Productivity Losses from the Attention toAggregate Uncertainty
Author: Diego Daruich Advisor: Josep Pijoan-Mas
CEMFI
June 12, 2012
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Intuition
• If agents have a limited amount of information-processingcapacity, they have to decide optimally how to allocate it.
• Entrepreneurs have to pay attention to:• Understand macro-aggregate conditions (e.g. inflation,
exchange rate), to do an optimal pricing.• Increase productivity (like Kirzner’s “alertness”).
• I study how the amount of volatility of macro conditionsaffects this trade off and its consequences on the levels ofproductivity and output.
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Motivation
ModelHouseholdsFirms
Model ImplicationsMoney Non-NeutralityPolicy FunctionAggregate Variables
Quantitative AnalysisCalibrationResults
Conclusions2 / 27
Outline
Motivation
Model
Model Implications
Quantitative Analysis
Conclusions
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Some Empirics
Table 1 (CS): Expected Sales Growth and Uncertainty in World Business Environment Survey (2000)
VARIABLES RE RE RE FE FE FE
Economic Unpredictability -2.108*** -1.889*** -2.190*** -2.039***
(0.646) (0.566) (0.700) (0.619)
Policy Unpredictability -1.246*** -0.260 -1.649** -0.192
(0.426) (0.666) (0.726) (0.680)
Observations 5,404 5,548 5,352 5,404 5,548 5,352
R-squared 0.007 0.004 0.007 0.007 0.005 0.007
Number of countries 53 69 53 53 69 53
Company characteristics Y Y Y Y Y Y
Country characteristics Y Y Y N N N
Legal Origin Y Y Y N N N
*** p<0.01, ** p<0.05, * p<0.1.
Robust standard errors in parentheses. Company characteristics: Foreign Owned, Government owned.
Country characteristics: GDP initial, GDP growth.
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Some Empirics
Table 2 (PD 5 year average): GDP Growth and Uncertainty, Within Groups Regression
VARIABLES (1) (2) (3) (4) (5) (6)
SD Inflation -1.100*** -0.560*** -0.649*** -0.503***
(0.149) (0.145) (0.147) (0.189)
SD Exchange Rate -0.259*** -0.210* -0.182* -0.231**
(0.097) (0.109) (0.100) (0.100)
SD M2 Growth -0.628*** -0.171 -0.134 -0.258**
(0.127) (0.122) (0.121) (0.115)
Observations 937 1,058 892 752 740 657
R-squared 0.370 0.215 0.224 0.293 0.315 0.419
Number of countries 135 137 129 119 117 108
Population N N N Y Y Y
Government N N N N Y Y
Economics N N N N N Y
*** p<0.01, ** p<0.05, * p<0.1
Robust standard errors in parentheses. All regressions control for year effects. Population: Pop., Pop. growth
and Education. Government: Gov. expenditure. Economics: Trade, Inv., Infl., Trade.4 / 27
Outline
Motivation
ModelHouseholdsFirms
Model Implications
Quantitative Analysis
Conclusions
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Model
• Static model.
• Representative money-holding consumer with Dixit-Stiglitzpreferences and endogenous labour.
• Monetary source of uncertainty.• The aggregate state variables are the monetary policy variance
(observed) and the monetary shock (not observed).
• Continuum of goods produced monopolistically.• Attention choice with trade off between aggregate uncertainty
and individual productivity.
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Households
maxci ,L,M
[ln (C ) + γm ln
(MP
)− γl
L1+Ψ
1+Ψ
]subject to:
• Budget Constraint: M + PC = WL + D
• Total Consumption: C =
[1∫0
cθ−1
θi di
] θθ−1
• Aggregate Price Index: P =
[1∫0
p1−θi di
] 11−θ
The resulting conditions are:
• Goods Demand: ci =(
Ppi
)θC
• Money Demand: MP = γmC
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FirmsBasics
• Production function: y = Alα
• A = A (1 + ηZ ) where Z will be related to the time devotedto paying attention to productivity.
• T + Z = 1, time is allocated between understanding macroconditions (T ) or productivity (Z ).
• Paying attention to aggregate conditions, has a cost interms of productivity.
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Monetary Policy and Information StructureM = Meε where ε ∼ N
(− σ2
m2 , σ2
m
)Why?
s = ε + ζ where the noise term ζ is:
• Independent of A and M.
• Independent across firms.
