This is fairly common advice in the financial/sales world. Closely related, it's common to also hear in salary negotiations, "whoever mentions a number first loses" (e.g., here, or discussed critically at Forbes here).
As an example, Jim Schleckser of The CEO Project, writing at Forbes, suggests a negotiation technique of flinch-reflect-silence:
Flinch: When presented with terms or a price, resist the urge to nod or verbally agree. Instead, exhibit a nonverbal "flinch," such as
an audible "oomph" or a sucking of air through your teeth. This
initial reaction sets the tone for the rest of the negotiation.
Reflect: After flinching, emphasize your astonishment by reflecting on the offer. For example, "Did I hear correctly? $100,000
for this service?" This mirroring technique underscores your
dissatisfaction with the offer.
Go Silent: Following the flinch and reflection, allow silence to fill the room. Silence is a powerful tool. The person who breaks it
often concedes ground, reinforcing the mantra: "Whoever speaks first
loses."
The well-known strategy is somewhat more critically addressed in a Stanford Business Interview here:
Darius Teter: So — true or false: whoever speaks first loses.
Margaret Neal: Well, sometimes.
Turns out that, on average, about 80 percent of folks think that the
better outcome is to receive the first offer and they do so because
they are believing that they get an information advantage. And I may
learn when I receive the first offer that you may value the issues
quite a bit differently than I do, or I might even learn that you have
no clue what you’re talking about. So that’s a reason why you might
receive the first offer. But the counter is also powerful. That is
making the first offer. And when I make the first offer, I get to set
the standard of where we start...
We can see with Google NGram that use of the phrase started around 1970, predating its popularization by Jordan Belfort. The start of the last bump coincides with the release of the movie (2013), while the start of the second-to-last bump coincides with the release of the book of the same name (2007).
Among the earliest uses of the phrase, Google shows examples such as an article from Real Estate Today (1970), Managing Negotiations (1980), The Pelican (a monthly newsletter for employees of the Mutual Benefit Life Insurance Company, 1980), etc.