Here’s Tyler Cowen:

Is a strong dollar better than a weak dollar?

Yes, for Americans though not for the world as a whole.  For the relevant thought experiment, assume an exogenous shift in noise trading boosts the value of the dollar.  That increases the wealth of individuals and institutions that are long dollars, and presumably this is the case for this country overall.  If you owned lots of ponies, would you not want the price of ponies to go up?

A weak desire to substitute into imports could blunt this result somewhat.  Or in other words, American tourists will benefit to a disproportionate degree.

I can imagine three scenarios:

A.  The dollar is currently below its optimal value for maximizing the welfare of Americans.

B.  The dollar is equal to its optimal value for maximizing the welfare of Americans.

C.  The dollar is above its optimal value for maximizing the welfare of Americans.

In case A, dollar appreciation makes Americans better off.

In case B and C, dollar appreciation makes Americans worse off.

The probability of case B is roughly 0%. So without knowing anything more I’d say there is a 50-50 chance of Tyler being right. His chance of being right is more than 50% if we can clearly establish the case for some sort of market or policy failure that results in the dollar usually being too weak for optimal welfare.  That’s possible, but it’s not obvious to me exactly what that distortion is.  And if true, it would suggest that “reverse beggar-thy-neighbor” policies might be optimal.

PS.  His noise trading assumption can be viewed as an exogenous increase in dollar demand, not motivated by fundamentals.  One can imagine other ways of getting a stronger dollar, such as a random drop in national saving.  His assumption seems aimed at getting a move in the dollar with the smallest deviation from the “other things equal” assumption.  I think his approach is plausible, and hence I do not object to the thought experiment on “reason from a price change” grounds.

Update:  It just occurred to me that my analysis only applies to tiny changes in the value of the dollar.  For large changes, random moves will push it in the wrong direction more than 50% of the time.