Reconciling Micro-Data and Macro Estimates of
Price Setting
Adam Cagliarini, Tim Robinson and Allen Tran
Reserve Bank of Australia (RBA)
October 21, 2009
Adam Cagliarini, Tim Robinson and Allen Tran
Reconciling Micro-Data and Macro Estimates of Price Setting
Puzzle
Estimates of Average Duration Between Price Resetting
US
Micro
Macro
4.3 months ≈ 6 quarters
Sources: Bils and Klenow (2004), Gali and Gertler (1999)
Adam Cagliarini, Tim Robinson and Allen Tran
Reconciling Micro-Data and Macro Estimates of Price Setting
Importance
The extent of nominal rigidities considerably influences the
real impact of monetary policy.
The Calvo framework is extensively used in central bank
models. Resolving this puzzle gives us greater understanding
of these models.
Help determine how to use the micro data as priors in
estimation.
Adam Cagliarini, Tim Robinson and Allen Tran
Reconciling Micro-Data and Macro Estimates of Price Setting
Summary
AIM: Reconcile the micro data on price setting with estimates from
a macro model.
Adam Cagliarini, Tim Robinson and Allen Tran
Reconciling Micro-Data and Macro Estimates of Price Setting
Summary
AIM: Reconcile the micro data on price setting with estimates from
a macro model.
METHOD:
Introduce into a standard model:
heterogeneity across firms, and,
a richer production structure, incorporating intermediate
goods.
Adam Cagliarini, Tim Robinson and Allen Tran
Reconciling Micro-Data and Macro Estimates of Price Setting
Summary
AIM: Reconcile the micro data on price setting with estimates from
a macro model.
METHOD:
Introduce into a standard model:
heterogeneity across firms, and,
a richer production structure, incorporating intermediate
goods.
Calibrate the model using the micro data, and simulate macro
aggregates.
Adam Cagliarini, Tim Robinson and Allen Tran
Reconciling Micro-Data and Macro Estimates of Price Setting
Summary
AIM: Reconcile the micro data on price setting with estimates from
a macro model.
METHOD:
Introduce into a standard model:
heterogeneity across firms, and,
a richer production structure, incorporating intermediate
goods.
Calibrate the model using the micro data, and simulate macro
aggregates.
Estimate the aggregate New-Keynesian Phillips curve (NKPC)
using the simulated macro data.
Compare and assess these macro estimates to the calibrated
true values.
Adam Cagliarini, Tim Robinson and Allen Tran
Reconciling Micro-Data and Macro Estimates of Price Setting
Results
The aggregate Phillips curve overstates price stickiness.
The slope of the NKPC in calibrated models often is too flat.
Ignoring heterogeneity in pricing has consequences.
Adam Cagliarini, Tim Robinson and Allen Tran
Reconciling Micro-Data and Macro Estimates of Price Setting
Results
The aggregate Phillips curve overstates price stickiness.
The slope of the NKPC in calibrated models often is too flat.
Ignoring heterogeneity in pricing has consequences.
When there is both a rich production structure and
heterogeneity the conventional measure of real marginal costs
(the cyclical variable in the NKPC) is no longer appropriate.
Adam Cagliarini, Tim Robinson and Allen Tran
Reconciling Micro-Data and Macro Estimates of Price Setting
The NKPC
πt =
(1 − βθ)(1 − θ)
rmct + βIEt (πt+1 )
θ
where:
πt is inflation; rmct real marginal costs,
β is the consumer’s discount factor, and,
The Calvo parameter, θ, which is the probability that a firm
cannot change its price.
The average duration of a price is
D(θ) =
Adam Cagliarini, Tim Robinson and Allen Tran
1
.
1−θ
Reconciling Micro-Data and Macro Estimates of Price Setting
Heterogeneity
Most models capture heterogeneity temporarily via Calvo
pricing - some firms temporarily cannot change prices.
