EC3115MonetaryEconomics...intersection of demand and supply). Firms are assumed to have the ability...

EC3115 :: L.10 : Old Keynesian macroeconomics Almaty, KZ :: 20 November 2015

EC3115 Monetary EconomicsLecture 10: Old Keynesian macroeconomics

Anuar D. Ushbayev

International School of EconomicsKazakh-British Technical University

https://anuarushbayev.wordpress.com/teaching/ec3115-2015/

Tengri Partners | Merchant Banking & Private [email protected] – www.tengripartners.com

Almaty, Kazakhstan, 20 November 2015

ISE – KBTU A.D. Ushbayev (2015)

https://anuarushbayev.wordpress.com/teaching/ec3115-2015/

EC3115 :: L.10 : Old Keynesian macroeconomics - 2 / 62 -

Relevant reading

Book treatment

B. McCallum. (1989). Monetary Economics, Chapters 9 & 10.

F. Mishkin. (2016). The Economics of Money, Banking and Financial Mar-kets, 11th edition, Pearson Education, Web Chapter 1 and its Appendix.

Must-read articles

B. Bernanke, A. Blinder. (1988). “Credit, Money, and Aggregate Demand”,American Economic Review, Vol. 78, No. 2, pp. 435-439.


https://media.pearsoncmg.com/intl/global/ema_ge_mishkin_econmbfm_11/webchapters/M01_MISH4199_11_GE_Ch01_Web.pdf

http://www.ssc.wisc.edu/~mchinn/bernanke_blinder_AEAPP1988.pdf

EC3115 :: L.10 : Old Keynesian macroeconomics - 3 / 62 - The basic sticky-wage Keynesian model

Section 1

The basic sticky-wage Keynesian model



Keynesian aggregate supply function

An early model of nominal rigidities was that of sticky nominal wages.Labour unions were argued to negotiate wages on a yearly basis,which would not allow nominal wages to adjust instantaneously tochanges in market conditions.

Like in the classical model, output here is produced from capital andlabour, and firms employ workers up to the point where the marginalproduct of labour is equal to the marginal cost, the real wage.

However, unlike in the classical model, labour employed, and henceoutput produced, only depends on labour demand (not on theintersection of demand and supply).

Firms are assumed to have the ability to choose how much labour toemploy, even if this is more than workers wish to supply at theprevailing real wage.

This could happen, for example, by firms asking, or forcing, labour towork overtime. Similarly, if the demand for labour by firms was belowthat which workers wish to supply, this will result in unemployment.



The aggregate supply curve in the economy is then going to beupward sloping.

If the nominal wage is fixed at W ∗ , an increase in the price level willcause the real wage, W ∗/P , to fall, resulting in higher labour demand.

More labour employed (if firms have the right to manage work forcesupply1) will lead to more output supplied, implying anupward-sloping aggregate supply schedule.

However, in the long run, wages will be renegotiated to the marketclearing level, at which point employment, output and other realvariables are determined by tastes and technology, not the price level.

The long-run aggregate supply schedule is then vertical as in theclassical model.

1Only needed when the real wage is below the labour market-clearing wage rate.ISE – KBTU A.D. Ushbayev (2015)


Graphical depiction of the mechanics of the basic Keynesian model



The effect of monetary policy in a model with sticky wages

In the above diagram set:The middle left panel shows the labour market when the nominalwage is fixed at W ∗.

The bottom left panel shows the standard production function withdiminishing marginal returns to labour.

The top right diagram shows the IS-LM curves.

The middle right panel shows aggregate demand and supply. Notethat aggregate supply is upward sloping as explained above.

Expansionary monetary policy causes the aggregate demandschedule to shift out and also causes the LM curve to shift to the right.

Since the AD shift causes a price rise, this will tend to reduce realmoney balances, causing a partial offsetting of the outward LM shift.



As in the classical model, a monetary expansion causes the labour demandcurve to shift out.The increase in the price level reduces the real wage for any given nominalwage, leading to an increase in labour demand. However, since the nominalwage is fixed, and given the “right to manage” assumption, firms employ morelabour so that employment increases to l ′′ and output increases to y ′′.A monetary expansion therefore has real effects caused by nominal wagesbeing sticky.In the long run, however, the nominal wage will be bid up as workersrenegotiate their contracts to counter the fall in their real wage, and thusemployment will remain at l ′, output will remain at y ′ and the monetaryexpansion simply causes a one-for-one movement in prices and nominalwages.The assumption of sticky nominal wages can easily explain the short-run realeffects of monetary policy. However, this implies that the real wage isstrongly countercyclical.Again, there is some controversy here, but evidence seems to suggest that thereal wage is weakly procyclical.



