Political Calculations
Unexpectedly Intriguing!
16 August 2022

According to atmospheric carbon dioxide concentration data collected at the remote Mauna Loa Observatory, Earth's economy continued to cool in July 2022.

That outcome can be seen in the latest update to Political Calculations' chart tracking the pace at which CO₂ accumulates in the Earth's air.

Trailing Twelve Month Average of Year-Over-Year Change in Parts per Million of Atmospheric Carbon Dioxide, January 2000 - July 2022

A falling rate of carbon dioxide accumulation in the atmosphere corresponds to falling levels of economic output. It also occurs as China's economy strengthened following the lifting of its government's zero-COVID lockdowns in several regions and as the U.S. economy likely continued shrinking or stagnating in real terms. The falling rate of CO₂ accumulation points to the established negative trend in the U.S. economy more than offsetting China's economic rebound.

All in all, it's pretty amazing what you can see about the global economy from the side of a remote volcano!

Mauna Loa Observatory at Sunset - Source: NOAA - https://www.esrl.noaa.gov/gmd/obop/mlo/pictures/sunsetmaunaloa1.jpg


National Oceanographic and Atmospheric Administration. Earth System Research Laboratory. Mauna Loa Observatory CO2 Data. [Text File]. Updated 5 August 2022. Accessed 5 August 2022.

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15 August 2022

After dipping nearly 23 points from its previous week's close, the S&P 500 (Index: SPX) jumped 2.1% on Wednesday, 10 August 2022 after the Bureau of Labor Statistics reported inflation slowed in July 2022. The index went on to reach 4,280.15 by the end of trading on Friday, 12 August 2022, nearly 3.3% higher than where it closed a week earlier.

In doing that, investors fixed their attention more fully on the distant future quarter of 2023-Q1 in setting current day stock prices. The latest update to the alternative futures chart shows that development.

Alternative Futures - S&P 500 - 2022Q3 - Standard Model (m=-2.5 from 16 June 2021) - Snapshot on 12 Aug 2022

This week's inflation news suggests the Federal Reserve's campaign to slow inflation by slowing the economy is finally having its desired effect. Investors are now looking at 2023-Q1 as the quarter in which the Federal Reserve's ongoing series of rate hikes will peak.

That can be seen in how the CME Group's FedWatch Tool projections of the Fed's future interest rate hikes have changed. Investors are now anticipating a half point rate hike in September 2022 (2022-Q3), down from the three-quarter point rate hike they anticipated last week. The FedWatch tool indicates it will followed by another half point rate hike in November (2022-Q4), then a quarter point rate hike in December (2022-Q4), which may now mark the end with the Fed's target Federal Funds Rate topping out in the 3.50-3.75% range. After that, FedWatch tool anticipates it will hold that level through July 2023, but with a growing likelihood of rate cuts as more time passes and as economic growth slows.

More stuff than that happened during the week that was. Here's our recap of the otherwise quiet news week's market-moving headlines:

Monday, 8 August 2022
Tuesday, 9 August 2022
Wednesday, 10 August 2022
Thursday, 11 August 2022
Friday, 12 August 2022

The Atlanta Fed's GDPNow tool's forecast for real GDP growth in 2022-Q3 surged to 2.5%, up from last week's projection of 1.4%.

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12 August 2022

There's been a remarkable development in the field of ecology. An established belief that chaotic dynamics are a relatively rare factor in shaping ecosystems has turned out to not be true.

The story of how that discovery was made is just as interesting as the discovery itself. Here's how Quanta Magazine's Joanna Thompson tells it:

Tanya Rogers was looking back through the scientific literature for recent studies on chaos in ecosystems when she discovered something unexpected: No one had published a quantitative analysis of it in over 25 years. “It was kind of surprising,” said Rogers, a research ecologist at the University of California, Santa Cruz and the new study’s first author. “Like, ‘I can’t believe no one’s done this.’”

So she decided to do it herself. Analyzing more than 170 sets of time-dependent ecosystem data, Rogers and her colleagues found that chaos was present in a third of them — nearly three times more than the estimates in previous studies. What’s more, they discovered that certain groups of organisms, like plankton, insects and algae, were far more prone to chaos than larger organisms like wolves and birds.

The signs of chaos had been there all along, lurking within the reams of accumulated ecological data. But earlier researchers had missed it because their models were too simple. It wasn't until Rogers and her fellow researchers applied more complex models that the telltale signs of chaotic influences could be teased out.

The new results from Rogers, Munch and their Santa Cruz mathematician colleague Bethany Johnson, however, suggest that the older work missed where the chaos was hiding. To detect chaos, the earlier studies used models with a single dimension — the population size of one species over time. They didn’t consider corresponding changes in messy real-world factors like temperature, sunlight, rainfall and interactions with other species that might affect populations. Their one-dimensional models captured how the populations changed, but not why they changed.

But Rogers and Munch “went looking for [chaos] in a more sensible way,” said Aaron King, a professor of ecology and evolutionary biology at the University of Michigan who was not involved in the study. Using three different complex algorithms, they analyzed 172 time series of different organisms’ populations as models with as many as six dimensions rather than just one, leaving room for the potential influence of unspecified environmental factors. In this way, they could check whether unnoticed chaotic patterns might be embedded within the one-dimensional representation of the population shifts. For example, more rainfall might be chaotically linked to population increases or decreases, but only after a delay of several years.

In the population data for about 34% of the species, Rogers, Johnson and Munch discovered, the signatures of nonlinear interactions were indeed present, which was significantly more chaos than was previously detected. In most of those data sets, the population changes for the species did not appear chaotic at first, but the relationship of the numbers to underlying factors was. They could not say precisely which environmental factors were responsible for the chaos, but whatever they were, their fingerprints were on the data.

