Traded Intermediate Inputs, Aggregate Productivity
Growth and Allocative Efficiency
Charlotte Sandoz∗
September 2016
PRELIMINARY AND INCOMPLETE
PLEASE DO NOT CIRCULATE
Abstract
Firms evolve in a globalized market and traded inputs are key factors of production today. Literature has shown that TFP dispersion reveals resource misallocation induced
by market frictions, but few studies have introduced traded inputs in these frameworks.
I provide new evidence that traded inputs generate misallocation through firm-specific
variable trade costs. I estimate a structural model using a comprehensive dataset of
French firms in manufacturing industries to measure firm-level distortions. I then implement a TFP decomposition to quantify the impact of trade openness on the evolution
of allocative efficiency in France between 1999 and 2011.
JEL classification: XXX, YYY.
Keywords: aggregate productivity, resource allocation, international trade, Firm level data.
∗
Banque de France, Université Paris 1-Sorbonne and Paris School of Economics.
lotte.sandoz at banque-france.fr
E-mail : char-
1.
Introduction
Since the last two decades, increasing trade openness in advanced economies has considerably changed the firm business environment by increasing input supply and aggregate
spending. Nowadays, firms easily outsource and offshore production. Production processes
are more and more globalized. One of the major impact of this phenomena is to widen
market pressure on firms and push them to rethink their strategy in terms of production organization. Price-to-performance ratio of inputs is a key parameter of firm competitiveness.
The Chinese entry at the WTO has boosted opportunities to lower input costs. However
only few firms are able to import some products due to their higher variable trade costs.
Does improvement access of foreign markets improve competitiveness? Does access to lower
price foreign inputs improve aggregate productivity in advanced economies? How does firm
heterogeneity matter?
Overcoming the "chicken-and-egg" situation about trade and aggregate productivity is
a key challenge in international economics. On one hand, only the most productive firms
have access to foreign markets (M. Melitz, 2003). On the other hand, trade induces reorganization of the production that raises domestic productivity (Melitz and Redding, 2014).
Recent literature exploring the link at micro level shows that improved access to foreign
inputs has increased firm productivity (Amiti and Konings (2007) for Indonesia, Kasahara
and Rodrigue (2008) for Chile and Goldberg et al. (2010) for India). Vandenbussche and
Viegelahn (2016) complete previous studies by showing that trade liberalization in India has
boosted productivity thanks to within-firm reallocation of output towards production using
non-protected inputs. With a broader approach, Berthou, Manova, and Sandoz (2016) show
that trade induces within-firm productivity gains, but only exports generate within-sector
reallocation of resources. In the theoretical literature, Melitz and Redding (2014) propose a
tractable framework to quantify productivity gains coming from traded intermediate inputs.
Halpern, Koren, and Szeidl (2011) use the same initial settings to measure firm productivity
gains from importing intermediates. They attribute one-quarter of Hungarian productivity
growth between 1993 and 2002 to imported inputs.
However models in international trade usually suppose no market friction, and thus an
efficient allocation of resources across firms. This contrasts with most of the macro studies
(Hsieh and Klenow, 2009 (2009), Gopinath et al., 2015 (2015)), in which market frictions
matter and generate substantial resource misallocation. Misallocation is measured by the
wedge between firm marginal revenues and a positive variance of revenue-based productivity.
Many empirical studies have been done on French data. For instance, Libert (2016) shows a
expanding variance of TFPR in manufacturing sector in 2000s (about 1% per year). Fontagné
1
and Santoni (2015) validate this result by pointing a significant increase in the average labor
gap during the same period. Bellone et al. (2014) and Osotimehin (2012) are focusing on the
dynamics of aggregate productivity and show that misallocation tends to slightly increase
