business cycles the basic short run model summaries

Empirically, changes in stock prices and in housing prices tend to be followed by changes in
output in the same direction. In part this reflects that higher asset prices lead to higher
investment. This chapter explains the links between asset prices and investment.
2. A firm seeking to maximize the wealth of its owners will choose an investment plan which
maximizes the market value of the firm's assets. The value of the firm, referred to as the
fundamental stock value, is the present discounted value of the expected future dividends
paid out by the firm. This follows from the shareholder's arbitrage condition which says that
the expected retum to shareholding, consisting of d ividends and capital gains on shares,
must equal the return to bondholding plus an appropriate risk premium.
3. When share prices reflect the fundamental value of firms, there are three possible reasons for
the observed volatility of stock prices: (i) fluctuations in (the growth rate of) expected future
dividends, (ii) fluctuations in the real interest rate, and (iii) fluctuations in the required risk
premium on shares. There is indirect evidence that the required risk premium fluctuates quite
a lot.
4. The evidence suggests that the rate of return on stocks is tied to the rate of return on bonds
over the long term. This accords with the view that stock prices reflect the fundamental value
of firms. However, many observers believe that stock prices can sometimes deviate from
fundamentals. The analysis in this chapter abstracts from such 'bubbles' in stock prices.
5. Increases in the firm's capital stock imply adjustment costs (ins1allation costs), including costs
of installing new machinery, costs of training workers to use the new equipment, and perhaps costs of adapting the firm's organization. These installation costs will typically increase more
than proportionally to the firm's level of investment.
6. The value-maximizing firm will push its investment to the point where the shareholder's capital
gain from a unit increase in the firm's capital stock is just offset by the dividend he must forgo
to enable the firm to purchase and install an extra unit of capital. Because the marginal installation
cost is increasing in the volume of investment, this investment ru le implies that the firm's
optimal level of investment will be higher, the higher a unit increase in the firm's capital stock
is valued by the stock market. An increase in the ratio of stock prices to the replacement cost
of the firm's assets will therefore stimulate its investment.
7. The market value of stocks relative to the replacement value of the underlying business assets
is referred to as Tobin's q. Our theory of investment may be summarized by saying that
business investment is an increasing function of Tobin's q.
8. Stock prices reflect expected future dividends which tend to be positively affected by a rise
in current profits. The value of Tobin's q therefore tends to vary positively with current profits,
which in turn vary positively with the output- capital ratio. Hence investment is an increasing
funr.tion of r.urrP.nt outrut !lncl !l dP.r.rP.!lsing funr.tion of thP. P.xisting r.!lrit!ll stor.k.
9. Ceteris paribus, a rise in the real interest rate implies that expected future dividends are
discounted more heavily, leading to a fall in Tobin's q via lower stock prices. Thus a higher real
interest rate tends to depress investment. A rise in the required risk premium on shares,
generated by more uncertainty about the future, will have a similar negative impact on
investment.
10. A version of the q-theory can explain investment in owner-occupied housing. When the
market price of residential property increases relative to the cost of housing construction, it
becomes profitable for firms in the construction sector to increase the supply of new housing
units. As a consequence, housing investment (construction activity) goes up. There is strong
empirical evidence in favour of this hypothesis.
11. In the short run, the market price of housing varies positively with current income and negatively
with the real interest rate and with the existing housing stock. Since construction
increases with the market price of housing, it follows that housing investment is an increasing
function of income and wealth and a decreasing function of the real interest rate and the
current housing stock.

Consumption, income and wealth
Private consumption is by far the largest component of the aggregate demand for goods and
services. A satisfactory theory of private consumption must explain the paradoxical stylized
facts that the average propensity to consume is a decreasing function of disposable income
in microeconomic cross-section data, whereas it is roughly constant in long-run macroeconomic
time series data.
