Download Protection for Sale Under Monopolistic Competition

Protection for Sale Under Monopolistic Competition: An Empirical
Investigation
Pao-Li Chang∗
Myoung-Jae Lee
School of Economics and Social Sciences
Singapore Management University, Singapore 259756
April 26, 2005
Abstract
Previous cross-sectional empirical work based on Grossman and Helpman (1994) has often
adopted homogeneous (perfect competition) market structure. Nonetheless, Chang (2005) suggests that the endogenous protection structure under the political framework of G-H changes
systematically when the underlying market structure is characterized by monopolistic competition instead of perfect competition. In this paper, we adopt a general empirical specification that
accommodates both monopolistically competitive sectors and perfectly competitive sectors. Our
results favor the general specification of heterogeneous market structures over the homogeneous
perfect competition specification. This empirical finding thus suggests an intricate relationship
between import protection and import penetration: it depends on whether the sector is perfectly
competitive or monopolistically competitive and whether the sector is politically organized or
not.
Keywords: endogenous trade policy; campaign contribution; monopolistic competition; intraindustry trade; import penetration
JEL classification: F12; F13
∗
Tel: +65-6822-0830; fax: +65-6822-0833. E-mail address: [email protected] (P.-L. Chang).
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1.
INTRODUCTION
Chang (2005) suggests that the endogenous protection structure under the political framework
of Grossman and Helpman (1994) (henceforth G-H) changes systematically when the underlying
market structure is characterized by monopolistic competition instead of perfect competition. First,
the benchmark welfare-maximizing import tariff is strictly positive, in contrast with the free trade
prediction under perfect competition. Secondly, lobbying efforts spent by competing interest groups,
each representing the owners of the factor specific to a sector, work to raise import protection levels
in organized sectors (represented by a lobby) and lower import protection levels in unorganized
sectors (not represented by a lobby), relative to the benchmark levels. The endogenous tariff
level, nonetheless, will not fall below zero in unorganized sectors. This is contrary to G-H where
unorganized sectors will be afforded negative protection. Lastly, the level of import protection is
predicted in Chang (2005) to vary inversely with the degree of import penetration, regardless of
whether the sector is organized or not. In other words, sectors with higher import penetration will
receive lower protection. This negative relationship applies only to organized sectors in G-H; in
unorganized sectors, higher import penetration leads to higher protection (or more precisely, less
negative protection).
The last theoretical prediction is especially of interest to empirical researchers. The general
perception before the G-H model was that a sector badly injured by imports would tend to receive
higher protection. This perception was supported by most of the empirical work conducted before
G-H; however, their findings were often derived using ad hoc regression models without theoretical
underpinnings. The G-H model presented a challenge to this conventional view, as it predicts
the otherwise for organized sectors. Several authors (Goldberg and Maggi, 1999; Gawande and
Bandyopadhyay, 2000; Eicher and Osang, 2002) have hence estimated the G-H model and put
this prediction to test. In general, their findings are supportive of the G-H model. The results of
Chang (2005) offer a picture completely at odd with the conventional view, as the import protection
actually falls with import penetration, regardless of whether the sector is organized or not. This
difference in findings between G-H and Chang (2005) suggests that the predictions of the G-H-type
model in this regard will depend on the nature of the market structure. Hence, a correctly-specified
empirical model relating to the G-H model should allow for heterogeneous responses of protection
to import penetration across sectors depending on the nature of the market structure. This has
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not been considered in previous cross-sectional G-H-type empirical work.
Our paper attempts to account for this heterogeneity explicitly in the estimation model. To do
this, we adopt the G-H model for perfectly competitive sectors and the Chang (2005) model for
monopolistically competitive sectors. It remains to be seen whether the Chang (2005) model will be
borne out by the data, and if it is, whether the general specification allowing both market structures
will provide a better fit to the data than the homogeneous perfect competition model. If the answers
are both positive, we may thus accept the estimates of the underlying political parameters derived
based on the general specification as being more representative of the economy under study than
suggested by previous estimates derived based on homogeneous perfect competition models.
The rest of the paper is organized as follows. In Section 2, we review the basic elements of G-H
and Chang (2005) and integrate the two models. In Section 3, we formulate the empirical model
for the general specification allowing heterogeneous market structures and explain the estimation
methodology. The general specification is then compared against the homogeneous perfect competition specification based on non-nested hypothesis tests. The results are given in Section 3.5.
Section 4 concludes. Technical notes regarding the estimation methodologies are given in the appendices.
2.
THE PROTECTION-FOR-SALE MODEL WITH
HETEROGENEOUS MARKET STRUCTURE
In this section, we integrate the original Protection-for-Sale model by Grossman and Helpman
(1994) and the modified model by Chang (2005). This construct allows the market structure to
be potentially heterogeneous across sectors. Thus, a sector can be either perfectly competitive or
monopolistically competitive. Suppose that a country is populated by individuals with identical
preferences, given by:
U = C0 +
n
X
Ui (Ci )
(1)
i=1
where Ci denotes consumption of good i, C0 denotes consumption of the numeraire good, and
Ui is an increasing concave function. The demand for good i implied by the preferences in (1)
0
is denoted Di (Pi ), where Di (·) is the inverse of Ui (·). The indirect utility of an individual with
P
income E is given by V = E + ni=1 Si (Pi ), where Si (Pi ) = Ui (Di (Pi )) − Pi Di (Pi ) is the consumer
3
surplus derived from good i. If sector i is a monopolistically competitive industry, Ci represents
the aggregate consumption of differentiated goods in sector i, with the aggregation following the
Dixit-Stiglitz functional form (Dixit and Stiglitz, 1977):
∗
mi
mi
X
X
1
%i
i
Ci = (
chi,k +
cf%i,k
) %i
k=1
0 < %i < 1
(2)
k=1
where chi,k (cf i,k ) is the consumption of home (foreign) variety k of good i and mi (m∗i ) is the
number of varieties of good i produced at home (abroad). The corresponding aggregate price level
Pi for the differentiated goods in sector i is:
∗
mi
mi
X
X
1
1−σi
i 1−σi
Pi = (
phi,k +
pf1−σ
i,k )
k=1
(3)
k=1
where phi,k (pf i,k ) is the consumer price for home (foreign) variety k of good i, and σi =
1
1−%i
>1
is the elasticity of substitution among different varieties of good i.
Good 0 (the numeraire) is taken to be a homogeneous good, produced one-to-one from labor,
and traded freely and costlessly, so that the wage is equal to one at home and abroad. Production
of the other goods requires labor and a sector-specific input. If sector i is a perfectly competitive
sector, the production technology exhibits constant returns to scale, and the various specific inputs
are available in inelastic supply. If sector i is a monopolistically competitive sector, each variety of
the differentiated goods is assumed to require a fixed amount of the sector-specific factor ki in order
to produce at all; after that, there is a constant unit labor requirement of θi . Thus, the number
of varieties produced at home in sector i is mi = K̄i /ki , where K̄i is the amount of sector-specific
factor i that the country is endowed with. The technology abroad to produce the differentiated
products is assumed to be the same as at home. Thus, the number of varieties produced abroad
in the same sector is m∗i = K̄i∗ /ki , where K̄i∗ is the amount of sector-specific factor i the foreign
country is endowed with.
