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EC3115 :: L.11 : New Keynesian macroeconomics Almaty, KZ :: 4 December 2015

EC3115 Monetary EconomicsLecture 11: New 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, 4 December 2015

ISE – KBTU A.D. Ushbayev (2016)

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

EC3115 :: L.11 : New Keynesian macroeconomics - 2 / 69 -

Relevant reading

Book treatment

W. Carlin and D. Soskice. (2006). Macroeconomics: Imperfections, Insti-tutions and Policies. Oxford University Press, Chapters 3, 5, 15.

N. Mankiw. (2012). Macroeconomics, 8th edition, Worth Publishers, Chap-ter 15.

Must-read articles

D. Romer. (2000). “Keynesian Macroeconomics without the LM Curve”,Journal of Economic Perspectives, Vol. 14, No. 2, pp. 149–169.

W. Carlin and D. Soskice. (2005). “The 3-equation New Keynesianmodel – A graphical exposition”, BE Journals in Macroeconomics: Contri-butions, Vol. 5, No. 1, pp.1-38.

P. Bofinger, E. Mayer and T. Wollmershäuser. (2006). “The BMW Model:A New Framework for Teaching Monetary Economics”, Journal of Eco-nomic Education, Vol. 37, No. 1, pp. 98-117.


http://eml.berkeley.edu/~dromer/papers/JEP_Spring00.pdf

http://discovery.ucl.ac.uk/16060/1/16060.pdf

http://discovery.ucl.ac.uk/16060/1/16060.pdf

http://economia.unipv.it/pagp/pagine_personali/lorenza.rossi/bmw_modelo_basico.pdf

http://economia.unipv.it/pagp/pagine_personali/lorenza.rossi/bmw_modelo_basico.pdf

EC3115 :: L.11 : New Keynesian macroeconomics - 3 / 69 -

Recommended articles

J. Taylor. (1993). “Discretion Versus Policy Rules in Practice”, Carnegie-Rochester Conference Series on Public Policy, 39, pp. 195-214.

N. Kiyotaki and J. Moore. (1997). “Credit cycles”, Journal of Political Econ-omy, Vol. 105, No.2, pp. 211-248.

R. Clarida, J. Gali and M. Gertler. (1999). “The science of monetary policy:A new Keynesian perspective”, Journal of Economic Literature, Vol. 37, pp.1661-1707.

B. Bernanke, M. Gertler and S. Gilchrist. (1999). “The financial acceleratorin a quantitative business cycle framework”, Chapter 21, in: J. Taylor andM. Woodford (eds.), Handbook of Macroeconomics, Volume 1, Elsevier.

C. Walsh. (2002). “Teaching inflation targeting: An analysis for interme-diate macro”, Journal of Economic Education 33 (Fall): 333-46.

P. Howells. (2009). “Money and banking in a realistic macro-model”, in:G. Fontana and M. Setterfield (eds.), Macroeconomic Theory and Macroe-conomic Pedagogy, London: Palgrave Macmillan, pp. 169-187.


http://web.stanford.edu/~johntayl/Papers/Discretion.PDF

http://www-users.york.ac.uk/~psm509/ULB2012/KiyotakiMooreJPE1997.pdf

http://www.econ.nyu.edu/user/gertlerm/science.pdf

http://www.econ.nyu.edu/user/gertlerm/science.pdf

http://www.econ.nyu.edu/user/gertlerm/BGGHandbook.pdf

http://www.econ.nyu.edu/user/gertlerm/BGGHandbook.pdf

http://www.unich.it/~vitale/Walsh-2002.pdf

http://www.unich.it/~vitale/Walsh-2002.pdf

http://eprints.uwe.ac.uk/12643/2/Money_and_Banking.pdf

EC3115 :: L.11 : New Keynesian macroeconomics - 4 / 69 - The IS-PC-MR model

Section 1

The IS-PC-MR model



Previously we’ve looked at standard textbook Keynesian models thatassume monetary base as the policy instrument for the central bank.

However, modern macroeconomic research has recognized that thisis far removed from the actual practice of monetary policyimplementation.

The prevailing policy instrument of real-world central banks is theshort-term interest rate managed via open market operations.

Pure classical models suggest that money has no real effects at anyhorizon. If we introduce nominal and real frictions or relax some otherkey assumptions of the classical model, such as rational expectations,then monetary policy can have real effects in the short run.

Now we turn to studying a simplified 3-equation new Keynesianmacro model. By introducing nominal (price) frictions into this modelwe will allow for short-term real effects of monetary policy.



Romer (2000) showed that the standard IS-LM / AD-AS frameworkis unable to deal with a monetary policy that uses the interest rate asits operating target.

Walsh (2002) argued that it is not at all well-suited for an analysis ofinflation targeting.

New Keynesian macro models inspired by Clarida, Gali and Gertler(1999) have formed the base of the now-mainstream family of modelsreferred to as Dynamic Stochastic General Equilibrium models.

