Paul Gomme

Inflation and GDP

Posted on April 26, 2024 by Paul Gomme

By Paul Gomme and Peter Rupert

The Bureau of Economic Analysis announced that, on an annualized basis, the personal consumption expenditures (PCE) price index increased 3.94% and core PCE (excluding food and energy) — the Fed’s preferred measure — rose 3.86%, up from 3.24% in the previous month. As we have commented many times, the monthly numbers are quite volatile and therefore we calculate a “trend” measure that we feel better captures the underlying trend, shown in red below. Both the trend measures indicate an uptick in inflation. These higher PCE inflation numbers were foreshadowed by the CPI release from about two weeks ago.

Earlier in the week the Bureau of Economic Analysis released its advance estimate for first quarter GDP. Output growth has decelerated from 4.9% in the third quarter of 2003 to 3.4% in the fourth quarter of 2023 and 1.6% in the most recent quarter. Personal consumption expenditures increased 2.5% in the first quarter after increasing 3.3% in the previous quarter. Indeed, consumer spending on services was a driving force in the most recent report. Investment increased 3.2% with the residential component increasing 13.9%, the largest increase since the fourth quarter of 2020.

The table below breaks down output growth by the contributions of its major components. The contribution of, say, investment (0.6 percentage points) is given by its growth rate (3.2%) weighted by its share of GDP (18%). Between 2023Q3 and 2024Q1, output growth has fallen by 3.3 percentage points. Of this decline, 0.4 percentage points (2.1 – 1.7) is due to consumption. Investment contributed 1.2 percentage points; government 0.8 points; and exports and imports have both contributed 0.5 points. This tells us that the fall in output growth has occurred due to all components of output, with particularly large contributions by investment and government spending.

Date	Output	Consumption	Investment	Government	Exports	Imports
2023Q3	4.9%	2.1	1.8	1.0	0.6	-0.6
2023Q4	3.4%	2.3	0.1	0.8	0.6	-0.3
2024Q1	1.6%	1.7	0.6	0.2	0.1	-1.1

Notes: Output (GDP) growth, and contributions by its major components.

Outlook

Over the last few months the likely prospect of several interest rate cuts became dimmer due to a rise in the underlying inflation trend. Has the deceleration in GDP growth over the last couple of quarters increased the likelihood of a rate cut? Given the rising trend in inflation it does not seem likely that a rate cut will happen any time soon.

Our measure of trend core PCE inflation now stands at 3.5% — considerably higher than the FOMC’s 2% target, and moving in the wrong direction. Some may point to the slower output growth numbers as a signal of lower future inflation. But, arguably the right thing to do at this stage is to raise interest rates. However, the FOMC has painted itself into a corner with earlier promises of lower interest rates. While it’s tempting to point to the real side weakness to justify a rate cut, in the longer term, addressing inflation is the better course of action as we learned in the 1970s when the U.S. was hit by stagflation — a stagnating real side along with high inflation.

February PCE Inflation

Posted on March 29, 2024 by Paul Gomme

Uh oh! While the year-over-year inflation rate as measured by the PCE deflator was essentially unchanged in February (it rose slightly, from 2.43% in January to 2.45%), the annualized month-over-month inflation rate, at 4.1%, is still running well above the Fed’s 2% target. Our measure of trend inflation rose half a point, from 2.6% to 3.1%. It bears repeating that our measure of trend inflation is designed to filter out much of the high frequency movements in the month-over-month inflation rate while responding in a timely fashion to changes in the trend.

The outlook is not much better when the “volatile” food and energy components of the PCE deflator are removed: The month-over-month inflation rate dropped from 5.6% to 3.2% (good), but is still well above the Fed’s 2% target (bad). The year-over-year inflation rate fell slightly, from 2.9% to 2.8%. And our measure of trend inflation was essentially unchanged, coming in at 3.16%.

The Policy Outlook

In a sense, the latest core PCE inflation numbers are not a surprise: they were foreshadowed by core CPI inflation which came out a couple of weeks ago. For the first two months of 2024, trend core inflation is up and is considerably higher than the Fed’s 2% target. If the monthly inflation rate continues to come in on the high side, expect to see the year-over-year inflation rate start to rise — just as it did in 2020-21. Along side the solid GDP growth and labor market, recent inflation makes it easier for those building a case for raising (or not lowering) interest rates.

