Short Run Gravity∗
James E. Anderson
Boston College and NBER

Yoto V. Yotov
Drexel University

November 14, 2018

Abstract
The short run gravity model is based on mobile labor combined with fixed bilateralcapacities (marketing capital). Efficient capacity allocation yields long run gravity.
Rising efficiency of bilateral capacity allocation is estimated to raise world manufacturing trade 162% in the globalization era, 1988-2006. Counter-factual calculation oflong run efficient capacity allocation reveals real income gains to all countries from
25% to 47%. Results give solutions to the ‘distance puzzle’ and the ’missing globalization puzzle’. The estimated short run trade elasticity is about 1/4 the long run tradeelasticity, 1/4 being the micro-founded buyers’ incidence elasticity parameter.

JEL Classification Codes: F13, F14, F16
Keywords: export networks, gravity, inefficiency.
∗

Acknowledgements will be added later. Contact information: James E. Anderson, Department of Economics, Boston College, Chestnut Hill, MA 02467, USA. Yoto V. Yotov, School of Economics, Drexel University, Philadelphia, PA 19104, USA.

1

Introduction

The short run gravity model developed in this paper solves several time invariance puzzles
posed by the recent empirical gravity literature. In brief, where is the globalization?1 The
model and its application give an answer. Invariant gravity coefficients are consistent withtrade costs that vary with volume in the short run due to diminishing returns to a variablefactor paired with a bilaterally specific fixed factor. Log-linear gravity results under plausible
restrictions as a static equilibrium structure that shifts over time as capacities (marketing
capital allocations) move. The structure of the model makes natural a new question – how far
can globalization go? The estimated model implies that increasing efficiency of allocationof marketing capital in 1988-2006 manufacturing increased world trade 162%. The 2006
equilibrium is nevertheless a long way from efficiency. Counterfactual long run efficientequilibrium allocation of marketing capital implies real income gains to countries ranging
from 25% to 47% relative to the 2006 base.
Short run gravity nests (the now-standard) long run gravity model interpreted here as
characterized by efficient allocation of marketing capital. Short run shipments from origin ito destination z at time τ relative to hypothetical frictionless shipments (size-adjusted tradeflows) are shown below to be given by:[Long Run Gravity(i, z)]ρ λ(i, z, τ )1−ρ .
1(1)Gravity’s emergence from the shade [e.g. Head and Mayer (2014)] highlights empirical and conceptual
puzzles. On one hand gravity-fitted bilateral trade flows come very close to the data and estimated coefficientsare stable over time. On the other hand, this fit and stability violate intuition and observation about trade
cost behavior over time. Secular invariance of coefficients is a puzzle in light of big technological improvements
in transportation and communications over the past 60 years. Cyclic invariance is a puzzle in light of cyclic
variation of shipping rates and delivery lags. Coe et al. (2002) define the ‘Missing Globalization Puzzle’
as “the failure of declining trade-related costs to be reflected in estimates of the standard gravity model ofbilateral trade” (p.1). Higher frequency invariance and good fit is further puzzling in light of business cycle
movement of ocean shipping rates and delivery lags. Imperfectly correlated national expenditures over thebusiness cycle and big secular shifts in the location of economic activity suggest cyclical and trend variationin bilateral trade costs over time and space. Time invariance also appears to conflict with the richly patterned
adjustment over time in bilateral trade links of French export firms emphasized by Chaney (2014), and therandom entry and exit in US 10-digit trade emphasized by Besedes and Prusa (2006).

[Long Run Gravity (·)] is the standard gravity model expression for the trade depressing
effect of bilateral relative to multilateral resistance in the long run equilibrium.2 λ(i, z, τ )is a bilateral capacity variable – the ‘marketing capital’ allocation. An important part ofλ(i, z, τ ) is origin-destination-specific investment in bilateral links.3 ρ is the buyers’ short run
incidence elasticity, the fraction of trade cost variation borne by buyers.4 ρ is a combinationof the elasticity of substitution in demand and the elasticity of supply, itself micro-founded in
the joint supply of output delivered to many destinations at increasing cost due to diminishingmarginal product of a variable factor on each link. The model encompasses heterogeneous
productivity, of industries (as in Eaton and Kortum (2002)) or of firms (as in Chaney (2008)).
When λ(i, z) is at efficient levels everywhere, short run gravity trade flows equal their longrun gravity values – long run gravity is the outer envelope of short run gravity.
The key conceptual object introduced in this paper is the micro-founded incidence elasticity parameter ρ ∈ (0, 1) in (1) that distinguishes the short run trade elasticity from the longrun trade elasticity. We seek an estimate of ρ from the movement of bilateral trade patterns
over the era of globalization 1988-2006 when traders everywhere plausibly increased efforts
to find foreign counter-parties. Inference of ρ requires disentangling the speed of adjustmentof λ(i, z, τ )s from the magnitude of the effect of λ(i, z, τ ) changes on bilateral trade changes
2

As demonstrated by Arkolakis et al. (2012), [Long Run Gravity(·)] derives from a wide array oftheoretical microfoundations. Anderson (1979) is the first to offer a theoretical economic foundation for thegravity equation in an Armington-CES setting. Other early contributions to gravity theory include Krugman(1980) and Bergstrand (1985), who obtain gravity from a monopolistic competition and a Heckscher-Ohlin
foundations, respectively. Eaton and Kortum (2002), who derive gravity in a Ricardian framework withintermediate goods, and Anderson and van Wincoop (2003), who popularize the Armington-CES model andemphasize the importance of the general equilibrium effects of trade costs, are arguably the most influential
gravity theories. More recently, the gravity model has been derived in a heterogeneous firm setting by
Chaney (2008) and Helpman et al. (2008). See Anderson (2011), Arkolakis et al. (2012), Head and Mayer(2014), and Costinot and Rodriguez-Clare (2014), and Yotov et al. (2016) for recent surveys of the evolutionof the theoretical gravity literature.
3
Bilateral capacity here is a notion consistent with the network link dynamics modeled by Chaney (2014)
and with the link between managers’ experience in previous firms and the export performance of their current
company described by Mion and Opromolla (2014) as well as the ‘marketing capital’ notion of Head et al.
(2010). The property of rising short run marginal cost of trade here resembles the increasing cost model of
Arkolakis (2010), but differs in the cause. Rising long run trade cost in Arkolakis (2010) is due to increasing
difficulty of reaching new customers. Long run trade costs are constant in our model.
4
The term incidence elasticity is chosen to distinguish it from the passthrough elasticity used to describe
incomplete incidence of exchange rate changes on prices, a higher frequency behavior that may reflect othercauses than are the focus of this paper.

2

from origin i to destination z. Thus some dynamic structure is needed.
There is no settled theory of trade link dynamics. Our approach is thus to combine simple
ad hoc dynamic devices with the short run gravity model to allow econometric inference.
Our strategy is to lean heavily on structural gravity and associated regularities of geography
while being agnostic about dynamic structure in our panel data. In contrast, Sampson (2016)
develops and calibrates a technology flows structural dynamic gravity model, made feasible
only by assuming uniform sized countries and uniform trade costs.
A reduced form dynamic approach uses cross-border-time fixed effects with panel gravity
data to control for the effect of globalization. The estimated border-time fixed effects movesmoothly over time while the gravity coefficients are stable. In the context of the short
run gravity model, this suggests that a single dynamic adjustment parameter combineswith ρ to fit the data. An external adjustment parameter estimate then yields an estimateof ρ from the reduced form approach. An alternative ad hoc structural dynamic device(explained below) infers the effect of globalization from lagged dependent variables, withstandard treatments for endogeneity. The same external value of the speed of adjustment
combined with the estimated structural model yields another estimate of ρ. Using theresults of the two approaches simultaneously yields a third estimate of ρ and an estimate of
the speed of adjustment. The various estimates of ρ are close to each other. This empirical
success is presumably because the era of globalization is so dominated by smooth adjustment
toward greater cross-border trade that any plausible dynamic model with a constant rate ofadjustment comes close to the trade data. Concerns about the ad hoc dynamic devices arethus mitigated.
Application of the model to manufacturing trade data for 52 countries yields a good fit
with intuitively plausible parameters. The reduced form results suggest that the growing
efficiency of trade capacity increased trade volume by 162%. Our estimation procedures
suggests ρ ∈ (0.20, 0.37), narrowed to (0.20, 0.24) in our favored specifications with a preferred value 0.24. In all robustness checks ρ is significantly far below 1, statistically and3economically. Most importantly, the consistency of results on ρ and the goodness of fit tend
to confirm that a parametric incidence elasticity comes close to the data. Beyond the present
paper the results suggest the usefulness of short run gravity in modeling bilateral trade evenin eras where dynamic adjustment may be more complex.
The focus of the paper on marketing capital efficiency naturally leads to the question of
how far globalization can go. To provide an answer the estimates of ρ and the other gravity
parameters are used to quantify the potential real income gain from long run efficient allocation of marketing capital. The counterfactual experiment compares two static equilibria,
one short run and the other the long run hypothetical equilibrium with base endowments,
preferences, trade costs and parameters held constant except for efficient reallocation of marketing capital. Gains from efficient globalization are universally big – real manufacturingincome rises everywhere, ranging from 25% to 47%.
The paper also contributes to the literature on measuring trade elasticities. Cross section
trade elasticity estimates are usually interpreted as long run elasticities. Expression (1)implies that the standard cross section gravity model may suffer from omitted variable bias,
but will be an unbiased estimator of long run elasticities when standard covariates adequately
control for the missing bilateral capacities λ(i, z, τ ). Short run gravity given by (1) alongwith the no bias property generates a simple prediction about the relationship between shortrun (SR) and long run (LR) gravity elasticities:

βlSR = βlLR ρ,(2)

where l denotes any gravity covariate, e.g. distance, tariffs, etc. A test statistic based onequation (2) yields results below consistent with no bias in long run elasticities from thestandard gravity literature. Long run elasticity estimates usually range between 4 and 12.
Our estimates of ρ around 1/4 suggest a range for short run elasticities between 1 and 3.55

See Eaton and Kortum (2002), Anderson and van Wincoop (2003), and Broda et al. (2006). The
corresponding short run elasticities from the IRBC macro literature are usually between 1 and 2. See
Backus et al. (1994), Zimmermann (1997), Heathcote and Perri (2002) and Feenstra et al. (2012).

4

Equation (2) is a time-invariant relationship between short run and long run trade elasticities. The related literature in contrast links short run time-varying to static long run
elasticities. Ruhl (2008) reconciles the difference between short run and long run elasticities
in a model based on cyclical fluctuations being temporary whereas trade cost changes arepermanent. Arkolakis et al. (2011) offer an explanation capable of handling the many country gravity context. A fraction of boundedly rational (myopic) consumers switch to cheaper
suppliers at each point in time. In contrast, our model assumes perfectly efficient spatial
equilibrium given the marketing capital allocation. Closest to our model, Crucini and Davis(2016) explain the discrepancy between the short run and long run elasticities with distribution capital that is specific to the origin of the good, domestic or foreign. In comparison
to our model, theirs allows for CES production of distribution whereas ours restricts theelasticity of substitution to 1 (i.e. Cobb-Douglas). This simplification buys time-invarianceof the short run trade elasticity. (Their structure is embedded in a two country real businesscycle model and their application calibrates the model to moments of price dispersion datafor 6 sectors in 13 US cities.)
A second implication of equation (2) suggests an explanation of the broad ‘missing globalization puzzle’ (Coe et al., 2002): the effects of geographic impediments such as distanceand other geographic impediments to estimated gravity equations have been stable, or evenincreasing over time. Time invariance of estimated coefficients of standard cross section gravity regressions is explained by iceberg trade cost proxies that control well for the omitted
bilateral capacity variables. Bilateral capacity adjusts over time toward an efficient level thatis shown below to depend on the same iceberg trade costs as in the standard cross section
model.6 We estimate highly significant declining border effects associated with rising investment in cross-border capacities relative to domestic capacities. The missing globalization
is in the omitted dynamic adjustment of bilateral capacities driven by the same geographic
6

The puzzles of time-invariant gravity estimates have attracted significant attention in the literature. A
series of papers have proposed purely empirical solutions to the puzzles. See Buch et al. (2004), Carrre andSchiff (2005), Brun et al. (2005), Boulhol and de Serres (2010), Lin and Sim (2012), Yotov (2012) Carrre etal. (2013), Bergstrand et al. (2015) and Larch et al. (2016).

5

forces that drive spatial variation of bilateral trade flows. The omission is concealed bystandard static gravity estimation that is an unbiased estimate of long run gravity.
The short run gravity model also implies a theory of the many zeroes observable inbilateral trade flows, some persistent and some flickering on and off. (Empirical investigationof the theory of zeroes is left to future research.) Changes in persistent zeroes are due
to investments in bilateral capacity on the extensive margin as capacity moves toward an
efficient long run extensive margin of markets served. Flickering zeroes are due to demandchanges combined with period-by-period fixed cost components of variable trade costs suchthat the origin-destination pair representative firm flips from one side to the other of the
break-even point for serving a particular destination. In the heterogeneous firms version of
the model, the breakeven point for not serving a destination applies to the least productive
active firm on an interior extensive margin.7
Section 2 presents the basic theoretical model of joint trade costs of production and delivery to many destinations. Section 3 applies the model to the multi-country setting, yielding
the short run gravity model. Section 4 develops and tests two complementary empiricalversions of the model. Supplemental online Appendix A shows that the basic model encompasses heterogeneous productivities (as in Eaton and Kortum (2002)) and heterogeneousfirms (as in Chaney (2008)). Appendix A also draws out the implications of model for atheory of endogenous trade costs such as may be applied to model inference from price comparisons for homogeneous goods across many locations. Supplemental Appendix B reports
on sensitivity experiments with the main empirical models. The main results are robust.
7

Helpman et al. (2008) (HMR) offer the first model of zeroes based on fixed export costs. Firms draw
productivities from a Pareto distribution with an upper bound such that zeroes are explained by a sufficiently
low upper bound such that no firm at a particular origin receives a draw high enough to cover the fixed
cost of entering a particular destination market. Our model for short run zeroes differs only in that fixedcapacity implies increasing opportunity cost of serving small markets, hence a U-shaped full average cost
curve that can lie everywhere above a small destination market’s willingness to pay, even with an unbounded
Pareto productivity distribution. The equilibrium extensive margin thus depends only on technology andtaste parameters. Short run entry and exit flickering on the extensive margin are induced by demand or
technology shocks that can have any distribution. Other models use demand systems with choke prices to
explain zeroes, e.g. quadratic as in Melitz and Ottaviano (2008), or translog as in Novy (2013). While chokeprices are realistic, such systems appear to do worse (according to Novy’s, 2013, results) at fitting the data
than the standard CES gravity equation.

6

2

A Model of Joint Trade Costs

An origin region produces and ships a product to potentially many destinations. Distribution
on each link requires labor and capital in variable proportions, multiplicatively amplified
by iceberg trade and production cost factors. The scalar iceberg cost factors differ acrossdestinations according to bilateral geographical features such as distance and borders andother familiar variables in the gravity literature. Cost-minimizing allocation of resources
implies that bilateral trade destinations are imperfect substitutes. One factor is variablein the short run (labor that can be freely allocated across destination markets that havepositive capacity) and one is fixed in the short run (capacity in each potential network link).
The variable labor requirement to each destination served includes a fixed labor component, interpretable as an office staff required to monitor trade on each active bilateral link.
The fixed labor requirement is normalized to one for expositional ease. For simplicity theoffice staff labor is perfectly substitutable for ‘line’ labor assigned to produce and distribute
goods on each link. Labor, including the office staff labor, is mobile in the short run acrossproduction for destinations actively served.
The trade activity also requires destination-specific “marketing capital” that is committed(sunk) before the allocation of labor, though it is variable ex ante. Marketing capital is thusbilaterally specialized and fixed in the short run. The details of destination specialization,
while interesting and important (e.g., Chaney, 2014), are outside the scope of this paper.
“Marketing capital” is left vague to encompass both human capital in the form of network
connections and physical capital particularized to serve a particular destination. The ideaof a retail network in Crucini and Davis (2016) is similar.
Bilateral production and trade of a generic firm in a generic origin and sector to destination z is formally modeled as a Cobb-Douglas function of line (non-office) labor L(z) − 1
and capital K(z): x(z) = (1/t(z))K(z)1−α (L(z) − 1)α . The functional form implies that theoffice staff of 1 unit, is required.8 x(z) is delivered product. t(z) > 1 is the technological8

The office staff story is just one justification of the formal requirement of a fixed labor cost for each7

iceberg-melting parameter from the given origin to destination z, a penalty imposed by ‘nature’ relative to the frictionless benchmark t = 1. t(z) also reflects a productivity penalty
in the usual sense that would apply to all destinations z uniformly. With all inputs variable(in the long run), the production function exhibits economies of scale. In the short run with
K(z) fixed, decreasing returns dominate.9 For now, all firms are identical in any origin,aggregating to an industry with the generic firm’s characteristics. Appendix Section A.1.1
shows that the short run gravity model extends in all essentials to include the heterogeneousfirms model with firm productivities drawn from a Pareto distribution. (Essentially thesame short run gravity model extends to incorporate fixed infrastructure at each locationand time, adding location-time-specific productivity shifters controlled for econometricallywith location-time fixed effects.)
For the generic sector as a whole, labor is drawn from a national labor market in an
amount satisfying the value of marginal product condition at the national wage rate. The
P
labor market constraint on short run allocation across destinations is L = n0 L(z), where
L is labor supply to the sector and destination z = n is at the extensive margin. n units ofoffice staff labor assigned to a total of n destinations are included in L. Labor is efficiently
allocated across destination activities with value of marginal product equal to the common
wage. Office staff are drawn from the common labor pool and are paid the common wage.
The price for delivered output at destination z is p(z). Delivered price p(z) in competitive
equilibrium covers costs: w[L(z) − 1] + r(z)K(z) + w = p(z)x(z) where r(z) is the realized(residual) return on the specific capital for delivery to destination z. The first term on theleft hand side of the equation is the line workers wage bill, the second term the payments tosector specific capital and the third term the payment to the office staff.
The extensive margin destination n is reached when the wage required for the office staff
destination served. Normalization of the fixed cost input to 1 unit of labor is a harmless convience. Heterogeneity across destinations in the amount of fixed input required is readily introduced, whence the production
function has the Stone-Geary form.
9
To see the long run economies of scale, consider a scalar expansion of K(z), L(z). The elasticity of x(z)with respect to a one % rise in K(z), L(z) is equal to 1 − α + αL(z)/[L(z) − 1] > 1 in the long run. The
marginal product of labor is diminishing in the short run, ∂ 2 x(z)/∂L(z)2 = (α − 1)αx(z)/[L(z) − 1] < 0.