Here we will follow Carlin and Soskice (2005) to build a simplifiedversion of a canonical New Keynesian model, which, despite itssimplicity, can carry the main insights of the New Keynesianmacroeconomics to an intermediate level and deal with issues such asinflation targeting, monetary policy rules, and central bank credibility.



Analytical structure

New Keynesian DSGE models employ the methodologicalfoundations of RBC models, but at the same time incorporate:

imperfect competition in the goods marketnominal rigidities in the face of shocks (prices and nominal wages cannotadjust continuously)

This approach is (sort of) the modern consensus in mainstream macroin the sense that it combines:

ability of monetary policy (by means of short-term rates) can beeffective to stabilize inflation & real output (after Keynes) in the short runthe neutrality of money (after the ‘classics’) in the long run.

The main building blocks in all New Keynesian DSGE models are:1. (IS) – an IS equation, that links the output gap to the real interest rate,

2. (NKPC) – a (New Keynesian) Phillips curve, that relates the inflation rateto the output gap, and

3. (MR) – a monetary policy rule that is evaluated in terms of or derivedfrom a social loss function.



Typically, a NK-DSGE model develops a framework of forward lookinghouseholds, firms and policy-makers and therefore the IS curve, thePhillips curve and the monetary policy reaction function are forwardlooking – that is, expectations about future real output and inflationmatter when setting optimal consumption, production and monetarypolicy.

For the sake of simplicity, Carlin and Soskice (2005, 2006) firstpresent a case with a backward looking IS and Phillips curves1 (that is,looking at what has happened in the previous period when makingcurrent decisions), before providing extensions.

The central bank, however, is forward-looking when deciding the levelof short-term interest rates by taking the Phillips and IS curves asconstraints.

1This is the version of the model that we will follow in this section. It is of course animportant simplification and departure from the standard analysis of New Keynesian DSGEmodels. Other than its usefulness for simplicity, backward looking IS and Phillips curves canbe to some extent justified by the presence of consumers who form habits in theirconsumption decisions.



The IS curve is given by:

yt = At − art−1

whereyt – is the actual real output,

rt – is the real interest rate, and

At – is an autonomous exogenous demand.

Redefined in terms of the output gap, this gives:

x t ≡ yt − ye =�

At − ye

�

− art−1

where ye is equilibrium (trend, long-term) output.



Define the so-called natural, ‘stabilizing’ or Wicksellian interest rate, rs , asone that would prevail if the economy was at full employment and thatwould be compatible with trend (or long-term) output such that the outputgap is zero:

yt − ye =�

At − ye

�

− ars = 0

⇒�

At − ye

�

= ars

ye = A− ars

This allows us to redefine the IS curve in terms of the natural interest rate:

x t = yt − ye = −a�

rt−1 − rs

�

(IS curve)

The central bank makes changes its policy in accordance to this natural rate,whenever the rate of inflation deviates from its target or the real outputdeviates from its trend output.



The Phillips curve is given by:

πt = πt−1 +αx t = πt−1 +α�

yt − ye

�

(NKPC curve)

where the inflation process, πt , is inertial so that current inflation is afunction of lagged inflation and the output gap.

Remember, ye reflects the level of real output associated with thestructural features of the economy such as the degree of competitionin the goods market and the nature of the labour markets.

Inflation persistence may be a reflection of backward lookingexpectations, lags in wage/price setting behaviour, consumptionhabits and other types of real/informational imperfections notdiscussed here.



The Central Bank loss function is given by:

L = β�

πt −πT�2+�

yt − ye

�2

β > 1 describes the importance of inflation against output gap for thecentral bank.

Thus the central bank minimizes this loss function subject to thePhillips cirve above, i.e. such that next period inflation is close to atarget inflation level and next period real output is close to the ‘trend’output subject to IS and PC equations.



Timing of the model

The assumption that the central bank can control real rates ensures thatthe central bank uses forecasts of the future inflation rate and output gapwhen setting the policy instrument.



The monetary rule equation can be expressed in two ways:

It can be in the form that shows how output (chosen by the centralbank through its interest rate decision) should respond to inflation (or,as will be seen, to forecast inflation). We call this form the monetaryreaction (MR) function.

It can also be expressed as an interest rate rule indicating how thecurrent real interest rate should be set in response to the currentinflation rate (and sometimes in response to the current output gap aswell, as in the famous Taylor rule). We call this form the interest rate(IR) rule equation.

Either form of the monetary rule can be derived from the other.



The central bank minimizes the loss by choosing the�

rt−1 − rs

�

.

