The Taylor rule is the celebrity of monetary policy rules, frequently touted as the go-to framework for central banks, especially the Federal Reserve. Its simplicity is its charm: set interest rates based on how far inflation deviates from the target and how much the economy is straying from its potential output.

However, let’s not kid ourselves into thinking the Taylor rule is the Holy Grail of monetary policy. It’s more of an empirical snapshot of what the Fed has done in the past rather than a universal panacea.

Enter the Mankiw rule—a somewhat underappreciated cousin in the monetary policy family. Greg Mankiw introduced this gem in his paper “Monetary policy during the 1990s”.

The appeal of the Mankiw rule is its simplicity. Mankiw argues that the Federal Reserve during the 1990s adjusted the federal funds rate based on the difference between core inflation (measured by the Personal Consumption Expenditures, or PCE, index) and the unemployment rate.

Yes, you heard that right: inflation and unemployment, which of course aligns with the Fed’s dual mandate.

Mankiw’s original formula is:

Federal funds rate = 8.5 + 1.4 (Core inflation – Unemployment)

In Mankiw’s paper, he states that “The parameters in this formula were chosen to offer the best fit for data from the 1990s”, but as the graph below shows, some slightly better parameters could probably have been chosen.

Obviously, Mankiw never argued that this was a perfect fit or even that it had been statistically estimated, but that’s not really important. We see from the graph that the rule fairly well captures the ups and downs in the Fed’s policy rate from the late 1980s to the early 1990s.

And the model is very simple – and that to me is certainly part of the charm of the model. The Fed’s two mandates expressed in a simple fashion pretty much dictated during the 1990s what the Fed did with interest rates.

A Slightly More Complicated Story

While the simplicity of the Mankiw rule is its main attraction, it is also the main problem with the rule, and it is in no way given that the structures in the US economy are stable over time.

I would particularly stress three factors that have not been stable over time and which are likely not to be stable over time.

Firstly, the Federal Reserve has changed its monetary policy targets numerous times over time before eventually implementing a 2% inflation target over the past decade.

Secondly, for the Fed it should be important to realise that looking at unemployment as a measure of inflationary pressures would be wrong if it fails to take into account that structural unemployment has changed over time.

Thirdly, the real natural interest rate, which is closely related to potential real GDP, has also changed over time.

Therefore, to fully understand why the Mankiw rule actually makes sense, we need to incorporate these factors in what I here call a Theoretical Mankiw Rule.

Now the Mankiw rule is somewhat less simple, but we can make it simple again.

Hence, if we look at the period from 1985 until 2000, then we can make assumptions about the variables in the theoretical Mankiw rule.

Now the Mankiw rule is somewhat less simple, but we can make it simple again.

Hence, if we look at the period from 1985 until 2000, then we can make assumptions about the variables in the theoretical Mankiw rule.

The Congressional Budget Office (CBO) makes estimates for potential real GDP growth and NAIRU, and I have used these estimates, around 3.5% and 5.5% respectively, and it is probably fair to assume that the Fed’s de facto inflation target at the time was 3%, and if I at the same time assume α equal to 1.5 (close to Mankiw’s assumption of 1.4), then I can insert these values into our Theoretical Mankiw Rule, and then I get the following rule:

Hence, we are now back at a simple version of the Mankiw rule, but based on a clearer definition of the theoretical foundation – and as we see from the graph below, this Theoretical Mankiw Rule (the red line) with these parameters gives a much better fit to the actual Fed funds rate than the original Mankiw rule does.

The Mankiw Rule: Has It Stood the Test of Time?

But how have the Mankiw Rule – and the Theoretical version – done over time? Does the Mankiw rule still provide useful guidance on what the Fed should do with interest rates, and can we use the Mankiw rule to predict Fed policy changes?

The graph below shows both versions of the Mankiw rule and the actual Fed funds rate since 1960.

The first thing we notice is that the two versions of the Mankiw rule – the original one and the theoretical one – are remarkably similar over time. Secondly, we see that both models have done a fairly good job explaining the ups and downs in the Fed funds rate over time – particularly until the major shocks in 2008-9 and 2020-22.

Somewhat disappointingly for somebody who wants to have a theoretical explanation as well as an empirical explanation, the original Mankiw rule does a slightly (and it is really slightly) better job in terms of correlation and fit (measured by R2 and MSE) in explaining the development in the Fed funds rate.

That said, I feel a lot more comfortable using a policy rule for analysis and prediction when I understand it and it is not just a black box.

Both Versions of the Mankiw Rule Are in Agreement – It Is Time for the Fed to Cut Rates

One thing is how the Mankiw Rule has done historically – another thing is what it is saying now and what it predicts for the future.

Let’s first zoom in on developments in recent years.