8

exceeds the value of sales minus the wage bill for line workers labor; i.e., profits are negative.
Even with positive profits, destination z may not be served if K(z) = 0, no destinationspecific capital is allocated. Destination-specific capital K(z) is allocated prior to production
P ∗and delivery to n∗ ≥ n potentially active destinations, accounting for K = n0 K(z) unitsof capital. The allocation shares of capital are λ(z) = K(z)/K. Long run efficient allocationof capital and its extensive margin n∗ is analyzed in Sections 3.2-3.3.
The value of production at delivered prices in the generic region and sector is the sum
over destinations z of the payments to labor (line and office staff) and the payment tonon-managerial capital given by10

Y = (L − n)α K 1−α C,

(3)

n
X
C≡[
λ(z)(p(z)/t(z))1/(1−α) ]1−α .

(4)

where
0

The real activity level
R = (L − n)α K 1−αin (3) is multiplied by a price index C embedding efficient allocation of the joint activity todelivered output at the many destinations. The setup thus yields a Constant Elasticity ofTransformation (CET) joint revenue function for delivered output. (The level of activity R
can be taken as exogenous for gravity model purposes, hence it is not necessary to assume
that activity R is a Cobb-Douglas function of labor and specific human capital.)
The equilibrium share of sales to each destination z that is served, by Hotelling’s Lemma
10

The setup here extends the specific factors production model of Anderson (2011) to include a fixed cost.
In Anderson (2011) the environment is a GDP function where z denotes a sector in a continuum of fixed
size, t(z) is a productivity penalty and there is no fixed cost.
Competitive equilibrium implies that labor is paid a common wage in serving all markets, equal to thevalue of marginal product of labor in each market. Aggregate labor employed is L, taken as an endowment
in solving for Y in (3) below. Price index C(·) results from solving the labor market clearance condition for
the wage, then replacing the wage with the resulting reduced form in evaluation aggregate revenue.

9

(applied to (3) using (4)), iss(z) = λ(z)p(z)/t(z)C1/(1−α).

(5)

It is convenient for later purposes to sort destinations by rank order, beginning with thelargest (so in equation (5) z ∈ [0, n]). The local delivery market is s(0) by convention
because empirically it is almost universally the largest.
The short run extensive margin n is determined by the value of marginal product of labor
in sector n falling below its value on the intensive margin for sectors z < n. This implies
that the extensive margin is efficient in the sense of maximizing (3) with respect to n. For
simplicity, temporarily think of a continuum of destinations (with ‘shares’ being densities)
and differentiate (3) with respect to n. The first order condition yields

αY /(L − n) = (1 − α)s(n)Y.

The left hand side is the value of marginal product of line labor, equal to the wage. The righthand side is the value of marginal product of the extensive margin office staff. Manipulating
the first order condition, the implication is:
Proposition 1: Extensive Margin. The smallest market served in short run equilibriumis unique and characterized by:n = {z : s(z) =α[L − z]−1 }.
1−α

(6)

Ordering markets by decreasing size, the extensive margin is the smallest market that can beserved.
Equation (6) implies that office staff paid w exhausts the entire residual payment insector n. The wage = αY /(L − n) is rising in n, while (1 − α)s(n)Y decreasing in n; hence
the equilibrium extensive margin exists and is unique. (6) readily rationalizes the flickering
10

on and off of bilateral trade that is observable in highly disaggregated data: capacity is inplace but insufficient revenue to cover the overhead cost of office staff indicate temporary
shutdown. Section 3.2 analyzes the long run extensive margin of installed capacity.
An implication of extensive margin model (6) is that volume equations for positive trade
are not subject to selection bias. That is because firms are identical, in contrast to heterogeneous firms literature. When the model is extended to heterogeneous firms with productivities drawn from an unbounded Pareto distribution following Melitz (2003), the volume of
positive trade on any link combines smooth action on both extensive and ‘interior’ intensive
margins in a closed-form structural gravity equation. With proxies for fixed costs that differ
from the proxies for iceberg trade costs, the action can be decomposed into the component
intensive and extensive margins. (The condition (6) for the extensive margin destination
remains the same, with the slight complication that the simple fixed cost normalized to 1
for each destination served is replaced by the mass of firms S(z) that are productive enoughRn
to serve destination z. n in (3) becomes N = 0 S(z)dz, the accumulated mass of all firms
serving active destinations. The details are developed below in Appendix Section A.1.1.)
For any market that is served, the equilibrium delivered price p(z) is endogenously determined by the supply side forces described in (3)-(5) interacting with demand forces describedby Constant Elasticity of Substitution preferences or technology (in the case of intermediate
goods). The intuitive notion of a bilateral trade cost corresponds to p(z)/p(0), a clear idea
when t(0) = 1, so bilateral trade cost is endogenous. In practice, this is a dangerous simplification because internal delivery costs are not zero, differ across countries and are endogenous
just as the bilateral costs are endogenous, cf. Agnosteva et al. (2014) and Ramondo et al.
(2016).
Description of the demand side of the market requires an expansion of notation to designate the location of the originating sector. The CES expenditure share for goods from origin

11

i in destination z is given by
X(i, z)=E(z)β(i)p(i, z)
P (z)

1−σ
.

(7)

Here, X(i, z) denotes the bilateral flow at end user prices, E(z) denotes the total expenditure
in destination z on goods from all origins serving it, β(i) is a distribution parameter of the
CES preferences/technology, σ is the elasticity of substitution, and P (z) is the CES priceindex for destination z.
The market clearing condition for positive bilateral trade from i to z is

Y (i)s(i, z) = X(i, z).

Using (5) for s(i, z) and (7) for X(i, z) in the market clearing condition to solve for theequilibrium price p(i, z) yields:
E(z)P (z)σ−1 β(i)1−σ [t(i, z)C(i)]η
p(i, z) =Y (i)λ(i, z)1/(η+σ−1),(8)where η = 1/(1 − α) > 1 is the supply elasticity. The short run equilibrium price in an active
origin-destination pair in (8) is an intuitive constant elasticity function of demand shifters
E(z)P (z)σ−1 , supply shifters Y (i) and C(i), and the exogenous bilateral friction componentsin t(i, z) and the contemporaneously exogenous bilateral capacity λ(i, z).
Incidence of trade costs to buyers is incomplete: the buyers’ incidence elasticity isd ln p(i, z)/d ln t(i, z) = η/(η + σ − 1) ≡ ρ. The incidence elasticity ρ (dropping “buyers” for brevity) plays a key role in the gravity representation of the model. ρ has a deep
micro-foundation as a combination of the demand elasticity parameter σ and the supply
elasticity parameter η, itself microfounded in the equilibrium of distribution based on the
Cobb-Douglas specific factors model. ρ is increasing in η and decreasing in σ.11
11Equation (8) can, in principle, account for substantial variation in prices across time and space. Rents
to the sector specific factor similarly vary (see Section 3.2). Rents are competitive in the model, so pricing to12

3Gravity in Short Run and Long Run

The gravity representation of short run equilibrium trade yields a gravity model with a short
run trade cost elasticity equal to the product of the long run trade cost elasticity times theincidence elasticity ρ. The short run elasticity applies everywhere. The short run trade flow
and multilateral resistance equations are additionally altered relative to long run gravity by
the volume effects of bilateral specific capacity everywhere.
Multilateral resistance for sellers is derived from the global market clearing condition for
Y (i). Substitute (8) into (7), then multiply by E(z) and sum over z to obtain the global
demand for Y (i). Collect the terms for Y (i) on the left hand side of the market clearance
condition and simplify the exponents 1−ρ(σ−1)/η = ρ on Y (i) and (σ−1)/(η+σ−1) = 1−ρon λ(i, z). The result is

Y (i)ρ = [β(i)C(i)]ρ(1−σ)X[E(z)P (z)σ−1 ]ρ t(i, z)ρ(1−σ) λ(i, z)1−ρ .

zDivide both sides by Y ρ . The result is


Y (i)
Y

ρ

= [β(i)C(i)Π(i)]ρ(1−σ) ⇒Y (i)= [β(i)C(i)Π(i)]1−σ ,Y(9)where outward multilateral resistance(1−σ)ρΠ(i)=X  E(z) ρ  t(i, z) (1−σ)ρ
z

Y

P (z)

λ(i, z)1−ρ .

(10)The left hand side of (9) is recognized as a CES share equation for a hypothetical world buyer
on the world market, with a world market price index for all goods equal to 1. Short run
multilateral resistance in (10) is a CES function of bilateral relative trade costs t(i, z)/P (z),where the elasticity of short run substitution is (1 − σ)ρ. Π(i) is homogeneous of degree one
market behavior in the usual sense is not implied. The model can be extended to monopolistic competition
by treating each origin i as a firm. With CES demand, markups are constant when firms shares are small.

13

in {t(i, z)} for given {P (z)}.
The gravity representation of trade also requires a relationship between the buyers’
price index and relative trade costs. Substitute (8) in the CES price definition P (z)1−σ =P
1−σ. Then use (9) to substitute for [β(i)C(i)]1−σ in the resulting equation.
i [β(i)p(i, z)]After simplification this gives the short run price index as

P (z)(1−σ)ρ


=

E(z)
Y

−(1−ρ) X
i

Y (i)
Y



t(i, z)Π(i)(1−σ)ρ

λ(i, z)1−ρ .

Buyers’ price index P (z) is the product of a size effect [E(z)/Y ]−(1−ρ) and a CES functionof the set of bilateral buyers’ incidences:Pe(z)(1−σ)ρ =X Y (i)  t(i, z) (1−σ)ρ
i

Y

Π(i)

λ(i, z)1−ρ , ∀z,(11)with short run elasticity of substitution (1 − σ)ρ . Pe(z) is the buyers’ short run multilateralresistance, also interpreted as the buyers’ short run incidence of trade costs. Simplifying the
CES price index, P (z) = [E(z)/Y ](1−ρ)/(σ−1)ρ Pe(z). Higher relative demand E(z)/Y raises
P (z) given Pe(z) due to fixed capacities {λ(i, z)Y (i)}. In long run gravity, as effectively
η → ∞, ρ → 1 and the buyers’ market size effect vanishes from the price index P (z).
Use P (z)(1−σ)ρ = [E(z)/Y ]−(1−ρ) Pe(z)(1−σ)ρ in sellers’ multilateral resistance (10) to yield
the more intuitive equivalent form

Π(i)(1−σ)ρ =X E(z)zYt(i, z)Pe(z)!(1−σ)ρ
λ(i, z)1−ρ , ∀i.

(12)

The final step in deriving short run gravity is to substitute the right hand side of (8) for
p(i, z) in (7) and use (9) to substitute for [β(i)C(i)]1−σ in the resulting expression. Aftersimplification using incidence elasticity ρ = η/(η + σ − 1), this gives:1212X(i, z) = E(z)(β(i)p(i, z))1−σ= E(z)ρ [t(i, z)/P (z)](1−σ)ρ λ(i, z)1−ρ H(i) where H(i) =(1−σ)ρ
1−ρ
[β(i)C(i)]Y (i) . Substitute [Y (i)/Y Π(i)1−σ ]ρ for [β(i)C(i)](1−σ)ρ in H(i) and replace P (z)(1−σ)ρ
−(1−ρ) e
with [E(z)/Y ]P (z)(1−σ)ρ . Rearranging the result yields equation (13).

14

Proposition 2: Short Run Gravity. Short run gravity is a geometric weighted averageof long run gravity and a bilateral capacity variable λ(i, z) . Short run gravity trade flows
are given by:"#(1−σ)ρ
Y (i)E(z)t(i, z)X(i, z) =λ(i, z)1−ρ .
eY
Π(i)P (z)(13)

where the multilateral resistances Π(i), Pe(z) are given by (11)-(12)The first term on the right hand side of (13) is the frictionless benchmark flow at given
sales {Y (i)} and expenditure {E(z)}. The middle term is the familiar effect of gravity
frictions, the ratio of bilateral to the product of buyers’ and sellers’ multilateral resistance.
The difference is that the short run trade elasticity is reduced in absolute value to (1 − σ)ρ.
The last term λ(i, z)1−ρ is the ‘friction’ due to inefficient investment in capacity on link i, z.
Dividing both sides of (13) by the frictionless benchmark, size adjusted trade is"#(1−σ)ρ
t(i, z)X(i, z)=λ(i, z)1−ρ ,eY (i)E(z)/YΠ(i)P (z)a geometric weighted average of long run gravity frictional displacement and inefficient link
capacity allocation.
Intuition about short run gravity system (11)-(13) is aided by considering an equiproportionate change in all bilateral trade costs t(i, z): t1 (i, z) = µt0 (i, z). Intuitively, bilateral
trade flows should be unchanged because no relative price changes. Checking the system(11)-(12), {Pe(z), Π(i)} are homogeneous of degree 1/2 in {t(i, z)}, hence buyers’ and sellers’
multilateral resistances change by µ1/2 so indeed bilateral trade flows are constant. As withlong run gravity, system (11)-(12) solves for multilateral resistances up to a normalization.
Multilateral resistances retain their interpretation as sellers’ and buyers’ incidence of trade
costs.
Over time the allocation of destination specific capital {λ(i, z)} presumably moves toward
the efficient level analyzed below in Section 3.2. The efficient allocation matches the long15

run demand pattern, so that the short run gravity equation (13) approaches the long run
gravity equation, intuitively equivalent to ρ → 1.
The preceding derivation of (13) combined with (10) and (11) uses for simplicity theArmington CES/endowments setup of Anderson and van Wincoop (2003), but the same short
run gravity structure derives from two alternative structures with endogenous production andheterogeneous productivities. Online Appendix Section A.1.1 shows that the form of short
run gravity in equations (10)-(13) holds for the alternative interpretation of gravity based onheterogeneous productivity draws in a Ricardian model due to Eaton and Kortum (2002).
It also extends to the heterogeneous firms gravity model of Chaney (2008),13 understandingthat the composite supply elasticity combines intensive margin elasticity η above with anextensive margin elasticity based on the dispersion parameter θ of the Pareto productivity
distribution. The composite supply elasticity is η̃ = η(1 + θ − η) > η for the intuitive caseθ > η, the necessary and sufficient condition for the extensive margin of firms serving adestination to be rising in price. The incidence elasticity becomes ρ̃ = η̃/(η̃ + σ − 1) > ρ forθ > η. Thus, the short run gravity adjustment developed here applies to the wide class ofmodels that have been described in Arkolakis et al. (2012).

3.1

Short vs. Long Run Gravity Elasticities

Short run gravity (13) nests long run gravity and thus can address three prominent empirical
puzzles. Gravity-based inference of the effect of a bilateral friction on a cross section ofbilateral trade is interpretable as a long run elasticity under the no-bias hypothesis. Panelgravity estimation of the short run model with the methods described below yields a short
run elasticity.
Bilateral trade costs t(i, z) are specified as a loglinear function of standard gravity variables:
13

The extension is exact for competitive firms and a close approximation for monopolistically competitive
firms.

16

t(i, z) =LY
(1 + tar(i, z))d(i, z)ψl l ,l=1

where tar(i, z) denotes ad valorem tariffs and the vector d(i, z) includes a set of binary andcontinuous determinants of bilateral trade. Proposition 2 delivers the relationship between
short run (SR) gravity coefficients and their long run (LR) counterparts as:

βlSR = (1 − σ)ψl ρ = βlLR ρ.

(14)

Notably, the relationship between short run and long run elasticities in (14) is time invariant.14 Equation (14) under the constraint ρ ∈ (0, 1) applied to direct price shifters such as
tariffs at least partially resolves the empirical puzzle posed by estimates of the trade elasticity in cross-section gravity estimations that are much larger than short run estimates used in
the macro literature. (See Footnote 5.) (14) combined with estimates of ρ partly reconciles
the difference, with remaining differences isolated from that due to the missing incidence
elasticity. Some portion of remaining difference may be due to incomplete passthrough tohigh frequency price changes.
Second, equation (13) helps resolve the time invariant distance elasticity puzzle. Supposethat the iceberg trade cost proxies control very well for the capacity variables in (13) that areomitted from the standard cross section gravity regression. Time invariant estimated trade
cost elasticities may be found by standard gravity regressions in that case. We replicate thatfinding below. The intuition that the effect of distance on trade should be falling over time
can be interpreted here as intuition that marketing capital λ relative to its efficient level,
having started lower in more distant destination markets, is rising faster in the globalizationera. Then the effect of distance on trade, including its effect on capacity, should be falling
14

Equation (8) is the short run gravity model buyers’ price equation, as developed further in Appendix A.
The model assumes perfect arbitrage equilibrium in the background, and in the foreground imposes structure
on production-cum-distribution restrictive enough to yield short run elasticities that are time-invariant.
Imperfect arbitrage (e.g. due to search frictions) or non-Cobb-Douglas production-cum-distribution structure(e.g. Crucini and Davis (2016)) can lead to short run time-varying trade elasticities.

17

in absolute value in a globalization era. In contrast, uniform globalization reduces trade
cost at all distances equiproportionately, an inference that cannot be rejected in our results
below.
Third, the missing globalization puzzle is the broader version of the distance puzzle,
applying to all the long run gravity covariates together. This paper finds the missing globalization in the evolution of marketing capital allocation, but in a sense the puzzle is removed
to the black box labeled λ.
Given ρ estimates, equation (14) offers several opportunities to test the hypothesis thatstandard gravity variables control for the omitted λs in standard long run gravity estimation.
(14) suggests the test β SR − ρβ LR = 0, one for each of the gravity regressors in vector d(i, z).
Structural estimation can identify ρ under assumptions discussed below.

