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The phrase "a downward influence" is correct and usable in written English
It can be used to describe a negative or adverse effect that something has on a situation, person, or group. Example: "The economic downturn had a downward influence on consumer spending, leading to a decrease in sales for many businesses."
Exact(3)
A downward influence is thus exercised on primary product prices.
We have previously found a strong association between patella bone lead and cardiovascular mortality (Weisskopf et al. 2009), which could exert a downward influence on the effect estimates found here, possibly leading to the inverse association with AVCD.
The association with mortality was weaker for tibia bone lead, thus a downward influence on the associations reported here between tibia lead and ECG characteristics is less likely; however, were it to be present, it would suggest that the adverse associations we found would be underestimates.
Similar(57)
In essence, the larger context within which lower-level processes are nested generally exerts a stronger downward influence, while the lower-level variables generally exert a weaker upward influence (Hitt et al., 2007).
The large amount of capital shifted into oil and gas production during shocks—and the very small amount of labor that follows produces a net downward influence on employment, and thus effective demand.
In understanding today's economy, one powerful dynamic cannot be overstated: accelerating technological advances are, paradoxically, exerting a major downward influence on GDP.
After prices have risen for a prolonged period, the bears have sold all their shares, so their downward influence on price is lessened.
Mr. May noted in a report that euro zone inflation "has recently slowed less sharply than that in the U.K. and U.S., perhaps suggesting that the economic slowdown is not having quite the downward influence that we anticipated".
Wu and her research community discovered that the decrease in sea ice cover in the BKS region and the associated warming of the overlying atmosphere by the heat released from the exposed ocean weakens the stratospheric polar vortex, and the "downward influence" from the stratosphere to the troposphere weakens the retaining-wall properties of the AO.
"I believe they influence the whole ethics of an organisation in a downward spiral and influence the people around them," he said.
All this risks creating a downward spiral in British influence, which the country would need to counter by being more effective in the areas in which it remains.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com