Carvalho, 2006: Heterogeneity in the Calvo parameter affects
aggregate dynamics
Real impact of monetary policy is larger.
To match the impulse responses of a heterogenous economy
with a homogeneous one, the Calvo parameter needs to be
increased threefold.
Adam Cagliarini, Tim Robinson and Allen Tran
Reconciling Micro-Data and Macro Estimates of Price Setting
Heterogeneity
Most models capture heterogeneity temporarily via Calvo
pricing - some firms temporarily cannot change prices.
Carvalho, 2006: Heterogeneity in the Calvo parameter affects
aggregate dynamics
Real impact of monetary policy is larger.
To match the impulse responses of a heterogenous economy
with a homogeneous one, the Calvo parameter needs to be
increased threefold.
Our model assumes heterogeneity in pricing and technology.
Adam Cagliarini, Tim Robinson and Allen Tran
Reconciling Micro-Data and Macro Estimates of Price Setting
Heterogeneity in Micro Data
Micro Data studies report the average duration prices remain
fixed for each sector
The Calvo probability is typically calculated from the average
duration across sectors, say the jth
D(θj ) =
Adam Cagliarini, Tim Robinson and Allen Tran
1
.
1 − θj
Reconciling Micro-Data and Macro Estimates of Price Setting
Heterogeneity in Micro Data
Micro Data studies report the average duration prices remain
fixed for each sector
The Calvo probability is typically calculated from the average
duration across sectors, say the jth
D(θj ) =
1
.
1 − θj
Recall Jensen’s inequality: if g is convex, IE(g (x)) ≥ g (IE(x)).
Since D(θj ) is convex and increasing in θ, we can apply
Jensen’s inequality:
D(θ̂MICRO ) = IE(D(θj )) > D(IE(θj ))
⇒ θ̂MICRO > IE(θj ).
Adam Cagliarini, Tim Robinson and Allen Tran
(1)
Reconciling Micro-Data and Macro Estimates of Price Setting
Heterogeneity in Macro Data
Suppose we can write the NKPC as the sum of sectoral
NKPCs
πt =
N
X
j=1
wj
(1 − θj )(1 − βθj )
mcj,t + βIEt πj,t+1
θj
and the slope coefficient can be decomposed as follows
λ(θj , β) =
(1 − βθj )(1 − θj )
= λ̄ + eλ,j
θj
We can write
πt = λ̄mct + βIEt πt+1 +
X
wj eλ,j mcj,t ,
j
Adam Cagliarini, Tim Robinson and Allen Tran
Reconciling Micro-Data and Macro Estimates of Price Setting
Heterogeneity in Macro Data
If we get a “good” estimate of λ̄, we can compute the
corresponding Calvo probabiity, θMACRO
Since λ(θj ) is convex and decreasing in θ, we can apply
Jensen’s inequality
λ(θ̂MACRO ) = IE(λ(θj )) ≥ λ(IE(θj ))
⇒ θ̂MACRO ≤ IE(θj ).
Adam Cagliarini, Tim Robinson and Allen Tran
(2)
Reconciling Micro-Data and Macro Estimates of Price Setting
The Puzzle Gets Bigger
(1) and (2) imply that:
θMACRO ≤ IE(θ) ≤ θMICRO
Adam Cagliarini, Tim Robinson and Allen Tran
Reconciling Micro-Data and Macro Estimates of Price Setting
The Puzzle Gets Bigger
(1) and (2) imply that:
θMACRO ≤ IE(θ) ≤ θMICRO
But...
Avg Duration from NKPCs ≈ 6 quarters
Avg Duration from Micro Data ≈ 1-2 quarters.
Adam Cagliarini, Tim Robinson and Allen Tran
Reconciling Micro-Data and Macro Estimates of Price Setting
Implications for Calibration/Bayesian Estimation
It’s clear that the Calvo parameters from the micro and macro
data should not be the same if heterogeneity is present.