3.2

Long Run Efficient Allocation

The allocation of capital to destinations z is outside the static model developed above under
the realistic assumption that investment is predetermined and generally inefficient relative tocurrent realizations of random variables. It is nevertheless useful to construct a benchmark
efficient allocation as an aid to intuition and to learning something about the inefficiency of
allocation. A key, though in some sense obvious result is that the general gravity model underinefficient investment nests the standard iceberg trade cost model as a special case of efficient
allocation. The difference between actual and hypothetical efficient allocation is presumably
due to un-modeled frictions hampering investment in the face of various risks and imperfect
information about realizations of natural bilateral resistance and other components of therealized equilibrium. The development of the benchmark allocation provides structure to theeconometric application that generates inferred differences between actual and benchmark
allocations as residuals.
Economic intuition suggests that standard iceberg trade costs should emerge as a reduced
form of all efficient equilibrium production and distribution models because it is consistent18

with the envelope theorem in the allocation of all relevant resources in distribution. Effectively, geography dictates the allocation of capital as well as the distribution of goods giventhat efficient allocation of capital. Development of the benchmark special case demonstrates
how this works.
Efficient capital allocation achieves equal returns on investment in each destination
served. The average return on investment for the generic sector and economy of Section
2 is given by r̄ = YK = (1 − α)Y /K. The return on capital relative to the average for destination z is given by s(i, z)/λ(i, z) (Anderson, 2011). If investors perfectly foresee bilateralnatural trade costs and the extensive margin, then λ(i, z) = s(i, z) in the capital allocation equilibrium actually realized. Then λ∗ (i, z) = s(i, z) = λ∗ (i, z)[p(i, z)/t(i, z)C(i)]η ⇒p(i, z) = t(i, z)C(i). Combine this restriction with equation (8) for the market clearing priceto solve for the efficient allocationE ∗ (z)λ (i, z) = ∗
Y (i)
∗



β(i)C ∗ (i)t(i, z)
P ∗ (z)1−σE ∗ (z)=Y∗t(i, z)∗Π (i)P ∗ (z)

1−σ
.

(15)

Note that (15) is a general equilibrium concept: the multilateral resistances imply that
all origins solve for efficient allocation simultaneously. Efficient allocation share λ∗ (i, z) isdecreasing in the cross section of trade pairs in natural trade friction t(i, z), increasing indestination market potential E(z)P (z)σ−1 and origin utility weight β(i)1−σ . Each of theseeffects is intuitive. It is also increasing in the ‘average economic distance’ of the origin from its
markets, Π∗ (i), implying that for markets actually served, relationship-specific investments
must be larger to overcome the average resistance.
Notice that η = 1/(1 − α) plays no role in the efficient allocation equilibrium. This
arises because no short run reallocation of labor is needed; the trade flows are generated by
efficiently allocated bilateral capacities as well as bilateral labor, yielding the standard longrun gravity model. The long run trade cost elasticity is 1 − σ, which exceeds in absolutevalue the ‘short run’ elasticity (1 − σ)η/(η + σ − 1) = (1 − σ)ρ, a familiar implication of the19envelope theorem. The short run gravity model of Section 2 is related to the long run modelas the elasticity of transformation η is infinite, corresponding to the Ricardian case where
there is instantaneous efficient reallocation of specific investment.

3.3

Efficient Extensive Margin

In efficient equilibrium, the extensive margin is determined by equation (6) with s(i, n) =λ∗ (i, n). Order the destinations with ordering Z(i) such that the efficient destination investment shares defined by (15) are decreasing in z: Z(i) = P({z}): dλ∗ (i, z)/dz < 0, whereP({z}) denotes a permutation of the ordering of {z}. Then n(i)∗ is defined byn∗ (i) = z : L(i) − z −α= 0; z ∈ Z(i).
(1 − α)λ∗ (i, z)

Existence and uniqueness of the fixed point n∗ (i) is guaranteed because

L(i) − z −α(1 − α)λ∗ (i, z)

is decreasing in z. More intuitively,s∗ (i, τ ) =α[L(i, τ ) − n∗ (i, τ )]−1 .
1−α

(16)

Evidently the efficient equilibrium extensive margin n(i)∗ is increasing in origin size L(i)and increasing in origin average economic distance Π∗ (i), the latter effect because it reduces
the relative difficulty of entering the marginal market t(i, z)/Π∗ (i). A more steeply risingprofile of bilateral trade costs for an origin country reduces its extensive margin. Destination
size distribution (market potential) E(z)P (z)σ−1 affects all exporters equally; as markets are
more equal, more are served by every origin. The intuitive results on origin and destination
size accord with observed characteristics of the extensive margin of trade. The more subtle
implications of (16) remain to be explored in applications. Notice that this theory of the20extensive margin imposes no structure on the distribution of productivity that contributes
implicitly to the variation of t(i, z).

4

Empirical Analysis

Short run gravity theory generates a series of testable predictions. Taking the predictions
to data faces two challenges. First, there is no direct data on bilateral capacity. Proxies
must be found to substitute for missing data. Second, there is no fully developed theory of
the investment trajectory.15 To maintain focus on short run forces, the application abstracts
from details about the progress of formal globalization aside from treatment of FTA implementation and tariff changes. Results here should be viewed as ‘proof of concept’ rather thanan accounting exercise. Knowledge gained will guide further empirical tests and extensionsof SR gravity, discussed in the conclusion and the Appendices.
The application focuses on the intensive margin, for two reasons. First, equation (13)for positive trade flows is central as a theory nesting long run gravity with forces departingfrom long run gravity. Second, the key incidence elasticity parameter ρ can be inferred fromequation (13). The empirical investigation of SR gravity on the intensive margin is a natural
first step.
Start from the idea that bilateral capacities are approaching efficient capacity allocationin the era of globalization. Uncoordinated buyers’ and sellers’ agents grope forward to form
links, expanding high rent links and contracting low rent links. Extend short run gravity
model (13) to add a time dimension τ :Y (i, τ )E(z, τ )X(i, z, τ ) =Y (τ )

t(i, z, τ )Π(i, τ )P (z, τ )15

1−σ !ρ

λ(i, z, τ )1−ρ .

(17)

The investments that plausibly form parts of λ(i, z) are the result of uncoordinated decisions of many
actors on N 2 links where N is the number of countries. See Chaney (2014) for evidence on export dynamics
of French firms. Information network theories of links suggest search and random matching conditioned on
anticipated probabilities of a match. Full rational expectations development is a chimera. Simple ad hoc
structures are thus applied here to empirically fit an investment trajectory.

21

Established econometric techniques and standard proxies control for bilateral trade costs(t(i, z, τ )), the multilateral resistances (Π(i, τ ) and P (z, τ )), and the size effects (Y (i, τ ),E(z, τ ), and Y (τ )). The unobservable bilateral capacity variable λ(i, z, τ ) evolves over time,
and the pattern of bilateral trade shifts with it at rate 1 − ρ. The challenge is to infersomething ρ from panel trade data based on specification (17) combined with some simple
dynamic device that gives information about the rate of change of unobservable λ(i, z, τ ).
We use two complementary approaches. The reduced form approach uses cross-bordertime fixed effects to pick up the trade volume effect of evolving bilateral capacity.16 A fully
general bilateral-time fixed effect set fits the data perfectly but gives no information about
economic structure, so restriction is necessary to discover anything. The restricted set applied here uses uniform cross-border fixed effects that vary over time without restriction toallow for non-smooth effects of globalization. The evidence suggests a smooth evolution of
the estimated fixed effects, and hence suggests that a single dynamic adjustment parameter combines with ρ. Applying an external adjustment parameter estimate then yields anestimate of ρ.
The alternative structural approach models the dynamics of λ(i, z, τ ) based Lucas andPrescott (1971) who model a parametric adjustment elasticity. Sales shares proxy the unobservable λs based on the efficient allocation theory of Section 3.2. The inferred parameteris a combination of the adjustment parameter and ρ, so in combination with an external
adjustment parameter it yields an estimate of ρ. The advantages and disadvantages of thetwo approaches are discussed with the findings in sections 4.2 and 4.3, respectively. Before
that we briefly describe the data.
16

Bergstrand et al. (2015) also use time-varying border dummies, designed to capture the impact of
globalization on bilateral trade. A similar border-time fixed effects strategy is used by Head et al. (2010)
to estimate the decline in ‘marketing capital’ in the trade of ex-colonies with their former masters relative
to continuously non-colonial international trade. In contrast to the current approach, these earlier reduced
form specifications have no theoretical foundation pointing to structural interpretation of the estimated fixed
effects.

22

4.1

Data: Description and Sources

In order to obtain the main empirical results we use the dataset of Baier et al. (2016), which
covers total manufacturing bilateral trade among 52 countries over the period 1988-2006.17
In addition to spanning over a relatively long time period, the dataset of Baier et al. (2016)
has two advantages. First, it includes data on intra-national trade flows.18 As will become
clear shortly, availability of intra-national trade flows data is crucial for the implementationof the reduced form approach to test SR gravity theory. Second, the dataset includes dataon applied tariffs, which will enable us to identify the estimate of the trade elasticity of
substitution directly from the empirical gravity specification, and to compare it between the
short run vs. long run gravity specifications. The original source of the tariff data is theUnited Nation’s TRAINS database. In addition to trade and tariff data and a rich set of
fixed effects, we also employ data on standard gravity variables (bilateral distance, colonial
ties, etc.), which come from the CEPII distances database (see Mayer and Zignago (2011)),and data on free trade agreements (FTAs), which come from the NSF-Kellogg Database on
Economic Integration Agreements of Jeff Bergstrand. For further description of the main
dataset we refer the reader to Baier et al. (2016).
In the sensitivity analysis we also experiment with an alternative database. Specifically,
we employ the latest edition of the WIOD database, which covers 43 countries over theperiod 2000-2014. Similar to the dataset from Baier et al. (2016), the WIOD data includes
consistently constructed international and intra-national trade flows.19 The disadvantages of
17

The 52 countries/regions in the sample include: Argentina, Australia, Austria, Bulgaria, BelgiumLuxembourg, Bolivia, Brazil, Canada, Switzerland, Chile, China, Colombia, Costa Rica, Cyprus, Germany,
Denmark, Ecuador, Egypt, Spain, Finland, France, United Kingdom, Greece, Hungary, Indonesia, Ireland,
Iceland, Israel, Italy, Jordan, Japan, South Korea, Kuwait, Morocco, Mexico, Malta, Myanmar, Malaysia,
Netherlands, Norway, Philippines, Poland, Portugal, Qatar, Romania, Singapore, Sweden, Thailand, Tunisia,
Turkey, Uruguay, United States
18
Intra-national trade flows are constructed as apparent consumption, i.e. as the difference between the
gross value of total production and total exports. The original trade data come from the UN COMTRADE
database, accessed via WITS. The data on total gross production come from the CEPII TradeProd databaseand UNIDO IndStat database.
19
The intra-national trade flows in the WIOD database are constructed using input-output linkages. See
Timmer et al. (2015) and Timmer et al. (2016) for further details.

23

WIOD dataset, as compared to the data used to obtain the main results, are that the WIOD
data cover a shorter time period and a smaller number of countries. However, the WIOD
dataset also has two main advantages. First, it offers a complete sectoral coverage for eachof the countries in the sample. Thus, summing across all sectors will enable us to cover total
trade (including international and intra-national trade flows) for each country in the sample.
Second, on a related note, we will use the WIOD data to test our theory at the sectorallevel. We do take advantage of these features of the WIOD data in the sensitivity analysis
that we present in Appendix B, where we demonstrate that our findings are confirmed with
the WIOD dataset.

4.2

A Reduced Form Approach to Short Run Gravity

Start with the intuition that in an era of globalization (1988-2006 or 2000-2014 depending on
the dataset), cross-border trade capacities λ(i, z, τ ) are inefficiently small (network links are
inefficiently sparse) while domestic capacities λ(i, i, τ ) are inefficiently large (trade links are
relatively too dense). Over time capacity investment presumably evolves toward efficiency,
so cross-border investment in trade links rises relative to domestic investment in trade links.
The reduced from approach looks for evidence in cross-border time fixed effects without
imposing any time path of adjustment.
Cross-border-time fixed effects averaged over the cross-destination variation for an origin
are structurally interpreted as:[λ(i, z, τ )/λ(i, i, τ )]1−ρ = [λ(i, z, 0)/λ(i, i, 0)]1−ρ µ(i, τ ), z 6= iwhere µ(i, τ ) > 1 is the growth factor of [λ(i, z, τ )/λ(i, i, τ )]1−ρ .20 No structure is imposedover time, so µ(i, τ )/µ(i, τ − 1) is not restricted over τ . Initially we average across all cross20

P
The adding up condition z λ(i, z, τ ) = 1 combined with the uniform growth factor assumption implies
that d ln λ(i, z) = µ(i, τ )λ(i, i, τ ) and d ln λ(i, i, τ ) = −µ(i, τ )[1 − λ(i, i, τ )]. In the panel gravity regressions
the effect of λ(i, i, τ ) on d ln λ(i, z, τ ) is absorbed by the origin-time fixed effects.

24border pairs at each point in time, µ(i, τ ) = µ(τ ). Subsequently we allow for differential
rates of adjustment for origin countries specialized to a difference between developed anddeveloping countries. Other uniformity restrictions are plausible as well in order to supply
degrees of freedom to identify the average time variation of primary concern. Idiosyncratic
variation of growth of λ(i, z, τ )/λ(i, i, τ ) that deviates from the uniform growth assumption
is associated with effects that go into the error term of the gravity equation.
A useful benchmark estimation is a panel gravity model that does not control for theefficiency improvements to be looked for based on the short run gravity theory. Thus ρ = 1
and the econometric model run in logs with OLS is:21

LN Xij,τ= β1 LN DISTij + β2 CN T Gij + β3 CLN Yij + β4 LAN Gij + β5 F T Aij,τ +β6 LN T ARIF Fij,τ + β7 IN T L BRDRij + πi,τ + χj,τ + ij,τ ,(18)

The dependent variable in (18) is the logarithm of nominal bilateral trade flows. The regressors are the standard gravity variables including the logarithm of bilateral distance between
countries i and j (LN DISTij ), and indicator variables for contiguous borders (CN T Gij ),common language (LAN Gij ), colonial ties (CLN Yij ), and free trade agreements (F T Aij,τ ).
In addition, we include the log of applied tariffs (LN T ARIF Fij,τ ).22 IN T L BRDRij is anindicator variable that takes a value of one for international trade and it is equal to zerofor internal trade. Specification (18) includes exporter-time and importer-time fixed effects
to control for the multilateral resistances of Anderson and van Wincoop (2003) and will absorb any other observable and unobservable country-specific characteristics on the exporterand on the importer side, respectively. Finally, following the recommendation of Cheng andWall (2005), we use 3-year intervals instead of consecutive years in order to obtain our main
21
Specification (18) is consistent with the traditional empirical approach to estimate gravity with the OLS
estimator. We show in the sensitivity experiments that our results are robust to using the PPML estimator
instead, which, as demonstrated by Santos Silva and Tenreyro (2006, 2011), simultaneously accounts forheteroskedasticity and takes into account the information contained in zero bilateral trade flows.
22
Since tariffs are a direct price shifter, the estimate of the tariff elasticity equals the trade elasticity σ.

25estimates.23
Estimates obtained from specification (18) are reported in column (1) of Table 1. Withan R2 = 0.88, gravity delivers its usual strong fit. In addition and as expected, distanceand tariffs24 are strong impediments to trade, while the presence of colonial ties, sharing
a common official language, and having FTAs in force all promote bilateral trade. The
negative, large, and significant estimate on IN T L BRDR is also expected, and it confirms
the strong presence of international borders, even after controlling for the impact of distanceand tariffs. Apart from the insignificant estimate on CN T G, all other estimates from column(1) of Table 1 are readily comparable to corresponding estimates in the literature (see themeta analysis estimates from Head and Mayer (2014)). In sum, the results from column (1)of Table 1 are long run benchmarks that confirm the representativeness of our sample andprovide long run responses to compare to the short run responses that follow.
The estimates from column (2) of Table 1 are obtained with time-varying cross-borderP
trade fixed effects. A series of year-specific border dummies, 2006
τ =1991 βτ IN T L BRDR τij ,are introduced to (18):
LN Xij,τ = β1 LN DISTij + β2 CN T Gij + β3 CLN Yij + β4 LAN Gij + β5 F T Aij,τ + β6 LN T ARIF Fij,τ +β7 IN T L BRDRij +2006
X

βτ IN T L BRDR τij + πi,τ + χj,τ + ij,τ ,(19)

τ =1991

The theoretical interpretation of each of the time-varying border estimates is βτ = (1 −ρ)∆ ln[λ(i, z, τ )/λ(i, i, τ )] = (1 − ρ)∆ ln µ(τ ) and, by construction, these estimates should beinterpreted as deviations from the estimate of β7 . Due to perfect collinearity, we omit theborder for the first year of the sample, 1988.
The estimates in column (2) of Table 1 show that the estimates on IN T L BRDRij are
all positive, statistically significant, and gradually increasing over time. SR gravity theory in23

We demonstrate in the sensitivity experiments below that our main results and conclusions are robust
to using all years in the sample. We refer the reader to Head and Mayer (2014) and Yotov et al. (2016) for
further discussion of the challenges with the estimation of empirical gravity models and their solutions.
24
The estimated tariff elasticity suggests a value of σ that is low relative to previous estimates. We suspect
this is due to aggregation bias for such a heterogeneous sector as manufacturing.

