NCO and NX correlation. Or, alternatively, One more than the model

Can't wait my next post will be titled economists do it with models. Now though, I have one more idea to bring about and it is pretty much the same idea as real interest rates or real purchasing power. Now it is real versus nominal exchange rates. As a well known economist said Par- tee! (OK it was Bart Simpson)

Nominal exchange rates would be the ones when you check in to a foreign country. I go to Thailand and the bank will give me 33.69 baht for every OG G-Dub I give them. Probably not as there will be a bid-ask spread, so the bank can make their crumbs off of me and some other schnook.

To complicate matters you can express the rate in two ways that both mean the same thing. That is, you can express it in your home currency per foreign currency or you can do it the opposite with foreign currency per your dollar. Unfortunately, places use them interchangeably or if it has become established market practice than it can go either way. If you follow the link you can see that Great Britain's pounds and the European Union's Euros are both quoted as X dollars per 1 unit of either of them. On the other hand most other currencies are quoted as X _____ per dollar.

Now then there is kind of a sticky point which needs bearing out. So if I say that the dollar has appreciated with regard to the Canadian Loonie, that is one dollar will now by more loonies. One could erroneously believe that because you have more loonies you can buy more things, thus the Loonie has appreciated. This is wrong. The fact is that it now takes more Loonies to buy the same American dollar. If you want to remove the dollar from the equation think about it this way. I have an apple grown in upstate NY that I am going to sell to a Canadian. Yesterday I sold an apple for .9 Loonies. Now today because the dollar appreciated, it will cost a Canadian a full Loonie to buy my apple. Thus, the Canadians have lost purchasing power.

Now to determine the real exchange rate we must observe another input, similarly to the example just provided. We need to put goods into the equation. So the Canadian from above is considering purchasing an apple. He can buy one from a Canadian farmer or an American one, and both apples have the same quality. To determine which price is best he must Use this formula:

Real exchange rate = (Nominal Exchange Rate x Domestic Price)/Foreign Price.

Let us state that the nominal exchange rate is 1.1 Loonies per dollar, the price of the Canadian apple is 1.0 and the American apple is 1.23.

Entering those variables into the equation we find:

Real exchange rate = (1.1 x 1)/1.23 = 0.89 Canadian apples per American apple. This real exchange rate will decide how much a country imports and exports. That is, economists look at price levels on a whole to decide how exchange rates should move to reflect the underlying trading reality.

So if you were interested in taking a medical vacation to Thailand, you might base your decision by using the real exchange rate. You would compare the price of a surgery stay in your hometown measured in dollars and compare it to the cost of the medical stay in Thailand in baht and then include the exchange rate between the two countries.

An interesting side shoot of this has been work done by The Economist magazine. They have what they call the Big Mac index. Positing that McDonald's is a large multinational and that the inputs to a Big Mac are the same the world over, the Big Mac Index should work to predict real exchange rates and tell you what countries' currency is over or under-valued.



So what this chart does is tell you America is the base case. A Big Mac costs $3.57 locally. It then compares the price in local currency and then it does the conversion for you by using the local currency price and converting it into dollars per the exchange rate. This can then be compared to the actual exchange rate for nationwide goods/services giving the reader a proxy for over and under-valued currencies. As of this edition of the index July 16, 2009 the worst place for Americans to spend their dollars is in Norway or Switzerland whose currencies are overvalued by 72 and 68%, respectively. The best places to spend your Uncle Sam's would be in Asia with Hong Kong, China, Malaysia and other leading the pack.

One reason this occurred in such a specific region, excluding the Ukraines of the world, it is theorized is that China pursues a mercantilist trade policy to keep its currency value down (dollars can buy more Yuan than they should) and other mercantilist countries, like the rest of Asia follow suit. This creates a large instability because to keep these currency valuations down the countries respective NCO must follow their NX up. Thus, they must purchase lots of US dollars. This intertwines the economies of Asia and America to a degree with which a contortionist could be proud.

These last three paragraphs and the chart have been using an idea called both purchasing power parity and the law of one price. I start with the latter.

