Firm-level Productivity Spillovers in China’s Chemical
Industry: A Spatial Hausman-Taylor Approach
Badi H. Baltagi
(Center for Policy Research, Syracuse University, Syracuse, NY 13244-1020)
Peter H. Egger
(ETH Zurich, CEPR, CESifo, GEP)
Michaela Kesina
(ETH Zurich)
September, 2013
Abstract: This paper assesses the role of intra-sectoral spillovers in total
factor productivity across Chinese producers in the chemical industry. We use
a rich panel data-set of 12,552 firms observed over the period 2004–2006. We
model output by the firm as a function of skilled and unskilled labor, capital,
materials, and total factor productivity, which is broadly defined. The latter is
a composite of observable factors such as export market participation, foreign
as well as public ownership, the extent of accumulated intangible assets, and
unobservable total factor productivity. Despite the richness of our data-set, it
suffers from the lack of time variation in the number of skilled workers as well
as in the variable indicating state ownership. We introduce spatial spillovers in
total factor productivity by allowing the error term across firms to be spatially
interdependent. We extend the Hausman and Taylor (1981) estimator to allow
for spatial correlation in the error term. This approach permits estimating
the effect of time-invariant variables which are wiped out by the fixed effects
estimator. We find evidence of positive spillovers across chemical manufacturers
and a large and significant detrimental effect of public ownership on total factor
productivity.
Key Words: Technology spillovers; Spatial econometrics; Panel data econometrics; Firm-level productivity; Chinese firms
JEL Classification: C23; C31; D24; L65
1
Introduction
There is now broad firm-level evidence suggesting that total factor productivity
(TFP) is contagious and prone to spillovers which are geographically bounded.
Evidence from Europe includes Smarzynska Javorcik (2004), Görg, Hijzen, and
Murakozy (2006), Ebersberger and Lööf (2005), and Lööf (2007), to mention a
few. Evidence from the United States includes Keller and Yeaple (2003), Bloom,
Schankerman, and van Reenen (2005), and Branstetter (2006), to mention a
few. For South America, see Aitken and Harrison (1999), and for China, see
Hu, Jefferson, and Jinchang (2005), Chen and Swenson (2006), Hale and Long
(2006), and Blonigen and Ma (2007), to mention a few examples.
Important transmission channels of TFP spillovers are worker flows, cooperation in research and development across firms, and other (not directly measurable but geographically bounded) forms of dissemination of knowledge and
productivity.1 A primary cause of TFP spillovers is the technology gap between
the leading firm in an industry and the other firms, and the catching-up of the
followers to the leader which is facilitated by a small geographical distance for
the above-mentioned reasons and by higher absorptive capacity of the followers (see Griffith, Redding, and van Reenen, 2004). Most of the empirical work
on TFP spillovers within an industry adopts at least one of the following two
assumptions: TFP spillovers are possible only from the industry leader to the
other firms; or, for developing countries and economies in transition (such as
China), TFP spillovers happen only from foreign-owned to domestic firms. Yet,
empirically it is difficult to distinguish between spillovers from leading foreignowned versus leading domestically-owned entities to other firms (see Lööf, 2007,
for a survey).
The data utilized in this study are based on the universe of all firms in
China’s chemical industry with a turnover exceeding about 700,000 US dollars
1 As pointed out by Smarzynska Javorcik (2004) and, in particular, by Bloom, Schankerman,
and van Reenen (2005), what is dubbed technology spillovers in empirical work consists of
two main components: technology transmission in a narrow sense and interdependence across
firms by market structure. Empirical work seldomly disentangles these components and should
therefore speak of spillovers in a broad sense.
1
over the period 2004–2006. The data-set covers 12,552 firms and 37,656 observations. Our focus on the period 2004-2006 is dictated by the quality of data in
recent periods and the availability of data on skilled workers. The chemical sector is relatively important in many countries of transition such as China (UNEP
Chemicals Branch, 2009; it accounts for about 8 percent of employment of all
Chinese manufacturing firms). The average firm in that sector is relatively large
(about 257 employees). Although the number of publicly-owned firms account
for a little more than 5 percent of all firms in that sector in China between 2004
and 2006, they employ on average 793 employees as compared to 166 employees
for domestically-owned firms; see also Szamosszegi and Kyle (2011).
One main goal of the study is disentangling the role of production factors
such as skilled and unskilled labor, capital, and material inputs, on the one
hand, from observable and unobservable determinants of TFP defined in a broad
sense. We account for four observable shifters of TFP: export status, foreign
ownership, the extent of intangible assets accumulated by a firm, and public
ownership status. Export market contact has been found to affect TFP through
competitive pressure as well as learning (see Baldwin and Gu, 2006; Girma,
Greenaway, and Kneller, 2004; and Greenaway and Kneller, 2004, 2007). Foreign
ownership of firms in developing countries and economies in transition offers
access to better technologies of foreign subsidiaries and even of other firms
in host countries. The beneficiaries include input suppliers (see Smarzynska
Javorcik, 2004; and Smarzynska Javorcik and Spatareanu, 2009) and firms which
receive worker flows from more productive, foreign-owned units (see Görg and
Strobl, 2005). For the foreign subsidiaries themselves, foreign ownership may
also lead to specialization on less-advanced production stages. Hence, foreign
ownership may impede knowledge transfer, if foreign owners fear the loss of
intellectual property through involuntary dissemination of knowledge to other
firms (see Puttitanun, 2006), or if foreign entities do not have the absorptive
capacity to utilize more advanced technologies available from the parent (see
Keller, 2004; and Peri, 2005). The corporate finance literature suggests that
the degree of asset (in)tangibility is an important factor in determining access
2
to external credit, opportunities to finance investments with little collateral
value such as research and development (R&D), in sustaining growth, especially,
of young companies (Himmelberg and Petersen, 1994; Hall and van Reenen,
2000; Hall and Lerner, 2010), and in facilitating knowledge absorption. Finally,
public ownership is commonly regarded as a stepping stone to technological
advancement due to the lack of competitive pressure (see González-Páramo and
Hernández Cos, 2005).
Apart from these shifters, we allow TFP for a particular firm to depend
spatially on other firms within a geographical neighborhood. We model the
extent of spatial TFP spillovers to decline with distance. This is done by using
information on a firm’s geographical location as available from the data (by
way of a six-digit ZIP code). We estimate our model using a spatial panel
GMM methodology derived by Kapoor, Kelejian, and Prucha (2007). However,
the presence of time-invariant variables – such as skilled labor input and public
ownership – and their possible correlation with unobservable firm-specific effects
require us to adopt a Hausman and Taylor (1981) estimation approach, hereafter
denoted by HT. Unlike the fixed effects estimator, the Hausman and Taylor
estimator does not wipe out the time-invariant variables. Instead, it uses the
between variation of the time-varying exogenous variables to instrument for
endogenous time-invariant regressors. Our estimation methodology modifies
the HT methodology to allow for spatial effects à la Kapoor, Kelejian, and
Prucha (2007). The proposed estimator has been shown to perform well in
small samples (see Baltagi, Egger, and Kesina, 2012).
Our findings can be summarized as follows: For China’s chemical industry,
a high degree of asset intangibility, a high foreign ownership ratio, and exportmarket participation are statistically significant and lead to a positive shift in
TFP. Second, public ownership is associated with dramatically lower TFP than
private ownership. Clearly, publicly-owned firms are relatively large (in terms
of assets and employees), they account for a significant share of the industry’s
output, but their output is relatively small once controlling for their factor usage.
We estimate that the average publicly-owned firm’s TFP is about 75-80 percent
3
lower than the average privately-owned firm’s TFP. The data suggest that shocks
in TFP are contagious within the industry. Hence, negative TFP shocks do not