Revisiting the Phillips curve

Despite the ability of the above model to explain the existence ofunemployment, it sheds very little light on to the mechanism bywhich wages are determined. If wages are predetermined in thecurrent period, then changes in the economy must be reflected inwages in the next period.

Remember that Phillips (1958) “overcame” the problem of assumingexogenously fixed wages by assuming2 that the nominal wagedepends on recent values of unemployment.

Intuitively, if unemployment was high, trade unions, and labour ingeneral, could not negotiate larger pay increases since firms wouldhave a large pool of unemployed with which to fill its vacancies. Whenunemployment is high, labour tends to be in a weak bargainingposition.

2Phillips extrapolated from the money wages-unemployment relationship to a priceinflation-unemployment one, although in reality even the link between rate of change ofmoney wages and unemployment is highly nonlinear.



The specification Phillips gave for the relationship was:

ln Wt︸︷︷︸

:=wt

= ζ�

ut−1

�

+ ln Wt−1

⇒∆wt = ζ�

ut−1

�

with ζ′ < 0

Firms that maximise profits will set the marginal product of labour equal tothe real wage, Wt/Pt , which implies that an increase in the nominal wagewill be associated with an increase in the price level.

Extrapolating from∆wt to∆pt :

∆p = ζ�

ut−1

�

with ζ′ < 0

The relationship states that there is a permanent trade-off betweeninflation and unemployment.



It appeared that all policy makers had to do to lower unemployment andincrease output was to allow inflation to rise.



However, in the 1970s the Phillips curve relationship broke down andthis was explained, and indeed predicted, by Friedman (1968)3 andPhelps (1970)4 who emphasised the importance of inflationexpectations, which had been ignored thus far.The introduction of the Phillips curve, as a fundamental structuralrelationship that characterises the wage adjustment process, intoeconomic analysis marked a shift from the original Keynesiandefinition of full employment in terms of job openings to job seekersratio to one that assumed an existence of trade-off between inflationand unemployment.The original Phillips curve is no longer used because of itsover-simplification of reality, but expectations-augmented Phillipscurve-like relations figure even in modern New Keynesian DSGEmodels.

3M. Friedman. (1968). “The role of monetary policy”, American Economic Review, Vol. 58,No. 1, pp.1-17.

4E. Phelps. (1970). Microeconomic Foundations of Employment and Inflation Theory. NewYork: Norton.



Friedman and Phelps claimed that agents cared, not about their nominalwage, but about their real purchasing power, and thus the real wage.

By augmenting the original Phillips curve with inflation, unemployment inperiod t − 1 would determine changes in real wages:

∆wt −∆pt = ζ�

ut−1

�

However, since there is no current information about∆pt (inflation is onlyrealised after nominal wages have been negotiated), its future realisedvalue has to be anticipated.

Denoting by∆pet the expectation formed at date t − 1 of inflation at date

t , the expectations-augmented Phillips curve can be written as:

∆wt = ζ�

ut−1

�

+∆pet with ζ′ < 0



The expectations augmented Phillips curve explained the breakdownof the simple version that occurred in the 1970s. There were argued tobe a number of short-run Phillips curves, one for each level ofexpected inflation.

Unexpected inflation would move you along a given short-run Phillipscurve but in the long run there would be no trade-off betweenunemployment and inflation. As people’s expectations of inflationincreased to meet actual inflation we would move to anothershort-run Phillips curve.

In equilibrium, when inflation was equal to expected inflation,unemployment would be constant at its natural rate.

In the long run, any attempt to reduce unemployment to below itsnatural rate would simply be inflationary.



The reason the Phillips curve broke down was because of thepersistent and high inflation of the 1970s.

This was caused partly by policy makers trying to exploit the Phillipscurve to reduce unemployment and partly by the supply side shocksin the form of large oil price rises in 1974.

Incidentally, this is a good example of Goodhart’s law in action: when astable relationship is discovered and starts to be used, it breaks down5.

The high inflation caused expectations of inflation to increase, causingthe existing ‘stable’ Phillips curve to shift.

In the period 1861 to 1957, although there were periods of notableprice rises and falls, inflation, and therefore expected inflation, was onthe whole rather stable.

5Original formulation: “any observed statistical regularity will tend to collapse oncepressure is placed upon it for control purposes” – C. Goodhart. (1975). “Problems of MonetaryManagement: The U.K. Experience”, Papers in Monetary Economics, Reserve Bank of Australia.



Okun’s lawThe basic Keynesian model suggests exists is a somewhat negative relationshipbetween unemployment and the output gap,

�

yt − y∗�

.

This is known as Okun’s law, which can be applied to the expectations-augmentedPhillips curve to transform it into:

∆pt = γ�

yt − y∗�

+∆pet with γ′ > 0

⇒ yt = y∗ +1

γ

�

∆pt −∆pet

�

Note that this is similar to the Lucas ‘misperceptions’ model:

yt = y∗ + d�

Pt −Et−1

�

Pt

��

where d = 1/γ, and where the unanticipated change in the price level has beenreplaced by the unanticipated change in inflation.

