Sunday, November 2, 2014

Guest Post: Estimating Monetary Policy Rules Around The Zero Lower Bound

I hope you enjoy this guest post contributed by Jon Hartley

As the Federal Reserve moves closer to normalizing monetary policy and moving toward a federal funds rate “lift-off” date, I’ve created MonetaryPolicyRules.org, a new website that provides up-to-date interactive graphs of popular monetary policy rules.

Since the federal funds rate has hit the zero lower bound, Taylor rules have received a lot of criticism in large part because many Taylor rules have prescribed negative nominal interest rates during and after the global financial crisis. Chicago Fed President (and prominent monetary policy scholar) Charles Evans stated about the Taylor Rule that “The rule completely breaks down during the Great Recession and its aftermath”.

The discretionary versus rules-based monetary policy debate endures, most recently with the Federal Reserve Accountability and Transparency Act being introduced in Congress, followed by a series of dueling Wall Street Journal op-eds by John Taylor and Alan Blinder. Rather than thinking about Taylor rules as a prescription for monetary policy (in a normative economics sense), what has been left out of the discussion is how Taylor rules can accurately be a description of monetary policy regimes (in a positive economics sense) even if the central bank does not explicitly follow a stated rule.

Tim Duy has accurately pointed out in a recent post that using the GDP and inflation forecasts also provided by the FOMC for 2014 through 2017 (and beyond), no traditional monetary policy rule captures the median of the current fed fund rate forecasts (commonly known as the “dot plots” released by the Federal Reserve on a quarterly basis as part of their Delphic forward guidance) which are considerably lower than either the Taylor (1993), Taylor (1999), Mankiw (2001), or Rudebusch (2009) rules would estimate.

What’s also worth noting is that in the early to mid-2000’s the federal funds rate was considerably lower than what any of the above classic monetary policy rules would estimate. This in large part is because all of these rules were estimated using data from the “Great Moderation” of the 1990’s, which was then led by a very different Federal Reserve than we have today (note those rules fit the federal funds effective rate data very accurately during the 1990’s).
Source: Tim Duy
The real question is how can we estimate a monetary policy rule that describes the Bernanke-Yellen Fed, while also addressing the problem of the zero lower bound for nominal interest rates?

One interesting idea that has gained some popularity recently is the idea of measuring a “shadow federal funds rate” (originally hypothesized by Fisher Black in a 1995 paper, published just before his death, which uses fed funds futures rates and an affine term structure model to back out a negative spot rate). The idea nicely estimates the potential effects of quantitative easing on long-term rates  while the federal funds rate is at the zero lower bound (and for that reason I’ve included the Wu-Xia (2014) shadow fed funds rate on the site). With the shadow fed funds rate in hand, one can now estimate a monetary policy rule with a standard OLS regression. One issue with this methodology is how there is a lack of consensus around what to use as input data for a shadow rate which can give you very different results (Khan and Hakkio (2014) observed that the Wu-Xia (2014) shadow fed funds rate looks remarkably different from the rate calculated by Krippner (2014)).

Wu-Xia (2014) and Krippner (2014) Shadow Federal Funds Rates (in %)Source: Khan and Hakkio (2014), Federal Reserve Board of Governors, Krippner (2014), Wu-Xia (2014)

One other solution to the problem of estimating a monetary policy rule at the zero lower bound is an econometric one. Fortunately, we have Tobit regressions in our econometric toolbox (originally developed by James Tobin (1958)) which allow us to estimate Taylor rules while censoring data at the zero lower bound.

In my Taylor rule that is estimated with federal funds rate from the Bernanke-Yellen period, censoring data at the zero lower bound using a Tobit regression, I use both y/y core CPI inflation and unemployment. In another version, I use the Fed’s new Labor Market Conditions Index (LMCI) as a labor market indicator though both yield relatively similar results*. Importantly, these estimates indicate that the Bernanke-Yellen Fed puts a much higher weight on the output/unemployment gap than the Mankiw (2001) rule estimated with data from the Greenspan period.

Tobit Taylor Rule Using Unemployment Rate and Core CPI as Inputs:
Federal Funds Target Rate = max{0, -0.43 + 1.2*(Core CPI y/y %) – 2.6*(Unemployment Rate-5.6)}

Using unemployment and inflation forecast data from the latest Federal Reserve FOMC meeting’s Survey of Economic Projections, I input these data as inputs into the Tobit Rule and Mankiw (2001) Rule. Matching these federal funds rate targets implied by the rules with the median federal funds forecasts provided by both the Federal Reserve “dot plots” and the Survey of Primary Dealers (note: the expected Fed Funds rate path from Survey of Primary Dealers has significantly fallen below the Fed dot plot Fed Funds rate path as noted by Christensen (2014)). Unfortunately, we do not have precise data on which dots belong to which Fed officials (otherwise, we could try to construct a Taylor rule for each Fed president and board member). Compared to the Mankiw (2001) rule, the estimated Tobit rule much better matches the median forecasts provided by the dot plots and the Survey of Primary Dealers.

Federal Reserve Forward Guidance/Survey of Primary Dealers Fed Funds Rate Forecasts versus Tobit Rule and Mankiw (2001) Rule Using Fed Unemployment and CPI Forecasts


Janet Yellen has spoken fondly of the Taylor (1999) rule in the past as she has previously stated in a 2012 speech that “[John] Taylor himself continues to prefer his original rule, which I will refer to as the Taylor (1993) rule. In my view, however, the later variant--which I will refer to as the Taylor (1999) rule--is more consistent with following a balanced approach to promoting our dual mandate.”

It is no surprise that the Tobit rule estimated with more recent data comes much closer to accurately describing the Fed’s forward guidance than the Taylor (1993) rule. However, what is really interesting is that the Tobit Rule is also much closer to describing the Fed’s current forward guidance than the Taylor (1999) rule, which remains far off.

Footnote:
*An important issue which has been addressed recently with the introduction of the Fed’s new Labor Market Conditions Index (LMCI) is how do we measure improvement (or lack thereof) in the labor market? While the U.S. unemployment rate for September was 5.9% (the lowest level since July 2008), the figure fails to capture a number of fractures in the economy remain which are not reflected in the unemployment rate. One item included in the LMCI (but not reflected in the unemployment rate) is the high U-6 unemployment rate (which factors in individuals who are underemployed, working part-time for economic reasons and would rather have full-time jobs) currently at 11.8%. Another is subdued wage growth that is not commensurate with drops in the unemployment rate as history would suggest. The labor force participation rate is at historical lows of 62% (in large part due to the number of retirements (a secular demographic trend) and to some extent due to discouraged workers (a cyclical trend) according to a recent Philly Fed study).

A previous post on this blog astutely points out that correlation of 12-month changes in LMCI with 12-month changes in the unemployment rate is -0.96, suggesting that “the LMCI doesn’t tell you anything that the unemployment rate wouldn’t already tell you”. While the economists who developed the LMCI list on the Fed’s website the correlations of 12-month changes (which tell you the tendency of large 12-month figures moving together), I would argue that this is accurate of long-term labor market trends, while the correlations of monthly changes with the LMCI is a more accurate representation of the extent the measures move together in small short-term labor market movements. Doing so indicates that the monthly level of the LMCI has a -0.82 correlation with the unemployment rate, suggesting that the LMCI is not completely redundant in short-term labor market movements, incorporating some parts of the mixed economic narrative told by dampening wage growth, low labor force participation, and high amount of underemployed part-timers.

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