26

an era of globalization is consistent with this finding, hence the model provides a structuralinterpretation of the “missing globalization” that places the “puzzle” in a plausible marketing
capital black box. Second, the estimates of the standard gravity variables are statisticallyunchanged from column (1), implying that the uniform growth assumption imposed in (19)
is approximately valid (non-uniform growth would likely be correlated with cross-section
variation in bilateral distance, etc.). Third, the R2 is essentially the same in columns (1)and (2).25 The reason is that the border-time fixed effects control for globalization effects
that were controlled for in column (1) by the origin-time fixed effects. Omitted variable bias
in the benchmark specification is thus confined to the origin-time fixed effects.26 This result
is intuitively consistent with exporters altering λs to exploit the globalization opportunity,
although the analytic comparative static derivative is too complex for proof.
The estimates from column (3) of Table 1 are obtained after allowing for the effects
of distance to vary over time. Specifically, we interact the distance variable with dummy
variables for each year on our sample.27 In order to ease the interpretation of our results,
we keep the original distance variable and do not include the distance variable for 1988.
Thus, the estimate on LN DIST should be interpreted as the effect of distance in 1988,
and all other time-varying distance estimates should be interpreted as deviations from theestimate on LN DIST . Column (3) implies that distance elasticities are stable over time.
The “distance puzzle” of non-declining distance elasticities in international trade (Disdierand Head (2008)) remains.
The estimates from columns (4) and (5) of Table 1 employ pair fixed effects. The motivation for the use of the time-invariant bilateral dummies is twofold. First, these variables
will completely account for the impact of all observable and unobservable determinants ofbilateral trade, cf. Agnosteva et al. (2014) and Egger and Nigai (2015). Second, on a related
25

We thank Thomas Chaney for pushing us to explain this.
Examination of the origin- and destination-time fixed effects (not shown) for columns (1) and (2) reveal
almost no change in the destination-time fixed effects and substantial changes in the origin-time fixed effects.
27
In principle, we could allow for the effects of all gravity variables to vary over time. We chose to focus on
distance only for expositional simplicity and because the distance variable has been used most prominently
to capture trade costs and their changes.
26

27

note and as demonstrated by Baier and Bergstrand (2007), the use of the pair fixed effects
will help mitigate endogeneity concerns related to the trade policy variables in our specification. The main findings from columns (4) and (5) are that (i) the estimates of the trade
policy variables are unchanged across the two specifications; and (ii) we observe the gradualand economically and statistically significant increase in the estimates on the international
border dummies. Exponentiating the border-time cumulative efficiency change estimate incolumn (5) of Table 1 (0.965) yields an overall efficiency of trade gain from 1988-2006 of
162%: world cross-border trade is 162% larger in 2006 than it would have been with themore inefficient bilateral capacities of 1988.
For purposes of generating estimates of the key incidence parameter ρ, we average theµ(τ )s to a smooth exponential increase in efficiency, µ̃(τ ) = ebτ τ where bτ equals 1 − ρtimes the growth rate of λ(i, z)/λ(i, i). Smooth growth actually turns out to be a close
approximation in our results below. We first recover b̂τ = (1 − ρ)δ as the slope of the fitted
line of the estimates of the changes in the effects of international borders, from our preferred
specification with paired fixed effects from column column (5) of Table 1. The best-fit linein the βτ –τ coordinate space is plotted in Figure 1. The regression implies that the slope isb̂τ = 0.046. In combination with an external value of δ = 0.061,28 the estimate b̂τ = 0.046
enables us to recover ρ̂ = 1 − b̂τ /δ = 0.246.
Column (6) relaxes the uniform efficiency growth restriction to allow for efficiency growth
to vary across ‘rich’ vs. ‘poor’ exporters, as classified by the World Bank.29 The estimatesfrom column (6) of Table 1 reveal significant efficiency improvements for each group of coun28

This value for δ is the average adjustment cost parameter estimate from the structural gravity settingof Anderson et al. (2015), obtained under the same assumptions for investment. Specifically, Anderson etal. (2015) recover δ from a second stage regression that links trade openness to capital accumulation. Theseauthors also obtain a distribution of country-specific capital adjustment cost parameters that vary between
1.6 and 13.6.
29
Note that non-uniform efficiency growth does not violate the structural assumptions used to specify
short run gravity. In principle origin-specific estimates of the efficiency-improvement effects βτ (i)’s can be
identified from variation across destinations z under a uniformity condition imposed on the external (foreign)destinations vs. internal trade. The original World Bank classification includes five income categories:‘High Income OECD’, ‘High Income Non-OECD’, ‘Upper Middle Income’, ‘Lower Middle Income’, and ‘Low
Income’ countries. We used the top three categories to form our sample of ‘rich’ countries, and the bottom
two categories to form the group of ‘poor’ countries.

28

tries captured by the positive, significant, and gradually increasing over time estimates on
IN T L BRDR HIGH and IN T L BRDR LOW . More importantly, low income countries
have converged faster toward more efficient trade during the period of investigation. (Theresult may not be robust to further country level disaggregation, plausibly being driven by
few outliers such as China. The difference between high income and developing countries
may also an artifact of composition effects, as the sectoral composition of manufacturingchanges differently across countries. Sectoral disaggregation is indicated as part of investigating country differences.)
A series of sensitivity experiments demonstrate the robustness of our main results, summarized here with a full report in Appendix B. Motivated by the work of Santos Silva andTenreyro (2006, 2011) advocating the PPML estimator as an alternative to OLS with thelog of gravity, Table 2 replaces the main estimates from Table 1 with those based on the
PPML estimator. PPML estimates confirm the OLS results: all border-time estimates are
positive, significant and increasing over time. Another experiment uses size-adjusted tradeas the dependent variable. The size-adjusted dependent variable specification is consistent
with theory and tends to reduce the problem of heteroskedasticity associated with the levelof trade specification (19). The OLS and PPML estimates using size-adjusted trade as dependent variable confirm the robustness of our main findings. A third experiment uses data
for all years rather than 3 year intervals. The OLS and PPML results are very similar to
the main estimates from Table 1. The next experiment employs the newly available 2016
WIOD data.30 Again, the main results from Tables 1 and 2 are closely matched with OLS
and PPML estimators respectively. Finally, exploiting the sectoral dimension of the WIOD
data we reproduce our main results for Crop and Animal Production, Forestry and Logging,
Fishing and Aquaculture, Mining and Quarrying, Manufacturing, and Services. The results
naturally vary by sector, but the main finding for the presence of efficiency improvement ispresent in each sector.
30

See Data section for a description and details on the WIOD data.

29

4.3

A Structural Approach to Short Run Gravity

The complementary structural approach to estimating short run gravity adds a simple ad
hoc theory of investment in bilateral capacity. The investment structure in combination
with external values of an adjustment speed parameter enables inference about the buyers’
incidence parameter ρ. This can be compared with inference of ρ from the reduced form
model as a consistency check between the two complementary approaches.31 Alternatively,
inference from the two approaches simultaneously provides estimates of ρ and the adjustment
parameter. The structural and the reduced form approaches come quite close in the estimatesof ρ detailed below. The structural model also permits tests of implication (14).
Suppose that intensive margin investment in pair-specific capital moves the current levelfrom its past level toward the efficient level at some rate of log-linear adjustment that is
implied by a Cobb-Douglas function of efficient and past levels.32 The adjustment process
specification is inspired by inter alia Lucas and Prescott (1971), Hercowitz and Sampson(1991), and Anderson et al. (2015) and Eaton et al. (2016) in the gravity context:

λ(i, z; τ ) = λ∗ (i, z)δ λ(i, z; τ − 1)1−δ ; δ ∈ (0, 1).

(20)

The parameter δ reflects both costs of adjustment and depreciation, the higher is δ the fasterthe movement to the efficient level. In the steady state, λ = λ∗ .
31

There are advantages and disadvantages to the treatment of efficiency improvements with border-time
dummies. A big advantage is that dummy variables are exogenous by construction, hence avoid the endogeneity issues raised by the complementary structural approach to dynamic adjustment. Another advantageof the dummy variable approach relative to the structural approach is a comprehensive accounting for allforces that could have contributed to improved efficiency over time, including those omitted from the structural approach. Thus, while (19) imposes a uniform efficiency improvement across destinations z 6= i ateach time τ , the specification does not impose any pattern whatever on efficiency variation over time. The
disadvantage of the efficiency treatment with border-time dummies is that it does not permit identificationof ρ, but only the effect of adjustment of cross-border capacity toward the long run over time.
32
The approach developed here is a first cut at a difficult problem. It leaves out plausibly important effects.
Investment in bilateral trade may be systematically affected in a differential fashion by a number of variables
reflecting allocations subject to credit constraints. Exchange rate risk’s effects on trade flows can be hedged
for many sectors with minimal cost, but hedging over longer intervals appropriate for fixed commitments isexpensive. This suggests that bilateral exchange rate volatility may significantly affect investment in bilateral
trade but not variable trade cost. Similarly, bilateral covariance of business cycles may affect investment but
not variable trade cost. Such refinements are beyond the scope of this project.

30

Operationalization of the adjustment process requires finding observables to replace theunobservable λs. The agents know that efficient allocation implies that λ∗ (i, z) = s∗ (i, z).
This suggests that λ(i.z, τ ) → s(i, z, τ ). Groping ahead toward the eventual efficient allocation suggests a specification of the dynamic process replacing s∗ (i, z) with s(i, z, τ ). Moving
toward operationality, replace the unobservable λ∗ (i, z) = s∗ (i, z) in (20) with s(i, z, τ ). Similarly, replace the unobservable λ(i, z, τ − 1) with s(i, z, τ − 1). (Note that λ(i, z) is likely
unobservable by individual competitive firms in i exporting to multiple zs, as well as by
the econometrician.) Then the costly adjustment specification in the spirit of Lucas andPrescott is:33
λ(i, z, τ ) = s(i, z, τ )δ s(i, z, τ − 1)1−δ .
The steady state of this process reaches the efficient allocation of long run gravity, is plausible as an approximation to more sophisticated expectations mechanisms, and its simplicity
preserves the simple loglinear features of structural gravity.
Substitute the right hand side of the preceding equation for the (implicit) contemporaneous value of λ(i, z, τ ) in gravity equation (13). The result is#(1−σ)ρ
"i1−ρ
ht(i, z, τ )Y (i, τ )E(z, τ )s(i, z, τ )δ s(i, z, τ − 1)1−δ.
X(i, z, τ ) =Y (τ )
Π(i, τ )Pe(z, τ )The presence of contemporaneous trade share s(i, z, τ ) on the right hand side of the preceding
equation requires solution for contemporaneous bilateral trade flows to yield:

X(i, z, τ ) = Y (i, τ )E(z, τ )Y (τ )11−δ(1−ρ)"t(i, z, τ )Π(i, t)Pe(z, τ )33# (1−σ)ρ 
1−δ(1−ρ)X(i, z, τ − 1)
Y (i, τ − 1)

 (1−δ)(1−ρ)
1−δ(1−ρ). (21)The specification here is in part an expedient to deal with the problem of unobservable capacity allocations, but on a conceptual level it violates rational expectations. The alternative of super-humanly rational
expectations is implausible considering the extremely high dimensionality where each bilateral link has potentially many uncoordinated agents and there are very many links with simultaneous interaction. In a
simpler environment of perfect information, Anderson et al. (2015) combine the Lucas-Prescott adjustment
mechanism with the consumer’s inter-temporal maximization problem to derive the optimal accumulationof country-specific physical capital. In contrast, the present case involves a bilateral capacity adjustment oneach link, N 2 adjustment paths compared to N in the simpler case.

31

Use the standard gravity proxies for bilateral trade costs introduced in the previous section, log-linearize specification (21), and add an error term in order to obtain the econometricmodel:34
LN Xij,τ = β̃1 LN DISTij + β̃2 CN T Gij + β̃3 CLN Yij + β̃4 LAN Gij + β̃5 F T Aij,τ + β̃6 LN T ARIF Fij,τ +β̃7 IN T L BRDRij + β̃8 LN Xij,τ −1 + π̃i,τ + χ̃j,τ + ˜ij,τ .

(22)Note that the exporter-time fixed effects in the preceding expression will absorb and control
for all contemporaneous as well as lagged exporter-specific characteristics, including thestructural contemporaneous and lagged size terms, that may affect bilateral trade.35
The structural interpretation of the estimated coefficient on LN Xij,τ −1 is:β̃8 =(1 − δ)(1 − ρ).
1 − δ(1 − ρ)(23)(23) is used below to recover the structural efficiency parameter ρ in combination withinformation on δ.
Specification (22) for short run gravity estimation differs in two important ways from longrun gravity specification (18).36 The first difference between the two estimating equations is
the appearance of the lagged dependent variable as a regressor in the SR gravity specification(22). From an econometric perspective short run gravity implies that the standard estimationof gravity without lagged variables may suffer from omitted variable bias. Hypothesizingthat the standard gravity estimator controls also control for the omitted capacity variables,
the standard estimator may be an unbiased estimator of long run gravity. The no-bias
34

Similar to the analysis in the previous section, in the sensitivity analysis we also experiment by estimating
the model with the PPML estimator.
35
In contrast, exporter specific δi must be treated with exporter-specific β1 − β8 . An exporter-type
δi consistent with the evidence that border-time fixed effects differ between high income and developing
economies. We impose a common δ here since our use of aggregate manufacturing trade confounds dynamic
adjustment cost effects with changing composition effects that vary across exporters. A proper investigationof origin variation in δ should be done with disaggregated data.
36
In addition to the two estimation-related differences, the structural interpretation of the fixed effects
will also be different in the SR gravity specification since the size variables no longer appear with unitaryelasticities in the theoretical SR gravity model. However, this has no consequences for gravity estimations.

32

hypothesis can be tested jointly with the structural implications of short run gravity, thesecond difference between specifications (18) and (22).
The theoretical relationship between long run and short run gravity coefficients in Corollary 2.1, extended to accommodate the theory of investment developed here is:β̃SR = βLRρ,
1 − δ(1 − ρ)(24)

where, the subscripts SR and LR denote estimates from the short run (SR) and from thelong run (LR) empirical gravity specifications, respectively. For any given gravity variable
coefficient, the combination of equations (23) and (24) enable a joint test of SR gravity
structure and the no-bias hypothesis for estimates of long run gravity by checking whether:β̃SR= 1 − β̃8 .
βLR

(25)

Because the gravity specifications include six gravity covariates, test (25) is performed six
times, and reported below.
The natural starting point for estimation is a standard/long run gravity model:
LN Xij,τ = β1 LN DISTij + β2 CN T Gij + β3 CLN Yij + β4 LAN Gij + β5 F T Aij,τ + β6 LN T ARIF Fij,τ +β7 IN T L BRDRij + πi,τ + χj,τ + ij,τ ,(26)

The only difference between specifications (22) and (26) is the absence of lagged trade in thelatter specification. The standard gravity estimates from column (1) of Table 3 are readily
comparable to their counterparts from the previous section. The estimates from column (2)of Table 3 are obtained from specification (22) with a lagged dependent variable.
An important potential issue is the dynamic panel bias from the use of a lagged dependent
variable, i.e. the Nickell (1981) bias. As explained in Roodman (2009a), the use of sufficiently
long time spans may mitigate and even eliminate the Nickell bias by construction. The

33

analysis in this section employs every year in the dataset37 motivated by this observation.
Importantly, even if the time coverage is not long enough to eliminate the dynamic panel
bias completely, the ‘naive’ OLS results from column (2) are useful for our purposes because
they establish an upper bound for the key estimate of the coefficient β̃8 on the structural
efficiency term LN Xij,τ −1 .38 This, in combination with expression (23), will enable us todraw inference about the bounds for the structural efficiency parameter ρ. In particular, we
will use the estimates from column (2) to establish a lower bound for ρ. Finally, note that the
OLS results from column (2) will be supported by the findings from the more sophisticatedeconometric specifications that we employ below.
The estimates in column (2) of Table 3 reveal a positive and significant estimate ofβ̃8 = 0.788 (std.err. 0.009). While the estimate of β̃8 seems fairly large in magnitude, it isquite low to be explained solely by the capital adjustment cost δ from our theory. Capitalizeon the structural restriction (23) in combination with an external estimate δ = 0.061 in orderto recover the incidence elasticity parameter ρ = 0.202 (std.err. 0.008). Three implications
follow.
First, column (2) of Table 3 implies that gravity estimates that do not control for efficiency
improvements and adjustment may suffer significant biases. The estimates from column (1)are very significantly larger than the estimates from column (2). This result reinforces thefindings of Olivero and Yotov (2012) and Eichengreen and Irwin (1996) who conclude thatthey “will never run another gravity equation that excludes lagged trade flows” (p.38). But
the possible bias may be one of interpretation under a valid ‘no-bias’ hypothesis that standard
gravity covariates also control for variation of the omitted variable.
Second, SR gravity theory as captured by equation (24) implies at least partial solution
to the trade elasticity puzzle – the gap between estimates of the trade elasticity σ from the37

In the sensitivity experiments we also employ the 3-year interval data from the previous section and we
demonstrate that our main results are robust to employing this alternative sample.
38
Specification (26) will deliver an upward bound for the estimate on β̃8 due to positive correlation between
the lagged dependent variable and the pair fixed effects in the error term, which will inflate the estimate on
LN Xij,τ −1 by attributing additional predictive power to it. See Roodman (2009a) for further details and avery informative discussion.

34

trade and the macro literatures, cf. Ruhl (2008), Arkolakis et al. (2011) and Crucini andDavis (2016).
Third, column (2) of Table 3 implies support for the quantitative structural predictionsof SR gravity theory and the ‘no-bias’ hypothesis. Expression (25) implies the hypothesistest:
1 − β̃8 − β̃SR /βLR = 0(27)

The test statistic in column (3) of Table 3 uses the estimated coefficients of columns (1)-(2)of Table 3 in (27) for each of the gravity variables. The null hypothesis cannot be rejected
at high levels of significance for all six tests.39
The results from the lagged dependent variable empirical model are complements to theborder-time dummy variable model under the strong assumption that the Lucas-Prescottadjustment model (20) applies to both. In that case, the border-time dummy variable
coefficient β7 +βτ should in theory be declining at rate bτ = (1−ρ)δ.40 The lagged dependent
variable model implies β8 = (1 − ρ)(1 − δ)/[1 − δ(1 − ρ)]. This structure can be used in two
ways. First, for a given δ, compare the implied value of ρ from the lagged dependent variable
model to the implied value of ρ from the border-time dummy variable model. Second, solve
the two equations simultaneously for the unique values of ρ and δ that satisfy the equations:ρ̂ = (1 − β̂8 )(1 − b̂τ ) and δ̂ = b̂τ /[β̂8 + b̂τ (1 − β̂8 )].
We first recover b̂τ = (1 − ρ)δ as the slope of the fitted line of the estimates of the changes
in the effects of international borders, from our preferred specification with paired fixed effects
from column column (5) of Table 1. The best-fit line in the βτ –τ coordinate space is plottedin Figure 1. The regression implies that the slope is b̂τ = 0.046. In combination with the
adopted value of δ = 0.061, the estimate of b̂τ = 0.046 enables us to recover ρ̂ = 1 − b̂τ /δ =39

The largest estimate that we obtain in column (3) is for CLN Y . However, as can be seen from columns(1) and (3) of Table 3, the estimate of the effect of sharing a common border is insignificant to start with.
Thus, even though the corresponding estimate in column (3) is insignificant and supports our theory, we
discount this finding.
40
Divide both sides of (20) by λ(i, z, τ − 1) to yield λ(i, z, τ )/λ(i, z, τ − 1) = [λ∗ (i, z)/λ(i, z, τ − 1)]δ withgrowth rate δ.

