... but they never seemed to have any impact/effect.

[WilliamTaft]

But when the Wall Street Crash of 1929 struck less than eight months after he took office, Hoover abandoned his ideological opposition to government intervention and tried to combat the ensuing Great Depression in the United States with large-scale government public works projects such as the Hoover Dam.
But the world economy continued to collapse and most of Hoover’s initiatives were ineffective.
He was a firm believer in balanced budgets, as were most Democrats, and was unwilling to run a budget deficit to fund welfare programs, instead increasing taxes on the wealthy, but the budget went into deficit anyway.
Hoover did pursue many proactive Federal policies in his attempts to pull the country out of the Depression, but they never seemed to have any impact.

Source: Herbert Hoover The Great Depression Begins (1929 - 1933), YouTube

What's the difference if I say "effect" in this context?

 

[teechar]

Those words are similar, but note that:
1- "effect" is broader.
2- "impact" can in some contexts have a negative connotation, whereas "effect" is generally neutral.
3- "impact" is stronger/more dramatic than "effect". This point is relevant to the above context.