Feburary CPI

Posted on March 13, 2024 by Paul Gomme

The annual (12 month-over-12 month) inflation rate as measured by the CPI rose marginally, from 3.11% to 3.17% in February. Taking out the volatile food and energy components, core CPI inflation was down marginally, from 3.87% to 3.76%. So, overall no change? As we have emphasized in the past, annual inflation rates respond sluggishly to changes in trend. The monthly annualized CPI inflation rate rose smartly, from 3.73% to 5.44% while annualized core CPI inflation fell from 4.81% to 4.39%. As we have previously discussed, monthly inflation rates are quite variable. Our trend measure of CPI inflation popped up from 3.06% to 3.85%; trend core CPI inflation saw an upturn from 3.89% to 4.06%.

Policy Outlook

The FOMC tends to look at core PCE inflation, not CPI inflation. However, the PCE data for February will be released in a couple of weeks. Given the overlap in the goods and services covered by the CPI and PCE, the February CPI report provides some “news” regarding the likely direction of the upcoming PCE data. Sorry folks, but the short term prospects for interest rate cuts are dim. At the horizons we report, PCE inflation for January exceeded the Fed’s 2% target, whether overall or the core measure. Given that the February CPI data shows an increase in inflation, it seems unlikely that PCE inflation for February will be heading down towards 2%, and may well be up from January. The Fed is unlikely to let inflation get out of hand as it did in 2020. At this juncture, it’s easier to make a case to raise, not lower, interest rates, especially since the real economy (labor market, productivity and GDP) has not shown signs of weakening.

Q4 GDP and PCE inflation

Posted on January 27, 2024 by Paul Gomme

On January 25, the BEA released its Advance Estimate for 2024Q4 GDP. The key headline number: GDP grew at an annualized rate of 3.3% in the fourth quarter, down from 4.9% in the third quarter. The recent number, though down from the fourth quarter, was the largest since the first quarter of 2022. Moreover, surveyed economists from the Wall Street Journal forecast 2% growth.

A useful way to think about this drop in output growth is in terms of the contributions of the major components of GDP. These contributions are the growth of a component multiplied by its share of GDP. The 1.6 percentage point decline in GDP growth is chiefly due to investment (contributing 1.4 percentage points, that is, falling from 1.8 to 0.4) with lesser contributions due to government spending (0.4 points) and consumption (0.2 points). Offsetting contributions were recorded by imports (-0.3 points) and exports (-0.1 points).

The quarterly personal consumption expenditures price index (PCE) fell to 1.7%, continuing an impressive decline starting in Q3 of 2022.

The BEA reports that the PCE price index increased 0.2% in December, up from -0.1% in November. At annual rates, these work out to 2.0% (December) and -0.8% (November). Our measure of trend PCE inflation rose, at an annual rate, from 1.4% in November to 1.6% in December. The earlier CPI report foreshadowed these increases. On a year-over-year basis, PCE inflation was essentially unchanged between November and December at 2.6%.

Our measure of trend core PCE inflation was up slightly, from an annualized 1.9% (November) to 2.0% (December). On a monthly basis, core PCE inflation shot up from 0.8% to 2.1% while the year-over-year rate fell from 3.2% to 2.9%. All in all, core PCE inflation looks to be settling into the Fed’s target of 2.0%. It will simply take a few months for the year-over-year rate to catch up with recent developments.

December CPI

Posted on January 12, 2024 by Paul Gomme

The December CPI (Consumer Price Index) report, released by the BLS (Bureau of Labor Statistics) is bad news on the inflation front. By almost any measure, CPI inflation is up. By our recently discussed “constant gain” measure of trend inflation, it rose by 0.4 percentage points for the overall CPI, and by 0.15 percentage points for core CPI (excluding food and energy). On a year-over-year basis, overall CPI rose 0.2 percentage points while core CPI fell by 0.1 points. The figures below show that the one-month annualized inflation rates are also up.

For monetary policy, what presumably matters is not what’s happening with CPI inflation but rather PCE (Personal Consumption Expenditures) price inflation since core PCE inflation is what the Fed looks at. Although it is probably the case that the CPI works to influence the policy makers. The PCE data won’t be released for another two weeks. However, given the broad similarity in the goods covered by the CPI and PCE deflator, it’s a reasonable guess that (core) PCE inflation will also be up. If so, the Fed will be faced with some difficult choices: Do they treat December as (maybe) an aberration and stand pat, or will they view December as the harbinger of another inflationary pulse? Or, cognizant of the long and variable lags associated with the effects of monetary policy, will the Fed leave rates unchanged since they’re already added enough tightening? Having said that, the “trend” line has not risen by much and for the core is basically flat. Therefore, from a long and variable lag perspective it seems doubtful that the Fed will alter their current stance at the meeting at the end of the month.