• Gaussian white noise with variance σ2ζ (1− T )τ = σ2
ζ Z τ
A timeline of the sequence of events for the firms would be:
Decision
Observed
Not Observed
Signal Quality(
σ2ζ
)Policy(σ2m)
Attention (Z )
Signal (s)
Shock (ε)
Price (p)
Output (y)
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FirmsAttention Problem: Second Stage
V (s; w , Z ) = maxp(s;w ,Z )
Eε|s,Z
[(p(s;w ,Z )
P y − wP l)]
s.t.
• Production Function: y = Alα
• Households’ Demand: y = c =(
Pp(s;w ,Z )
)θC
• Households’ Money Demand: MP = γmC
• Aggregate Price: P =
[1∫0
p (s; w , Z )1−θ ds
] 11−θ
• Money Supply: M = Meε where ε ∼ N(− σ2
m2 , σ2
m
)• Signal: s = ε + ζ where ζ ∼ N
(0, σ2
ζ Z τ)
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FirmsAttention Problem: First Stage
maxZ
∫V (s; w , Z ) f (s |Z ) ds
subject to:
• Productivity: A = A (1 + ηZ ) with (Z ∈ [0, 1])
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Equilibrium
DefinitionGiven the monetary shock, ε, an equilibrium for this economy is aset of decision rules, p (s; w , Z ) and Z ; quantities L, Md , ci and lifor all i ∈ [0, 1]; and a wage w such that:
1. Given the wage and prices, Md , L and ci for all i ∈ [0, 1]solve the households’ problem.
2. Given the wage, p (s; w , Z ) and Z solve the firms’ problem.
3. Good i market clears, for all i ∈ [0, 1] .
4. Labour market clears, L =1∫0
lidi .
5. The money market clears, Md = Ms = Meε
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Computational Methodology
1. Generate many shocks from ε ∼ N(− σ2
m2 , σ2
m
).
2. For each shock:
2.1 Guess wage w .2.2 Build a grid of Attention levels Z . For each Z :
2.2.1 Build a grid of signals from si = ε + ζi and ζi ∼ N(
0, σ2ζ Z
τ)
and solve nonlinear system for policy function.- Approximate unknown function p (s;w ,Z ) with a finitenumber of elements of the polynomial base.- Using Gauss-Hermite Quadrature to approx expectations.
2.2.2 Compute expected profits, again using Gauss-Hermite andpolicy function.
2.3 Choose Z that maximizes expected profits.2.4 Using policy function, simulate many firms. Obtain
equilibrium output, prices and labour demand and supply.2.5 If labour market clears, stop. Otherwise, try new w and
restart (bisection method).
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Outline
Motivation
Model
Model ImplicationsMoney Non-NeutralityPolicy FunctionAggregate Variables
Quantitative Analysis
Conclusions
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ImplicationsMoney Neutrality
Money is neutral only when there is no uncertainty:
1. Monetary policy is fixed: σ2m = 0 (exogenous).
2. By definition there is no noise: σ2ζ = 0 (exogenous).
3. Full Attention to Macro conditions: Z = 0 (endogenous).
Figure: Aggregate output and Monetary shock in non-neutral case.
Competition in Quantities Competition in Prices
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ImplicationsPrice or Quantity Competition
The difference is due to the non-linearities in the problem:
In Quantities
• Policy Function: y (s; w , Z )
• Aggregation:
C =
[1∫0
y (s; w , Z )θ−1
θ ds
] θθ−1
• P = G (C , M)
In Prices
• Policy Function: p (s; w , Z )
• Aggregation:
P =
[1∫0
p (s; w , Z )1−θ ds
] 11−θ
• C = H (P, M)
Equivalent as θ approaches one, since each firm becomes anactual monopolist in its own product and does not need to
predict what the other firms are doing.
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ImplicationsAttention and Uncertainty
Figure: Effects of Aggregate Uncertainty
Attention to Productivity Aggregate Output
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ImplicationsPolicy Functions
Figure: Policy Functions p (si ; w , Z )
Low Uncertainty High Uncertainty
The higher the uncertainty, the more attention is paid to macroconditions, making the signal more reliable. Then, the policy
function is more sensible to the signal.16 / 27
Implications
Figure: Aggregate Variables and Monetary Shock
Nominal Wages Aggregate Price
Real Labour Income Real Firm Income
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Outline
Motivation
Model
Model Implications
Quantitative AnalysisCalibrationResults
Conclusions
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Calibration
In order to calculate the monetary policy volatility I fit a modifiedGARCH(1,1) on the money growth gm,t
gm,t =σ2m,t
2 + εt
εt ∼ N(− σ2
m,t
2 , σ2m,t
)σ2m,t = c + β1
(ε2t−1 − σ2
m
)+ β2
(σ2m,t−1 − σ2
m
)σ2m = c
1−β1−β2
To estimate the noise, I assume that:
σ2ζ,t = kσ2
m,t
Then use time series of σ2m,t , εt and HP-filtered output cycles to
recover 3 parameters (η, τ and k).
