Uribe (2021) investigates the nature and empirical importance of monetary policy shocks that produce neo-Fisherian dynamics, i.e. move interest rates and inflation in the same direction over the short run. To that end, the author estimates a standard small-scale New-Keynesian model with price stickiness and habit formation, augmented with seven structural shocks.

Three of the shocks are to monetary policy, which is described by the following policy rule:

where $I_t$ the nominal interest rate, $Y_t$ is aggregate output, ${\mathrm{\Pi }}_t$ is the inflation rate, ${\mathrm{\Gamma }}_t$ is the inflation-target, $X_t$ is a nonstationary productivity shocks, and $z_t^m$ is a stationary interest-rate shock. The inflation target is defined as

where $X_t^m$ and $z_t^{m2}$ are permanent and transitory components of the inflation target. It is assumes that $X_t^m$ and $X_t$ grow at a rates $g_t^m$ and $g_t$, respectively.

There are two preference shocks affecting the lifetime utility function of the representative household, given by

where $C_t$ is consumption, ${\tilde{C}}_t$ is the cross sectional average of consumption, $h_t$ is hours worked, ${\xi }_t$ is an intertemporal preference shock, and ${\theta }_t$ is a shock to labor supply.

In addition to $X_t$, there is also a stationary productivity shock $z_t$, which affects the production technology according to

The five stationary shocks (${\xi }_t$, ${\theta }_t$, $z_t$, $z_t^m$, and $z_t^{m2}$ ) and the growth rates of the two non-stationary shocks ($g_t$ and $g_t^m$) are all assumed to follow first-order autoregressive processes.

Uribe (2021) estimates the model using quarterly US data on three variables: per capita output growth ($\mathrm{△}{y}_t$), the interest-rate-inflation differential ($r_t=i_t-{\pi }_t$), and the change in the nominal interest rate ($\mathrm{△}{i}_t$). All variables are assumed to be observed with measurement errors.