1 Keynesian Models for Analysis of Macroeconomic Policy 1 Keshab R Bhattarai Business School University of Hull, Hu6 7RX, UK ABSTRACT This paper reviews the Keynesian IS-LM model and the neoclassical and endogenous economic growth models that are widely used in analysing fluctuations of output in the short run and economic growth in the long run. Numerical examples are provided to evaluate impacts to fiscal and monetary policy measures on aggregate demand with a sensitivity analysis of model results to various parameters contained in the model. It is an overview of simple macroeconomic models that are often applied for policy analysis. Key words: Keynes, Macroeconomic policy JEL Classification: E12, E63 September 2005 1 Correspondence address: Business School, University of Hull, HU6 7RX, UK. E-mail: [email protected]Phone: 01482-463207 and Fax: 01482-643484.
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1
Keynesian Models for Analysis of Macroeconomic Policy1
Keshab R Bhattarai Business School
University of Hull, Hu6 7RX, UK
ABSTRACT This paper reviews the Keynesian IS-LM model and the neoclassical and endogenous economic growth models that are widely used in analysing fluctuations of output in the short run and economic growth in the long run. Numerical examples are provided to evaluate impacts to fiscal and monetary policy measures on aggregate demand with a sensitivity analysis of model results to various parameters contained in the model. It is an overview of simple macroeconomic models that are often applied for policy analysis.
Key words: Keynes, Macroeconomic policy
JEL Classification: E12, E63
September 2005
1 Correspondence address: Business School, University of Hull, HU6 7RX, UK. E-mail: [email protected] Phone: 01482-463207 and Fax: 01482-643484.
2
I. Introduction
Macroeconomic models have been in use for formulation of economic policy
almost in every country in the world. These models not only provide an analytical
framework to link the demand and supply sides and the resource allocation process in
an economy but also may help in reducing fluctuations and enhancing the economic
growth, which are two major aspects of any economy. Classical, Keynesian, new
classical and new Keynesian approaches have evolved over time to analyse
fluctuations of output, employment and price level over years (Keynes (1936), Hicks
(1986), Taylor (1987), Taylor (1993), Sargent and Ljungqvists (2000), Minford and
Peel (2002), Blake and Weal (2003), Garratt, Lee, Pesaran and Shin (2003)) contain
techniques how rational expectation could improve predictions from a
macroeconomic model.
Secondly Keynesian models lack sufficient micro foundation to explain the
optimising behaviour of consumers and producers in a market economy. Though all
endogenous variables are determined simultaneously the equations for consumption,
investment, exports and imports or taxes, or interest rates or demand for money are
not derived from the optimising framework. Therefore the results of a standard
Keynesian model cannot determine whether a solution obtained from the model is
optimal one from the perspective of millions of households and firms in the economy.
The new classical and new Keynesian models that have appeared in the last two
decades have attempted to remedy this problem by explicitly incorporating the
optimising framework in the model (Mankiw and Romer (1993)).
Thirdly early Keynesian models lacked a good dynamic structure though some
attempts were made in this direction by Samuelson (1939), Phillips (1958), Phelps
(1968) and Friedman (1968). Model forecasts depended more on backward looking
adaptive expectation framework or on simple autoregressive structure despite the fact
that Ramsey (1928) already had developed an explicit dynamic structure for a
growing economy with single representative household.
Unhappy with Keynesian pre-occupation with short run fluctuations Harrod
(1939), Domar (1947) and Solow (1956) analysed growth taking the Keynesian set up.
28
These growth models involve maximising the utility of the infinitely lived household
dtC
e tt∫∞ −
−
−0
1
1 σ
σρ subject to the technology constraint αα −= 1
tttt NKAY and capital
accumulation process ttttt KCNYK δ−−=& . When simplified, assuming 1=tA 1=tN ,
the optimisation problem is often formulated in the form of a current value
Hamiltonian as
( ) [ ]1
1
1,, −
−
−−+−
= tttt KCK
CKcH δθ
σθ α
σ
where C is consumption, a control variable; K is the capital stock, a state variable, θ
is the shadow price of the capital stock in terms of the utility, a co-state variable.