between the end of 1990s and the begin of 2000s in France.
My contribution is to bridge the gap between trade and macroeconomic literature. I
investigate how improved access to foreign inputs contributes to productivity growth in
presence of firm heterogeneity. I then identify through which margins productivity gains
occurred in presence of firm-level distortions.
First, I estimate a structural model of importer firms on French data. Following Halpern,
Koren, and Szeidl (2011), I formulate a model where firms use differential inputs to produce
a final good. Imported inputs affect firm productivity through higher price-adjusted quality
and imperfect substitutability. These two forces get incentive for firms to use relatively more
imported inputs than domestic ones. However they confer a comparative advantage to the
most productive firms. This advantage in foreign markets allows them to import more high
price-adjusted quality inputs and disproportionately increases their revenue-based productivity. The presence of firm-level distortions on intermediate input market creates some resource
misallocation. I measure it as the wedges between the firms’ value of marginal products and
this is translated by a positive standard deviation of the revenue-based productivity.
Once firm production functions are defined, the next challenge is to derive the link between firms and aggregate productivity dynamics. Aggregate productivity has to capture
variations in output due to firm productivity gains and variations of firm-level distortions.
I define the aggregate production function as the relation between aggregate output and
inputs for a given allocation of inputs as in Osotimehin (2012). My contribution relatively
to Osotimehin (2012) is to exploit a production function with three production factors which
are capital, labor and intermediate inputs. It allows me to capture productivity changes due
to variations of firm-level trade costs on intermediate inputs.
I then quantify the contribution of intermediate input reallocation on within-sector allocative efficiency. To do this, I rework the decomposition of aggregate productivity proposed
by Osotimehin (2016) with a third production factor (intermediate inputs). The goal is to
document the role played by traded intermediate inputs in sectoral TFP growth and to
quantify their contribution in allocative efficiency dynamics. One of the added values of
Osotimehin’s decomposition comes from the use of aggregate productivity rather than average productivity. The allocative efficiency is defined relatively to the optimal allocation of
resources, i.e. when marginal products are equalized across firms within a sector.
I estimate the decomposition on French firm-level data in manufacturing sectors between
1999 and 2011. I find that the positive growth rate of sectoral productivity over the period
2
(on average 0.2% per year) is mainly explained by positive growth rates between 2003 and
2006 (on average 2.2% per year) due to enhancing allocative efficiency (more than 60% of the
annual TFP growth). Even if firm-level distortions on intermediate input market are almost
unchanged during the studying period, allocative efficiency of intermediates relatively to the
output is substantially improving and this is the main driver of the total allocative efficiency
growth.
The rest of this paper is organized as follow. Section 2, I develop a simple model of
importer-producers and derive the decomposition of sectoral TFP. Section 3, I describe
data, estimation methods and results. Section 4 concludes.
2.
Theoretical Framework: an Industry Equilibrium Model
of Imported Inputs
In this section, I show in a simplified framework how trade affects aggregate productivity. I use a standard model of monopolistic competition with heterogeneous firms to
illustrate gains from trade coming from a higher allocative efficiency of resources. I present
the discussion from the point of view of the home country1 .
2.1. Demand and Preferences
Preferences across varieties have the standard CES form, with a constant elasticity of
substitution, σ. Utility for a representative agent is derived from the consumption of a
continuum of differentiated variety with elasticity σ > 1 :
σ/(σ−1)