As the graph above shows, both versions of the Mankiw rule have had a hard time explaining why interest rates were as low as they were until 2020, but this is not really what we are interested in here as there is general consensus that numerous factors such as negative demographics, financial regulation and likely also a de facto acceptance from central banks around the world that inflation was going to undershoot inflation targets without central banks taking any actions to do anything about this.

But the important thing is what happened from 2020 onwards.

In early 2020, the lockdown shock hit the US (and global) economy and caused unemployment to skyrocket. As a consequence, the Mankiw rule(s) stipulated that the Fed should cut rates strongly. The Fed did this and once it hit the Zero Lower Bound, it started – in my view correctly – to undertake massive quantitative easing of monetary policy.

However, as we also see, the US economy responded swiftly to the reopening of the economy as well as the massive monetary and fiscal stimulus. As a consequence, unemployment dropped very fast in the second half of 2020 and the Mankiw rules are quite clear – the Fed should have started the interest rate hiking cycle already in 2021. The Fed, as we know, didn’t do that and that in my view is the main reason inflation shot up sharply starting already in 2021.

However, in 2022 the Fed started to undo its mistakes and the Fed funds rate was hiked significantly, and during 2022 and 2023 the actual rate and the Mankiw rules have approached each other – and presently mid-2024 the theoretical Mankiw rule is basically exactly at the same level as the actual Fed funds rate.

But it is also notable that the theoretical Mankiw rule is slightly closer to the actual policy rate than the original Mankiw rule is.

An Updated Mankiw Rule

But if we want a simple rule of thumb, we really would like an updated version of the simple Mankiw rule.

We can calculate that by using the theoretical version of the Mankiw rule and assuming that the inflation target is 2%, that NAIRU is 4% and potential real GDP growth is 2.5%.

Then we get the following reduced form for the Mankiw rule:

We then assume that (core) inflation will have returned to 2% by the end of the year (we are already quite close) and that unemployment will have increased slightly to 4.5% also by the end of 2024.

Then we can calculate a “target” for the Fed funds rate over the next 6-12 months:

The current federal funds rate is set in the range of 5.25% to 5.50%, which means that the (updated) Mankiw rule indicates that the Fed should cut rates by as much as 1.50 percentage points over the coming year.

That could sound like a lot, but this is in fact extremely close to actual market pricing as illustrated by the table below from CME Group.

As we see, the most likely scenario (32.4%) is that the Fed will cut its key policy rate to 3.75-4.00 over the coming 12 months. Exactly as indicated by the updated Mankiw rule.

In conclusion, even though the Mankiw rule is extremely simple, it remains a rather useful—and easy to use—tool for assessing and predicting US monetary policy. This is especially true, in my view, if you use the updated parameterization of the rule.

The crucial question going forward is, of course, whether we will return to the “predictable 1990s” or if we will once again be hit by major economic and financial shocks as we have seen since 2008. I am optimistic that these are very rare events and that it is likely that we are, in fact, returning to something similar to the Great Moderation that lasted from 1985 until 2008—and returned again in 2010-2012 until 2020.

If that is the case, we might find it useful to have an updated Mankiw rule in our toolbox.

PS I have build a simple Mankiw Rule Calculator using artifacts in Claude 3.5 Sonnet. You can test the Calculator here. With the calculator you can make your own predictions for the Fed funds rate based on your expectations for macroeconomic variables in the US.

If you want to know more about my work on AI and data, then have a look at the website of PAICE — the AI and data consultancy I have co-founded.

I think it is pretty clear to everybody who follows this blog and follows me on social media that I am deeply fascinated by AI and how we can use, for example, Large Language Models in economic research—and I am eager to spread the gospel.

Today, I spent a couple of hours building a simple macroeconomic simulation model in Claude 3.5 Sonnet (see more about that here).

The model is a rather simple AS/AD model for the US economy in its most simple form. Test the model here.

When I had done the model, it struck me that I could test the output (graphs) from the model to see whether Large Language Models like ChatGPT or Claude can do macroeconomic reasoning based on “looking” at graphs of economic data.

In the model, I simulated a cut in interest rates by the Fed. The model, among other things, produced the graphs below.

I then simply copied these two graphs directly into a prompt in ChatGPT 4o and asked it the following question:

“Tell me about this. From an economic-theoretical perspective, what type of shock is this?”

And this is how ChatGPT 4o replied:

The graphs show two time series: GDP growth (%) and inflation (%), each plotted against a time index. Here’s a detailed analysis from an economic-theoretical perspective:

GDP Growth (%)

• Initial State: At the beginning (from -5 to 0), GDP growth is relatively stable at around 2.00%.
• Shock Occurrence: At time 1, there’s a sharp increase in GDP growth, peaking around time 2.
• Post-Shock: After the peak, GDP growth declines and stabilises back to around the initial level by time 8, remaining stable thereafter.