Substitution the PC equation into the loss function we get:

L = β�

πt −πT�2+�

yt − ye

�2

= β�

πt−1 +α�

yt − ye

�

−πT�2+�

yt − ye

�2

Using unconstrained optimization with current period output as theargument, the first order condition is given by:

∂ L

∂ yt= 2βα

�

πt−1 +α�

yt − ye

�

−πT�

+ 2�

yt − ye

�

= 0

�

yt − ye

�

= −αβ�

πt−1 +α�

yt − ye

�

−πT�

Substituting the PC curve back into the above gives the monetary rule:

�

yt − ye

�

= −αβ�

πt −πT�

(MR curve)



Alternatively, substituting both the IS and PC equations into the centralbank loss function, we get:

L = β�

πt −πT�2+�

yt − ye

�2

= β��

πt−1 +α�

−a�

rt−1 − rs

��

−πT�2+�

−a�

rt−1 − rs

��2

Using unconstrained optimization with the interest rate as the argument,the first order condition is given by:

∂ L

∂�

rt−1 − rs

� = −2βαa�

πt−1 −αa�

rt−1 − rs

�

−πT�

+2a2�

rt−1 − rs

�

= 0

Solving for�

rt−1 − rs

�

:

2βαa�

πt−1 −αa�

rt−1 − rs

�

−πT�

= 2a2�

rt−1 − rs

�

2βαa�

πt−1 −πT�

− 2βαa�

αa�

rt−1 − rs

��

= 2a2�

rt−1 − rs

�



2βαa�

πt−1 −πT�

= 2a2�

rt−1 − rs

�

+ 2βαa�

αa�

rt−1 − rs

��

2βαa�

πt−1 −πT�

=�

rt−1 − rs

� �

2a2 + 2βα2a2�

�

rt−1 − rs

�

=2βαa

2a2 + 2βα2a2

�

πt−1 −πT�

=��2βαa

��2βαa�

aβα+αa

�

�

πt−1 −πT�

Which gives the Interest rate rule2:

rt−1 − rs =1

a�

α+ 1αβ

�

�

πt−1 −πT�

(IR equation)

2This is the interest rate rule as a response to deviations from target inflation and outputgap. For e.g. a = α= β = 1 the rule becomes:

�

rt−1 − rs�

= 0.5�

πt−1 −πT�



By setting out the central bank’s problem in the above way, we haveidentified the key role of forecasting: the central bank must forecastthe Phillips curve and the IS curve it will face next period.

Even though the central bank observes a shock in period t − 1 andcalculates its impact on current output and next period’s inflation, dueto the lagged effect of interest rates on aggregate demand and outputit cannot fully offset the impact of the shock in the current period.

In this model, according to the ‘rule’, interest rates need to increasewhenever actual inflation exceeds target inflation and vice versa.

In reality, the central bank may want to target the average rate ofinflation over a longer period of time, rather than the current periodinflation alone.


EC3115 :: L.11 : New Keynesian macroeconomics - 19 / 69 - Shocks in the IC-PC-MR model

Section 2

Shocks in the IC-PC-MR model



Basic setup

Consider a simplified version of the model presented above, with only twotime periods, numbered 0 and 1, such that the system is described by:

y1 − ye = −a�

r0 − rs

�

(IS)

π1 = π0 +α�

y1 − ye

�

(PC)

r0 − rs =1

a�

α+ 1αβ

�

�

π0 −πT�

(IR)



Graphical exposition

The lower panel shows the vertical long-run Phillips curve at the equilibrium outputlevel, ye .

We think of labour and product marketsas being imperfectly competitive so thatthe equilibrium output level is where bothwage- and price-setters make no attemptto change the prevailing real wage or rela-tive prices.

Each Phillips curve is indexed by the pre-existing or inertial rate of inflation πI =π−1.

The economy is in a constant inflationequilibrium at the output level of ye .

Inflation is constant at the target rate ofπT .



Graphical exposition (cont.)

The upper panel shows the goods marketequilibrium characterised by the IS equa-tion.

The stabilising (or Wicksellian) interestrate, rs , will produce a level of aggregatedemand equal to equilibrium (trend) out-put, ye .

The interest rate axis in the IS diagram islabelled r−1 to capture the lag structure inthe IS equation.



Analysis of a shock to aggregate demand

As a consequence of a positive aggregatedemand shock, the IS curve shifts to theright: a positive output gap (y > ye) abovethe trend output is generated, and infla-tion rises to 4% above the target level of2% (π0 > π

T ). Economy is at point A.

The central bank’s job is to set the interestrate, r0, in response to this new informa-tion about economic conditions.

In order to do this, it must first make a fore-cast of the Phillips curve next period, sincethis shows the set of output-inflation pairsthat it can choose from by setting the in-terest rate now.

Note: changing the interest rate now onlyaffects output next period.



Analysis of a shock to aggregate demand (cont.)

Given that inflation is inertial, the centralbank’s forecast of the Phillips curve in pe-riod 1 will be PC (πI = 4) as shown by thedashed line in the Phillips curve diagram.

Note: only points on this Phillips curvewith inflation below 4% entail lower out-put, i.e. a negative output gap (y1 < ye).

