Shiraz Robinson is a grad student in data science at the University of Virginia, who came to our attention shortly after the Christmas holiday for his Merry Christmans equations. Unfortunately, that was too late to feature his tradition of blending math formulas and holiday celebrations together, at least for that holiday, but he's back in time for Valentine's Day with another holiday-appropriate math formula!

Here's the equation, suitable for sharing with that special someone who appreciates math as much as you do! And before you ask, yes, it's safe for work....

x² + [y - (x²)¹^/³]² = 1

While the mathematically inclined will immediately interpret this equation of love, others may need to plot it on a graph to truly appreciate its romantic message. We recommend checking out this GeoGebra version because you can play with the parameters d'amour.

Previously on Political Calculations

• Picking the Right Date for Valentine's Day
• The Indisputable Inter-Age Rule for Dating
• Happy Valentine's Day!
• The Maths of Love
• The Most Romantic Shape in Mathematics
• A Formula for Love
• Conway's Game of Love

The employment situation for U.S. teens was little changed in January 2026.

Overall, the seasonally-adjusted employment of Americans Age 16-19 came in at 5,448,000, which is 38,000 lower than the previous month's figure. The employed-to-population ratio for this demographic correspondingly dipped from 30.8% to 30.6% in January 2026.

Dividing the employment data up between younger teens (Age 16-17) and older teens (Age 18-19), reveals a mixed outcome. Younger teens saw their numbers among the employed increase by 35,000 to a seasonally adjusted 1,973,000, representing 20.9% of the Age 16-17 population. Older teens meanwhile saw their employment numbers drop by 69,000 to 3,478,000 in January 2026, falling from 42.9% to 41.6% of the nation's population of 18 and 19 year-olds.

The following pair of charts presents the latest data for teen employment in the U.S., covering the period from January 2021 through January 2026.

For the entire Age 16 and older population, the number of people counted as being employed rose from a seasonally adjusted 163,992,000 in December 2025 to 164,520,000 in January 2026. Working teens make up about 3.3% of the total number of employed people in the United States.

References

U.S. Bureau of Labor Statistics. Labor Force Statistics (Current Population Survey - CPS). [Online Database]. Accessed: 11 February 2026.

Image credit: Wanted ad on OpenClipArt. Public domain image.

Estimating median household income in the U.S. is normally a pretty boring affair. Since July 2025 however, we've seen a significant divergence in the available monthly estimates, which suggests something not-so-boring is taking place in that data.

One source of estimates is provided by Motio Research as part of the analytical firm's Household Income Series. Motio Research's estimates are developed from income data collected by the U.S. Census Bureau for its monthly Current Population Survey.

Political Calculations generates the other series of timely median household income estimates on a monthly basis. Our estimates are produced using aggregate wage and salary income data published by the Bureau of Economic Analysis and population estimates reported by the Census Bureau each month, which complements the survey-based estimates produced by Motio Research.

Normally, these two sets of estimates come in pretty close to each other, but that changed last year. Starting in July 2025, Motio Research's survey-based estimates notably spiked up above our estimates. What's more, they have maintained that difference through the end of 2025, even as our estimates have plodded along on a much more steady trajectory. This divergence suggests some factor is greatly affecting the survey-based income data, without affecting aggregate earned income data much at all.

There aren't many factors that can have that kind of effect. One that might however points to the Trump administration's efforts to deport the citizens of foreign countries who have been living and working in the United States without fully complying with U.S. laws throughout 2025.

One of the first things the administration did after President Trump was sworn into office on 20 January 2025 was to establish greater control over U.S. borders. That effort has greatly reduced the number of attempted unlawful border crossings. In the months that followed, the Trump administration expanded its efforts to get foreign nationals who unlawfully entered the U.S. or who have outstayed their visas prior to January 2025 to leave.

The administration claims it has successfully removed "nearly three million" such individuals. Over 625,000 of that claimed number is through the Department of Homeland Security's highly visible deportation efforts, while most of the rest has been through "self-deportation", which the Trump administration incentivized with an offer of free travel and a $1,000 cash bonus for foreign nationals to leave if they take the option. At the end of 2025, the administration even temporarily boosted the cash incentive to $3,000 to encourage more self-deportation before the end of the year.