Inflation (%)

• Initial State: Inflation is stable at 2.00% from time -5 to 0.
• Shock Occurrence: A significant increase in inflation begins at time 1, peaking at time 3 and stabilising at a high level until time 6.
• Post-Shock: Post time 6, inflation sharply decreases and stabilises around its initial level by time 8, similar to GDP growth.

Type of Economic Shock

Given the patterns observed in both GDP growth and inflation, the economic shock depicted in these graphs can be analysed as follows:

Supply-Side Shock (Supply Shock)

• Characteristics: A supply shock, such as a sudden increase in productivity or an external factor reducing production costs, can lead to a temporary increase in GDP growth and inflation. This is because the economy can produce more goods and services, thus boosting GDP, while the increased supply might temporarily push prices up.
• Recovery Phase: Once the effects of the shock dissipate, both GDP growth and inflation return to their previous levels, as seen in the graphs.

Demand-Side Shock (Demand Shock)

• Characteristics: A demand-side shock, such as an increase in consumer spending or investment, typically raises both GDP growth and inflation. The initial increase in demand drives up production (GDP growth) and prices (inflation).
• Recovery Phase: Once the demand pressure subsides, both GDP growth and inflation return to their prior states, matching the pattern observed in the graphs.

Conclusion

The graphs suggest a positive demand-side shock due to the simultaneous increase in both GDP growth and inflation. This type of shock might be caused by factors such as increased government spending, tax cuts, or a surge in consumer confidence leading to higher spending. The temporary nature of the shock, with both GDP growth and inflation eventually returning to their baseline levels, supports the identification of a demand-side shock.

Additional Considerations

• Monetary Policy Response: Central banks might respond to such shocks by adjusting interest rates to manage inflation, which can also influence GDP growth.
• External Factors: External economic events, such as changes in global trade policies or commodity prices, could also contribute to these observed patterns.

Overall, the graphs illustrate a typical economic response to a temporary positive demand-side shock.

I know a lot of economists who would answer a lot less correctly than this, and even though I am quite bullish, to say the least, on the abilities of Large Language Models, I must say that I am extremely positively surprised by this. It should be remembered that ChatGPT 4o is not a model designed or trained to be able to do macroeconomic reasoning, but we clearly see here that it can perform this task rather well.

Imagine then when you train a model specifically for macroeconomic reasoning. We are getting quite close to virtual economists—and imagine what that will do, for example, in finance and central banking.

If you want to know more about my work on AI and data, then have a look at the website of PAICE — the AI and data consultancy I have co-founded.

Here are two sets of high-frequency US economic data: first, the daily US “inflation” numbers as measured by Truflation.com and the Weekly Economic Index (Lewis-Mertens-Stock), which is a very good weekly indicator of US real GDP growth.

What are we seeing?

Inflation is sharply down…

… and (proxy) real GDP growth is sharply up.

This started in May and has accelerated in June.

I would love to say this is AI-driven, but I have no evidence that that is the case. However, the numbers are truly positive.

So, if you can ignore US politics for a moment and instead look at the US economy, you will see a very positive story unfolding.

Yesterday, in my post “Fed’s hidden strategy: Implementing new dual NGDP targets”, I introduced a weekly NGDP growth proxy for the United States and proposed a medium-term NGDP target rule.

Today, I want to push this analysis further by exploring how the US yield curve might be functioning as a policy instrument in the Federal Reserve’s implicit NGDP targeting strategy.

Recapping Yesterday’s Insights on US Monetary Policy

Before we go into today’s analysis of the US economy, let’s quickly recap the key points from yesterday:

1. We introduced a weekly US NGDP growth proxy combining market expectations for US 5-year-5-year forward inflation and the Weekly Economic Indicator (WEI) from the Federal Reserve Bank of New York.
2. We proposed a medium-term NGDP target rule for the US: n_target_t = n* – λ(n_MA_t-2 – n), where n is 4.5% and λ is 0.75.
3. We observed that the Federal Reserve seems to have been implicitly following a rule similar to our proposed medium-term NGDP target rule, especially since 2022.

The US Yield Curve as a Policy Instrument

Today, I want to propose a new perspective: what if the US yield curve itself is functioning as a policy instrument in the Fed’s implicit NGDP targeting strategy? Here’s how I’m thinking about it:

The Federal Reserve directly controls the short end of the US yield curve through its setting of the federal funds rate (effectively by controlling the money base). By doing so, it influences the entire US yield curve, which in turn affects US economic activity and, consequently, US NGDP growth. Furthermore, the long end of the curve is at least partly a reflection of long-term NGDP growth (the Fed’s implicit long term NGDP target).