Note that although both the Lucas model and Okun’s law have similar predictions –i.e. real effects of unanticipated monetary policy caused by an upward-slopingaggregate supply curve – they have different microfoundations.

The Lucas supply curve is based on imperfect information on the sources of good specific pricechanges that affects real output and employment fluctuations are voluntary, whereas the Phillipscurve assumes nominal rigidities that lead to involuntary employment fluctuations.


EC3115 :: L.10 : Old Keynesian macroeconomics - 17 / 62 - A sticky-price Keynesian model

Section 2

A sticky-price Keynesian model



The case of sticky prices

We now turn to studying a McCallum (1989) economy with sticky prices,where the aggregate demand expression is derived from the standard ISand LM equations:

yt = β0 + β1

�

mt − pt

�

+ β2Et−1

�

pt+1 − pt

�

+ vt

whereyt – log of real output at time t ,

mt – log of nominal money balances,

pt – log the price level,

vt – a random demand shock with zero mean (i.e. an element ofaggregate demand that is not picked up by real money balances orexpected inflation),

β0, β1 and β2 – are positive parameters.

Et−1 [·] – is the expectations operator denoting expectations offuture values of a variable formed at time t − 1.



In rational expectations, agents not only take all available informationinto account when they form their expectations, but theirexpectations are also consistent with the way in which the variablesactually evolve (i.e. agents “know the model”).

Therefore rational expectations are sometimes also known as “modelconsistent” expectations.

The above equation states that aggregate demand depends positivelyon real money balances and positively on expected inflation.

For any given nominal interest rate, higher inflation implies a lowerreal interest rate, making investment cheaper.



Aggregate supply is a little trickier to specify because of the assumptionthat prices are set at the beginning of the period, with supply beingdemand determined.

Denote the goods market-clearing price at time t by p∗t , and themarket-clearing level of output by y∗t .

We assume that the prices pt – that the firms set at time t − 1 to beoperational in the market at time t – are their expectations of themarket-clearing prices for time t , such that:

pt = Et−1

�

p∗t�

Since random demand shocks, vt , are not known in advance and havezero mean, they do not figure in the price-setting equation.

Then, if the price equals that which allows markets to clear, bydefinition markets must clear and so y∗t must equal the demandwhenever pt = p∗t :

y∗t = β0 + β1

�

mt − p∗t�

+ β2Et−1

�

pt+1 − p∗t�

+ vt



Rearranging the above:

y∗t = β0 + β1mt − β1p∗t + β2Et−1

�

pt+1

�

− β2 Et−1

�

p∗t�

︸︷︷︸

=pt

+vt

= β0 + β1mt + β2Et−1

�

pt+1

�

+ vt − β1p∗t − β2pt

Now, noting that with market clearing we have pt = p∗t :

y∗t = β0 + β1mt + β2Et−1

�

pt+1

�

+ vt −�

β1 + β2

�

p∗t

And therefore solving for p∗t gives:

p∗t =β0 − y∗t + β1mt + β2Et−1

�

pt+1

�

+ vt

β1 + β2



We now need an expression for the dynamics of the market-clearing /full-employment level of output, y∗t .

The model of McCallum (1989) uses the following dynamic equationfor y∗t :

y∗t = δ0 +δ1 t +δ2 y∗t−1 + ut

which includes a linear time trend and also a term that depends onthe last period’s full employment output level, plus a zero-meanrandom supply shock.

The presence of δ2 y∗t−1 allows persistence of full employment output.

To see this compare the above with an equation that only includes atime trend

y∗t = δ0 +δ1 t + ut

y∗t+1 =�

δ0 +δ1

�

+δ1 t + ut+1

where the expression for the next period market-clearing output doesnot include the previous-period ut term, so the shock is short-lived.



In contrast, when the equation for y∗t includes its own lagged value,we have:

y∗t = δ0 +δ1 t +δ2 y∗t−1 + ut

y∗t+1 =�

δ0 +δ1

�

+δ1 t +δ2 y∗t + ut+1

=�

δ0 +δ1

�

+δ1 t +δ2

�

δ0 +δ1 t +δ2 y∗t−1 + ut

�

+ ut+1

=�

δ0 +δ1 +δ0δ2

�

+�

δ1 +δ1δ2

�

t +δ22 y∗t−1 + δ2ut + ut+1

Thus the shock is long-lived: e.g. a positive value of ut increases y∗t bythe same amount, which in turn increases y∗t+1 by δ2ut , which in turnincreases y∗t+2 by δ2

2ut and so on.

If full employment output is high today, it is likely to be high tomorrow.