Let the domestic import policy τi denote one plus the ad valorem import tariff rate and the domestic export policy si represent one plus the ad valorem export subsidy rate for sector i. Similarly,
let τi∗ and s∗i represent the corresponding foreign import and export policy for sector i, defined in
a similar way.
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Suppose sector i is a perfectly competitive sector and the world price is Pi∗ . Then, the domestic
price in sector i is Pi = τi Pi∗ if sector i is an import competing sector, and is Pi = si Pi∗ if sector i
is an export sector. The returns to specific factor i depend only on Pi and are denoted by Πi (Pi ).
0
It follows that the supply function of good i is Yi (Pi ) = Πi (Pi ).
Suppose sector i is a monopolistically competitive sector. Assume that there are a large number
of varieties (home and foreign combined) available to the consumer in sector i. Given the preferences
specified in (2), each variety’s producer faces an approximately constant elasticity of demand, σi .
Thus, with profit maximization, the producer of each variety charges the same price: phi,k =
phi = pf∗i =
θi σi
σi −1 ,
where pf∗i is the producer (and consumer) price in the foreign market for each
foreign variety of good i. Since the producer prices of the home and foreign varieties are the same,
the difference in the consumer prices of the home and foreign varieties in the domestic market
reflects the government interventions in trade: pf i =
τi
s∗i phi .
Thus, the aggregate price index for
differentiated good i in (3) can be simplified as:
Pi = phi (mi + m∗i (
1
τi 1−σi 1−σ
)
) i.
∗
si
(4)
The utility function Ui in (1) for monopolistically competitive sectors is assumed to take the functional form: Ui = Ei lnCi . This amounts to assuming that an individual allocates a fixed amount of
expenditure Ei on good i. The rest of the world is assumed to share the same preference structure,
but with a possibly different allocation of expenditure on various goods, Ei∗ . Given this, we can
derive the demand for a representative home and foreign variety of good i as:
chi =
1
Ei
∗
phi mi + mi ( sτ∗i )1−σi
(5)
i
cf i
( sτ∗i )1−σi
Ei
i
=
.
pf i mi + m∗i ( sτ∗i )1−σi
i
Similarly, a foreign individual will consume a representative home and foreign variety of good i
5
according to:
τ∗
chi∗
( sii )1−σi
Ei∗
= ∗
∗
phi mi ( τi )1−σi + m∗
i
si
cf∗i =
where phi∗ =
τi∗ ∗
s i pf i
(6)
Ei∗
1
∗
pf∗i mi ( τi )1−σi + m∗
i
si
is the consumer price abroad for a representative home variety of good i. Given
the domestic and foreign demand for its product, a representative home producer of differentiated
good i will produce at the scale of (N chi + N ∗ chi∗ ), where N (N ∗ ) is the total home (foreign)
population. Thus, the returns to the specific factor used in differentiated sector i are: Πi (τi , si ) =
mi (phi − θi )(N chi + N ∗ chi∗ ).
The net tariff revenue from sector i, expressed on a per capita basis, is given by:
1
Xi ]
N
N∗
1
cf i −
mi (1 − )phi chi∗ ]
N
si
Ri =(1 − Iim )(Pi − Pi∗ )[Ci −
+Iim [m∗i (τi − 1)
phi
s∗i
(7)
where Xi = Yi (Pi ) is the domestic output of good i in a perfectly competitive sector, and Iim is an
indicator variable, which equals one if sector i is a monopolistically competitive sector and equals
P
zero otherwise. It is assumed that the government redistributes the revenue R = ni=1 Ri from
trade policy evenly to each individual.
Summing indirect utilities over all individuals, and noting that aggregate income is the sum of
labor income, returns to specific factors and tariff revenue, one obtains aggregate welfare as:
W =N+
n
X
Πi + N
i=1
n
X
(Ri + Si ).
(8)
i=1
Next we describe the political structure. Suppose that in some subset of sectors L ⊂ {1, 2, · · · n}
the owners of specific factors are able to form a lobby. Let αi denote the fraction of population
that owns specific factor i. Assume that each individual owns a unit of labor and at most one type
of specific factor. Summing indirect utilities over all individuals who belong to lobby i, we obtain
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lobby i’s aggregate well-being:
Wi = αi N + Πi + αi N
n
X
(Ri + Si ).
(9)
i=1
Lobbies compete noncooperatively for the government’s favor and propose contribution schedules,
Ci (τ, s), contingent on the trade-policy vector set by the government, (τ, s). Lobby i’s objective
is to maximize the net aggregate well-being given by Wi − Ci . Given the contribution schedules
offered by the lobbies, the government in turn selects a trade-policy vector (τ, s) to maximize its
politically-motivated objective function, which is a combination of welfare and contributions:
G=
X
Ci + aW
(10)
i∈L
where a ≥ 0 captures the weight of welfare in the government’s objective relative to campaign
contributions. As shown in G-H, if the contribution schedules offered by lobbies are truthful, the
government’s objective function in (10) is equivalent to:
G̃ =
X
Wi + aW.
(11)
i∈L
To find the equilibrium trade policies, one can rewrite G̃ as:
G̃ = (a + αL )N +
n
X
(a + Ii )Πi + (a + αL )N
i=1
where αL ≡
P
i∈L αi
n
X
(Ri + Si ).
(12)
i=1
denotes the fraction of population that is represented by a lobby, and Ii is
an indicator variable that equals one if sector i is organized and zero otherwise. We focus on the
endogenous import policy henceforth, and refer interested readers to Chang (2005) for details on
the endogenous export policy. Let ti ≡ τi − 1 denote the ad valorem import tariff rate. Taking
first-order derivative respect to (12) yields the following results:
PROPOSITION 1 (Endogenous Protection Structure) If the contribution schedules of the
lobbies are truthful, the import policy that will emerge in the political equilibrium for a perfectly
competitive sector i satisfies
toi
Ii − αL zio
=
,
1 + toi
a + αL eoi
7
(13)
where zio = Xio /Mio is the equilibrium ratio of domestic output to imports, eoi = −Mio 0 Pio /Mio is the
elasticity of import demand, Pio = (1 + toi )Pi∗ is the domestic price for both domestic output and
imports, and Pi∗ is the world price.
On the other hand, the import policy that will emerge in the political equilibrium for a monopolistically competitive sector j satisfies
σj −1
toj
Ij + a
σj
=
o
1 + tj
a + αL σj +
1
z̃jo
(14)
where z̃jo = phj mj chjo / pfoj m∗j cfoj is the equilibrium market share of domestic products relative to
the market share of foreign products at the consumer price in the home market, and σj is the
constant elasticity of substitution between domestic and foreign products (which is approximately
the elasticity of import demand ei ). Specifically, mj chjo is the total domestic demand for home
differentiated goods in sector j, m∗j cfoj is the total domestic demand for (and imports of ) foreign
differentiated goods in sector j, and phj and pfoj are respectively the domestic consumer price of the
home and foreign variety in sector j.
