Asymmetric Inventory Dynamics and Product Market Search Linxi Chen - - PowerPoint PPT Presentation

Asymmetric Inventory Dynamics and Product Market Search

Linxi Chen November 29, 2017

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Asymmetric Inventory Dynamics and Product Market Search

Linxi Chen November 29, 2017

2017-11-29

Asymmetric Inventory Dynamics and Product Market Search

...indeed, to a great extent, business cycles are inventory fluc- tuations. Alan Blinder, 1981

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...indeed, to a great extent, business cycles are inventory fluc- tuations. Alan Blinder, 1981

2017-11-29

Asymmetric Inventory Dynamics and Product Market Search

• 1. Economists knew inventory movements

...indeed, to a great extent, business cycles are inventory fluc- tuations. Alan Blinder, 1981 Everything that needs to be said has already been said. But since no one was listening, everything must be said again. Andre Gide

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...indeed, to a great extent, business cycles are inventory fluc- tuations. Alan Blinder, 1981 Everything that needs to be said has already been said. But since no one was listening, everything must be said again. Andre Gide

2017-11-29

Asymmetric Inventory Dynamics and Product Market Search

• 1. Economists knew inventory movements

Importance of Inventory Investment

20 40 60 80 100 percent

GDP Level

20 40 60 80 100 percent

GDP Growth

20 40 60 80 100 percent

GDP Growth Variance

Real GDP Decomposition, 1954−2007

Consumption Fixed Investment Inventory Investment Government Expenditure Net Export Covariance

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Importance of Inventory Investment

Real GDP Decomposition, 1954−2007

2017-11-29

Asymmetric Inventory Dynamics and Product Market Search Importance of Inventory Investment

• 1. Inventory investment is a component of GDP
• 2. Clarification: inventory means stock, II means the change (flow)
• 3. and it’s known as CIPI, change in private inventory

Introduction

Document and explain two new stylized facts:

1

Inventory investment accounts for much larger share of GDP change in recessions than expansions

2

Inventory-sales ratio lags GDP for four quarters

Standard inventory models (e.g. Wen 2011) fail to account for them This paper:

Based on stockout-avoidance motive for inventory (Kahn 1987). Augment with product market search Matches the two new stylized facts and existing ones.

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Introduction

Document and explain two new stylized facts:

Inventory investment accounts for much larger share of GDP change in recessions than expansions

Inventory-sales ratio lags GDP for four quarters Standard inventory models (e.g. Wen 2011) fail to account for them This paper: Based on stockout-avoidance motive for inventory (Kahn 1987). Augment with product market search Matches the two new stylized facts and existing ones.

2017-11-29

Asymmetric Inventory Dynamics and Product Market Search Introduction

Fact 1: Asymmetric Share of Inventory Investment

Inventory investment accounts for 72% of GDP decline in recessions This part motivates research on inventory But only 8% of GDP increase in expansions This part is mostly ignored Inventory-investment-to-GDP ratio is negatively skewed Stylized facts are determined by behaviors in expansions

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Fact 1: Asymmetric Share of Inventory Investment

Inventory investment accounts for 72% of GDP decline in recessions This part motivates research on inventory But only 8% of GDP increase in expansions This part is mostly ignored Inventory-investment-to-GDP ratio is negatively skewed Stylized facts are determined by behaviors in expansions

2017-11-29

Asymmetric Inventory Dynamics and Product Market Search Fact 1: Asymmetric Share of Inventory Investment

Fact 1: Inventory Investment in the 1981 Recession

−200 −100 100 1981q3 1981q4 1982q1 1982q2 1982q3 1982q4 date GDP Consumption Fixed Investment Inventory Investment

Billions of 2009 Dollars, Peak to Trough 1981 Recession Figure: GDP and its Components,Change Relative to Peak

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Fact 1: Inventory Investment in the 1981 Recession

Billions of 2009 Dollars, Peak to Trough 1981 Recession Figure: GDP and its Components,Change Relative to Peak

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Asymmetric Inventory Dynamics and Product Market Search Fact 1: Inventory Investment in the 1981 Recession