We now have the four equations that close the model.

Aggregate demand:

yt = β0 + β1

�

mt − pt

�

+ β2Et−1

�

pt+1 − pt

�

+ vt

Aggregate supply:

pt = Et−1

�

p∗t�

p∗t =β0 − y∗t + β1mt + β2Et−1

�

pt+1

�

+ vt

β1 + β2

y∗t = δ0 +δ1 t +δ2 y∗t−1 + ut



Taking expectations of the last expression for aggregate supply y∗t :

Et−1

�

y∗t�

= Et−1

�

δ0 +δ1 t +δ2 y∗t−1 + ut

�

= δ0 +δ1 t +δ2 y∗t−1 +Et−1

�

ut

�

︸︷︷︸

:=0

= δ0 +δ1 t +δ2 y∗t−1

⇒ Et−1

�

y∗t�

= y∗t − ut

Taking expectations of the expression for aggregate demand at fullemployment (i.e. at y∗t ):

Et−1

�

y∗t�

= Et−1

�

β0 + β1

�

mt − p∗t�

+ β2Et−1

�

pt+1 − p∗t�

+ vt

�

= β0 + β1Et−1

�

mt

�

− β1 Et−1

�

p∗t�

︸︷︷︸

=pt

+β2Et−1

�

pt+1

�

− β2 Et−1

�

p∗t�

︸︷︷︸

=pt

+Et−1

�

vt

�

︸︷︷︸

:=0

= β0 + β1

�

Et−1

�

mt

�

− pt

�

+ β2

�

Et−1

�

pt+1

�

− pt

�



Thus we have:

Et−1

�

y∗t�

= β0 + β1

�

Et−1

�

mt

�

− pt

�

+ β2

�

Et−1

�

pt+1

�

− pt

�

Noting also that from the expectation of aggregate supply we have:

Et−1

�

y∗t�

= y∗t − ut

Then, combining, we get:

y∗t = β0 + β1

�

Et−1

�

mt

�

− pt

�

+ β2

�

Et−1

�

pt+1

�

− pt

�

+ ut

Subtracting the above from the expression for aggregate demand we haveand equation for the output gap:

yt − y∗t = ��β0 + β1

�

mt −��pt

�

+(((((((

(((β2

�

Et−1

�

pt+1

�

− pt

�

+ vt −

−��β0 − β1

�

Et−1

�

mt

�

−��pt

�

−(((((((((

(β2

�

Et−1

�

pt+1

�

− pt

�

− ut

= β1

�

mt −Et−1

�

mt

��

+ vt − ut



Monetary policy in a McCallum (1989) economy

Imagine that the central bank uses the money supply as the policyinstrument,and sets its level according to the following rule:

mt = µ0 +µ1mt−1︸︷︷︸

systematic component

+ et︸︷︷︸

random shock component

Taking expectations gives:

Et−1

�

mt

�

= µ0 +µ1 Et−1

�

mt−1

�

︸︷︷︸

known at time t−1

+Et−1

�

et

�

︸︷︷︸

:=0

= µ0 +µ1mt−1

Therefore the unexpected part of the money supply at time t is equal to:

mt −Et−1

�

mt

�

= et



Substituting this into the expression for the output gap gives:

yt − y∗t = β1

�

mt −Et−1

�

mt

��

+ vt − ut

= β1et + vt − ut

We observe that the systematic component of monetary policy,�

µ0 +µ1mt−1

�

has no effects on the output gap in this model.

This is because at time t − 1, when prices for time t are set, firms takeinto consideration what they expect the monetary authorities will do.

If they expect the money supply to increase, knowing that moneyshould have no real effects, they will increase their prices for time taccordingly.

Only the random component of monetary policy, the monetarypolicy shock et , will have real effects since this is realised after theprices have been set.



This apparent result, that the systematic component of monetarypolicy has no real effect is known as the “policy ineffectivenessproposition”.

The fact that unanticipated monetary policy, in the form of the shock,et , has real effects, is essentially because prices are fixed for oneperiod.

Prices are set at time t − 1 for the market at date t . Any eventoccurring, relevant for the market at date t, after prices have been setwill naturally be reflected in real variables such as output andemployment.



Multi-period pricing

Now we turn to considering what happens when prices are set for twoperiods.

Let there be two types of firms, type A and type B firms, of equalproportion. Both set prices for two periods, but at different times.

At time t − 2 (based on the information available at that time) type Afirms set, possibly different, prices for the market at times t − 1 and t .

Type B firms also set prices for two periods but do so 1 period later (i.e.at times t − 1 they set prices for the market at times t and t + 1).



At date t − 2, type A’ firms set their prices (for the market at t − 1 andt) at the level they expect will clear the market.

Type B firms set their prices at time t − 1 for t and t + 1 similarly.