Empirical Evidence: The US Yield Curve and NGDP Growth

To support our hypothesis about US monetary policy, I’ve conducted some preliminary analysis, focusing on the period from 1985 to the present. This timeframe is particularly significant as it marks the beginning of what economists call the Great Moderation – a period of reduced macroeconomic volatility in the US that many attribute to improved Federal Reserve policy.

Let’s examine the following scatter plot of US data:

This graph illustrates the relationship between the US yield curve (specifically, the spread between 10-year and 2-year US Treasury yields, T10Y2Y) and the residuals of US NGDP growth from our medium-term target. Here are the key observations:

1. Optimal Lag: The analysis reveals that the US yield curve lagged by 9 months has the strongest correlation with US NGDP growth residuals. This suggests that changes in the US yield curve precede changes in US NGDP growth by about three quarters.
   
2. Negative Correlation: The regression line (y = -2.61x + 3.41) shows a clear negative relationship between the US yield curve spread and US NGDP growth residuals.
   
3. Explanatory Power: With an R² value of 0.50, the US yield curve explains about half of the variation in US NGDP growth residuals. This is a significant finding, suggesting that the yield curve indeed plays a crucial role in the Federal Reserve’s implicit NGDP targeting.

Interpreting the Results in the Context of US Monetary Policy History

As a market monetarist, I’m not surprised that the US financial market, represented here by the yield curve, provides such valuable information about future US NGDP growth. But what’s particularly intriguing is how these results align with our understanding of post-1985 US monetary policy.

The period we’ve analyzed, starting from 1985, coincides with what my friend Bob Hetzel has termed the Federal Reserve’s “Lean-Against-the-Wind (LAW) with credibility” monetary standard.

This approach, which emerged during the Great Moderation, represents a shift towards more rule-based monetary policy in the US.

Our findings suggest that this policy framework has remained largely intact, despite significant challenges:

1. Monetary Policy Response: When there’s a negative shock to US NGDP growth, the Fed responds by cutting rates. This action causes the US yield curve to steepen (higher T10Y2Y spread). Over the coming 9 months, this steeper yield curve contributes to a pickup in US NGDP growth, bringing it back towards the target. This mechanism aligns perfectly with the LAW approach.
   
2. Predictive Power: The 9-month lag we observe in our US data aligns remarkably well with Milton Friedman’s observations about the US economy. Friedman often spoke of a lag period of around 9 months from changes in US monetary policy to the impact on nominal demand (NGDP growth). This consistency adds credibility to our findings and underscores the importance of forward-looking monetary policy for the US economy.
   
3. “Automatic Stabilizer”: The negative relationship we see in the data suggests that the US yield curve acts as an automatic stabilizer for US NGDP growth. When NGDP growth falls below target, the Fed’s response steepens the yield curve, which then works to bring NGDP growth back up. Conversely, when US NGDP growth is above target, the flattening or inversion of the yield curve helps to moderate growth. This stabilizing effect is a hallmark of the Great Moderation period in the US and reflects the credibility aspect of the Fed’s LAW policy.
   
4. Policy Continuity: Perhaps most importantly, our analysis indicates that despite significant policy mistakes in 2008-9 and 2020-21, the overall US monetary policy framework remains broadly the same and maintains its credibility. This suggests a remarkable resilience in the Federal Reserve’s approach to monetary policy over the past four decades.

The Federal Reserve’s Challenge: Forward-Looking Policy in a Credible Framework

The key challenge for the Federal Reserve, highlighted by our analysis of the US economy, is to control the US yield curve approximately 9 months (give or take a few months) before the desired impact on US NGDP growth.

This underscores a fundamental tenet of market monetarism and aligns with the forward-looking nature of the LAW policy: US monetary policy must be forward-looking.

The Fed needs to set policy today based on where it wants US NGDP growth to be in about 9 months. This is no easy task, but our analysis suggests that by carefully managing the US yield curve, the Fed can indeed influence future US NGDP growth in a predictable manner.

This 9-month lag also emphasizes the importance of the Fed avoiding policy errors.

A mistake in yield curve management could have consequences that only become fully apparent after a significant delay, potentially leading to undesired fluctuations in US NGDP growth.

However, the overall stability we observe suggests that the Fed has, by and large, managed to navigate this challenge successfully for the US economy since 1985. Hence, we can likely talk about a rather robust monetary standard despite the obvious policy blunders in 2008-09 and 2020-21.

Refined Policy Rule for the US

Given these empirical findings about the US economy, we can refine our proposed policy rule:

This formulation captures the lagged relationship we observed and the negative correlation between the US yield curve and US NGDP growth residuals.

Conclusion: The Enduring Legacy of Rule-Based Monetary Policy in the US

Our analysis strongly supports the market monetarist view that US financial markets provide crucial information about future US economic conditions. The US yield curve, in particular, seems to be a powerful predictor of future US NGDP growth.

