Beyond the liquidity trap: ineffectiveness of monetary policy as an instrument
to neutralize demand and supply shocks
Adam Koronowski *
Abstract:
The aim of this paper is to discuss limitations, other then nominal zero bound, to effectiveness
of monetary policy as an instrument to neutralize a negative impact that demand or supply
shocks may have on production and employment. Firstly, intent to boost economy with
expansionary monetary policy may contradict central bank’s primary target of stable prices.
The paper asserts this may be a case even when nominal and real interest rates are positive
and the economy experiences a severe contraction. Secondly, counterbalancing negative
shocks may require negative real interest rates. However, negative real interest rates would
create costs of wasteful use of capital. A question arises whether monetary policy should set
under any circumstances negative real interest rates. A conclusion comes that monetary policy
cannot neutralize negative supply shocks without increase in inflation. “Negative” demand
shocks – increase in propensity to save – allow for lower real interest rates in equilibrium and
are welfare improving as long as there is no problem of the nominal zero bound. This
inference allows for non-Keynesian effects of fiscal contraction. The paper presents also
limitations to smooth functioning of a currency union when there are considerable differences
in regional (national) savings patterns.
*
National Bank of Poland, Faculty of Economics – University of Warsaw
Comments welcome: Adam.Koronowski@mail.nbp.pl
Views expressed in this paper are those of the author and not necessarily represent those of
the National Bank of Poland.
1
I Introduction
Ineffectiveness of monetary policy as an instrument to counteract recessionary
pressures is typically related to the concept of liquidity trap. This traditional concept asserts
that monetary policy is ineffective in a situation when increase in money supply does not
result in falling interest rate but merely in growth of idle balances; the interest rate elasticity
of demand for money becomes infinite. According to Keynesian tradition this is the case
when individuals believe that bond prices are too high and therefore will fall and,
correspondingly, that interest rates are too low and must rise. This interpretation is awkward
and obsolete when considered from the perspective of endogenous money supply. A central
bank can generally cut the rate if it believes it is too high and it really wants to boost the
economy via more expansionary monetary policy. Such an expansion is inefficient in
promoting more spending only in a situation when nominal interest rate is zero; individuals
could avoid negative interest rates by holding more money. This is nominal zero bound
problem which may be considered as a modern interpretation of the liquidity trap.1
The aim of this paper is to discuss other possible limitations to effectiveness of
monetary policy as an instrument to neutralize a negative impact that demand or supply
shocks may have on production and employment.
Firstly, intent to boost economy with expansionary monetary policy may contradict
central bank’s primary target of stable prices. This may be a case even when nominal and real
interest rates are positive and the economy experiences a severe contraction.2 Such a situation
is beyond the scope of these concepts and models which consider inflation (recession) as an
effect of spending that is excessive (deficient) as compared to a certain potential level of
production so that nominal and real developments have the same expansionary or
recessionary direction. This attitude is clearly unrealistic as a general paradigm and it is
enough to call the notion of stagflation to prove this opinion.
Secondly, counterbalancing negative shocks may require negative real interest rates.
In case of sufficiently high nominal interest rates (and rates of inflation) the nominal zero
bound may not constitute a problem. However, negative real interest rates would create costs
of wasteful use of capital. A question arises whether monetary policy should set under any
1
2
Compare Svensson (1999)
This possibility was noted by Summers (1991) and Wilson (2000)
2
circumstances negative real interest rates. This is not a technical problem, as in the case of
nominal zero bound, but a matter of policy optimization.3
In the second part of this paper a simple model of macroeconomic production and
equilibrium is developed. The third and fourth parts present within the structure of the model
the consequences of supply and demand shocks respectively and formulate conclusions on
whether monetary policy can neutralize their impact on production or employment. The fifth
part takes short notice of some outcomes of the model which shed light on functioning of a
monetary union. The article ends up with a resume.
II Model
The first and central equation of the model is production function:
1.
Y = aKL ,
where 

In eq. 1 Y stands for the real domestic production (income) and K and L for capital
and labor engaged in production.