Market clearing, implicit in the budget constraint, implies that output is either
consumed or invested. The optimal path of capital accumulation is found using four
first order conditions:
0=∂∂
tCH ttC θσ =− (47)
t
ttt K
H∂∂
−= ρθθ& [ ]δαθρθθ α −−= −1tttt K& (48)
tttt KCKK δα −−=& (49)
and the transversality condition 0=∞→
−tt
t Ket
Limθρ (50)
The first equation denotes the shadow price of capital in terms of the marginal
utility of consumption. The second shows how the shadow price is sensitive to
subjective discount factor and accumulation constraint. The final terminal condition
implies no need for capital accumulation at the end of the planning horizon. Capital
stock, consumption and the shadow price of capital remain constant in the balanced
growth path; cgCC=
&; Kg
KK
=&
and θθθ
gt
t =&
. Proof of this follows from (48)
[ ]δαρθθ α −−= −1K
t
t&
δθθ
ρα α +−=−
t
tK&
1 (51)
This is the most important equation for deriving the equilibrium in this model. It
simply states that the marginal productivity of capital should equal the cost of capital,
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where the shadow price measures the opportunity cost of capital. By assumption the
RHS in (51) is constant. This implies that the LHS also should be a constant,
therefore, 0=KK& . Then from the production function, if the capital stock is not growing
then the output is also not growing; and so 0=YY& . From the budget constraint when
output and capital stocks are not growing the consumption is also not growing;
thus 0=CC& . The shadow price also is not changing in the steady state as is obvious by
the log differentiation of (47) t
t
t
t
CC&&
σθθ
−= 0=t
t
θθ& .
The values of capital stock and output in the steady state can be solved from (51):
αδρα +
=−1tK 1
1
* −
+=
α
αδρK and
αα
δρα −
+
=1
*Y .
Though the capital stock does not grow the economy needs positive saving to
maintain the capital stock intact: *** KKC δα −=
The saving rate ( )
+
=
+
==
−
−−
δραδ
δραδδδ
α
αα
1
11
1**
*
KYK (52)
The major difference of this optimal growth model from the standard Keynesian
growth model is that the saving rate is determined in terms of parameters of
preferences and technology rather than being assumed as a constant fraction of the
national income. The higher discount rate for future consumption implies lower
saving rate and more productive capital implies higher saving rate. Higher discount
rate of capital reduces the steady state capital but raises the level of saving in the
steady state.
The transitional dynamics show a process where by the economy converges
towards the steady state once it is disturbed from that path. From the second first
order condition derived above, ( )δαρθθ α +−= −1ttt K& for 0=tθ& , since
30
0>tθα
δρα −
+
=1
1
*K can be used in the ( )tt K,θ space for the transition dynamics of
the shadow price tθ relative to the steady state capital stock as shown in Figure 1.
Figure 4: Transition dynamics for shadow price of capital stock
0=tθ& 0<tθ& 0>tθ&
tθ
K* Capital stock can be increased above the steady state only by raising the shadow price
of capital above its steady state value or if the shadow price is lowered it will reduce
the capital stock. Similarly the transition dynamics of the tK in the ( )tt K,θ space
relative to the steady state of the shadow price tθ can be found using FOC (1);
ttC θσ =− σθ1
−= ttC ; ttttt KCNKK δα −−=& σα θδ
1−
−−= tttt KKK&
σα θδ1
−=− ttt KK (53)
Figure 5: Transition dynamics for capital stock
0=K& 0>K& θ
ttC θσ =− 0<K&
α
δρα −
+
=1
1
*K α
δα −
=
11
'K α
δ−
=
11
1K
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For sufficiently large value of K there is no θ for which (53) will be satisfied. The
largest such value of K can be found by setting the right hand side of (53) to zero.
tt KK δα = α
α
δδ
−−
==
11
11 1K (54)
*KK > since 1<α and the 1>ρ .
Figure 6: Saddle path for Steady State Solutions 0=K& 0=θ& θ I II
ttC θσ =− IV III
α
δρα −
+
=1
1
*K α
δα −
=
11
'K α
δ−
=
11
1K
The saddle points for this model consists of points in ( )tt K,θ space where the
economy will converge to its steady state as shown by lines with arrows in region I
and II in Figure 6. The 0=K& path shows set of values of θ , for which there will be no
change in the stock of capital. Capital stock is rising above this line and falling below
this line. Similarly 0=θ& shows capital stock where there is no change in value ofθ .
The shadow price θ is rising to the right of this and falling to the left of this line.
Right balance between the shadow price and accumulation is obtained only by the
parameter sets in region I and III which guarantee the convergence of the system to
the steady state.
As seen from above derivations the long run growth path of the economy is
determined by a set of parameters in preferences and technology. Values of these
parameters are determined by cultures and institutions. Economies with a hard drive
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for growth have lower discount rates for future consumption and higher rates of
saving than economies that value current consumption more. More efficient
economies produce more from the given sets of inputs.
