"It's still consumer driven, and we are seeing that it's still holding up," Abney said on "Squawk Alley." "It may not be as strong an increase as last year, but we still feel pretty good about what we are seeing."
"Of course we'd like to see industrial production and manufacturing increase, but consumer is holding on right now," he added. Consumer activity accounts of about two-thirds of the U.S. economy.
However, the economist behind the University of Michigan's monthly consumer sentiment survey said on Friday, "Despite the high levels of confidence, consumers have also expressed rising levels of economic uncertainty."
The final reading on September consumer sentiment showed a small increase, but a near-record number of consumers cited trade policies as a negative factor weighing on growth.
Meanwhile, the ISM's purchasing managers index fell in September to its lowest reading since June 2009 and the second straight month in contraction. The August contraction ended a 35-month expansion period.
The decline in manufacturing is seen as the latest sign that President Donald Trump's trade war with China is dragging on the American economy. The trade dispute also is considered to be a factor in a broader global economic slowdown. U.S. and Chinese officials are set to resume high-level trade talks on Oct. 10.
At UPS, Abney said the shipping giant is seeing "headwinds" internationally, citing both the trade conflict and worries over Brexit as the U.K. continues to try to negotiate a smooth departure from the European Union trading bloc.
Abney's cautiously optimistic tone, following UPS' better-than-expected second-quarter earnings back in July, contrasts with pessimism at rival FedEx, which last month reported quarterly earnings and revenue that missed estimates. FedEx also lowered full-year guidance for fiscal 2020.
On the post-earnings call with analysts, FedEx Chairman and CEO Fred Smith said, "I think there is a lot of whistling past the graveyard about the U.S. consumer and the United States economy versus what's going on globally."
Shares of UPS and FedEx were under pressure Tuesday in a down market. However, year-to-date UPS stock is up 19%, while FedEx stock in 2019 is down 11%.