Therefore, at time t , the price level will be the average of the pricesset by type A and type B firms:

pt =Et−1

�

p∗t�

+Et−2

�

p∗t�

2

remembering that we assume that the prices pt – that the firms setahead of future markets – are their expectations of themarket-clearing prices for future periods.



Here we will use two simplifications such that:inflation expectations of agents do not affect aggregate demand (i.e.β2 = 0):

yt = β0 + β1

�

mt − pt

�

+ vt

market clearing output level is deterministic with a linear trend:

y∗t = δ0 +δ1 t

The market clearing level of output will therefore equal aggregate demandat the market clearing price level:

y∗t = β0 + β1

�

mt − p∗t�

+ vt

Taking expectations of the above conditional on information available atthe time of price-setting by type A and type B firms gives:

Et−2

�

y∗t�

= β0 + β1Et−2

�

mt − p∗t�

Et−1

�

y∗t�

= β0 + β1Et−1

�

mt − p∗t�



Noting thatEt−1

�

y∗t�

= Et−1

�

y∗t�

= y∗tsince y∗t is purely deterministic here with y∗t = δ0 +δ1 t , and taking the

average for two types of firms we have:

y∗t = β0 +1

2β1Et−2

�

mt − p∗t�

+1

2β1Et−1

�

mt − p∗t�

= β0 +1

2β1

�

Et−2

�

mt

�

+Et−1

�

mt

��

−1

2β1

�

Et−2

�

p∗t�

+Et−1

�

p∗t��

︸︷︷︸

=2pt

Subtracting the resulting expression for aggregate market-clearing outputfrom the expression for aggregate demand we get:

y− y∗t =��β0+β1mt−��β1pt+vt−��β0−1

2β1

�

Et−2

�

mt

�

+Et−1

�

mt

��

+��β1pt

y − y∗t = β1mt −1

2β1

�

Et−2

�

mt

�

+Et−1

�

mt

��

+ vt



Which can be rearranged as:

y − y∗t =1

2β1mt +

1

2β1mt −

1

2β1

�

Et−2

�

mt

�

+Et−1

�

mt

��

+ vt

=1

2β1

�

mt −Et−2

�

mt

��

+1

2β1

�

mt −Et−1

�

mt

��

+ vt

Using the same monetary policy rule as before:

mt = µ0 +µ1mt−1 + et

= µ0 +µ1

�

µ0 +µ1mt−2 + et−1

�

+ et

=�

µ0 +µ0µ1

�

+µ21mt−2 + et +µ1et−1

Taking expectations of the above conditional on information available atthe time of price-setting by type A and type B firms gives:

Et−2

�

mt

�

=�

µ0 +µ0µ1

�

+µ21Et−2

�

mt−2

�

Et−1

�

mt

�

= µ0 +µ1Et−1

�

mt−1

�



Therefore the unexpected parts of the money supply at time t is equal to:

mt −Et−1

�

mt

�

= et

mt −Et−2

�

mt

�

= et +µ1et−1

Plugging these into the expression for the output gap we find:

y − y∗t =1

2β1

�

mt −Et−2

�

mt

��

+1

2β1

�

mt −Et−1

�

mt

��

+ vt

=1

2β1

�

et +µ1et−1

�

+1

2β1

�

et

�

+ vt

= β1et +1

2β1µ1et−1 + vt



Let’s compare the case of one- and two-period pricing with no supplyshocks:

(1-period pricing) y − y∗t = β1et + vt

(2-period pricing) y − y∗t = β1et +12β1µ1et−1 + vt

It is clear that, in this model, multi-period pricing allows monetary policyshocks to have real effects not only contemporaneously, but also in thenext period.

The reason why it affects output at t − 1 is the fact prices for themarket at t − 1 were set at both t − 2 (by type A firms) and t − 3 (bytype B firms), and thus a shock at time t − 1 will cause output tochange at t − 1.

However, once the shock has been realised, only type B firms can takethis into account when they set period t prices. Type A firms cannottake et−1 into consideration since their period t prices were alreadyset at time t − 2.



Thus, since not all firms can change strategies after the realisation ofnew market conditions, the shock at time t − 1 will have real effects atdate t .

With multi-period pricing, monetary shocks can have real and, moreimportantly, persistent effects.The more periods for which a firm setsits prices, the longer and more persistent any monetary shocks will be.

Not only that, but also the output gap,�

y − y∗t�

, now depends on theparameters of the monetary policy rule, µ1.

Thus, unlike under one-period pricing, multi-period pricing allows thesystematic component of monetary policy to have real effects (bydetermining the persistence of any shocks).

Nevertheless, the choice of the monetary policy parameters will notcause permanent deviations of output from its full-employment level.Money, in the long run, is still neutral.