This mechanics implies that a disinflation-ary policy will be costly in the sense thatoutput must be pushed below equilibriumin order to achieve the desired result.

Note: In NK models demand shocks donot necessarily lead to a trade-off be-tween output and inflation. The CB canstabilise inflation by stabilising the outputgap. (See e.g. Clarida et al. (1999)).



How is the policy maker going to choose the r0 along the new(forecast) Phillips curve?

This depends on the stabilisation preferences of the central bank: ifthe central bank cares more about inflation stabilisation than theoutput gap, then the preference parameter β in the loss function willhave a higher value.

Given that the interest rate choice, (r0 − rs), determines the outputgap which in turn determines the rate of inflation, the moreinflation-averse the central bank is, the more it is willing to sacrificeoutput (y1 − ye) to achieve its inflation objective.



Monetary policy choice

CB will choose point B where its indiffer-ence curve (loss function) and the fore-cast PC will be tangent. Thus the the newdesired output level y1 is the aggregatedemand target according to the optimalmonetary policy rule.

The MR function connects point B andthe zero loss point at Z, where inflation isat target and output is at equilibrium.

The next step is to forecast the IS curve(IS′) associated with desired output, y1.

The dashed line in the upper panel showsthe central bank interest rate, r ′0, in agree-ment with the new desired output to sta-bilise the inflation. Clearly, interest rateneeds to increase.



Monetary policy choice (cont.)

In the absence of further IS shocks, theincrease in the interest rate leads to a fallin output to y1 and inflation starts to fall.

The CB repeats the steps above to achievethe target inflation. Both preferences ofthe CB and the Phillips curve represent theinflation output trade-off the CB faces.

Given the policy instrument, the short-term rate, the central bank stabilisesthe economy through aggregate demandmanagement following an IS (demand)shock.

Note: Other random shocks may disturbthe economy in period 1 but they do notenter CB decision rule in period 0, sincethey are unforecastable.



Monetary policy choice (cont.)

To complete the example, we tracethrough the adjustment process.

Following the increase in the interest rate,output falls to y1 and inflation falls to π1.

The central bank forecasts the new Phillipscurve, which goes through point C in thePhillips diagram (not shown) and it will fol-low the same steps to adjust the interestrate downwards so as to guide the econ-omy along the IS′ curve from C’ to Z’.

Eventually, the objective of inflation atπT = 2% is achieved and the economy isat equilibrium output, where it will remainuntil a new shock or policy change arises.



Temporary or permanent demand shocks

Above we analyzed an aggregate demand (IS) shock, but was it atemporary or a permanent one?

In order for the central bank to make its forecast of the IS curve, thecentral bank needs to decide whether the demand shock is atemporary or permanent one.

If the central bank believes that the shock would persist for anotherperiod, central bank policy rate, r ′0, should be higher than the newstabilising interest rate, r ′s .

If the central bank’s forecasts are such that the output will insteadrevert to its initial level, then it will increase the interest rate by lesssince the stabilising interest rate would have remained unchanged atrs (i.e. its chosen interest rate would have been on the IS pre-shockcurve in rather than on the IS curve).



Analysis of a shock to aggregate supply

Structural changes in the economy maylead to a shift in the trend output thereforea shift in the vertical (long-run) PC curve.

Prominent examples of such structuralchanges are changes in the wage- or price-setting behaviour (curbing labour unionpower for instance), a change in tax regimeor benefits or changes in the nature of thegoods market competition such that theprice mark-up changes.

Suppose that the degree of competitionintensifies which leads to a shift in the ver-tical Phillips curve to the right. Equilibriumoutput shifts from original ye to y ′e associ-ated with a stabilising interest rate declineto r ′s at Z’.



Analysis of a shock to aggregate supply (cont.)

As a consequence of a positive aggregatesupply shock, the short-run Phillips curvecorresponding to inflation equal to the tar-get – shown by the Phillips curve (πI =2%, ye) – shifts to the right as well.

First, inflation falls from target inflationlevel of 2% to 0% as the economy movesfrom equilibrium point A to B, with outputunchanged at ye . This is observed by theCB in period 0.

Second, the CB forecasts the Phillips curveconstraint (πI = 0%, ye)) for the next pe-riod and chooses the optimal level of out-put as shown by point C.



Analysis of a shock to aggregate supply (cont.)

To raise output to this level, the CB has tocut the interest rate in period 0 to r ′ asshown in the IS diagram.

Note: Since the stabilizing interest ratehas fallen to r ′s , the central bank reducesthe interest rate below this in order toachieve its desired output level of y ′.

The economy is then guided along theMR–AD curve to the new equilibrium at Z.

The positive supply shock is associated ini-tially with a fall in inflation and a rise inoutput – in contrast to the initial rise inboth output and inflation in response tothe aggregate demand shock.



