How many cats are prowling outside in your neighborhood? Or in your city? Or in your country?

That's a remarkably difficult question to answer, where the Wall Street Journal indicates the best estimates scientists have of the outdoor population of Felis catus, better known as the domestic house cat, are very far from being either accurate or precise:

In the U.S., estimates range from 40 million to 60 million; 30 million to 80 million; and 20 million to 120 million.

"It's a huge window," said Tyler Flockhart, an ecologist with the University of Maryland Center for Environmental Science. "And they're not even estimates. They're expert guesses based on very limited data."

At the end of the day, he said, scientists have to shrug and say this is the best information they have.

It's an important question to answer because Felis catus is a predator species, one whose prey includes birds and small mammals. To the extent that these hunted species overlap the list of endangered or threatened species, knowing the number of outdoor cats would better define the extent to which the populations of endangered animals are negatively impacted by their hunting habits, which in turn, could lead to more effective conservation efforts.

The WSJ article goes on to describe an effort to get an accurate count of the population of outdoor cats in the District of Columbia, which uses motion sensing cameras to conduct a census of the local cat population during a set period of time.

Accounting for the outdoor cats is the most complex part of the research. The project uses cameras to count cats in a given area over a certain period. Then, using a mathematical formula, the project extrapolates the total number of cats in the area by seeing what portion of the photographed cats show up on camera again.

The article provides the following infographic to describe the math developed by U.S. Geological Survey's Andy Royle to more accurate estimate the population of cats in the surveyed region from the sampling of images obtained by the network of motion-sensing cameras:

We built the following tool to do that math, so if you want to estimate the size of a population you're interesting in tracking from a sample of it observed over a limited period of time, you can do the same math. If you're accessing this article on a site that republishes our RSS news feed, you can choose to either click through to our site to access a working version of the tool or to view a static screen shot of the tool with its results for the default input data.

The results of running the tool with the default input data confirms the results presented in the WSJ's infographic, but the cool thing about it is that the math can be applied to estimate the size of other difficult-to-measure populations, such as the endangered species that are believed to be negatively impacted by predatory house cats. Or even the total unsheltered members of a region's homeless population, whose numbers are currently counted in the U.S. during a single night in January each year by community canvassers.

Alone, such a canvassing approach is affected by the limitations of the canvassers, who might miss significant portions of the homeless population during the single period where they perform their count, resulting in an undercount in the official figures. Adopting a dual-period measurement approach could provide a better indication of how accurate the canvassers single-period counts are while also leading to a better overall estimate of the total homeless population using this kind of math.

Tim Harford has a second round of his podcast series on the BBC, 50 Things That Made The Modern Economy, which rolling out new episodes weekly. The first season's episodes were collected into book form, where the new second season is extending the list of short stories about technologies that have changed how people live and what they do.

We highly recommended the series, where last week's episode on the humble electronic spreadsheet is a standout among all the episodes of the entire series, which has included tales of items such as the Billy Bookcase and the Index Fund.

What makes the 11-minute episode stand out how it ties into modern concerns of how jobs change when new technologies make old ways of doing things obsolete. What can happen to people when robots can take over their jobs?

It's not necessarily what you might think, if 40 years of computerized spreadsheets are the example to go by for answering the question. Do check it out!

Meanwhile, if you'd like to find out a little bit more about the early history of the electronic spreadsheet, Business Insider met up with the two guys who invented it!

Previously on Political Calculations

• Elevators that Go Up, Down, Left and Right....
• Jack Bogle on Investing

On 22 December 2017, President Donald Trump signed the Tax Cuts and Jobs Act of 2017 into law. Here's a brief overview of the major changes, which we've condensed from a lengthier discussion at CPA Journal:

Tax Rate Reduction

The linchpin to this tax legislation is a reduction in individual tax rates. While the current number of tax brackets has been retained, each one has been reduced slightly.