The condition  expresses decreasing returns to scale. This condition is
crucial for the model. Only limited amounts of labor and capital can be engaged in production
due to decreasing returns which must cover some given prices of the factors of production. As
a consequence, domestic product may remain below full utilization of available resources.
When the amount of capital is fairly flexible at least in a longer term – due to investment and
capital depreciation – the factor of production which may remain idle is labor; the model
allows for unemployment.
Since the condition has much importance for the model and it is not the conventional
assumption of constant returns to scale, it needs some justification. It seems fairly
uncontroversial that there should be at least one factor of production other then labor and
capital (such as land, human capital, natural resources). Let’s assume its amount is constant.
This means diminishing returns of capital and labor. If the factor(s) of production nonspecified in the production function is Z then
3
Since zero bound problem is treated as a technical problem there is a streak in literature that develops ideas
how to “fool” he markets and make them responsible to negative nominal interest rates. An example of such
attitude are Krugman (1999), Svensson (2000), Wojtyna (2001).
3
2.
where 
Y = a*KLZ ,
Since Z is a constant eq. 2 is none other then eq. 1 with the condition of decreasing
returns to scale given only two factors of production are considered openly (they define the
scale).
From eq. 1 we get
3.
MPK =  aKL
4.
MPL = aKL,
and
where MPL and MPK is marginal product of capital and labor respectively.
Marginal product of labor equals real wages (w) which for simplicity and to focus
attention on monetary aspects are assumed to be constant.4
5.
MPL = w.
Marginal product of capital must cover the real cost of capital which equals real
interest rate (r) and the rate of capital depreciation (
6.
MPK = r + .
Eq.. 3 – 6 give
7.
(r + / w = MPK / MPL = L / K
8.
K = wL / (r + .
and
Eq. 8 and eq. 3-6 allow to determine the amounts of capital and labor used at its’
given costs:
9.
4
L = [w / a] [(r + / w]
and
The level of w must only satisfy the condition that demand for labor should be lower then its supply.
4
10.
K = [(r + / a] [w(r + ].
Eq. 7, 9 and 10 have some important properties. Interest rate cut brings about – as eq.
10 predicts - more capital engaged in production. It also leads to higher employment
according to eq. 9. However, technology becomes more capital-intensive (eq. 6). It is easy to
show that product increases. Similarly, wage reduction leads to higher employment, more
capital engaged, more labor-intensive technology and production increase.
Eq. 9 and 10 describe the amounts of labor and capital that can be effectively used in
production. This need not be consistent with full employment. Moreover, none of the
equations above touches upon the issue of equilibrium in the market for goods and services.
This problem may be addressed as in eq. 11 which is a condition for equilibrium in the goods
market. This resembles the respective condition in Solow’s model, however, it is not
expressed in terms “per labor unit”.5
11.
mY,
where m is a constant and 0<m<1.
Eq. 11 – together with eq. 1, 8, 10 – determines a level of the interest rate consistent
with goods market equilibrium. This interest rate level is described by eq. 12.
12.
r / m) – 1]
The equilibrium interest rate from eq. 12 (through eq. 1, 8, and 9) determines how
much capital and labor is engaged in production and how big the product is.6
Let’s notice here that the equilibrium interest rate may take negative values. However,
since m<1 it always holds that r> – 1). Moreover, extreme and improbable case when
m=1 (savings and investment in equilibrium is equal income) shows that sufficiently low
negative equilibrium interest rate must reduce consumption which is price for wasteful use of
capital in a steady state. 
In Solow’s model the respective condition of equilibrium is always binding and it determines the amount of
capital (per labor unit) engaged in production in a steady state. In the model presented in this paper the amount
of capital depends on real interest rate and it sets the value of investment (equal capital depreciation). Savings
and investment may be equal only due to a separate condition – eq. 11 which is not self-imposing.
6
More sophisticated savings function (in particular dependent directly on interest rate) could also produce more
than one solution - a single level of equilibrium interest rates. In such a case multiple equilibrium interest rates
could be ranked with regard to production levels. Some of these equilibria would render undesirable features –
interest rate increase above an equilibrium rate would give rise to inflation.