On measuring trend inflation

Posted on January 11, 2024 by Paul Gomme

One of the challenges over the past couple of years has been measuring trend inflation. As shown in the figure below, monthly inflation rates are volatile; 12-month inflation rates are much smoother, but only slowly reflect changes in trend inflation. Previously, we’ve focused on the 3-month inflation rate.

As shown below, the 3-month inflation rate is approximately the average of three 1-month inflation rates. This means that each month, the 3-month inflation rate adds the current 1-month inflation rate, and drops the 1-month inflation rate from 4 months ago. Consequently, the 3-month inflation rate can drop precipitously if the inflation rate being dropped is relatively high.

A different way of putting the issue is that the calculation for the 3-month inflation rate assigns a weight of 1/3 to each of the past 3 months’ inflation rates, and a weight of 0 to inflation rates 4 or more months ago. Why such a discrete change in weights? Why not a more gradual decline in weights?

The remainder of this post gets into the guts of an alternative measure of trend inflation in which the weights on monthly inflation rates decline with their age. Readers uninterested in the details should feel free to jump to the end which presents our new measure of trend inflation.

The 3-month inflation rate as an average of 1-month inflation rates

Consider the calculation of the gross 3-month (non-annualized) inflation rate for November,

$1+\tilde\pi^{(3)}_{November} = \frac{P_{November}}{P_{August}}$

where $P$ is the price level (for a given month), and the superscript indicates the horizon over which the inflation rate is computed (3 months in this case). The `tilde’ over $\pi$ indicates that the measure of inflation is not annualized. Similarly, 1-month (non-annualized) inflation rates are given by

$1+\tilde\pi^{(1)}_{September} = \frac{P_{September}}{P_{August}}$

$1+\tilde\pi^{(1)}_{October} = \frac{P_{October}}{P_{September}}$

$1+\tilde\pi^{(1)}_{November} = \frac{P_{November}}{P_{October}}$

From the above, it follows that

$1+\tilde\pi^{(3)}_{November} = \left(1+\tilde\pi^{(1)}_{September}\right) \left(1+\tilde\pi^{(1)}_{October}\right) \left(1+\tilde\pi^{(1)}_{November}\right)$

The gross 3-month inflation rate is the product of the three immediate past 1-month inflation rates. Taking the natural logarithm,

$\ln\left(1+\tilde\pi^{(3)}_{November}\right) = \ln\left(1+\tilde\pi^{(1)}_{September}\right) + \ln\left(1+\tilde\pi^{(1)}_{October}\right) + \ln\left(1+\tilde\pi^{(1)}_{November}\right)$

we obtain

$\tilde\pi^{(3)}_{November} \simeq \tilde\pi^{(1)}_{September} + \tilde\pi^{(1)}_{October} + \tilde\pi^{(1)}_{November}$

where the approximation arises from $\ln(1+x) \simeq x$ for $x$ close to zero.

If we wish to work with annualized inflation rates, then

$1+\pi^{(3)}_{November} = \left(\frac{P_{November}}{P_{August}}\right)^{4}$

Again taking the natural logarithm, we obtain

$\pi^{(3)}_{November} \simeq 4 \tilde\pi^{(3)}_{November}$

The 1-month inflation rates will have “12” in the place of “4”. We now have

$\pi^{(3)}_{November} \simeq \frac{1}{3} \left[\pi^{(1)}_{September} + \pi^{(1)}_{October} + \pi^{(1)}_{November}\right]$

In other words, the 3-month annualized inflation rate for November is (approximately) the average of the three 1-month annualized inflation rates.

A related problem: computing an average

Given 3 observations on some variable, the sample average or mean is

$\overline x^{(3)} = \frac{1}{3} \left[x_{1} + x_{2} + x_{3}\right]$

Now, if we add a fourth observation,

$\overline x^{(4)} = \frac{1}{4} \left[x_{1} + x_{2} + x_{3} + x_{4}\right]$

However, computing $\overline x^{(4)}$ as above discards the “work” done in calculating $x^{(3)}$ . From the calculation of $\overline x^{(3)}$ ,

$x_{1} + x_{2} + x_{3} = 3 \overline x^{(3)}$

Substituting into the formula for $\overline x^{(4)}$ ,

$\overline x^{(4)} = \frac{1}{4} \left[ 3 \overline x^{(3)} + x_{4} \right]$

or,

$\overline x^{(4)} = \frac{3}{4} \overline x^{(3)} + \frac{1}{4} x_{4}$

This leads to a well-known formula for recursively computing an average:

$\overline x^{(t)} = \frac{t-1}{t} \overline x^{(t-1)} + \frac{1}{t} x_{t}$

where t is the number of observations. It says that the mean at date t is a weighted average of the previous mean, and the current (date t) observation.