only affect firms that are hit by those shocks but also their geographic neighbors.
Using inverse geographical distance to parameterize the spatial weights matrix
across firms, we estimate the spatial dependence parameter at about 0.29 in the
preferred models. This parameter is statistically significant at 1 percent and is
estimated on a spatial weights matrix which is full and of size 12, 552 × 12, 552.
One of the merits of the generalized moments approach is that it can cope with
spatial problems of this size. We find that restricting the scope of spillovers to
firms within a smaller neighborhood – say, within a radius of 50, 100, or 200
miles – does not change the results much. The spatial spillover effect suggests
that a one-percent positive shock applied to all firms leads to an ultimate gain
of about 1.41 percent in TFP accruing to unobservable factors.
The remainder of the paper is organized as follows. The next section introduces the econometric model and the spatial Hausman and Taylor (1981)
approach (SHT). That section puts the SHT estimator in context with its spatial random effects (SRE) and spatial fixed effects (SFE) counterparts and also
presents variants of SHT in the spirit of Amemiya and MaCurdy (1986) as well
as Breusch, Mizon, and Schmidt (1989) which have been suggested in the nonspatial literature. In a spatial context, we will refer to these estimators as the
SAM and SBMS variants of SHT. Section 3 summarizes the empirical results for
non-spatial as well as spatial (cum spillover) translog models. The last section
concludes with a summary of the key findings.
2
Econometric model
In this section, we specify an econometric error components model with spatially
autocorrelated disturbances and right-hand side variables that are correlated
with the time-invariant firm effects.
4
2.1
Model outline
Consider a large cross section of N spatial units (firms), which are observed
repeatedly across a small number of T time periods.2 We use the subscript
i = 1, ..., N to refer to individual units, and t = 1, ..., T to refer to time periods.
We specify a Cliff-Ord-type spatial model to describe the interaction between
firms at period t as follows:
yt
= Xt β + Zγ + ut = Zt δ + ut
(1)
ut
= ρWut + εt ,
(2)
εt = µ + ν t
0
where Zt = [Xt , Z], and δ = β 0 , γ 0 . Here, yt = (y1t , ..., yN t )0 is an N ×
1 vector of observations on the dependent variable at time t, Xt is an N ×
K matrix of time-varying regressors for period t, Z is an N × R matrix of
time-invariant regressors. As described below, for the Hausman and Taylor
(1981) model, some of the regressors in Zt are allowed to be correlated with
µ. W is an N × N observed non-stochastic weights matrix whose properties
will be specified below. ut = (u1t , ..., uN t )0 is the N × 1 vector of regression
disturbances, and εt = (ε1t , ..., εN t )0 is an N × 1 vector of innovations which
consist of two components: a time-invariant µ = (µ1 , ..., µN )0 and a time-variant
ν t = (ν1t , ..., νN t )0 component. The vector Wut represents a spatial lag of ut .
The scalar ρ denotes the spatial auto-regressive parameter, while β and γ are
K × 1 and R × 1 vectors of regression parameters.3
In matrix form, we sort the data first by time t (the slow running index) and
2 The data available in this study do not permit distinguishing between common factors
and spatial correlation in a more narrow sense. The former are in the limelight of a recent
literature in theoretical econometrics which focuses on data situations with a relatively large
number of time periods (see Pesaran, 2006; Pesaran and Tosetti, 2011; or Pesaran, Smith,
and Yamagata, 2013; for a few recent examples of such research).
3 Kelejian and Prucha (1999) and Kapoor, Kelejian, and Prucha (2007) use the subscript N
to indicate that the elements of all data vectors and matrices as well as of all parameters may
depend on the cross section sample size N . We skip this subscript to avoid index cluttering.
5
then by firms i (the fast running index) as follows:
y
= Xβ + (ιT ⊗ Z)γ + u = Zδ + u
(3)
u
= ρ(IT ⊗ W)u + ε,
(4)
ε = Zµ µ + ν,
where ιT denotes a T × 1 vector of ones and IT denotes a T × T identity matrix.
Zµ = ιT ⊗ IN is an N T × N selector matrix of ones and zeroes. For subsequent
use, it is convenient to define d ≡ (ιT ⊗ Z)γ + u.
2.2
Assumptions
We follow the standard assumptions given in Kapoor, Kelejian, and Prucha
(2007) for the random effects spatial panel model, but we allow for correlation
of some of the regressors with the individual time-invariant effects as in Hausman
and Taylor (1981).
(i) (Assumptions on the error components):
µi ∼ i.i.d.(0, σµ2 ), νit ∼ i.i.d.(0, σν2 ), and µi and νit are independent of each other
for all i and t. Hence, the covariance of εit and εjs is as follows: Cov(εit εis ) =
σµ2 + σν2 for i = j and t = s; Cov(εit εis ) = σµ2 for i = j and t 6= s; and
Cov(εit εis ) = 0 otherwise, see Baltagi (2008). The variance components are
uniformly bounded away from zero and from infinity, and the (4+η)-th moments
of the error components are finite for some η > 0, as in Badinger and Egger
(2011).
(ii) (Assumptions on W and admissible parameter space):
All diagonal elements of W are zero, and W is row-sum normalized. ρ ∈ (−1, 1)
and the matrix IN − ρW is nonsingular.
(iii) (Hausman and Taylor assumptions:)
The regressor submatrices may be decomposed into X = [XU , XC ] and Z =
[ZU , ZC ], where Xf is N T × Kf and Zf is N × Rf for f = U, C. In Hausman
and Taylor’s (1981) notation, [XC , ιT ⊗ ZC ] are correlated with µ, whereas
A = [XU , ιT ⊗ ZU ] are not. All columns of Z are assumed to be uncorrelated
6
with ν. Define the (between) projection matrix Q1 = JT ⊗ IN , where JT ≡
T −1 JT and JT = ιT ⊗ ι0T . Also, define the sweeping (within transformation)
matrix Q0 = IT N − Q1 with IT N = IT ⊗ IN (see Baltagi, 2008). In this case,
E(X0 Q0 u) = 0, E(X0U u) = 0, E((ιT ⊗ ZU )0 u) = 0, but E((ιT ⊗ ZC )0 u) 6= 0
and E(X0 Q1 u) 6= 0 due to E(X0C u) 6= 0. We assume that the Hausman and
Taylor (1981) order condition for identification, i.e., RC ≤ KU holds throughout
our analysis.
Notice that Assumption (i) ensures that the central limit theorem underlying
the estimator in Kapoor, Kelejian, and Prucha (2007) applies. This is needed
for the asymptotic distributions of our estimators to conform with the properties
and analysis in Kapoor, Kelejian, and Prucha (2007) and Badinger and Egger
(2011). Assumption (ii) is a standard normalization of W which ensures that
the shocks in the interdependent system have finite consequences, and it allows
the researcher to infer directly from the estimate of ρ whether this is the case.
Assumption (iii) is a standard order condition for identification.
2.3
The spatial Hausman-Taylor estimator
STEP 1 - Estimate β. From the assumptions of our model, one can estimate
β consistently using the fixed effects estimator βbF E = (X0 Q0 X)−1 X0 Q0 y. This
provides a consistent estimate of the residuals d ≡ (ιT ⊗ Z)γ + ut given by
b ≡ y − Xβ
b .
d
FE
STEP 2 - Estimate γ: Now one can retrieve a consistent estimate γ which
was wiped out by the fixed effects estimator. First, we average the residuals
b over time by computing Q1 d.
b Then, we run 2SLS of Q1 d
b on Z using
in d
A = [XU , ιT ⊗ ZU ] as our instruments. This is the two-step Hausman and
b where P =
b 2SLS = (Z0 PZ)−1 Z0 PQ1 d,
Taylor estimator and it is given by γ
A(A0 A)−1 A0 is the projection matrix on the matrix of instruments A. This
estimator is consistent but not efficient, since it ignores the error component
structure of the data.
STEP 3 - Estimate ρ, σν2 , and σµ2 : From step 2 we now have consistent
7
b = y − XβbF E − (ιT ⊗ Z)b
b , s we can
estimates of u given by u
γ 2SLS . Using these u
directly apply the moment conditions in Kapoor, Kelejian, and Prucha (2007) to
obtain estimates of ρ and the variance components σν2 and σµ2 .4 This is true even
though the columns in Z are correlated with u (see Kelejian and Prucha, 2004;
Drukker, Egger, and Prucha, 2010; and Badinger and Egger, 2011; for a set
of assumptions accommodating the endogenous regressors in Z). The moment
conditions are given by
1
ε0 Q0 ε
N (T − 1)
1
ε0 Q0 ε
N (T − 1)
1
ε0 Q0 ε
N (T − 1)
1 0
ε Q1 ε
N
1 0
ε Q1 ε
N
1 0
ε Q1 ε
N
= σν2
= σν2
=
1
tr(W0 W)
N
0
= σ12
= σ12
=
1
tr(W0 W)
N
0,
where ε ≡ (IT ⊗ W)ε and σ12 = T σµ2 + σν2 . These can be rewritten in terms of
u using the fact that ε = (IT ⊗ [IN − ρW])u = u − ρu whereby u ≡ (IT ⊗ W)u
and ε ≡ (IT ⊗ W)(IT ⊗ [IN − ρW])u = u − ρu with u ≡ (IT ⊗ W)u.
The resulting moment conditions are then stacked and solved as a solution
to the system of six equations in three unknowns. More formally, γ − Γα = 0,
4 Note
that this is different from the pooled OLS residuals used in Kapoor, Kelejian, and
Prucha (2007). In the Hausman and Taylor (1981) case, the OLS residuals would lead to
inconsistent estimates of u due to the correlation of [XC , ιT ⊗ ZC ] with µ.
8
where