Comparing the effects of demand and supply shocks

The positive supply shock is associated initially with a fall in inflation,in contrast to the initial rise in both output and inflation in response tothe positive aggregate demand shock.

In the aggregate demand case, the central bank has to push outputbelow equilibrium during the adjustment process in order to squeezethe higher inflation caused by the demand shock out of the economy.

Conversely in the aggregate supply shock case, a period of outputabove equilibrium is needed in order to bring inflation back up to thetarget from below.

In the new equilibrium, output is higher than its initial level in thesupply shock case whereas it returns to its initial level in the case ofthe aggregate demand shock.

In the new equilibrium, inflation is at target in both cases.

However, whereas the real interest rate is higher than its initial level inthe new equilibrium following a permanent positive aggregatedemand shock, it is lower following a positive aggregate supply shock.


EC3115 :: L.11 : New Keynesian macroeconomics - 34 / 69 - Simple monetary policy rules

Section 3

Simple monetary policy rules



We will now analyze cases when a central bank implements policyaccording to a rule or formula that is chosen to be applicable over alarge number of periods.

These are simple rules thus by definition not reflecting optimal choiceof the monetary policy instrument given the state of the economy asdone in the previous sections.

Following a rule is transparent: by committing to follow a rule, policymakers can communicate and explain their policy actions easily andshould at least in principle enhance the accountability and credibilityof the central bank.

Despite reducing the inflation bias (to be discussed later in the course),possibly to zero, depending on the rule, such policy will not be able tocounter the productivity shocks that hit the economy.



If the economy is prone to productivity shocks of large variance, itmay be desirable for the monetary authorities to lean against the windusing expansionary monetary policy in a time of negative productivityshocks, for example.

However, to do so will require discretion on the part of the authorities,but this will naturally lead to inflation bias.

In the argument of rules versus discretion we have to weigh up the costof using discretion (the inflation bias) with the cost of using a rule(inability to counter productivity shocks).



Taylor rules

In Taylor (1999)3 an interest rate rule of the form:

Rt = πt + g�

yt − y∗�

+ h�

πt −π∗�

+ r∗

whereRt – is the nominal interest rate,πt – is inflation,π∗ – is the target rate of inflation,�

yt − y∗�

– is the output gap,r∗ – is the estimate of the equilibrium real interest rate, andg and h – are the relative importance weights given by the CB to theoutput and inflation gaps.

was argued to be a valid representation of how CBs do and shouldrespond to developments in inflation and macroeconomic activity byadjusting their policy interest rate, in a variety of monetary regimes.

3J. Taylor, (1999), “A Historical Analysis of Monetary Policy Rules” in Monetary Policy Rules,ed., John B. Taylor (Chicago: University of Chicago Press, 1999), pp. 319–341.


http://www.nber.org/chapters/c7419.pdf


The Taylor rule above can be rewritten as4:

Rt = πt + g�

yt − y∗�

+ h�

πt −π∗�

+ r∗

= (r∗ − hπ∗) + g�

yt − y∗�

+ (1+ h)πt

When fitting this model to US data from 1987:Q1 to 1997:Q3 in Taylor(1999), the coefficients g and h were estimated to be equal to 0.765and 1.533, respectively.

The fact that these are positive, and for the case of the coefficient oninflation, greater than unity, were found to be important for thestability of the economy – since it was Taylor (1999) finds that moreresponsive policy rules lead to greater economic stability.

4Also note that when both output and inflation gaps are zero, the Taylor rules collapses tothe simplified Fisher equation.



Consider a fall in demand that causes output to fall below trend level,y∗, with no immediate impact on inflation.

A positive g coefficient implies that nominal interest rates set by themonetary authorities should fall, since

�

yt − y∗�

is now negative.

With no change in inflation, the fall in nominal rates will decrease realrates and so encourage investment spending and aggregate demand.

Output should then return to the full employment level.

Now consider the case where inflation has increased above the targetrate, π∗.

If the h coefficient on inflation is greater than unity, then the increase innominal interest rates will be greater than the increase in inflation.

This causes real interest rates to increase, leading to reduced investmentspending and so reduces the inflationary pressure in the economy.



With positive coefficients for g and h (causing (1+ h), the coefficienton inflation, to be greater than unity) we should see stability in theeconomy, with output tending to be at its full employment level andinflation staying close to the target rate.

If the coefficient on inflation in was found to be less than one (i.e.h< 0), then an increase in inflation will be met by a less thanone-for-one rise in nominal rates.

This will cause real rates to fall, encouraging investment and aggregatedemand that will cause further inflationary pressure. The economicsystem in this case would be unstable.