We think these initiatives are affecting the survey-based income data. Assuming that most of those who are being deported or are choosing to self-deport are very low income-earners, their departure from the U.S. is very likely contributing to the apparent boost in median household income captured by Motio Research's analysis. If the incomes of people at the lowest end of the income spectrum are no longer being captured in the survey because they have left the U.S., the median will skew higher in favor of the higher incomes earned by those who are still living and working in the U.S.

At the same time, there would be a small, downward effect on aggregate earned income resulting from the departure of those who had been earning very low incomes. Which is what we see in the data. The aggregate income data shows a slightly slower rate of growth during 2025 than in 2024, which would be consistent with that dynamic.

The following chart shows how Motio Research's and Political Calculations' median household income estimates compare over the four full years from December 2021 through December 2025.

The data suggests the combination of incentives introduced in May 2025 with increased resources for enforcement that were passed by the U.S. Congress in early July 2025 could explain why the two median household income series diverged from July 2025 onward with the patterns we've described.

But would that really affect the survey-based median household income estimates? The answer is yes, given the math behind how medians are calculated as this following video lesson from the Khan Academy demonstrates using a simple example involving golf scores:

Of the two DHS initiatives, the DHS' incentive program for foreign nationals to voluntarily self-deport to receive free travel and a cash reward has been more successful in achieving its objectives. On 21 January 2026, the Trump administration boosted its cash incentive to $2,600 to encourage more such departures.

The standard disclaimer for this kind of analysis is that correlation isn't causation, which is to say there may be factors beyond these contributing to what we observe in the data. Whatever those additional factors might be, they would not appear to be evident in the years preceding these initiatives, which means they would have to have become significant at the same time as the DHS' initiatives. If the hypothesis the DHS' initiatives are behind it doesn't hold, what other factors would be capable of producing the observations we have for the divergence of median household income estimates in 2025?

Image credit: Department of Homeland Security. "Limited Time Offer". Public domain image.

The S&P 500 has sustained a mostly orderly, upward trend since the end of 2023.

That's a really strange thing to consider because the index nearly saw order within the market break down in early 2025. The first leg down toward chaos came with the unveiling of China's DeepSeek AI system on 19 February 2025 deflated whatever bubble had been forming among U.S. tech companies in response to the potential for artificial intelligence technologies. It took a month for the overall index to show signs of stabilization.

The DeepSeek shock was followed by President Trump's 2 April 2025 "Liberation Day" global tariff announcement, which sent the index stocks plunging by a similar amount. Had it lasted longer, the one-two punch of these two hugely negative shocks would have broken the state of relative order that had become well established going into mid-February 2025. But order didn't break down, as the shocks proved to just be short-lived outliers. The S&P 500 recovered from the shocks and has since continued to grow, which you can see in the following chart.

Through Friday, 6 February 2026, we find that period of order has real staying power, despite the stock market's day-to-day volatility.

Image Credit: Microsoft Copilot Designer. Prompt: "An editorial cartoon of a Wall Street bull looking at a chart showing a diagonal narrow channel running from the lower left to upper right that is labeled 'GOOD' with the upper left labeled 'TOO GOOD' and the lower right labeled 'HERE THERE BE DRAGONS'". We made some minor modifications to the chart.

Wall Street bulls got something of a scare in the first trading week of February 2026. After starting the week strong, the S&P 500 (Index: SPX) got clobbered between Tuesday and Thursday before rebounding to end the week at 6,932.30, up 0.24% from where it closed out the final trading week of January 2026.

What clobbered the market in the middle of the week was tightly targeted on companies making big capital expenditures in building out their investments in Artificial Intelligence (AI) technologies. Google (NASDAQ: GOOGL) led the market down early in the week after revealing they were doubling their capital expenditures to $185 billion to support building their AI systems. That was followed up by Amazon's announcement they plan to spend $200 billion this year on its AI infrastructure.