1
0
N (T −1) u Q0 u






γ=















Γ=













1
0

N (T −1) u Q0 u 
,
1 0

N u Q1 u


1 0

N u Q1 u

1 0
u
Q
u
1
N

0
1
N (T −1) u Q0 u
ρ

 2
 ρ
α=
 2
 σν

σ12




.



0
−1
N (T −1) u Q0 u
0
−1
N (T −1) u Q0 u
1
0
N trW W
0
−1
N (T −1) u Q0 u
0
2 0
N u Q1 u
2 0
N u Q1 u
−1 0
N u Q1 u
−1 0
N u Q1 u
0
0
−1 0
N u Q1 u
0
2
0
N (T −1) u Q0 u
0
2
N (T −1) u Q0 u
1
0
N (T −1) (u Q0 u
1
0
N (u Q1 u
+ u0 Q0 u)
+ u Q1 u)
(5)
1

0
0






0


.
1


1
0

trW
W
N



0

0
(6)
For estimation, u, u, and u are replaced by their corresponding consistent estimates û, û, and û. As in Kapoor, Kelejian, and Prucha (2007):
α̂ = (ρ̂, σ̂ν , σ̂1 ) = arg
min
σν2 ∈Sν ,σ12 ∈S1 ,ρ∈Sρ
γ̂ − Γ̂α̂
0
Ĵ γ̂ − Γ̂α̂
,
(7)
where Sν , S1 , and Sρ denote the respective admissible parameter spaces of σν2 ,
σ12 , and ρ, and Ĵ denotes a suitable estimate of the true weighting matrix of
the moment vector, J. In a data-set which is as large as ours and involves a
matrix W of size 12, 552×12, 552, it is advisable to solve the moment conditions
in two parts. First, solve the three moment conditions involving Q0 (using a
moments weighting matrix I3 ) for ρ̂ and σ̂ν2 , and subsequently the remaining
moment conditions or just one of them for σ̂12 . With these estimates at hand,
calculate the weighting matrix matrix Υ̂

