Monetary Policy, 16/3 2017

Henrik JensenDepartment of EconomicsUniversity of Copenhagen

“0.”Finish the Auberbach/Obsfeld model (last lecture’s slides, 13 March, pp. 13—)

1. Money in the short run: Incomplete nominal adjustment (I)

Sticky Prices and Wages: Early models

Literature: Walsh (Chapter 6, pp. 225—241 – plus relevant appendix)

Note that these slides are accompanied by the note “Technical notes to Walsh (2010), Chapter 6”

c© 2017 Henrik Jensen. This document may be reproduced for educational and research purposes, as long as the copies contain this notice and are retained for personaluse or distributed free.

Introductory remarks• Flex-price models covered so far cannot account for short-run dynamics of real output followingmonetary shocks

In case there were any real effects, the magnitude appears modest

Some “sand in the wheels”are necessary to explain the effects of money on output seen in data

• Obvious candidate is incomplete nominal adjustment. In flex-price models, money neutralityholds both in the short and long run

—If money neutrality fails in the short run due to incomplete nominal adjustment, the impact ofmoney will clearly be stronger

• Two types of incomplete adjustment have been considered:

One highlights the role of imperfect information

—While still allowing prices– technically– to be flexible; lack of information makes economic agentsact such that aggregate money and prices do not move proportionally

=> Lucas’“misperceptions model”

Another highlights the role of sticky prices and wages

—Then, a change in the nominal money stock has real effects by definition (as in e.g. standardIS/LM models)

1

• In the Lucas “misperceptions model,”money shocks have real effects due to imperfect information.Prices are flexible

Most, however, believe that short-run price flexibility is a strong assumption: Lots of empiricalevidence on price- and wage inflexibility

• I.e., some nominal rigidity prevails in the short run

—If this is the case, monetary phenomena will have much stronger impact

—E.g., with rigid nominal prices, expansive monetary policy will likely translate directly into higherproduction

—E.g., with rigid nominal wages, monetary policy affects prices, thus directly affecting the realwage and employment

• Lot of research therefore examines the consequences of nominal rigidities in wages and/or prices for

—the transmission of monetary policy shocks

—the possibility of using monetary policy to stabilize the economy against other shocks

2

Sticky wages in MIU model

• A log-linearized version of the stochastic MIU model of Chapter 2 with endogenous labor supply isused to assess the idea and implications

• Simplifications:

—Utility function parameters: b = Φ; with flexible prices, money is superneutral(changes in real money holdings do not affect the marginal utility of consumption and thus theconsumption-leisure choice)

—No capital

Hence, any real effects of money will have to arise from nominal rigidities

• Nominal rigidity is introduced– in the simplest possible form– by assuming that the nominalwage for period t is set in period t− 1. It cannot change in period t (e.g., for contractual reasons)

Wage determination: the nominal wage is set such that the expected real wage equals the expectedmarginal product of labor

With Cobb-Douglas production function Yt = eetN 1−αt , 0 < α < 1, the marginal product is

(1− α) eetN−αt = (1− α)Yt/Nt

3

• In log-deviations from steady-state, the real-wage-equals-the-marginal-product is

wt − pt = yt − nt (6.3)

(lower-case letters are logs)

To attain this condition in expectations, the nominal wage is in period t− 1 set as:

wct = Et−1pt + Et−1yt − Et−1nt (6.9’)

—Higher expected prices, higher contract wage to secure the real wage target

—Higher Et−1yt− Et−1nt, higher contract wage to “match”higher expected marginal product

• Actual employment for given contract wage is therefore

nt = yt − (wct − pt)

= yt − (Et−1pt + Et−1yt − Et−1nt − pt)= (yt − Et−1yt) + (pt − Et−1pt) + Et−1nt

Actual employment is higher than expected if

—yt > Et−1yt as the marginal product then is higher than expected, which the contract wage failsto “incorporate”

—pt > Et−1pt as the actual real wage then is lower than expected, making firms hire more labor

4

• Implications of wage rigidity on actual output:

yt = (1− α)nt + et (6.1)

Insert the expression for employment:

yt = (1− α) [(yt − Et−1yt) + (pt − Et−1pt) + Et−1nt] + et

αyt = − (1− α) [Et−1yt − (pt − Et−1pt)− Et−1nt] + et

αyt = Et−1et − (1− α) [Et−1yt − (pt − Et−1pt)− Et−1nt] + et − Et−1et= Et−1yt − (1− α) [Et−1yt − (pt − Et−1pt)] + et − Et−1et

Therefore:

yt = a (pt − Et−1pt) + Et−1yt + (1 + a) εt, (6.11’)

εt ≡ et − Et−1et, a ≡ (1− α) /α > 0

Output exceeds the expected value if pt > Et−1pt. I.e., if prices are surprisingly high (and/or ifproductivity shock is higher than expected)

5

• Simple numerical example shows that the impact of a monetary shock is much larger that in theflexible price model

If aggregate demand is (ignoring velocity changes)

yt = mt − pt (6.13)

output isyt = (1− α) (mt − Et−1mt) + Et−1yt + εt (6.14’)

One percent positive money shock, st ≡ mt− Et−1mt,

=> (1− α) percent increase in output

=> With 1− α = 0.64 (labor’s typical share of income), a significant increase in output

• What about the persistent effect of money shocks found in data?