• Tax brackets. The brackets for individuals are cut to 10%, 12%, 22%, 24%, 32%, 35%, and 37%. The top tax rate applies to joint filers with taxable income over $600,000 (single filers over $500,000).
• Tax rates for owners of pass-through entities. There is no special tax rate or cap for taxes on pass-through income. There is, however, a new 20% deduction for business income, although many restrictions apply that prevent this break from being claimed by most attorneys, accountants, and many other professionals.
• Capital gains and dividends. The 15% and 20% tax rates on long-term capital gains and qualified dividends have been retained; those in the 10% or 12% tax brackets pay zero tax on these gains and dividends.

Deductions

The personal and dependency exemptions are repealed, while the deduction for student interest that had been slated for repeal is retained. Other changes to deductions include the following:

• Standard deduction. The standard deduction increases to $24,000 for joint filers, $18,000 for heads of households, and $12,000 for other filers; these amounts are indexed for inflation after 2018. [Note: The new standard deduction amounts are nearly double what the previous tax law provided.]
• Itemized deductions. Many of the itemized deduction rules have changed:
• The medical deduction is retained, with the 7.5% of AGI floor retained for all taxpayers for 2017 and 2018. After 2018, the threshold returns to 10% of AGI.
• The cap for deducting mortgage interest for buying or building a home is reduced from the current $1 million cap to $750,000; no interest is deductible for home equity debt.
• The deduction for state and local income, property, and sales taxes (SALT) is capped at $10,000. This is a substantial reduction from the former rule allowing all property taxes, plus all state and local income or sales taxes, to be itemized. Prepaying 2018 state and local income taxes in 2017 will not help; no deduction in 2017 is allowed for such prepayment.

Most Americans would have noticed some of the changes prompted by the new tax law in mid-February 2019, when new tax withholding rules took effect and changed the amount of money they could take home after taxes on their paychecks. But the bigger changes from changes in the standard deductions wouldn't be noticed until they filed their income taxes for 2018, which were due on 15 April 2019.

Tax preparer H&R Block (NYSE: HRB) itemized the overall year-over-year changes that millions of their middle-class household clients who had filed their annual returns by the end of March 2019 were seeing for their annual federal tax bills.

H&R Block data through March 31, 2019 shows the size of its clients’ tax refunds is up 1.4 percent under the first year of tax reform and new withholding tables, while overall tax liability is down 24.9 percent.

As H&R Block notes, that combination of smaller refunds and dramatically lower tax bills (or tax liability, as H&R Block describes it) is directly attributable to the changes in tax withholding rates, which shrank the size of refunds by letting Americans keep more of their pay without giving the U.S. government an overly generous interest-free loan by overwithholding their income taxes throughout the year.

Meanwhile, corporations saw roughly a 30% reduction in their tax liabilities during 2018 as a direct result of changes made by the new tax law.

So what effect did the Tax Cuts and Jobs Act have on the U.S. government's tax revenues? In the following chart, we've calculated the trailing twelve month total of the U.S. government's tax revenues from all its major sources from December 2016 through April 2019, as reported by the U.S. Treasury Department each month.

The trailing twelve month totals gives us a pretty good sense of how tax revenues have changed over all this time while smoothing out month-to-month volatility. What we see is that through April 2019, which captures the majority of tax returns filed for the 2018 calendar year, the U.S. government's total tax revenues from all its major sources is nearly the same as in April 2017, when the old, higher tax rates applied for those filing taxes.

At the same time, we see a shift from corporation income taxes, which decreased, toward individual income taxes, which increased by a similar amount to offset a large percentage of the reduction in corporation income tax revenues. That is at least partly attributable to what businesses did with the extra money they gained from their reduced tax rates, some of which found its way to their employees in the form of bonuses or higher wages, while some found its way to their shareholding owners in the form of higher dividend payments and share buybacks.

These latter two categories would boost the federal government's revenues from individual income taxes through dividend taxes and through capital gains taxes, both of which are reported on individual income tax returns. We'll be curious to see how much the government collected through these personal income taxes when the IRS updates its Statistics of Income to include the details for the 2018 tax year, which will happen sometime in the next two years.