35

0.246. This value is somewhat larger but comparable in magnitude to the preceding estimateof ρ = 0.202 from the structural approach above. Finally, use the estimates of β̂8 and b̂τ inthe simultaneous equations ρ̂ = (1 − β̂8 )(1 − b̂τ ) and δ̂ = b̂τ /[β̂8 + b̂τ (1 − β̂8 )] in order tosimultaneously recover unique values of ρ̂ = 0.202 (std.err. 0.008) and δ̂ = 0.058 (std.err.
0.001). ρ is statistically and quantitatively indistinguishable from the estimate of using theexternal value of δ = 0.061 while the internally generated estimate of δ differs statisticallysignificantly but quantitatively insignificantly from the external value. The close magnitudesof the various inferences of the value of ρ are compelling. Pushing inference to the limit, wenote that the lower value of δ̂ = 0.058 obtained from the simultaneous solution corresponds
more closely to the interest rate values that are used for calibrations in the macroeconomic
literature.
Estimates of ρ̂ imply restrictions on the deep structural parameters of supply η anddemand σ because
1/ρ − 1 = (σ − 1)/η.
Using the estimate ρ̂ = 0.20 ⇒ η̂ = (σ − 1)/4. Estimate of σ in the literature41 range from 4
to 10, implying η̂ ∈ [0.75, 2.25]. The finite short run supply elasticities implied pass a smell
test (with heterogeneous firms, η̃ < 1 is readily possible) and provide an intuitive foundation
for thinking about short run gravity.
Columns (4)-(8) of Table 3 report results from alternative estimators. Columns (4)and (5) use pair fixed effects for two reasons. First, the pair fixed effects will absorb andcontrol for any omitted time-invariant determinants of bilateral trade. Second, the useof pair fixed effects has proven to be a useful method to address possible endogeneity of
FTAs and trade policy in general. In the context of dynamic panel bias caused by thelagged dependent variable (Roodman (2009a)), an additional advantage of pair fixed effects is
mitigation of the dynamic panel bias. The so-called Least Square Dummy Variable (LSDV)
treatment of the Nickell bias is especially effective for samples with long time coverage.
41

The estimate of 1 − σ inferred in our regressions is lower but we assume it is biased downward.

36

Finally, as demonstrated in Roodman (2009a), in case the LSDV estimator does not eliminate
completely the bias in the estimate of the lagged dependent variable, then the remaining bias
would be a downward bias owing to a negative correlation between the lagged dependent
variable and the remaining error. This, in combination with expression (23), enables us toestablish an upper bound for ρ. Using external value δ = 0.061, the result in column (5)give an upper bound ρ̄ = 0.371 (std.err. 0.011) to pair with the lower bound from column(2) ρ = 0.202.
Two further results stand out from columns (4)-(6). First, the SR gravity theory test (27)reported in column (6) offer strong support for the theory. Second, in combination with theestimates from the border-time dummy variable model, the results from column (5) implyρ̂ = 0.368 (std.err. 0.011) and δ̂ = 0.072 (std.err. 0.001). The incidence elasticity estimateof ρ is almost unchanged by the switch from externally to structurally generated δ.
The relatively long time coverage of our sample attenuates endogeneity bias in the LSDV
estimator of SR gravity of column (5), but may not eliminate it. Column (7) of Table 3 thus
implements an IV estimation along the lines of Frankel and Romer (1999). We construct an
instrument for lagged trade by using a reduced form gravity specification that only includes
the standard gravity variables, which are exogenous by definition, and also exporter andimporter population, which also are arguably exogenous. We use the second to fifth lagsof the newly constructed trade variable as instruments for the lagged dependent variable inspecification (22). The estimation results from column (7) support our theory. First, theinstruments are good since, based on the specification tests that we perform in the bottomof Table 3, they pass all IV tests. Second, once again, we obtain a positive and significant
estimate on the lagged trade term. In combination with (23) and the external value ofδ = 0.061, ρ = 0.242 (std.err. 0.120). We calculate ρ̂ = 0.242 (std.err. 0.118) and δ̂ = 0.061(std.err. 0.009) when we combine the estimates from column (7) with those from the main
results from the border-time dummy variable model. The close approximation of the two
estimated parameter vectors is remarkable. Pushing the results of the various specifications

37

hard, our preferred range for the key incidence elasticity is ρ ∈ (0.20, 0.24) and our preferredvalue is 0.24, while we report a conservative range ρ ∈ (0.20, 0.37).
Note finally that the SR test for the LSDV IV estimation reported in column (8) weakly
supports the theory. We cannot reject the null hypothesis for the FTA variable. In contrast,
the test statistic on LN T ARIF F rejects the null. We are suspicious of all estimates of thetariff parameter due to aggregation bias and low variation.
We conclude with a brief description of robustness checks. Detailed results and descriptions for each experiment can be found in Appendix B. The first experiment uses interval
data instead of yearly data. The second experiment uses size-adjusted trade as the dependent variable. Use of the trade share instead of the level of trade tends to reduce the problemof heteroskedasticity. The third sensitivity experiment uses international trade data only.
All three experiments confirm robustness of the main findings. We also experiment with the
PPML estimator, yielding estimates that correspond to the upper and lower bound resultsfrom Table 3. The next experiment employs the system-GMM estimator of Arellano andBond (1991) and Arellano and Bover (1995)/Blundell and Bond (1998). Here the results forρ are higher, though remaining well inside the unit interval. (We suspect the poorer small
sample properties of the system-GMM estimator are to blame.) Finally, the main results
are reproduced with the aggregate WIOD data as well as for each of the main sectors thatare covered in the WIOD dataset. In each case, the new estimates are consistent with andcomparable to the main results from Table 3.

4.4

Real Income in the Short vs. Long Run

The model is next used to quantify the potential real income gain from long run efficient
allocation of marketing capital – gains from globalization in the limit. The counterfactual
experiment compares two static equilibria, one short run that represents the 2006 estimatedshort run model of the economy and the other long run with all parameters and variables
except for marketing capital held constant. Importantly, constancy means all 2006 bilateral38

links that are empty remain empty in the long run. Results suggest that gains are universally
big – welfare rises everywhere, ranging from 25% to 47%. This impression seems likely to beright given the model, though details would change as the many variables held constant inthis counter-factual analysis would change during any actual transition to the long run.
The computation proceeds in three steps. First, the structural approach from Section 4.3
is used in combination with our preferred estimate of the efficiency parameter ρ, to solve theshort run gravity model in baseline year 2006 (i.e., the last year in our sample). Second, we
solve the standard gravity system in the long run equilibrium. Third, we construct countryspecific real income measures as the ratio of real expenditure in the short run equilibrium toreal expenditure in the long run equilibrium. This ratio measures how far countries currently
are from where they could be with universally efficient (i.e. long run) allocation of marketing
capital. Details on the construction of the real income (welfare) percentage changes that we
present and describe here are included in Section B.3 of the Supplementary Appendix.
Our findings are presented in Table 4, which reports in percentage terms for the countries listed how far they were in 2006 from the level of real income they could achieve in auniversally efficient world economy. All indexes of the real income changes are significantly
smaller than one. With an average value of 61.5%, and ranging between 53% and 75%, theindexes imply welfare gains of 25% to 47% are possible from efficient allocation of ‘marketing
capital’. The variation across countries in real income percentage changes in Table 4 suggeststhat smaller and less developed countries are further from efficient equilibrium. Such countries (e.g., Malta, Philippines, Ireland, and Costa Rica) are mostly in the lower tail of the
distribution while the upper tail contains some larger and more developed economies (e.g.
the United States and the United Kingdom). In contrast, Qatar, Ecuador and Colombia
are relatively closer to the LR equilibrium. An at least partial explanation for Qatar’s starranking is its exports dominated by natural gas and oil exported to other Asian economies
in close proximity. Deeper explanations are beyond the scope of this paper.

39

5Conclusion and Extensions

Short run gravity features (i) joint trade costs endogenous to bilateral volumes, (ii) long run
gravity as a limiting case of efficient investment in bilateral capacities, (iii) tractable shortand long run models of the extensive margin, and (iv) a structural ratio of short run to longrun trade elasticities. Despite the complexity, bilateral trade is a geometric weighted averageof long run gravity and a bilateral capacity variable, where the weight on long run gravity
is the short run buyers’ incidence elasticity. The incidence elasticity is itself micro-founded.
The theoretical short run gravity model finds strong support in the data and the empiricalanalysis resolves several empirical puzzles.
The short run gravity model here suggests several extensions. (i) The model can be applied at the firm level, where indeed its assumption of a common Cobb-Douglas distribution‘production’ function is most natural. (ii) Another potential extension is to the explanationof income inequality. The rents to destination-specific managerial labor may be linked toinefficient investment and costs of adjustment, inducing income inequality within firms andacross firms in a sector. (iii) The model also extends upward to embedding in a multi-sector
general equilibrium setting. The stock of labor and human capital is simply the sectoral
allocation, possibly with differentials due to search costs. (iv) Empirical implementationand tests of the short run and long run extensive margin implications of SR gravity is an
important challenge.
More challenging, perhaps leading outside the scope of the present model, is opening
the black box of bilateral capacity. This paper treats capacity investment as effectively
on the exporter side only. Since some investment is on the importer side, this may affectthe short run statics and dynamics of the model. Firm level data and modeling suggests
more carefully modeling the ‘manager’ input, sources of heterogeneity across markets andalso across modes of organization: arms length contracting, joint ventures or horizontal
integration in a multinational structure. The Arkolakis (2010) model extended to a dynamic
setting may be a useful starting point.
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44

Table 1: SR Gravity with Efficiency Improvements, OLS Estimates
LN DIST
CNTG
CLNY
LANG
FTA
LN TARIFF
INTL BRDRINTL BRDR 1991
INTL BRDR 1994
INTL BRDR 1997
INTL BRDR 2000
INTL BRDR 2003
INTL BRDR 2006
LN DIST 1991
LN DIST 1994
LN DIST 1997
LN DIST 2000
LN DIST 2003
LN DIST 2006

(1)
Standard-1.184(0.049)∗∗-0.047(0.189)0.460(0.159)∗∗0.782(0.107)∗∗0.413(0.062)∗∗-1.723(0.443)∗∗-3.235(0.299)∗∗(2)
Efficiency-1.185(0.049)∗∗-0.048(0.189)0.459(0.159)∗∗0.782(0.107)∗∗0.406(0.062)∗∗-1.704(0.442)∗∗-3.733(0.324)∗∗0.215(0.091)∗
0.462(0.098)∗∗0.622(0.122)∗∗0.685(0.132)∗∗0.722(0.149)∗∗0.799(0.160)∗∗(3)
DistPuzzle-1.183(0.057)∗∗-0.047(0.189)0.460(0.159)∗∗0.781(0.107)∗∗0.419(0.065)∗∗-1.719(0.445)∗∗-3.737(0.336)∗∗0.381(0.116)∗∗0.551(0.158)∗∗0.508(0.166)∗∗0.664(0.174)∗∗0.713(0.197)∗∗0.680(0.209)∗∗-0.051(0.030)+-0.027(0.040)0.034(0.037)0.006(0.038)0.002(0.041)
0.035(0.042)INTL BRDR HIGH 1991

(4)
PairFEs(5)
Efficiency2(6)Development

0.165(0.041)∗∗-1.311(0.308)∗∗0.147(0.041)∗∗-1.283(0.306)∗∗0.139(0.041)∗∗-0.990(0.260)∗∗0.231(0.092)∗0.511(0.098)∗∗0.713(0.121)∗∗
0.812(0.131)∗∗0.864(0.144)∗∗0.965(0.158)∗∗0.314(0.237)INTL BRDR HIGH 1994
0.589
(0.187)∗∗INTL BRDR HIGH 1997
0.800
(0.258)∗∗INTL BRDR HIGH 2000
1.009
(0.262)∗∗INTL BRDR HIGH 2003
1.065
(0.267)∗∗INTL BRDR HIGH 2006
1.287
(0.306)∗∗INTL BRDR LOW 1991
0.438
(0.177)∗0.939
INTL BRDR LOW 1994
(0.214)∗∗INTL BRDR LOW 1997
1.235
(0.226)∗∗INTL BRDR LOW 2000
1.237
(0.275)∗∗
1.351
INTL BRDR LOW 2003
(0.322)∗∗INTL BRDR LOW 2006
1.520
(0.351)∗∗
N
18345
18345
18345
18344
18344
18336
r2
0.880
0.881
0.881
0.935
0.936
0.955
Notes: This table reports results from the international-borders dummy variable approach to test SR gravity theory. All estimates are obtained with the OLS estimator and with exporter-time and importer-time
fixed effects, whose estimates are omitted for brevity. The dependent variable in each specification is thelog of nominal bilateral trade. Column (1) reports standard (long run) gravity estimates. The estimatesfrom column (2) are obtained with time-varying international border dummies, designed to capture relative
efficiency improvements. Column (3) allows for time-varying distance effects, in addition to the time-varying
border dummies. Columns (4) and (5) reproduce the results from columns (1) and (2) but with pair fixed
effects. Finally, column (6) uses the specification from column (5) but allows for heterogeneous efficiency
improvements across developed vs. developing countries. Standard errors are clustered by country pair andare reported in parentheses + p < 0.10, ∗ p < .05, ∗∗ p < .01. See text for further details.

45

Table 2: SR Gravity with Efficiency Improvements, PPML Estimates
LN DIST
CNTG
CLNY
LANG
FTA
LN TARIFF
INTL BRDRINTL BRDR 1991
INTL BRDR 1994
INTL BRDR 1997
INTL BRDR 2000
INTL BRDR 2003
INTL BRDR 2006
LN DIST 1991
LN DIST 1994
LN DIST 1997
LN DIST 2000
LN DIST 2003
LN DIST 2006

(1)
Standard-0.648(0.065)∗∗0.488(0.148)∗∗-0.049(0.109)0.325(0.139)∗0.142(0.123)-7.438(1.167)∗∗-2.635(0.154)∗∗(2)
Efficiency-0.662(0.065)∗∗0.500(0.146)∗∗-0.064(0.108)0.343(0.138)∗0.073(0.118)-6.803(1.227)∗∗-3.032(0.152)∗∗0.202(0.023)∗∗0.324(0.028)∗∗0.449(0.044)∗∗0.543(0.055)∗∗0.491(0.062)∗∗0.510(0.065)∗∗(3)
DistPuzzle-0.640(0.074)∗∗0.500(0.145)∗∗-0.066(0.108)0.345(0.138)∗0.073(0.117)-6.859(1.238)∗∗-3.069(0.164)∗∗0.182(0.057)∗∗0.297(0.055)∗∗0.394(0.086)∗∗0.595(0.106)∗∗0.561(0.106)∗∗0.621(0.090)∗∗0.011(0.023)0.013(0.023)0.028(0.031)-0.029(0.036)-0.039(0.038)-0.061(0.036)+INTL BRDR HIGH 1991

(4)
PairFEs(5)
Efficiency2(6)Development

0.318(0.077)∗∗-4.842(0.588)∗∗0.112(0.067)+-2.699(0.547)∗∗0.214(0.062)∗∗-2.122(0.448)∗∗0.147(0.016)∗∗0.249(0.024)∗∗0.401(0.035)∗∗0.481(0.041)∗∗0.498(0.043)∗∗0.570(0.040)∗∗0.436(0.054)∗∗INTL BRDR HIGH 1994
0.750
(0.078)∗∗INTL BRDR HIGH 1997
0.967
(0.150)∗∗INTL BRDR HIGH 2000
0.988
(0.227)∗∗INTL BRDR HIGH 2003
0.972
(0.208)∗∗
1.118
INTL BRDR HIGH 2006
(0.205)∗∗INTL BRDR LOW 1991
0.512
(0.084)∗∗INTL BRDR LOW 1994
1.162
(0.123)∗∗INTL BRDR LOW 1997
1.368
(0.132)∗∗INTL BRDR LOW 2000
1.520
(0.172)∗∗INTL BRDR LOW 2003
1.900
(0.187)∗∗INTL BRDR LOW 2006
2.062
(0.193)∗∗
N
18928
18928
18928
18928
18928
18928
Notes: This table reports results from the international-borders dummy variable approach to test SR gravity theory. All estimates are obtained with the PPML estimator and with exporter-time and importer-time
fixed effects, whose estimates are omitted for brevity. The dependent variable in each specification is nominal bilateral trade. Column (1) reports standard (long run) gravity estimates. The estimates from column(2) are obtained with time-varying international border dummies, designed to capture relative efficiency
improvements. Column (3) allows for time-varying distance effects, in addition to the time-varying borderdummies. Columns (4) and (5) reproduce the results from columns (1) and (2) but with pair fixed effects.
Finally, column (6) uses the specification from column (5) but allows for heterogeneous efficiency improvements across developed vs. developing countries. Standard errors are clustered by country pair and arereported in parentheses + p < 0.10, ∗ p < .05, ∗∗ p < .01. See text for further details.

46

Table 3: SR Gravity & Efficiency
LN DIST
CNTG
CLNY
LANG
FTA
LN TARIFF
INTL BRDR
L.LN TRADE(1)
Standard-1.186(0.049)∗∗-0.036(0.189)0.457(0.158)∗∗0.773(0.105)∗∗0.418(0.062)∗∗-1.513(0.378)∗∗-3.229(0.297)∗∗(2)
SR Gravity-0.248(0.016)∗∗0.005(0.039)0.092(0.034)∗∗0.147(0.022)∗∗0.108(0.013)∗∗-0.348(0.100)∗∗-0.635(0.064)∗∗0.788(0.009)∗∗
46868
0.959
0.202
(0.008)∗∗(3)SR Test1
0.003(0.0080.358(1.097)0.112(0.074)0.022(0.028)- 0.046(0.032)- 0.018(0.066)0.015(0.019)

(4)
LSDV

(5)
SR LSDV(6)
SR Test2(7)
LSDV IV(8)SR Test3

0.170(0.037)∗∗-1.114(0.259)∗∗0.070(0.016)∗∗-0.446(0.118)∗∗- 0.024(0.097)0.014(0.105)0.029(0.017)+-0.579(0.149)∗∗0.081(0.130)-0.265(0.097)∗∗0.614(0.011)∗∗
46868
0.964
0.371
(0.011)∗∗0.746(0.124)∗∗
N
49916
49916
35411
R2
0.882
0.936
0.964
ρ
0.242
(0.120)∗∗Under Id χ2
13.595p-val(0.009)
Weak Id χ2
3.394
p-val
(0.009)Over Id χ2
1.350
p-val
(0.717)
Notes: This table reports results from the structural investment approach to test SR gravity theory. All estimates are
obtained with exporter-time and importer-time fixed effects, whose estimates are omitted for brevity. The dependent
variable in each specification is the log of nominal bilateral trade. Column (1) reports standard (long run) gravity
estimates. The estimates from column (2) are obtained with lagged trade added as a covariate. Column (3) reports
the results from a test of the SR gravity theory according to equation (27). Columns (4)-(6) reproduce the resultsfrom columns (1)-(3) but with pair fixed effects, thus implementing the LSDV estimator. Column (7) implements an
IV LSDV estimation, and column (8) reports the results from test (27). The “weak identification” (Weak Id) statistics
are based on Kleibergen-Paap Wald F values, which are appropriate when the standard error i.i.d. assumption is not
met and the usual Cragg-Donald Wald statistic is no longer valid. (The corresponding Cragg-Donald Wald F statistic
is 3.781.) Robust standard errors are reported in parentheses + p < 0.10, ∗ p < .05, ∗∗ p < .01. See text for further
details.