The properties of the aggregate consumption function may be derived by studying the
behaviour of a representative consumer who must allocate his consumption optimally over
time, subject to his intertemporal budget constraint. With perfect capital markets, this con·
straint implies that the present value of lifetime consumption cannot exceed the sum of the
consumer's initial financial and human wealth. Human wealth is the present value of current
and future disposable labour income.
3. In the consumer's optimum, the marginal rate of substitution between present and future con·
sumption equals the relative price of future consumption, given by one plus the real rate of
interest. When disposable income varies over time, the optimizing consumer will want to
smooth the time path of consumption relative to the time path of income. There is evidence
that such consumption smoothing does indeed take place.
4. Given the assumption of perfect capital markets, the optimal intertemporal allocation of con·
sumption implies that current consumption is proportional to total current wealth (the sum of
financial and human wealth). The propensity to consume current wealth depends on the real
interest rate, the consumer's rate of time preference, and on his intertemporal elasticity of
substitution, defined as the percentage change in the ratio of futu re to present consumption
implied by a 1 per cent change in the consumer's marginal rate of substitution.
5. A rise in the real interest rate will have offsetting income and substitution effects on the
propensity to consume current wealth. If the intertemporal substitution elasticity is greater
than 1, reflecting a strong willingness of consumers to substitute future for present con·
sumption, the substitution effect will dominate. A rise in the real interest rate will then reduce
the propensity to consume current wealth. The opposite will happen if the intertemporal sub·
stitution elasticity is smaller than 1 . Even if a change in the interest rate does not significantly
affect the propensity to consume a given amount of wealth, it may reduce current consump·
tion by reducing the present value of future labour income, that is, by reducing human wealth,
and by reducing the market value of the consumer's stockholdings and housing wealth.
6. For an optimizing consumer, the average propensity to consume current income will vary
positively with the ratio of current financial wealth to current income. There is strong empirical
evidence that such a positive relationship exists. The rough long· run constancy of the average
propensity to consume observed in macroeconomic time series data may be explained by the
fact that the wealth-income ratio, the growth rate of real income, and the real rate of interest
tend to be roughly constant over the long run.
7. The negative correlation between income and the average propensity to consume observed
in microeconomic cross-section data may be explained by the fact that, in any given period,
many consumers will have a relatively low current income relative to their average income over
the life cycle. Such consumers will therefore have a high level of current consumption relative
to their current income, because they expect higher future incomes, or because they have
accumulated wealth by saving out of higher past incomes.
8. A tax cut which is expected to be permanent will have a stronger positive impact on current
consumption than a tax cut which is believed to be temporary. When the real interest rate
equals the rate of time preference, a permanent tax cut will induce a corresponding rise in
current consumption.
9. The government's intertemporal budget constraint implies that the present value of current
and future taxes must be sufficient to cover the present value of current and future government
spending plus the initial stock of government debt. For given levels of current and future
government spending, a tax cut today must therefore be offset by a future tax increase of
equal present value.
10. If consumers have rational expectations they will realize the implications of the intertemporal
government budget constraint. This means that a cut in current (lump sum) taxes which is not
accompanied by a cut in present or future public spending will have no effect on private consumption:
consumers will save all of the current tax cut to be able to finance the higher future
taxes without having to reduce future consumption. This equivalence between tax finance and
debt finance of current public spending is referred to as Ricardian equivalence.
11. In practice, consumers are unlikely to save the full amount of a current tax cut, even if they
realize that lower taxes today must imply higher taxes in the future. First of all, consumers may
believe that some of the future taxes will be levied on future generations. Second, some consumers
may be credit-constrained. A switch from current to future taxes will help these individuals
to achieve a desired rise in current consumption at the expense of futu re consumption.
The use of redistributive and distortionary taxes also means that a switch from tax finance to
debt finance of current public spending is likely to have real effects on current consumption
and labour supply.
12. The theory of private consumption is summarized in the generalized consumption function
which states that aggregate consumption is an increasing function of current disposable
income, of the expected futu re growth rate of income, and of the current ratio of financial
wealth to income. A rise in the real interest rate has a theoretically ambiguous effect, although
it is likely to reduce current consumption due to its nega1ive impact on human and financial
wealth.