Fact 1: Inventory investment In the 1982-1990 Expansion

500 1000 1500 2000 2500 1982q3 1984q3 1986q3 1988q3 1990q3 date GDP Consumption Fixed Investment Inventory Investment

Billions of 2009 Dollars, Trough to Peak 1981−90 Figure: GDP and its Components,Change Relative to Trough

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Fact 1: Inventory investment In the 1982-1990 Expansion

Billions of 2009 Dollars, Trough to Peak 1981−90 Figure: GDP and its Components,Change Relative to Trough

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Asymmetric Inventory Dynamics and Product Market Search Fact 1: Inventory investment In the 1982-1990 Expansion

Fact1: Peak-to-trough Declines

Peak Trough Inven.Inves. GDP Share 1948:4 1949:4

• 40.66
• 30.68

132% 1953:2 1954:2

• 24.47
• 62.77

39% 1957:3 1958:2

• 21.19
• 84.98

25% 1960:2 1961:1

• 21.38
• 9.06

236% 1969:4 1970:4

• 35.84
• 7.19

498% 1973:4 1975:1

• 80.06
• 169.95

47% 1980:1 1980:3

• 67.26
• 142.02

47% 1981:3 1982:4

• 120.51
• 169.73

71% 1990:3 1991:1

• 46.87
• 118.38

39% 2001:1 2001:4

• 24.09
• 40.20

59 % 2007:4 2009:2

• 213.07
• 636.23

33% Avg*:72%

Table: Peak-to-trough Declines in All Postwar Recessions. Note: Units in billions of 2009 dollar, annualized quarterly

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Fact1: Peak-to-trough Declines

Peak Trough Inven.Inves. GDP Share 1948:4 1949:4

• 40.66
• 30.68

132% 1953:2 1954:2

• 24.47
• 62.77

39% 1957:3 1958:2

• 21.19
• 84.98

25% 1960:2 1961:1

• 21.38
• 9.06

236% 1969:4 1970:4

• 35.84
• 7.19

498% 1973:4 1975:1

• 80.06
• 169.95

47% 1980:1 1980:3

• 67.26
• 142.02

47% 1981:3 1982:4

• 120.51
• 169.73

71% 1990:3 1991:1

• 46.87
• 118.38

39% 2001:1 2001:4

• 24.09
• 40.20

59 % 2007:4 2009:2

• 213.07
• 636.23

33% Avg*:72% Table: Peak-to-trough Declines in All Postwar Recessions. Note: Units in billions of 2009 dollar, annualized quarterly

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Asymmetric Inventory Dynamics and Product Market Search Fact1: Peak-to-trough Declines

Fact 1: Trough-to-peak Increases

Trough Peak

• Inven. Inves.

GDP Share 1949:4 1953:2 33.28 588.80 6% 1954:2 1957:3 20.94 345.24 6% 1958:2 1960:2 22.89 320.36 7% 1961:1 1969:4 30.15 1613.21 2% 1970:4 1973:4 76.25 754.12 10% 1975:1 1980:1 33.01 1232.47 3% 1980:3 1981:3 115.93 279.97 41% 1982:4 1990:3 84.35 2490.81 3% 1991:1 2001:2 7.16 3844.74 0.1% 2001:4 2007:4 120.34 2286.52 5% Avg: 8%

Table: Trough-to-peak Increases in All Postwar Expansions Note: Units in billions of 2009 dollar, annualized quarterly

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Fact 1: Trough-to-peak Increases

Trough Peak

• Inven. Inves.

GDP Share 1949:4 1953:2 33.28 588.80 6% 1954:2 1957:3 20.94 345.24 6% 1958:2 1960:2 22.89 320.36 7% 1961:1 1969:4 30.15 1613.21 2% 1970:4 1973:4 76.25 754.12 10% 1975:1 1980:1 33.01 1232.47 3% 1980:3 1981:3 115.93 279.97 41% 1982:4 1990:3 84.35 2490.81 3% 1991:1 2001:2 7.16 3844.74 0.1% 2001:4 2007:4 120.34 2286.52 5% Avg: 8% Table: Trough-to-peak Increases in All Postwar Expansions Note: Units in billions of 2009 dollar, annualized quarterly

