Theory of discounting and monetary policy

• The concept of a “discount rate” is central to economic analysis … Because of this centrality, the choice of an appropriate discount rate is one of the most critical problems in all of economics. And yet, to be perfectly honest, a great deal of uncertainty beclouds this very issue. … The most critical single problem with discounting future benefits and cost is that no consensus now exists, or for that matter has ever existed, about what actual rate of interest to use. (Weitzman, 2001, p. 260)

• The main problem in the theory of discounting is that “an economist who knows the literature well” is “able to justify any reasonable social discount rate by some internally consistent story”.

Some puzzles (Puzzle 1)

• The borrowing rates for banks are very low. But the credit card interest rates that banks can charge their customers are very high. How can the large interest rate differential be maintained over a long time?

• From another perspective, individuals can obtain a line of credit or mortgage at much lower interest rate than the credit card interest rate. Why do so many people still maintain a large amount of credit card debt, without replacing it with a line of creditor or mortgage refinaning?

Puzzle 2

• Most economists are staunch proponents on the efficiency of markets, especially when a market is very liquid and transparent. The short term money market is among the most liquid and transparent markets in the world.

• Yet, most economists support that the short term discount rate, possibly the most important factor affecting economic performance, should be determined by a small group of “independent” professionals from central banks.

• Does that mean the market is only capable of being efficient on minor issues and not on major issues?

Puzzle 3

• In general, yield curves slope upward. Loans with longer maturity pay higher interest rates than loans with shorter maturity. At the same time, empirical evidence suggests that humans discount the long term future at lower rates than the short term future. This pattern is called hyperbolic discounting. Many policy papers also advocate discounting long term projects at lower rates than short term projects.

• Why do market discount rates and psychological and policy discount rates move at different directions with the increase of project duration?

Puzzle 4

• It is free to accumulate any amount of credit card debt, which often pay interest as high as 30%? The is defended as freedom of choice.

• Why it is mandatory for people to save for retirement, which typically yield very low return?

Human discounting rates

• Experiments– Depending on the designs of the experiments,

results vary.– If showed pictures of beautiful ladies before

surveys, discount rates can be extremely high for men

• Credit card rates can be 30%.

What determine human psychological discount rates?

• For human beings, it is from our evolutionary past.

• In old times, the probability of death is high.

• Hence the high discount rate.• People feel high interest rate charge is

natural. So they are willing to pay high interest rate on credit card debts.

• This resolves the first puzzle.

Government bond yields

• Currently, 10 year Canadian bond yield is below 3%

• Similar yields for many other government bonds

The role of government

• Government is the largest equity holder of the society.

• Housing: Privately owned?• What happened if you do not pay property tax

for three years?• Private housing can be more precisely

understood as long term leasing from the government. Property tax is the rent.

• There is really no chasm between public and private ownership.

• As equity owner, the government prefer high rate of economic growth and high equity value so it can generate more tax revenue and other types of revenues.

• From our earlier calculation, low discount rate environment increase equity value and encourage economic growth.

• So government prefer low discount rate policy.

• Government preferred discount rate is lower than human psychological discount rate. Hence low discount rate needs to be actively managed by central banks instead of directly determined by financial markets.

• This resolves the second puzzle.

A consequence of low discount rate policy

• Low discount rate policy benefit borrowers instead of lenders.

• As a result, saving rates in countries of low discount rates, which are all the wealthy countries, are low.

Exercise

• A company has a choice to select one of the two projects. The first project requires an initial spending of 10 million dollars. For the next ten years, the project will generate 3 million dollar profit each year. The second project requires an initial spending of 20 million dollars. The project will generate 3 million dollar profit the first year. The profit from the project will increase 10% from each previous year. The project will last ten years. The criterion of selection is NPV of a project. If the discount rate is 12%, which project you will choose? If the discount rate is 5%, which project you will choose?

• Tax base is the total net profit over the project’s life. Calculate tax bases for both projects.

• If the government attempts to maximize tax base, which discount rate the government will choose?