JS
X
1/σ (σ−1)/σ 
Ut = 
Vit Yit
,σ > 1
(1)
i=1
where it denotes manufacturing varieties i at time t, Js is the set of varieties produced, Yit the
Ps
demand for the ith product from this set and Vit a demand shifter. I normalize Ji=1
Vit = 1.
The price index for manufactures at home, Pst , is defined over the prices of individual
varieties Pit :

1/(1−σ)
JS
X
(1−σ) 
Pt = 
Pit
(2)
i=1
1
see Bustos (2011)
3
These preferences generate a demand function of individual varieties i :
(σ−1)
Yit = Pit−σ Yt Pt
(3)
where Yt is the aggregate spending.
2.2. Technology and Firm Behaviors
In each sector S, firm i produces a differentiated good. Entry and exit are exogenous
and Iit < 0 indicates an active firm, Iit ≥ 0 an inactive firm and Nst = {i|Iit ≤ 0} is the set
of active firms. The number of active firms in a sector is denoted nst = Card(Nst ). Sector
P
P
P
inputs are denoted by Lst = i∈Nst Lit , Kst = i∈Nst Kit and Xst = i∈Nst Xit . Sectoral
output is given by the CES aggregate2 :
!1/θ
θ−1
θ
X
Yst = nst
Yitθ
(4)
i∈Nst
Where 0 < θ < 1 and the elasticity of substitution within sector s equals 1/(1 − θ) 3 . To
simplify notations, time subscripts t are omitted on sector-specific variables.
The sector s is composed by firms indexed by i = {1, ..., n}. Firms use Cobb-Douglas
technology for producing a differentiated final good:
Yit = Ωit Kitα Lβit
Y
γ
Xijtj
(5)
Firm i combines intermediate composite good Xijt with labor Lit and capital Kit . Ωit is the
Hicks-neutral total factor productivity. The Cobb-Douglas weight γj measured importance
of intermediate input i for production, as in Halpern et al (2015). The total weight of
P
all intermediate goods is γ =
i γj . The firm faces constant returns to scale such as
α + β + γ = 1. The factor elasticities and the set of intermediate inputs are assumed to be
identical within a sector.
Capital is internationally mobile with price Ri and input share α. The labor factor is
an internationally immobile primary factor with prices wi and input shares β. The third
factor of production is a composite intermediate good with price PX and input share γ.
They could be either produced domestically or imported. They are a CES composite of a
2
As in Osotimehin (2016), the CES aggregate is normalized by the number of firms nst to eliminate the
variety effect and avoid having total output increase in the number of firms.
3
As in Osotimehin (2016), I assume that each good has the same weight in the aggregation and hence
abstract from firm-specific demand shocks.
4
f
d
domestic variety, Xijt
, and a foreign one Xijt
, with relative efficiency (i.e. quality advantage)
of foreign inputs given by Bij which I suppose time-invariant. 4 I set Bij = 0 for nontradable
inputs.
h
i1/κ
f κ
d κ
Xijt = (Xijt
+ (Bij Xijt
)
(6)
Producers are price-takers in intermediate input market. The price of domestic and
foreign inputs are respectively denoted PXhjt and PXijt . By solving the cost-minimization
problem associated with equation (6), the effective price of composite good Xij if the firm
decide to import variety i :
PXijt =
(1−κ)
[PXhjt
1−κ 1/(1−κ)
+ (dj tPXf jt /Bij )
]
= PXhjt [1 +
Aij
(1 + dijt )
κ−1
]1/(1−κ)
(7)
Where dit is iceberg variable trade costs time t in firm i which captures firm-specific trade
frictions. Aij = Bij PXhj /PXf j is the price-adjusted quality advantage of foreign inputs j in
firm i. I set dijt > 0 for traded inputs. If Aij>1 , foreign inputs have higher quality than
domestic ones, and vice versa. If Aij = 0, foreign input price is infinitely high and this is
the case for non-tradable goods. I make the simplifying assumptions that the price-adjusted
quality Aij of all tradeable goods used by the firm i is the same across inputs used within a
firm: Aij = Ai . All firms are able to import foreign variety. The quantity of inputs chosen by
firms is determined by the tradeoff between differences in price-adjusted quality advantage
and variable trade cost across input varieties. The price index of composite goods used in
firm i is a geometric mean of composite prices:
PXit
M
N
Y
Y
(γj /γ)
(−γj /γ)
=
(γj /γ)
PXijt
j=1
(8)
j=1
1/(1−κ)
Regarding equation (8), Pijt = PXhjt [1 + Aκ−1
for tradeable inputs, otherwise Pijt =
ijt ]
PXhjt .
log[1+
I then denote aijt =
Ai
(1+dijt )κ −1
1−κ
PXit = Υ
M
Y
]
and Υ =
(γj /γ)
PXhjt
j=1
4
mj
Y
QN