Moreover, it appears that the Federal Reserve has been implicitly using the yield curve as a policy instrument to target US NGDP growth, consistent with Hetzel’s characterization of the post-1985 US monetary standard. This aligns with our long-standing argument that NGDP targeting is a superior framework for US monetary policy.

What’s particularly encouraging is the resilience of this framework. Despite significant economic shocks and occasional policy missteps, the fundamental approach has remained intact and credible. This suggests that the benefits of rule-based monetary policy, which contributed to the Great Moderation in the US, continue to provide a strongly stabilizing force in the US economy.

The challenge for the Federal Reserve going forward is to explicitly recognize and refine this implicit NGDP targeting approach for the US economy. By formalizing its use of the yield curve and market signals, the Fed could potentially enhance its policy outcomes and communication, further cementing the gains of the past four decades in US economic stability.

PS The Yield Curve: A Robust Indicator Amidst Structural Changes

Our focus on the yield curve spread, rather than absolute interest rates, offers a key advantage: it sidesteps the challenge of estimating the natural interest rate (r*), a concept dating back to Knut Wicksell. While r* may fluctuate due to structural economic changes, the yield curve spread remains a reliable indicator of monetary policy stance.

This approach aligns with market monetarist principles, emphasizing market signals over unobservable variables. It suggests our findings on the relationship between the yield curve and future NGDP growth are robust to economic evolution.

Ultimately, the yield curve provides the Federal Reserve with a dependable tool for assessing monetary policy and its potential impact on NGDP growth, even as the underlying economic structure shifts.

Note: The drawing above is created based on the article above by ChatGPT/DALL-E.

Are you interested in my new AI and data venture, PAICE? Then have a look here and here.

Traditionally, central banks have focused on inflation targeting, but NGDP level targeting provides a more comprehensive picture by encompassing both inflation and real GDP growth over time.

However, real-time data on NGDP is not readily available. This challenge led me to develop a proxy for weekly NGDP growth.

In January 2024, I introduced this approach in my blog post “Did Jay Powell just deliver a near-perfect soft landing? Get the surprising answer from a new weekly NGDP indicator.”

This NGDP growth proxy has become an invaluable tool for real-time economic analysis for me – now I just hope the Fed would adopt it as well.

Constructing Our Weekly NGDP Growth Proxy

Our weekly NGDP growth proxy is constructed using a combination of high-frequency data points that reflect real-time economic activity. Specifically, we use:

1. Market expectations for US 5-year-5-year forward inflation: This is a forward-looking indicator that reflects market expectations of inflation over a future five-year period, starting five years from now.
2. Weekly Economic Indicator (WEI) from the Federal Reserve Bank of New York: The WEI combines several high-frequency data points, such as retail sales, unemployment claims, and consumer sentiment indices, to provide a near real-time indicator of economic activity.

By combining these indicators, we can track the growth rate of nominal spending with a high degree of accuracy and timeliness. Historically, this combination has tracked actual NGDP growth very well, providing a robust tool for economic analysis and policy formulation.

Our weekly NGDP growth proxy can be formally expressed as:

n_proxy_t = Inflation_Expectations_t + WEI_t

Where n_proxy_t is our NGDP growth proxy and WEI_t is inflation expectations.

We can see from the graph below that our NGDP proxy has closely followed the actual development in NGDP growth over the last 15 years. However, it has the significant advantage of providing us with near real-time, week-by-week data. Additionally, because we use market expectations for inflation, the proxy is also leading in relation to the actual NGDP growth.

The Rule for Targeting NGDP Growth

Market monetarists like Scott Sumner, David Beckworth and myself traditionally argue for an NGDP level target rather than an NGDP growth target.

However, our proposed medium-term growth target represents a more pragmatic approach to ensure economic stability.

To guide monetary policy, I propose a rule-based framework that targets a long-term NGDP growth rate of 4.5%.

This target is grounded in the Federal Reserve’s official 2% inflation target and an assumed potential real GDP growth rate of around 2-2.5%.

However, a purely growth-based target may not adequately address historical deviations from the target path. To compensate for periods of undershooting or overshooting, I introduce a medium-term NGDP target rule, which can be formally expressed as:

n_target_t = n* – λ(n_MA_t-2 – n*) (2)

Where:

• n_target_t is the medium-term NGDP growth target at time t
• n* is the long-run NGDP growth target (4.5%)
• n_MA_t-2 is the 6-quarter moving average of NGDP growth, lagged by 2 quarters
• λ is an adjustment coefficient (set at 0.75 in our baseline model)

This formula adjusts the target based on the historical performance relative to the long-term target, effectively compensating for past deviations. If NGDP growth has been below target, the medium-term target allows for a period of higher growth to bring the economy back on track, and vice versa.