Υ̂ = 
1
4
T −1 σ̃v
0
0
σ̃14
9

 ⊗ I3 .
(8)
Replacing Ĵ with Υ̂ and applying nonlinear least squares to eq. (7) using all six
moment conditions yields an estimate for ρ (for details, see Kapoor, Kelejian,
and Prucha, 2007).
STEP 4 - The spatial Hausman-Taylor estimator: Let us denote the
variance-covariance matrices of u, ε, and ν by Ωu , Ωε , and Ων , respectively.
By the assumptions given in subsection 2.2:
Ων = σν2 IT N , Ωε = σµ2 (JT ⊗ IN ) + σν2 IT N ,
(9)
and
Ωu = [IT N − ρ(IT ⊗ W)]−1 [σµ2 (JT ⊗ IN ) + σν2 IT N ][IT N − ρ(IT ⊗ W)]−1 , (10)
see Baltagi (2008). Notice that premultiplying the model by [IT N − ρ̂(IT ⊗ W)],
where ρ̂ is obtained from step 3, leads to spatially Cochrane-Orcutt-transformed
variables y∗ , Z∗ , and u∗ . In general, variables with one star as a superscript,
e.g., vector y∗ , are defined as y∗ = [IT N − ρ̂(IT ⊗ W)]y. Next, we apply
the Fuller and Battese (1973, 1974) transformation which uses the fact that
−1/2
bε
σ̂ν Ω
= Q0 +
σ̂ν
σ̂1 Q1 ,
where σ̂ν and σ̂1 are obtained from step 3. We denote
such variables by two stars as a superscript and they reflect vectors such as
b −1/2
y∗ = (IT N − θ̂Q1 )y∗ with θ̂ = 1 −
y∗∗ = σ̂ν Ω
ε
σ̂ν
σ̂1 .
Since ιT ⊗ Z∗C in Z∗ is
still correlated with µ in u∗ , we still need an instrumental variable procedure
to estimate the double-starred transformed model. The Hausman and Taylor
(1981) spatially transformed set of instruments is given by:
A∗SHT
=
[Q0 X∗ , Q1 X∗U , ιT ⊗ Z∗U ]
(11)
P∗SHT
=
∗
−1 ∗0
A∗SHT (A∗0
ASHT .
SHT ASHT )
(12)
This estimator removes the error component structure as well as the spatial
autocorrelation from the process in equation 4. Note that (11) holds because
10
(IT ⊗ W)Qs = Qs (IT ⊗ W) for s = 0, 1. Also,
[IT N − ρ̂(IT ⊗ W)](ιT ⊗ ZU ) = (ιT ⊗ ZU ) − ρ̂(ιT ⊗ WZU ) = ιT ⊗ Z∗U , (13)
where Z∗U = ZU − ρ̂WZU . The spatial Hausman-Taylor estimator (SHT) is
then defined as a 2SLS estimator of y∗∗ on Z∗∗ with the matrix of instruments
A∗SHT . More formally:
0
0
δ̂ SHT = (Z∗∗ P∗SHT Z∗∗ )−1 Z∗∗ P∗SHT y∗∗ .
(14)
This can be contrasted with a spatial fixed effects (SFE) estimator (see Mutl
and Pfaffermayr, 2011) defined as
β̂ SF E = (X∗0 Q0 X∗ )−1 X∗0 Q0 y∗ .
(15)
The latter corresponds to a fixed effects estimator which is applied to the spatially Cochrane-Orcutt-transformed model. This has an advantage over the
standard fixed effects estimator in that it takes into account the spatial correlation. However, it shares the same disadvantage of the standard fixed effects
estimator in that it does not deliver an estimate of γ. Such estimates could
have been obtained with a spatial random effects estimator (SRE) of the form
δ̂ SRE = (Z∗∗0 Z∗∗ )−1 Z∗∗0 y∗∗ ,
(16)
but they would be inconsistent under the adopted assumptions. One way of
checking whether Z is correlated with µ, is to apply the Hausman (1978) test
m̂SH = (β̂ SRE − β̂ SF E )0 [V ar(β̂ SF E ) − V ar(β̂ SRE )]− (β̂ SRE − β̂ SF E ), (17)
where superscript “ − ” in eq. 17 refers to the generalized inverse. m̂SH is
distributed as χ2 (rank[V ar(β̂ SF E ) − V ar(β̂ SRE )]− ) under the null hypothesis
of no correlation between Z and µ. If the null is rejected, then δ̂ SRE is not
11
consistent. In this case, one can check the choice of [XU , ιT ⊗ ZU ], i.e., the
choice of regressors uncorrelated with µ, by applying the Hausman test based
on the contrast between β̂ SHT and β̂ SF E . This is given by:
m̂SHT = (β̂ SHT − β̂ SF E )0 [V ar(β̂ SF E ) − V ar(β̂ SHT )]− (β̂ SHT − β̂ SF E ) (18)
and is distributed as χ2 (KU − RC ) where KU − RC is the degree of overidentification.
Alternative sets of instruments to ASHT can be formulated in the spirit
of Amemiya and MaCurdy (1986) (ASAM ) and Breusch, Mizon, and Schmidt
(1989) (ASBM S ):
A∗SAM
=
0∗
∗
[Q0 X∗ , X0∗
U 1 , ..., XU T , ιT ⊗ ZU ],
A∗SBM S
=
0∗
0∗
0∗
∗
∗
[Q0 X∗ , Q0 X0∗
U 1 , ..., Q0 XU T , Q0 XC1 , ..., Q0 XCT , Q1 XU , ιT ⊗ ZU ],
where X0U t = XU t ⊗ ιT is a T N × KU matrices for all t = 1, ..., T .
3
3.1
Empirical analysis
Data and descriptive statistics
We use data on output, factor usage, ownership characteristics, and export market participation for 12,552 Chinese firms in the chemical industry as compiled
by the National Bureau of Statistics of China (NBS) over the period 2004-2006.
The data-set covers all Chinese firms with an annual turnover exceeding five
million Yuan (about 700,000 US dollars). In particular, we use data on log of
sales for firm i at year t (yit ) as the outcome variable of interest and model
it as a function of the following regressors: log of employment (lit ); the share
of high-skilled workers (hi ), which is defined as the fraction of workers with a
university or comparable education (it is only available for 2004 and treated as
time-invariant as indicated by the single subscript); log of capital used in production (kit ); and log of material inputs (mit ); a binary export status indicator
12
which takes the value one if the firm is an exporter, and zero otherwise (eit );
foreign ownership which is measured by the share of capital provided by foreign
investors (fit ); an indicator variable for the intensive use of intangible relative
to total assets (iit ); and a binary public ownership status indicator which takes
the value one if the firm is publicly-owned (i.e. state-owned) and zero otherwise
(pi ). The latter is time-invariant for the Chinese chemical industry and the
time-period covered by our data.
Apart from the main technology parameters, we are interested in estimating
the impact of public ownership on output, while allowing for spillover effects in
unspecified (remainder) total factor productivity across firms.
– Table 1 about here –
Table 1 summarizes the descriptive statistics for our data in two panels.
The upper panel reports the mean, standard deviation, minimum, and maximum for all variables, firms, and years covered. The lower panel reports the
mean and standard deviation for state-owned as compared to privately-owned
enterprises. Note that 5 percent of the firms in the data are state-owned, and
they have on average more employees than privately-owned firms (about 793
versus 166 employees on average). Second, about 24 percent of all firms considered participate in the export market. Also, export market participation
is higher for state-owned firms as compared to privately-owned enterprises (29
versus 23 percent). Third, many firms in that sector use intangible assets relatively intensively – which is consistent with the innovative pressure and the
relative patent intensity in the manufacturing of chemicals. The relative intangible asset intensity is relatively higher for state-owned units as compared to
privately-owned ones (59 compared to 42 percent). Fourth, about 19 percent
of all firms are at least partly foreign owned. The ratio of foreign capital to
total capital is 0.14 for all firms on average. It is lower for state-owned than for
privately-owned ones (0.06 versus 0.14).
This firm level data-set contains information about the postcodes of firms
which identify the geographical location of all entities uniquely in terms of the
13
longitude and latitude of a firm’s residence. The latter enables calculating great
circle distances between all units, using the so-called haversine formula.5
– Figures 1a and 1b about here –
We define counties as regional aggregates using the first four digits of the
postcode. This yields 2, 425 regional aggregates/counties all over China. Figure
1a colors counties according to the number of firms in the chemical industry,
while Figure 1b colors counties according to total employment in that industry.