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Asymmetric Inventory Dynamics and Product Market Search Fact 1: Trough-to-peak Increases

Fact 1: Skewnes As an Alternative Measure of Asymmetry

50 100 150 Density −.02 −.01 .01 .02 Inventory−Investment Relative to GDP

Skewness of Inventory Investment Relative to GDP

Skewness = -0.33

Figure: Histogram of Inventory-investment-to-GDP Ratio

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Fact 1: Skewnes As an Alternative Measure of Asymmetry

Skewness of Inventory Investment Relative to GDP Skewness = -0.33 Figure: Histogram of Inventory-investment-to-GDP Ratio

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Asymmetric Inventory Dynamics and Product Market Search Fact 1: Skewnes As an Alternative Measure of Asymmetry

Fact 2: Inventory-sales ratio lags GDP

Inventory-sales ratios lags GDP by four quarters Positive cross-correlation is the largest at fourth lag The lagging relationship is stable for the entire post-war period

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Fact 2: Inventory-sales ratio lags GDP

Inventory-sales ratios lags GDP by four quarters Positive cross-correlation is the largest at fourth lag The lagging relationship is stable for the entire post-war period

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Asymmetric Inventory Dynamics and Product Market Search Fact 2: Inventory-sales ratio lags GDP

Fact 2: Inventory-sales Ratio Lags GDP by Four Lags

−.1 −.05 .05 .1 1947q3 1964q3 1981q3 1998q3 2015q3 date Cyclical GDP, L4 Cyclical IS ratio

Figure: HP Filtered (1600)

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Fact 2: Inventory-sales Ratio Lags GDP by Four Lags

Figure: HP Filtered (1600)

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Asymmetric Inventory Dynamics and Product Market Search Fact 2: Inventory-sales Ratio Lags GDP by Four Lags

CAUTION

Inventory-sales ratio being countercyclical is NOT a stylized fact It ceases to be countercyclical since the 1990s. Countercyclicality is crucial for various important results Examples: (Bils Kahn 2000, Midrigran Krytsov 2013, Alessandria et

• al. 2013, Sarte et al. 2015 )

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CAUTION

Inventory-sales ratio being countercyclical is NOT a stylized fact It ceases to be countercyclical since the 1990s. Countercyclicality is crucial for various important results Examples: (Bils Kahn 2000, Midrigran Krytsov 2013, Alessandria et

• al. 2013, Sarte et al. 2015 )

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Asymmetric Inventory Dynamics and Product Market Search CAUTION

CAUTION

−1 −.5 .5 Moving Correlation 1947q3 1964q3 1981q3 1998q3 2015q3 date

Inventory−sales and GDP

Correlation = -0.24 before 1992, Correlation = 0.23 after 1992

Figure: HP Filtered, 40 Quarters Moving Window

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CAUTION

Inventory−sales and GDP Correlation = -0.24 before 1992, Correlation = 0.23 after 1992 Figure: HP Filtered, 40 Quarters Moving Window

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Asymmetric Inventory Dynamics and Product Market Search CAUTION

Model: Agents

1 Intermediate good producer: produced with labor only. 2 Variety good producer: produced with intermediate goods. 3 Household: “love for variety” 15 / 46

Model: Agents

2017-11-29

Asymmetric Inventory Dynamics and Product Market Search Model: Agents

Model: Matching at Product Level

Search and match protocol similar to the labor literature (Pissarides 1994, Diamond 2000). Measure 1 of HH matches with measure 1 of varieties. Each variety is produced by one monopolistic firm. Generate x matches with d aggregate search effort x = M(d, 1) and thus the rate at which HH finds varieties ΨD ≡ x d = M(1, 1 d )

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Model: Matching at Product Level

Search and match protocol similar to the labor literature (Pissarides 1994, Diamond 2000). Measure 1 of HH matches with measure 1 of varieties. Each variety is produced by one monopolistic firm. Generate x matches with d aggregate search effort x = M(d, 1) and thus the rate at which HH finds varieties ΨD ≡ x d = M(1, 1 d )

