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Central banks already come equipped with the dual goal of price stability and financial stability. In this post, I explore existing literature that explores the role of financial stability considerations in monetary policy, above and beyond its traditional financial stability tools.

Taylor Rule Galore

Let’s first talk about the Taylor rule and its variants. We will use this framework first to think about what the optimal policy rates should be.

1. Traditional Taylor Rule and Its Variants

   The traditional Taylor rule is not forward-looking and therefore reacts to contemporary deviations of inflation and output from target. It was introduced by John Taylor in 1993:

   

   The key point in the rule is that the weight on the deviation of inflation from target received a coefficient of 1.5 reflecting the “Taylor Principle” that when inflation rises above target the real interest rate should be increased more than one-for-one.

   Bernanke offered a modified version of the rule in 2015 by proposing two changes:

   1. Measuring inflation using the core PCE deflator rather than the GDP deflator
   2. Changing the weight on output from $0.5$ to $1.0$

2. Forward-Looking Expectations and Smoothing

   Clarida, Gali, and Gertler (2000) estimate a forward-looking policy rule for various monetary regimes in the United States. They also allowed for only partial adjustment towards target based on an interest rate smoothing equation:

   

   Here are the estimated parameters:

   

   So the smoothing parameter is around $0.8$ and the coefficient on output is $0.93$.

   More recently, Clarida explicitly endorsed an alternative policy rule:

   Consistent with our new framework, the relevant policy rule benchmark I will consult after the conditions for liftoff have been met is an inertial Taylor-type rule with a coefficient of zero on the unemployment gap, a coefficient of 1.5 on the gap between core PCE inflation and the 2 percent longer-run goal, and a neutral real policy rate equal to my SEP projection of long-run r*

3. Taylor Rule for Open Economies

   The baseline Taylor rule might also be inappropriate for open economies subject to external shocks, in which case it may be necessary instead to include other variables such as the ex- change rate.

   • Ball (1999) concluded that such an augmented rule was followed in Canada from 1975 to 2003, whilst Lubik and Schorfheide (2007) found that it was in the UK as well as Canada, but not in Australia and New Zealand.

   On the other hand, if the exchange rate fluctuations are responded with a different policy instrument, it may not be necessary for exchange rates to appear in the equation determining the policy rate.

   • Daude et al. (2016) pointed out that central banks in emerging markets with a flexible exchange rate regime frequently intervene in their foreign exchange market.
   • Eichengreen and Gupta (2016) also analyze the sudden stops in capital flows to emerging markets since 1991. They argue that the conventional wisdom — that EM central banks tighten monetary and fiscal policies to counter the drop in the exchange rate and in an effort to restore confidence — is evidence in only a minority of cases.
   • Kalemli-Özcan (2019) makes an argument on why domestic monetary policy may be ineffective.

Loss Function for Monetary Policy

Equipped with the Taylor Rule in mind, let us now specify the loss function for a given central bank’s monetary policy. Suppose that the central bank has a target rate based on a standard dual mandate under which it stabilizes the inflation rate around an inflation target and the unemployment rate around its long-run sustainable rate. It also observes a vector of asset prices $\mathbf{p}{t}$, and a vector of asset volatility **$\boldsymbol{\sigma}{t}$ in the financial markets.

Following the forward-looking versions of the Taylor rule, the target rate can be expressed as:

$$ i_{t}^{}=\alpha+\beta_{\pi}\left(\mathbb{E}{t}^{CB}\left[\pi{t+1}\right]-\pi^{}\right)+\beta_{y}\left(\mathbb{E}{t}^{CB}\left[Y{t+1}\right]-Y^{*}\right) $$

where $\pi_{t}$ is the inflation rate, $\pi^{}$ is the inflation target, $Y_{t}$ denotes output, and $Y^{}$ is the potential output. Importantly, $\mathbb{E}^{CB}\left[\cdot\right]$ denotes the central bank's expectations of future inflation and growth.