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  Investment and the Real Interest Rate, Exports and Autonomous Spending

Investment and the Real Interest Rate:

A business that commences an investment project always has alternative uses for the money. One alternative would be to take the money that would have been spent building the factory or buying the machines and place it instead in the financial markets—i.e. lending it out at the market real rate of interest.  Therefore the opportunity cost of an investment project is the real interest rate. The higher the interest rate signifies the fewer the number and value of investment projects that will return more than their current cost and the lower the level of investment spending.

However which interest rate is the relevant one? There are several different interest rates. First, the interest rate that is applicable for determining investment spending is a long-term interest rate. This distinction matters, for the reason that long and short-term interest rates are different and don’t always move in step. Seem at the shifts over time in the yield curve chart shows that different interest rates don’t always fluctuate together. It as well shows that long-term interest rates are usually higher than short-term ones.

Second the interest rate that is pertinent for investment spending decisions isn’t the nominal but the real interest rate. The nominal prices a business charges increase with inflation. If a business is enthusiastic to invest when the interest rate is 5% and inflation is 2% per year (and so the real interest rate is 3% per year), then the business must also be willing to invest when the interest rate is 10% and inflation is 7% per year (and as a result the real interest rate is still 3% per year).

Third there is risk. Lending money to a business for all time carries an element of risk. May be the borrower will go bankrupt before the loan is due. May be the creditors will find themselves last or nearly last, in line as a little amount of left-over post-bankruptcy assets are divided up. Financial institutions lending money are eagerly interested in the financial health of those to whom they lend. The riskier they consider the loan is--the larger the possibility of a bankruptcy or a debt rescheduling appears to be--the higher is the interest rate that lenders will demand to compensate them for risk.

Therefore to determine the level of investment spending take the baseline level of investment I0 (expected economic growth, determined by businesses’ optimism and a bunch of other factors for which the level of the stock market serves as a convenient thermometer). Deduct from this baseline level the interest sensitivity of investment parameter Ir times the relevant interest rate r. The relevant interest rate should be long-term because most investments are long-term. The relevant interest rate should be real because investment projects are real assets: their value increases with inflation. And the relevant interest rate should be risky because businesses borrowing to invest may go bankrupt. In the investment function:

I = Io - Ir x r
     
The relevant interest rate r is the real, long-term and risky interest rate.

Exports and Autonomous Spending:

Investment spending isn’t the only component of autonomous spending that is affected by the real interest rate. In the planned expenditure function:

E = A + MPE x Y
     
Autonomous expenditure includes gross exports as well:

A = Co + I + G + GX
     
Therefore we can expand the determinants of gross exports in the expression for autonomous spending:

A = Co + (Io - Ir x r) + G + (XfYf + Xε x ε)
 
The real exchange rate ε depends on the domestic real interest rate r (and on foreign-exchange speculators' opinions of fundamentals and foreign interest rates):

ε = εo - εr x (r - rf)
     
Alternating the determinants of the exchange rate into the autonomous spending equation:

1014_autonomous spending equation.jpg

It becomes obvious that there are two components of autonomous spending affected by changes in the real interest rate. A higher real interest rate decreases autonomous spending by reducing exports (Xεεr x r) as well as by reducing investment (Ir x r).
From the Real Interest Rate to the Change in Exports:

769_change in exports.jpg

Legend: A alter in the real interest rate has larger effects on aggregate demand than those through investment alone: a alter in the real interest rate changes the exchange rate, and thus changes net exports as well.

Why does a elevated domestic interest rate reduce exports? A elevated real interest rate makes investing in the home country more attractive: foreign exchange speculators try to take benefit of this opportunity to earn higher returns by shifting their portfolio holdings to comprise more home currency-denominated assets. This raise in demand for home currency-denominated assets and decrease in demand for foreign currency-denominated assets drives down the exchange rate which is the value of foreign currency.

A lesser value of foreign currency makes exports more expensive to foreigners: their currency buys less here for the reason that it is less valuable. It diminishes their aptitude to purchase exports. Ever since exports are a part of autonomous spending, a rise in the real interest rate diminishes autonomous spending through this channel as well. Therefore a change in interest rates has a bigger effect on output than one would think from the effect of interest rates on investment alone.

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