Implications for the interest rule in IS-PC-MR

Recall:

y1 − ye = −a�

r0 − rs

�

(IS)π1 = π0 +α

�

y1 − ye

�

(PC)

r0 − rs =1

a�

α+ 1αβ

�

�

π0 −πT�

(IR)

For a given deviation of inflation from target, and in each case, comparingthe situation with the basic case of a = α= β = 1 , we have:

a more inflation-averse central bank (β > 1) will raise the interest rateby more,

when the IS curve is flatter (a > 1), the central bank will raise theinterest rate by less, and

when the Phillips curve is steeper (α > 1), the central bank will raisethe interest rate by less.



Friedman’s rule of constant money growth

“[M]y conclusion [is] that monetary actions affect economic conditionsonly after a lag that is both long and variable.”

– Milton Friedman, (1961), “The Lag in Effect of Monetary Policy”, Journalof Political Economy, Vol. 69, No. 5, pp. 447-466.

Due to the long and variable lags associated with the formulation andimplementation of monetary policy, Milton Friedman suggested that tryingto control the economy through changing monetary variables, wouldpurely lead to greater instability.


http://www.jstor.org/stable/1828534


At date t0 a shock occurs that causes output to start to fall. The first recordeddata of such an event may become available at date t1.

However, the authorities need more than just one data observation beforechanging their policy – after all, the data reading could be a blip or involveconsiderable measurement error.



At date t2 enough data are available for the authorities to determine that adownturn is indeed happening and the decision is made to implement anexpansionary monetary policy.

Since it takes some time for the policy decision to take effect, output is onlyaffected at date t3, but this is the point when the economy is starting to recover.



The monetary expansion at a time when the economy is naturally starting toaccelerate could lead to a more volatile path for output.

Hence, Friedman suggested monetary policy should not be used to combatoutput fluctuations, not because of neutrality arguments but because of the longand variable lags involved with such an activist policy.


EC3115 :: L.11 : New Keynesian macroeconomics - 46 / 69 - Credit and the real economy I: financial accelerators

Section 4

Credit and the real economy I: financial accelerators



We have already learned banks are important for economic activityand have seen some simple models that incorporate the credit market(e.g. Bernanke-Blinder).

It has also been long recognized that credit-market conditions arethemselves a source factor in shaping economic activity.

There are many New Keynesian models that model credit marketimperfections in a general equilibrium setting.

Examples using asymmetric information are Bernanke and Gertler(1989) and the Bernanke et al. (1999) model where asymmetries ofinformation play a key role in borrower-lender relationships.



The Bernanke–Gertler–Gilchrist model

In this model5, financial contracts reflect the costs of gatheringinformation (“costly state verification”) about the quality of borrower’sinvestment project.

You may remember from your corporate finance courses that theModigliani-Miller theorem implicitly states that in the absence oftaxes, bankruptcy costs, agency costs, and asymmetric informationthe capital structure (equity/debt split) of a firm is irrelevant for itsvalue.

When credit markets are characterised by asymmetric information,the Modigliani–Miller irrelevance principle is of course no longer valid.

Several problems can occur in credit markets that may lead to aworsening of informational asymmetries and increases in theassociated agency costs and thereby lead to fewer projects receivingexternal financing. These then will have widespread real effects.

5The complete model is beyond the scope of this course, so we will just outline the logicand some stylized features and conclusions.



There are 3 types of agents: Households, Entrepreneurs, and Retailers.

Entrepreneurs play a key role in the model. These individuals areassumed to be risk-neutral and have finite horizons.

Specifically, we assume that each entrepreneur has a certain constantprobability of surviving (equivalently “dying”) to the next period.

Retailers act as an "aggregator": buy intermediate goods fromentrepreneurs, make diversified final output, which motivatesmonopolistic competition/enables sticky prices.

There is a partial equilibrium in the capital market. In each period tentrepreneurs acquire physical capital that is financed by eitherwealth (profits plus labour income) and borrowing (one period loancontracts) that is subject to external finance premium.

If the wealth or net worth is high, this allows for internal financetherefore entrepreneurs will be able to finance their investment rathercheaply, or equivalently if they seek external finance they can postthese as collateral, therefore financing the project is less risky.



As the external finance needs should be met via some form of lendingcontract and there are informational problems about the quality ofthe entrepreneurial project (agency problem – uncertain returns oncapital that are subject to both aggregate and idiosyncratic risk),uncollateralised external finance should be more expensive thancollateralised one.

The need to borrow from some credit institution is formalised as:

Q t Kjt+1 = N j

t+1 + B jt+1

At time t , the entrepreneur who manages firm j purchases capital foruse at t + 1.

The quantity of capital purchased is denoted K jt+1, with the subscript

t + 1 denoting the period in which the capital is actually used, and thesuperscript j denoting the firm.



The price paid per unit of capital good in period t is Q t . Capital ishomogeneous, and so it does not matter whether the capital theentrepreneur purchases is newly produced within the period or is old,depreciated capital.

At the end of period t (going into period t + 1) entrepreneur j has anavailable net worth, N j

t+1.

To finance the difference between his expenditures on capital goodsand his net worth he must borrow an amount B j

t+1.