Also during the week, privately held Anthropic unveiled a new generation of its Claude AI system tailored to automate the generation of computer code. That development prompted investors to not just beat the hell out of software development companies but also financial firms that have made large investments in them.

That downward action was mitigated by the end of the week as investors rotated toward dividend paying firms, benefitting the Dow Jones Industrials, which broke through the 50,000 mark.

Overall, the combination of things going on within the S&P 500 was enough to keep it on track with the dividend futures-based model's trajectory associated with investors focusing on the upcoming quarter of 2026-Q2. The latest update of the alternative futures chart shows the S&P 500 has kept within a few percent of that projected level.

Although we've already covered the week's biggest market-moving news, there was more that investors absorbed. Here are those additional headlines:

Monday, 2 February 2026

• Signs and portents for the U.S. economy:
• Oil falls 5% on US-Iran de-escalation
• OPEC+ agrees in principle to keep planned pause in oil output hikes for March, sources say
• Next Fed minion boss wants to shake things up at Fed:
• Warsh 'regime change' faces steep hurdles at sprawling US central bank
• Fed chair nominee Warsh may want smaller Fed holdings, but that's not easy to do
• Bigger stimulus developing in China:
• China's measures to shore up its indebted property sector
• China new home prices rise in January as government signals support, private survey says
• Growth signs developing in Japan:
• Japan's factory activity growth hits near 3-1/2-year peak, PMI shows
• Less bad, but still bigger trouble developing in Eurozone:
• Euro zone factory activity contracts in January but output rebounds, PMI shows
• Euro zone firms see deteriorating profits, ECB survey shows
• S&P 500 flirts with record high; chipmakers and small caps jump
• Slump in commodities rattles global markets
• Gold, silver fall further as CME margin hike stokes selling
• Bitcoin falls below $80,000, continuing decline as liquidity worries mount

Tuesday, 3 February 2026

• Signs and portents for the U.S. economy:
• India-US trade deal slashes tariffs; seen lifting exports, market sentiment
• US to cut tariffs on India to 18%, India agrees to end Russian oil purchases
• India to ramp up purchases of US oil, arms, aircraft
• Oil steadies as investors weigh supply, possible US-Iran de-escalation
• US refiners struggle to absorb sudden surge in Venezuelan oil imports
• Investors ramp up bets on steeper yield curve under Warsh-led Fed
• US homebuilders working on plan to develop as many as 1 million ‘Trump Homes,' Bloomberg News reports
• Fed minions say predicting the future is hard:
• Fed's Barkin says hard to know how long higher productivity will last
• Fed's Miran tells Fox Business he still wants rate cuts this year
• Bigger trouble developing in Japan:
• Japan PM's idle yen comments send finance bureaucrats scrambling
• Bigger trouble developing in Eurozone:
• Euro zone banks tightening access to business credit, ECB survey shows
• U.S. stocks finish lower as Wall Street sells tech despite positive Q4 results and a gold rebound
• Wall Street ends sharply down as traders fret about AI disruption
• Gold heads for biggest daily gain since 2008 as investors step in after steep selloff
• Walmart hits $1 trillion market value, joins club dominated by Big Tech giants

Wednesday, 4 February 2026

• Signs and portents for the U.S. economy:
• Oil prices climb 3% on report US officials reject Iran's request to change location of talks
• US services sector steady in January, supply constraints from AI data centers feared
• Trump says 'not much' doubt interest rates will be lowered, in NBC interview
• US Treasury's Bessent says he was wrong when he said tariffs could be inflationary
• Fed minions told they lost trust of Americans, new minion stops working second job:
• Bessent: Fed lost trust of American people over inflation, threatening independence
• Fed Governor Miran quits White House job
• Bigger stimulus developing in China, signs of growth:
• Automakers in China roll-out longer-term financing plans to spur demand
• China services activity picks up in January, hiring hits 6 month high, survey shows
• BOJ minions wish new Japan PM "good luck with that", growth signs develop in Japan:
• Exclusive: BOJ won't come to the rescue of a Takaichi-driven bond rout
• BOJ debated risk of being 'behind the curve' on inflation, January summary shows
• Japan's services activity hits fastest growth in nearly a year, PMI shows
• Bigger trouble developing in the Eurozone:
• Euro zone economic momentum wanes further in January, PMI shows
• Euro zone inflation dips in January as soft patch begins
• Nasdaq, S&P 500 extend losses amid suffering tech trade, weak jobs data
• Wall Street ends down as AI worries slam tech stocks
• US tech stocks hit with fresh wave of selling as chipmaker AMD tumbles
• How Anthropic achieved AI coding breakthroughs — and rattled business
• Nvidia's Huang dismisses fears AI will replace software tools
• Google Goes Wild After Hours After Beating Estimates, Projecting Mindblowing CapEx