To visualize how this rule works in practice, let’s examine the following graph:

This graph clearly demonstrates the relationship between actual NGDP growth (blue line), our proposed medium-term NGDP target (yellow line), and the long-term NGDP target of 4.5% (green dashed line).

Several key observations can be made:

1. Pre-pandemic period (2010-2019): Actual NGDP growth generally fluctuated around the 4.5% long-term target, with the medium-term target adjusting to compensate for deviations.
2. Pandemic shock (2020): We see a dramatic drop in NGDP growth, followed by a sharp rebound. The medium-term target adjusted significantly to compensate for this extreme deviation.
3. Post-pandemic recovery (2021-2022): NGDP growth overshot the target, leading to a period of monetary tightening.
4. Recent stabilization (2023-2024): As observed in early 2024, for nearly half a year, the Fed has been able to ensure very stable NGDP growth around the 4.5% target. This is evident in the convergence of all three lines towards the end of the graph.

This visual representation supports our argument that the Fed has implicitly been following a rule similar to our proposed medium-term NGDP target rule.

The medium-term target (yellow line) has consistently guided actual NGDP growth back towards the long-term 4.5% target, even in the face of significant economic shocks.

This does not mean that monetary policy has been flawless. For instance, it seems evident that monetary policy became overly expansionary during 2021 (the blue line was significantly above the yellow line). However, at least from 2022 onwards, the Fed managed to get back on track – a stance it has largely maintained to date.

Relation to the McCallum Rule

Our approach bears significant similarities to the McCallum rule, a monetary policy rule proposed by economist Bennett McCallum.

The McCallum rule focuses on adjusting the monetary base to achieve a target path for nominal GDP. It can be formally expressed as:

Δb_t = n* – Δv_a + λ(n* – n_t-1) (3)

Where:

• Δb_t is the change in the monetary base
• n* is the target NGDP growth rate
• Δv_a is the average growth rate of base velocity
• n_t-1 is the previous period’s NGDP growth rate
• λ is an adjustment coefficient

In essence, the McCallum rule aims to stabilize nominal GDP growth by adjusting the monetary base to offset changes in money velocity and align with real GDP growth. Both the McCallum rule and our medium-term NGDP target rule aim to stabilize nominal GDP growth.

Comparison of Coefficients

To understand the similarities and differences between our proposed medium-term NGDP target rule and the McCallum rule, it is useful to compare the coefficients in the respective equations.

Our Medium-Term NGDP Target Rule:
n_target_t = n* – 0.75(n_MA_t-2 – n*)

In this equation:

• The target NGDP growth rate is n* (4.5%)
• The coefficient for the deviation of the moving average of NGDP growth from the target is -0.75
• The adjustment is based on a 6-quarter moving average, lagged by 2 quarters

The McCallum Rule:
Δb_t = n* – Δv_a + λ(n* – n_t-1)

In this equation:

• The coefficient for the velocity of money is -1
• The coefficient for the deviation of NGDP growth from the target is λ (typically set around 0.5)
• The adjustment is based on the previous period’s NGDP growth

While both rules aim to stabilize NGDP, our medium-term target rule explicitly compensates for past deviations from the target through a specific coefficient (-0.75) and a lag (6-quarter moving average, lagged by 2 quarters), providing a structured way to return to the desired NGDP growth path.

In contrast, the McCallum rule focuses on adjusting the monetary base considering changes in the velocity of money and the most recent NGDP growth rate.

The choice of a -0.75 coefficient in our rule allows for a more aggressive adjustment compared to the typical λ value in the McCallum rule. This reflects our emphasis on medium-term stability and the need to compensate for cumulative deviations over time.

Furthermore, our use of a moving average lagged by two quarters provides a smoother adjustment process, reducing the impact of short-term fluctuations and allowing for a more gradual return to the target path.

Both rules share the fundamental principle of targeting NGDP growth, but our proposed rule is designed to be more forward-looking and to provide a clearer path for expectation formation among market participants.

By explicitly targeting a medium-term NGDP growth rate, our rule may be more effective in anchoring long-term expectations while still allowing for short-term flexibility in monetary policy.

Where We Are Now

The current state of the US economy illustrates the effectiveness of this implicit rule.

Our analysis shows that after a period of monetary tightening in response to high NGDP growth rates, the Federal Reserve’s policies have managed to stabilize NGDP growth around the long-term target of 4.5%. This has been achieved without official acknowledgment of following a rule akin to the McCallum rule.

Effectively, this means that monetary policy is now more or less perfectly balanced, ensuring a growth rate of nominal spending that will allow US inflation to return to 2% while avoiding a recession – the much-talked-about “soft landing”.

