Inflation and Unit Labor Cost Robert G. King Mark W. Watson Prepared - - PowerPoint PPT Presentation

Inflation and Unit Labor Cost

Robert G. King Mark W. Watson Prepared for Studienzentrum Gerzensee 25th anniversary conference

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Familiar New Keynesian Price Equation

• Single equation (Gali & Gertler, Sbordonne)
• Component of DSGE models (Smets and Wouters)
• Link between inflation and real cost measure
•  is real unit labor cost or modification of it indicated by

particular production/market structure

• “z” is other factors, sometimes given a structural

interpretation (such as price markup shocks in SW)

• NKPE provides a direct 4‐way breakdown (Decomposition

#1) into inertia, expectations, cost, and residual

t t t t f t b t

z E    

 

     

1 1

2

Inflation and rulc

[similar to Figure 6 in packet: internal validity sample period]

1960 1965 1970 1975 1980 1985 1990 1995 2000

• 5

5 10 15 Percent per year, Percent deviation Inflation and Real Unit Labor Cost GDP inflation NFB real ULC

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Evolving project:

• ur starting questions
• What account do modern NK‐DSGE models

provide about forces which drive inflation?

– On average, during estimation period (60‐99) – During particular episodes – Before and afterward

• How does conclusion depend on whether one

looks directly at NKPE or its rational expectation solution?

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Why is NKPE attractive?

• Theoretical foundations (Calvo model)
• Near neutrality with respect to inflation trends
• Forward‐looking elements inevitable with sticky

prices

• Empirically tractable
• Real unit labor costs allows side‐step of difficult

task of measuring capacity output in a world of changing technology

• Allows ready consideration of implications of

alternative inflation targeting policies

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Decomposition 1: What are sources of inflation? Figure 10’s direct answer from NKPE using GG measure of parameters and cost

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Conclusions from Decomposition #1

• Inflation dominated by expectations
• Small direct contribution of cost (which is sole channel

for monetary policy and aggregate demand)

• Not too much inflation inertia
• Robust: parameters (GG versus SW); cost measures (GG

versus SW); inflation forecasting (GG‐VAR, SW‐DSGE)

• Robust to levels or deviations from trend (using 1‐sided

HP filter to remove trend)

• Inflation shocks are not dominant

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Decomposition #2: Fundamental Inflation

• History It was precisely this type of decomposition in

the work of Gali‐Gertler (1999) and Sbordonne (2002) that generated impetus toward NKPE in DSGE models.

• Example of Interpretation of single equation or block of

equations within a DSGE model. Focuses on inflation impact of DSGE modeling assumptions.

– Our 1996 REStat study yielded disappointing results for an NKPE+DSGE framework – It contained Calvo pricing w/o inflation inertia mechanism – But the rest of the DSGE was very different from SW: much simpler core neoclassical structure (e.g., no consumption habit) well as no nominal wage rigidity

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Insert GG Figure 2

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Figure 12: Replicating the potential displayed in GGS

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Decomposition #2: Mechanics of Fundamental Inflation (RE forward solution)

t j j t t j t t t t z t t t

d M I L E L d

1 1 1 1 t t

] [ ) 1 ( ) 1 ( DSGE]

• r

[VAR u Md d vectors] data , [selection

      

         



             

   

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Figure 18: Unexpected (to us) results in SW

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Switching from accounting to diagnosis What are the candidates?

• 1. Parameters ()
• 2. Measure of cost (
• 3. Forecasting model (M)

a) 2 variable VAR in GG b) DSGE solution in SW c) Implied 2 variable VAR for SW (population approximation or empirical)

• 4. Various combinations of above: Fundamental

inflation is complicated function of , M so we’ll develop a simple approximation

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Parameters in NKPE

b f  GG 0.25 0.68 0.153 SW 0.19 0.81 0.082

Parameters in Fundamental Inflation

   z GG

0.32 0.876 0.197 5.14

SW

0.23 0.998 0.101 4.91

Figure 15: Cost Measures

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• Overhead corrections (model consistent) to rulc in SW, which we call

modified unit labor cost (mulc) and some differences in data since they are modeling GDP rather than NFB

