Wednesday, September 23, 2009

Real Interest Rates and Net Capital Outflow



Last post I was talking about the identity of Net Exports equaling Net Capital Outflow or in fancy math NX=NCO. I stopped the post short because I wanted to talk about real interest rates before proceeding to build a model for how NCO affects NX and vice versa.

Intuitively NCO will be affected by the real interest rate in the domestic country (wherever you are currently) and the real interest rate in the foreign country with whom you are doing trade. But what exactly is the real interest rate and how does it differ from the nominal interest rates? Well to answer the last question first the real interest rate is the nominal interest rate adjusted for inflation. A man named Fisher first studied and brought this effect to the attention of the economic community.

One more thought on why you should care about nominal interest rates versus real ones. Nominal interest rates affect how much interest your money earns over time. Real interest rates however will track how much purchasing power your money gains or loses over time. Its the same as when we talked about inflation here.

To figure out the relationship for real interest rates, nominal interest rates and inflation we will need three variables. Fisher used r, i and π. Basically he said that i =r + π. However, to really get at the derivation we need to add one to each term. So it should be written as

(1 + i)= (1 + r) * (1 +π)

So then depending on what you know it easy to derive the unknown, usually this will be the real rate of interest. So we can put

((1 + i)/(1 + π)) - 1 = r

So if you know that your savings account gained 4 % last year and CPI calculated by the BLS raised by 2%, we can deduce that the real rate of interest is 1.96%. So your purchasing power of your account moving from 100 to 104, really netted you an increase of about 1.96 dollars of increased purchasing power.

Now back to the beginnings of a model. So now we have a model of the the economy where:
Y = GDP
C = Consumption
G = Government Purchases
I = Investments
NX = Net Exports (Exports - Imports)

Y= C + G + I + NX

So before when it was a closed economy we could just state that Savings equals Investment. Now with our new variables, or toys, or tools (which ever you prefer) we should investigate how NCO and NX are affected by real interest rates.

In the early post we reformed our formula to look like this:

Y - C - G = I and S = Y - C - G

but as I said we will now add NX. So it looks like this:

Y - C - G = I + NX

Thus we can state that Savings equals Investments plus Net Exports, or

S = I + NX and we know that NX = NCO, therefore

S = I + NCO

So it becomes apparent that the entire reason we use the term net capital outflow is because national savings will equal domestic investments plus net capital outflow.

We can theorize what happens in some different circumstances. So if Savings is greater than domestic investments, I, then its capital will be exiting the country through NCO. Restated that the country is buying assets abroad. On the other hand when Savings is less than domestic investment it is because foreign capital is helping meet the demand of domestic investment by purchasing our assets.

One last way of viewing this is through the Net Exports account. So if Germany (domestic) is running a trade surplus by selling more goods to foreign countries than it buys (NX +) than its capital must be leaving its country to purchase foreign assets (NCO +). Likewise when New Zealand purchases more foreign goods than it sells(NX -), it must then sell its assets to bring in capital (NCO -).

Finally, we should consider how a current account deficit should work and whether it is a good or bad thing. So the current account deficit occurs when we import more than we sell, thus our net capital account decreases and the current account deficit widens. But there are a couple of variables at play. Is the current account increasing because investment has increased as a percentage of GDP? Or is the current account growing because the government is running a budget deficit, thus dis-saving for the domestic economy. (S = (Y - t - C) + (t - G), where an increase in G keeping everything else static will decrease national savings) Both of these situations put the deficit in completely different lights.

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