Proposition 1 indicates that import protection will decrease with higher import penetration
(1/zi ) in an organized sector and will increase with higher import penetration in an unorganized
sector, if the sector is perfectly competitive. On the other hand, in monopolistically competitive
sectors, import protection always decreases with higher import penetration (1/z̃i ), regardless of
whether the sector is organized or not. This difference can be explained by the fact that both
organized and unorganized sectors under monopolistic competition are protected by positive import
tariffs. In this case, the effect of the size of the domestic industry is similar to that for organized
sectors under perfect competition, which receive positive tariffs. In sectors with a larger presence
of domestic firms, specific-factor owners have more to gain from an increase in tariff, while the
economy has less to lose from protection with lower volume of imports. The degree of political
representation αL has similar effects on the endogenous protection level, regardless of the market
structure. As more people are politically represented, the general protection level decreases. Finally,
as the government values welfare more (a larger a), the endogenous protection level approaches the
welfare-maximizing level, which is free trade in perfectly-competitive sectors and is a positive import
tariff
(σj −1)/σj
σj +1/z̃jo
in monopolistically competitive sectors.
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3.
THE ECONOMETRIC MODEL
If heterogeneity in market structure is ignored and all sectors are taken to be perfectly competitive,
equation (13) as derived originally by Grossman and Helpman (1994) applies to all sectors. This
theoretical specification has been the basis of previous empirical research such as Goldberg and
Maggi (1999), Gawande and Bandyopadhyay (2000), and Eicher and Osang (2002). For example,
Goldberg and Maggi (1999) form the following structural equation from (13):
Ii − αL
ti
ei =
zi + ²p,i
1 + ti
a + αL
= γp zi + δp Ii zi + ²p,i
(15)
where γp = −αL /(a + αL ) and δp = 1/(a + αL ). We will call this specification the homogeneous
perfectly competitive model (PC). On the other hand, if all sectors are taken to be monopolistically
competitive, equation (14) applies to all sectors. A structural equation based on (14) can be derived
in parallel with (15) as:
Ii + a ei − 1
ti
ei =
+ ²m,i
1 + ti
αL + a ei + z̃1
i
= γm wi + δm Ii wi + ²m,i
where γm = a/(a + αL ), δm = 1/(a + αL ), and wi =
ei −1
ei + z̃1
(16)
. In this paper, we consider a generalized
i
specification of endogenous protection structure based on Proposition 1, which accommodates both
potential market structures:
ti
ei = (1 − Iim ){γp zi + δp Ii zi + ²p,i } + Iim {γm wi + δm Ii wi + ²m,i }.
1 + ti
(17)
As the parameters, γp , δp , γm , and δm , are functions of the underlying political parameters, a and
αL , they are related such that −γp + γm = 1 and δp = δm . We will call this generalized specification
the heterogeneous market structure model (HC). We are interested to learn whether this generalized
HC specification will provide a statistically better fit to the data than the homogeneous PC model
frequently used in previous empirical studies, and if this is the case, what are the implied values
for the underlying political parameters a and αL given the estimated HC model.
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3.1
Data and Measurement
We briefly discuss the measurement and endogeneity issues associated with estimation of the specifications (15) and (17). The data we used are kindly provided by Eicher and Osang (2002), which
is a reconstruction of the data set described in Goldberg and Maggi (1999). We refer the reader
to these two sources for detailed explanations of the data set. In brief, the sectors investigated are
106 United States manufacturing sectors at the 3-digit SIC level. The coverage ratios for nontariff
barriers (NTB) in year 1983, instead of tariffs, are used to proxy for the noncooperative endogenous protection level predicted by the above theories. This is in view of the fact that tariff levels in
reality are set cooperatively among nations in international trade negotiations. Since the coverage
ratio can only take values between 0 and 1, the protection variable ti is censored. We follow the
benchmark mapping in Goldberg and Maggi (1999) between the latent protection level and the
nontariff barrier, that is, for coverage ratios less than 1, they reflect the equivalent tariff level. For
latent equivalent tariffs higher than 100 percent, they are mapped onto a coverage ratio of 1.
The trade elasticity estimates from Shiells et al. (1986) are used to measure both the import
elasticity in (15) for perfectly competitive sectors, and the elasticity of substitution in (16) for
monopolistically competitive sectors. The import elasticity measure is brought to the left-hand
side of the estimating equation for perfectly competitive sectors in Goldberg and Maggi (1999),
because the variable is endogenous by theory (13) and no suitable instrumental variables can be
clearly identified. The elasticities of substitution for monopolistically competitive sectors, however,
are not endogenous by theory (14). To facilitate estimation and comparison, however, we also phrase
the structural equation for monopolistically competitive sectors in a similar fashion such that the
left-hand side variable is also a composite of the protection measure and the elasticity measure
as in perfectly competitive sectors. The elasticity terms that remain on the right-hand side of
the structural equation for monopolistically competitive sectors (16) can be taken as exogenous by
theory (14).
The inverse import-penetration ratio zi for perfectly competitive sectors in (15) is measured by
the ratio of the value of shipments over imports as in Goldberg and Maggi (1999). The alternative
import-penetration ratio z̃i for monopolistically competitive sectors in (16), however, requires slight
modifications. It is measured as the ratio of the value of shipment to the domestic market over
imports (= (value of shipment - exports)/imports). Because both the import and domestic pro10
duction level depend on the protection level, these two inverse penetration ratios are endogenous.
We follow Goldberg and Maggi (1999) in the selection of the explanatory variables for the inverse
penetration ratio, zi . These include physical capital, inventories, engineers/scientists, white-collar
worker, skilled labor, semiskilled labor, cropland, pasture, forest, coal, petroleum, and minerals
(the explanatory variables used for import penetration in Trefler, 1993), as well as seller concentration, buyer concentration, seller number of firms, buyer number of firms, scale, capital stock,
unionization, geographic concentration, and tenure (a selection of the explanatory variables used
for import protection in the same source). This set of explanatory variables is also used for the
composite inverse penetration ratio, wi .
The political-organization dummy Ii is exogenous in theory, but is empirically measured based
on sectoral political contributions. Goldberg and Maggi (1999) construct the dummy using the
threshold level of $1,000,000,000 for political action committee (PAC) contributions. A sector is
considered politically organized for trade-policy purposes, if the sector’s PAC contribution is above
the threshold. Although by constructing the organization dummy in such a way implies that Ii
should be treated as endogenous since the political contribution level Ci is endogenous, we will not
pursue this extra estimation rigor here, for technical reasons given in Appendix A.