j=1 (γj /γ)
(−γj /γ)
exp(−ait γj /γ)
j=1
see Bas and Berthou (2013) ; Halpern, Koren and Szeidl (AER, 2015)
5
and thus:
(9)
The relative importance for production of the inputs the firm chooses to import is denoted:
Pmi
j=1
Gi =
γj
(10)
γ
And I finaly get :
PXit = PXt eait Gi
(11)
Q
(γj /γ)
Where PXt = Υ M
j=1 PXhjt is the industry input price index. The price of inputs face
by the firm depends on their ability to integrate foreign inputs in production (Bij ), iceberg
variable trade costs (dit ), the substituability between inputs (Gi ).
Profits are given by :
Y
πit = Pit Ωit Kitα Lβit
γ
Xijtj − Rit Kit − wit Lit − PXit
j
Y
γ /γ
Xijtj
(12)
j
Profit maximisation yields the standard condition that the firm’s output price is a fixed
price over its marginal cost 5 :
σ
Pit =
σ−1
Rit
α
α wit
β
β PXt eait Gi
γ
γ
1
Ωit
(13)
The firm marginal revenue products of capital and labor can be written :
Pit Yit
= Rit
Kit
Pit Yit
M RP Lit = β
= wit
Lit
M RP Kit = α
(14)
If there is no friction in capital and labor markets (Rit = R) and (wit = w), the marginal
revenue products are equalized across firms and resources are efficiently allocated. If firms
face distortions, the marginal revenue products are no longer equalized: Rit = R(1 + τkit )
and wit = w(1 + τwit ). Capital and labor are not efficiently allocated across firms due to
distortions at firms-level. Here, distortion is defined as the wedge in the first-order condition
of the first-best allocation of resources.
The marginal revenue product of inputs is proportional to the input prices and depends
5
Due to CES preferences and monopolistic competition, the constant markup of price over marginal cost
ensures that higher firm productivity is passed on fully to consumers in the form of a lower prices. Since
demand is elastic, this lower price implies higher revenue for more productive firms (Melitz and Redding,
2015).
6
on per product import gain (ait ) and import share measure (Gi ):
M RP Xit = γ
Pit Yit
= PXt eait Gi
Xit
(15)
However I do not observe Xit in the data, but Mit = XitPPXtXit and marginal revenue product
of inputs measured is then:
Pit Yit
= eait Gi
(16)
M RP Mit = γ
Mit
The marginal product of inputs are not equalized across firms. Per product import gains are
not identical across firms due to their imperfect substitutability and firm-specific variable
trade costs. This generates distortions and resource misallocation. Domestic and foreign
inputs are not efficiently allocated within sector.
Finally, I do not observe Yit in the data but YitPstPit .Using the assumption about the demand
function pit /Pst = (nst Yit /Yst )( θ − 1), the firm-level TFP is then:
Ωit =
(Pit Yit /Pst )1/θ
Kitα Lβit Mitγ
Yst
nst
(θ−1)/θ
(17)
2.3. Sectoral Production Functions and aggregate productivity
For aggregating the production functions, I follow the methodology proposed by Osotimehin (2016). I first aggregate the firm-level production function at the sectoral level and
then aggregate the sectoral production functions6 . In fact, the sectoral production function
Ys = Fs (Ls , Is , As , τs ) as the same functional form as the individual production functions :
β
α β
Fst (Lst , Ist , Ast , τst ) = T F Pst Kst
Lst Xst
With
θ
θ−1
T F Pst = nst
X
i∈Nst
Ωθi
Kit
Kst
αθ Lit
Lst
βθ Mit
Mst
γθ !1/θ
(18)
Where Kit /Kst , Lit /Lst and Mit /Mst are functions of the vector of firm-level productivities
Ωt = {Ωit , it ∈ Nst } and at = {ait , i ∈ Nst }.
6
First, we derive the aggregate production function for a given allocation rule, which define how inputs
are allocated across firms. We parametrise the allocation rules as a function of firm-level distortions (i.e. the
difference from the first order condition of the best allocation of resources). We then aggregate the sectoral
production functions and take into account the heterogeneity between sectors.
7
2.4. Decomposition of sectoral TFP growth
Regarding to the decomposition proposed by Osotimehin (2016), sectoral TFP growth
(∆T F Pst = lnT F Pst − lnT F Pst−1 ) can be decomposed into changes in technical efficiency
(∆T Es ), changes in allocative efficiency (∆AEs ) and changes at the extensive margin (∆EXs )
such as :
∆T F Ps = ∆T Es + ∆AEs + ∆EXs
(19)
The changes in firm-level productivity can be approximated as a combination of weighted
average of the firm-level productivity changes7 :