Once the model parameters are specified it is possible to trace the growth
paths of consumption, output and capital stock in this model. There can be too much
capital if solutions lie in the region II and too little capital if the solution remains in
region IV. Analysis of data on economic growth suggests that OECD and many
middle income economies fall in convergence regions I and III. Fast growing
economies of East Asia belong to region II and they are accumulating too much
capital. Growth disaster economies such as those of Sub-Saharan Africa have not
saved enough and caught in poverty trap in region IV of the above figure.
Implications of the Keynesian models are closer to the conclusions of
endogenous models of economic growth that have become more popular after Lucas
(1988) and Romer (1989) in which the rate of economic growth need not to be limited
by the diminishing rate of marginal productivity of capital as in the above neoclassical
model when accumulated knowledge resulting from work of researchers in
universities or research laboratories is applied in the production process. Infinite
elasticity of supply assumed under the Keynesian models have same implications as
in these endogenous growth models as the demand can drive the rate of economic
progress. The stock of knowledge that exists in the form of designs, formulas or
models is a non-rival good with positive externality as it can be borrowed from the
library. These models assume separate production functions for research, intermediate
and the final goods sector while illustrating the endogenous process of technical
progress and its impact in economic growth. Workers in the research sector produce
new ideas that they sell to an intermediate sector, which apply them in production of
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final goods. Productivity of workers in the final goods sectors rises when they get
better tools to work with. Economic growth is ultimately the result of human
resources employed in the research sector such as universities and research
laboratories. The production function is similar to the labour augmenting technology
in the Solow model with a standard neoclassical production function, ( )βαYALKY = .
Now technology A is the result of efforts of researchers working in the knowledge
sector. Total labour resource (L) can either be used in the knowledge sector AL or in
the production of final goods sector yL : Ay LLL += . As presented in Jones (1995)
any change in the stock of knowledge depends upon the number of people employed
in the knowledge sector, AL , average productivity in the research sector δ and the
stock of existing knowledge A as λφδδ ALA= and φ
λδ−== 1A
LA
dAa A . By log
differentiating this equation one finds that the growth rate of technology is determined
by the rate of population growth in the steady state, φ
δ−
=1
na . Higher rate of growth
of population is beneficial rather than harmful for economic growth because the
economy can afford to put more people in research. This type of endogenous growth
model shows increasing return to scale relative to all inputs used in production. Since
there is imperfect competition in the intermediate goods sector it is possible that
inventors can extract profits by selling patent rights to producers of intermediate
goods. Protecting research in terms of patent rights or subsidies to researchers
becomes optimal as research drives up productivity by increasing the stock of
knowledge in the whole economy. More demand drives higher growth rate both in
Keynesian and endogenous growth models.
34
The real economic growth process is much more complicated than explained
by the above models. Growth involves structural transformation in production, trade
and consumption. Conclusions received from simple single sector models are elegant
but can provide little intuition for actual policy analysis that involves assessments of
the underlying factors that determine demand and supply in the various sectors of the
economy and evaluation of redistribution impacts of policies implemented by public
authorities. Analysis of structural change requires more details on technologies
production across sectors and system of trade, preferences of households and about
the process of capital accumulation and finance. There has been some progress in
constructing more disaggregated dynamic general equilibrium models in recent years.
Sargent and Ljungqvists (2000) have shown how dynamic programming techniques
can be used to provide a consistent dynamic structure of an economy.
Fourth, the majority of Keynesian macro models only have a single good and a
representative firm and a household and lack structural details of an economy required
for evaluation of a policy that can affect various sectors and sections of the economy
in many different ways. Multi-sectoral multi-period dynamic general equilibrium
models developed in recent years provide both micro foundation and inter-temporal
optimising frameworks required for a policy model (Fullerton, Shoven and Whalley
(1983), Auerbach and Kotlikoff (1987), Perroni (1995), Rutherford (1995), Bank of
England, NIESR) Bhattarai (1997, 1999), Kehoe, Srinivasan and Whalley (2005)).
V. Conclusion
This paper briefly reviews the Keynesian IS-LM model and the neoclassical
and endogenous economic growth models that are widely used in analysing
fluctuations of output in the short run and economic growth in the long run.
Numerical examples are provided to evaluate impacts to fiscal and monetary policy
35
reforms and to assess the importance of model parameters that describe the
behavioural aspect of the economy. Discussion here provides an overview of the
macroeconomic models often applied for policy analysis in the literature.
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