Policy Ineffectiveness Proposition

Since the central bank usually acts to compensate the variouseconomic disturbances in order to stabilize prices, a significant part ofits behaviour can be regarded as systematic and thus can lend itselfreasonably well to expectation by the public, if the public and thecentral bank share the same information set.

The remainder of the money supply can be considered as a shock tomonetary conditions, arising as a result of a mistake or a change in themonetary policy rule, or from a change in the microstructure offinancial markets and agent preferences.

As we saw in the case of the McCallum economy, it is possible formonetary shock to have real effects, while at the same time thepredictable systematic component of monetary policy has no effecton real output, since agents will adjust their prices in anticipation ofthe change in monetary policy.



In fact we also saw before that one does not need to assume stickyprices for monetary shocks to have real effects in the short run, cf. theLucas “misperceptions” model with flexible prices and real effects ofmoney.

So even when prices are perfectly flexible, monetary shocks can havereal effects, caused e.g. by the asymmetric information assumption ofthe Lucas model.

The predictable component of monetary policy, showing how theauthorities change the money supply (in the simplistic frameworkwhich assumes that the central bank monetary base a the policyinstrument) depending on the state of the economy, has no effect atall on real variables.

This is known as the policy ineffectiveness proposition (PIP).

A policy of the form�

mt = µ0 + et

�

will have the same effect on theeconomy as when money depends on lagged money, inflation,output, and so on.



The role of rational expectations

In both the sticky price and the Lucas models, we assumed thatagents had rational expectations when forming estimates of futurevariables, which made the deviation of actual from the expectedmonetary policy stance simply noise:

mt −Et−1

�

mt

�

= et

hence giving rise the PIP.

In fact, however, not all rational expectations (RE) models exhibit suchbehaviour.

Replace the McCallum economy aggregate demand function

yt = β0 + β1

�

mt − pt

�

+ β2Et−1

�

pt+1 − pt

�

+ vt

byyt = β0 + β1

�

mt − pt

�

+ β2 Et

�

pt+1 − pt

�

+ vt

such that expectations are formed contemporaneously instead of oneperiod in advance.



If we continue to make the same assumptions of:price-setting in accordance with the expectations of futuremarket-clearing prices:

pt = Et−1

�

p∗t�

the market clearing output being deterministic with a linear trend:

y∗t = δ0 +δ1 t

We can deduce that the expression for the market-clearing level of outputwill be given by:

y∗t = β0 + β1

�

mt − p∗t�

+ β2Et

�

pt+1 − p∗t�

+ vt



Taking expectations of the above, remembering:that y∗t is deterministic:

Et−1

�

y∗t�

= Et−1

�

δ0 +δ1 t�

= δ0 +δ1 t = y∗tand

the tower property of the expectations operator:

Et−1

�

Et

�

p∗t��

= Et−1

�

p∗t�

we get:

Et−1

�

y∗t�

= β0 + β1

�

Et−1

�

mt

�

−Et−1

�

p∗t��

+ β2

�

Et−1

�

Et

�

pt+1

��

−Et−1

�

p∗t��

y∗t = β0 + β1

�

Et−1

�

mt

�

− pt

�

+ β2

�

Et−1

�

pt+1

�

− pt

�

Which produces a slightly different expression for the output gap:

yt − y∗t = β1

�

mt −Et−1

�

mt

��

+ β2

�

Et

�

pt+1

�

−Et−1

�

pt+1

��

+ vt



The monetary shock term, mt −Et−1

�

mt

�

, is present just as before, but herealso a change in the predictable component of monetary policy can have realeffects by altering agents’ expectations of the future price level.

If a change in the predictable component of monetary policy causes a changein expectations (between times t − 1 and t ) of pt+1 , then PIP no longer holdseven though rational expectations are assumed.

Monetary policy can then have real effects, but again only in the short run.Prices are set at time t − 1 for time t and so can only contain informationavailable up until time t − 1.

Aggregate demand, on the other hand, depends on the expectation ofinflation made at time t (relevant for investment decisions through the Fisherequation).

Firms, setting their prices at the level they expect to clear the market, have tomake an expectation of this term but do so at time t − 1.

The fact that expected inflation can rise with new information meansaggregate demand can be greater than firms initially anticipated, causingoutput to increase.



The Lucas critique

Due to Robert Lucas who won Nobel Prize in 1995 for his work onrational expectations.

For some time, central banks have been building largemacroeconometric models, which until recently were large versions ofthe IS-LM or AD-AS model.

They would then use these models to provide simulations for theeffects of various different kinds of policies, estimated with historicaldata.

Lucas pointed out that it may be unwise to believe in the invariance ofthe model parameters and in the validity of such models’ predictionssince policy changes would likely alter agents’ expectations in a waythat changes the fundamental relationships between variables.



Example:Prediction (based on past experience): An increase in the money growthrate will reduce unemployment.