Implications of an Implicit McCallum Rule

The realization that the Federal Reserve has been implicitly following a McCallum-like rule has significant implications for both policymakers and market participants.

Firstly, it underscores the importance of NGDP targeting as a superior policy framework compared to traditional inflation targeting.

NGDP targeting inherently adjusts for both real economic growth and inflation, providing a more broad-based measure of economic health.

Secondly, this approach highlights the need for central banks to compensate for past deviations from their targets.

By ensuring that periods of undershooting are followed by periods of overshooting, central banks can maintain a more stable economic environment. This is particularly important in avoiding the pitfalls of purely reactive policies that can exacerbate economic volatility.

The Path Forward: Embracing a Rule-Based Approach

For the Federal Reserve, openly acknowledging and embracing a rule-based approach to NGDP targeting could lead to more effective monetary policy.

By clearly communicating its targets and the rules governing policy adjustments, the Fed can enhance its credibility and effectiveness.

This transparency would allow market participants to better understand the Fed’s actions, reducing uncertainty and fostering a more stable economic environment.

This approach would make monetary policy fully rule-based, reducing the need for extensive Fed communication or in-house forecasting. The market would then take care of most of the heavy lifting in monetary policy.

Moreover, if the Fed keeps NGDP growth close to 4-4.5% and we simultaneously see an acceleration in productivity, inflation might drop below 2%. This should be welcomed as long as it reflects higher productivity growth, further underlining why the Fed should target NGDP growth rather than inflation alone.

The adoption of a rule-based framework aligns with the principles of market monetarism, which advocate for predictable and transparent monetary policy. This approach can help prevent the kind of monetary imbalances that lead to economic disruptions, ensuring a more stable and prosperous economy for all.

A concrete way forward for the Fed could be:

1. Embrace a high-frequency indicator of nominal spending growth, such as the one proposed in this article.
2. Announce that it will track this indicator closely to ensure 4-4.5% growth in nominal spending in the long run.
3. In the short term, use monetary policy instruments to hit the medium-term target for NGDP, which might be higher or lower than the long-term target, to make up for past policy mistakes (overshooting or undershooting relative to the long-term target).
4. Continue to use interest rates as its primary policy instrument, but communicate in terms of a further interest rate path relative to market pricing.
5. Pre-announce that if the zero lower bound on interest rates is hit, the Fed will initiate quantitative easing as long as the NGDP proxy is below the medium-term NGDP target.

By adopting this framework, the Federal Reserve would be acknowledging and formalizing the McCallum-like rule it has been implicitly following, leading to more transparent, predictable, and effective monetary policy.

Note: The drawing above is created based on an article by ChatGPT/DALL-E.

Are you interested in my new AI and data venture, PAICE? Then have a look here and here.

Abstract

This blog post examines the effectiveness of real rate rules in stabilizing inflation expectations using quarterly data from 10-year Treasury yields and inflation data from 1988 to 2024.

We estimate the relationship between inflation deviations from the target and the expected average deviation of future inflation, following the methodology outlined in “Robust Real Rate Rules” by Bundesbank economist Tom D. Holden. Our findings indicate a significant and positive relationship, supporting the use of real rate rules for effective monetary policy.

Introduction

Inflation stability is a key objective for central banks worldwide. Real rate rules, which adjust nominal interest rates based on real rates and inflation deviations, have been proposed as robust tools for achieving this goal. This study extends the analysis by using 10-year Treasury yields and inflation expectations to estimate the impact of inflation deviations on future inflation expectations.

Data Sources and Methodology

Data Sources

The data used in this study are sourced from the Federal Reserve Economic Data (FRED) database, maintained by the Federal Reserve Bank of St. Louis. The datasets include the Consumer Price Index (CPI), 10-Year Treasury Constant Maturity Rate (DGS10), and 10-Year Expected Inflation (EXPINF10YR). The data are provided quarterly and cover the period from 1988 to 2024.

Model Specification

To reflect the 10-year expectations, we use a rolling window of 40 quarters (10 years) to calculate the expected deviation.

Note: To address an unusual spike in Q4 2018 due to technical factors related to the shock 10 years earlier (2008), we adjusted the yt​ value for Q4 2018 to the average of Q3 2018 and Q1 2019 values. This adjustment ensures the model’s stability and accuracy.

Results

Regression Summary

• Inflation Deviation Coefficient (θ): 0.0227 (statistically significant at the 0.000 level)
• R-squared (uncentered): 0.362
• F-statistic: 57.19 (p-value: 1.87e-11)

Diagnostic Tests

• Durbin-Watson Statistic: 2.033 (no significant autocorrelation)
• Omnibus Test: 5.378 (p-value: 0.068)
• Jarque-Bera Test: 6.501 (p-value: 0.0388)

Visual Analysis

The actual and predicted values of yt are plotted against the date, showing that the model captures the overall trends and significant deviations effectively.