To assign sectors into perfectly competitive ones and monopolistically competitive ones, we try
a few alternative criteria. The first and most simplistic criterion suggested by the data is based
on the elasticity measure. For theory (14) for monopolistically competitive sectors to hold, the
elasticity of substitution must be greater than one. Thus, sectors with trade elasticity measures
less than or equal to one are considered perfectly competitive (Iim = 0 if ei ≤ 1), while sectors
with elasticity measures larger than one are considered monopolistically competitive (Iim = 1 if
ei > 1). We also explore alternative measures of Iim using cluster analysis, to further partition the
sectors with elasticity measures larger than one into perfectly competitive ones and monopolistically
competitive ones. The details are discussed later as we present the extended results. There are
good reasons to suspect that the trade elasticity measures are noisy, and sectors that should be
categorized as monopolistically competitive are categorized as perfectly competitive because the
elasticity estimates fall below one. However, given that there is no obvious way to get around this
problem, we regard the elasticity estimates and the derived dummy Iim as the best approximation
available.
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3.2
The Full Econometric Model
Let SF and RF stand for ‘structural form’ and ‘reduced form’, respectively. Given the above
discussion, the full econometric model for the homogenous perfectly competitive (PC) model we
consider is, with c̄i = 12 ei > 0,
y SF
:
yi = max{0, min(yi∗ , c̄i )}
y ∗ SF
:
yi∗ =
t∗i
ei = γp zi + δp Ii zi + ²p,i
1 + t∗i
zi = ζp0 Zi + up,i
observed
:
yi , zi , Ii , Zi , ei , c̄i , i = 1, ..., n, iid across i.
where up,i and ²p,i are dependent. The latent variable t∗i indicates the true level of protection,
which is censored at zero and one when measured by the NTB coverage ratio. It follows that the
upper censoring point for y ∗ SF is c̄i , which varies across i. The vector Zi consists of one and the
explanatory variables for the inverse penetration ratio zi .
The heterogeneous market structure (HC) model, on the other hand, takes the following form:
y SF
:
yi = max{0, min(yi∗ , c̄i )}
y ∗ SF
:
yi∗ =
t∗i
ei = (1 − Iim ){γp zi + δp Ii zi + ²p,i } + Iim {γm wi + δm Ii wi + ²m,i }
1 + t∗i
0
0
zi = (1 − Iim ){ζpp
Zi + upp,i } + Iim {ζpm
Zi + upm,i }
0
0
wi = (1 − Iim ){ζmp
Zi + ump,i } + Iim {ζmm
Zi + umm,i }
observed
:
yi , zi , wi , Ii , Iim , Zi , ei , c̄i , i = 1, ..., n, iid across i.
where upp,i and ²p,i are dependent, and so are umm,i and ²m,i . In this model, heterogeneity in market
structure across sectors is explicitly taken into account. In particular, we allow the protection
structure yi∗ , the inverse penetration ratio zi , and the composite inverse penetration ratio wi to
behave differently in perfectly competitive sectors (Iim = 0) from in monopolistically competitive
sectors (Iim = 1), with the structural equation for yi∗ explicitly guided by Proposition 1. Without
any further constraints, this system of specifications would be equivalent to two independent systems
of specifications, one for each group of sectors belonging to the same market structure, and each
12
with only the relevant structural component in y ∗ SF and the relevant reduced form specification
for either zi or wi . However, as discussed earlier, the structural parameters under the two market
structures in a given economy are related, and should be subject to the constraints that −γp +γm = 1
and δp = δm when the HC model is estimated.
3.3
Estimation
In view of the iid assumption, the subscript i will be omitted often in the following. The goal is to
estimate the SF parameters γp and δp in the PC model, and γp , δp , γm , and δm in the HC model
subject to the constraints that −γp + γm = 1 and δp = δm . There are two econometric problems in
pursuing the goal. One is the censoring in the y SF and the other is the endogeneity of z and w.
Each problem on its own is not difficult to deal with, but the combination of the two has been a longstanding problem in econometrics. The z- (and w-) equation regressor vector Z that includes unity
is essentially an instrument vector for z (and w), but due to the nonlinearity caused by the censoring,
the usual instrumental variable estimator (IVE) for linear models is not applicable. As explained
in Appendix A, there are four potential methods available, depending on whether the censored
maximum likelihood estimator (CMLE) or the censored least absolute deviation estimator (CLAD)
is used to estimate the y SF equation, and whether the minimum distance estimator (MDE) or the
two-stage least square estimator (2SLS) is used to incorporate the z- (and w-) equation. The full
information maximum likelihood estimator (FIML) is still another option. In the current context,
the relatively small sample size, coupled with the relatively large number of parameters, precludes
us from arriving at reliable estimates using the nonparametric CLAD method, the MDE method,
or the FIML method. Thus, we choose to proceed with the 2SLS-CMLE method.
Let σa and ρa,b stand for, respectively, the standard error of variable a and the correlation
between variables a and b. For the PC model, denoting the LSE for ζp and σup in the z- equation
as ζ̂p and σ̂up , and substituting the z- equation into the y ∗ SF, we get the y ∗ RF for the PC model
and the variance of its associated error:
y ∗ RF
σv2p
:
y ∗ = γp ζ̂p0 Z + δp I ζ̂p0 Z + {(γp + δp I)up + ²p }
≡ V ({·}|Z, I) = (γp + δp I)2 σ̂u2p + 2(γp + δp I)ρup ,²p σ̂up σ²p + σ²2p .
13
(18)
(19)
The error term in {·} is heteroscedastic depending on I and consists of two errors. The resulting
y RF can be estimated with the usual CMLE with an adjustment owing to the heteroscedasticity
of the variance. The log-likelihood function for the y RF of the PC model is
Lp =
X
{ 1[yi = 0] ln Φ(
i
−γp ζ̂p0 Zi − δp Ii ζ̂p0 Zi
)
σvp,i
+1[0 < yi < c̄i ] ln
+1[yi = c̄i ] ln Φ(
φ((yi − γp ζ̂p0 Zi − δp Ii ζ̂p0 Zi )/σvp,i )
σvp,i
γp ζ̂p0 Zi + δp Ii ζ̂p0 Zi − c̄i
) },
σvp,i
(20)
which is to be maximized for γp , δp , σ²p , and ρup ,²p . Denote the resulting estimates (γ̇p , δ̇p , σ̇²p , ρ̇up ,²p ).
