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					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
• 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?
     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
• 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
       The role of government
• Government is the largest equity holder of the
• 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
• 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
• 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.
•   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
• If the government attempts to maximize
  tax base, which discount rate the
  government will choose?

 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
• 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
  – The excuse is that these projects will have
    massive long term benefits.
  – How do you know?
Preconditions for low discount rate
• Economic growth has to be possible
  – The key constraint is the availability of natural
• 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
      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
• 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
• This means we should stimulate economy
  when resource is abundant and slow down
  economy when resource is scarce.
• WACC is the standard method we have
  learned in the classes. So we will discuss
• 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
             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
• This illustrate the importance of duration in
  funding processes.
• There is a continuation from short term to
  long term funding. No chasm between
• Banking industry illustrate this clearly.

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