Presented on June 12th 2012 at CEMFI

1. Productivity Losses from the Attention to
Aggregate Uncertainty
Author: Diego Daruich Advisor: Josep Pijoan-Mas
CEMFI
June 12, 2012
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2. Intuition
• If agents have a limited amount of information-processing
capacity, 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 conditions
affects this trade off and its consequences on the levels of
productivity and output.
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3. Motivation
Model
Households
Firms
Model Implications
Money Non-Neutrality
Policy Function
Aggregate Variables
Quantitative Analysis
Calibration
Results
Conclusions
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4. Outline
Motivation
Model
Model Implications
Quantitative Analysis
Conclusions
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5. 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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6. 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.
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7. Outline
Motivation
Model
Households
Firms
Model Implications
Quantitative Analysis
Conclusions
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8. Model
• Static model.
• Representative money-holding consumer with Dixit-Stiglitz
preferences 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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9. Households
M 1+ Ψ
max ln (C ) + γm ln P − γl L+Ψ
1
ci ,L,M
subject to:
• Budget Constraint: M + PC = WL + D
θ
1 θ −1
θ −1
• Total Consumption: C = ci θ
di
0
1
1 1− θ
• Aggregate Price Index: P = pi1−θ di
0
The resulting conditions are:
θ
• Goods Demand: ci = P
pi C
• Money Demand: M = γm C
P
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10. Firms
Basics
• Production function: y = Al α
¯
• A = A (1 + ηZ ) where Z will be related to the time devoted
to paying attention to productivity.
• T + Z = 1, time is allocated between understanding macro
conditions (T ) or productivity (Z ).
• Paying attention to aggregate conditions, has a cost in
terms of productivity.
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11. Monetary Policy and Information Structure
2
¯ 2
M = Me ε where ε ∼ N − σ2 , σm
m Why?
s = ε + ζ where the noise term ζ is:
• Independent of A and M.
• Independent across firms.
2 2
• Gaussian white noise with variance σζ (1 − T )τ = σζ Z τ
A timeline of the sequence of events for the firms would be:
Not Observed Shock (ε)
2
Policy σm )
Observed 2 Signal (s ) Output (y )
Signal Quality σζ
Decision Attention (Z ) Price (p )
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12. Firms
Attention Problem: Second Stage
p (s;w ,Z )
V (s; w , Z ) = max Eε|s,Z P y − wl
P s.t.
p (s;w ,Z )
• Production Function: y = Al α
θ
• Households’ Demand: y = c = P
p (s;w ,Z )
C
• Households’ Money Demand: M = γm C
P
1
1 1− θ
1− θ
• Aggregate Price: P = ˜
p (s ; w , Z ) ˜
ds
0
2
¯ 2
• Money Supply: M = Me ε where ε ∼ N − σ2 , σm
m
2
• Signal: s = ε + ζ where ζ ∼ N 0, σζ Z τ
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13. Firms
Attention Problem: First Stage
max V (s; w , Z ) f (s |Z ) ds
Z
subject to:
¯
• Productivity: A = A (1 + ηZ ) with (Z ∈ [0, 1])
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14. Equilibrium
Definition
Given the monetary shock, ε, an equilibrium for this economy is a
set of decision rules, p (s; w , Z ) and Z ; quantities L, M d , ci and li
for all i ∈ [0, 1]; and a wage w such that:
1. Given the wage and prices, M d , 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] .
1
4. Labour market clears, L = li di.
0
¯
5. The money market clears, M d = M s = Me ε
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15. Computational Methodology
2
2
1. Generate many shocks from ε ∼ N − σ2 , σm .
m
2. For each shock:
2.1 Guess wage w .
2.2 Build a grid of Attention levels Z . For each Z :
2
2.2.1 Build a grid of signals from si = ε + ζ i and ζ i ∼ N 0, σζ Z τ
and solve nonlinear system for policy function.
- Approximate unknown function p (s; w , Z ) with a finite
number of elements of the polynomial base.
- Using Gauss-Hermite Quadrature to approx expectations.
2.2.2 Compute expected profits, again using Gauss-Hermite and
policy 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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16. Outline
Motivation
Model
Model Implications
Money Non-Neutrality
Policy Function
Aggregate Variables
Quantitative Analysis
Conclusions
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17. Implications
Money Neutrality
Money is neutral only when there is no uncertainty:
2
1. Monetary policy is fixed: σm = 0 (exogenous).
2
2. By definition there is no noise: σζ = 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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18. Implications
Price or Quantity Competition
The difference is due to the non-linearities in the problem:
In Quantities In Prices
• Policy Function: y (s; w , Z ) • Policy Function: p (s; w , Z )
• Aggregation: • Aggregation:
θ 1
1 θ −1 1 1− θ
θ −1 1− θ
C = y (s; w , Z ) θ ds P= p (s; w , Z ) ds
0 0
• P = G (C , M ) • C = H (P, M )
Equivalent as θ approaches one, since each firm becomes an
actual monopolist in its own product and does not need to
predict what the other firms are doing.
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19. Implications
Attention and Uncertainty
Figure: Effects of Aggregate Uncertainty
Attention to Productivity Aggregate Output
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20. Implications
Policy Functions
Figure: Policy Functions p (si ; w , Z )
Low Uncertainty High Uncertainty
The higher the uncertainty, the more attention is paid to macro
conditions, making the signal more reliable. Then, the policy
function is more sensible to the signal.
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21. Implications
Figure: Aggregate Variables and Monetary Shock
Nominal Wages Aggregate Price
Real Labour Income Real Firm Income
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22. Outline
Motivation
Model
Model Implications
Quantitative Analysis
Calibration
Results
Conclusions
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23. Calibration
In order to calculate the monetary policy volatility I fit a modified
GARCH(1,1) on the money growth gm,t
2
σm,t
gm,t = 2 + εt
2
σm,t
ε t ∼ N − 2 , σm,t 2
2
σm,t = c + β 1 ε2−1 − σm + β 2
2 2 2
σm,t −1 − σm
t
2 = c
σm 1− β 1 − β 2
To estimate the noise, I assume that:
2 2
σζ,t = kσm,t
2
Then use time series of σm,t , ε t and HP-filtered output cycles to
recover 3 parameters (η, τ and k).
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24. 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

