Lecture 7
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Lecture 7. Monetary policy in New Keynesian models - Introducing nominal rigidities ECON 4325 Monetary policy and business fluctuations Hilde C. Bjørnland and Steinar Holden, University of Oslo. Wage rigidity in a Money In Utility (MIU) model. Want a model with a role for monetary policy

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Lecture 7

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Lecture 7

Monetary policy in

New Keynesian models - Introducing nominal rigidities

ECON 4325 Monetary policy and business fluctuations

Hilde C. Bjørnland and Steinar Holden,

University of Oslo


Wage rigidity in a Money In Utility (MIU) model

  • Want a model with a role for monetary policy

    • To analyse monetary policy

    • Because of empirical evidence that money has real effects

    • Flex-price models provide implausible or too small effects of money

  • Introduce nominal wage and price rigidities. (menu costs, contracts)

  • Start out from general equilibrium with optimizing behaviour (as in classical models). Solve for flex-price solution. Consider effect of nominal rigidities

  • Here: Assume that nominal wages are set at start of each period and are unresponsive to developments within period

  • Utility separable in consumption and money holdings, implying no effect of money under flexible prices

  • Capital stock fixed, no investment - not important source of business cycles(?)


  • Linear approximation to MIU model plus one period nominal wage contract (see variables definition in Walsh, chpt. 5. All variables are deviations from steady state (SS)).

  • When prices are flexible, monetary shocks no effect on output

  • Classical dichotomy, real variables determined independent of money supply and money demand factors

  • Suppose that nominal wage is set prior to the start of each period, at level expected to give the real wage that equates labour supply and labour demand.


Flex-price equilibrium (flexible wages)

  • Equate labour demand (3) and labour supply (5) and use (1) and (2) to find flex-price equilibrium employment n* and real wage *:

  • Define contract nominal wage as


  • Firms equate MPL (yt-nt) to real wage (wt-pt), so (3) implies that employment follows


  • Employment deviates from expected flex price equilibrium level when there are unexpected movements in prices

  • An unexpected productivity shock () raises MPL and leads to employment increase

  • Substituting (12) into the production function (1) one obtains

  • Monetary shocks that produce unanticipated price movements affect output


  • Assume serially uncorrelated disturbances, i.e. Et-1et =0 and from (9 )

    ,(14) reads

  • With the demand side defined by quantity equation (interest elasticity of money demand goes to zero), (6) can be written as:

  • (8) and (16) imply

  • Which substituted into (15) yields


Implications of model

  • Assume =0.36, then a 1% deviation of p from expected value will cause a 1.8% [(1-)/] deviation of output, see equation (15).

  • 1% money surprise increases output by (1-) = 0,64%, see equation (18).

  • Surprise depends on parameter on production function, in contrast to Lucas’s misperception model, where impact on price surprise depends on variance of shock.

  • However, the effect of a money shock lasts only one period (i.e. the duration of the rigidity)


Persistent effects of money

  • Want model in which a money shock has persistent effects on output.

  • Taylor (1979, 1980): Staggered wage setting

    • Contract wage set for two periods

    • Half of all contracts set in each period

  • Real effects of a money shock last longer than duration of contract


Taylor’s staggered adjustment model

  • Average wage equal to average of log contract wagex set in this and the previous period. Prices are set as a constant mark up on wages (markup set to zero)

  • Average expected real wage over the life of the contract

  • Expected average real contract wage is increasing function of output


  • Price level is given by

  • Rearranging yields an expression for inertia in the price level, depending both on the history and future

  • As prices are persistent, a negative monetary shock will have long-lasting effects on output (e.g. assume that aggregate demand is y= m – p)


  • However, no inherent persistence in the inflation rate.

  • Persistence in inflation must be caused by persistence in the money stock

  • “Disinflation” is not costly. A reduction in the growth rate of nominal money need not lead to lower output.

  • Both implications in contrast to empirical evidence


Fuhrer and Moore’s model: explaining inflation persistence

  • Real value at time t, of contracts negotiated at time t

  • An index of average real contract wages in contracts still in effect at time t

  • In deciding on t, agents compare with the expected average of the real contract index over the two period life of the contract; 1/2(vt +Etvt+1), plus the effect of the business cycle; (kyt)


  • Which can be written as

  • (compares to (22) in Taylor’s model – but not more plausible than Taylor).

  • In terms of the rate of change of the contract wage

  • Note that t=1/2(xt+ xt-1), t then equals

  • Which can be compared to (25). Hence the Fuhrer and Moore specification implies that inflation is persistent (see next page for how to derive (31).


  • Note that (31) is slightly different from the Walsh textbook, in that I get ½ in front of the term t.


Conclusion of Fuhrer and Moore

  • Sluggish inflation adjustment, not relying on persistence in driving force

  • Inflation is inflexible with regard to new information

  • Backward looking nature in inflation process implies that reductions in money growth will be costly in terms of output. Hence; disinflation is costly.

  • Price stickiness and inflation stickiness is an empirical issue, not yet solved.

  • Taylor model plus non-rational behaviour may imply stickiness as in Fuhrer and Moore

  • Implications for cost of policies to lower inflation


Calvo pricing

  • Alternative to Taylor’s model of staggered price adjustment, yielding more convenient analysis.

  • In each period, all firms face a constant probability (1-ω) that it can adjust its price (independent of length of time since price was set – unrealistic, but convenient).

  • Expected time between price adjustments is 1/(1-ω).

  • Opportunities occur randomly, so span of time between prices are adjusted will be a random variable.

  • Representative firm i set prices so as to minimize a quadratic loss function that depend on difference between actual price pit and optimal price p*

  • subject to when the firm will actually be able to adjust price


  • Focus on the price set at time t

  • since ωj is the probability that firm has not adjusted after j periods, so price at t holds at t+j. The FOC for the optimal choice of pit requires that

  • xt denotes the optimal price set at time t by all firms that adjust, i.e.

  • Or if we let the target price depend on aggregate price and output:


  • With a large number of firms, fraction (1-ω) will adjust price each period, so aggregate price level can be expressed as

  • and aggregate inflation can be described as (see Walsh, p 227)

  • Which is close to (25) in the Taylor model. Coefficient on output in (38) depends on frequency with which prices are adjusted.


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