47

Figure 1: Evolution of International Borders, 1988-2006.

Note: This figure plots the evolution of the international border estimatesfrom column (5) of Table 1, which are obtained with the OLS estimator andpair fixed effects, over time. The figure also reports the slope of the fitted line,
which corresponds to the parameter bτ from the main text.

Table 4: Real Income in SR Relative to LR(1)
Country
MLT
PHL
IRL
CRI
CHL
URY
DNK
MMR
IDN
SGP
THA
FIN
TUN
HUN
MYS
AUT
ARG

(2)
Ratio (%)
52.76154.52555.96256.04756.11556.14756.34856.71157.27157.40357.65257.87957.90758.05758.19858.37658.544(3)
Country
ISR
SWE
KWT
PRT
NLD
BGR
ISL
BOL
NOR
MAR
JPN
KOR
CHE
CAN
MEX
POL
EGY

(4)
Ratio (%)
58.59858.91959.51
60.32
60.44660.50260.51660.56
61.35561.48561.89162.41362.44262.75362.76263.19663.43(5)Country
CHN
ROM
BRA
DEU
CYP
FRA
AUS
ITA
GRC
JOR
ESP
GBR
TUR
COL
ECU
USA
QAT

(6)
Ratio (%)
63.88
63.92864.02164.19564.45564.60764.76864.94765.04965.10165.62266.09566.83768.48568.93371.71974.738Notes: This table reports the ratio (in percent) between the short-sun welfare indexes andthe corresponding long run welfare indexes based on the structural estimates from Section
4.3. Columns (1), (3), and (5) list the countries in our sample and columns (2), (4), and(6) list the corresponding welfare indexes. Countries are ranked based on how far they are,in terms of welfare, from the hypothetical long run equilibrium. For further details on theconstruction of the welfare indexes and for a discussion these results, see Section 4.4 of themain text and Section B.3 of the Supplementary Appendix.

48

Supplementary Appendix
This document is the Supplementary Appendix to “Short Run Gravity” (2018), by J. E.
Anderson and Y. V. Yotov. The appendix is not intended for publication and will appear
on the authors’ web sites.

Appendix A: Theoretical Extensions
A.1

Heterogeneous Productivities and Short Run Gravity

Short run gravity can equivalently represent a foundation based on heterogeneous productivities generated by a probability distribution (Eaton and Kortum, 2002). With productivity
draws from a Frechet (Type II extreme value) distribution, it is well known that the same
long run gravity equation system results with the trade cost elasticity 1 − σ reinterpreted
as the dispersion parameter θ of the Frechet distribution and the taste parameter βi reinterpreted as the location parameter of the productivity distribution for origin i. The CES
demand system is used in the Eaton-Kortum model but σ ends up in a background constantterm due to the infinite elasticity of transformation of the Ricardian model.
The simplicity of the Cobb-Douglas production model here allows short run long run
gravity to be interpreted in terms of either foundation. For the Eaton-Kortum interpretation,
each origin supplies potentially an infinite number of varieties to each destination. Eachvariety has the same basic Cobb-Douglas production function up to a productivity draw
parameter divided by an iceberg trade factor. The proportion of draws favorable enough topermit shipments to destination j relative to shipments from all origins to destination j isa CES-type share function of unit cost of delivered output from origin i relative to an index
of unit costs of delivered output to j from all origins. The key link between the two models
is that the unit cost of delivered output in equilibrium in the short run model plays thesame role in either model. Note also that the long run Cobb-Douglas model with efficient
capacities becomes Ricardian, as in the Eaton-Kortum model.
49

Feenstra (2016) following Chaney (2008) shows that with constant iceberg bilateral trade
costs and Melitz (2003) Pareto distributed productivities, a version of the structural gravity
model emerges, with the trade cost elasticity having a different interpretation and fixed
costs playing a role. The key step in reaching this conclusion is that the combination of
Pareto distribution and iceberg bilateral costs leads to a log-linear closed form solution forthe productivity of the least productive firm in any origin able to serve each destination fromthat origin. The Pareto distribution then yields a log-linear expression for the proportion offirms from each origin that serve each destination.
For purely competitive firms with Pareto distributed productivities, fixed costs of exporting to a destination, and the increasing variable bilateral trade costs modeled in this paper,
Section A.1.1 below shows that the optimized (restricted) profit function has a constantelasticity with respect to productivity. This implies a closed form solution for the minimum
productivity firm and thus the proportion of firms that can serve any market. In this case,the heterogeneous purely competitive firms model again yields a standard structural gravity
equation. The trade cost elasticity is now a function of the elasticity of substitution σ, thePareto distribution dispersion parameter θ and the elasticity of transformation 1/(1 − α).
The monopolistic competition case is examined in Section A.1.3. Unfortunately, thecombination of heterogeneous productivities and selection of monopolistically competitive
firms due to fixed costs does not lead to a tractable short run gravity model. There is
generally no closed form solution for the productivity of the least productive firm able toserve a destination. This is because in monopolistic competition the elasticity of optimized(restricted) revenue with respect to productivity is smaller than the elasticity of optimized
variable cost with respect to productivity. The implicit relationship between the proportionof firms serving a market on the one hand and market size and origin wage on the other
hand retains the qualitative properties of the Melitz-Chaney model, but the implicit function
substantially departs from log-linearity. Nevertheless, Section A.1.3 shows that the purelycompetitive firms model closely approximates the monopolistic competition model as σ is50

large. Numerical evaluation reveals the two models are close.

A.1.1

Short Run Gravity with Competitive Heterogeneous Firms

Each firm draws a Hicks-neutral productivity scalar % ≥ 1 from a Pareto distribution G(%) =1 − %−θ . Index the firms in an (implicit) origin by their productivity draws ρ. Firms
have (by assumption) previously committed capital K(z) to each destination z in the same
pattern based on expected demand because prior to receiving their productivities, all firms
are identical. The profit of firm % is%p(z)L(z, %)α K(z)1−α − wL(z, %).
t(z)Profit maximization by a price taking firm implies the restricted profit function %1/(1−α) R̄(z)where
R̄(z) =p(z)t(z)

1/(1−α)K(z)[αα/(1−α) − w−α/(1−α) α1/(1−α) ]is the variable profit of the least productive firm (whether it ships to destination z or not).
The zero profit cutoff value of % occurs at%(z) = [f (z)/R̄(z)]1−α

where f (z) is the fixed cost of exporting to z. The proportion of firms with % ≥ % is givenR∞by 1 − G(%) = % θ%−θ−1 d%. Then the aggregate value shipped to destination z is given by


p(z)
t(z)

1/(1−α)

K(z)αα/(1−α) S(z)(28)

where the mass of firms serving destination z
Z ∞S(z) =

θ%%

1/(1−α)−θ−1

θ
d% =
θ+1−η

51



f (z)
R̄(z)

η−θ
(29)

using η = 1/(1 − α). Relative to the text version of short run gravity, S(z) enters everywherethat K(z) = λ(z)K appears. R̄(z) is proportional to [p(z)/t(z)]η . Using this expression in(29), p(z)/t(z) affects the extensive margin of trade through S(z) with elasticity η(θ − η).
The intensive margin response to a fall in trade cost t(z) acts to crowd out the extensive
margin response in (29), completely so at θ = η. The mass of active firms falls and average
productivity rises when η > θ, which is the famous Melitz (2003) case where effectively
η → ∞.
(29) combines in (28) with the effect of p(z)/t(z) on the intensive margin of trade withelasticity η. The combined effect of p(z)/t(z) on shipments has composite supply elasticityη̃ = η(1 + θ − η). This composite supply side elasticity combines with the demand side
elasticity in the short run equilibrium model of the text to yield a buyers’ incidence elasticity
equal toρ̃ =

η(1 + θ − η)>ρη(1 + θ − η) + σ − 1(30)for θ > η, the intuitive case where the extensive margin of firms S(z) is increasing in pricep(z). In the special case θ = η, the responses of firms on the intensive and extensive margins
are perfect substitutes.
The extensive margin of destinations is essentially the same as in the identical firms case.
The normalization to 1 of the fixed labor requirement to serve a destination is replaced by themass of firms productive enough to serve that destination S(z). Suppressing the variationf (z) introduced above and normalizing it to 1, the fixed labor requirement n for the identicalRnfirms case becomes N = 0 S(z)dz. Condition (6) yielding the smallest destination able tobe served becomesαY
S(n) = (1 − α)s(n)Y.
L−N

This has the same meaning, only adding the slight complication that the mass of firms
requiring a fixed labor input S(z) is presumably falling as z → n.
In empirical applications, the extensive margin component can be identified if proxies52for fixed export costs can be found that are not also proxies for variable trade costs. In theabsence of such proxies, estimated trade elasticities have to be considered combinations ofintensive and extensive margin responses.

A.1.2

Empirical Implications

The development of the firm level model here points to a rationale for the simple econometric
procedure adopted for the empirical work. First, the λ(z) allocations are assumed to be thesame for any firm, under the assumption that all heterogeneity is in % draws. We can
extend the logic to assume that all z > 0 external markets are ex post under-supplied to a
uniform extent, λ(z) is too small by a common fraction and correspondingly λ(0) is too large.
This permits drawing inferences from multiple observations on the movement of external vs.
internal trade over time.
A second aspect of the model with empirical content is that the zeroes in bilateral tradeflows can simply be rationalized as the absence, for whatever reason, of a finite positive λ.

A.1.3

Monopolsitic Competition Case

The production function for delivered output by monopolistic competitive firm % to destination z from a representative origin is the same as in the competitive case, y(z, %) =%L(z, %)α K(z)1−α /t(z), where K(z) is assumed to be committed before % is drawn from thePareto distribution with dispersion parameter θ. The firm faces willingness to pay for its
shipments to destination z equal top(z, %) = y(z, %)−1/σ E(z)1/σ P (z)1−1/σ .

Once % is drawn, the firm hires labor (including the manager) to maximize profits (including
the premium paid to the manager). The efficient level of labor is such that the wage w is53

equal to the marginal revenue product of labor:L(z, %) = %(1−1/σ)/(1−α(1−1/σ)) α(1 − 1/σ)E(z)1/σ (P (z)/t(z)1−1/σ K(z)(1−α)(1−1/σ) /w

1/(1−α(1−1/σ))(31)

The wage bill of firm % on shipments to z is w times the right hand side of (31). The
value of sales at destination prices follows from substituting the right hand side of (31) into
the production function for delivered output and the willingness to pay function for delivered
output. The restricted profit function is equal to sales minus the wage bill. It is convenient
for present purposes to define the sales y(z) and labor L(z) of the minimally productive firmwith % = 1, suppressing the unnecessary details. The restricted profit function of firm % on
sales to z isR(z, %) = y(z)%(1−1/σ)(1+α)/(1−α(1−1/σ)) − L(z)%(1−1/σ)/(1−α(1−1/σ)) .

(32)

The least productive firm able to serve market z must be productive enough to pay fixed
cost f (z). The cutoff firm has productivity%(z) = min % : R(z, %) − f (z) = 0.

The definition imposes a plausible restriction that the monopolistic competitive firm willfind the smallest root % when there are multiple roots solving the equation.
Expression (32) does not yield a closed form solution for % for a given profit level, so it
will not yield a convenient structural gravity equation for the mass of firms serving market
z from the origin in focus here. In contrast, perfectly competitive firms yield a closed form
solution. The monopolisitic competition case comes close to the competitive case as σ grows
large, hence 1 − 1/σ → 1 in the exponents of (32).
Quantitatively, the difference between the monopolistic competition case and the purecompetition case can be numerically evaluated by comparing solutions for %(z) given rea-54

sonable range values of σ with the competitive equivalent solution with σ → ∞. Plugging
the pair of solutions for into equation (29), the ratio of the mass of sales of monopolistic
to competitive firms can be computed, given a value of θ. A representative evaluation caseused f /Y = 0.5, wL/y = 0.6, α = 0.67, θ = 4. At σ = 2, monopolistic firms total sales
are 91% of competitive firms sales. At σ = 10, they are 99% of competitive firms sales. The
ratio is monotonic (and equilibrium % is unique), convex and ‘nearly’ linear in σ ∈ (1, ∞).

A.2

Short Run Trade Cost Endogeneity

The short run gravity model implies a theory of short run endogenous trade costs. Equation (8) yields a structure that potentially connects inference about trade costs from pricevariation to inference from trade flow variation.
Relative price T (i, z) ≡ p(i, z)/p(i, i) is common direct measure of trade cost variation.
Use (8) and the result on the CES price index P (z) = (E(z)/Y )−(1−ρ) Pe(z) from Section
3 where Pe(z) is the buyer’s multilateral resistance. Simplify the exponents of the result togive:T (i, z) =t(i, z)t(i, i)ρ λ(i, z)λ(i, i)

−ρ/η

Pe(z)
Pe(i)

!1−ρ 

E(z)
E(i)

1/η
.

(33)

T (i, z) → t(i, z)/t(i, i) as λ(i, z)/λ(i, i) adjusts to its efficient level (see Section 3.2). t(i, z)/t(i, i)
is inferred from standard (i.e. long run) gravity equations, while (33) implies that spatial
variation of T (i, z) includes the effect of inefficient bilateral capacities and the spatial variation of demand conditions. Demand variation in the last two terms on the right is direct inE(z)/E(i) and indirect through its general equilibrium effects on buyers’ relative multilateral resistance Pe(z)/Pe(i). (33) can potentially reconcile the time invariance of t(i, z) inferredfrom gravity and the obvious time variation of direct price measures, and also differencesin elasticities inferred from the spatial variation of prices and the spatial variation of tradeflows. Future research on disaggregated price and trade flow data can test the consistency55

of (13) and (33).42
Spatial arbitrage is assumed to be perfect in (33). Violations of the Law of One Priceare are unimportant in the empirical work reported in this paper if they are unsystematic.
Higher frequency data on disaggregated price and trade flow data is likely to reveal systematicdeviations from the Law of One Price, with intertemporal behavior that is informative about
dynamics of arbitrage.

42
The application of this paper to aggregate manufacturing data is not suitable for use of (33) because
composition effects contaminate the spatial variation of manufacturing price indexes.

56Appendix B: Empirical Analysis
This appendix reports the results from a series of sensitivity experiments that demonstrate
the robustness of our main results. Following the development of the exposition in the main
text of the manuscript, we present successively robustness experiments for each the two
econometric methods that we employ to test the SR gravity theory.

B.1

Sensitivity Experiments: Econometric Approach

We start this section with a brief summary of the main empirical findings from Section 4.2,
where we tested the short run gravity theory with an estimation approach that employed international border dummies under the assumption that cross-border trade capacities λ(i, z, τ )are inefficiently small, while domestic capacities λ(i, i, τ ) are inefficiently large and, over time,
capacity investment evolves toward efficiency so that cross-border investment in trade links
rises relative to domestic investment in trade links. The two main findings from the estimatesin Section 4.2 were that (i) the estimates of the standard gravity variables remained statistically unchanged once we introduced the bilateral border dummies; and, more importantly
for our purposes, (ii) we obtained estimates on the bilateral border dummies that were all
positive, statistically significant, and gradually increasing over time, which, consistent with
our theory we interpreted as improvement in efficiency. The following experiments confirm
the robustness of our main findings from Section 4.2:
• The estimates in Table 5 are obtained with size-adjusted trade, Xi,z,τ /Yi,τ , as dependent variable. The motivation for using size-adjusted trade is twofold. First, suchspecification is consistent with theory. Second, using size-adjusted trade as dependent
variable mitigates heteroskedasticity concerns by construction, cf. Anderson and van
Wincoop (2003). The estimates from columns (1)-(4) of Table 5 are obtained with the
OLS estimator. Columns (1) and (2) reproduce the estimates with standard gravity
variables from columns (1) and (2) of Table 1. Columns (3) and (4) reproduce the57estimates with pair fixed effects from columns (4) and (5) of Table 1. Columns (5)-(8)reproduce the estimates from columns (1)-(4) with the PPML estimator. All results
are obtained with exporter-time and importer-time fixed effects, whose estimates areomitted for brevity. Both the OLS and the PPML estimates from Table 5 confirm thetwo main findings as summarized at the beginning of this section.
• Figure 2 reports estimates of the evolution of the international border estimates fromcolumn (2) of Table 1, which are obtained with OLS and standard gravity variables,
over time. The figure also obtains the slope of the fitted line, which corresponds tothe parameter bτ from the main text. The estimate of bτ = 0.036 from Figure 2 issmaller but comparable to the estimate of bτ = 0.046 from the main text. The resultsin Figure 3 are constructed based on the estimates from column (5) of Table 2, which
are obtained with the PPML estimator and pair fixed effects, over time. Once again,
we obtain a similar value for the parameter bτ = 0.028.
• Table 6 reproduces the main results from Table 1 with data for all years. The estimatesfrom columns (1)-(4) are obtained with the OLS estimator. Columns (1) and (2) reproduce the estimates with standard gravity variables from columns (1) and (2) of Table
1. Columns (3) and (4) reproduce the estimates with pair fixed effects from columns(4) and (5) of Table 1. Columns (5)-(8) of this table reproduce the estimates fromcolumns (1)-(4) of the same table with the PPML estimator. All results are obtainedwith exporter-time and importer-time fixed effects, whose estimates are omitted forbrevity. In addition, also for brevity, we have omitted the estimates on the bilateralborder dummies for the odd years in the sample. These are available by request. The
estimates from Table 6, once again, confirm our main findings as summarized at the
beginning of this section.
• Table 7 reproduces the results from column (3) of Table 1 with data for all years.
We remind the reader that the estimates from column (3) of Table 1 depicted and58

resolved the ‘distance puzzle’ in international trade. The estimates in column (1) of
Table 7 are obtained with the OLS estimator and the estimates in column (2) of Table
7 are obtained with the PPML estimator. All results are obtained with exporter-timeand importer-time fixed effects, whose estimates are omitted for brevity. In addition,
also for brevity, we have omitted the estimates on the time-varying distance variables
and the estimates on the bilateral border dummies for the odd years in the sample
for each group of countries. The omitted estimates are available by request. In eachcase we allow for time-varying distance effects and, in each case, we find no evidence
for time-varying effects of distance. This is consistent with the distance puzzle ininternational trade. However, similar to the discussion of our main results, our theory
suggests that the correct interpretation of the effects of distance should combine thejoint impact that is captured by the distance estimates and by the estimates of theefficiency improvements. Thus, combined with the decreasing border effects (capturedby the positive, significant and increasing estimates on the border dummies), our theory
implies that the impact of distance have steadily decreased over time. In sum, theestimates from Table 7 confirm that our theory can indeed resolve the famous ‘distance’and ‘missing globalization’ puzzles in the international trade literature.
• Table 8 reproduces the results from column (6) of Table 1 with data for all years. We
remind the reader that the estimates from column (6) of Table 1 distinguished between
capacity improvement for the developed vs. developing countries in our sample. The
estimates in column (1) of Table 8 are obtained with the OLS estimator and theestimates in column (2) of Table 8 are obtained with the PPML estimator. In eachcase we allow for different efficiency improvement rates depending on whether a country
is developed or developing. All results are obtained with exporter-time and importertime fixed effects, whose estimates are omitted for brevity. In addition, also for brevity,
we have omitted the estimates on the bilateral border dummies for the odd years inthe sample for each group of countries. The omitted estimates are available by request.
59