5
5
The model does not describe situations which emerge in case of interest rates below or
above the equilibrium interest rates. It is only assumed here that interest rate above the level
specified by eq. 12 implies that aggregate demand is insufficient to uphold current production
and it results in recession (prices are inelastic downward), interest rate below the level fuels
inflation. In this sense the interest rate from eq. 12 is natural.
Eq. 11 assumes a very simple form of consumption (and savings) function. Savings
are not determined within a general equilibrium model based on micro-foundations. As a
consequence, the model pertains only to steady-states when investment equals depreciation. It
allows for comparative static only.7 If the economy experiences macro disequilibrium, within
the model a necessary condition to restore equilibrium is a change of the interest rate set by
the central bank (changing fiscal stance not explicitly included in the model). The model does
not supply a dynamic description of disequilibrium and in particular of a mechanism which
could restore a recessionary steady-state in absence of monetary policy reaction. In case of
overheating, a natural interpretation is that rising prices reduce real consumption and
investment in relation to the levels planned in nominal terms of a previous period. As long as
real interest rate is falling (nominal rate is constant) it results in ever growing inflation8. In
case of recession a mechanism which should restore equilibrium might be looked for in
dynamic feedbacks among savings, income and income expectations. Such analysis would
require much more attention paid to the savings function than in the presented form of the
model. However, it needs to be openly expressed that the model purposefully is not a general
equilibrium model. In fact it is rather admitted here that recessionary pressure may lead to
abandonment of first best procedures of micro-optimization: only its violation may lead to a
new steady state of a recessionary macro-equilibrium. In particular, deficient demand may
entail job reduction and - at constant capital in a short period – a fall in output combined with
rising marginal productivity of capital. This would support investment and reduce savings (in
parallel with income) and restore a macro-equilibrium. The conditions expressed by eq. 3 and
4 would, however, not be met in this case.9 Of course, this a simple suggestion and it is not
alleged here that during real life recession capital stock and investment would not fall. The
7
However, it would be easy to amend the model so that it encompass economic growth due to increase in total
factor productivity (increase in the amount of non-specified factors Z).This would be consistent with the analysis
applied and conclusions drawn with regard to supply shocks discussed in the next part of the paper and it would
not change main lessons from the model.
8
Compare Friedman(1968)
9
Labor would receive remuneration below its marginal product and – as a consequence – entrepreneurs would
receive incomes above the marginal product of capital.
6
example is only to show what role can be played by changing proportions of factors of
production when disequilibrium is transferred from macro to micro level.
In this context it is worth noticing that savings levels (determined with respect to
micro-optimization) would always be consistent with macro-equilibrium if they were
dependent on endogenous interest rate that should match savings and investment. Any
autonomous shift of the savings function would lead to a change of the interest rate consistent
with macro-equilibrium. In such a case natural and actual interest rates would be the same.
However, in modern economies nominal interest rates – and in consequence real ones - are
exogenously set by central banks (and money supply is endogenous, not the opposite).
The formula for the natural interest rate given by eq. 12 does not contain real wages.
However, more sophisticated consumption (and savings) function would make the natural
interest rate depend on real wages. Then flexible wages could – formally – constitute a factor
which allows for macro-equilibrium for any given level of interest rate set by the central bank.
Even so, elastic wages considered as a subject to micro-optimization consistent with labor
market equilibrium would not help much with regard to macro-equilibrium. On the one hand,
labor market equilibrium may not be compatible with recessionary macro-equilibrium (or
simply with the steady state balance between savings and investment) but at a particular
(natural) level of interest rate; macro-equilibrium remains the task of the central bank (given
fiscal stance). On the other hand, even though – due to changes in techniques and amount of
capital employed – there may be a level of wages that guarantee macro-equilibrium for any
given interest rate it would not be consistent either with micro-optimization or full
employment. There is no reason why wages should be a factor which restores macroequilibrium.10 Moreover, if wage changes were to restore macro-equilibrium at any interest
rate there would be nothing like the natural rate of interest. It seems thus reasonable to
approve of the feature of the model that wages are not considered as a factor which allows for
macro-equilibrium; wages are assumed to be inelastic. Also a form of savings function which
eliminates wages from the formula for the natural interest rate is accepted.
