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, \(\Pi_t\) is the inflation rate, \(\Gamma_t\) 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 \(g^m_t\) 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 \(g^m_t\)) 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 (\(\triangle y_t\)), the interest-rate-inflation differential (\(r_t=i_t - \pi_t\)), and the change in the nominal interest rate (\(\triangle i_t\)). All variables are assumed to be observed with measurement errors.