The estimates from columns (1) and (2) of Table 8 deliver results that are very similar
to our main corresponding findings from Table 1. Specifically, and most important,
we do observe efficiency improvements for both groups of countries. In addition, we
see that the low income countries have actually converged faster toward more efficient
trade during the period of investigation.
• Table 9 reproduces the main results from Table 1 with with the latest edition of the
WIOD data, as described in the data section. The WIOD dataset covers the period
2000-2014 and we use 2-year intervals to obtain the estimates in Table 9. The estimates from columns (1)-(4) are obtained with the OLS estimator. Columns (1) and(2) reproduce the estimates with standard gravity variables from columns (1) and (2)of Table 1. Columns (3) and (4) of Table 9 reproduce the estimates with pair fixed
effects from columns (4) and (5) of Table 1. Columns (5)-(8) of Table 9 reproduce theestimates from columns (1)-(4) of the same table with the PPML estimator. All results are obtained with exporter-time and importer-time fixed effects, whose estimates
are omitted for brevity. The estimates from Table 9 confirm our main findings, assummarized at the beginning of this section, with the WIOD data.
• Table 10 reproduces the main results from Table 1 by capitalizing on the sectoral
dimension of the latest edition of the WIOD data, as described in the data section.
Once again, we use 2-year interval data. For brevity, for each of the six main sectors in
the WIOD database (including Crop and Animal Production, Forestry and Logging,
Fishing and Aquaculture, Mining and Quarrying, Manufacturing, and Services), weonly reproduce the main specifications with pair fixed effects, which correspond to thosein columns (4) and (5) of Table 1. All results are obtained with the OLS estimatorand with exporter-time and importer-time fixed effects, whose estimates are omitted forbrevity. The main finding from the results in Table 10 is that the estimates of the timevarying bilateral border dummies are positive, statistically significant, and increasing60

over time for each sector in our sample. These results are consistent with our main
findings and support the SR gravity theory. In addition, we note that while there
is certain heterogeneity in the bilateral border estimates across sectors, the efficiency
improvements have been significant at the sectoral level and similar in magnitude.
In sum, based on the sensitivity experiments that we employed in this section, we conclude
that our main findings from Section 4.2 represent robust results.

B.2

Sensitivity Experiments: Structural Approach

We start this section with a brief summary of the main empirical findings from Section 4.3,
where we tested the short run gravity theory by developing a formal model of investment,
which resulted in the addition of the lagged dependent variable as a covariate in the estimating equation for SR gravity. Three main findings stood out from the estimates in Section
4.3. First, we obtained a large, positive and statistically significant estimate of the coefficienton the structural efficiency term. Second, we recovered estimates of the structural efficiency
parameter ranging from 0.202 to 0.371. Third, as predicted by the SR gravity theory, theestimates that controlled for efficiency improvements were significantly smaller in magnitude as compared to their long run counterparts. The following experiments confirm therobustness of our main findings from Section 4.2:
• Table 11 uses 3-year interval data to reproduce the results from Table 3 of the maintext. All results are obtained with exporter-time and importer-time fixed effects, whose
estimates are omitted for brevity. The dependent variable in each specification is
the log of nominal bilateral trade. Column (1) reports standard (long run) gravity
estimates. The estimates from column (2) are obtained with lagged trade added asa covariate. Column (3) reproduces the results from column (2) but with pair fixed
effects, thus implementing the LSDV estimator. Column (4) implements an IV LSDV
estimation. Finally, column (5) implements the Arellano-Bond estimator. In sum, the61estimates from Table 11 are in support of all main findings listed at the beginning of thissection. Specifically: (i) We obtain positive and significant estimates of the structural
efficiency term; (ii) Taking into account the use of 3-year interval data, which implies
3(1−ρ), we recover ρ̂ ∈ [0.250, 0.534] across the different specifications, which
β̃8 = (1−δ)
1−δ(1−ρ)can be found in the bottom panel of Table 11; (iii) The estimates from each specificationthat controls for efficiency improvements are significantly smaller in magnitude ascompared to their long run counterparts from column (1) of Table 11. Finally, we notethat the bounds for ρ that we obtain with sample that includes all years are tighter ascompared to the bounds with the 3-year interval data. This is evidence in support ofusing the full sample over using data with intervals.
• Table 12 uses size-adjusted trade as dependent variable and reproduces the results from
Table 3 of the main text. All results are obtained with exporter-time and importer-time
fixed effects, whose estimates are omitted for brevity. The dependent variable in eachspecification is the log of nominal bilateral trade. Column (1) reports standard (longrun) gravity estimates. The estimates from column (2) are obtained with lagged trade
added as a covariate. Column (3) reproduces the results from column (2) but withpair fixed effects, thus implementing the LSDV estimator. Column (4) implements
an IV LSDV estimation. The estimates from Table 12 confirm our main results assummarized at the beginning of this section.
• Table 13 reproduces the results from Table 3 of the main text with 3-year interval dataon international trade only. All results are obtained with exporter-time and importertime fixed effects, whose estimates are omitted for brevity. The dependent variable ineach specification is the log of nominal bilateral trade. Column (1) reports standard(long run) gravity estimates. The estimates from column (2) are obtained with lagged
trade added as a covariate. Column (3) reproduces the results from column (2) but
with pair fixed effects, thus implementing the LSDV estimator. Column (4) implements62

an IV LSDV estimation. Once again, the estimates from Table 13 confirm our main
results as summarized at the beginning of this section.
• Table 14 uses the system-GMM estimator, which will account for the dynamic featuresof our model.43 The estimates from column (1) of Table 14 are obtained with data for
all years and pass the Arellano-Bond test for autocorrelation in the disturbances by
rejecting (as expected) the null hypothesis of no AR(1) errors with z = −10.268, but
passing the test for second-order serial correlation AR(2) with z = 1.302. However,
the instruments do not pass the Sargan test of overidentifcation restrictions with χ215 =
168.99 (p-value=0.025). Furthermore, we obtain a suspiciously small estimate of thecoefficient on LN Xij,τ −1 (β̃8 = 0.254, std.err. 0.045), which is clearly outside of thebounds that we established in columns (2) and (4) of Table 3 from th main text. The
Arellano-Bond estimates from column (2) of Table 14 are obtained with 3-year interval
data and they improve on the estimates from column (1) by delivering an estimate
on LN Xij,τ −1 (β̃8 = 0.603, std.err. 0.161), from which we recover ρ̂ = 0.303 (std.err.
0.178), which is not statistically different from our main estimates.
• Table 16 uses the latest edition of the WIOD data and reproduces the results from
Table 3 of the main text. All results are obtained with exporter-time and importertime fixed effects, whose estimates are omitted for brevity. The dependent variablein each specification is the log of nominal bilateral trade and we use 2-year interval
data. Column (1) reports standard (long run) gravity estimates. The estimates fromcolumn (2) are obtained with lagged trade added as a covariate. Columns (3) and43

Anderson and Hsiao (1982) are the first to achieve consistency in short time period setting by using
appropriate lagged levels and differences of the dependent variable as instruments for the lagged dependent
variable. Arellano and Bond (1991) and Arellano and Bover (1995)/Blundell and Bond (1998) extend theAnderson-Hsiao estimator to the difference-GMM and the system-GMM estimators, respectively, which
use larger sets of orthogonality conditions in order to obtain consistent estimates in dynamic panels withlagged dependent variable such as ours. We refer the interested reader to Roodman (2009a) for a detailed
discussion and step-by-step implementation of alternative dynamic estimators in Stata. Roodman (2009b)
An additional advantage of this estimation method for our analysis is that it will enable us to obtain estimatesof the coefficient of all gravity variables, which will be used to perform test (27) multiple times. discusses
problems associated with the proliferation of instruments in similar settings.

63

(4) reproduce the results from columns (1) and (2) but with pair fixed effects, thus
implementing the LSDV estimator. The estimates with the WIOD data are consistent
with the main results and they deliver ρ̂ ∈ [0.070, 0.598]. Both the upper and the lower
bounds for ρ are wider as compared to the main estimates, but they are within thetheoretical limits. We offer two possible explanations for the wider bounds. First, themain sample has longer time coverage, which, according to Roodman (2009a) leads
to more precise estimates. Second, similar to the estimates with the 3-year interval
sample of the main data, the WIOD estimates from Table 16 are obtained with 2-year
interval data.
• Table 17 reproduces the main results from Table 3 by capitalizing on the sectoral
dimension of the latest edition of the WIOD data, as described in the data section.
For brevity, for each sector we only focus on reproducing the main specifications (i)with lagged trade and standard gravity variables and (ii) with lagged trade and pair
fixed effects. All results are obtained with 2-year interval data, with the OLS estimator,
and with exporter-time and importer-time fixed effects, whose estimates are omitted
for brevity. The sectoral SR gravity estimates are relatively homogeneous and they
confirm our main findings.
In sum, based on the sensitivity experiments that we employed in this section, we conclude
that our main findings from Section 4.3 represent robust results.

B.3

Welfare Calculation Metods

This section describes the methods that we employ in order to construct the welfare indexes
from Table 4, which we presented and discussed in section 4.4 of the main text. We proceed
in three steps.
1. Take the last year in the sample, i.e., 2006, as baseline and solve the system in the shortrun. Let R(i, sr) denote the initial/baseline value of Y (i, 2006) with the units choice64

C(i, sr) = 1. Base expenditures are given in the data, but imply an awkward empiricalreality of trade imbalance everywhere. Closing the counterfactual model is met with aP
crude static mechanism E(z) = ψ(z)Y (z) subject to z ψ(z)Y (z) = Y where the baseequilibrium calibrates ψ(z) = E(z, 2006)/Y (z, 2006) for each destination z as a set of
positive parameters, to be held constant in the counterfactual simulation.
Use the costly adjustment specification of Lucas-Prescott for the structural short run
model from Section 4.3,

λ(i, z, τ )1−ρ = (X(i, z, 2006)/Y (i, 2006))δ(1−ρ) (X(i, z, 2005)/Y (i, 2005))(1−δ)(1−ρ)/[1−δ(1−ρ)] ,to solve for the short run multilateral resistances from equations (11) and (12) in
Section 3. Then, impose market clearance with the units choice C(i, sr) = 1. The
baseline SR gravity system becomes:P̆ (z, sr)(1−σ)ρ
1−δ(1−ρ)=Xi

R(i, sr)Pi R(i, sr)t(i, z, sr)Π(i, sr)(1−σ)ρ  1−δ(1−ρ)

X ψ(z)R(z, sr) t(i, z, sr)PΠ(i, sr)=P̆ (z, sr)z R(z, sr)
z
1
 1−σ

R(i, sr)Pβ(i)Π(i, sr) =i R(i, sr)(1−σ)ρ
1−δ(1−ρ)X(i, z, 2005)
Y (i, 2005)(1−σ)ρ
! 1−δ(1−ρ)
 (1−δ)(1−ρ)
1−δ(1−ρ)X(i, z, 2005)
Y (i, 2005)(, 34)
 (1−δ)(1−ρ)
1−δ(1−ρ)
(35)
,
(36)

System (34)-(36) is a system of 3 × N equations and 3 × N unknowns, which include
the 2 × N SR multilateral resistances and the N preference parameters β(i). As usual,solving system (34)-(36) requires a normalization. Our choice is
X
i

1−σ

Π(i)


X  R(i)
σ−1
P
=1=
β(i)
.
i R(i)
i(37)

Finally, to solve system (34)-(36) we use initial output data, R(i, sr), lagged tradedata, X(i, z, 2005), and lagged output data, Y (i, 2005). In addition, we need values for65the short run and for the long run bilateral trade costs, as well as for the parametersψi , σ, δ, and ρ.
• ψ(i) is calibrated as described above, i.e., ψ(i) = E(i, 2006)/Y (i, 2006).
• σ = 7 is a representative value for the elasticity of substitution from the existing
trade literature, e.g., see Head and Mayer (2014).
• As discussed in the main text, δ = 0.061 is from Anderson et al. (2015).
• The estimate of the bilateral trade costs and the efficiency parameter ρ = 0.242
come from the most preferred structural specification from the empirical analysis
in Section 4.3.
The solution to system (34)-(36) subject to normalization (37) delivers estimates for the
SR multilateral resistances as well as for the preference parameters β(i). In addition,using the estimates of the inward SR multilateral resistance, we also obtain the SR
 (1−δ)(1−ρ)
(σ−1)ρ)P
ideal consumer price index P (i, sr) = P̆ (i, sr) ψ(i)R(i,sr).
R(i,sr)i

2. Obtain LR multilateral resistances and endogenous C(i)s in the LR equilibrium by
setting ρ = 1 and by solving the following LR gravity system:(1−σ)t(i, z, sr)
ψ(i)C(z, lr)R(z, sr)PΠ(i, lr)=,
P (z, lr)z ψ(z)C(z, lr)R(z, sr)z
X C(i, lr)R(i, sr)  t(i, z, sr) (1−σ)
(1−σ)
P
,
P (z, lr)=
C(i,lr)R(i,
sr)
Π(i,
lr)
i
i
1

 1−σ
C(i, lr)R(i, sr)P
C(i, lr)β̂(i)Π(i, lr) =.
i C(i, lr)R(i, sr)
(1−σ)

X

(38)
(39)
(40)

System (38)-(40) is a system of 3 × N equations and 3 × N unknowns, which include
the 2 × N LR multilateral resistances and the N endogenous C(i, lr).44 The 3 × N
equations have to be solved simultaneously. The only new vector of parameters needed
44

Equation (38) contains ψ(z) weights in the denominator as a result of closing the model by relating expenditures to income via E(z) = ψ(z)Y (z). Global adding up is automatically met in the
P initial equilibrium,
hence the ψ(z) weights are omitted in the denominator of (35). Global adding up z E(z)1 = Y in the66

to solve the LR gravity system is the vector of β̂(i)’s. These values are denoted with‘ˆ’ because they come directly from the baseline solution of the SR gravity system in
Step 1.
The solution to system (38)-(40) delivers estimates for the LR multilateral resistances
as well as for the endogenous LR price indexes C(i,lr). In this case, the CES priceindex coincides with the inward multilateral resistance.
3. Construct percentage changes between real expenditure in the short run vs. long run
for each country in our sample:
1
P (i, lr)
E(i, sr)/P (i, sr)
× 100 =
× 100
E(i, lr)/P (i, lr)
P (i, sr) C(i, lr)
These are the indexes that appear in Table 4 of the main text.

counter-factual equilibrium implies that
ψ(z)C(z)1 R(z)E(z)1 = PY.
1z ψ(z)C(z) R(z)67

Table 5: SR Gravity & Efficiency, Size-adjusted TradeOLS Estimator
PPML Estimator
Efficiency
PairFEs
Efficiency2 Standard Efficiency
PairFEs
Efficiency2
(2)
(3)
(4)
(5)
(6)
(7)
(8)
LN DIST-1.185-0.711-0.723∗∗∗∗∗∗(0.049)(0.066)(0.067)
CNTG-0.0480.559
0.554(0.189)(0.150)∗∗(0.151)∗∗
CLNY
0.459
0.060
0.055
(0.159)∗∗(0.122)(0.121)
LANG
0.782
0.537
0.541
(0.107)∗∗(0.117)∗∗(0.117)∗∗
FTA
0.406
0.165
0.147
0.122
0.043
0.321
0.108
(0.062)∗∗(0.041)∗∗(0.041)∗∗(0.064)+(0.070)(0.066)∗∗(0.063)+
LN TARIFF-1.704-1.311-1.283-8.345-7.981-2.545-1.420(0.442)∗∗(0.308)∗∗(0.306)∗∗(0.757)∗∗(0.794)∗∗(0.398)∗∗(0.326)∗∗-3.733-3.178-3.501INTL BRDR(0.324)∗∗(0.179)∗∗(0.174)∗∗INTL BRDR 1991
0.215
0.231
0.168
0.148
(0.091)∗(0.092)∗(0.027)∗∗(0.018)∗∗
0.462
0.511
0.358
0.316
INTL BRDR 1994
(0.098)∗∗(0.098)∗∗(0.028)∗∗(0.025)∗∗INTL BRDR 1997
0.622
0.713
0.412
0.450
(0.122)∗∗(0.121)∗∗(0.048)∗∗(0.032)∗∗INTL BRDR 2000
0.685
0.812
0.472
0.528
(0.132)∗∗(0.131)∗∗(0.060)∗∗(0.039)∗∗INTL BRDR 2003
0.722
0.864
0.511
0.597
(0.149)∗∗(0.144)∗∗(0.064)∗∗(0.041)∗∗INTL BRDR 2006
0.799
0.965
0.440
0.663
(0.160)∗∗(0.158)∗∗(0.070)∗∗(0.039)∗∗
N
18345
18345
18344
18344
18928
18928
18928
18928
R2
0.801
0.801
0.892
0.893
0.974
0.975
Notes: This table reproduces the main results from Table 1 with size-adjusted trade Xi,z,τ /Yi,τ as dependent variable.
The estimates from columns (1)-(4) are obtained with the OLS estimator. Columns (1) and (2) reproduce the estimateswith standard gravity variables from columns (1) and (2) of Table 1. Columns (3) and (4) reproduce the estimates with pair
fixed effects from columns (4) and (5) of Table 1. Columns (5)-(8) of this table reproduce the estimates from columns (1)-(4)of the same table with the PPML estimator. All results are obtained with exporter-time and importer-time fixed effects,
whose estimates are omitted for brevity. Standard errors are clustered by country pair and are reported in parentheses +p < 0.10, ∗ p < .05, ∗∗ p < .01. See text for further details.
Standard(1)-1.184(0.049)∗∗-0.047(0.189)0.460(0.159)∗∗0.782(0.107)∗∗0.413(0.062)∗∗-1.723(0.443)∗∗-3.235(0.299)∗∗68

Figure 2: Evolution of International Borders, 1988-2006.