2017-11-29

Asymmetric Inventory Dynamics and Product Market Search Model: Matching at Product Level

Household: Second Stage Problem

First stage decides varieties x and consumption level ˜ c Each variety i: maximum quantity available for sale zi and prices pi Demand shocks vi to each variety Expenditure minimization problem: min

ci

x picidi s.t. ci ≤ zi ˜ c ≤ x v

1− 1

ρ

i

c

1 ρ

i di

ρ

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Household: Second Stage Problem

First stage decides varieties x and consumption level ˜ c Each variety i: maximum quantity available for sale zi and prices pi Demand shocks vi to each variety Expenditure minimization problem: min

x picidi s.t. ci ≤ zi ˜ c ≤ x v

c

ρ

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Asymmetric Inventory Dynamics and Product Market Search Household: Second Stage Problem

Household: Second Stage Problem

Demand for variety i: ci = min

• zi, vi

pi p

• ρ

1−ρ

c

• where c =

˜ c xρ =

• 1

x

x

0 v 1− 1

ρ

i

c

1 ρ

i di

ρ Average price index: p = 1 x x vi (pi + µi)

1 1−ρ di

1−ρ where µi is the Lagrange multiplier associated with ci ≤ zi Total expenditure: x picidi = pxc

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Household: Second Stage Problem

Demand for variety i: ci = min

• zi, vi

pi p

• ρ

c

• where c =

• 1

x

c

ρ Average price index: p = 1 x x vi (pi + µi)

1−ρ where µi is the Lagrange multiplier associated with ci ≤ zi Total expenditure: x picidi = pxc

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Asymmetric Inventory Dynamics and Product Market Search Household: Second Stage Problem

Household: First Stage Problem

Solves the following Bellman’s equation: H (a) = max

c,d,n,a′,x u(xρc, d, n) + βEH

• a′

s.t. a′ = wn + a (1 + Π) − pcx x = ΨDd Consume x varieties with average level c, search for varieties with effort d, work for wage w, receive profit from all firms Π, save with stock purchase a′ (numeraire). ΨD is variety finding rate, household take as given.

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Household: First Stage Problem

Solves the following Bellman’s equation: H (a) = max

• a′

s.t. a′ = wn + a (1 + Π) − pcx x = ΨDd Consume x varieties with average level c, search for varieties with effort d, work for wage w, receive profit from all firms Π, save with stock purchase a′ (numeraire). ΨD is variety finding rate, household take as given.

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Asymmetric Inventory Dynamics and Product Market Search Household: First Stage Problem

Variety Producer

Monopolistic competitive, unit measure. With probability x, the variety producer have access to final good producer’sdemand (“matched”). Once matched, draw demand shock vi. vi is i.i.d. across time and across varieties Decide on pricing and ordering before knowing these shocks. Thus generate the incentive to hold inventories.

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Variety Producer

Monopolistic competitive, unit measure. With probability x, the variety producer have access to final good producer’sdemand (“matched”). Once matched, draw demand shock vi. vi is i.i.d. across time and across varieties Decide on pricing and ordering before knowing these shocks. Thus generate the incentive to hold inventories.

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Asymmetric Inventory Dynamics and Product Market Search Variety Producer

Variety Producer

Solves the following problem: V (ei) = max

yi,pi,e′

i

−pMyi + x cipi + Em

′V (e ′

i )

• F v(dvi)

+ (1 − x)Em′V (e

′

i )

s.t. ci = min

• vic

pi p

• ρ

1−ρ

, zi

• zi = ei + yi

e

′

i =

• (1 − δe) [ei + yi − ci]

”matched” (1 − δe) [ei + yi] ”unmatched” zi is the amount of good i made available to buyers pM price of intermediate goods, yi the order

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Variety Producer

Solves the following problem: V (ei) = max

−pMyi + x cipi + Em

• F v(dvi)

+ (1 − x)Em′V (e

s.t. ci = min

• vic

pi p

• ρ

, zi

• zi = ei + yi

e

• (1 − δe) [ei + yi − ci]