∆T Est ≈

pit−1 Yit−1
Kit−1
Lit−1
Mit−1 
1 X ∆Ωit 
 X

− αθ X
− βθ X
− γθ X

1−θ
Ωit−1 
p
Y
K
L
M
it−1
it−1
it−1
it−1
it−1
i∈Cs t
i∈Cst
i∈Cst
i∈Cst
(20)
i∈Cst
Where Cst is the set of continuing firms in sector s at time t. Here, the technical efficiency
component includes both the effects of changes in firm-level productivity with firms’ input
shares constant and the effect of the implied changes in input shares for a given level of
allocative efficiency. Furthermore, technical efficiency is also affected by the composition of
intermediate inputs used. Firms with access to high productive inputs have higher technical
efficiency 8 .
The changes in allocative efficiency is a combination of weighted averages of the firm-level
changes in distortions :

∆AEst ≈ −

X ∆τKit  pit Yit
α
Kit
Lit
Mit 
 X

− (1 − (1 − α)θ) X
− βθ X
− γθ X


(1 − θ)
τKit−1
pit Yit
Kit
Lit
Mit
i∈Cs t
i∈Cs t
i∈Cs t
i∈Cs t
i∈Cs t

−

X ∆τLit  pit Yit
β
Lit
Kit X
Mit 
 X

Kit − (1 − (1 − β)θ P
−
αθ
− γθ X

(1 − θ)
τLit−1 
L
it
p
Y
M
i∈C
t
s
it
it
it
i∈Cs t
i∈Cs t
i∈Cs t
i∈Cs t

−

X ∆ eait Gi  pit Yit
γ
Kit
Lit
Mit 
 X

− αθ X
− βθ X
− (1 − (1 − γ)θ) X


a
G
it−1
i
(1 − θ)
e
pit Yit
Kit
Lit
Mit
i∈Cs t
i∈Cs t
i∈Cs t
i∈Cs t
i∈Cs t
(21)
The allocative efficiency measures the effect of changes in input allocation across firms on
aggregate productivity. In the general case, allocative efficiency change equals zero if the
7
More details in appendix.
the technical efficiency is also likely to reflect other shocks than technology upgrading such as demand
shocks or factor utilization. When goods are heterogeneous the firm’s productivity is also a function of
firm-specific demand shocks (see Osotimehin, 2016).
8
8
level of distortions is unchanged or if the change in the distortions is identical across firms
(i.e. firms’ marginal productivity remains relatively unchanged). If variable trade costs are
highly dispersed, more productive firms will get a comparative advantage on foreign markets.
Higher productive inputs are disproportionately allocated toward these firms which already
have high marginal productivities. It leads to decrease allocative efficiency. The fact that
some firms have specific advantages creates distortions and generate resource misallocation.
The contribution of the extensive margin depends on the average output and input used
by entering and exiting firms :

∆EXst ≈


est 
1 

nst θs 
1
est
X
pit Yit
i∈st
1
cst
X
pit Yit





− 1
 − α
1
est
+


xst 
1 

nt θs 
1
xst
X
1
cst
1
cst
X
pit Yit
X
Kit





− 1
−β
1
est





− 1
 − α
i∈Ct
1
xst
X
Kit
i∈χst
1
cst
X
Kit
i∈Ct
X
Lit
i∈st
1
cst
i∈Cst
pit Yit
i∈χst
Kit
i∈st
i∈Cst

X
X
Lit





− 1
−γ
1
est
1
cst




− 1
−β
1
xst
X
Lit
i∈χst
1
cst
X
i∈Ct
Lit
X
Mit





− 1
−γ
1
xst
X
Mit

Mit


− 1

i∈χst
1
cst
X
i∈Cst
With Cst the set of continuing firms, st the set of entering firms, χst the set of exiting firms,
and ct , et and xt the number of continuing, entering and exiting firms each year9 .
Empirical framework
I estimate the decomposition by using firm-level data to measure how decreasing trade
costs have modified the allocative efficiency and contributed to the productivity growth.
In this section, I describe the data used, the estimation strategy and the results of the
decomposition.
3.1. Data description
To implement the decomposition, I use French firm-level dataset collected by the Banque
de France, called Fiben. This database includes all firms with a turnover of at least 750 000
euros between 1995 and 2013. It gathers accounting and financial data from firm balance
sheets, which includes measures of firms’ value added, investment expenditures, number of
employees and raw material costs.
Each firm is assigned by an identification number (Siren) which allows us to detect
potential entries and exits. However Fiben is not the appropriate database to study the
9
When firms face constant returns to scale (as assumed here), the contribution of entry and exit does not
depend on the number of firms (see Osotimehin, 2016).
9


− 1

i∈Cst
(22)
3.

Mit
i∈st
i∈Cst

X
extensive margin due to the presence of turnover threshold. That is why I am focusing on
continuing firms and sector-level TFP growth. I assume that industries in my framework
correspond to the 2-digit industry-level of the NACE revision 2 classification. I exclude
agricultural and mining sectors and remove sectors which do not provide market services
(i.e. education, health, education and non-profit sectors). I then exclude from the sample
firms whose productivity changes are in the bottom and top 2 percentiles by sector.
The sample contains about 140 000 active firms per year and 49 sectors. I measure labor
cost as wedge bill and intermediate inputs as material costs deflated by the corresponding
value-added price index from Eurostat. I compute the capital stock as the book value
of tangible fixed assets, deflated by the industry price deflators from Eurostat. Finally, I
measure production with turnover (gross output) deflated by the corresponding value-added
deflators from Eurostat.
3.2. Estimation method of sectoral aggregate TFP and decomposition
In this section, I describe method used to estimate firm-level distortions, factor elasticities
and productivities.
3.2.1.
Estimation of firm-level distortions
Distortions facing by firms are described in equations (14) et (16). They are the wedges
between the firm marginal productivities and the frictionless value. As shown by Osotimehin (2016), the impact of the distortions on aggregate productivity only depends on the
relative marginal productivity of firms. This property simplifies the estimation of firm-level
distortions that can be computed from firm-marginal productivities in nominal terms :
M V P Kit
Rst Pst
M V P Lit
(1 + τwi ) =
wst Pst
M
V P Mit
eai Gi =
Pst
(1 + τKi ) =
10
(23)
Substitute in equation (21), allocative efficiency is then:

