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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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