Things are even more complicated. National savings should contain public savings or
deficits. As a consequence a mutual relation between balances of private and public sectors
should also be included in the analysis – for example in the form of the Ricardian
equivalence. This problem is not formally recognized within the model.
10
In case of deficient demand wages should fall due to rising unemployment; however, this would turn
techniques less capital intensive and would temper the process of return to a steady state.
7
It is a useful extension of the model to lift the implicit assumption of closed economy.
Eq. 11 and 12 may be easily transformed to forms which should comprehend current account
balance. Current account developments due to changes in absorption and in relative price
levels (real exchange rates) – for example as a result of excessive demand – could be a short
and medium term adjustment mechanism which restores internal equilibrium. This in turn
opens questions on long term current account sustainability. Since this is not a task and
ambition of the paper to present a coherent theoretical general equilibrium model ranging
from dynamic, short term micro-optimization on the one hand to long-term current account
sustainability on the other hand, the issue of balance of payment is not formally recognized in
the model. It is enough to say here that excessive demand results not only in inflationary
pressures but also in widening of current account deficits at fixed exchange rates.
Summing up, the model is not a general equilibrium model rooted in microfoundations but it could be subject to some interpretations (or extensions) featuring dynamic
mechanisms which should allow for recessionary macro-equilibrium (steady state) or lead to
inflationary explosion. However, what is important here is not these mechanisms but the role
that monetary policy can play to counterbalance shocks and restore equilibrium before any
medium- or long-term endogenous mechanisms find their way.
III Supply shocks
A negative supply shock is interpreted here as a decline in production achieved form
given amounts of the factors of production (capital and labor). Marginal products of capital
and labor diminish and they are above their cost. Since diminishing returns of scale are a
feature of the model, quantities of both factors engaged in production shrink as a result of a
negative supply shock so that marginal products should grow and meet the factor costs again.
In this context there are two important questions; 1. whether monetary policy can offset the
shock and allow to maintain the level of production and/or employment, 2. what monetary
policy stance is needed to maintain equilibrium.
A negative supply shock in terms of the model means the parameter a of the
production function has decreased; a2<a1. Let’s assume that the aim of monetary policy is a
constant level of employment, L2 = L1. Using eq. 8 for two different values of the parameter a
and two different interest rates under the condition of stable employment we obtain
15.
r2 + r1 +  (a2/a1) 1/ .
8
Eq. 15 shows that lower interest rate (r2< r1) is needed to compensate for the impact
a negative supply shock exerts on employment. It is easy to prove that the condition of
constant production gives the same solution (eq. 15).
A few conclusions are worthwhile. Firstly, even when r1>0 it is possible that r2<0; it
may need negative real (and probably nominal) interest rate to counter the shock. Secondly,
the shock has no impact on natural interest rate given by eg. 12. Should interest rate be cut
with respect to employment and production considerations, it would give rise to excessive
demand and – as a consequence - inflationary pressures and current account deficit widening.
This is intuitively understandable; at a constant level of production and savings (given the
assumed savings function), at lower interest rate, higher capital engaged and higher
investment there must be excessive demand. Thirdly, in case of a modest monetary reaction to
the shock and interest rate set between r1 and r2 there should be both economic contraction
and inflation – the model admits stagflation. Fourthly, it is worth lifting the assumption of
inelastic real wages to note that wage reduction could boost production and employment – it
could offset the real effects of the shock – at a constant, natural interest rate.11
IV Demand shocks
A negative/positive demand shock can be expressed in terms of the model as
decrease/increase of the propensity to save (m2>m1 or m2<m1 respectively). First of all let’s
notice that in face of a demand shock monetary policy has to react to disequilibrium and not
to fall in equilibrium level of output, which was the case of a negative supply shock.
In the case of decrease in propensity to save natural rate of interest is rising. To stop
inflationary pressures central bank has to raise its interest rate. Until now interpretation of this
situation is easy – excessive demand leads to inflationary pressures and monetary policy
contraction. A part of such interpretation might be, however, inference that demand has
grown above the level of potential product and interest rate hike has returned demand and
production to its’ previous levels. This inference is false; as interest rate is raised to its new
natural level, product declines. Anti-inflationary monetary policy as a reaction to consumption
boom entails costs in real terms. This conclusion reflects the fact that the model encompasses
both supply and demand aspects of economy.