∆AEs ≈ −

X ∆M V P Kit  pit Yit
α
Kt
Lt
Mt 
 X

− (1 − (1 − α)θ) X
− βθ X
− γθ X


(1 − θ)
M V P Kit−1
pit Yit
Kt
Lt
Mt
i∈Cs t
i∈Cs t
i∈Cs t
i∈Cs t
i∈Cs t

−

X ∆M V P Lit  pit Yit
β
Kt
Lt
Mt 
 X

X
X
X
−
αθ
−
(1
−
(1
−
β)θ)
−
γθ

(1 − θ)
M V P Lit−1 
p
Y
K
L
M
it
it
t
t
t
i∈Cs t
i∈Cs t
i∈Cs t
i∈Cs t
i∈Cs t

−

X ∆M V P Mit  pit Yit
γ
Kt
Lt
Mt 
 X

− αθ X
− βθ X
− (1 − (1 − γ)θ) X


(1 − θ)
M V P Mit−1
p
Y
K
L
M
it it
t
t
t
i∈Cs t
i∈Cs t
i∈Cs t
i∈Cs t
i∈Cs t
(24)
In equations (20) and (24), technical efficiency is computed as a Laaspeyres index and
allocative efficiency as a Paasche index for simplicity. To tackle this arbitrary choice, I
compute allocative efficiency and technical efficiency as Fischer indexes in the do-file.
3.2.2.
Estimation of production functions
The estimation of production function is tricky in presence of resource misallocation.
I can not implement the Olley and Pakes (1996) semi-parametric method, as in Halpern
et al (2015). In this framework, firm decision depends on its productivity but also on
factor distortions. Olley and Pakes approach can only deal with a unique unobservable state
variable and it is not appropriate here because firm-level distortions are also unobserved.
Following Osotimehin (2016), I assume that input price heterogeneity is the only source
P 1
P 1
1
=
1
and
of average distortions ( T1 t 1+τ
t eeit Gi = 1). Then I can use labor income and
T
t
raw material cost shares to estimate labor and input elasticities :
βs =
γs =
1 X wst Lst
T t Pst Yst
1 X PXst Xst
T
t
(25)
Pst Yst
Assuming constant return to scale, αs = 1 − βs − γs . Sectoral productivity is given by the
standar Solow residual:
Yst
T F Pst = α β γ
(26)
Kst Lst Mst
9
See more details in appendix.
11
To estimate TFP at firm-level, I have to deal with unobservable firm prices. I use the
common assumption about the demand function, Pit /Pst = (nst Yit /Yst )θ−1 and the estimate
firm productivity is :
(θ−1)
θ
(Pit Yit )1/θ Yst
(27)
Ωit = α β γ
Kit Lit Mit nst
Where Pst is measured by the sectoral deflator and Yst is the sector nominal value added.
I set a within-sector elasticity of substitution at θ = 3, coming from Broda and Weistein
(2006). Important limitations of the measure of firm productivity Ωi are that it doest not
capture only technical productivity, but also firm-specific demand shocks, shifing in factor
utilization and other measurement issues. [TO BE DEVELOPED]
3.3. Results
In this section, I investigate how the booming trade of intermediate inputs from China
between 2002 and 2007 has impacted aggregate productivity in France. In December 2001,
China became a member of WTO. This integration has considerably decreased the cost of
importing from China for France. For that country, this period corresponds to a positive
growth of aggregate productivity (see figure 1). In the first subsection, I look at the decomposition of the French aggregate productivity growth of continuing firms and quantify
the relative importance of allocative efficiency in productivity gains. I then evaluate the
importance of decreasing trade cost of inputs on allocative efficiency.
3.3.1.
Productivity growth at sector level and allocative efficiency
French manufacturing industries experiment a TFP growth by 0.2% between 1999 and
2011 in the sample of continuing firms 10 , but the growth path is not linear. Figure 1 reveals
that the main sub-period of positive growth rates is between 2003 and 2006 (by 2.2% on
average). This sub-period coincides with massive arrivals of imported inputs from China,
which raised by an average of 16% per year.
How do allocative efficiency and technical efficiency contribute to aggregate productivity
growth in French manufacturing sectors between 1999 and 2011? Table 1 shows the contribution of each components in aggregate TFP growth computing for continuing firms in
manufacturing industry. Allocative efficiency appears to be the main source of aggregate
productivity gains, but there is a large heterogeneity across sectors. For instance, 65% of
aggregate productivity growth is explained by a better allocation of resources across firms
10
Due to the entry threshold in the Fiben database, I choose to exclude the extensive margin and be focus
on the intensive margin analysis.
12
in textile industry against -18% in chemicals. The variations in within-firm productivity
(∆T E) play a less sizable role for the dynamics of sectoral productivity. On average technical efficiency reduces the growth of sectoral TFP by 20%, but in some sectors its contribution
is positive and substantial. For instance, technical efficiency represents more than 50% of
TFP gains in wood, chemical and fabricated metal product industries.
Table 1: Average contribution to sectoral TFP growth by sector, 1999-2007
Manufacturing sectors
Food products
Beverage products
Textiles
Wearing apparel
Leather products
Wood products
Paper products
Printing and reproduction
Chemical products
Basic pharmaceutical products
Rubber and plastic products
Other nonmetallic products
Basic metals
Fabricated metal products
Electronic products
