Foreign Shocks as Granular Fluctuations Julian di Giovanni 1 Andrei A. Levchenko 2 Isabelle Mejean 3 1 FRBNY, ICREA-UPF, BGSE, CREI and CEPR 2 University of Michigan, NBER, CEPR 3 CREST-Ecole Polytechnique and CEPR September, 2019
International Business Cycle Shock Propagation Textbook: cross-country propagation through relative prices, representative firm e.g. BKK (1992), Kose and Yi (2006), Johnson (2014), ... Data: importing and exporting i) relatively rare; ii) strongly concentrated among largest firms e.g. Freund and Pierola (2015), di Giovanni et al. (2017, 2018), ... “Micro of Macro”: role of large firms, idiosyncratic shocks in aggregate fluctuations Gabaix (2011), di Giovanni et al. (2014), Carvalho an Grassi (2015), ... 2/22
A firm-level view of international shock propagation Foreign shocks (even purely aggregate) affect firms differentially depending on the extent and nature of their international linkages 3/22
A firm-level view of international shock propagation Foreign shocks (even purely aggregate) affect firms differentially depending on the extent and nature of their international linkages Elasticity of GDP w.r.t. a foreign shock: � ω f ω , ǫ f � ǫ Y = ǫ + Cov ���� � �� � Average Granular Propagation Foreign shocks affect predominantly the largest firms ⇒ Aggregate (granular) fluctuations 3/22
A firm-level view of international shock propagation Foreign shocks (even purely aggregate) affect firms differentially depending on the extent and nature of their international linkages Elasticity of GDP w.r.t. a foreign shock: � ω f ω , ǫ f � ǫ Y = ǫ + Cov ���� � �� � Average Granular Propagation Foreign shocks affect predominantly the largest firms ⇒ Aggregate (granular) fluctuations This paper: � ω f ω , ǫ f � 1. Provide evidence that Cov > 0 2. Quantify the size of the granular propagation term 3/22
This paper Quantitative model with heterogeneous firms, multiple countries, multiple sectors Implemented directly on firm-level data Census of French firms appended with WIOD (40 countries, 32 sectors) Simulate two types of (aggregate) shocks: A productivity shock and a preference shock w.r.t French varieties Granular propagation term accounts for 40 − 60% of the total effect of a shock Individual firms’ strategies on where to export / where to source inputs from have important consequences for the economy’s exposure to various foreign shocks 4/22
Literature Micro origins of macro fluctuations Input-output networks: Carvalho (2010), Acemoglu et al. (2012), Barrot and Sauvagnat (2016), Baqaee (2016), Carvalho et al. (2016), Atalay (2017), Baqaee and Farhi (2018), Grassi (2018), Kikkawa et al. (2018) Large firms: Gabaix (2011), di Giovanni et al. (2014), Carvalho and Grassi (2015) Business cycle transmission at the firm level Kleinert et al. (2015), Boehm et al. (2019), Cravino and Levchenko (2017), di Giovanni et al. (2017, 2018), Blaum (2018) Ghironi and Melitz (2005), Alessandria and Choi (2007) 5/22
Data sources France (firm level): Fiscal administration: firm tax forms from INSEE-Ficus: value added, sales, intermediate usage, industry Statistics by sector Customs: partner-country exports and imports (Trade in goods ) World (sector level): WIOD: global input-output matrix, 40 countries, 32 sectors Firm-level coefficients normalized to match WIOD at the sector level 6/22
Fact 1: Larger firms more sensitive to foreign GDP (1) (2) (3) (4) Dep. Var.: Log change in firm VA 0.175 a 0.173 a 0.105 a 0.118 a Firm’s size × World GDP growth (0.017) (0.017) (0.018) (0.019) -0.024 a -0.024 a -0.025 a -0.025 a Firm’s size (0.001) (0.001) (0.001) (0.001) -1.025 a World GDP growth (0.105) -0.030 b Firm’s size × French GDP growth (0.014) Observations 3,632,281 3,632,281 3,632,281 3,632,281 # years 11 11 11 11 # firms 655,596 655,596 655,596 655,596 Adjusted R 2 0.009 0.013 0.020 0.020 Fixed Effects – Year Sector × Year Sector × Year A doubling of firm size increases the elasticity of firm growth to world GDP by about 0.12 7/22
Fact 2a: Larger firms more likely to export 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 Unweighted Weighted 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Sources: French customs and balance-sheet data, for 2005. Restricted to T sectors. Foreign sales share is the share of exports in total sales 8/22