The entrepreneur borrows from a financial intermediary that obtainsits funds from households.

The financial intermediary faces an opportunity cost of funds betweent and t + 1 equal to the economy’s riskless gross rate of return, Rt+1.



The riskless rate is the relevant opportunity cost because in theequilibrium, the intermediary holds a perfectly safe portfolio (itperfectly diversifies the idiosyncratic risk involved in lending).

Because entrepreneurs are risk-neutral and households arerisk-averse, the loan contract the intermediary signs hasentrepreneurs absorb any aggregate risk.

Lenders have to pay a fee (auditing, accounting, legal and so on) toverify the state of the entrepreneur, so they incur costs by lending.

In equilibrium, Bernanke et al. (1999) show that for an entrepreneurwho is not fully self-financed, the return to capital will be equated tothe marginal cost of external finance, i.e.:

Et

�

Rkt+1

�

= s

�

N jt+1

Q t Kjt+1

�

Rt+1



The ratio s (·) of the cost of external finance to the safe rate – which isthe discounted return to capital but may be equally well interpreted asthe external finance premium – depends inversely on the share of thefirm’s capital investment that is financed by the entrepreneur’s ownnet worth.

It shows that capital expenditures by each firm are proportional to thenet worth of the entrepreneur, with a proportionality factor that isincreasing in the expected discounted return to capital:

Et

�

Rkt+1

�

Rt+1= s

�

N jt+1

Q t Kjt+1

�

s′ (·)< 0

A high s reduces the default probability and entrepreneurs can take onmore debt and expand the size of the firm, thus economy expands,and vice versa.

In other words, financial (or equivalently credit) constraints can lead tostronger downturns than when these constraints are absent; hence itworks as a financial accelerator.


EC3115 :: L.11 : New Keynesian macroeconomics - 54 / 69 - Credit and the real economy II: cycles

Section 5

Credit and the real economy II: cycles



Above we’ve used asymmetric information and costly stateverification among heterogeneous to capture credit marketimperfections.

An alternative is to use collateral constraints as in e.g. Kiyotaki andMoore (1997):

uses heterogeneous agents,

produces co-movement of amount of credit, asset prices and aggregateoutput,

creates a propagation mechanism that produces persistence andamplification of a shock,

produces pro-cyclical productivity even if technology does not change,

able to explain cross-industry co-movements.



The Kiyotaki-Moore model

This is a model6 of a dynamic economy in which credit constraintsarise naturally because lenders cannot force borrowers to repay theirdebts unless the debts are secured.

Durable assets such as land, buildings, and machinery play a dual role:not only are they factors of production, but they also serve ascollateral for loans.

Borrowers’ credit limits are affected by the prices of the collateralizedassets.

At the same time, these prices are affected by the size of the creditlimits.

The dynamic interaction between credit limits and asset prices turnsout to be a powerful transmission mechanism by which the effects ofshocks persist, amplify, and spread out.

6Once again, the complete model is beyond the scope of this course, so we will justoutline the intuition together with some stylized features and conclusions.



The transmission mechanism

Consider an economy in which land is used to secure loans as well asto produce output, and the total supply of land is fixed.

Some firms are credit constrained, and are highly levered in that theyhave borrowed heavily against the value of their landholdings, whichare their major asset.

Other firms are not credit constrained.

Suppose that in some period t the firms experience a temporaryproductivity shock that reduces their net worth.

Being unable to borrow more, the credit-constrained firms are forcedto cut back on their investment expenditure, including investment inland.

This hurts them in the next period: they earn less revenue, their networth falls, and, again because of credit constraints, they reduceinvestment.



The transmission mechanism (cont.)

The knock-on effects continue, with the result that the temporaryshock in period t reduces the constrained firms’ demand for land notonly in period t but also in periods t + 1, t + 2, etc.

For the market to clear in each of these periods, the demand for landby the unconstrained firms has to increase, which requires that theiropportunity cost, or user cost, of holding land must fall.

Given that these firms are unconstrained, their user cost in eachperiod is simply the difference between that period’s land price andthe discounted value of the land price in the following period.

This anticipated decline in user costs in periods t , t + 1, t + 2, and soon is reflected by a fall in the land price in period t – since price equalsthe discounted value of future user costs.



The transmission mechanism (cont.)

The fall in land price in period t has a significant impact on thebehavior of the constrained firms. They suffer a capital loss on theirlandholdings, which, because of the high leverage, causes their networth to drop considerably.

As a result, the firms have to make yet deeper cuts in their investmentin land. There is an intertemporal multiplier process: the shock to theconstrained firms’ net worth in period t causes them to cut theirdemand for land in period t and in subsequent periods.

For market equilibrium to be restored, the unconstrained firms’ usercost of land is thus anticipated to fall in each of these periods, whichleads to a fall in the land price in period t .

This in turn reduces the constrained firms’ net worth in period t stillfurther.