The Calvo used in many calibrated models is likely to be too
high or the priors in Bayesian estimation inappropriate if made
with reference to the micro data.
Adam Cagliarini, Tim Robinson and Allen Tran
Reconciling Micro-Data and Macro Estimates of Price Setting
Roadmap
Look at effects of including heterogeneity and roundabout
production in a standard macro model.
Assess their consequences for econometric estimates of the
NKPC.
Adam Cagliarini, Tim Robinson and Allen Tran
Reconciling Micro-Data and Macro Estimates of Price Setting
The Model
The model contains standard New-Keynesian features with
Heterogeneity across sectors
Calvo pricing in the intermediate goods producers.
Roundabout production
Adam Cagliarini, Tim Robinson and Allen Tran
Reconciling Micro-Data and Macro Estimates of Price Setting
The Model
The model contains standard New-Keynesian features with
Heterogeneity across sectors
Calvo pricing in the intermediate goods producers.
Roundabout production
Production in a modern economy is not well represented by a
tiered production process.
Firms produce output that can be consumed or used as a
factor in production (Basu (1995)).
Roundabout production means one firms real marginal costs
depends on the pricing decision of another.
Nakamura and Steinsson (forthcoming) show that roundabout
production increases the real effects of monetary policy.
Adam Cagliarini, Tim Robinson and Allen Tran
Reconciling Micro-Data and Macro Estimates of Price Setting
The Model
The model contains standard New-Keynesian features with
Heterogeneity across sectors
Calvo pricing in the intermediate goods producers.
Roundabout production
Production in a modern economy is not well represented by a
tiered production process.
Firms produce output that can be consumed or used as a
factor in production (Basu (1995)).
Roundabout production means one firms real marginal costs
depends on the pricing decision of another.
Nakamura and Steinsson (forthcoming) show that roundabout
production increases the real effects of monetary policy.
Adam Cagliarini, Tim Robinson and Allen Tran
Reconciling Micro-Data and Macro Estimates of Price Setting
Model Diagram
Households
Labour: lt
Final Good: cj,t
Intermediate Goods Firms
Final Goods Firms
Intermediate Good used in consumption: ct(i)
Intermediate Good used in production: mk,t(i)
Adam Cagliarini, Tim Robinson and Allen Tran
Reconciling Micro-Data and Macro Estimates of Price Setting
Calibration and Estimation
Table: Calvo probabilities for each sector
Sector
Agriculture
Construction
Manufacturing
Mining
Utilities
Wholesale and Retail Trade
Transport and Storage
Business Services
Household Services
Tourism
Avg. Duration (Q)
4
1.33
2
4
4
1
4
4
4
4
Calvo
0.75
0.25
0.50
0.75
0.75
<0.25
0.75
0.75
0.75
0.75
Source: RIA/RBA Pricing Survey (D’Arcy, Rayner and Park, Forthcoming)
Adam Cagliarini, Tim Robinson and Allen Tran
Reconciling Micro-Data and Macro Estimates of Price Setting
Simulated data
Table: Moments of observed and simulated series (1993Q1 to 2007Q4)
Parameter
Var (gt )
Var (πt )
Var (it )
Corr (gt , πt )
Corr (gt , rt )
Corr (it , πt )
Corr (gt , gt−1 )
Corr (rt , rt−1 )
Corr (πt , πt−1 )
Adam Cagliarini, Tim Robinson and Allen Tran
Actual
0.33
0.05
0.04
-0.01
-0.12
0.27
-0.04
0.93
0.42
Simulation
0.38
0.06
0.03
-0.08
-0.01
0.24