We'll also be interested to see how much additional taxes were collected because of the new cap on the amount of state and local taxes that can be deducted on federal tax returns in 2018, which primarily affects people with high incomes who live in high tax states.

Finally, the U.S. government's tax revenues were boosted during the period in which the Tax Cuts and Jobs Act has been in effect by smaller increases in employee and employer-paid Social Security and Medicare taxes, Excise taxes and Customs Duties (Tariffs).

It doesn't happen often, but sometimes, we find ourselves almost perfectly situated to capture two snapshots in time for the S&P 500 (Index: SPX).

We presented the first snapshot in time early in the morning of Monday, 13 May 2019, where we summed up what had happened to S&P 500 as it had been "knocked about by noisy U.S.-China trade negotiations" during the trading week ending on 10 May 2019 with just two charts and two paragraphs:

The S&P 500 (Index: SPX) set no new records during the week of trading ending on Friday, 10 May 2019, where stock prices mostly appeared to react to the noise generated by trade negotiations between the United States and China.

Overall, the index stayed within the typical range of values our dividend futures-based model would project if investors were primarily focused on the distant future quarter of 2020-Q1. Not uncoincidentally, this period coincides with the expectation that the Fed will next act to cut its Federal Funds Rate during that quarter, according to the latest probabilities indicated by the CME Group’s Fedwatch Tool.

The second snapshot in time comes from the end of trading on Monday, 13 May 2019, when after having been triggered by China's new retaliatory tariffs, investors responded by shifting a portion of their forward-looking focus from 2020-Q1 back toward the nearer-term future of 2019-Q4 and the more negative expectations associated with that point of time in the future. For our dividend futures-based model of how stock prices work, that shift in how far forward investors are looking was sufficient to send the S&P 500 sinking.

Having dropped below the range we would expect the S&P 500 to be if investors were focusing on 2020-Q1 in setting current day stock prices, or rather, the expectations for dividend growth that are associated with that distant future quarter, we would describe the current level of the S&P 500 as being consistent with investors splitting their attention between 2018-Q4 and 2020-Q1.

Not uncoincidentally, the sudden shift toward the earlier quarter of 2018-Q4 coincides with the heightened expectation that the Fed will next act to cut its Federal Funds Rate during that quarter, according to the latest probabilities indicated by the CME Group’s Fedwatch Tool. The following image shows how those probabilities have changed during the course of just one trading day:

As for why investors would suddenly be betting on the Fed cutting short term U.S. interest rates sooner rather than later, the Fed's minions have been priming their expectations for what they would do if the U.S.-China trade war slows the U.S. economy. Here's a sampling of relevant headlines since Thursday, 9 May 2019:

• Fed's Bostic says scheduled tariff hike could fuel inflation
• Tariff tumult boosts view that Fed may cut U.S. rates
• Fed's Bostic says tariff hikes could prompt rate cut if consumers pull back
• Fed can lower rates if U.S.-China trade spat causes slowdown: Rosengren

Now the question is will something happen to shift their attention back toward 2020-Q1 and prompt a rebound in stock prices? Or will they come to more closely focus upon 2019-Q4 and potentially send the S&P 500 down even more? If you can predict which point in time will come to capture the attention of today's investors and can set up your investing strategy accordingly, you could stand to benefit from what a behavioral finance expert like Robert Shiller might call irrational behavior, but which is really anything but.

The S&P 500 (Index: SPX) set no new records during the week of trading ending on Friday, 10 May 2019, where stock prices mostly appeared to react to the noise generated by trade negotiations between the United States and China.

Overall, the index stayed within the typical range of values our dividend futures-based model would project if investors were primarily focused on the distant future quarter of 2020-Q1. Not uncoincidentally, this period coincides with the expectation that the Fed will next act to cut its Federal Funds Rate during that quarter, according to the latest probabilities indicated by the CME Group’s Fedwatch Tool.