• Log indexes adjusted to common mean

More on cost differences

• Differences large in trend, smaller detrended
• Irony: real unit labor cost has some similar issues to
• utput gaps

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Approximating Fundamental Inflation

• 1. Estimate bivariate VAR (d=[ 

a) Just as in GG b) Simplification for SW

• 2. Use this VAR to form FI solution

3. Sum the FI solution coefficients  on  and 

• 4. Compute approximation to as
• 5. Approximation emphasizes trends

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t t t

    

 

) 1 ( ) 1 ( ~  

t t

d M I L

1 1

] [ ) 1 (

 

       

 

Figure 15: Approximation for GG fundamental inflation

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Figure 19: Approximation for SW Fundamental Inflation

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Key findings

• Approximation is quite good
• Parameters are not responsible for large

differences between GG and SW

• Both approximating VAR thru beta and cost

data help explain large differences

• But the rest of the SW DSGE model is not the

source of the puzzle: it fits the moments of the SW data quite well.

• Robustness in table 5

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Key findings from approximation (cont’d)

• GG fundamental inflation

– places positive weight on both  and  – Reference approximation for FI is .85 +.15  – Triangular shape in “inflation trend” and downward “cost trend” yields main historical inflation patterns

• SW fundamental inflation

– places bigger positive weight on measured cost and negative weight on actual inflation – Reference approximation for FI is 1.45  ‐ .7  – Approximation closely captures puzzling picture, linking SW‐FI to trends in inflation and modified rulc

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Inside the SW model

• Elements of their Historical Decompositions

– As SW emphasize, structural wage and price markup shocks are the key drivers of inflation – But price markup shocks also are very important for SW marginal cost measure, which we are calling modified real unit labor cost (MRULC)

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Figure 7: SW inflation historical decomposition

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Figure 8: SW cost historical decomposition

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Four impulse responses

• Revision in inflation path due to structural

price shock (z)

• Revision in present discounted value forecast

z of structural price shock (same sign, larger)

• Revision in modified real unit labor cost (very

persistent; offsetting z effect)

• Revision in fundamental inflation (opposite

sign to z)

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SW impulse responses for structural shock, inflation and cost

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SW model impulse responses for fundamental inflation and z

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Why pattern in SW model?

• Take 1: Price markup shock and inflation targeting pattern

– Would be “neutral” if just right “flexible inflation target” moves in z – Inflation shock z rises in a persistent manner (ARMA(1,1) with ar=.9 and ma=.7) and discounted z rises as well (more than one‐for‐one) – Inflation  does not rise much (policy rule behind this…) and thus “fundamental inflation” must fall.

• Take 2: Price markup shock and real activity pattern

– The components of SW modified rulc (real wage, labor input, and

• utput) all fall in response , but compensation falls by more than
• utput principally due to real wage declines

– Real marginal cost is still roughly “inverse of markup” as in simpler models – there is a very slow equilibrating process for the wage and mrulc because the markup is very persistent (.9^12=.24)

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External validity: Continuing decline in real unit labor cost/labor share (Figure 23)

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Recent Decade: GG model (Figure 24A)

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Recent decade: SW model (Figure 24B)

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Comments

• Standard NKPE in GG form is hit by decline in real

ulc, as SW form is hit by even more pronounced decline in modified rulc.

• SW had to grapple with this phenomenon earlier,

due to early 1990s data revisions (which make

• ur replication of GG look less good than their

Figure 2) and longer estimation interval (through 2004:4, which includes some of pronounced recent decline in labor’s share)

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Another interpretation and its implications

• Labor’s share and labor substitution
• Possibility: roughly constant inflation, roughly

constant correctly measured costs, trend down in labor’s share

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ate indetermin Shares ] y wN [ ce indifferen Factor w/x q logs no : Note ) ( y qs s xN a y       



Summary

• We have studied the link between inflation

and unit labor cost, through the NKPE lens

• We have shown how SW model identifies

trend declines in modified real unit labor costs as positive price shocks so as to satisfy NKPE

• We have illustrated how labor substitution in

the production function could lead to major declines in labor’s share/real unit labor cost without pronounced declines in inflation

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