11
This conclusion, however, crucially depends on the form of savings function.
9
Since public spending is12 not explicitly considered in the model it may be useful to
admit interpretation when rising consumption is a result of higher public spending. In this
case the model envisages deterioration of policy mix. Higher public deficits force the central
bank to raise interest rate in search of price stability – as a consequence income declines. This
remark is in line with often empirically observed non-Keynesian effects of fiscal
consolidations.
In the case of rising propensity to save natural interest falls and the central bank
should lower its interest rate to maintain equilibrium. This leads to more investment, higher
employment and bigger product. A “negative” demand shock – decline in consumption levels
– should bring about positive results when equilibrium is preserved due to easier monetary
policy.
However, as it has been already noted, natural interest rate might turn negative in
nominal and/or real terms. A supposition is that savings have an ambiguous role. On the one
hand rising savings allow for interest rate cut, more resources employed and bigger product
received at stable prices. On the other hand high propensity to save may turn monetary policy
ineffective in light of negative real (and possibly nominal) natural interest rate.
The case of nominal zero bound is subject to rich literature and not to this paper. A
question which matters here is thus what policy would be optimal in the case of negative real
(and positive nominal) natural interest rate? Is it rational to set negative real interest rates
which cause wasteful use of capital?
More capital engaged in production of course gives higher product. The problem is
that marginal product of capital is lower than depreciation and – at a steady state – it brings
costs in terms of consumption. However, more capital allows also for more employment and
further rise in product. A negative interest rate does not necessarily diminish consumption and
is irrational. Moreover, as it has been already suggested, there must be a real natural interest
rate level such that lower rates would diminish consumption. Let’s find such a level of natural
interest rate.
Firstly, let’s check how increase in capital changes income when eq. 3 and 4 hold.
Using eq. 1, 8 and 10 we get
16.
12
dY/dK = a (r +a .
For more on these observations and their interpretation look, for example, Giavazzi, Cotis (2005).
10
We know that at steady state dI/dK =  We also want that income should rise faster
than investment leaving room for increase in consumption (what can be expressed as
dY/dK>dI/dK). As a consequence we get a condition

r > (

Eq. 17 states that income growth is higher than increase in investment if only interest
rate were above the level given by the right hand side of eq. 17. It is easy to show that the
right hand side of this equation has a negative value and is higher than the minimum formally
possible natural interest rate rm=1= – 1), which confirms our earlier suggestion. This
proves that in decreasing natural - and actual - interest rates are welfare improving as long as
natural interest rate is not lower than its negative value given by eq. 17. Moreover, natural
interest rate would assume values lower than the left hand side of eq. 17 only when
m>, which is unreasonable.
In different words, in a reasonable scenario, monetary policy can accommodate a
“negative” demand shock and restore equilibrium at a higher level of income and
consumption even though it may call for negative real interest rate. It means that such a shock
might entail recessionary pressures which cannot be overcome by monetary policy only in
case of nominal zero bound. In the case of zero nominal bound expansionary fiscal policy
would increase natural interest rate and thus it could restore equilibrium at zero natural
interest rate. In this case expansionary fiscal policy would be thus welfare improving although
earlier in part it has been noticed that higher deficits deteriorate policy mix if they push up
natural interest rate which is not beyond reach of the central bank.
V Monetary unions in light of the model
It appears from the model (and its non-formal extensions) that in a monetary union
characterized with different regional (national) savings patterns and as a consequence
different natural interest rates there must be also regional differences in inflation rates and
current account developments.
It has been already suggested in this paper that current account developments may
constitute a factor which mitigates disequilibrium in the domestic market in a short run and
puts saving patterns more in line in a long run. This kind of accommodation is envisaged in
11
European Commission (2005). It does not mean that the process of getting in line would not
be painful. In fact, high expenditures leading to inflation, current account deficits and flawed
competitiveness may require in future periods deep contraction in spending and economic
activity which would keep external debt and current account deficits within reasonable
boundaries. High consumption spending may thus turn out to have been excessive in terms of
inter-temporal optimization and from the perspective of its recessionary consequences.