”matched” (1 − δe) [ei + yi] ”unmatched” zi is the amount of good i made available to buyers pM price of intermediate goods, yi the order

2017-11-29

Asymmetric Inventory Dynamics and Product Market Search Variety Producer

Variety Producer

Pricing Decision: pi = ǫi ǫi − 1(1 − δe)Em′P

′

M

where the price elasticity of expected sales is given by: ǫi = ρ 1 − ρ v∗

i

ci(pi, ni, vi)F v(dvi) v∗

i

ci(pi, ni, vi)F v(dvi) +

• 1 − F v(v∗

i )

• [ei + F(ni)]

The cut-off point of stockout v∗

i is given by:

ci(pi, ni, v∗

i ) = zi

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Variety Producer

Pricing Decision: pi = ǫi ǫi − 1(1 − δe)Em′P

where the price elasticity of expected sales is given by: ǫi = ρ 1 − ρ v∗

ci(pi, ni, vi)F v(dvi) v∗

ci(pi, ni, vi)F v(dvi) +

• 1 − F v(v∗

• [ei + F(ni)]

The cut-off point of stockout v∗

ci(pi, ni, v∗

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Asymmetric Inventory Dynamics and Product Market Search Variety Producer

Variety Producer

Availability decision: (b − rI)x[1 − F v(v∗

i )] = 1 − rI

where b = pi w/pM and rI ≡ (1 − δe) Em′ p

′

M

pM . rI captures return on holding inventory in the absent of stock-out x is endogenous unlike standard stockout model Information structure → all varieties choose the same zi and pi

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Variety Producer

Availability decision: (b − rI)x[1 − F v(v∗

where b = pi w/pM and rI ≡ (1 − δe) Em′ p

pM . rI captures return on holding inventory in the absent of stock-out x is endogenous unlike standard stockout model Information structure → all varieties choose the same zi and pi

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Asymmetric Inventory Dynamics and Product Market Search Variety Producer

Intermediate Producer

Perfectly competitive, unit measure Solves the static problem: max

n

pMF(n) − wn Production function F(n) Allows for exact aggregation despite heterogeneous vi

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Intermediate Producer

Perfectly competitive, unit measure Solves the static problem: max

pMF(n) − wn Production function F(n) Allows for exact aggregation despite heterogeneous vi

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Asymmetric Inventory Dynamics and Product Market Search Intermediate Producer

Equilibrium

Agents solve their respective optimization problems Variety goods, intermediate goods and labor markets clear All variety producers choose the same price ... and same amount of goods available Solved with 3rd order perturbation.

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Equilibrium

Agents solve their respective optimization problems Variety goods, intermediate goods and labor markets clear All variety producers choose the same price ... and same amount of goods available Solved with 3rd order perturbation.

2017-11-29

Asymmetric Inventory Dynamics and Product Market Search Equilibrium

Functional Forms

Production Function: F(n) = An1−α Utility (Generalized GHH 1988, search behavior): u(cxρ, d, n) = log

• cxρ − ζ n1+υn

1 + υn − ξd

• Distribution of demand shocks vi Pareto(vmin, σV ):

Fvi(v) = 1 − (vmin vi )σv Matching function (den Hann et al. 2000): M(D, 1) = D (Dι + 1ι)1/ι

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Functional Forms

Production Function: F(n) = An1−α Utility (Generalized GHH 1988, search behavior): u(cxρ, d, n) = log

• cxρ − ζ n1+υn

1 + υn − ξd

• Distribution of demand shocks vi Pareto(vmin, σV ):

Fvi(v) = 1 − (vmin vi )σv Matching function (den Hann et al. 2000): M(D, 1) = D (Dι + 1ι)1/ι

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Asymmetric Inventory Dynamics and Product Market Search Functional Forms

Calibration

Parameter Name Value Target Source β Discount Rate 0.99 4% Return Data υn Labor Elasticity 0.75 Frish Elas. Chetty 2011 α Labor Share 0.67 Data ζ Labor Disutility 1.5 1/3 time worked ATUS vmin

• Loc. vi

0.04 Mean 1 σv Shape vi 1.05 S.O. Prob=5% Bils 2004 ρ

• Elas. of Subs.