• Not present here.....

—. . . after a shock, wages have adjusted fully after one period

—. . . even with persistent shocks

• Is missing capital accumulation the cause?

—No; remember the weak persistence in flex-price model– applies here as well

6

• Hence, while introduction of wage rigidity in the MIU model gives much stronger effects of monetaryshocks (compared to the flex-price versions), the effects are not persistent

• Also, the transmission mechanism implies a countercyclical real wage; not in accordance withdata (real wages are a-cyclical, or mildly pro-cyclical)

• Moreover, the introduction of a nominal rigidity raises the issue: Who is setting the nominal variable?

—To address this, one must explicitly model price- or wage setting agents

—This, on the other hand, must involve introducing monopoly power into the model

• Monopoly power (and persistence) is therefore addressed (here, in a price-setting model)

—Monopoly power does not in itself create monetary non-neutrality

—Therefore, prices are assumed to be fixed for some time

• Also, they are assumed to be set (and reset), in an asynchronized – “staggered”– fashion; i.e., allmonopolists do not set/reset prices at exact same dates

—The latter feature is there to generate persistent effects of money shocks

7

“Staggered”price setting and persistence of money shocksModel of price setting under imperfect competition

• The economy has two sectors

—A final goods sector operating under perfect competition, using intermediate goods as inputs

—An intermediate goods sector, where a continuum of monopolists set the price on their uniqueintermediate good

• Production function for final goods producers:

Yt =

[∫ 1

0

Yt (i)q di]1q

, 0 < q ≤ 1 (6.20)

where Yt is final good and Yt (i) is intermediate good i, i ∈ [0, 1]

• Profits of final goods producers:

PtYt −∫ 1

0

Pt (i)Yt (i) di

where Pt is price on final good and Pt (i) is price on intermediate good i

By the production function, profits are

Pt

[∫ 1

0

Yt (i)q di]1q

−∫ 1

0

Pt (i)Yt (i) di

8

• Final goods producers take all prices as given (perfect competition), and choose profit-maximizingdemands. First-order condition:

Pt

[∫ 1

0

Yt (i)q di]1−q

q

Yt (i)q−1 = Pt (i) , i ∈ [0, 1]

Marginal revenue of each intermediate good equals its marginal cost

• This is rewritten by use of the production function:

PtY1−qt Yt (i)q−1 = Pt (i) i ∈ [0, 1]

This gives demand functions for intermediate goods:

Yt (i) =

[PtPt (i)

] 11−q

Yt i ∈ [0, 1] (6.21)

Demand of good i is falling in the relative price (1/ (1− q) is elasticity of substitution)

Tedious algebra shows that zero profits in the final goods sector requires (see Section 1 of “Technicalnotes . . .”)

Pt =

[∫ 1

0

Pt (i)qq−1 di

]q−1q

. . . the aggregate price index

9

• Each intermediate goods producer has the profit function

πt (i) = Pt (i)Yt (i)− rtKt (i)−WtLt (i) = [Pt (i)− PtVt]Yt (i)

where Vt is the minimized real costs of producing one unit of the good. PtVt thus denotes the nominalmarginal cost of Yt (i)

The intermediate producer has monopoly power, and sets its price so as to maximize profits, takinginto account the demand function for its product. I.e., it maximizes

πt (i) = [Pt (i)− PtVt][PtPt (i)

] 11−q

Yt︸ ︷︷ ︸= Y t(i)

with respect to Pt (i) (taking as given Pt; thereby the term monopolistic competition)

• From the first-order condition one recovers the familiar monopoly-theory result:

Pt (i) =1

qPtVt,

1

q> 1 (6.24)

Price is set as amark-up, 1/q > 1, over marginal costs

—Note that q → 1 implies that intermediate goods become perfect substitutes

—No monopoly power, and mark up becomes 1 (case of perfect competition arises)

10

• Imperfect competition does not cause monetary non-neutrality (but ineffi ciently low production)

In a symmetric equilibrium, Pt (i) = Pt, Lt (i) = Lt and proportional changes in prices and nominalwages have no real effects

• Assume therefore that price setters cannot adjust prices freely (this may even be optimal under “menucost”arguments)

The model with time dependent, staggered price setting

• Intermediate goods producers set a price, which has a “duration”of two periods

• Prices are set in staggered fashion: Half of the producers set prices in a given period, the other halfin the next period:

—Half sets prices in t, t + 2, t + 4, t + 6, ....