Thursday, 5 February 2026

• Signs and portents for the U.S. economy:
• Oil falls more than 1% on easing supply concerns after US, Iran agree to talks
• US job openings drop to more than five-year low in December
• Fed minions thinking about doing nothing with interest rates, even though they understand their policy is restrictive:
• Fed's Cook says it's time to 'wait and see' on rates
• Fed's Cook says policy rate 'ever so mildly' restrictive
• Bigger trouble, stimulus developing in China:
• China faces higher prices for further U.S. soybean buys to please Trump
• JapanGov minion starting to think fiscal discipline might be important:
• Japan PM Takaichi's reflationist aide calls for fiscal discipline
• ECB minions do nothing with Eurozone interest rates, as expected. Also say they’re okay with weaker US dollar:
• ECB keeps rates unchanged, signal comfort with dollar weakness
• Wall Street sells off due to AI capex fears and disappointing jobs data
• Wall Street ends sharply down as AI worries weigh
• Google Goes Wild After Hours After Beating Estimates, Projecting Mindblowing CapEx
• Amazon sees 50% boost to capital spending this year; shares tumble
• Silver tumbles, oil drops in commodity sell-off

Friday, 6 February 2026

• Signs and portents for the U.S. economy:
• Oil prices stable after U.S. and Iran hold nuclear talks
• Interest rate outlook comes under scrutiny next week with jobs, inflation data on deck
• Anthropic’s breakout moment: how Claude cracked AI for business
• Fed minions see weak labor market as giving room for rate cuts:
• Exclusive: Fed's Daly sees labor market vulnerabilities, room to cut interest rates
• Fed's Daly says job market feels 'precarious,' eyes rate cuts
• Fed's Jefferson cautiously optimistic about economy, sees job market stabilizing, inflation falling
• Bigger trouble developing in Japan:
• Japan's biggest banks ready to increase JGB holdings despite growing losses
• Former Japan currency chief says FX intervention should be backed by rate hikes
• ECB minions see bailouts as growth opportunity; Eurozone minions see crypto-Euro as key to their growth:
• ECB's safety net is part of EU plan to court new allies
• Exclusive: Euro zone ministers to weigh euro-stablecoins, more joint debt issuance to boost role of euro
• Dow reaches 50K, ends at record high as U.S. stocks rise on NVDA lift
• Dow closes above 50,000, Nvidia soars as traders focus on AI spending
• Nvidia leads chip stocks higher as broader market gains after software sell-off
• Gold rebounds as volatility continues; exchange operator CME again raises margins

The CME Group's FedWatch Tool continued projecting the Fed will keep holding the Federal Funds Rate steady until 17 June (2026-Q2) when it forecasts a quarter point rate cut. The tool anticipates another quarter point reduction on 16 September (2026-Q3). The expected timing of both these projected rate cuts have held steady for the last several weeks.

The Atlanta Fed's GDPNow toolestimates real GDP growth in the U.S. during 2025-Q4 is unchanged at +4.2%, with no updates in the last week. Updates are on tap for the upcoming week.

Image credit: Microsoft Copilot Designer. Prompt: "An editorial cartoon of a young Wall Street bull who is shocked and scared after a jack-in-the-box pops open to show a bear holding a sign that says 'AI CAPEX'".