1.17 20% markup Data δe

• Deprec. Inven,

0.015 6% annual Wen 2011 ι Match Elasticity 1.18 0.35 elas. Broda et al 2011 ξ Search Disutility 0.01 1 hr shopping ATUS ρA TFP Pers. 0.96 SF-FED TFP σA TFP Vola. 0.02

Table: Calibration

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Calibration

• Loc. vi

• Elas. of Subs.

• Deprec. Inven,

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Asymmetric Inventory Dynamics and Product Market Search Calibration

Performance: Fact 1

Stat. Data Model Wen 2011 corr( Inven. Inves.

GDP

,GDP) 0.66 0.58 0.57 AR(1) of Inven.

Sales

0.75 0.89 0.77 corr( Inven.

Sales ,GDP)

• 0.43
• 0.30
• 0.68

skewness( Inven. Inves.

GDP

)

• 0.30
• 0.46

0.11

Table: Inventory Stylized Facts Performance

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Performance: Fact 1

Stat. Data Model Wen 2011 corr( Inven. Inves.

,GDP) 0.66 0.58 0.57 AR(1) of Inven.

0.75 0.89 0.77 corr( Inven.

• 0.43
• 0.30
• 0.68

skewness( Inven. Inves.

)

• 0.30
• 0.46

0.11 Table: Inventory Stylized Facts Performance

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Asymmetric Inventory Dynamics and Product Market Search Performance: Fact 1

Performance: Fact 1

Examine peak-trough shares of inventory investment. Dating turning points:

Treat the model as generating demeaned growth rates Define recessions to be at least two consecutive periods with GDP contraction rate as large as recessions in the data Matches share of recession periods in data: 20%. Model depress on avg. four quarters and expands 13 quarters

Recession: inventory investment is 54% of output decline (data 72%) Expansion: 25% of output expansion (data 8%) Robust to various business cycle dating schemes

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Performance: Fact 1

Examine peak-trough shares of inventory investment. Dating turning points: Treat the model as generating demeaned growth rates Define recessions to be at least two consecutive periods with GDP contraction rate as large as recessions in the data Matches share of recession periods in data: 20%. Model depress on avg. four quarters and expands 13 quarters Recession: inventory investment is 54% of output decline (data 72%) Expansion: 25% of output expansion (data 8%) Robust to various business cycle dating schemes

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Asymmetric Inventory Dynamics and Product Market Search Performance: Fact 1

Performance: Fact 2

20 40 60 80 100 120 140 160 180 200

• 0.05

0.05

• 0.1

0.1

IS Ratio Output Lag 5

Figure: Inventory-sales Ratio Lags Output by 5 Quarters (Model)

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Performance: Fact 2

• 0.05

• 0.1

Figure: Inventory-sales Ratio Lags Output by 5 Quarters (Model)

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Asymmetric Inventory Dynamics and Product Market Search Performance: Fact 2

Performance: Fact 2

• 20
• 15
• 10
• 5

5 10 15 20 Lag

• 0.6
• 0.4
• 0.2

0.2 0.4 0.6 0.8 Sample Cross Correlation Cross Correlation: IS Ratio versus Output

Figure: Inventory-sales Ratio Lags Output by 5 Quarters (Model)

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Performance: Fact 2

• 20
• 15
• 10
• 5

• 0.6
• 0.4
• 0.2

Figure: Inventory-sales Ratio Lags Output by 5 Quarters (Model)

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Asymmetric Inventory Dynamics and Product Market Search Performance: Fact 2

Data: Fact 2

−1.00 −0.50 0.00 0.50 1.00 −1.00 −0.50 0.00 0.50 1.00 Cross−correlations of HP_ln_rISratio and HP_ln_rGDP −20 −10 10 20 Lag

Cross−correlogram Figure: IS Ratio Lags Output by 4 Quarters (Data)

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Data: Fact 2

Cross−correlogram Figure: IS Ratio Lags Output by 4 Quarters (Data)

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Asymmetric Inventory Dynamics and Product Market Search Data: Fact 2

Mechanism: Fact 1, Role of Product Market Friction

Benchmark Statistics ξ = 0.006 ξ = 0.010 ξ = 0.012 Steady State Varieties, ¯ x 0.91 0.88 0.75 Peak-to-trough Share 0.40 0.54 0.71 Trough-to-peak Share 0.29 0.25 0.12 Skewness( Inven. Inves.