Electrical equipment
Machinery
Motor vehicles
Other transport equipment
Furniture
Other manufacturing products
Repair and installation of machinery
Source:.
13
∆T Es
∆AEs
-1.78
-2.26
0.35
0.33
0.42
0.70
0.20
0.14
1.18
0.15
0.09
-2.05
-0.18
1.70
-0.02
0.40
-0.24
0.46
-0.08
0.54
0.41
-0.39
2.78
3.26
0.65
0.67
0.58
0.93
0.80
0.86
-0.18
0.85
0.91
3.05
1.18
-0.70
1.02
0.60
1.24
0.54
1.08
0.46
0.59
1.39
Fig. 1. Dynamics of aggregate productivity and imported inputs in France
Note: This figure gives the average annual growth rates of aggregate productivity, total
imported inputs and total imported inputs from China in manufacturing sectors. Aggregate
TFP growth is measured by an average of annual growth rate of TFP at sector level computed
on continuing firms.
Fig. 2. Average contribution to sectoral TFP growth over time
Note: This figure gives the average annual growth rates of aggregate productivity, allocative
efficiency and technical efficiency which are computed at sector-level.
14
Figure 2 shows the dynamics of technical and allocative efficiency over time in manufacturing sectors. It confirms previous results and stresses the importance of allocative efficiency
in productivity dynamics. However, sectoral volatility is mainly driven by firm-level productivity gains in Osotimehin (2016). Samples are not identical and are coming from different
sources. In the Banque de France database using here, the threshold on turnover creates
endogenous firm selection. Only the biggest firms are referenced, and so the most productive
ones, which may reinforce the allocative term.
3.3.2.
Allocative efficiency and firm-level distortions on inputs
The next questions are why allocative efficiency is improving between 2003 and 2006 and
which inputs are better allocated. First, I look at the evolution of firm-level distortions. I
estimate firm-level distortions on labor, capital and intermediate inputs by using equations
(23). I then compute the average annual growth rate and plot them in Figure 3. Intermediate
inputs distortions are slightly decreasing in 2001 and 2002. Between 2002 and 2007, they
grow by 0.7% per year. Capital distortions are lowering between 2001 and 2003, while labor
distortions are continuously rising over the entire period, excepted in 2008. At first glance,
the arrival of Chinese inputs seems to have been related to a reduction of distortions across
continuing firms in manufacturing sectors in France, but the magnitude remains small.
Fig. 3. Average firm-level distortions over time
Note: This figure gives the average annual growth rate of firm-level distortions. Firm-level
distortions are computed as in equations 23. I then compute the average annual growth rate.
In Figure 4, allocative efficiency is decomposed by types of inputs used by firms relatively
to their turnover. The rapid growth of allocative efficiency is mainly due to an improvement
15
Fig. 4. Dynamics of allocative efficiency by types of inputs
Note: This figure gives the decomposition of allocative efficiency dynamics by types of inputs
used by continuing firms relatively to their turnover (see equation 24) in manufacturing
sectors.
of allocation of intermediate inputs across continuing firms in manufacturing industries. In
2006, 63% of the improvement of allocative efficiency is explained by shifting of intermediate
inputs across firms.
4.
Conclusion
This paper examines the impact of traded intermediate inputs on aggregate productivity
growth. I find that allocative efficiency is an important determinant of sectoral productivity
growth and the reallocation of intermediate inputs across continuing firms plays a significant
role at the begin of 2000s. This work sheds light on the productivity gains from trade in
presence of firm-level variable trade costs on intermediate inputs.
[TO BE DEVELOPED]
16
References
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[3] Antoine Berthou, Kalina Manova, and Charlotte Sandoz. “Productivity, Misallocation
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(2010), pp. 1727–1767 (cit. on p. 1).
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17
[14] Sophie Osotimehin. “Aggregate productivity and the allocation of resources over the
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18
5.
Appendix
[TO BE COMPLETED]
5.1. Exact decomposition of sectoral TFP
Regarding to the method proposed by Osotimehin (2016), the decomposition of productivity growth is given by :
T F Pst
= IIN IEX
(28)
T F Pst
Where IIN is the intensive margin and IEX is the extensive margin.
By using equations (??), (??) and (17), I rewrite RVA, capital, labor and inputs used as
function of firm-level productivity and distortions :
θ
αθ
βθ
γθ
βθ
γθ
g Y (Ai , τi ) = Ωit1−θ (1 + τitK )− 1−θ (1 + τitL )− 1−θ (eait Gi )− 1−θ
θ
g K (Ai , τi ) = Ωit1−θ (1 + τitK )−
θ
1−θ
L
1−(1−α)θ
1−θ
αθ
− 1−θ
g (Ai , τi ) = Ωit (1 + τitK )
θ
1−θ
(1 + τitL )− 1−θ (eait Gi )− 1−θ
(1 + τitL )
−
1−(1−β)θ
1−θ
)
(e
βθ
αθ
(29)
γθ
ait Gi − 1−θ
g X (Ai , τi ) = Ωit (1 + τitK )− 1−θ (1 + τitL )− 1−θ (eait Gi )−
1−(1−γ)θ
1−θ
And :