According to Figures 1a and 1b, 1, 610 of the 2, 425 counties in China do not host
any chemical producer. Most of all inhabited regions host less than 10 firms.
As expected, coastal regions have a higher density of firms. This pattern also
holds for the number of employees in the chemical sector. In general, Figure 1b
looks quite similar to Figure 1a. However, careful inspection of the data shows
that Wenzhou in the coastal province of Zhejiang is the region with the largest
number of chemical producers, while Jinjiang in the coastal province of Fujian
is the biggest regional employer in the chemical industry.
3.2
Specification
For estimation, we use a flexible translog production technology, which also
nests the more restrictive Cobb Douglas technology. The vectors of inputs k,
l, ιT ⊗ h, and m, represent primary production factors; while the vectors e,
f , i, and ιT ⊗ p, along with the disturbance term u, reflect measurable and
unmeasurable aspects of total factor productivity. The time-invariant variables
are Z = [h, h2 , p], and the right-hand-side regressors for the primal translog
5 The haversine formula is particularly suited for calculating great circle distances between
two points i and j on the globe, if these two points are very close to each other. Denote the
haversine function of an argument ` by h(`) = 0.5(1 − cos(`)), and use φi , φj , and ∆λij to
refer to the latitude of i, the latitude of j, and the difference in longitudes between i and j
which are all measured in radians. Then, the haversine distance between i and j is defined
1/2
as dij = D · arcsin(Hij ), where D is the diameter of the globe (e.g., measured in miles) and
Hij = h(φi − φj ) + cos(φi ) cos(φj )h(∆λij ).
14
production function are as follows:
[X, ιT ⊗ Z]
=
[k, l, ιT ⊗ h, m, k2 , l2 , m2 , (ιT ⊗ h)2 , k ◦ l,
k ◦ m, l ◦ m, (ιT ⊗ h) ◦ k, (ιT ⊗ h) ◦ l, (ιT ⊗ h) ◦ m,
e, f , i, ιT ⊗ p],
(19)
where ◦ denotes element-wise products.6 In general, we do not enforce linear
homogeneity of the technology by restricting the parameters on the quadratic
and interactive terms to sum up to unity (see Greene, 2008). Linear homogeneity
of the production technology is refuted by the data at hand.
The Cobb Douglas counterpart to this model would have the following regressors:
[X, ιT ⊗ Z] = [k, l, ιT ⊗ h, m, e, f , i, ιT ⊗ p],
which restricts the quadratic and interactive terms in to be zero. Since the Cobb
Douglas model is generally rejected for the data at hand, we will only report
parameter estimates for the more flexible translog model.
In the next subsection, we consider the case where W0 is full, so that any
distance matters and spillovers may occur between all firms in the chemical
industry. We consider three alternative cases for the elements of W0 in a sen0
sitivity analysis. The first alternative specifies wij
= 0 if dij > 200 miles, the
0
second alternative specifies wij
= 0 if dij > 100 miles, and the third alternative
0
specifies wij
= 0 if dij > 50 miles.
3.3
Estimation results
We report parameter estimates of translog production functions in primary form
in Tables 2 and 3. These tables contain parameters and test statistics for fixed
6 Notice that we do not interact vectors e, f , i, ι ⊗ p. There is no principal argument
T
against allowing for even more flexibility in interacting these vectors with each other and with
the primary production factors. However, e, i, ιT ⊗ p represent vectors of binary variables
so that using an even more flexible form drastically increases the degree of multicollinearity
among the regressors. Therefore, we choose the form in (19) (see Burkett and Škegro, 1989;
and Liang, 2008; for earlier examples in that vein).
15
effects (FE), random effects (RE), Hausman and Taylor (HT), and Breusch,
Mizon, and Schmidt (BMS) type models. Table 2 reports parameter estimates
and test statistics for specifications assuming that there are no spillovers in u
so that ρ = 0, while Table 3 reports parameter estimates and test statistics for
specifications allowing that ρ 6= 0.7
– Table 2 about here –
The results in Table 2 can be summarized as follows: First, the Hausman
tests generally reject the absence of correlation of the regressors and the timeinvariant error term. Hence, there is evidence of misspecification in the RE
and SRE results, and the corresponding parameter estimates are inconsistent
and subject to misleading inference. Second, for the HT and BMS instrument
set, we find a high joint degree of relevance in the first-stage regression (with
triple-digit F-statistics) and both sets of instruments pass the Hausman test as
shown in Table 2.
Third, export market participation (eit ), foreign ownership (fit ) , and state
ownership (pit ) are found to be statistically significant, while intensive use of intangible assets (iit ) does not display a significant impact on TFP. In fact, export
market participation and foreign ownership raise TFP, while state ownership reduces it. The comparison among the RE, HT, and BMS models suggests that
state ownership is endogenous and its effect can not be estimated consistently
by way of the RE model.
However, it should be borne in mind that the test statistics and standard
errors in Table 2 are misleading (inconsistent) in case of an ignored spatial
autocorrelation (ρ 6= 0) in u.
– Table 3 about here –
Table 3 describes the results when accounting for spatial correlation in the
error term and applying the procedure described in Section 2.8 The standard
7 In Table 2, 3, and 4 the elements of X
U are m, m ◦ m, h ◦ m, e; the elements of XC are
l, l ◦ l, l ◦ h, k, k ◦ k, k ◦ h, k ◦ l, f , i; the elements of ZU are h, h ◦ h; the element of ZC is p.
8 For the SHT estimator, we use the residuals from the HT model to estimate ρ for the
subsequent spatial Cochrane-Orcutt transformation. Similarly, for the SFE and the SBMS
16
error of ρ is estimated by following Badinger and Egger (2013). Our estimates of
the spatial autocorrelation parameter on Wb
u, ρb, are 0.386 and 0.389 for the SFE
and SRE estimators, and 0.291 and 0.338 for the SHT and SBMS estimators,
respectively. All estimates of ρ are statistically significant. As in the nonspatial models, the set of instruments performs well in terms of significance.
The Hausman test does not reject the SHT and the SBMS model using this set
of instruments.
The estimates of all measurable shifters of TFP are statistically significant
in the SHT and SBMS models. Exporting, foreign ownership and the intensive
use of intangible assets raise TFP, while public ownership reduces it.
The spatial model suggests that publicly-owned companies’ TFP is between
100 · (exp(−1.167) − 1) ≈ 70 and 100 · (exp(−1.602) − 1) ≈ 80 percent lower
than that for privately-owned companies in China’s chemical industry. Hence,
significant efficiency gains could be had with privatization in that industry.
Shocks in TFP display significant spillover effects across firms, and they are
geographically bound. Providing a more detailed assessment of the geographical
reach of such spillovers is the goal of the next subsection.
3.4
Sensitivity checks and quantification of spillovers
In this section, we explore the sensitivity of our estimates to alternative weights
matrices differing by the specification of the spatial decay function.9 We report
the sensitivity checks in Table 4 focusing on the SHT estimator.
– Table 4 about here –
The three columns of Table 4 involve weights matrices that are based on positive cell entries wij if firms i and j are closer than 50 miles (W50 ), 100 miles