Similarly, for the HC model, denoting the LSE for ζpp , σupp , ζmm , and σumm in the z- and w- equation as ζ̂pp , σ̂upp , ζ̂mm , and σ̂umm , and substituting the z- and w- equation into the y ∗ SF, we get
the y ∗ RF for the HC model and the variance of its associated error:
y ∗ RF
:
0
0
0
0
y ∗ = (1 − I m )(γp ζ̂pp
Z + δp I ζ̂pp
Z) + I m (γm ζ̂mm
Z + δm I ζ̂mm
Z)
+{(1 − I m )(γp + δp I)upp + I m (γm + δm I)umm + ²}
σv2h
(21)
≡ V ({·}|Z, I, I m ) = (1 − I m )[(γp + δp I)2 σ̂u2pp + 2(γp + δp I)ρupp ,²p σ̂upp σ²p + σ²2p ]
+I m [(γm + δm I)2 σ̂u2mm + 2(γm + δm I)ρumm ,²m σ̂umm σ²m + σ²2m ]
(22)
where ² = (1 − I m )²p + I m ²m . The error term in {·} is heteroscedastic depending on I, I m , and
consists of four errors. The resulting log-likelihood function for the y RF of the HC model is
Lh =
0 Z + δ I ζ̂ 0 Z) − I m (γ ζ̂ 0
0
X
−(1 − I m )(γp ζ̂pp
p pp
m mm Z + δm I ζ̂mm Z)
{ 1[yi = 0] ln Φ(
)
σvh,i
i
0 Z + δ I ζ̂ 0 Z) − I m (γ ζ̂ 0
0
φ((yi − (1 − I m )(γp ζ̂pp
p pp
m mm Z + δm I ζ̂mm Z))/σvh,i )
+1[0 < yi < c̄i ] ln
σvh,i
+1[yi = c̄i ] ln Φ(
0
0 Z + δ I ζ̂ 0 Z) + I m (γ ζ̂ 0
(1 − I m )(γp ζ̂pp
m mm Z + δm I ζ̂mm Z) − c̄i
p pp
) },
σvh,i
(23)
which is to be maximized for γp , δp , σ²p , γm , δm , σ²m , ρupp ,²p , and ρumm ,²m , subject to the constraints
that −γp +γm = 1 and δp = δm . Denote the resulting estimates (γ̈p , δ̈p , σ̈²p , γ̈m , δ̈m , σ̈²m , ρ̈upp ,²p , ρ̈umm ,²m ).
The standard errors of the CMLE parameter estimates are derived numerically, with the first-stage
14
estimation errors (of ζ̂p or of ζ̂pp and ζ̂mm ) taken into account. The details are explained in Appendix B.
3.4
Hypothesis Testing
To test the validity of these two competing models, we apply the J-test procedure proposed by
Davidson and MacKinnon (1981) for strictly non-nested hypotheses. Define f (Z, I, γp , δp , ζp ) ≡
γp ζp0 Z + δp Iζp0 Z, which is the corresponding regression function of the PC model in (18). Similarly,
0 Z +δ Iζ 0 Z)+I m (γ ζ 0
0
define g(Z, I, I m , γp , δp , γm , δm , ζpp , ζmm ) ≡ (1−I m )(γp ζpp
p pp
m mm Z +δm Iζmm Z),
which is the corresponding regression function of the HC model in (21). Then, the J-test for the
PC model as the null proceeds as follows. First, create an artificially augmented regression function
of f :
f˜ ≡ f (Z, I, γp , δp , ζp ) + µh ĝ,
where ĝ = g(Z, I, I m , γ̈p , δ̈p , γ̈m , δ̈m , ζ̂pp , ζ̂mm ) is the fitted value based on the parameter estimates
from the HC model. Next, obtain the 2SLS-CMLE based on a modified likelihood function L̃p as
in (20) but with the augmented regression function f˜. Tests for µh = 0. If µh = 0 is rejected, then
the PC model is rejected to the direction of the HC model. The J-test for the HC model as the
null can be done analogously. Form an artificially augmented regression function of g:
g̃ ≡ g(Z, I, I m , γp , δp , γm , δm , ζpp , ζmm ) + µp fˆ,
where fˆ = f (Z, I, γ̇p , δ̇p , ζ̂p ) is the fitted value based on the parameter estimates from the PC
model. Obtain the 2SLS-CMLE based on a modified likelihood function L̃h as in (23) but with the
augmented regression function g̃. Tests for µp = 0. If µp = 0 is rejected, then the HC model is
rejected to the direction of the PC model.
3.5
Result
Table 1 presents the first estimation results. For the PC model, the parameter estimates of γp
and δp are of correct signs in accordance with the theory (13) and are significant. According to
these estimates, the weight of welfare in the government’s objective (β ≡
a
1+a )
is 0.9890 while
the fraction of the population represented by a lobby (αL ) is 0.7981. The results are broadly
15
consistent with those of Goldberg and Maggi (1999), and serve as our benchmark against which
to evaluate the HC model. In this exercise, the clustering of sectors for the HC model is based on
the simplistic criterion, whereby a sector is considered monopolistically competitive if its elasticity
measure is greater than one and perfectly competitive otherwise. By this criterion, there are 59
monopolistically competitive sectors and 47 perfectly competitive sectors. The parameter estimates
of γp and δp (and the implied γm and δm ) are also of correct signs in accordance with the theories
(13) and (14), although they are not statistically significant. This may be accounted for by the fact
that the degree of freedom is reduced with the sample broken into two regimes. According to these
estimates using the HC model, the weight of welfare in the government’s objective (β ≡
a
1+a )
is
higher at 0.9988 while the fraction of the population represented by a lobby (αL ) is lower at 0.4545.
The relatively higher weight of welfare in the government’s objective implied by the HC model
may be explained by the fact that the welfare-maximizing tariff for a monopolistically competitive
sector is positive.1 Thus, even if a government were not politically motivated (with a β = 1),
a monopolistically competitive sector would still receive a positive level of protection. Thus, for
a given level of observed protection, it would imply a higher weight of welfare placed by the
government if the sector is classified as a monopolistically competitive one than if it is classified as
a perfectly competitive one. The treatment of all sectors as perfectly competitive ones causes the
parameter estimate of a to bias downward.
Next, the results of the J-test in Table 1 indicate that neither model is a correct specification
of the underlying endogenous protection structure, as either model when considered as the null
hypothesis is rejected at the 5% significance level. This negative result points to two potential
directions of investigation. First, neither theoretical model is complete; important structures or
variables are omitted. Second, the market structure dummy under the HC model is not correctly
specified and there is room for improvement. We leave the first task to future research and investigate the second possibility below. Indeed, the summary statistics in Table 1 indicate that the
derived market structure dummy I m based on the simplistic criterion is less than satisfactory. The
average degree of seller competition (scomp), which is measured by the seller number of firms in a
sector divided by industry sales, is higher in monopolistically competitive sectors than in perfectly
competitive sectors, when in theory the ranking should be reversed. Thus, there is a need to further
1
The welfare-maximizing tariff for a monopolistically competitive sector is implied by (14) with a → ∞.
16
refine the market structure dummy.
Toward this end, we attempt two alternative methods. In the first alternative, we use the
STATA “cluster kmeans” routine to separate sectors into two groups with respect to the degree
of seller competition, and construct the dummy kmeans(scompi ). The dummy is set equal to one
if the sector belongs to the group with a lower average degree of seller competition and zero vice
versa. Then, the market structure dummy is defined; a sector is considered a monopolistically
competitive sector, if the elasticity measure is greater than one and if the sector faces relatively
lower degrees of competition (I m = 1, if ei > 1 and kmeans(scompi ) = 1). The results based
on this refined market structure dummy are reported in Table 2. The number of monopolistically
competitive sectors is now reduced to 50, and these sectors now have the theoretically-desired lower
degree of seller competition (0.1500) on average than perfectly competitive sectors (0.3175). With
the refined market structure dummy, the parameter estimates of γp and δp (and the implied γm and
δm ) are still of correct signs in accordance with the theories (13) and (14), but remain statistically
insignificant. The conclusion from the J-test, however, still rejects both of the PC and the HC
models.