This is exactly the kind of study that spawns new research. The effort to find out what factors are at play and how they interact with each other will shape generations of work in the now understood to be underdeveloped field of ecological population growth dynamics.

We would expect the initial phase of that new work to resemble the equivalent of a design of experiments in statistics to verify which factors are most influential, followed by more detailed studies into the effects of their interactions over time. It's an exciting development for a field that's now coming out of a period of stagnation no one knew it was in as a result of the discovery.

More Information

For some basic information on how chaos can influence ecological population dynamics, we found Numberphile's 19-minute video on the Feigenbaum constant provides a nice introduction to the surprisingly simple population modeling math that produces chaotic outcomes:

For more background, we've also built a tool to model the chaotic growth of the population of a species over time. Our post also features Veratiseum's video exploring the logistic map and its role in the emergence of complexity.

We can also point you to HHMI Bioactive's Population Dynamics simulator, which features a good primer on the simpler logistic growth model math that wasn't capturing the extent of chaotic influences found by Rogers, Johnson and Munch.


Rogers, T.L., Johnson, B.J. & Munch, S.B. Chaos is not rare in natural ecosystems. Nature Ecology & Evolution. Volume 6, pp 1105–1111. (2022). DOI: 10.1038/s41559-022-01787-y.

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11 August 2022

How do big changes in mortgage rates affect new home sales?

That question has become very relevant to the U.S. economy with the Federal Reserve scrambling to contain President Biden's inflation by hiking short term interest rates. Their actions have directly impacted 30-year conventional fixed mortgage rates, which have risen from December 2021's average of 3.1% to June 2022's 5.4% because of the Fed's rate hikes.

That's a big change in a relatively short period of time for mortgage rates. One that's bound to impact the sales of new homes. In our first chart, we've sought to quantify how much that impact might be by plotting the percentage change in year-over-year new home sales against the year-over-year change in mortgage rates using fifty years worth of monthly data.

Change in New Home Sales vs Change in 30-Year Conventional Fixed Mortgage Rates, June 1972 - June 2022

A simple linear regression shows that changes in mortgages rates have an inverse relationship with changes in new home sales. Rising mortgage rates tend to coincide with negative changes in the sales of new homes, while falling mortgage rates coincide with increases in new home sales.

That makes sense because mortgage rates have a direct impact on the cost that homeowners pay on their mortgages. Given the same sale price, higher rates means a higher cost of ownership.

But the correlation between changes in mortgage rates and new home sales isn't as strong as you might think. The correlation coefficient (R²) is 0.182, which is relatively weak. In looking at the chart, it occurred to us that there's quite a lot of noise in the data associated with relatively small mortgage rate changes, which is where most of the changes are concentrated.

What would happen if we simply omitted the data where the absolute year over year change in mortgage rates was less than 1.0%? The next chart shows the results of that analysis.

Change in New Home Sales vs Change in 30-Year Conventional Fixed Mortgage Rates, Omitting Small Changes in Mortgage Rates, June 1972 - June 2022

Here, the correlation shows a moderately strong relationship between these two factors. Interestingly, there's little change in the linear regression itself after omitting the data, which still shows that for a given year-over-year change in mortgage rates, new home sales will move in the opposite direction by 8.5-9.0%. For June 2022, the most recent month for which we have initial data for new home sales, the 2.6% increase in mortgage rates over the past year corresponds to a negative 20% change in new home sales, which is nearly in line with what the linear regression would predict.

There's still quite a lot of noise in the underlying data however, so for us, it's not yet worth developing into a forecasting tool. Moderately strong correlations are mainly good for putting you in the right ballpark, so while they're useful for answering questions like how big mortgage rate changes affect new home sales, they come with a wider than desirable margin of error for telling you the exact change to expect when they occur.

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10 August 2022

For a job market that was reported to be much, much stronger than expected, you wouldn't know it from teen employment data.

To show how unexpected last week's jobs numbers were, here are two headlines from Reuters. The first headline was published the evening before the July 2022 employment situation report was released on 5 August 2022, the second headline was published minutes after the July report hit the wires:

Here's the lead paragraph of the July 2022 report:

Total nonfarm payroll employment rose by 528,000 in July, and the unemployment rate edged down to 3.5 percent, the U.S. Bureau of Labor Statistics reported today. Job growth was widespread, led by gains in leisure and hospitality, professional and business services, and health care. Both total nonfarm employment and the unemployment rate have returned to their February 2020 pre-pandemic levels.

Now, square that with what the Bureau of Labor Statistics reported for teen employment, two-fifths of whom find work in the leisure and hospitality service sector of the U.S. economy identified for its July 2022 job gains, for whom we've updated our teen employment chart:


And also our chart tracking the teen employment-to-population ratio to take any potential changing age demographics into account:


The seasonally-adjusted teen employment data isn't squaring up with the reported increase in payroll employment. Younger teens (Age 16-17) are continuing to see their numbers among the employed fall from their recent peak in April 2022, while older teens (Age 18-19) saw their numbers hold steady month over month. Consequently, the combined total for the full Age 16-19 population continued its downward trend in July 2022.

When you consider that July represents the height of teen availability for employment in the U.S., the falling seasonally-adjusted teen employment figures suggest a developing weakening that contradicts the headline jobs numbers.

Previously on Political Calculations

Here are the other posts in our "Teen Canaries in the Coal Mine" series on teen employment trends, presented in chronological order:


U.S. Bureau of Labor Statistics. Labor Force Statistics (Current Population Survey - CPS). [Online Database]. Accessed: 5 August 2022.

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