i've heard some people say that it would be best to keep the euro and the dollar at a 1:1 exchange rate. why would this be good? why might it be bad?
The Euro is currently at about $1.22. The last time it was significantly lower than this was in late 2003. The last time it was as low as $1.00 was in October 2002. So what you are hearing are proposals for a substantial depreciation of the Euro.
Why do people want this? I don't think it's any more complicated than (1) Europe, like the US, continues to see employment and output held down by inadequate aggregate demand, (2) political elites in Europe (especially Germany) are resistant to any effort to boost either public or private consumption, leaving exports as the only potential source of increased demand, and (3) net exports are assumed to respond to relative prices, and relative prices are assumed to move with exchange rates.
Folks like Dean Baker and Paul Krugman have been making similar arguments for the US -- that given the lack of political support for further expansion of public spending, getting back to full employment will require a big improvement in the current account, meaning a big depreciation of the dollar. (Krugman tends to express this -- unhelpfully IMO -- in terms of Chinese "manipulation" of the yuan-dollar exchange rate, but the argument is the same.) Baker even gives the same figure you're hearing -- 20 percent -- as an appropriate amount for the dollar to fall.
First, since the US and the Euro area are both so large in world trade, it might be hard for both currencies to depreciate simultaneously. This is less of a problem than you might think, since there's surprisingly little direct trade between the US and Euroland -- less than 20 percent of the exports of each go to the other. (The US sells more to Canada's 33 million residents than to the Euro area's 330 million.) But it's still the case that if the Euro is to fall against the dollar while the dollar itself is depreciating, both would have to fall even more against third-country currencies, which might be harder to achieve, and more disruptive if it were.
Second, the two cases are not symmetric. The US is starting from a position of big current account deficits, which have to be financed by large financial inflows which, arguably, contributed to the financial crisis. There is a plausible argument that, given the lack of international institutions to regulate capital flows, stable growth is more likely if countries remain in rough current account balance. So -- by this logic -- an improvement in the US current account wouldn't just increase demand in the US, it would help prevent future financial crises. The Euro area, on the other hand, is in rough balance already -- since 1999, the Euro area has run a current account deficit averaging just 0.2 percent of GDP. So an improvement in the Euro-area current account would mean a movement toward big surpluses, i.e. toward larger trade imbalances that would have to be financed by larger international capital flows. In other words, it would require the Euro area to assume a (larger) net creditor position towards its trade partners, i.e. to recapitulate the dynamic between Germany and Greece, Spain, etc. earlier in this decade. Perhaps the folks you are talking to feel that was a big success?
Third, leaving aside the desirability of an improvement in the Euro-area current account, there's a question of how effective a tool Euro depreciation would actually be to realize it. I don't have any estimates of exchange-rate elasticity for the Euro area handy. But for the US, estimates of import elasticity generally fall between 0.1 and 0.3 and export elasticity between 0.6 and 0.8, meaning that the Marshall-Lerner-Robinson condition is satisfied weakly at best, and a depreciation would produce little or no improvement in the trade balance. Of course the more favorable starting trade balance works in Europe's favor here, making it more likely that a depreciation would improve the current account. But in the absence of concrete evidence for reasonably high exchange-rate elasticities, one shouldn't just assume -- as too many people do -- that exchange rate changes reliably produce the "right" effect on trade.
So those are some arguments against. A few more issues.
One, why parity specifically? The argument one sometimes hears is that the goal should be PPP parity. Personally, I don't buy that either -- it assumes there are no systematic divergences in the ratio of tradable and non-tradable prices between the US and Euroland -- but at least it has some principled basis. The International Comparison Program of the World Bank, which is the main source of PPP estimates, gives a range from $1.08 to the Euro for Germany to $1.25 Euro to the dollar for Spain (price levels vary across the Euro area) but there's no major Euro country for which the PPP Euro is as weak as $1.00, let alone for the area as a whole. So 1 euro = 1 dollar looks like undervaluation by any standard.
Two, is this an argument mainly about the level of the Euro, or is it also about the desirability of fixing the Euro-dollar exchange rate? There's a huge literature on fixed vs. floating exchange rates, which I'm not going to try to summarize here.
Finally, there's the question of how a lower Euro would actually be achieved. For various reasons, I suspect the tool might be lower short-term interest rates, rather than (or in addition to) direct foreign-exchange market intervention. In that case, a policy of weakening the Euro might in effect be an excuse for the ECB to take a more expansionary stance than it is willing to do on domestic grounds. Ten years ago, the ECB's attempts to strengthen the Euro were defeated by the perception that the higher interest rates involved would reduce European growth. (See here.) The opposite could happen now -- lower interest rates, by increasing domestic demand and growth prospects, could increase imports and foreign investment into the Euro area, resulting in the current account moving more towards deficit rather than surplus -- the opposite of the intended result. Which, ironically, would be the one good argument in favor of the policy.