In the second alternative, we use the STATA “cluster kmedians” routine instead to cluster
sectors with respect to the degree of seller competition. The routine is similar to the previous
one, except that now the distance to be minimized between one sector and the potential group the
sector will join is based on the median, instead of the mean, of the existing group members. A
similar dummy kmedians(scompi ) is constructed, which is set equal to one if the sector belongs
to the group with a lower average degree of seller competition and zero vice versa. The market
structure dummy is then defined in a similar fashion as in the previous alternative (I m = 1, if
ei > 1 and kmedians(scompi ) = 1). The results based on this final set of market structure
dummy are given in Table 3. In this case, the number of monopolistically competitive sectors
is further reduced to 45, with a even lower average degree of seller competition (0.1213) than
perfectly competitive sectors (0.3249). A higher fraction of monopolistically competitive sectors
are politically organized (0.4667) than perfectly competitive sectors (0.3934). Simultaneously, the
monopolistically competitive sectors also receive a higher average protection level (0.1424) than
perfectly competitive sectors (0.1296), which is contrary to the previous scenario (in Table 2). The
results of the J-test now clearly reject the PC model but support the HC model. Thus, we consider
17
the HC model in combination with the final set of market structure dummy as providing the best
fit to the data. Under this combination of specifications, the parameter estimates of γp and δp
(and the implied γm and δm ) are of correct signs. They indicate that the weight of welfare in the
government’s objective (β ≡
a
1+a )
is 0.9988 and the fraction of population politically represented
(αL ) is 0.5107.
These results suggest a higher weight on welfare placed by the government (β) than indicated by
previous studies in the literature based on the G-H type homogeneous perfect competition models
(0.986 in Goldberg and Maggi, 1999; 0.96 in Eicher and Osang, 2002). This is consistent with our
earlier discussion that misspecification of a monopolistically competitive sector as a perfectly competitive sector tends to assign the supposedly welfare-driven component of protection as politically
motivated and bias upward the estimate of the government’s weight on political contribution, or in
other words, bias downward the government’s emphasis on aggregate welfare. The estimates of the
degree of political representation (αL ) vary a lot in the literature, ranging from 0.98 in Gawande and
Bandyopadhyay (2000), 0.88 in Goldberg and Maggi (1999), to 0.26 in Eicher and Osang (2002).
Our estimate of αL at 0.5107 suggests an intermediate degree of political participation.
4.
CONCLUSION
The results of the paper support the heterogeneous market structure hypothesis, where the protection structure is deemed to behave in systematically different ways according to Proposition 1 in
selected sectors characteristic of monopolistic competition from sectors of perfect competition, and
reject the homogeneous perfect competition hypothesis, where all sectors are deemed to be perfectly competitive and share the same protection structure according to Grossman and Helpman
(1994). Thus, the Chang (2005) model is borne out by the data for monopolistically competitive
sectors, while the predictions of G-H remain valid for the subset of perfectly competitive sectors.
This empirical finding thus suggests an intricate relationship between import protection and import penetration: it depends on whether the sector is perfectly competitive or monopolistically
competitive and whether the sector is politically organized or not. When all these different facets
of heterogeneity are taken into account, the resulting estimates imply that the government’s weight
on aggregate welfare is higher than previously suggested by the literature (with similar estimation
18
framework) and is close to being a welfare maximizer. On the other hand, the degree of political representation falls in the intermediate range; around half of the population is politically represented
in the arena of trade policy.
Caution is warranted when one would like to take the results given here and stand to applaud the
benevolence of the U.S. government in their trade policy making, for one important sector is missing
here from the sample: the agriculture sector. The sample studied here and in previous G-H-type
empirical papers has focused mainly on manufacturing sectors, where the general protection level
is low, and excluded the agriculture sector, where heavy protection persists. With the agriculture
sector included, the conclusions are likely to change toward finding a more special-interest driven
government.
APPENDIX A:
ESTIMATION METHODOLOGY FOR TOBIT
MODEL WITH ENDOGENOUS REGRESSORS
Define an indicator function 1[A] = 1 if A holds and 0 otherwise. Let SF and RF stand for
‘structural form’ and ‘reduced form’, respectively. Suppose the equations under consideration are,
with c > 0,
y SF
:
yi = max{0, min(yi∗ , c)},
wi = zi0 ηw + vwi ,
where y ∗ SF is yi∗ = βw wi + βdw di wi + ui ,
where vwi and ui are dependent
di = 1[d∗i > 0], where d∗i = zi0 ηd + vdi , vdi and ui are dependent,
observed
:
(Model 1)
di , zi , wi , yi , i = 1, ..., N , iid across i.
In view of the iid assumption, the subscript i will be omitted often in the following. The goal is
to estimate the SF parameters βw and βdw . The upper censoring point c can be allowed to vary
across i so long as ci is observed and independent of yi . A simpler version of Model 1 is obtained
if d is exogenous:
same as Model 1 but d is exogenous under independence between vd and u.
19
(Model 2)
In this case, the slope of w in y ∗ = (βw +βdw d)w +u shift exogenously depending on d. Substituting
the w equation into the y ∗ SF, we get the y ∗ RF:
y ∗ RF : y ∗ = z 0 (βw ηw ) + dz 0 (βdw ηw ) + {(βw + βdw d)vw + u}
where the error term in {·} is heteroscedastic depending on d and consists of two errors.
Write the y ∗ RF simply as yi∗ = x0i α + εi =⇒ yi = max{0, min(x0i α + εi , c)} where xi is an
exogenous regressor vector, α is a parameter vector, and εi is an error term. Under the independence
of ε from x and the normality ε ∼ N (0, σε2 ), the Censored MLE (CMLE ) is obtained with the loglikelihood function
X
−x0 α
φ((yi − x0i α)/σε )
x0 α − c
{1[yi = 0] ln Φ( i ) + 1[0 < yi < c] ln{
} + 1[yi = c] ln Φ( i
)}
σε
σε
σε
i
which is maximized with respect to (wrt) α and σε . CMLE converges reasonably well.
Denoting the conditional median of ε|x as M ed(ε|x), a semiparametric estimator requiring only
M ed(ε|x) = 0 while allowing an unknown form of heteroskedasticity is the Censored Least Absolute
Deviation estimator (CLAD) of Powell (1984). For the double censoring case, CLAD minimizes
wrt α
X
|yi − max{0, min(x0i α, c)}|.
i
The requisite assumption for CLAD is much weaker than that for CMLE. Also, no ‘nuisance parameter’ such as σε appears for CLAD. The non-smooth minimand may not behave well in computation.
To get around this nonconvexity problem, one may apply the nonparametric algorithm of Lee and
Kim (1998).
Eicher and Osang (2002) apply Minimum Distance Estimator (MDE) as explained in Lee
(1996a). But MDE requires a somewhat different model from above: instead of the d equation,
suppose
dw equation : di wi = zi0 ηdw + vdwi .
20
Then, substituting the above w equation and this dw equation into the above y ∗ SF yields
y ∗ RF-MDE
yi∗ = βw (zi0 ηw + vwi ) + βdw (zi0 ηdw + vdwi ) + ui ≡ zi0 ηy + vy , where
:
vy ≡ βw vwi + βdw vdwi + ui
MDE Restriction
:
and
ηy = βw ηw + βdw ηdw .
