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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