A new keynesian perspective of the US economy

This entry is an English translation of a previous post in this very same blog originally written in Portuguese for my usual Brazilian public. If you happen to have enjoyed this content, make sure to let me know so I can shift gears to English posts in the future.

I intend to dedicate this entry to the analysis of the American macroeconomic outlook. Using the most basic New Keynesian model, it is possible illustrate the core details of the Fed’s current monetary policy debate, the main sources of uncertainty shared between most US economy analysts, and to build an organized way of thinking about the future.

To start off, I anticipate that all data used for this post was extracted from the FRED. I will also leave a public Excel spreadsheet for this analysis available at the end of the post. Lets get to it then.

Describing the model and our baseline scenario

Our new keynesian model will count with four simultaneous dynamic equations, with quarterly frequency sourced data.

The first equation is an IS Curve, which will describe the path for short-run economic activity:

Here, ‘y’ is the output gap, ‘i’ is the Fed Funds rate, ‘t5y(trend)’ is the HP-filtered 5-year treasury bond yield trend and ‘gb’ is the federal gov’t budget balance

The second equation, a Phillips Curve, in charge of the inflation dynamics:

Where ‘π’ is the quarterly annualized, and seasonally adjusted change to CPI prices, ‘oil’ is the same according change (no seasonal adjustment required here) to WTI crude oil prices, ‘E(t)π(t+4)’ denotes inflation expectations for the next four quarters (I take an average of surveys and market breakeven inflation, details available on the spreadsheet)

The third equation is a Taylor rule, which will be behind the upcoming policy rate movements by the US Fed:

‘π(s)’ is an inflation signal, basically an average of multiple current and forward looking inflation metrics, π(target) is the Fed’s target, 2%

The fourth and final equation, a simple law of motion for inflation expectations:

Here, we define 0<b1<1, the closes b1 is to 1, the less anchored to the target inflation is, resulting into more sticky inflation

To get our model going, we need to calibrate the parameters {c1, c2… c10, b1}. I made the calibration based on three fundamental criteria, in no order of importance: 1) adjustment to historical data, 2) respect to the most widely accepted theory for the relationship between the variables, and 3) adjustment to Fed projections and market expectations for the base scenario.

Here, MAD represents the median absolute deviation of the residuals, the measure of choice for fitting historical data

In addition to calibrating the parameters, for the projections we will also need to assume trajectories for the exogenous variables of the model. These are my baseline assumptions for the WTI oil and the 5-year treasury yield:

Here, it is assumed that WTI should follow the expected US inflation from its last observed average price of 2022Q1 (approx. $95/pb), for the 5-year US treasury yield we go with a small convergence towards 0.3% real annual returns (above the 2% target)

The yielding baseline scenario from our assumptions above is then:

All estimates within the sample are conditioned to the value observed immediately before, to avoid the accumulation of t-1 errors

As a final adjustment to the model, I needed to calibrate shocks in the IS curve for the next two quarters to bring the GDP projection closer to the most up to date market expectation for growth this year (between 2.5–3.5%). The other projections have no short-term shocks whatsoever, therefore being driven by their equations alone.

Right away, we can interpret some observations implied by the results obtained:

1. The consensus and the US Fed do not expect the economy to overheat so far (output gap is not expected to tread into positive territory);
2. The Fed chose to stray away from the recommendations of our Taylor rule for about three quarters (since 2021 Q2), when inflation started to accelerate due to the sharp acceleration in the oil price. The lack of anticipation of the commodities scenario may have cost the central bank’s credibility to the inflation target objective in the short-term;
3. The Fed is expected to run into contractionary interest rate levels later this year to prevent an even higher inflation deviation from its target of 2% per year on average;
4. The peak pace of this most recent cycle of accelerated growth is also expected to have been reached in the latest quarter (2022 Q1). Going forward, the economy should slow down to grow around potential (1.8–2% per year).

Sources of uncertainty and alternative scenarios

There are many sources of uncertainty currently. Russia’s invasion of Ukraine has brought great volatility to commodity prices, which translates into different scenarios for short-term inflation. If overshooting current inflation happens to erode agents’ medium-term expectations, the Fed will be forced to act more aggressively than is currently expected, raising interest rates faster or in greater magnitude.

To represent this source of uncertainty however, it would be as easy as shocking our projections with new trajectories for the oil price or adding periodical shocks to the results of our Phillips Curve. For this post, however, I’d like to try to answer a different question: what if in an unchanged baseline scenario, the Fed simply decides to change its reaction function?

The reaction function of a central bank can be represented by the term ‘(1-c8)’ in our Taylor rule. The magnitude of the coefficient ‘c8’ will calibrate the speed with which a central bank chooses to act and address the cyclical conditions of the economy. A coefficient ‘c8’ close to unity would represent a very slow and cautious central bank response (more typical of the Fed), while a coefficient closer to zero would give us an aggressive central bank that over-reacts to data at the margin (less usual). We can play around with this coefficient and assess how monetary policy (and the rest of the economy) moves in a non-negligible way because of it.

Let us allow for the central bank in our model to move a little faster than what is usually suggested by historical US data:

In this calibration, all coefficients remained identical, with the exception of c8 = 0.75, 0.1 less than in our baseline shown previously

Under these new circumstances, a change in the Fed’s stance would force agents to perceive a greater number of increases in monetary policy this year:

More reactive, the Fed would deliver 3% interest rates for an identical baseline scenario

To enlighten the impacts to the rest of our modelled economy, I plotted this impulse-response graph for this more reactive monetary policy.

An advantage for the Fed to consider a less gradual policy reaction approach than the current one is to speed up the closing of the inflation deviation from its target and allow for a quicker convergence to the economy’s steady-state, preventing more shocks from accumulating before the old shocks dissipate. Naturally, this also depends that the Fed manages to convince the broad public that tighter monetary policy won’t create a self-fulfilling prophecy that the economy is going into recession. Long story short, agents’ expectations matter.

Does it make sense to think that the Fed would consider such a stance in the face of international geopolitical uncertainties? I leave the answer to this question to the reader.

Final thoughts

Forecasting the US economy is quite convenient given the abundance and accessibility of data, especially more so considering how hard it is to extract good estimates of unobservable output gaps or neutral policy rates. Despite having multiple public methods for computing a neutral rate estimate for the US economy, I chose to use my personal neutral interest methodology, as it already comes out with the model. At the end of the day, each analyst has his own, so feel free to replace it if you wish to in the spreadsheet available in this link. This will allow you to replicate this analysis and suit it to your personal interpretation of the current state of the economy.

It is also interesting to see how much can be achieved with systems of equations yielding simple linear relations. So much pointless debate and wordplay could be easily summarized by simplified modelling work.

This would be all for today’s entry. Thank you for making it this far.