—Other half sets prices in t + 1, t + 3, t + 5, t + 7, ....

—Generally, P t+j is a price fixed for periods t + j and t + j + 1

• Important:

—Any monopolist i setting prices in a period, cares about the relative price of its product, Pt (i) /Pt

in the period it sets the price and the expected next-period relative price

—Two-period profit-maximization will therefore lead to a price-setting rule depending on currentand expected future aggregate prices

11

• From the first-order condition for two-period profit maximization, one gets the optimal price set in t(in log deviations from steady state) (see Section 2 of “Technical notes”):

pt =1

2(pt + Etpt+1) +

1

2(vt + Etvt+1) (6.29)

Indeed pt depends on current aggregate prices and real marginal costs, as well as expected futurevalues

The aggregate price is by definition a function of the prices set in the period, as well as the prices setin the previous period:

pt =1

2(pt + pt−1)

Therefore, the optimal price in period t depends on past period’s optimal prices and expected futureoptimal prices:

pt =1

2pt−1 +

1

2Etpt+1 + (vt + Etvt+1)

This will account for potential gradual adjustment of aggregate prices, and thus potential persistenceof monetary shocks

12

• Implications of this form of price rigidity is best analyzed under very simple assumptions (specialcases of the MIU equations):

—Real marginal costs are linearly related to output:

vt = γyt, γ > 0

—Aggregate demand is characterized by a quantity equation (ignoring velocity changes):

mt − pt = yt

—Nominal money supply follows a random walk:

Etmt+1 = mt

13

• With these assumptions one can solve for pt by the method of undetermined coeffi cients, to get (seeSection 4 of “Technical notes”):

pt = apt−1 + (1− a)mt, a =1−√γ1 +√γ, |a| < 1 (6.31)

The associated solution for aggregate prices, remembering pt = (1/2) (pt + pt−1), is

pt = apt−1 +1

2(1− a) (mt + mt−1)

Hence, for |a| 6= 0 aggregate prices exhibit inertia, implying prolonged real effects of a monetaryshock

• Important parameter for the degree of inertia is γ, the sensitivity of real marginal costs to output(could depend inversely on labor supply wage elasticity)

—Low sensitivity is often labelled a situation with high degree of real rigidity

14

• For γ = 1 (a = 0), highly sensitive real marginal costs, aggregate price adjustment is immediate; realeffect of money shock dies out after one period

—With γ = 1, a one percent increase in nominal money will for given prices increase output by onepercent. This increases real marginal costs by one percent, and all firms who can adjust pricesadjust by raising prices by one percent.

—Aggregate prices increase by 0.5 percent, and output increase by 0.5 percent

—In next period, when all firms have had the opportunity to adjust prices, the aggregate priceadjustment is complete, and y = 0 again

15

16

• For γ < 1 (a > 0), less sensitive real marginal costs, aggregate price adjustment is inertial; real effectof a money shock is persistent

—Hence, even after all firms have had the opportunity to adjust prices, aggregate price adjustmentis incomplete, and y has not returned to steady-state

—Source of inertia is the interplay between prices’dependence on past prices and expected futureprices

—Those adjusting in period t do not adjust fully to a monetary shock as their real marginal costdoes not rise suffi ciently. Hence, aggregate prices will adjust by less than half of the change inthe money supply

—This will feed into next period’s price adjustment, which will be dampened as it depends on thepast period’s dampened adjustment

—This is known by current price setters, and given that expected next-period prices are important,equilibrium adjustment of current prices are further reduced

—This process continues into the future, making adjustment gradual

17

• This case of staggered price-setting therefore provides a framework for generating persistent realeffects of monetary shocks

• The parameter γ, however, has to be rather low; i.e., a high degree of real rigidity is necessary

—This could be a situation where real labor market imperfections (effi ciency wage considerations,unionized wage setting), implies a rather rigid real wage. Then, real marginal costs will be ratherinsensitive to output

—So, a high degree of real rigidity (low γ), implies a high degree of persistence due to nominalrigidity

18

Summary

• Nominal rigidities give rise to substantial effects of monetary shocks as compared with flexible pricemodels

• One-period nominal wage (or price) contracts does not give rise to persistence of monetary shocks

• Modelling sticky price (or wage) setting calls for models of monopoly power

—Monopoly power in itself not a source of non-neutrality of money

—Particular price-setting structure important for the transmission of money shocks

—With staggered price setting, persistent effect of money shocks prevails; in particular with highdegrees of real rigidity

19

Plan for next lectures

Monday, March 20:Exercises in class, QUESTION 2 from the exam on June 15, 2006

Monday, March 27:

1. Money in the short run: Incomplete nominal adjustment (II)

Sticky Prices and Wages: Calvo and alternatives

Literature: Walsh (Chapter 6, pp. 241—261 – plus relevant appendix)

20