# How would inflation in the U.S. affect dolarized countries

Today I was reading about climbing inflation in the United States, so it got me wondering how would that affect (if at all) an small economy with the U.S dollar as its official currency.

As a bit of background, my country changed its currency for the U.S dollar around 20 years ago amidst an inflationary crisis that caused massive migration and other big problems.

So far, the main argument to keep our economy dollarized, -instead of having our own currency and the ability to depreciate it to be more competitives, etc.- has been that this provides a kind of cap to our inflation rate, which has made the policy quite popular given our recent past.

However, as a complete layman in Economics, I was wondering if a large inflation of the U.S dollar would have an impact over a small (dependent on commodity exports, quite informal, etc.) dollarized economy regardless of its government policies, or it would not be influenced at all. If the impact was inevitable, would there be some policy this country could take to reduce the damage?

Edit: The main effect I was thinking about is inflation itself, meaning a hyperinflation (taking it to the extreme) in the U.S. dollar because of policies in the U.S. would inevitably translate itself as a hyperinflation in the rest of the small dollarized countries or would it be a way of detachment. My country is Ecuador by the way.

$$p_{Ec} = p_{US} − θ_{US} + θ_{Ec} + \epsilon$$
where $$p_{Eq}$$ is price level in Ecuador, $$p_{US}$$ is US price level (determined by equilibrium on USD money market and treated as exogenously given here), $$θ_{US}$$ are structural factors of US economy (e.g. productivity and so on), $$θ_{Ec}$$ structural factors of Ecuador and $$\epsilon$$ are some idiosyncratic shocks.
Assuming structural factors $$\theta_i$$ won't change, the inflation (positive change in $$p_i$$) in the Ecuador should mimic that of the US plus some discrepancy caused by idiosyncratic shocks. For example, if Ecuador will happen to be hit by positive macro idiosyncratic shocks you would expect change in $$p_{Ec}$$ to be slightly higher than in the US, and if negative idiosyncratic shocks you would expect $$p_{Ec}$$ to be slightly lower. Of course, structural factors of US and Ec economy could change as well which could lead to larger differences between inflation rates, but structural factors are typically slow to change.