The Lucas critique points out that increasing the money growth rate mayraise expected inflation, in which case unemployment would notnecessarily fall.

The Lucas critique refers to the instability of reduced-formexpressions used for policy making or policy appraisal.

In the sticky price McCallum model above, the structural equationswere given by the aggregate demand equation, the price equation, theequation of the dynamics for market clearing output and themonetary policy reaction function.

When we solve for the output gap, the equation derived is one ofreduced-form (endogenous variable expressed in terms of exogenousor known lagged endogenous variables): a mixture of aggregatedemand, aggregate supply and the central bank’s’ reaction function.



Consider the expression for the output gap in the original one-periodprice-setting McCallum economy:

yt − y∗t = β1et + vt − ut

Replace the noise term et by mt −Et−1

�

mt

�

:

yt − y∗t = β1

�

mt −Et−1

�

mt

��

+ vt − ut

and open up the expectation of the money supply to give:

yt − y∗t = β1

�

mt −�

µ0 +µ1mt−1

��

+ vt − ut

= −β1µ0 + β1mt − β1µ1mt−1 + vt − ut

If we do not “know” that the economy indeed fundamentally follows this“law”, we could be tempted to simply employ econometrics to estimate anequation of such form, i.e.:

�

yt − y∗t�

= α+ γ1mt + γ2mt−1 + εt



Our estimation would establish the values of parameters α, γ1 and γ2 for agiven historical dataset.

Should we encounter a positive value of γ1, we might be led to believe thata monetary expansion causes output to increase.

However, once the central bank attempts to exploit this apparentrelationship and tries to increase the money supply by changing the policyrule from

mt = µ0 +µ1mt−1 + et

tom̂t = µ̂0 +µ1mt−1 + et

�

s.t. µ̂0 = µ0 + ξ�

, what would happen (if the underlying “true” model is indeed true, ofcourse), is that the “true” model’s parameters would change, resulting in:

yt − y∗t = −β1 µ̂0 + β1 m̂t − β1µ1mt−1 + vt − ut



We observe that the expansion of the money supply in this manner willhave two effects on output:

yt − y∗t = −β1µ̂0 + β1m̂t − β1µ1mt−1 + vt − ut

= −β1

�

µ0 + ξ�

+ β1

�

mt + ξ�

− β1µ1mt−1 + vt − ut

= −β1µ0 + β1mt − β1µ1mt−1 + vt − ut +��β1ξ−��β1ξ

Thus the two effects are mutually annihilating, output is unchanged andthe monetary expansion simply leads to an increase in prices.

The change in people’s expectations associated with this policy changethus causes the reduced form to break down and the predictions of amodel estimated on historical data become invalid.

The key problem here obviously is the assumption that parameters beingestimated are structural and independent of policy choices. In fact this is ageneric identification problem of RE models.



In practice, it is :often quite difficult after estimating empirical relationships todetermine whether they are structural or merely reduced-forms ofsome more fundamental model.hard to identify shocks in the data.hard to tell how outcomes would have been different had actualpolicies not been used.

The Lucas critique can be seen as a reformulation of Goodhart’s law thatnotes the fact that since the parameters of reduced-form models are notstructural (i.e. not policy-invariant), they will necessarily change wheneverpolicy changes.

“If policy makers attempt to take advantage of statistical relationships,effects operating through expectations may cause the relationships tobreak down. This is the famous Lucas critique.”

– David Romer, (2001), Advanced Macroeconomics, Second edition, Mc-Graw Hill Irwin.


EC3115 :: L.10 : Old Keynesian macroeconomics - 50 / 62 - Bernanke-Blinder model

Section 3

Bernanke-Blinder model



IS-LM plus credit

The model of Bernanke and Blinder (1988) is a extension of the standardstatic IS-LM framework that includes credit as a third asset in the model inaddition to money and government bonds.

We assume existence of no physical cash, and thus the monetary baseconsists only of reserves:

M = Rwhich the central manages by open market operations.The money supply thus also only consists of deposits:

M = D

Assume a bank credit (loan) demand function of the following kind:

Ld = L�

ρ, i, y�

where∂ L

∂ ρ< 0

∂ L

∂ y> 0

∂ L

∂ i> 0



Bank credit is imperfectly substitutable for bond finance.

The balance sheet of the banking sector consists of reserves, loans andbonds on the asset side, and deposits on the liability side:

R+ L + B = D

Reserves are made up of required reserves and excess reserves(non-remunerated):

R︸︷︷︸

E+τD

+L + B = D

E + L + B = (1−τ)D

where τ is the required reserves ratio.

The job of the bank is thus to choose an appropriate portfolio structure ofthe asset side of its balance sheet.



