The third-quarter numbers are on the books, and business travelers' ground transportation preferences have still not found equilibrium.

Ride hailing pierced the 50% market share level for the first time in the U.S., according to business expense software provider Certify.

Lyft and Uber accounted for 52% of the ground transportation market share in the quarter, up from 49% in the second quarter and just 34% a year earlier.

Meanwhile, taxis fell to just a 12% share of business traveler wallets among Certify customers, down from 22% a year earlier.

Share of Business Ground Transportation by Mode Among Certify's Client Base

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Source: Certify

Taking rental cars our of the equation, Uber's U.S. share has increased from 14% in the first quarter of 2014 to 76%. Lyft continues to be the fastest grower in percentage terms, but Uber still gained more share in the third quarter.

In the three-way comparison, taxis dropped below 20% market share in the U.S. for the first time, representing just 18% in last month (see chart below).

Since the first quarter of 2014, Uber's market share has increased to 74% in Boston from less than 10%, almost 54% in Chicago from 8% and 54% in New York from 9%. The sequential share losses for taxis in Chicago and New York were both near 10% in the third quarter.

Share of U.S. Business Traveler Trips in Certify's Client Base

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Source: Certify

The core problem for taxis is stark and remains daunting: Ride-hailing is both cheaper and rated as a higher-quality service experience than taxis (see table). Decades without competition left taxi medallion owners and drivers flat-footed when regulators suddenly allowed innovative competition into markets.

Customer Ratings and Average Trip Costs

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Source: Certify

Sequential share gains were observed for Uber alone versus taxis in all major cities except San Francisco, which at just a 6% market share, may have reached equilibrium (see chart below).

As noted previously, New York showed no share loss versus taxis in the second quarter after a 16% sequential drop in the first. The downward trend resumed in the third quarter, with an 8% drop.

Uber Business Traveler Share Gains: Third Quarter vs. Second Quarter

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Source: Certify

New York is the most insulated taxi medallion market in the country, owing to the long history of street hailing, high population density and many decades of population growth without a commensurate increase in taxis on the road.

But the introduction of ride hailing has still had a devastating effect. Trips and meter revenue data in New York continued to show significant year-over-year declines through July (see chart).

NYC Year-Over-Year Percentage Change in Yellow Taxi Trips and Meter Revenue Since 2012

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Source: Taxi & Limousine Commission

The prices at which medallions have changed hands in Chicago and New York reflect the declines in taxi cash flows and the elimination of taxi exclusivity (see chart). In New York, independent medallions and corporate (mini-fleet) medallions are down about 45% so far, while Chicago medallions are down 80%.

Taxi Medallion Transfer Price Trends in Chicago and New York ($000's)

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Sources: TLC and City of Chicago

Third-quarter financial reports haven't yet been released for the banks and credit unions most heavily exposed to taxi medallion loans, but the data through the second quarter show that loan performance, as one would expect, has continued to deteriorate with the breakdown in taxi medallion cash flows and values (see chart).

Medallion Financial has more than twice its book value tied up in taxi medallion loans and owned medallions and nearly half its managed assets. It recently cut its quarterly dividend by 80% and has seen its stock price drop 50% since July.

Business travelers tend to be earlier adopters, and thus their behavior leads that of the broader consumer population.

As such, the Certify data may suggest that market share gains for ride-hailing companies still have legs.

Equilibrium will eventually arrive, and taxis aren't going away. But the legacy debt service costs of taxi medallions purchased at much higher prices are under intense pressure already and will only get worse as cash flows for taxis continue to drop.

That isn't good news for taxi medallion owners or the banks that financed those purchases.

Credit Union Taxi Medallion Loan Performance Trends

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This article is commentary by an independent contributor. At the time of publication, the author held no positions in the stocks mentioned.