monetary policy and AD
The aggregate demand curve (the AD curve) is derived by combining the aggregate con·
sumption and investment functions with the goods market equilibrium condition that total
output must equal the total demand for output consisting of private consumption, private
investment and government demand for goods and services. Goods market equilibrium
implies that aggregate saving equals aggregate investment. The AD curve assumes that the
private sector savings surplus {savings minus investment) is an increasing function of the real
rate of interest. The evidence supports this assumption.
2. Because aggregate demand depends on the real rate of interest, it is crucially influenced by
the interest rate policy of the central bank. Historically some central banks have followed
Milton Friedman's suggested constant money growth rule, setting the short-term interest rate
with the purpose of attaining a steady growth rate of the nominal money supply. More
recently, the interest rate policy of many important central banks has tended to follow the rule
suggested by John Taylor according to which the central bank should raise the short-term real
interest rate when faced with a rise in the rate of inflation or a rise in output. If the money
demand function is stable, the constant money growth rule has similar qualitative implications
for central bank interest rate policy as the Taylor rule.
3. The central bank can control the short-term interest rate, but not the long-term interest rate.
The expectations hypothesis states that the long-term interest rate is a simple average of the
current and expected future short-term interest rates. If a change in the short-term interest
rate has little elfect on expected future short-term rates, it will also have little effect on the
long-term interest rate. The ability of the central bank to influence the long-term interest rate
therefore depends very much on its ability to affect market expectations.
4. The incentive to invest in a real asset depends on the expected cost of finance over the life·
time of the asset. Under debt finance a long-lived asset may be financed by a long-term loan
or by a sequence of short-term loans. Risk neutral investors will choose the mode of finance
which has the lowest expected cost. When the expectations hypothesis holds, the expected
cost of finance is the same whether real investment is financed by equity, by long-term debt,
or by a sequence of short-term loans. As a consequence, the ability of the central bank to
influence incentives for long-term real investment depends on its ability to influence the long·
term interest rate which in turn hinges on its ability to affect market expectations of future
short-term rates.

5. When expectations are static, the expected future short-term interest rates are equal to the
current short-term rate. A change in the current short-term rate will then cause a corresponding
change in the long-term interest rate, and the yield curve showing the interest rates on
bonds with different terms to maturity will be completely flat. The AD curve is derived on the
simplifying assumption that expectations are static so that the central bank can control longterm
interest rates through its control over the short-term rate.
6. Because of its empirical relevance, our theory of the aggregate demand curve also assumes
that monetary policy follows the Taylor ru le which implies that the central bank raises the real
interest rate when the rate of inflation goes up. A higher rate of inflation will therefore be
accompanied by a fall in aggregate demand, so the AD curve will be downward-sloping in
(y,.n) space. The AD curve will shift down if the central bank lowers its target rate of inflation
or if the economy is hit by a negative demand shock, due to a tightening of fiscal policy or a
fall in private sector confidence.

Inflation, unemployment and aggregate supply

The link between inflation and unemployment determines how the supply side of the economy
works. Some decades ago most economists and policy makers believed in the simple Phillips
curve which postulates a permanent trade-off between inflation and unemployment: a perma·
nent reduction in the rate of unemployment can be only achieved by accepting a permanent
increase in the rate of inflation, and vice versa.
2. Empirically the simple Phill ips curve broke down in the stagflation of the 1970s. This led to the
theory of the expectations-augmented Phill ips curve which says that the simple Phillips curve
is just a short-run trade-off between inflation and unemployment, existing only as long as the
expected rate of inflation is constant. When the expected inflation rate goes up, the actual
inflation rate increases by a corresponding amount, other things equal.
3. The expectations-augmented Phillips curve implies the existence of a 'natural' rate of unem·
ployment, defined as the level of unemployment which will prevail in a long-run equilibrium
where the expected inflation rate equals the actual inflation rate. Since any fully anticipated
rate of inflation is compatible with long-run equilibrium, the long-run Phillips curve is vertical.
