ECON 34104410 LECTURE 7 Aggregate demand dynamics

1
ECON 3410/4410 LECTURE 7 Aggregate demand
dynamics

• Ragnar Nymoen
• 4 October 2007

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Overview

• Review of aggregate demand and its components.
• Closed economy, open economy in a later lecture
• Determinants of aggregate investments (ch 15) and
  consumption (ch 16), important and volatile
  components of aggregate demand
• Aggregate demand put together,
• and how monetary policy affects aggregate demand
  (ch 17)---the transmission mechanism.
• Term structure of interest rates
• Regime dependency of AD curve
• Aggregate demand and aggregate supply
• Short and long-run versions of the closed economy
  AS-AD model

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Ch 15Private 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 cursory (you may drop it)

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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
• In this way, markets for financial captial and
  real captial becomes integrated.

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The fundamental value of a firm

• Successive substitution of Vetj 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
• What does this expression remind you of?
• Interpretation The fundamental value of the firm
  equals the present value of expected future
  dividends
• 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 ch. 17 the level of capital K is
  assumed constant and the notation changes
  slightly (? is the index of business confidence)

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Static investment function

• Note that the rationale for assuming K constant
  (despite KtKt-1 It) is that K is a stock
  variable, while I is a flow variable.
• Hence Kt is close to Kt-1 if the time period is
  short, even for large It
• However, as we shall see, It may still react
  dynamically because of dynamics elsewhere in
  the full model.

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Ch 16Private 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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Relationship to consumtion function in IDM

• In IDM we had a consumption function with fewer
  explanatory variables, essentially only
  arguments, only Y-T.
• We could have added r, for example, but left it
  out for simplicity.
• On the other hand we introduced lagged C of
  course
• The IDM specification thus assumes that
  adjustment of C to changes in Y-T for example is
  all done within the period of analysis.

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Ch 17Aggregate 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 long-run aggregate demand function in
log-linearized form

• Assume that for that all arguments in the demand
  function are at their long-run (steady state)
  values, then long-run aggregate demand function
  is
• The IAM textbook shows how the aggregate demand
  function Y can be log-linearized around its
  long-run equilibrium values to give

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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
• 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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The transmission mechanism Term structure of
interest rates

• Remember that the rate of interest r in the
  demand function is interpretaable as an yield on
  long term bonds (10 years for example), a so
  called long interest rates
• What monetary policy controls (directly or
  indirectly) is the very short interest rate, the
  money-market interest rate.
• How can the central bank control the interest
  rate which is relevant for aggregate demand?
• Answer No worry! When capital markets are
  operating according to theory a change in the
  money market rate will be transmitted
  automatically to the long rates!
• Arbitrage is (again) the mechanism

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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
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Whatever happened to the money market?

• The Taylor-rule pushes the money market that we
  know from the IS-LM model into the background.
• This is OK in many ways, as long as it does not
  lead to misunderstanding like
• There is no role for money in the model
• The money market is always, there it is only that
  it is not always specified explixtely.

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The money market in a period-to-period equilibirum
Real Money supply
i
Real money demand L(Yt,it)
Mt/Pt
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Consider a money targeting regime In each period
the money supply is set by the central bank.
Real Money supply in period t
i
Interest rate in peride t
Real money demand L(Yt,it)
Mt/Pt
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Interest rate function in a money targeting regime
The money graph in previous slide defines
it i(Yt, Mt/Pt) where Y and
M/P are regarded as determined outside the money
market, M/P being the policy instrument.

• If we define a long-run interest rate by
  inserting the long run values of the arguments in
  the i-function and then take the deviation
  between it and the long-run rate, we obtain a
  function that is qualitatively similar to the
  Taylor-rule. With one important difference
• In the money targeting regime the derivatives of
  the i-function are already given by the
  properties of the money demand function.
• In the Taylor-rule the corresponding parameters h
  and b transpires to be free parameters, to the
  chosen by the central bank (see next lecture)
• Note IAM p 504-506 contains a more detailed
  comparison/derivation of the two interest rate
  functions

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The money market with a policy determined
interest rate
If the coefficients of the Taylor-rule are
free-parameters, the money market operates like
this
i
Interest rate in period t
M/P
Real money supply In period t
Real money supply is then an endogenous variable.
Since the price level is pre-determined in any
given period, it is the nominal money stock that
adjusts immediately to bring the market into
equilibrium. The Central Bank does this by
market operations.
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The AD-schedule is regime dependent

• Although it is OK for some purposes to use the
  Taylor-rule as a catch all for monetary policy,
  as IAM does, it is also obscuring the important
  fact that
• The response of aggregate demand (the impact
  multipliers of you like) to for example an
  increase in g is dependent on the monetary policy
  regime.
• This point is going to be even more important
  when we later move to the open economy.

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Aggregate demand dynamics---where is it?

• This lecture was titled aggregate demand dynamics
  
• But the main impression is that we have
  simplified so much that dynamics have almost been
  removed from the demand side.
• Still there is one source of dynamics left the
  real interest rate is and expectations
  variable---which is a source of dynamics.
• In the next lecture we will utilize this to
  establish a long-run and a short-run version of
  the AD-AS model.
• We will also consider a different model
  altogether the real-business cycle model, where
  dynamics stems form other sources than
  expectations.