**Investments and the Real Interest Rate**

We started out finishing up investments. From the last class, we saw that the investment function for the US, from 1990-2007 (based on my crude analysis) was as follows: I = 6,337 – 83.50r. Thus, I_{0} = $6,337 billion, and I_{r} = $83.50 billion. Here’s the original graph, with the added trend-line:

Based on my crude analysis, and the information from the *Economist *that:

In America politicians and central bankers are focusing on policy stimulus. The Federal Reserve has cut short-term interest rates by 1.25 percentage points in recent weeks, to 3%. [link]

We can actually calculate the change in investment that would result from the decrease in real rates. Firstly, the rate the the Fed controls is not the lending rate. We can use the Prime Lending Rate instead. But is that related to the Fed Funds Rate? Take a look.

There is a clear correlation, and I am assuming that the prime rate = fed rate + 2.5%. In fact, the above figure also shows the relationship between investment (the green line) and the Fed Funds rate (the red line). Based on my crude analysis, my assumption that prime rate = fed rate + 2.5%, we can assume that if the fed decreases rates from 4.25% to 3%, the prime rate will go down from 6.75% to 5.5%. And given this information, we can conclude that investment will *increase* from $6,331.36b to $6,332.41b, a total increase of $1.05 billion.

**Government Spending**

We finally got to looking at government spending today. The key fact about government spending that we must take into account is that of * transfer payments*. These are the payments that are made by the government to the people – like social security, Medicare, etc. We view them as negative taxes. Other than this, we don’t look too deeply into how the government spends its money.

Finally, we look at the last component of GDP – that of net exports. Now, we know that net exports are gross exports minus imports. In mathematical terms, NX = GX – IM. We look at each of the components of net exports individually.

**Gross Exports**

We assume that gross exports are affected by two main factors: (1) the real exchange rate, and; (2) the level of income in the foreign country (or foreign GDP). To understand this better, let’s take a closer look at the relationship of both of these factors with gross exports. A cursory search on the Census Bureau’s website will reveal that the country that did the most trade with the US in 2007 was Canada ($44.23b) [1]. Looking at data on Canada, we first see how the real exchange rate affects net exports from the US.

For this graph, I took the values of gross exports and real exchange rate (1974-2004) from the BEA website, and added a trend-line to the data. The relationship is clearly positive. We call the slope of this line the factor by which exports are effected by exchange rates – it can be viewed as the marginal propensity to export based on the real exchange rate. For this graph, the value is $4,903m. That is, for each dollar increase in the real exchange rate, exports will increase by $4,903 million.

Next, we take a look at the relationship that the Canadian GDP per capita has on exports to Canada from the US.

As you might expect an increase in the real GDP per capita, will cause an increase in the gross exports to that country. The data here is once again from 1974-2004, and the slope of the trend-line is positive, indicating the positive relationship between these two. The marginal propensity to export based on the GDP per capita is $5,973 million. That is, for each dollar increase in the Canadian real GDP per capita, exports will increase by $5,973 million.

In sum, we add the two factors together, to get the following relationship between gross exports, the real exchange rate and foreign GDP.

Here, X_{f} is the marginal propensity to export based on the foreign GDP, and X_{?} is the marginal propensity to export based on the real exchange rate.

**Imports**

To examine this relationship, we start out by assuming that imports depend on the *home* (or domestic) GDP, and the real exchange rate. However, as the real exchange rate increases, the imports decrease, and vice versa. So, given enough time, imports will adjust to changes in the exchange rate, and we assume that the total dollar value of imports will remain constant. Thus, the real exchange rate does not affect imports. Finally, we just assume that imports are a constant proportion of the domestic GDP: **IM = IM _{y} Y**

To see this, we look at overall imports into the US, and the domestic GDP.

The slope of the trend-line is $119.2 billion. This means that for each billion dollar increase in real GDP, imports will increase by $119.2 billion. This stands to reason – as we get richer, we will buy more from abroad.

**Net Exports**

Now, if we put everything together, we can say something about net exports.

So, we know that **NX = GX – IM**.

And also that GX = X_{f} Y^{f} + X_{ε} ε

And also that IM = IM_{y} Y

Putting everything together, we get that **NX = X _{f} Y^{f} + X_{ε} ε – IM_{y} Y**

Thus, we can say that net exports depend on three things:

- Foreign GDP
- Domestic GDP
- Real Exchange Rates

Although I did talk a little bit about exchange rates and the effects of foreign exchange trading on exchange rates, we will revisit that in the next class.

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