(W100 ), or 200 miles (W200 ), respectively. Hence, the results based on W50 cormodels we employ the residuals of the FE and BMS estimators to do so, respectively. For the
SRE model we follow Kapoor, Kelejian, and Prucha (2007) and use the pooled OLS residuals.
9 However, there is limited scope for sensitivity checks, since estimating spatial models in
a data-set as large as ours and with a non-sparse weighting matrix of size 12, 552 × 12, 552 is
very computer intensive.
17
respond to the sparsest weights matrix considered, and in turn, all weights matrices W50 , W100 , and W200 are sparser than the original W matrix. With row
PN
PN
0
0
normalization, it will generally be the case that j=1 w50,ij
≤ j=1 w100,ij
≤
PN
P
N
0
0
j=1 w200,ij ≤
j=1 wij . Therefore, the positive individual cells of the respective matrices have the property 0 < wij ≤ w200,ij ≤ w100,ij ≤ w50,ij ≤ 1. If
spillovers were equally strong between far-away and closeby firms, this feature
would be consistent with the finding that ρ̂50 < ρ̂100 < ρ̂200 < ρ̂. Since this
is not the case but there is evidence of the opposite, we would conclude that
spillovers are stronger among closeby entities. Other than that, our findings
from Tables 3 and 4 are qualitatively unaffected by the choice of the weighting
scheme considered.
How strong are spillovers in China’s chemical industry? There are numerous
ways of assessing this question. One of them is to consider the impact of a
common shock on total factor productivity of all firms in the sample. Suppose,
we considered a shock of one percent in TFP. The specification of W – in
particular, its row normalization – suggest that such a uniform shock will trigger
a uniform response in output across all firms of
1
1−ρ̂
percent. Using the SHT
model in Table 3, we would conclude that the response is about 1.41 percent.
Hence, the results suggest that there is a multiplier to shocks of 1.41 due to
spillovers. Hence, TFP shocks will be amplified by more than one-third due to
spillovers among chemical producers in China.
4
Conclusions
This paper combines ideas put forward by Hausman and Taylor (1981) for estimating the coefficients of time-invariant regressors which may be correlated
with the firm effects, with those of Kapoor, Kelejian, and Prucha (2007) on
estimating random effects models with spatial interdependence. It applies the
spatial Hausman-Taylor model to the estimation of a translog production function for the Chinese chemical industry. The data-set utilized in this study
consists of a large cross section of 12,552 firms observed annually over the short
18
period of 2004–2006. The proposed estimator allows some of the regressors to be
time-invariant and perhaps correlated with the unobservable firm effects. This
estimator has some advantages over the spatial fixed effects or random effects
estimators. In fact, the spatial fixed effects estimator does not provide estimates
of the time-invariant variables since they are wiped out by the within transformation. Also, the random effects estimates suffer from bias and inconsistency
when the regressors are correlated with the firm effects.
The firms in the data are concentrated in the coastal area of China. We
estimate a translog production function in primal form and find that the Cobb
Douglas production function restrictions are rejected by the data, and so is the
assumption of linear homogeneity of the technology. The estimated size of the
spatial autocorrelation parameter suggests that there are important spillover
effects across firms. We estimate that a common shock on all producers is amplified by more than one-third due to geographical spillovers. While the strength
of spillovers could have been estimated by means of a spatial fixed effects estimator, our results unveil insights that could not have been drawn from fixed
effects estimates. For instance, we are able to discern permanent and transitory
elements of observable and unobservable components in total factor productivity and find that time-invariant components dominate. This is not possible with
spatial fixed effects estimates, since they wipe out the time-invariant primary
production factors such as skilled labor in our data and the time-invariant determinants of total factor productivity such as public ownership. We find evidence
of significant detrimental effects of public ownership on total factor productivity.
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5
Tables and Figures
24
Table 1: Descriptive statistics
All firms
Variable
Total sales (in logs)
Mean
Std.dev.
Minimum
Maximum
10.341
1.275
4.382
16.749
9.862
Employment (in logs)
4.525
1.094
1.609
Skilled labor ratio (fraction)
0.175
0.188
0
1
Capital used in production (in logs)
8.823
1.686
2.303
15.954
Material (in logs)
9.828
1.349
2.565
16.356
State-owned (binary indicator)
0.053
0.224
0
1
Foreign-owned-to-total-capital ratio (fraction)
0.140
0.320
0
1
Exporter (binary indicator)
0.236
0.425
0
1
Intangible assets intensity (binary indicator)
Number of firms
0.431
0.495
12552
0
1
37656
Number of observations
State-owned vs. non-state owned firms
Variable
Total sales (in logs)
Employment (in logs)
Skilled labor ratio (fraction)
State-owned firms
Mean
Non state-owned firms
Std.dev.
Mean
Std.dev.
10.889
1.931
10.311
1.221
5.625
1.482
4.464
1.034
0.226
0.184
0.172
0.187
Capital used in production (in logs)
10.315
2.124
8.740
1.619
Material (in logs)
10.203
2.089
9.807
1.293
Foreign-owned-to-total-capital ratio (fraction)
0.064
0.186
0.144
0.326
Exporter (binary indicator)
0.292
0.455
0.233
0.423
Intangible assets intensity (binary indicator)
Number of firms
0.590
662
0.492
0.422
11890
0.494
Number of observations
1986
35670
Table 2 - Non-spatial translog specification: The Chinese chemical industry (2004-2006)
Dependent variable: total sales (in logs)
Non-spatial translog estimates
RE
HT
Acronym
FE
BMS
Capital (in logs)
kit
Labor (in logs)
lit
Skilled labor ratio (fraction)
hi
Material (in logs)
mit
Capital × capital
kitkit
Capital × labor
kitlit
Capital × skilled labor ratio
kithi
Capital × material
kitmit
Labor × labor
litlit
Labor × skilled labor ratio
lithi
Labor × material
litmit
Skilled labor ratio × skilled labor ratio
hihi
Skilled labor ratio × material
himit
Material × material
mitmit
0.126***
(0.021)
0.619***
(0.031)
-0.184***
(0.021)
0.007***
(0.001)
0.020***
(0.003)
-0.056**
(0.018)
-0.028***
(0.002)
0.018***
(0.003)
0.228***
(0.026)
-0.091***
(0.003)
-0.262***
(0.014)
0.082***
(0.001)
0.158***
(0.013)
0.489***
(0.018)
0.951***
(0.081)
0.032*
(0.014)
0.011***
(0.001)
0.016***
(0.002)
0.049***
(0.009)
-0.038***
(0.002)
0.030***
(0.002)
0.222***
(0.014)
-0.082***
(0.002)
0.078
(0.044)
-0.216***
(0.009)
0.076***
(0.001)
0.066**
(0.024)
0.533***
(0.037)
1.662***
(0.126)
-0.203***
(0.025)
0.011***
(0.002)
0.022***
(0.004)
-0.016
(0.019)
-0.029***
(0.003)
0.026***
(0.004)
0.272***
(0.030)
-0.088***
(0.004)
-0.181**
(0.067)
-0.227***
(0.016)
0.084***
(0.002)
0.095***
(0.022)
0.568***
(0.033)
1.489***
(0.110)
-0.152***
(0.021)
0.011***
(0.001)
0.019***
(0.003)
-0.015
(0.017)
-0.030***
(0.002)
0.026***
(0.004)
0.275***
(0.026)
-0.090***
(0.003)
-0.074
(0.058)
-0.222***
(0.014)
0.083***
(0.001)
0.043*
(0.018)
0.021**
(0.007)
0.004
(0.006)
-
0.065***
(0.007)
0.019***
(0.005)
-0.006
(0.004)
-0.101***
(0.011)
0.048*
(0.019)
0.014*
(0.007)
0.010
(0.007)
-1.625***
(0.112)
0.057***
(0.017)
0.016**
(0.006)
0.009
(0.006)
-1.132***
(0.078)
2
Total specified TFP (fit,eit,pi,uit)
y
2
P
2
T
1.626
-
1.626
1.492
0.001
1.626
1.579
0.133
1.626
1.546
0.065
Between component of unspecified TFP
Within component of unspecified TFP
2
2