∆T F Pst =
nst
nst−1
θ−1
θ
X
g Y (Ait , τit )
 θ1 
i∈Nst
X
−α
i∈Nst
−β 
L
g (Ait , τit )
 i∈Nst

X



g L (Ait−1 , τit−1 )
i∈Nst
Where
X
g K (Ait , τit )
  i∈Nst

 i∈Nst
 X

X
 


Y
K
g (Ait−1 , τit−1 )
g (Ait−1 , τit−1 )


X
g Y (Ait , τit )
X
−γ
X
(30)
g (Ait , τit )
 i∈Nst

X



g C (Ait−1 , τit−1 )
i∈Nst
 θ1 
X
g K (Ait , τit )
−α
 i∈Cst
  i∈Cst

 X

X
IIN = 

 

g Y (Ait−1 , τit−1 )
g K (Ait−1 , τit−1 )
i∈Cst

X
i∈Cst
L
−β 
g (Ait , τit )
 i∈Cst

X



g L (Ait−1 , τit−1 )
i∈Cst
X
−γ
g (Ait , τit )
 i∈Cst

X



g X (Ait−1 , τit−1 )
i∈Cst
19
X
(31)
And

IEX =
nst
nst−1
X
g Y (Ait , τit )
X
g Y (Ait−1 , τit−1 )
 θ1
θ−1

θ 
i∈Cst
 i∈Nst

X
 X Y

Y

g (Ait−1 , τit−1 )
g (Ait−1 , τit−1 ) 
i∈Nst−1

X
i∈Cst
X
K
K
−α
L
−β
g (Ait−1 , τit−1 )
g (Ait , τit )


i∈Cst

 i∈Nst
X

 X K

g (Ait−1 , τit−1 )
g K (Ait−1 , τit−1 ) 
i∈Nst−1

X
i∈Cst
X
L
g (Ait , τit )
g (Ait−1 , τit−1 )


i∈Cst
 i∈Nst

X
 X L

L

g (Ait−1 , τit−1 ) 
g (Ait−1 , τit−1 )
i∈Nst−1

X
i∈Cst
g X (Ait , τit )
X
g X (Ait−1 , τit−1 )
−γ


i∈Cst

 i∈Nst
X
X


X
X

g (Ait−1 , τit−1 ) 
g (Ait−1 , τit−1 )
i∈Nst−1
i∈Cst
20
(32)