This is all well and good if the population average is constant. But what if the population average changes periodically. If we knew when these changes in population average occur, we would simply discard all the old observations, and start computing the average afresh. When we don’t know when changes in the population average occur, an alternative approach is to apply a constant “gain” or weight to new observations:

$\overline x^{(t)} = w x_{t} + (1-w) \overline x^{(t-1)}$

where $w$ is the constant weight.

Application: Trend inflation

The discussion above suggests measuring trend inflation via

$\pi^{T}_{t} = w \pi^{(1)}_{t} + (1-w) \pi^{T}_{t-1}$

In words: trend inflation is a weighted average of the current one-month inflation rate (with weight w), and the previous trend inflation rate (with weight 1-w). Solving this equation backwards gives

$\pi^{T}_{t} = w \sum_{j=0}^{\infty} (1-w)^{j} \pi^{(1)}_{t-j}$

That is to say, the measure of trend inflation at t is a weighted average of all past inflation rates, and that the weights decline geometrically with time. Put differently, there is a smooth drop off in the importance attached to previous inflation rates. By way of example, for w=1/3, the weight associated with the current inflation rate is 1/3 = 0.333; with the previous month’s inflation rate, 2/9 = 0.222; with the inflation rate 2 months ago, 4/27 = 0.148; and with inflation 12 months ago, roughly 0.00257 — very small.

Our new measure of trend inflation

The figure below plots our `constant-gain’ measure of trend core PCE inflation for a weight of 1/3 on the latest observation, along with the monthly, 3-month, and annual inflation rates. Relative to the 3-month inflation rate, this measure of trend inflation is somewhat smoother while still responding in a timely fashion to apparent changes in trend inflation.

November PCE Inflation

Posted on December 29, 2023 by Paul Gomme

Bottom line: core PCE (Personal Consumption Expenditure) inflation is down. The monthly annualized inflation rate fell from 1.8% in October to 0.7% in November; the year-over-year rate fell from 3.4% to 3.2%; and our preferred three month annualized rate fell from 2.3% to 2.2%. Ignoring the very noisy monthly rate, these declines are in keeping with our “prediction” of small changes in core PCE inflation based on the earlier CPI (Consumer Price Index) report for November.

Looking at overall PCE price inflation, the three month annualized rate plunged from 3.1% in October to 1.4% in November; the year-over-year rate fall was more modest, from 2.9% to 2.6%. These declines are in line with those of the earlier CPI report.

Given the continued decline in almost all measures of inflation it seems that the Fed will be looking closely at the “real” side of the economy. In fact, the recent revision of GDP by the BEA showed that the third (and final) estimate came in at 4.9%, down from 5.2% in the second estimate. According to the BEA the downward revision primarily reflected a decline in consumer spending, from 3.6% to 3.1%.

In its most recent announcement, the Fed noted,

Recent indicators suggest that growth of economic activity has slowed from its strong pace in the third quarter. Job gains have moderated since earlier in the year but remain strong, and the unemployment rate has remained low. Inflation has eased over the past year but remains elevated.

The latest revision to the third quarter tells us that the third quarter wasn’t quite as strong as previously reported. The Fed puts a lot of resources into nowcasting the US economy, so FOMC’s statement about slowing growth in the fourth quarter is probably a good read on the economy. The downward revision in the third quarter suggests that the fourth quarter may be even weaker than the Fed thought. With core PCE inflation edging closer to the Fed’s 2% target, and a weaker real side to the US economy, further hikes in the Fed funds rate seem unlikely.

November CPI inflation

Posted on December 14, 2023 by Paul Gomme

According to the latest Bureau of Labor Statistics release, CPI (Consumer Price Index) inflation fell between October and November. While the one month annualized rate rose from 0.5% to 1.2%, the three month rate plunged from 4.4% to 2.2% and the 12 month rate was down marginally, from 3.2% to 3.1%.

Core CPI inflation was unchanged at the three month (3.4%) and 12 month (4%) horizons; the one month rate rose from 2.8% to 3.5%.

The FOMC (Federal Open Market Committee) focuses on inflation as measured by the core PCE deflator. However, November data for that measure of prices will not be released for two weeks. The scatter plot below shows that there’s a positive correlation between 3-month core CPI inflation and 3-month core PCE inflation. Given the marginal declines in 3-month and 12-month core CPI inflation, our best guess is that the corresponding core PCE inflation measures will also fall slightly. With the October 3-month core PCE inflation rate having come in at 2.4%, prospects look promising for core PCE inflation to settle in near the Fed’s 2% target.