0.279
0.036
0.062
0.036
0.171
0.036
0.113
0.036
Primary production factors
Elements of total factor productivity (TFP)
Foreign-owned-to-total-capital ratio (fraction)
fit
Exporter (binary indicator)
eit
Intangible asset intensity (binary indicator)
iit
Publicly-owned (State-owned; binary indicator)
pi
Variance components
Dependent variable (yit)
Primary production factors
Hausman test/Hausman and Taylor test
2-statistic
928.221
4.447
41.152
Degrees of freedom
15
3
33
p-value
0.00
0.22
0.16
First stage
F-statistic for joint instrument relevance
376.264
376.264
Degrees of freedom
4
4
p-value
0.00
0.00
Notes: *, **, and *** refer to significant parameters and test statistics at 5%, 1%, and 0.1%, respectively. FE refers to fixed effects, RE
to random effects, HT to Hausman and Taylor (1981) and BMS to Breusch, Mizon, and Schmidt (1989). Elements of XU: m, m◦ m,
h◦m, e. Elements of XC: l, l◦l. l◦h, k, k◦k, k◦h, k◦l, f, i. Elements of ZU: h, h◦h. Elements of ZC: p. There are 12,552 firms and 37,656
observations.
Table 3 - Spatial translog specification: The Chinese chemical industry (2004-2006)
Dependent variable: total sales (in logs)
Spatial translog estimates
SRE
SHT
Acronym
SFE
SBMS
Capital (in logs)
kit
Labor (in logs)
lit
Skilled labor ratio (fraction)
hi
Material (in logs)
mit
Capital × capital
kitkit
Capital × labor
kitlit
Capital × skilled labor ratio
kithi
Capital × material
kitmit
Labor × labor
litlit
Labor × skilled labor ratio
lithi
Labor × material
litmit
Skilled labor ratio × skilled labor ratio
hihi
Skilled labor ratio × material
himit
Material × material
mitmit
0.096***
(0.020)
0.629***
(0.031)
-0.168***
(0.021)
0.005***
(0.001)
0.020***
(0.003)
-0.032
(0.018)
-0.023***
(0.002)
0.021***
(0.003)
0.186***
(0.026)
-0.093***
(0.003)
-0.248***
(0.014)
0.079***
(0.001)
0.142***
(0.013)
0.493***
(0.018)
0.943***
(0.081)
0.027
(0.014)
0.010***
(0.001)
0.016***
(0.002)
0.050***
(0.009)
-0.035***
(0.002)
0.031***
(0.002)
0.222***
(0.014)
-0.083***
(0.002)
0.064
(0.044)
-0.215***
(0.009)
0.074***
(0.001)
0.037
(0.023)
0.540***
(0.035)
1.665***
(0.125)
-0.190***
(0.024)
0.011***
(0.001)
0.021***
(0.004)
-0.008
(0.018)
-0.026***
(0.002)
0.030***
(0.004)
0.237***
(0.028)
-0.090***
(0.004)
-0.182**
(0.068)
-0.221***
(0.015)
0.082***
(0.001)
0.054**
(0.021)
0.569***
(0.031)
1.547***
(0.113)
-0.154***
(0.020)
0.011***
(0.001)
0.019***
(0.003)
-0.007
(0.016)
-0.026***
(0.002)
0.030***
(0.003)
0.236***
(0.025)
-0.093***
(0.003)
-0.098
(0.062)
-0.217***
(0.013)
0.081***
(0.001)
0.043*
(0.017)
0.026***
(0.007)
0.010
(0.006)
-
0.066***
(0.007)
0.023***
(0.005)
0.002
(0.004)
-0.102***
(0.011)
0.052**
(0.018)
0.019**
(0.006)
0.016*
(0.006)
-1.602***
(0.113)
0.060***
(0.016)
0.022***
(0.006)
0.015**
(0.006)
-1.167***
(0.083)
y
2
P
2
T
2
1.547
-
1.546
1.403
0.001
1.563
1.500
0.126
1.555
1.457
0.067

