Title: LECTURE 6 Aggregate demand and its components
1LECTURE 6 Aggregate demand and its components
- Øystein Børsum
- 21rst February 2006
2Overview 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
3PART 1Private investment
4Overview 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
5Pricing 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
6The 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.
7The 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
8The 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
9Optimal level of investment depends on q
- Maximization of Vt taking qt as given gives the
following first-order conditions
10An 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
11The 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)
12PART 2Private consumption
13Overview 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.
14Intertemporal 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
15Intertemporal 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
16Human 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
17Optimal 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
18Optimal intertemporal consumption
- In optimum, the marginal rate of substitution
between present and future consumption (MRS) must
equal the relative price of present consumption
(1r)
19Example 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
20Example 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.
21The 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)
22PART 3Aggregate demand
23Overview 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
24Equilibrium 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
25Evidence 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
26The 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
27The 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
28The 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).
29Evidence 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
30Policy 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.
31Aggregate 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
32The 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)
33ADDITIONAL MATERIALTerm structure of interest
rates
34The 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
35In 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