LECTURE 6 Aggregate demand and its components

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LECTURE 6 Aggregate demand and its components

• Øystein Børsum
• 21rst February 2006

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Overview of forthcoming lectures

• Lecture 6 Aggregate demand and its components
• Determinants of aggregate investments and
  consumption, important and volatile components of
  aggregate demand
• Aggregate demand put together The AD curve
• Lecture 7 Aggregate demand and aggregate supply
• Macroeconomic dynamics in the AS-AD model
• Lecture 8 Stabilization policies
• Goals for stabilization policies Stable output
  and inflation
• Optimal policy rule Demand and supply shocks
• Lecture 9 Limits to stabilization policies
• Rational expectations and the Policy
  Ineffectiveness Proposition, the Ricardian
  Equivalence Theorem and the Lucas Critique
• Policy rules versus discretion Credibility of
  economic policy

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PART 1Private investment
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Overview of Q-theory of investment

• The market value of a firm is determined by
  discounting future dividends to the owners
• By investing in capital, the firm grows and hence
  its capacity to generate dividends increases
• The cost of investing one unit of capital is
  exogenous
• This provides an incentive for firms with a high
  market value per unit of capital to invest
• Definition q the ratio between the market
  value of the firm (V) and the replacement value
  of its capital stock (K)
• Note Q-theory applied to housing investment
  (section 15.4) is self-study

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Pricing by arbitrage condition

• Arbitrage condition In every period, stocks and
  bonds must yield the same risk-adjusted rate of
  return
• Vt real stock market value of the firm at the
  start of period t
• Vet1 expected real stock market value of the
  firm at the start
• of period t1
• De real expected dividend at the end of the
  period t
• r real interest rate on bonds
• ? risk premium on shares

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The fundamental value of a firm

• Successive substitution gives
• Assume that the future value of the firm Vet1
  cannot rise faster than r ? (else it would be
  of infinite value), i.e.

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The fundamental value of a firm

• Then the infinite sum can be written as
• Interpretation The fundamental value of the firm
  equals the present value of expected future
  dividends
• Implications Stock prices may fluctuate because
  of changes in
• expected future dividends
• the real interest rate
• the risk premium between stocks and bonds
• The role of the interest rate We only assume
  that the expected return on shares is
  systematically related to the return on bonds
• What about investments? The firm must decide
  whether to pay out its profits now (as dividends)
  or invest it in order to increase profits
  (dividends) later Maximize Vt with respect to It

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The decision to invest

• Definition qt Vt / Kt the ratio between the
  market value of the firm and the replacement
  value of its capital stock
• Expected value of the firm tomorrow
• ? where we have used
  and
• Cash flow constraint
• ?e expected profit
• c installation costs
• Assume the following installation cost function

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Optimal level of investment depends on q

• Maximization of Vt taking qt as given gives the
  following first-order conditions

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An example of the investment function

• Assume that in order to simplify the
  value of the firm to
• Assume furthermore that and
• ? expected dividend pay-out ratio
• ? constant profit share
• Using the definition of q this gives the
  investment function

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The general investment function

• Abstracting from the functional form the general
  investment function is
• E index of business confidence
• Note that the risk premium is omitted
• Note that in chpt. 17 the level of capital K is
  assumed constant and the notation changes
  slightly (? is the index of business confidence)

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PART 2Private consumption
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Overview of intertemporal consumption theory

• Diminishing marginal utility of consumption
  provides an incentive for consumption smoothing
  over time.
• Through the capital market, consumers can save or
  borrow and thus separate consumption from current
  income.
• The discounted value of disposable lifetime
  income (human wealth) plus the initial stock of
  financial wealth represents the consumers
  lifetime budget constraint.
• In optimum the consumer is indifferent between
  consuming an extra unit today and saving that
  extra unit in order to consume it tomorrow.
• Current consumption will be proportional with
  wealth not income.
• Note Issues on debt-financed tax cuts and
  ricardian equivalence will be treated later on in
  the course.

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Intertemporal consumer preferences

• Representative consumer with a two-period utility
  function
• Properties of the utility function
• the marginal utility of consumption in each
  period is positive, but diminishing (provides an
  incentive for consumption smoothing)
• the consumer is impatient the rate of time
  preference ? is positive

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Intertemporal budget constraint

• Period 1 budget constraint
• Period 2 budget constraint
• The consumers intertemporal budget constraint
• V financial wealth
• r real rate of interest
• YL labour income
• T net tax payment (taxes minus transfers)
• C consumption

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Human wealth and financial wealth

• V1 represents the consumers initial financial
  wealth
• The present value of disposable lifetime income
  can be thought of as human wealth (or human
  capital) H
• This simplifies the notation of the intertemporal
  budget constraint

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Optimal intertemporal consumption

• Utility over the consumers life-time becomes (as
  a function of C1)
• Maximization of U with respect to C1 gives the
  following first-order conditions
• The Keynes-Ramsey rule

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Optimal intertemporal consumption

• In optimum, the marginal rate of substitution
  between present and future consumption (MRS) must
  equal the relative price of present consumption
  (1r)

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Example of the consumption function with CES
utility

• The constant (intertemporal) elasticity of
  substitution utility function
• u(Ct) Ct-1/?
• Insert this into the Keynes-Ramsey rule

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Example of the consumption function with CES
utility

• Insert the expression for the optimal C2 in terms
  of C1 into the intertemporal budget constraint.
• Current consumption C1 is proportional to total
  current wealth (not current income).
• The propensity to consume wealth is positive, but
  less than one.