2

2
0.249
0.034
0.060
0.035
0.164
0.035
0.114
0.035

0.386***
(0.005)
0.389***
(0.002)
0.291***
(0.012)
0.338***
(0.008)
Primary production factors
Elements of total factor productivity (TFP)
Foreign-owned-to-total-capital ratio (fraction)
fit
Exporter (binary indicator)
eit
Intangible asset intensity (binary indicator)
iit
Publicly-owned (State-owned; binary indicator)
pi
Variance components
Dependent variable (y it)
Primary production factors (k it,lit,hi,mit)
Total specified TFP (f it,eit,pi)
Between component of unspecified TFP
Within component of unspecified TFP
Spatial autocorrelation parameter
Hausman test/Hausman and Taylor test
2
 -statistic
1295.709
3.248
36.642
Degrees of freedom
15
3
33
p-value
0.00
0.35
0.30
First stage
F-statistic for joint instrument relevance
377.442
377.783
Degrees of freedom
4
4
p-value
0.00
0.00
Notes: *, **, and *** refer to significant parameters and test statistics at 5%, 1%, and 0.1%, respectively. FE refers to fixed effects, RE
to random effects, HT to Hausman and Taylor (1981) and BMS to Breusch, Mizon, and Schmidt (1989). Elements of XU: m, m◦ m,
h◦m, e. Elements of XC: l, l◦l. l◦h, k, k◦k, k◦h, k◦l, f, i. Elements of ZU: h, h◦h. Elements of ZC: p. There are 12,552 firms and 37,656
observations.
Table 4 -Spatial translog specification: The Chinese chemical industry (2004-2006)
Dependent variable: total sales (in logs)
Acronym
Spatial translog Hausman Taylor estimates
W200
W100
W50
Primary production factors
Capital (in logs)
kit
Labor (in logs)
lit
Skilled labor ratio (fraction)
hi
Material (in logs)
mit
Capital × capital
kitkit
Capital × labor
kitlit
Capital × skilled labor ratio
kithi
Capital × material
kitmit
Labor × labor
litlit
Labor × skilled labor ratio
lithi
Labor × material
litmit
Skilled labor ratio × skilled labor ratio
hihi
Skilled labor ratio × material
himit
Material × material
mitmit
0.046
(0.024)
0.543***
(0.036)
1.667***
(0.126)
-0.195***
(0.025)
0.012***
(0.002)
0.021***
(0.004)
-0.011
(0.018)
-0.027***
(0.002)
0.029***
(0.004)
0.250***
(0.029)
-0.090***
(0.004)
-0.187**
(0.068)
-0.223***
(0.015)
0.083***
(0.002)
0.053*
(0.024)
0.539***
(0.037)
1.664***
(0.126)
-0.199***
(0.025)
0.012***
(0.002)
0.021***
(0.004)
-0.013
(0.019)
-0.027***
(0.002)
0.028***
(0.004)
0.258***
(0.029)
-0.089***
(0.004)
-0.187**
(0.067)
-0.224***
(0.016)
0.083***
(0.002)
0.058*
(0.024)
0.537***
(0.037)
1.665***
(0.126)
-0.201***
(0.025)
0.012***
(0.002)
0.021***
(0.004)
-0.014
(0.019)
-0.028***
(0.003)
0.027***
(0.004)
0.264***
(0.030)
-0.089***
(0.004)
-0.186**
(0.067)
-0.226***
(0.016)
0.084***
(0.002)
0.051**
(0.019)
0.017**
(0.007)
0.014*
(0.007)
-1.649***
(0.115)
0.050**
(0.019)
0.015*
(0.007)
0.012
(0.007)
-1.651***
(0.114)
0.049*
(0.019)
0.015*
(0.007)
0.012
(0.007)
-1.646***
(0.114)
y2
P2
T2
1.579
1.528
0.134
1.594
1.546
0.135
1.606
1.559
0.135
2
2
0.171
0.035
0.172
0.036
0.172
0.036

0.312***
(0.014)
0.304***
(0.015)
0.292***
(0.016)
Elements of total factor productivity (TFP)
Foreign-owned-to-total-capital ratio (fraction)
fit
Exporter (binary indicator)
eit
Intangible asset intensity (binary indicator)
iit
Publicly-owned (State-owned; binary indicator)
pi
Variance components
Dependent variable (yit)
Primary production factors (kit,lit,hi,mit)
Total specified TFP (fit,eit,pi)
Between component of unspecified TFP
Within component of unspecified TFP
Spatial autocorrelation parameter
Hausman test/Hausman and Taylor test
2-statistic
2.601
3.442
3.994
Degrees of freedom
3
3
3
p-value
0.46
0.33
0.26
First stage
F-statistic for joint instrument relevance
372.159
365.322
359.006
Degrees of freedom
4
4
4
p-value
0.00
0.00
0.00
Notes: *, **, and *** refer to significant parameters and test statistics at 5%, 1%, and 0.1%, respectively. W50, W100, and
W200 refer to weights matrices whose elements are zero if distance>50 miles, distance>100 miles, and distance>200
miles, respectively. Elements of XU: m, m◦m, h◦m, e. Elements of XC: l, l◦l. l◦h, k, k◦k, k◦h, k◦l, f, i. Elements of ZU: h,
h◦h. Elements of ZC: p. There are 12,552 firms and 37,656 observations.