25. 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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26. Calibration
Parameters
Table 2: Parameters values
Calibrated
η Productivity return 0.069
τ Non-linearity of noise reduction 19.75
k Noise-Signal ratio 1.95
Obtained from Literature
γl Utility multiplier of leisure 0.94
γm Utility multiplier of real money 1
Ψ Utility leisure Non-linearity 3
θ Consumption Aggregation 4
α Production Function Non-linearity 0.8
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27. Results
Model Capacity
Figure: Data and Model output percentage deviation
Argentina Chile
Ecuador Mexico
Data (Blue, solid) and Model (Red, dashed) 22 / 27

28. Results
Model Capacity
Table: Model Capacity
Country Correlation Explains
Argentina 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 Ecuadorian
data, capturing almost perfectly the 1989 hyper-inflation
and 1999 banking crisis, respectively.
• The model fit for Mexico is the poorest, probably because its
cycles are less related to monetary policy (Garriga, 2010).
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29. Results
Importance of Uncertainty vs. Shock
I test model with expected shock instead estimated one, therefore
evaluating the importance of uncertainty alone in good fit.
Table: Model Capacity without shock
Country Correlation Explains
Argentina 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 is
most important driving source for the fit.
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30. Results
Figure: Consumption losses (%) from monetary uncertainty.
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31. Results
Table: Consumption losses from Uncertainty
Country Maximum Loss Annual Average Loss
Argentina 24.13% 5.01%
Chile 18.15% 3.34%
Ecuador 10.49% 2.00%
Mexico 9.22% 1.58%
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32. Outline
Motivation
Model
Model Implications
Quantitative Analysis
Conclusions
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33. Conclusions and Comments
• Empirical analysis suggests negative relation between
uncertainty and welfare. However, previous literature
(Barlevy, 2005) was generally unable to generate this relation.
• I build a model with interesting features (e.g. money
endogenously determined non-neutrality and price-quantity
non-equivalence) which does and also provides a rationale for
relationship observed between monetary volatility and
aggregate output in Latin-American countries.
• Model explains 43% of the output fluctuations and, with the
volatility observed, can generate output losses of up to
24%, and annual averages as high as 5%.
• Model could be extended for a “market for attention”,
heterogeneity in firms and attention effects on productivity
growth rather than level to evaluate its potential.
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34. Why Monetary Uncertainty?
• Modeling tool: Lucas Island model uses money to show
that nominal shocks can have real effects when people can’t
distinguish them perfectly. I will also use money as a tool to
generate 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 by
government.
• Empirical: Lucas (2003) finds that around 30 percent of
variation in output can be attributed to monetary shocks in
the US, where money grew at rate of 7% with 2%
std.deviation since 1960. Effect in Latin-American countries
should be much higher (for example, in Argentina money grew
at 60% with 42% standard deviation).
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