The structure of the asset side portfolio is given by:

E (i) = λE (i) (1−τ)D excess reserves demandLs�

i,ρ�

= λL

�

i,ρ�

(1−τ)D credit supply

B�

i,ρ�

=�

1−λE (i)−λL

�

i,ρ��

︸︷︷︸

λB(i,ρ)

(1−τ)D bond demand

where i is the bond interest rate, ρ is the loan interest rate,λE +λL +λB = 1 and:

∂ λE (i)∂ i

< 0∂ λL (i)∂ i

< 0∂ λB (i)∂ i

> 0

∂ λB (i)∂ ρ

> 0∂ λB (i)∂ ρ

< 0



The reserves of the commercial bank thus are:

R= τD+ E = τD+λE (i) (1−τ)D =�

τ+λE (i) (1−τ)�

D

The money multiplier therefore equals:

∆D

∆R= m (i) =

1

τ+λE (i) (1−τ)The multiplier thus depends on the bank’s portfolio considerations and isendogenously determined by the interest rate i.

Note, that i is determined on the bond market and the central bank is anagent in the bond market.

Money supply is given by the multiplier, M s = D = m (i)R, while themoney demand follows the standard assumptions Dd

�

i, y�

(with positivedependency on y and negative dependency on i).



The equilibrium in the money market is given by the LM curve:

Dd�

i, y�

= M = m (i)RThe equilibrium in the goods market is given by the IS curve:

y = Y�

ρ, i�

It is assumed that non-banks also hold a portfolio of bonds and money sothat the loan demand is determined by i (positively) and ρ (negatively).

The equilibrium on the credit market is determined by6:

Ld�

ρ, i, y�

= Ls�

i,ρ�

= λL

�

i,ρ�

(1−τ)Dwhich implies:

Ld�

ρ, i, y�

= Ls�

i,ρ�

= λL

�

i,ρ�

(1−τ)D

= λL

�

i,ρ�

(1−τ)m (i)R6Note: the bond market also clears, automatically, by Walras’ Law.



The above can be solves to give the equilibrium interest rate on loans, ρ:

ρ = φ�

i, y, R�

with∂ ρ

∂ y> 0 – an increase in loan demand pushes up the interest rate.

∂ ρ

∂ R< 0 – an increase in reserves, for a given money multiplier, results

in an increase in loanable funds7.

Thus the new IS curve – the CC (commodity-credit) curve – becomes:

y = Y�

φ�

i, y, R�

, i�

The Bernanke-Blinder model thus adds one more observable variable tothe IS-LM framework to allow better analysis of the dynamics of theeconomy and financial markets.

7Caution! No such thing in reality.ISE – KBTU A.D. Ushbayev (2015)


The CC curve has a negative slope similar to the IS curve.

Unlike the IS curve, however, the CC curve is affected by monetarypolicy (change in reserves) and by credit market shock that affecteither the L (·) or λ (·) functions.



If riskiness of the marginal investment project rises, the CC curve shifts in.

If the money multiplier falls, both the CC and LM curves shift in.

If some financial institutions fail, both the CC and LM curves shift in.



In reaction to above the central bank can either increase reserves, ordirectly lend to the financial institutions. This is shown above as a shiftoutward of the LM curve, and of the CC curve.



Effects of shocks on observable variables in the CC-LM model

Increase in Income Money Credit i on bondsBank reserves + + + -

Money demand - + - +Credit supply + + + +

Credit demand - - + -Commodity demand + + + +

Expenditure shock shifts CC like IS.

Money demand shock shifts LM.

Rise in bank reserves is expansionary through both LM and CC8.

Increase in credit supply shifts the CC-curve outward.

8Creates an identification problem.ISE – KBTU A.D. Ushbayev (2015)


Concluding remarks

Beyond the level of interest rates on government bonds, we can alsoobserve interest rate differentials (i.e. spreads).

Changes in these spreads are indications of the supply and demandfor credit and bonds.

The loan-bond spread, ρ − i, is a positive function of loan riskiness(not explicitly shown in the original model).

The CC curve reduces to the IS curve if a) bonds and loans areassumed to be perfect substitutes to borrowers or lenders, or b) ifcommodity demand is insensitive to the loan rate.

In case of a “liquidity trap”, where money and bonds are perfectsubstitutes9, the LM curve would become horizontal and hencemonetary policy could only work through the credit market directly,affecting the CC curve.

9Not exactly the original Keynes’ formulation.ISE – KBTU A.D. Ushbayev (2015)


IS-LM assumes money is special and has no close substitutes.

CC-LM allows credit to be special due to information problems infinancial markets and various balance sheet effects.

Credit-GDP relationship is more stable than Money-GDP-relationship,cf. Werner’s Quantity Theory of Credit.


EC3115MonetaryEconomics...intersection of demand and supply). Firms are assumed to have the ability...

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