The law of one price states that goods traded in different places must be priced the same otherwise arbitrageurs would buy in the cheaper market and sell in the other market. Imagine a tycoon buying up Big Macs in China to ship them over to the US. Of course, there is more to the argument than that, prices can differ slightly as there would be shipping and spoilage charges incurred in practicing this arbitrage. Because of the law of one price, which applies to currencies as well as Big Macs, it follows that a US dollar should trade for the same in all markets and we reach purchasing power parity. From these two ideas we can then see that nominal exchange rates should reflect the price levels ratios of any two countries.

One interesting fallacy that can be exposed in this model is expressed in the following idea first proposed by Larry Summers. People get so tied up into this idea of parity that imagine we have two bottles of ketchup that measure 12 ounces a piece. Then we have a third ketchup bottle from the same brand that measures 24 ounces. Economists will get so caught up in making sure that the two smaller bottles price together reflects the cost of the larger bottle. This causes a problem in that ... can you guess ...

that one is not looking into whether the input prices are over or under-valued. This is especially prevalent in financial assets and may be the reason we had such a spectacular blow off in 2008 in the financial sector. Everyone kept taking note of the fact that one house with 2400 square feet cost exactly double a house with 1200 square feet keeping all other factors constant. No one asked whether the price of the smaller home should have been selling for 3 times as much as the place could be rented for over the period of the mortgage.

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.

NX, what I've been missing

So, quite a few of my posts were about the model of the economy with no imports or exports. This was so that I could more easily investigate nuances of taxation, savings and investments. However, as most economies are not closed off to each other the model is only good for introductory looks at an economy. So to add to our burden we must now investigate the flow of goods and its effects on money and monetary policy.

1st the basics
Exports - goods/services produced domestically that are sold to foreign countries
Imports - goods/services produced abroad and consumed domestically.
Net Exports - the positive or negative value when comparing a country's imports and exports. If it imports more than it exports it has a trade deficit.

Conversely, if it exports more than it imports it has a trade surplus. This is called a country's trade balance. There are numerous factors that affect why a country should run a deficit or surplus some include:

• exchange rates
• tax policies
• wealth of citizens
• price of goods
• and, preference of citizens

The above chart shows the US trade balances from 1960 to 2008. The blue area is when the US ran a trade surplus and the red area is when it has run a trade deficit. The purple area is the null area where imports and exports equal each other. (Also in later years it is merely the exports as imports dwarf exports from 1976 onwards.) It is plainly obvious that the trade has become an increasingly large proportion of the economy. It is also true that the imports have become a larger portion of the economy than exports, you can draw your own reasons from the ones listed above as to why imports have grown more rapidly than exports.

Most economists would posit that trade has increased because of the better supply chains that have been initiated from standardized Twenty-foot equivalent units, that can be transferred onto trains, ships and trucks almost effortlessly, to universal product codes have helped make the world a global economy. Telecommunications and technology have intertwined to support the logistics of multinational corporations. Increasingly technocrats have listened to economists' advice that free trade will bring gains to all sides. All have contributed to why trade has grown to a larger portion of GDP.

There is another way that countries trade with each other and it is with financial instruments. A term called net capital outflow (NCO) works exactly like NX. So instead of an import it would be a purchase of a financial asset by a foreigner; conversely a purchase of a financial asset by a US citizen would be an export. So when a foreigner purchases either a factory or US treasury bill that represents a decrease in net capital outflow. The purchase of a factory would be a foreign direct investment and the purchase of the treasury security would be a foreign portfolio investment.

The reason it is important to consider NCO and NX together is that they form an identity, that is, NCO=NX and vice versa. They must equal each other. Here is an example to help think about why it is so.

Say you purchase a BMW from Germany, you even make a vacation of it. So you bring an import to the United States and in exchange you give the German company US dollars. That is net exports have decreased for the United States and decreased the net capital outflow.

Now BMW cannot use the US dollars to pay their employees. So maybe they would instead use their new dollars to buy an automobile assembly robot in the United States. This would increase the net capital outflow of the US and also increase exports, thereby increasing NX.

Tomorrow I will explore how this affects savings and then work on a model to show how this is affected by real interest rates.