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The general consumption function

• g growth rate of income (increases human
  wealth)
• Some consumers may be credit constrained, hence
  Y1d
• In chpt. 17 notation is slightly changed
• The value of financial wealth is treated
  implicitly in r
• ? is an index of consumer confidence (proxy for
  expected income growth)

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PART 3Aggregate demand
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Overview over aggregate demand theory with
endogenous monetary policy

• Private investments and consumption are sensitive
  to changes in the real interest rate, hence there
  is a potential for stabilization policy
• The government cares about stabilizing both
  output and inflation
• In order to achieve the governments objectives,
  the central bank sets the nominal short-term
  interest rate according to a Taylor rule
• The resulting aggregate demand curve will be
  downwards-sloping in (y?) space
• Important properties of the aggregate demand
  curve (the exact slope as well as the shift
  properties) will depend on the policy priorities
  (implied by the choice of coefficients in the
  Taylor rule)
• Note We will return to questions about fiscal
  policy (public consumption and taxes) later in
  the course

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Equilibrium condition in the goods market gives
the aggregate demand function Y

• Investments plus consumption aggregate private
  demand D
• Equlibrium condition for the goods market (closed
  economy)
• Properties of the aggregate private demand
  function

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Evidence from Denmark seem to confirm a close
relationship between private sector demand and
the real interest rate over time
The real interest rate and the private sector
savings surplus in Denmark, 1971-2000. Per cent
Source Erik Haller Pedersen, Udvikling i og
måling af realrenten, Danmarks Nationalbank,
Kvartalsoversigt, 3. kvartal, 2001, Figure 6
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The aggregate demand function on log-linearized
form

• The long run equilibrium values of aggregate
  demand
• The textbook shows how the aggregate demand
  function Y can be log-linearized around its
  long-run equilibrium values to give this very
  convenient form

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The real and the nominal interest rate

• The definition of the expected real interest rate
• As long as i and ? are close to zero, we can
  approximate the real interest rate
• Expectations play a central role in
  macroeconomics
• As a first approach we will assume static
  expectations

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The Taylor rule as a proxy for monetary policy

• History shows that governments care about
  stabilizing both output and inflation.
• As a proxy for these policy motives, we can use
  the following interest rate rule proposed by John
  Taylor
• With this rule, y, ? and r will be on their
  long-run equilibrium values on average.
• ? is interpreted as the inflation target (can be
  implicit or explicit).
• For the stability of this economy, the parameter
  must be h positive so that an increase in
  inflation triggers an increase in the real
  interest rate (the Taylor principle).

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Evidence from the euro area seems to confirm the
Taylor rule as a proxy for monetary policy
The 3 month nominal interest rate and an
estimated Taylor rate for the euro area,
1999-2003. Per cent
Source Centre for European Policy Studies,
Adjusting to Leaner Times, 5th Annual Report of
the CEPS Macroeconomic Policy Group, Brussels,
July 2003
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Policy priorities implied by the Taylor rule
coefficients seem to vary across countries
Estimated interest rate reaction functions of
four central banks
1. Source Richard Clarida, Jordi Gali and Mark
Gertler, Monetary Policy Rules in Practice
Some International Evidence, European Economic
Review, 42, 1998, pp. 10331067. 2. Source
Centre for European Policy Studies, Adjusting to
Leaner Times, 5th Annual Report of the CEPS
Macroeconomic Policy Group, Brussels, July 2003.
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Aggregate demand curve with endogenous monetary
policy

• The log-linearized version of the aggregate
  demand function Y and the Taylor rule can be
  combined to an aggregate demand curve in (y?)
  space

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The shape of the aggregate demand curve will
depend on the priorities of monetary policy
Illustration of the aggregate demand curve under
alternative monetary policy regimes (indicated by
the choice of coefficients h and b in the Taylor
rule)
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ADDITIONAL MATERIALTerm structure of interest
rates
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The expectations theory of the term structure of
interest rates

• Investment decisions depend on the expected cost
  of capital over the entire life of the asset
  (easily 10 years)
• To what extend does the short-term policy rate
  influence long-term interest rates?
• If short-term and long-term bonds are perfect
  substitutes (risk neutral investors) then the
  following arbitrage condition will hold
• Taking logs and using the approximation ln(1i) ?
  I
• Alternative Static interest rate expectations

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In 2001, U.S. long-term interest rates kept a
steady level as the short-term policy rate fell
The Federal funds target rate (U.S. policy rate)
and the yield on 10 year U.S. government bonds,
2001-2002. Per cent
Source Danmarks Nationalbank