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Calibration
Figure: Output Cycle and Monetary Uncertainty
Argentina Chile
Ecuador Mexico
Output Cycle (Blue, left axis) and Monetary Std. Dev. (Red, right axis) 19 / 27
Calibration
Figure: Calibration using Time Series of Chile
Output Cycle (Blue, left axis) and Monetary Std. Dev. (Red, right axis)
I have chosen this strategy because:• Computationally demanding.• Years close to each other.• Years display pattern the model tries to capture.
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CalibrationParameters
Table 2: Parameters values
Calibrated
η Productivity return 0.069τ Non-linearity of noise reduction 19.75k Noise-Signal ratio 1.95
Obtained from Literature
γl Utility multiplier of leisure 0.94γm Utility multiplier of real money 1Ψ Utility leisure Non-linearity 3θ Consumption Aggregation 4α Production Function Non-linearity 0.8
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ResultsModel Capacity
Figure: Data and Model output percentage deviation
Argentina Chile
Ecuador Mexico
Data (Blue, solid) and Model (Red, dashed) 22 / 27
ResultsModel Capacity
Table: Model Capacity
Country Correlation ExplainsArgentina 38.79% 43.99%
Chile 16.25% 49.10%Ecuador 42.11% 44.28%Mexico 12.31% 36.42%
Average 27.37% 43.44%
• The model fits very well the Argentinean and Ecuadoriandata, capturing almost perfectly the 1989 hyper-inflationand 1999 banking crisis, respectively.
• The model fit for Mexico is the poorest, probably because itscycles are less related to monetary policy (Garriga, 2010).
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ResultsImportance of Uncertainty vs. Shock
I test model with expected shock instead estimated one, thereforeevaluating the importance of uncertainty alone in good fit.
Table: Model Capacity without shock
Country Correlation ExplainsArgentina 38.79% 43.99%
Chile 16.25% 49.10%Ecuador 42.11% 44.28%Mexico 12.31% 36.42%
Average 27.37% 43.44%
It is very similar to previous one, suggesting uncertainty itself ismost important driving source for the fit.
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Results
Figure: Consumption losses (%) from monetary uncertainty.
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Results
Table: Consumption losses from Uncertainty
Country Maximum Loss Annual Average LossArgentina 24.13% 5.01%
Chile 18.15% 3.34%Ecuador 10.49% 2.00%Mexico 9.22% 1.58%
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Outline
Motivation
Model
Model Implications
Quantitative Analysis
Conclusions
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Conclusions and Comments
• Empirical analysis suggests negative relation betweenuncertainty and welfare. However, previous literature(Barlevy, 2005) was generally unable to generate this relation.
• I build a model with interesting features (e.g. moneyendogenously determined non-neutrality and price-quantitynon-equivalence) which does and also provides a rationale forrelationship observed between monetary volatility andaggregate output in Latin-American countries.
• Model explains 43% of the output fluctuations and, with thevolatility observed, can generate output losses of up to24%, and annual averages as high as 5%.
• Model could be extended for a “market for attention”,heterogeneity in firms and attention effects on productivitygrowth rather than level to evaluate its potential.
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Why Monetary Uncertainty?• Modeling tool: Lucas Island model uses money to show
that nominal shocks can have real effects when people can’tdistinguish them perfectly. I will also use money as a tool togenerate uncertainty in demand.Moreover, it is:
• Measurable: Clearly identifiable in the data.• Policy variable: it is not confused with other sources of
uncertainty (e.g. output variance) and it is controlled bygovernment.
• Empirical: Lucas (2003) finds that around 30 percent ofvariation in output can be attributed to monetary shocks inthe US, where money grew at rate of 7% with 2%std.deviation since 1960. Effect in Latin-American countriesshould be much higher (for example, in Argentina money grewat 60% with 42% standard deviation).
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