GDP

)

• 0.21
• 0.46
• 0.51

Table: Inventory Performance

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Mechanism: Fact 1, Role of Product Market Friction

Benchmark Statistics ξ = 0.006 ξ = 0.010 ξ = 0.012 Steady State Varieties, ¯ x 0.91 0.88 0.75 Peak-to-trough Share 0.40 0.54 0.71 Trough-to-peak Share 0.29 0.25 0.12 Skewness( Inven. Inves.

)

• 0.21
• 0.46
• 0.51

Table: Inventory Performance

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Asymmetric Inventory Dynamics and Product Market Search Mechanism: Fact 1, Role of Product Market Friction

Mechanism: Fact 1, Demand Curve

pi ci

Price Sales

zi zi p∗

A B ci = min

• zi, vic
• pi

p

ρ

1−ρ

high vi low vi

Figure: Demand Curve for Variety i

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Mechanism: Fact 1, Demand Curve

pi ci

Price Sales

zi zi p∗

A B ci = min

• zi, vic
• pi

p

ρ

1−ρ high vi low vi Figure: Demand Curve for Variety i

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Asymmetric Inventory Dynamics and Product Market Search Mechanism: Fact 1, Demand Curve

Mechanism: Fact 1, Optimal Markup

bi

zi c

Markup Safe Stock

ρr I bi =

ǫi ǫi−1r I,

bi ↓ ρr I as zi

c ↑ ∞

Figure: Optimal Choices For Markup

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Mechanism: Fact 1, Optimal Markup

bi

zi c

Markup Safe Stock

ρr I bi =

ǫi ǫi−1r I,

bi ↓ ρr I as zi

c ↑ ∞ Figure: Optimal Choices For Markup

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Asymmetric Inventory Dynamics and Product Market Search Mechanism: Fact 1, Optimal Markup

Mechanism: Fact 1, Optimal Markup + Optimal Buffer

bi

zi c

Markup Safe Stock

x(1 − Fv)(b − r I) = 1 − r I b =

ǫ ǫ−1r I

Figure: Joint Determination of Markup and Safe Buffer

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Mechanism: Fact 1, Optimal Markup + Optimal Buffer

bi

zi c

Markup Safe Stock x(1 − Fv)(b − r I) = 1 − r I b =

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Asymmetric Inventory Dynamics and Product Market Search Mechanism: Fact 1, Optimal Markup + Optimal Buffer

Mechanism: Fact 1, Peak vs Trough

b

zi ¯ c

Markup Safe Stock A A′ B B′

Figure: Asymmetric Responses: Peak v.s. Trough

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Mechanism: Fact 1, Peak vs Trough

b

zi ¯ c

Markup Safe Stock A A′ B B′ Figure: Asymmetric Responses: Peak v.s. Trough

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Asymmetric Inventory Dynamics and Product Market Search Mechanism: Fact 1, Peak vs Trough

Mechanism: Fact 1, Markup and Safe Stock TS

5 10 15 20 25 30 35 40

Periods From Shock

• 0.02
• 0.01

0.01

Prct From SS In Response to Positive TFP Shock

• 1

1 2

Markup Buffer Size

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Mechanism: Fact 1, Markup and Safe Stock TS

• 0.02
• 0.01

• 1

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Asymmetric Inventory Dynamics and Product Market Search Mechanism: Fact 1, Markup and Safe Stock TS

Mechanism: Fact 1, Higher r I

b

zi ¯ c

Markup Safe Stock

r I ↑ r I ↑

Figure: Increasing r I

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Mechanism: Fact 1, Higher r I

b

zi ¯ c

Markup Safe Stock

r I ↑ r I ↑

Figure: Increasing r I

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Asymmetric Inventory Dynamics and Product Market Search Mechanism: Fact 1, Higher r I

Mechanism: Fact 1

Nonlinearity exists in stock-out model, but unexplored. Allowing movement in x enhances the nonlinearity Peak and trough are further away along markup decision curve Generates quantitatively stronger asymmetry in inventory decision.