When the actual inflation rate exceeds the expected inflation rate, the actual unemployment
rate falls below the natural unemployment rate, and vice versa.
4. Several different theories of wage and price formation lead to the expectations-augmented
Phillips curve. One such theory is the 'sticky-wage model' in which nominal wage rates are
pre-set at the start of each period. In the sticky wage model presented in this chapter, money
wages are dictated by trade unions seeking to achieve a certain target real wage, given their
expectations of the price level which will prevail over the next period. Given the wage rate set
by unions, profit-maximizing monopolistically competitive firms set their prices as a mark-up
over marginal costs and choose a level of employment which is declining in the actual real
wage. According to this model, employment increases above its natural rate when the actual
price level exceeds the expected price level, and vice versa. The model also implies that, in
general, there is some amount of involuntary unemployment.
5. In the sticky-wage model the target real wage is a mark-up over the opportunity cost of
employment which is given by the rate of unemployment benefit. The wage mark-up factor -
and hence the target real wage - is higher the lower the wage elasticity of labour demand, and the lower lhe weight the union attaches to the goal of high employment relative to the
goal of a high real wage. The mark-up of prices over marginal costs is higher the lower the
price elasticity of demand for the output of the representative firm. The natural rate of unemployment
is higher the higher the wage and price mark-ups and the more generous the level
of unemployment benefits.
6. Another theory leading to the expectations-augmented Phill ips curve is the 'workermisperception
model' which assumes a competitive clearing labour market with fully flexible
wages. Labour demand is a declining function of the actual real wage, while labour supply is
an increasing function of the expected real wage, since workers are imperfectly informed
about the current general price level. This model also implies that employment rises above
the natural level when the actual price level exceeds the expected price level. However, for
any given amount of unanticipated inflation, the increase in employment is smaller in the
worker-misperception model than in the sticky wage model where nominal wage rates are
fixed in the short run. Even in the absence of nominal rigidities, unanticipated inflation will thus
generate deviations of employment from the natural rate, but nominal rigidities will amplify the
fluctuations in employment.
7. According to the hypothesis of static expectations, the expected inflation rate for the current
period equals the actual inflation rate observed during the previous period. Combined with
the expectations-augmented Phillips curve, the assumption of static expectations implies that
the rate of inflation will keep on accelerating (decelerating) when actual unemployment is
below (above) the natural unemployment rate.
8. So-called supply shocks in the form of fluctuations in productivity and in the wage and price
mark-ups create 'noise' in the relationship between inflation and unemployment. An
unfavourable supply shock implies an increase in the actual rate of inflation for any given levels
of unemployment and expected inflation. In the presence of supply shocks the natural
unemployment rate is defined as the rate of unemployment prevailing when inflation expectations
are fu lfilled and productivity as well as the wage and prce mark-ups are at their trend
levels.
9. An expectations-augmented Phillips curve with static inflation expectations is consistent with
US data on inflation and unemployment in the period from the early 1 960s to the mid 1 990s.
In the 'New Economy' of the late 1 ggos inflation was surprisingly low, given the low rate of
unemployment prevailing during that period. This experience may be seen as a result of a
favourable supply shock arising from the fact that target real wages were lagging behind the
accelerating rate of productivity growth.
10. The economy's short-run aggregate supply curve (the SRAS curve) implies a positive link
between the output gap and the actual rate of inflation, given the expected rate of inflation. The
SRAS curve may be derived from the expectations-augmented Phillips curve, using the production
function which links the unemployment rate to the level of output. The SRAS curve
shifts upwards when the expected inflation rate goes up, or when the economy is hit by an
unfavourable supply shock. When there are no supply shocks and expected inflation equals
actual inflation, the economy is on its long-run aggregate supply curve (the LRAS curve) which
is vertical at the natural level of output corresponding to the natural rate of unemployment.