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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) wage contract (see variables definition in Walsh, chpt. 5. All variables are deviations from steady state (SS)).

- 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 (y wage contract (see variables definition in Walsh, chpt. 5. All variables are deviations from steady state (SS)).t-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. E level when there are unexpected movements in pricest-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 level when there are unexpected movements in prices

- 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 level when there are unexpected movements in prices

- 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 level when there are unexpected movements in prices

- 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 level when there are unexpected movements in prices
- 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, level when there are unexpected movements in pricesno 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 level when there are unexpected movements in prices

- 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 level when there are unexpected movements in prices
- (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 textbook, in that I get ½ in front of the term

- 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 textbook, in that I get ½ in front of the term

- 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 textbook, in that I get ½ in front of the term 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 textbook, in that I get ½ in front of the term 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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