Monetary Approach to a depreciating currency I am currently doing some research on the monetary approach to the effects of currency fluctuations on trade balance. It's been a while since I took an int econ class back in the undergrad, so I hope I can glean some understanding from the gods of macroecon. I have a good understanding of the overall assertion being made by this approach (trade balance change dissapates in the LR), but am a bit confused by the details and how equilibria are reached. One of my old textbooks summarizes it as such: when the currency depreciates, money demand shifts up, and rates rise, trade balance improves. In the LR, investors will flock towards the higher rates, and the money supply shifts right, where equilibrium will return to the initial interest rate. This doesn't really make sense to me....


What is causing the currency to depreciate here? When I think of a devalued currency, I think of an expansionary policy/decrease in rates. But here, rates increase due to the depreciation
Where is the deviation from the net zero trade balance and where does it return in terms of the process of the money market changes?
How do foreign investors affect the supply of the currency? I thought that when higher rates existed, that the demand of the currency increased (which would explain why contractionary policy leads to currency appreciation)
More as a question about the theory in general, is there empirical evidence of this? The US has had a trade deficit for a very long time. Does this approach suggest that our net exports should be zero?


Thanks!
Let us call the country with the trade deficit, country A, which is our domestic country. If a country builds up a trade deficit, it is selling less goods to other countries than it buys from them. To do so, A must exchange its currency for foreign currency. This means more demand for the foreign currency and more supply for the domestic currency. More supply reduces the price of domestic currency relative to other currencies. More demand for foreign currency increases their price relaive to domestic currency. All this causes a depreciation of the domestic currency. For more detail on this see, for example, the answer to this question.
Currency values are fundamentally determined by supply and demand for currency (see answer above). Both of those are driven by both the goods and financial markets. So trade deficits have an effect here, as well as investors flocking to higher rates.
Foreign investors both affect and are affected by the exchange rates. If these investors want to invest in a foreign country with higher interest rates, they need the currency of that country in one way or another. So they sell their currency to buy the foreign currency, which like in the answer to 1) will have an effect on the value. Even if foreign investors have the foreign currency to invest, they will need to exchange it at some point in order to consume their earnings at home.
Solid empirical evidence is rather difficult when it comes to long term effects. It is true that the US has had a trade deficit for a long time. However, it is unclear how long a time is a long-run. Furthermore, before having a deficit, the US has had a surplus for a very long time, so it is natural it would eventually have a deficit. Whether this deficit has exceeded past built up surpluses is not necessarily clear.