This y ∗ RF in turn leads to
y RF-MDE : yi = max{0, min(zi0 ηy + vy , c)}.
The MDE proceeds in two steps. First, estimate ηy for the y RF-MDE with a censored model
estimator, and ηw and ηdw with Least Squares Estimator (LSE); denote the estimators as hy , hw ,
and hdw , respectively. Second, do the LSE of hy on hw and hdw to estimate the two scalars βw and
βdw , which works owing to MDE Restriction above.
The MDE procedure works well in practice. But the shortcoming is the linear model assumption
for dw, which is not tenable in principle because dw is not a continuous random variable due to
P (d = 0) = P (dw = 0) > 0. Recognizing this problem, one may apply a little different MDE; use
a censored model
di wi = max(0, zi0 ηdw + vdwi )
and estimate this with CMLE. This should provide a better approximation for dw, but leads to
a new problem that the MDE restriction—and consequently y RF-MDE—holds only on d = 1.
Estimating the y RF-MDE using only the subsample d = 1 causes the usual sample selection
problem if d is endogenous. If d is exogenous, then the MDE procedure works so long as the
estimation of the y RF-MDE is done with the d = 1 subsample. That is, the MDE procedure is
tenable under Model 2.
Lee (1996b) proposes a Two-Stage-LSE (2SLS) type approach for limited dependent variable
models with endogenous regressors. The idea is to replace each endogenous regressor with its
21
conditional mean given the instruments. For this, rewrite the y ∗ SF as
y ∗ SF-2SLS-1 : yi∗ = βw E(w|zi ) + βdw E(dw|zi )
+ui + βw {wi − E(w|zi )} + βdw {di wi − E(dw|zi )}
where the last three terms constitute the new (composite) error term. The conditional means
E(w|z) and E(dw|z) can be estimated nonparametrically. In practice, the LSE for wi = zi0 ηw + vwi
and di wi = zi0 ηdw + vdwi may do. The latter (practical) approach has the same problem as the
above MDE, because the linear model for the product dw is not tenable in principle.
The 2SLS approach can be similarly applied for Model 2. Rewrite the y ∗ SF as
y ∗ SF-2SLS-2 : yi∗ = βw E(w|zi ) + βdw di E(w|zi )
+ui + βw {wi − E(w|zi )} + βdw di {wi − E(w|zi )}
where the last three terms constitute the new (composite) error term. The conditional means
E(w|z) can be estimated using the LSE for wi = zi0 ηw + vwi . The problem mentioned above wrt y ∗
RF-MDE and y ∗ SF-2SLS-1 does not arise in this case. Thus, the 2SLS procedure is tenable under
Model 2. The y ∗ SF-2SLS leads straightforwardly to the y SF-2SLS, to which CMLE or CLAD can
be applied.
Considering our discussions so far, we can think of four methods to estimate βd and βdw :
CMLE
CLAD
MDE
y RF estimated, normality
y RF estimated, zero median
2SLS
y SF-2SLS estimated, normality
y SF-2SLS estimated, zero median
Other than the approaches in the table, one may also attempt to apply the full information
MLE to Model 1 under (u, vw , vd ) ∼ N (0, Ω), where the covariance matrix Ω has SD(u), SD(vw ),
COR(u, vw ), COR(u, vd ), and COR(vw , vd ); SD(vd ) is not identified. But this MLE has two
problems. First, with d endogenous, it seems difficult—if not impossible—to obtain the likelihood
function. Second, even if the likelihood function is found, estimating correlation coefficients (and
standard deviations) is notoriously difficult in multivariate MLE’s. In practice, often some correlations are assumed to be zero (e.g., COR(vw , vd ) = 0), or an equi-correlation assumption is imposed
22
(e.g., COR(u, vw ) = COR(u, vd )). It is not clear to us how Goldberg and Maggi (1999) proceed,
as they do not show the likelihood function nor the estimate for Ω for their MLE. Alternatively, if
Model 2 is adopted, the likelihood function becomes straightforward, and the size of the covariance
matrix is also greatly reduced. Overall, in view of the econometrics issues discussed above, we will
pursue Model 2 in the main text.
APPENDIX B:
ESTIMATION METHODOLOGY FOR THE
STANDARD ERRORS OF THE 2SLS-CMLE
Let α be the first stage parameter of dimension k1 × 1 and aN be the LSE. Let β be the likelihood
parameter of dimension k2 × 1 for the second stage, and bN be the MLE. Denote the second stage
score function as s(zi , α, β); omit zi for simplification. Define
∇α s(α, β) ≡
k2 ×k1
∂s(α, β)
∂α0
and ∇β s(α, β) ≡
k2 ×k2
∂s(α, β)
.
∂β 0
By the definition of bN , it holds that, using Taylor’s expansion,
0
=
=⇒
=⇒
=⇒
1 X
√
s(aN , bN )
N i
√
1 X
1 X
0' √
s(aN , β) + {
∇β s(α, β)} N (bN − β)
N
N i
i
X
√
1
1 X
N (bN − β) = −{
s(aN , β)
∇β s(α, β)}−1 √
N
N i
i
√
1 X
1 X
N (bN − β) = −{
s(α, β)s(α, β)0 }−1 √
s(aN , β).
N
N i
i
To account for the first-stage error aN − α, define
HN ≡
1 X
1 X
∇β s(α, β) =
s(α, β)s(α, β)0
N
N
i
and
i
Apply Taylor’s expansion to s(aN , β) in the above expression for
LN ≡
1 X
∇α s(α, β).
N
i
√
N (bN − β) to get
√
√
1 X
−1
· {√
N (bN − β) ' −HN
s(α, β) + LN N (aN − α)}.
N i
23
With ri denoting the first-stage LSE residual with Zi as the regressor, observe
√
N (aN − α) =
≡
1 X 1 X
√
(
Zi Zi0 )−1 Zi ri
N i N i
1 X
1 X
√
ηi , where ηi ≡ (
Zi Zi0 )−1 Zi ri .
N
N i
i
Hence
√
1 X
1 X
−1
s(α, β) + LN √
ηi }
N (bN − β) ' −HN
{√
N i
N i
X
−1 1
√
= −HN
{s(α, β) + LN ηi }
N i
X
−1 1
√
= −HN
qi , where qi ≡ s(α, β) + LN ηi .
N i
Therefore,
√
N (bN − β) Ã N (0, H −1 E(qq 0 )H −1 ) where H ≡ E{s(α, β)s(α, β)0 }.
Consistent estimators for H and E(qq 0 ) are
ĤN
≡
QN
≡
1 X
s(aN , bN )s(aN , bN )0 ,
N
i
1 X
{s(aN , bN ) + L̂N ηi }{s(aN , bN ) + L̂N ηi }0
N
i
where L̂N ≡
1 X
∇α s(aN , bN ).