Solution

0 1 2 3 4 5 6 7 8 9 10 tax base

-10 3 3 3 3 3 3 3 3 3 3 20

-20 3 3.3 3.63 3.99 4.39 4.83 5.31 5.85 6.4 7.1 27.8

Solution

• Lower discount rate generates more taxable income.

• The government will choose the lower discount rate

On the third puzzle

• Discounting and uncertainty

• For the same project, longer duration, higher uncertainty.

• For different projects, only low uncertainty projects are designed to last long.

Relation between discounting and other factors

• fixed cost

• duration

• uncertainty

• growth

Resolution of the third puzzle

• Low discount rate is associated with low uncertainty, long duration systems

• This resolves the third puzzle.

Policy implications

• One should not force low discount rate on long term issues if uncertainty is high.– Massive funding for climate change related

projects. – The excuse is that these projects will have

massive long term benefits. – How do you know?

Preconditions for low discount rate policy

• Economic growth has to be possible– The key constraint is the availability of natural

resources

• Effective selection and monitoring systems have to be developed to distinguish projects with genuine high growth potential and project with low probability of high growth potential. These systems will be highly expensive and prone to errors in long term forecasting.

• Examples: Various green energy projects

Past, Present and Future

• In the most time of past several hundred years, low discount rate, high fixed cost societies are more competitive and spread out. However, in the last several decades, the trend has reversed. High discount rate, low fixed cost societies are spreading out. It is time reconsider low discount rate policy.

Limits to low discount rate

• The biological value of a low discount rate is limited by its requiring the organism to detect which one of all the events occurring over a preceding period of hours or days led to a particular reinforcer. As the discounting rate falls, the informational load increases. Without substantial discounting, a reinforcer would act with nearly full force not only on the behaviors that immediately preceded it, but also on those that had been emitted in past hours or days. The task of factoring out which behaviors had actually led to reward could exceed the information processing capacity of a species. (Ainslie and Herrnstein, 1981)

High discount rate environment

• While low discount rate environment require active policy and institutional support, high discount rate environment require less active policy or institutional support. Hence it is a passive and low cost environment from institutional point of view. However, at this moment, we may not to wish the discount rate to be as high as human nature deems it to be. Institutions and policies will still work to keep interest rate lower than the pure market rate.

Policy recommendations

• Higher interest rate than now

• How much higher?

• Let the market take on more active roles. Governments only insure small depositors. Interest rate will increase to reflect the risk.

• In countries with two tier financial systems, such as in China, where it is often difficult for private businesses to obtain loans. Illegal but common practice is to set up private credit unions to attract deposits and make loans.

• Deposit rates are much higher than official rates from banks. This shows that discount rate without government guarantees are much higher.

• But doesn’t higher discount rate lower the rate of economic growth?

• If the amount of fuel is unlimited, driving at a higher speed will get you further.

• If the amount of fuel is limited, driving at 70km/hour will get you further than driving at 150km/hour.

•

• Low discount rate does stimulate economic growth over short term.

• However, with little growth prospect in real economy in most parts of the world, money, which is made abundant under low interest rate environment, is concentrated in real estates and commodity speculation.

• This is what caused eventual collapse of the financial system in 2008

• From our theory, we should adjust policy measures to adapt to the level of resource bases.

• This means we should stimulate economy when resource is abundant and slow down economy when resource is scarce.

WACC

• WACC is the standard method we have learned in the classes. So we will discuss more

• Definition of WACC:

• WACC is the weighted average of the cost of debt and the cost of equity.

• Cost of debt is the bond yield. Can we define the cost of equity as the dividend yield?

• It will make the definition of the cost of equity consistent with that of the cost of debt.

• Potential problem– Price change of equity.

• But bond price change as well, especially long bond.

Mortgage rate

• Do mortgage rates based on WACC?

• What is mortgage rate right now?

• What is WACC for banks?

• Why such big difference between mortgage rate and WACC?

What is capital?

• Capital is long term funding. • But bank cash flows are mainly short term

funding. • This illustrate the importance of duration in

funding processes. • There is a continuation from short term to

long term funding. No chasm between them

• Banking industry illustrate this clearly.