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Mechanism: Fact 1

Nonlinearity exists in stock-out model, but unexplored. Allowing movement in x enhances the nonlinearity Peak and trough are further away along markup decision curve Generates quantitatively stronger asymmetry in inventory decision.

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Asymmetric Inventory Dynamics and Product Market Search Mechanism: Fact 1

Mechanism: Fact 2, Hump-shape Responses

10 20 30 40

Periods From Shock

• 0.05

0.05 0.1 0.15 0.2 0.5 1 1.5 2 2.5

Prct From SS

• Prob. Match

Inventory Return Inventory

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Mechanism: Fact 2, Hump-shape Responses

10 20 30 40 Periods From Shock

• 0.05

0.05 0.1 0.15 0.2 0.5 1 1.5 2 2.5 Prct From SS

• Prob. Match

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Asymmetric Inventory Dynamics and Product Market Search Mechanism: Fact 2, Hump-shape Responses

Mechanism: Fact 2

With product search, expansion of varieties peaks first then the return on holding inventory holding return peak later Return on holding inventory has no direct impact on sales! Prolonged impact on buffer stock, thus inventories. But shorter-lived impact on sales. Generates the lagging relationship of inventory-sales ratio

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Mechanism: Fact 2

With product search, expansion of varieties peaks first then the return on holding inventory holding return peak later Return on holding inventory has no direct impact on sales! Prolonged impact on buffer stock, thus inventories. But shorter-lived impact on sales. Generates the lagging relationship of inventory-sales ratio

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Asymmetric Inventory Dynamics and Product Market Search Mechanism: Fact 2

Conclusion

Two new stylized facts poses challenges to popular DSGE inventory models. Product market search friction improve an off-the-shelf inventory’ model’s ability to be consistent with these two facts. Consistent with household shopping empirics:

Procyclical search effort Expansion of varieties and expenditure.

Consistent with aspects of business cycle asymmetry:

Positively skewed markup Negatively skewed employment

Companion empirical paper documents asymmetric effects of monetary policy shocks, more on asymmetry inventory dynamics

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Conclusion

Two new stylized facts poses challenges to popular DSGE inventory models. Product market search friction improve an off-the-shelf inventory’ model’s ability to be consistent with these two facts. Consistent with household shopping empirics: Procyclical search effort Expansion of varieties and expenditure. Consistent with aspects of business cycle asymmetry: Positively skewed markup Negatively skewed employment Companion empirical paper documents asymmetric effects of monetary policy shocks, more on asymmetry inventory dynamics

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Asymmetric Inventory Dynamics and Product Market Search Conclusion

Backup

Figure: Wen 2011

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Backup

Figure: Wen 2011

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Asymmetric Inventory Dynamics and Product Market Search Backup

Intuition: Hump-shape

10 20 30 40

Periods From Shock

• 0.1
• 0.05

0.05 0.1

Growth Rate Positive TFP Shock, Contrib. To rI

Hours Growth TFP Growth (abs) Wage Growth

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Intuition: Hump-shape

10 20 30 40 Periods From Shock

• 0.1
• 0.05

0.05 0.1 Growth Rate Positive TFP Shock, Contrib. To rI Hours Growth TFP Growth (abs) Wage Growth

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Asymmetric Inventory Dynamics and Product Market Search Intuition: Hump-shape

Related Literature

Broda et al. 2010:

1 UPC level data of HH consumption varieties (nondurable, 60% of

CPI basket).

2 Large turnover of varieties HH consumes (75% common good in 4

year period).

3 Procyclical net product creation driven by product entrance.

Suggests that substantial risk of “out-of-favor” for producers when deciding inventory.

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Related Literature

Broda et al. 2010:

CPI basket).

year period).

Suggests that substantial risk of “out-of-favor” for producers when deciding inventory.

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Asymmetric Inventory Dynamics and Product Market Search Related Literature