Persistence and amplification reinforce each other.



The transmission mechanism illustrated



The model assumptions are:discrete time,

infinitely lived agents,

two goods – a durable asset (land) and a non-durable commodity(fruit),

a constant interest rate,

no labor supply decision,

no capital accumulation,

only one asset that can be used for production, does not depreciateand is available in fixed supply in the aggregate.



Types of (risk-neutral) agents, with corresponding expected utility at date t :

farmers (productive)

Et

� ∞∑

s=0

β s x t+s

�

gatherers (unproductive)

Et

� ∞∑

s=0

β ′s x ′t+s

�

where x t+s and x ′t+s are the agents respective consumption of fruit atdate t + s, and the discount factors β and β ′ are 0< β < β ′ < 1.



The farmers have a linear constant returns to scale productiontechnology in capital, kt , only:

yt+1 = (a+ c) kt

Only a fraction akt of the produced goods is tradable, and the rest,ckt , cannot be traded but can be consumed by the farmer himself.

The farmer can finance his growing business by debt, but if he has alot of debt, he may find it advantageous to threaten his creditors bywithdrawing his labor and repudiating his debt contract.

Creditors protect themselves from the threat of repudiation bycollateralizing the farmer’s land. They are careful never to allow thesize of the debt (gross of interest) to exceed the value of the collateral.

Therefore the farmer is subjected to a credit constraint of the form:

Rbt ≤ qt+1kt

where qt is the price of fruit, R is the interest rate and bt is the size ofthe farmer’s debt.



The farmer can expand his scale of production by investing in moreland.

Consider a farmer who holds kt−q land at the end of date t − 1, andhas incurred a total debt of bt−1.

At date t he harvests akt−1 tradable fruit, which, together with a newloan bt , is available to cover the cost of buying new land and investingin new trees, as well as to repay the accumulated debt of Rbt−1 (whichincludes interest) and meet any additional consumption

�

x t − ckt−1

�

(over and above the automatic consumption of non-tradable outputckt−1).

The farmer’s flow-of-funds constraint is thus:

qt

�

kt − kt−1

�

+φ�

kt −λkt−1

�

+Rbt−1 +�

x t − ckt−1

�

= akt−1 + bt



Only a fraction π of the population can invest while a fraction (1−π)cannot.

For a farmer, investment is strictly better than consumption, so thathe will use all the funds available to invest, i.e. the constraintsx t ≥ ckt−1 and Rbt ≤ qt+1kt are in fact binding.

From substituting these in the flow of funds constraint above andrearranging it follows that:

kt =1

φ + qt −1

Rqt+1

��

a+ qt +λφ�

kt−1 − Rbt−1

�

︸︷︷︸

farmer’s net worth

Also, at each date t , with probability (1−π), a farmer may now facethe additional technological constraint kt ≤ λkt−1.

If the farmer does not invest, he keeps his stock of capital withoutdivesting, i.e. kt = λkt−1.



Since the dynamical expressions for capital obtained above are linearin kt−1 and bt−1, we can aggregate across farmers and us LLN tojustify the following law of motion for the aggregate capital:

Kt = (1−π)×�

λKt−1

�

︸︷︷︸

the non investing farmers

+ π×

1

φ + qt −1

Rqt+1

��

a+ qt +λφ�

Kt−1 − Rbt−1

�

︸︷︷︸

the investing farmers

And since no farmer consumes more than his nontradable output,from the flow-of-funds constraint we deduce the debt law of motion:

Bt = RBt−1 + qt

�

Kt − Kt−1

�

+φ�

Kt −λKt−1

�

− aKt−1



Finally, we add the gatherers behaviour.

Gatherers have a linear decreasing returns to scale productiontechnology in fruits – y ′t+1 = G

�

k′t�

.

A gatherer is not credit constrained, and so his demand for land isdetermined at the point at which the present value of the marginalproduct of land is equal to the opportunity cost of holding land.

The Euler equation for consumption determines the asset price:

u�

Kt

�

= qt −qt+1

R=

1

RG′�

K − Kt

�

where u�

Kt

�

is the user cost of capital7.

These equations are a first-order non-linear system.

There is an unique steady state�

q∗, K∗, B∗�

with associated steadystate user cost.

7Check the paper for details on market clearing.ISE – KBTU A.D. Ushbayev (2016)


Effect of an unanticipated, temporary productivity shock

Consider a productivity shock∆ = 0.01 in period 1.That is, there is a 1 percent increase in quarterly output of all the farmers and

gatherers.Prior to the shock, the economy is in the steady state.



Effect of an unanticipated, temporary productivity shock

The figure above shows simulation results for qr/q∗, Kt/K

∗, and Bt/B∗ – the

ratios of the land price, the farmers’ aggregate landholding, and their aggregatedebt to their respective steady-state values. Shocks exhibit persistence andamplification before the economy returns to a steady state.


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