-0.02
0.86
0.37
Reconciling Micro-Data and Macro Estimates of Price Setting
Results
Compare 4 models
Baseline, single sector and no roundabout production
Roundabout, roundabout production and no heterogeneity
Heterogeneous, multiple sectors but no roundabout production
Full model
Adam Cagliarini, Tim Robinson and Allen Tran
Reconciling Micro-Data and Macro Estimates of Price Setting
Impulse Response Functions
Preference shock on
interest rate
% pts
Policy shock on
% pts
interest rate
Technology shock on
% pts
0.06
0.04
0.04
0.02
0.00
0.02
0.00
-0.01
inflation
% pts
0.01
inflation
% pts
% pts
0.0
0.00
0.05
-0.2
-0.05
0.00
-0.4
0.10
growth
% pts
0.2
0.1
value added
%
%
% pts
0.4
0.3
0.2
value added
%
0.0
0.00
0.2
-0.1
-0.05
-0.2
-0.10
0.0
2
growth
0.1
0.0
0.3
0.1
inflation
-0.10
growth
% pts
0.1
0.0
-0.1
-0.2
-0.3
0.0
-0.1
-0.2
interest rate
value added
-0.3
-0.15
4 6 8 10
2 4 6 8 10
2 4 6 8
Quarter
Quarter
Quarter
–– Baseline –– Roundabout –– Heterogeneous –– Full
Adam Cagliarini, Tim Robinson and Allen Tran
10
Reconciling Micro-Data and Macro Estimates of Price Setting
Roadmap
Look at effects of including heterogeneity and roundabout
production in a standard macro model.
Assess their consequences for econometric estimates of the
NKPC.
Adam Cagliarini, Tim Robinson and Allen Tran
Reconciling Micro-Data and Macro Estimates of Price Setting
Monte Carlo Exercise
For each of the four models
Simulate model over T periods
Estimate hybrid aggregate NKPC using simulated data
πt =
βθ
ω
(1 − ω)(1 − βθ)(1 − θ)
mct +
IEt πt+1 + πt−1
φ
φ
φ
φ = θ + ω [1 − θ(1 − β)]
Save parameter estimates
Repeat N times
We estimate using GMM, instrumenting for:
expected inflation, and,
marginal costs.
Choice of instruments largely follows Gali and Gertler (1999).
Adam Cagliarini, Tim Robinson and Allen Tran
Reconciling Micro-Data and Macro Estimates of Price Setting
Estimates of the Aggregate NKPC
Table: GMM estimates of the aggregate NKPC from various models
Parameter
β
θ
ω
True
0.99
0.30
0.00
Baseline
0.72 (0.12)
0.31 (0.09)
0.01 (0.02)
Roundabout
0.82 (0.11)
0.33 (0.11)
0.03 (0.06)
Heterogeneous
0.38 (0.23)
0.87 (0.05)
0.05 (0.04)
Full
0.83 (0.16)
0.86 (0.11)
0.21 (0.07)
Median and standard deviation in brackets.
Instruments and estimation method replicate Gali and Gertler (1999).
Adam Cagliarini, Tim Robinson and Allen Tran
Reconciling Micro-Data and Macro Estimates of Price Setting
Monte Carlo Results
Figure: Estimates of θ
Density
Density
12
12
Heterogeneous
10
8
10
Baseline
8
6
6
Roundabout
4
4
Full
2
0
0.0
2
0.2
0.4
0.6
0.8
1.0
0
1.2
θ
Adam Cagliarini, Tim Robinson and Allen Tran
Reconciling Micro-Data and Macro Estimates of Price Setting
Monte Carlo Results
Figure: Estimates of ω
Density
Density
25
25
Baseline
20
20
15
15
Heterogeneous
10
10
Roundabout
5
5
Full
0
-0.1
0.0
0.1
0.2
0.3
0.4
0
0.5
ω
Adam Cagliarini, Tim Robinson and Allen Tran
Reconciling Micro-Data and Macro Estimates of Price Setting
Why does Heterogeneity affect estimates of the NKPC?
There are 3 possible explanations
Misweighting of marginal costs
Weak instruments
Lack of instrument exogeneity
Adam Cagliarini, Tim Robinson and Allen Tran
Reconciling Micro-Data and Macro Estimates of Price Setting
Misspecification
In the presence of heterogeneity, aggregate marginal costs is
not the aggregate labour share.