The Federal Reserve held the policy rate steady and the median projections pointed to three rate cuts in 2024 and more the next few years, ending with: 4.6% in 2024, 3.6% in 2025 and 2.9% in 2026. The financial markets went bonkers: Dow up 500 points crossing the 37,000 mark to set a record.

October PCE inflation and GDP revision

Posted on December 2, 2023 by Paul Gomme

On November 30, the Bureau of Economic Analysis (BEA) released PCE (Personal Consumption Expenditure) data for October 2023. The BEA notes a small monthly change in the PCE deflator (0.6% at an annual rate, down from 4.5% in September), and that the 12-month PCE inflation rate came in at 3.0% (down from 3.4% in September). These numbers largely mirror the earlier CPI (Consumer Price Index) release: the annualized monthly change fell from 4.8% to 0.5%; the 12-month rate from 3.7% to 3.2%. We prefer to look at the 3-month annualized inflation rate which also fell, from 3.7% to 3.2%; CPI inflation fell from 4.9% to 4.4%.

The cognoscenti know that the Fed’s preferred inflation measure is so-called core PCE inflation (taking out the food and energy components). By this measure, the monthly inflation rate fell from 3.8% to 2.0%, a larger decline than recorded by core CPI (3.9% to 2.8%). The 12-month inflation rate fell by 0.2 percentage points, to 3.5%; core CPI inflation fell by 0.1 percentage point to 3.0%. While our preferred 3-month annualized inflation rate fell, it was essentially unchanged at 2.4%. In contrast, the 3-month annualized change in core CPI rose in October, from 3.1% to 3.4%

In summary, the PCE inflation numbers for October confirm what was seen in the CPI inflation reported about two weeks earlier: inflation is down. How much depends on which series you focus upon. Keeping in mind that CPI inflation tends to run about 0.5 percentage points higher than PCE inflation, the data for October suggest that the US economy is approaching the Fed’s 2.0% inflation target.

Gross Domestic Product (Second Estimate)

On November 29 the BEA announced that real GDP for Q3 was revised up from 4.9% to 5.2%. While revisions to nonresidential fixed investment and state and local government spending were the leading causes of the increase, consumer spending was revised down.

Policy outlook

Given the continued decline in the inflation numbers and the continued strength in the output numbers, it appears the economy has digested the record increases in the Fed Funds rate without roiling the real side of the economy. There seems little doubt at this point that Fed policy is achieving its inflation reduction goal and may have reached the peak of the Fed Funds rate during this cycle. That is, nothing in the data points to the need for further increases in the rate and the market is suggesting some rate declines in 2024.

September CPI and PPI

Posted on October 12, 2023 by Paul Gomme

The recently released CPI (Consumer Price Index) numbers for September are a bit of a mixed bag for the inflation outlook. Our preferred 3-month annualized change in CPI rose from 4.0% in August to 4.9% in September. However, the monthly inflation rate fell from 7.8% to 4.9% at an annual rate. On a year-over-year basis, CPI inflation was essentially unchanged at 3.7%.

Those who prefer core CPI also confront a mix. On a 3-month basis, core CPI inflation rose form 2.4% to 3.1% (annualized) and the monthly inflation rate was up from 2.4% to 3.1%. On the other hand, the 12-month inflation rate was down from 4.4% to 4.1%.

Producer Price Index (PPI)

October 11 saw the release of PPI data for September. While the monthly rate of PPI inflation fell, from 9.4% to 6.3% at an annual rate, the 3-month rate rose from 5.6% to 7.7% while the 12-month change was up modestly, from 1.9% to 2.2%.

For what it’s worth, the monthly change in the personal consumption component of PPI fell from 39.2% to 16.9% (annualized) while its 3-month inflation rate rose from 15.2% to 19.3% (also annualized). On an annual basis, this measure of inflation rose from 1.4% to 2.1%.

Policy Implications

To be sure, there is good news from the CPI report: On a monthly basis, overall CPI inflation is down while the annual inflation rate is unchanged. Core CPI inflation is down at on an annual basis, but not at shorter horizons. However, both CPI and core CPI inflation are running hotter than the Fed’s 2% inflation target (granted, for (core) PCE inflation). PPI inflation tells much the same story as CPI inflation: down on a monthly basis, but up when measured over longer horizons. However, it’s not clear that PPI inflation signals future CPI inflation — particularly for the PPI for personal consumption. It seems unlikely that the PPI and CPI releases for September will change policyholders’ predilections.