Serial Inflation or the cost of inflation

Everyone knows that inflation is a bad thing; deflation may be worse but neither is desirable. What central banks shoot for is price stability, so that businesses and consumers can plan accordingly to maximize their utility. However, it was Mark Twain that said “It ain't what you don't know that gets you into trouble. It's what you know for sure that just ain't so.”

What do I mean? Well, inflation may be the cruelest tax but the drop in purchasing power may not be all that it is cracked up to be. See that is why people dislike inflation. It is ingrained in their head that if the dollar loses value, that their dollar purchases less goods and services. This is a bad thing, no? Here is their evidence.


Pretty rough. Since the advent of the Federal Reserve, the private bank has eroded each Americans wealth by 93.4%. The thinking described must advances a theory that American standard of living has dropped in step with the fall of the dollar. However, I don't remember seeing any HDTV, MRI machines, air conditioners during the 1913 period in my history textbooks. Not seeing these items is not direct proof per se, but until I see one I will assume they weren't prevalent, at least to the degree that they are today.

Another way of saying this would be that, the dollar is used to purchase goods and services. People provide goods and services at their job. Thus, the price level rising (the dollar's value declining) tends to net out because the inflation that drives down the purchasing power is also being inflated in the person's offered labor.

One last way of putting this is by numerical example. The CPI index states that inflation rose by 3% last year, (made up.) Last year, you received a 3% raise, so net net you are even. You have not lost purchasing power; your yearly bonus helps safeguard your standard of living.

**Addendum**
I re-read my post and it makes sense but I wanted to add flavor and nuance to the argument. So I needed a multi-year argument to further convince you. So I went and grabbed the Census department's median income in current (nominal) dollars and in real terms as well. I also added the BLS CPI price levels matching set of data from 1975 to 2008 year end.

So first I took a compound annual growth rate for both series, to bring about a unified number so that an apple to apple comparison could be made. To do this I took the last year of my data for each set and divided it by the initial year. I then raised it to 1 over the number of years difference, which is 1/33 years. I then subtracted by one to end up with a annual growth rate percentage. For median income it was 4.49% and for the CPI price level data it was 4.39%. What these two figures mean is that over the period between 1975 and 2008 on average, that is linearly, median income outpaced inflation (what the CPI price levels measure.) You may then draw the conclusion that standards of living have risen because income has outpaced inflation.


If you still do not believe me the Census bureau in the same data set provides the median income in real terms. From 1975 to 2008 the "real" amount of annual wealth accumulation has risen from $42,936 to $50,303. Meaning most households can purchase more than they could back in 1975, thus their standard of living has increased. (Note: I use median income because average income can be skewed by the Bill Gates-s of the world. Ever hear the quip, when Bill Gates walks into the room on average we are all billionaires?)

Though the fallacy should relieve you, inflation still does have an effect and can lower your standard of living in other ways. One is called shoe leather cost. It is the affect, where you have to change your paycheck into a store of value. That is instead of placing your paycheck into a demand deposit account, you because of your knowledge of inflation instead place your funds into a money market account. Now though you have to transfer funds back to the demand deposit account when you go to the restaurant or take the children to the amusement park. This isn't bad in the United States. However, imagine you were in Zimbabwe last year where inflation ran at 36,000%. The cost of your meal would be more the longer you ate, so I am positive that the Zimbabwe equivalent of McDonald's did brisk business last year.

Another is an effect called the menu effect, after restaurant menus. It means that businesses set prices and are reluctant to change them. Again our low inflation environment makes the effect a bit myopic but if inflation ran at a higher rate, businesses would be forced to change their "menu" more often so as to not be burned by their margin contraction as their inputs cost more while their own prices stayed the same.

Finally, there is one last way in which inflation can hurt you and it is in investing. Hypothetically, you buy a share of GM in 1971 for 100 dollars. Now almost 40 years later, after counting for splits the stock is worth 300 dollars. You would be assessed a capital gain tax on 200 dollars at a 20% rate. Here is where inflation stings. Look at the chart above. The dollar was worth 24 cents. Now it is worth 4.6 cents. It has lost almost 6 times its value. Meaning your 100 1971 dollars could buy almost 600 dollars today. So in fact your capital gain is not real, you have lost 50% of your money over the time period. Yet you are still taxed 40 dollars because taxes are assessed nominally and not indexed. Ouch!