In collecting the market-moving news headlines of the second week of May 2019, we've made of point of including U.S-China trade negotiation-related items, although they mostly contributed a lot of noise during the week where the trajectory of stock prices was concerned.

Monday, 6 May 2019

• Oil bounces up on Iran concern after touching one-month low on trade tensions
• Fed flags high U.S. business debt, asset prices in financial report
• Fed's Harker says trade tensions are weighing on U.S. businesses
• Fed's Harker sees downward inflation trend as 'transitory'
• Trade war eruption:
• Trump ratchets up pressure on China, threatens tariff hikes
• Factbox: Tariff wars - duties imposed by Trump and U.S. trading partners
• Explainer: Who pays Trump's tariffs - China and other exporters or U.S. customers?
• Explainer: Counting the cost of the U.S.-China trade war so far
• China considers canceling trade talks with U.S. after Trump vows new tariff hike: WSJ
• China's April export growth seen cooling, imports staying weak: Reuters poll
• China stocks fall most in over three years on tariff threats, yuan tumbles
• China says trade delegation is preparing to go to the U.S.
• Wall St. falls as White House vows to raise China tariffs

Tuesday, 7 May 2019

• Oil ends at lowest in a month on trade concerns, high U.S. crude supplies
• Fed's Clarida says there's no good case for rate hikes or cuts: Bloomberg
• Fed's Kaplan optimistic U.S., China will find ways to tackle trade issues
• U.S.: China reneged on trade commitments, sparking Trump tariff hike
• Wall Street slides as U.S.-China trade fears rise

Wednesday, 8 May 2019

• Oil rises 1% after surprise fall in U.S. crude stockpiles
• Bigger stimulus developing in China:
• Gaining traction: China's factory-gate inflation hits four-month high, food prices surge
• China April exports unexpectedly fall but imports rebound as fresh U.S. tariffs loom
• China launches green subsidies to spur investment in hinterland provinces
• Trade war negotiations heat up:
• U.S. to hike tariffs on $200 billion worth of Chinese imports: Federal Register
• China to retaliate if U.S. raises tariffs as planned: commerce ministry
• Exclusive: China backtracked on almost all aspects of U.S. trade deal - sources
• More of the Fed's minions share their views:
• Fed's Barkin: Low unemployment and interest rates mean low recession risk
• Brainard: Fed should consider targeting longer rates in a future downturn
• Wall St. falls as investors cautious on trade; Intel slides

Thursday, 9 May 2019

• Bigger stimulus developing in China:
• More China policy easing seen as lending slows, trade risks rise
• Getting traction: China's factory-gate inflation hits four-month high, food prices surge
• Noisy U.S.-China trade war negotiations:
• Trump says Beijing 'broke' trade talk deals, pledges to keep tariffs on Chinese goods
• U.S. goods trade deficit with China drops to five-year low
• Fed's Bostic says scheduled tariff hike could fuel inflation
• Oil rebounds as Trump says letter revives China trade hopes
• Trump says he has received 'beautiful' letter from China's Xi
• Wall St. dips as investors await outcome of U.S.-China trade talks

Friday, 10 May 2019

• Oil steady, ends week lower as trade tensions weigh
• U.S.-China trade talks stall over draft deal revisions: sources
• Trump says in 'no rush' for China trade deal, defends tariffs
• Trump says trade talks with China will continue, tariffs may or may not stay
• Chinese vice premier says trade talks with U.S. went 'fairly well': Bloomberg
• U.S.-China negotiators agree to meet again in Beijing: Global Times editor in chief
• Tariff tumult boosts view that Fed may cut U.S. rates
• Fed's Williams says U.S. economy strong despite trade tensions
• Fed's Bostic says tariff hikes could prompt rate cut if consumers pull back
• Wall St. snaps losing streak after Trump's upbeat trade comments

Barry Ritholtz grouped the week's major U.S. economy and markets stories into positives and negatives. Please click through to find out how many there were of each!