Fact 2b: Larger firms more likely to import 1 0.9 0.8 0.7 0.6 0.5 Unweighted Weighted 0.4 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Sources: French customs and balance-sheet data, for 2005. Foreign in- puts share is the share of foreign inputs in firms’ total input expenditure Labor Share Figure 9/22
Main ingredients Heterogeneous-firm, multi-country, multi-sector model of trade Time t , countries m , n , k , sectors i , j , firms f , g Rest of the world: no firm-level data ⇒ heterogeneity within a sector assumed away (see Costinot and Rodriguez-Clare, 2014) France: heterogeneity in i) productivity, ii) input linkages, iii) export patterns, and iv) labor shares Endogenous factor supply 10/22
Households M countries and J sectors ¯ L n households in country n (supply of primary factors) GHH preferences (Greenwood et al, 1988): � � � ∞ � � c n , t − ψ 0 ¯ ψ { c n , t , l n , t } ∞ δ t ν U = ψ l n , t t =0 ¯ t =0 � c ϑ j c n , t = n , j , t j �� � σ j σ j − 1 1 σ j − 1 σ j c n , j , t = µ mn , j c mn , j , t σ j m 11/22
Sectors and firms CES aggregate of firms from m selling to n in sector j : ρ j ρ j − 1 � ρ j − 1 1 ρ j Q mn , j , t ( f ) Q mn , j , t = ξ mn , j , t ( f ) ρ j f ∈ Ω mn , j Demand faced by firm f , expressed in expenditures: X mn , j , t ( f ) = ξ mn , j , t ( f ) p mn , j , t ( f ) 1 − ρ j X mn , j , t P 1 − ρ j mn , j , t � �� � π mn , j , t ( f ) 12/22
Firms Monopolistically competitive Productivity: a t ( f ) Taste shocks: { ξ mn , j , t ( f ) } n Firm-specific input bundle cost: � � 1 − λ � � 1 1 − λ , α m , j ( f ) w 1 − λ P M b m , j , t ( f ) = m , t + (1 − α m , j ( f )) m , j , t ( f ) �� � 1 � 1 − η γ km , ij ( f ) P 1 − η P M m , j , t ( f ) = km , i , t i k 13/22
Firms Monopolistically competitive Productivity: a t ( f ) Taste shocks: { ξ mn , j , t ( f ) } n Firm-specific input bundle cost: � � 1 − λ � � 1 1 − λ , α m , j ( f ) w 1 − λ P M b m , j , t ( f ) = m , t + (1 − α m , j ( f )) m , j , t ( f ) �� � 1 � 1 − η γ km , ij ( f ) P 1 − η P M m , j , t ( f ) = km , i , t i k Heterogeneity: � 1 − λ � 1 − ρ j � � 1 − λ ξ mm , j , t ( f ) a t ( f ) 1 − ρ j α m , j ( f ) w 1 − λ P M + (1 − α m , j ( f )) m , j , t ( f ) m , t π mm , j , t ( f ) = � 1 − λ � 1 − ρ j � � � 1 − λ g ∈ Ω mm , j ξ mm , j , t ( g ) a t ( g ) 1 − ρ j α m , j ( g ) w 1 − λ P M + (1 − α m , j ( g )) m , j , t ( g ) m , t 13/22
Equilibrium Goods market clearing: � � 1 − σ j � 1 � 1 µ mn , j P w n , t ψ − 1 L n + Π n , t + D n , t ¯ mn , j , t X mn , j , t = w n , t ϑ j 1 − σ j ψ 0 P n , t P n , j , t � � 1 − ρ i ρ i ξ nk , i , t ( f ) ρ i − 1 τ nk , i b n , i , t ( f ) a t ( f ) � � � ρ i − 1 (1 − π l n , i , t ( f )) π M + mn , ji , t ( f ) X nk , i , t 1 − ρ i ρ i P i f ∈ i k nk , i , t Price level and input shares Factor market clearing: � 1 � 1 � w n , t ψ − 1 L n = ¯ L n , j , t ψ 0 P n , t j � � 1 − ρ j ρ j ξ nk , j , t ( f ) ρ j − 1 τ nk , j b n , j , t ( f ) a t ( f ) � � = ρ j − 1 π l n , i , t ( f ) X nk , j , t 1 − ρ j ρ j P f ∈ j k nk , j , t 14/22
The role of heterogeneity Aggregate and firm-level value added: GDP � � ǫ Y = ω m ( f ) ǫ f Y m , t = Y m , t ( f ) → f f � ω m ( f ) � ǫ Y , ǫ f = ǫ + Cov ω 15/22
The role of heterogeneity Aggregate and firm-level value added: GDP � � ǫ Y = ω m ( f ) ǫ f Y m , t = Y m , t ( f ) → f f � ω m ( f ) � ǫ Y , ǫ f = ǫ + Cov ω Firm value added growth: � d ln a t ( f ) + π l d ln Y m , j , t ( f ) (1 − ρ j ) m , j , t ( f ) d ln w m , t + ≈ � � � (1 − π l m , j , t ( f )) π M + km , ij , t ( f ) d ln P km , i , t i k � � � τ mn , j � 1 − ρ j � + s mn , j , t ( f ) d ln � ξ mn , j , t ( f ) X mn , j , t P mn , j , t n 15/22
Calibration Transform model to growth rates, use sales shares data directly (Dekle, Eaton, and Kortum, 2008) DEK Use GDP deflator to express results in real terms 2 types of foreign shocks: demand ( ξ mn , j , t ( f )) or productivity ( a t ( f )); 2 foreign economies: the World or Germany Param. Value Source Related to ρ 3 Broda and Weinstein (2006) subst. elasticity btw. firms σ 1.5 Feenstra et al. (2018) Armington elasticity η 1 standard subst. elasticity btw. inputs λ 1 standard subst. elasticity btw. inputs and labor ψ 3 Chetty et al. (2012) Frisch elasticity π l n , i , t ( f ), π M mn , ji , t ( f ) labor and intermediate shares } ϑ j Our calculations based on final consumption shares π c French data and WIOD final trade shares mn , j , t π nk , j , t ( f ) intermediate use trade shares 16/22
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