N
i
In practice, s can be obtained by numerical derivatives, and ∇α s can be obtained using numerical
derivatives once more. If the first-stage LSE involves two equations, each with regressor Zji , residual
0 , η 0 )0 and
rji , ηji , and the parameter αj , j = 1, 2, then set α ≡ (α10 , α20 )0 , aN ≡ (a01N , a02N )0 , ηi ≡ (η1i
2i
proceed as above.
REFERENCES
Chang, P.-L., 2005. Protection for sale under monopolistic competition, forthcoming in Journal of
International Economics.
24
Davidson, R., MacKinnon, J. G., 1981. Several tests for model specification in the presence of
alternative hypothesis. Econometrica 49 (3), 781–93.
Dixit, A. K., Stiglitz, J. E., 1977. Monopolistic competition and optimum product diversity. American Economic Review 67 (3), 297–308.
Eicher, T., Osang, T., 2002. Protection for sale: An empirical investigation: Comment. American
Economic Review 92 (5), 1702–1710.
Gawande, K., Bandyopadhyay, U., 2000. Is protection for sale? Evidence on the Grossman-Helpman
theory of endogenous protection. Review of Economics and Statistics 82 (1), 139–152.
Goldberg, P. K., Maggi, G., 1999. Protection for sale: An empirical investigation. American Economic Review 89 (5), 1135–1155.
Grossman, G. M., Helpman, E., 1994. Protection for sale. American Economic Review 84 (4),
833–850.
Lee, M.-J., 1996a. Methods of moments and semiparametric econometrics for limited dependent
variable models. Springer Verlag, New York.
Lee, M.-J., 1996b. Nonparametric two stage estimation of simultaneous equations with limited
endogenous regressor. Econometric Theory 12, 305–330.
Lee, M.-J., Kim, H.-J., 1998. Semiparametric econometric estimators for a truncated regression
model: a review with an extension. Statistica Neerlandica 52, 200–225.
Powell, J. L., 1984. Least absolute deviations estimation for the censored regression model. Journal
of Econometrics 25, 303–325.
Shiells, C. R., Stern, R. M., Deardorff, A. V., 1986. Estimates of the elasticities of substitution
between imports and home goods for the United States. Weltwirtschaftliches Archiv 122 (3),
497–519.
Trefler, D., February 1993. Trade liberalization and the theory of endogenous protection. Journal
of Political Economy 101 (1), 138–160.
25
Table 1: clustering of sectors by elasticity
PC
HC
γp
δp
σ²p
ρup ,²p (ρupp ,²p )
γm
δm
σ²m
ρumm ,²m
-0.0088
0.0110
0.6693
-0.9149
(0.0032)
(0.0060)
(0.1037)
(0.6661)
-0.0005
0.0012
0.1219
-1
0.9995
0.0012
1.3093
-1
(0.0005)
(0.0010)
(0.0144)
a
αL
Lp (Lh )
J test:
µh (µp )
L̃p (L̃h )
90.1327
0.7981
-99.0480
(49.2445)
(0.3304)
849.0480
0.4545
-78.3968
(740.7163)
(0.4451)
0.6914**
-94.2304
(0.2868)
0.4271**
-76.0305
(0.1744)
(0.0005)
(0.0010)
(0.0432)
Summary Statistics: # of sectors
ēi
scomp
¯ i
I¯i
t̄i
m
Ii = 1
59
4.0337
0.2466
0.3898
0.1203
Iim = 0
47
0.4492
0.2283
0.4681
0.1535
Total
106
2.4443
0.2385
0.4245
0.1350
Note:
1. Iim = 1 if ei > 1. The variable “seller competition (scomp)” is the seller
number of firms in an industry scaled by industry sales.
2. Figures in brackets are standard errors.
3. A ∗ sign indicates significance at 10% level, a ∗∗ sign indicates significance at
5% level, and a ∗∗∗ sign indicates significance at 1% level.
26
Table 2: clustering of sectors by elasticity and seller competition (kmeans)
PC
HC
γp
δp
σ²p
ρup ,²p (ρupp ,²p )
γm
δm
σ²m
ρumm ,²m
-0.0088
0.0110
0.6693
-0.9149
(0.0032)
(0.0060)
(0.1037)
(0.6661)
-0.0007
0.0014
0.1326
-1
0.9993
0.0014
1.3507
-1
(0.0005)
(0.0010)
(0.0170)
a
αL
Lp (Lh )
J test:
µh (µp )
L̃p (L̃h )
90.1327
0.7981
-99.0480
(49.2445)
(0.3304)
696.3331
0.4718
-71.3375
(472.3585)
(0.3638)
0.7226**
-93.8804
(0.3052)
0.4307**
-68.1527
(0.1694)
(0.0005)
(0.0010)
(0.0489)
Summary Statistics: # of sectors
ēi
scomp
¯ i
I¯i
t̄i
m
Ii = 1
50
4.3010
0.1500
0.4400
0.1320
Iim = 0
56
0.7866
0.3175
0.4107
0.1378
Total
106
2.4443
0.2385
0.4245
0.1350
Note:
1. Iim = 1 if ei > 1 and kmeans(scompi ) = 1. The dummy kmeans(scompi ) is
obtained using the STATA “cluster kmeans” analysis with respect to the variable
“seller competition (scomp)”, which is the seller number of firms in an industry
scaled by industry sales.
2. Figures in brackets are standard errors.
3. A ∗ sign indicates significance at 10% level, a ∗∗ sign indicates significance at
5% level, and a ∗∗∗ sign indicates significance at 1% level.
27
Table 3: clustering of sectors by elasticity and seller competition (kmedians)
PC
HC
γp
δp
σ²p
ρup ,²p (ρupp ,²p )
γm
δm
σ²m
ρumm ,²m
-0.0088
0.0110
0.6693
-0.9149
(0.0032)
(0.0060)
(0.1037)
(0.6661)
-0.0006
0.0012
0.1242
-1
0.9994
0.0012
1.3957
-1
(0.0005)
(0.0010)
(0.0150)
a
αL
Lp (Lh )
J test:
µh (µp )
L̃p (L̃h )
90.1327
0.7981
-99.0480
(49.2445)
(0.3304)
825.5517
0.5107
-61.0028
(670.0232)
(0.4711)
0.7186***
-93.4296
(0.2735)
0.4105
-57.3074
(0.4183)
(0.0005)
(0.0010)
(0.0604)
Summary Statistics: # of sectors
ēi
scomp
¯ i
I¯i
t̄i
m
Ii = 1
45
4.4392
0.1213
0.4667
0.1424
Iim = 0
61
0.9727
0.3249
0.3934
0.1296
Total
106
2.4443
0.2385
0.4245
0.1350
Note:
1. Iim = 1 if ei > 1 and kmedians(scompi ) = 1. The dummy kmedians(scompi )
is obtained using the STATA “cluster kmedians” analysis with respect to the
variable “seller competition (scomp)”, which is the seller number of firms in an
industry scaled by industry sales.
2. Figures in brackets are standard errors.
3. A ∗ sign indicates significance at 10% level, a ∗∗ sign indicates significance at
5% level, and a ∗∗∗ sign indicates significance at 1% level.
28