Instead, aggregate marginal costs are gross revenue weighted
labour shares for each sector.
Adam Cagliarini, Tim Robinson and Allen Tran
Reconciling Micro-Data and Macro Estimates of Price Setting
Misspecification
Figure: Estimates of θ Using Correctly Measured Real Marginal Costs
Density
Density
10
10
Correct marginal costs
8
8
6
6
Aggregate labour share
4
4
2
2
0
0.6
0.7
0.8
0.9
1.0
0
1.1
θ
Adam Cagliarini, Tim Robinson and Allen Tran
Reconciling Micro-Data and Macro Estimates of Price Setting
Weak Instruments
The NKPC is plagued by weak instrument problems
(Mavroeidis, 2005 JMCB)
Sectoral NKPCs do not have heterogeneity problems but weak
instrument problems remain.s
Weak instruments only pose modest problems when
heterogeneity exists.
Table: GMM estimates of sectoral NKPCs
Parameter
β
θ
ω
Construction
Actual
Estimated
0.99
0.61 (0.15)
0.25
0.27 (0.06)
0.00
0.00 (0.01)
Adam Cagliarini, Tim Robinson and Allen Tran
Manufacturing
Actual
Estimated
0.99
0.75 (0.13)
0.5
0.55 (0.07)
0.00
0.04 (0.06)
Business Services
Actual
Estimated
0.99
0.85 (0.14)
0.75
0.80 (0.27)
0.00
0.32 (0.20)
Reconciling Micro-Data and Macro Estimates of Price Setting
Instrument Exogeneity
In our model, ignoring indexation, using
IEt (πt+1 ) = πt+1 + vt+1 , we can write
X
πt = λ̄mct + βπt+1 + βvt+1 +
wj eλ,j mcj,t
j
Using GMM to estimate the NKPC requires the moment
condition
X
IE(βvt+1 +
wj ej mcjt |zit ) = 0 ∀i
j
which is hard to satisfy for any relevant instruments when
instrumenting for marginal cost.
Adam Cagliarini, Tim Robinson and Allen Tran
Reconciling Micro-Data and Macro Estimates of Price Setting
Macroeconomic Implications - GMM Estimates are Similar
to the Full Model
Preference shock on
Policy shock on
interest rate
% pts
interest rate
% pts
Technology shock on
0.05
0.06
% pts
0.02
0.04
0.04
0.01
0.03
0.02
0.00
0.02
0.00
-0.01
inflation
% pts
inflation
0.06
% pts
-0.05
% pts
-0.01
0.04
-0.10
-0.02
0.02
-0.15
-0.03
0.00
-0.20
growth
growth
% pts
0.4
0.2
0.3
0.2
0.0
0.2
0.0
-0.2
0.1
-0.2
-0.4
0.0
-0.1
-0.3
-0.4
2
4 6 8
Quarter
% pts
0.0
value added
value added
%
0.0
-0.1
-0.2
10
inflation
-0.04
growth
% pts
%
0.3
0.2
0.1
interest rate
value added
%
0.00
-0.05
2
-0.10
-0.15
-0.20
4 6 8 10
2
Quarter
–– GMM estimate –– Full model
Adam Cagliarini, Tim Robinson and Allen Tran
4 6 8
Quarter
10
Reconciling Micro-Data and Macro Estimates of Price Setting
Conclusion
Heterogeneity and roundabout production affect dynamics in
a non-trivial manner
Estimates of the aggregate Calvo from Gali and Gertler
(1999) suggest that
the economy is populated by homogeneous firms resetting
every 6.5 quarters on average; OR
the average duration of price changes across heterogeneous
sectors is 2 quarters on average
The latter is more plausible and resolves the discrepancy
between the micro and macro-data
Adam Cagliarini, Tim Robinson and Allen Tran
Reconciling Micro-Data and Macro Estimates of Price Setting