Discussion

The results confirm a significant positive relationship between inflation deviation and future inflation expectations. The coefficient aligns with the findings in Holden’s study, validating the robustness of real rate rules. The R-squared value indicates that the model explains a substantial portion of the variation, though other factors may also influence inflation expectations.

Comparison with Holden’s Results

Holden’s study “Robust Real Rate Rules” provides a framework for understanding the relationship between inflation deviations and inflation expectations, primarily focusing on data from 2008 Q4 to 2023 Q2. Our study extends this analysis in several key ways:

1. Longer Time Period:
   • Holden’s Study: 2008 Q4 to 2023 Q2.
   • Current Study: 1988 to 2024.
   • Impact: By including a longer time period, our study captures a wider range of economic conditions, including multiple economic cycles and policy changes.
2. Data Frequency and Sources:
   • Holden’s Study: Uses quarterly data on CPI and TIPS breakeven inflation.
   • Current Study: Uses quarterly data on CPI, 10-Year Treasury yields, and 10-Year expected inflation rates from FRED.
   • Impact: The use of 10-Year Treasury yields and expected inflation rates provides a longer-term perspective on inflation expectations.
3. Key Findings:
   • Holden’s Study: Found a significant positive relationship between inflation deviation and future inflation expectations, with various coefficients for different models ranging from 0.033 to 0.130.
   • Current Study: Also finds a significant positive relationship, with a coefficient of 0.0227. This consistency reinforces the robustness of real rate rules.

Conclusion

This blog post reinforces the effectiveness of real rate rules in stabilizing inflation expectations using long-term data. The findings support the adoption of such rules for robust monetary policy, ensuring inflation targets are met under varying economic conditions.

References

• Holden, T. D. (2023). Robust Real Rate Rules. https://www.tholden.org/assets/files/RobustRealRateRulesOnlineAppendices.pdf
• U.S. Bureau of Labor Statistics, Consumer Price Index for All Urban Consumers: All Items [CPIAUCSL], retrieved from FRED, Federal Reserve Bank of St. Louis; https://fred.stlouisfed.org/series/CPIAUCSL, June 27, 2024.
• Board of Governors of the Federal Reserve System (US), 10-Year Treasury Constant Maturity Rate [DGS10], retrieved from FRED, Federal Reserve Bank of St. Louis; https://fred.stlouisfed.org/series/DGS10, June 27, 2024.
• Federal Reserve Bank of Cleveland, 10-Year Expected Inflation [EXPINF10YR], retrieved from FRED, Federal Reserve Bank of St. Louis; https://fred.stlouisfed.org/series/EXPINF10YR, June 27, 2024.

This blog post has been nearly entirely written by ChatGPT-4 based on my prompting and the output from the regression analysis I asked ChatGPT-4 to undertake.

Have a look at the website of my AI advisory Paice here.

Over the past year, I have increasingly dedicated my time to speaking, writing, and advising on the use of data, analytics, and artificial intelligence (AI). This includes workshops, lectures, and direct consultation with clients on introducing and using AI.

Initially, this wasn’t an active decision but rather driven by demand. My phone has been ringing quite frequently with requests for assistance with data and AI consulting. So when I was introduced to Christian Heiner Schmidt in January, it became clear that it was time to seriously go all-in on the AI revolution.

Christian and I both have backgrounds in finance and an extensive network in the Nordic financial sector.

Our skills complement each other: I excel in data, analytics, and communication, while Christian excels in IT solutions and project implementation. Christian has led several high-profile, business-oriented IT systems for companies including Nordea, Carnegie, and Saxo Bank.

So when Christian and I met in January, it was clear – we should start an AI and data consulting business together. And that’s how PAICE came into existence. The company was officially registered in March, and we have now been working on the first major projects for some time.

But what is it that we do at Paice?

I have often said that AI is not primarily about technology, but about solutions – and about identifying problems that can be solved using data, analytics, and AI (both machine learning and language models). And that’s what we do – we identify problems and help find solutions.

Our focus is primarily on finance and sectors undergoing “financialisation”, i.e. sectors that are increasingly resembling the financial sector in terms of data and algorithm usage. This includes retail and wholesale businesses. Here we see enormous potential for the use of AI and data-based solutions.

To ensure effective implementation of AI-based solutions, we have entered into a Joint Business Relationship agreement with PwC (Denmark), enabling us to offer both consulting and implementation of AI and data-based solutions.

If you want to know more about Paice, please visit our website (here) or send us an email (hello@paice.io).

You can also reach me by phone (+ 45 52 50 25 06).

P.S. And don’t worry – I will not stop occasionally writing on monetary policy on this blog.