Overheating and relatively high inflation lead to unavoidable slow down.13 It would be too
optimistic to assume that due to endogenous criteria of optimal currency area a monetary
union should quickly and at low cost overcome such problems.
These remarks suggest that fiscal policy eliminating differences in national saving
patterns (private and public together) could constitute an important factor providing more real
and nominal convergence in a monetary union. However, since the national differences might
be pervasive features of particular economies rather than only temporal, cyclical divergences
it might turn out that fiscal policy could not play this role, especially in environment of strict
fiscal rules. In particular, it is difficult to imagine that countries characterized with high
savings and low growth could run considerable expansionary fiscal deficits. Such deficits
would bring about growth of public debt and deterioration of their long term credibility or
which would violate rules such as Stability and Growth Pact. It is equally improbable that
other countries of a union would be ready to maintain fiscal surplus in a long run.
This suggests that a successful monetary union is possible only in case of fairly
homogenous societies.14 Future will show whether Europe meets this criterion.
VI Resume
The paper formally proves that intent to counteract economic contraction with
expansionary monetary policy may contradict central bank’s primary target of stable prices.
This may be a case in a situation of a negative supply shock. Counterbalancing negative
shocks may require negative real interest rates. “Negative” demand shocks – increase in
propensity to save – allow for lower real interest rates in equilibrium and they are welfare
improving as long as there is no problem of the nominal zero bound. Although negative real
interest rates bring social cost of wasteful use of capital it seems that falling real natural
13
This remark pertains only to excessive spending and resulting disequilibria and not to such phenomena as
Balassa-Samuelson effect.
14
Free movement of factors of production is an important optimum currency area criterion. Asymmetric
positions of particular economies could theoretically encourage migration – however this needs even more
12
interest rates would allow for gains in consumption due to rise in employment, at least in a
reasonable range of negative rates. A conclusion comes that there are two situations in which
monetary policy is ineffective: this is a negative supply shock and a case of the nominal zero
bound. Wit exception of the latter situation the inference is that fiscal contraction brings about
non-Keynesian effects.
Another conclusion from the paper states that differences in regional (national)
savings patterns constitute important limitations to smooth functioning of a currency union.
References:
European Commission, Directorate General for Economic and Financial Affairs, Growth
differences in the euro area, 2005
M. Friedman, The role of monetary policy, American Economic Review, no. 58/1968
F. Giavazzi, J.-P. Cotis, Political economy of strong fiscal adjustments, a paper presented at
the conference of the National Bank of Poland Fiscal policy and the road to the
euro, July 2005
P. Krugman, Thinking about the liquidity trap, http://web.mit.edu/krugman, 1999
D. Laidler, The Demand for Money, Theories, Evidence, Problems, Harper Collins College
Publishers, 1993
J. Smithin, Controversies in Monetary Economics; Ideas, Issues and Policy, Edward Elgar,
1994
L. Summers, How Should Long-term Monetary Policy Be Determined? Journal of Money,
Credit and Banking, August 1991, Part 2
L. E.O. Svensson, How Should Monetary Policy Be Conducted in an Era of Price Stability,
In: New Challenges for Monetary Policy, A Symposium Sponsored by The Federal
Reserve Bank of Kansas City, Jackson Hole, August 1999
L. E.O. Svensson, The Zero Bound in an Open Economy: a Foolproof of Escaping from a
Liquidity Trap, NBER Working Paper 7957, October 2000
D. Wilson, Japan’s Slowdown: Monetary versus Real Explanations, Oxford Review of
Economic Policy, no 2/20000
A. Wojtyna, Skuteczność polityki pieniężnej w warunkach niskiej inflacji: problem zerowej
granicy nominalnych stop procentowych, Bank i Kredyt nr 7/2001
profound social homogeneity. It is unrealistic to assume that large scale migration of “Germans” to “Ireland”
would be possible or politically acceptable for either party.
13
14