government budget constraint and a linear version of Cagan’s portfolio balance equation. The model contains a continuum of equilibria with “sunspot equilibria.” Closed forms for the solutions are found. Even though there is a continuum of equilibria, the model is overidentified econometrically, so that the model restricts time series data on price levels and currency stocks. We describe how the free parameters of the model can be estimated, including some parameters that serve to index particular members of the continuum of equilibria. The sunspot equilibria hold out some promise of explaining anomalies in the observed behavior of inflation and real balances during hyperinflations.

In a general equilibrium setting, we study versions of the proposal to pay interest on reserves at the market rate. We argue that the proposal makes the demand for total reserves indeterminate whether interest is paid on total reserves or on required reserves only. One consequence is that tax financing of the proposal gives rise to a continuum of equilibria, equilibria which differ in real returns and consumption allocations. Another consequence is that an attempt to finance the proposal through earnings on the central bank’s portfolio either gives rise to an equilibrium with a zero nominal interest rate or fails to give rise to an equilibrium.