Note: This figure plots the evolution of the international border estimatesfrom column (2) of Table 1, which are obtained with OLS and standard gravity
variables, over time. The figure also reports the slope of the fitted line, whichcorresponds to the parameter bτ from the main text.

Figure 3: Evolution of International Borders, 1988-2006.

Note: This figure plots the evolution of the international border estimatesfrom column (5) of Table 2, which are obtained with the PPML estimator andpair fixed effects, over time. The figure also reports the slope of the fitted line,
which corresponds to the parameter bτ from the main text.

69

Table 6: SR Gravity & Efficiency, All Years: 1988-2006
OLS Estimator
PPML Estimator
Efficiency
PairFEs
Efficiency2 Standard Efficiency
PairFEs
Efficiency2
(2)
(3)
(4)
(5)
(6)
(7)
(8)
LN DIST-1.187-0.643-0.656(0.049)∗∗(0.065)∗∗(0.065)∗∗CNTG-0.0360.492
0.500(0.189)(0.145)∗∗(0.143)∗∗
CLNY
0.457
-0.056-0.070(0.158)∗∗(0.110)(0.110)
LANG
0.773
0.346
0.362
(0.106)∗∗(0.137)∗(0.136)∗∗
FTA
0.412
0.170
0.155
0.127
0.072
0.282
0.102
(0.062)∗∗ (0.037)∗∗(0.036)∗∗(0.117)(0.113)(0.073)∗∗(0.065)-1.497-1.114-1.091-7.444-6.894-4.391-2.383
LN TARIFF(0.377)∗∗ (0.259)∗∗(0.257)∗∗(1.092)∗∗(1.157)∗∗ (0.631)∗∗(0.539)∗∗INTL BRDR-3.746-2.652-3.043(0.323)∗∗(0.154)∗∗(0.153)∗∗INTL BRDR 1990
0.183
0.195
0.180
0.137
(0.061)∗∗(0.060)∗∗(0.022)∗∗(0.016)∗∗INTL BRDR 1992
0.343
0.381
0.226
0.170
(0.088)∗∗(0.091)∗∗(0.023)∗∗(0.018)∗∗
0.463
0.515
0.324
0.250
INTL BRDR 1994
(0.098)∗∗(0.098)∗∗(0.028)∗∗(0.024)∗∗INTL BRDR 1996
0.548
0.633
0.382
0.326
(0.115)∗∗(0.116)∗∗(0.039)∗∗(0.032)∗∗INTL BRDR 1998
0.657
0.769
0.479
0.459
(0.126)∗∗(0.122)∗∗(0.047)∗∗(0.037)∗∗INTL BRDR 2000
0.689
0.816
0.543
0.490
(0.132)∗∗(0.130)∗∗(0.055)∗∗(0.042)∗∗INTL BRDR 2002
0.653
0.789
0.455
0.459
(0.146)∗∗(0.139)∗∗(0.057)∗∗(0.041)∗∗INTL BRDR 2004
0.723
0.883
0.486
0.538
(0.152)∗∗(0.148)∗∗(0.062)∗∗(0.042)∗∗INTL BRDR 2006
0.807
0.975
0.509
0.585
(0.160)∗∗(0.157)∗∗(0.066)∗∗(0.041)∗∗
N
49916
49916
49916
49916
51376
51376
51376
51376
R2
0.882
0.882
0.936
0.936
Notes: This table reproduces the main results from Table 1 with data for all years. The estimates from columns (1)-(4)are obtained with the OLS estimator. Columns (1) and (2) reproduce the estimates with standard gravity variables fromcolumns (1) and (2) of Table 1. Columns (3) and (4) reproduce the estimates with pair fixed effects from columns (4)and (5) of Table 1. Columns (5)-(8) of this table reproduce the estimates from columns (1)-(4) of the same table with the
PPML estimator. All results are obtained with exporter-time and importer-time fixed effects, whose estimates are omitted
for brevity. In addition, also for brevity, we have omitted the estimates on the bilateral border dummies for the odd years
in the sample. The omitted estimates are available by request. Standard errors are clustered by country pair and arereported in parentheses + p < 0.10, ∗ p < .05, ∗∗ p < .01. See text for further details.
Standard(1)-1.186(0.049)∗∗-0.036(0.189)0.457(0.158)∗∗0.773(0.105)∗∗0.418(0.062)∗∗-1.513(0.378)∗∗-3.229(0.297)∗∗70

Table 7: SR Gravity & Efficiency, All Years: 1988-2006(1)(2)
PuzzleOLS
PuzzlePPML
LN DIST-1.184-0.634(0.057)∗∗(0.074)∗∗
LN DIST 1990
-0.0050.016(0.027)(0.021)-0.0610.000
LN DIST 1992
(0.031)∗(0.023)-0.0270.012
LN DIST 1994
(0.040)(0.023)
LN DIST 1996
0.032
0.029
(0.039)(0.028)0.008-0.037
LN DIST 1998
(0.039)(0.032)0.006-0.032
LN DIST 2000
(0.038)(0.037)0.013-0.041
LN DIST 2002
(0.041)(0.034)0.004-0.051
LN DIST 2004
(0.041)(0.034)
LN DIST 2006
0.033
-0.063(0.042)(0.036)+
CNTG-0.0350.501(0.189)(0.142)∗∗
CLNY
0.458
-0.072(0.158)∗∗(0.110)
LANG
0.772
0.365
(0.105)∗∗(0.136)∗∗
FTA
0.425
0.072
(0.065)∗∗(0.113)
LN TARIFF-1.509-6.953(0.379)∗∗(1.167)∗∗-3.754-3.081INTL BRDR(0.336)∗∗(0.164)∗∗INTL BRDR 1990
0.200
0.152
(0.097)∗(0.055)∗∗INTL BRDR 1992
0.543
0.225
(0.129)∗∗(0.056)∗∗
0.549
0.300
INTL BRDR 1994
(0.159)∗∗(0.055)∗∗INTL BRDR 1996
0.443
0.325
(0.167)∗∗(0.076)∗∗
0.628
0.546
INTL BRDR 1998
(0.170)∗∗(0.091)∗∗
0.668
0.599
INTL BRDR 2000
(0.174)∗∗(0.108)∗∗INTL BRDR 2002
0.608
0.528
(0.192)∗∗(0.094)∗∗INTL BRDR 2004
0.707
0.579
(0.201)∗∗(0.089)∗∗INTL BRDR 2006
0.693
0.624
(0.209)∗∗(0.091)∗∗
N
49916
51376
R2
0.882
Notes: This table reproduces the results from column (3) of
Table 1, where we use our theory to resolve the ‘distance puzzle’ of trade, with data for all years. The estimates in column(1) of this table are obtained with the OLS estimator and theestimates in column (2) are obtained with the PPML estimator.
In each case we allow for time-varying distance effects. All results are obtained with exporter-time and importer-time fixed
effects, whose estimates are omitted for brevity. In addition,
also for brevity, we have omitted the estimates on the timevarying distance variables and the estimates on the bilateralborder dummies for the odd years in the sample for each groupof countries. The omitted estimates are available by request.
Standard errors are clustered by country pair and are reported
in parentheses + p < 0.10, ∗ p < .05, ∗∗ p < .01. See text for
further details.
71

Table 8: SR Gravity & Efficiency, All Years: 1988-2006(1)(2)
DvlpmntOLS
DvlpmntPPML
FTA
0.148
0.171
(0.036)∗∗(0.049)∗∗LN TARIFF-0.870-1.826(0.227)∗∗(0.435)∗∗
0.329
0.341
INTL BRDR HIGH 1990
(0.109)∗∗(0.041)∗∗
0.572
0.636
INTL BRDR HIGH 1992
(0.163)∗∗(0.085)∗∗INTL BRDR HIGH 1994
0.603
0.774
(0.185)∗∗(0.075)∗∗
0.759
0.882
INTL BRDR HIGH 1996
(0.253)∗∗(0.147)∗∗INTL BRDR HIGH 1998
0.998
1.068
(0.250)∗∗(0.184)∗∗
1.023
1.019
INTL BRDR HIGH 2000
(0.258)∗∗(0.228)∗∗INTL BRDR HIGH 2002
0.904
0.937
(0.283)∗∗(0.197)∗∗INTL BRDR HIGH 2004
1.023
1.044
(0.289)∗∗(0.187)∗∗INTL BRDR HIGH 2006
1.300
1.168
(0.304)∗∗(0.207)∗∗
0.252
0.339
INTL BRDR LOW 1990
(0.160)(0.067)∗∗INTL BRDR LOW 1992
0.636
0.714
(0.215)∗∗(0.098)∗∗INTL BRDR LOW 1994
0.946
1.166
(0.212)∗∗(0.123)∗∗INTL BRDR LOW 1996
1.116
1.144
(0.194)∗∗(0.132)∗∗INTL BRDR LOW 1998
1.132
1.488
(0.257)∗∗(0.160)∗∗INTL BRDR LOW 2000
1.232
1.565
(0.271)∗∗(0.172)∗∗INTL BRDR LOW 2002
1.323
1.710
(0.296)∗∗(0.193)∗∗
1.478
2.079
INTL BRDR LOW 2004
(0.327)∗∗(0.189)∗∗INTL BRDR LOW 2006
1.528
2.133
(0.347)∗∗(0.193)∗∗
N
49914
51376
R2
0.956
Notes: This table reproduces the results from column (6) of
Table 1, which distinguished between capacity improvement forthe developed vs. developing countries in our sample, with data
for all years. The estimates in column (1) of Table 8 are obtainedwith the OLS estimator and the estimates in column (2) of Table
8 are obtained with the PPML estimator. In each case we allow
for different efficiency improvements depending on whether acountry is developed or developing. All results are obtained with
exporter-time and importer-time fixed effects, whose estimates
are omitted for brevity. In addition, also for brevity, we haveomitted the estimates on the bilateral border dummies for the
odd years in the sample for each group of countries. The omitted
estimates are available by request. Standard errors are clusteredby country pair and are reported in parentheses + p < 0.10, ∗p < .05, ∗∗ p < .01. See text for further details.

72

Table 9: SR Gravity & Efficiency, Aggregate WIOD Data
OLS Estimator
PPML Estimator
Efficiency
PairFEs
Efficiency2Standard
Efficiency
PairFEs
Efficiency2
(2)
(3)
(4)
(5)
(6)
(7)
(8)
LN DIST-1.268-0.845-0.846(0.055)∗∗(0.042)∗∗(0.042)∗∗
CNTG
0.342
0.317
0.317
(0.112)∗∗(0.106)∗∗(0.106)∗∗
CLNY
0.524
0.244
0.247
(0.134)∗∗(0.103)∗(0.103)∗LANG-0.0340.393
0.395(0.122)(0.104)∗∗(0.105)∗∗
RTA
0.402
0.172
0.156
0.180
0.180
0.121
0.023
(0.081)∗∗(0.062)∗∗(0.062)∗(0.065)∗∗(0.065)∗∗(0.043)∗∗(0.045)INTL BRDR-3.909-3.568-3.621(0.288)∗∗(0.107)∗∗(0.107)∗∗INTL BRDR 2002
0.075
0.081
-0.053-0.033(0.038)∗(0.038)∗(0.011)∗∗(0.009)∗∗INTL BRDR 2004
0.288
0.309
0.008
0.046
(0.075)∗∗(0.077)∗∗(0.018)(0.016)∗∗INTL BRDR 2006
0.410
0.433
0.046
0.104
(0.095)∗∗(0.097)∗∗(0.020)∗(0.018)∗∗INTL BRDR 2008
0.503
0.526
0.065
0.147
(0.103)∗∗(0.105)∗∗(0.024)∗∗(0.020)∗∗INTL BRDR 2010
0.487
0.511
0.044
0.130
(0.107)∗∗(0.110)∗∗(0.025)+(0.022)∗∗INTL BRDR 2012
0.577
0.609
0.096
0.185
(0.120)∗∗(0.123)∗∗(0.024)∗∗(0.021)∗∗INTL BRDR 2014
0.548
0.581
0.097
0.189
(0.126)∗∗(0.127)∗∗(0.026)∗∗(0.021)∗∗
N
14792
14792
14792
14792
14792
14792
14792
14792
R2
0.890
0.891
0.978
0.978
1.000
1.000
Notes: This table reproduces the main results from Table 1 with the latest edition of the WIOD data, as described in the data
section. The estimates from columns (1)-(4) are obtained with the OLS estimator. Columns (1) and (2) reproduce the estimateswith standard gravity variables from columns (1) and (2) of Table 1. Columns (3) and (4) reproduce the estimates with pair
fixed effects from columns (4) and (5) of Table 1. Columns (5)-(8) of this table reproduce the estimates from columns (1)-(4)of the same table with the PPML estimator. All results are obtained with exporter-time and importer-time fixed effects, whose
estimates are omitted for brevity. Standard errors are clustered by country pair and are reported in parentheses + p < 0.10, ∗p < .05, ∗∗ p < .01. See text for further details.
Standard(1)-1.267(0.055)∗∗0.343(0.112)∗∗0.524(0.134)∗∗-0.034(0.122)0.406(0.081)∗∗-3.553(0.247)∗∗73

74

ForestryLogging
PairFEs
SR PairFEs
(3)
(4)
0.202
0.186
(0.078)∗∗(0.077)∗0.083(0.048)+0.331(0.087)∗∗0.480(0.115)∗∗0.544(0.118)∗∗0.525(0.145)∗∗0.613(0.165)∗∗0.566(0.181)∗∗
14104
14104
0.969
0.969

FishingAquaculture
PairFEs
SR PairFEs
(5)
(6)
0.301
0.283
(0.085)∗∗(0.084)∗∗0.091(0.044)∗0.293(0.089)∗∗0.458(0.113)∗∗0.586(0.131)∗∗
0.535(0.140)∗∗0.605(0.153)∗∗0.635(0.149)∗∗
14104
14104
0.966
0.966

MiningQuarrying
PairFEs
SR PairFEs
(7)
(8)
0.136
0.116
(0.079)+(0.077)0.155(0.047)∗∗0.400(0.086)∗∗0.568(0.107)∗∗0.671(0.117)∗∗0.641(0.120)∗∗0.746(0.136)∗∗0.707(0.141)∗∗
14792
14792
0.972
0.972

Manufacturing
PairFEs
SR PairFEs
(9)
(10)
0.159
0.141
(0.059)∗∗(0.058)∗0.098(0.040)∗0.322(0.075)∗∗0.459(0.098)∗∗0.550(0.108)∗∗0.563(0.113)∗∗0.651(0.127)∗∗0.638(0.133)∗∗
14792
14792
0.979
0.979

Table 10: SR Gravity & Efficiency, Sectoral WIOD Data
Services
PairFEs
SR PairFEs
(11)
(12)
0.181
0.164
(0.067)∗∗(0.066)∗0.087(0.038)∗0.324(0.082)∗∗0.443(0.101)∗∗
0.552(0.108)∗∗0.526(0.112)∗∗0.618(0.124)∗∗0.594(0.127)∗∗
14792
14792
0.976
0.976

Notes: This table reproduces the main results from Table 1 by capitalizing on the sectoral dimension of the latest edition of the WIOD data, as described in the data section. For brevity,for each sector we focus on reproducing the main specifications with pair fixed effects, which are reported in columns (4) and (5) of Table 1. All results are obtained with the OLS estimatorand with exporter-time and importer-time fixed effects, whose estimates are omitted for brevity. Standard errors are clustered by country pair and are reported in parentheses + p < 0.10,∗
p < .05, ∗∗ p < .01. See text for further details.

N
R2

INTL BRDR 2014

INTL BRDR 2012INTL BRDR 2010

INTL BRDR 2008

INTL BRDR 2006

INTL BRDR 2004

INTL BRDR 2002

RTA

CropAnimal
PairFEs
SR PairFEs
(1)
(2)
0.130
0.112
(0.072)+(0.071)
0.106(0.046)∗0.309(0.079)∗∗0.445(0.098)∗∗0.562(0.106)∗∗0.579(0.123)∗∗0.680(0.132)∗∗0.643(0.135)∗∗
14792
14792
0.970
0.970

Table 11: SR Gravity & Efficiency, 3-year Intervals

LN DIST
CNTG
CLNY
LANG
FTA
LN TARIFF
INTL BRDR
L.ln trade(1)
Standard-1.184(0.049)∗∗-0.047(0.189)0.460(0.159)∗∗0.782(0.107)∗∗0.413(0.062)∗∗-1.723(0.443)∗∗-3.235(0.299)∗∗(2)
LagTrade-0.404(0.026)∗∗0.019(0.066)0.146(0.058)∗0.238(0.036)∗∗0.200(0.025)∗∗-0.802(0.286)∗∗-0.992(0.105)∗∗0.651(0.014)∗∗
15551
0.940
0.250
(0.015)∗∗

(3)
LSDV

(4)
LSDV IV

0.111(0.033)∗∗-0.868(0.260)∗∗0.077(0.054)-1.195(0.433)∗∗0.630(0.276)∗
N
18345
10122
R2
0.880
0.955
ρ̂
0.273
(0.304)
UnderId χ2
7.092
p-val
(0.069)
Weak Id χ2
2.345
p-val
(0.071)
Over Id χ2
4.056
p-val
(0.131)
Notes: This table uses 3-year interval data to reproduce theresults from Table 3 of the main text. All results are obtainedwith exporter-time and importer-time fixed effects, whose estimates are omitted for brevity. The dependent variable ineach specification is the log of nominal bilateral trade. Column (1) reports standard (long run) gravity estimates. The
estimates from column (2) are obtained with lagged trade
added as a covariate. Columns (3) reproduces the results fromcolumn (2) but with pair fixed effects, thus implementing the
LSDV estimator. Column (4) implements an IV LSDV estimation. Robust standard errors are reported in parentheses+ p < 0.10, ∗ p < .05, ∗∗ p < .01. See text for further details.

75

0.397
(0.017)∗∗
15549
0.953
0.534
(0.020)∗∗Table 12: SR Gravity & Efficiency, Size-adjusted Trade

LN DIST
CNTG
CLNY
LANG
FTA
LN TARIFF
INTL BRDR
L.ln trade y(1)Standard-1.186(0.049)∗∗-0.036(0.189)0.457(0.158)∗∗0.773(0.105)∗∗0.418(0.062)∗∗-1.513(0.378)∗∗-3.229(0.297)∗∗(2)
LagTrade-0.248(0.016)∗∗0.005(0.039)0.092(0.034)∗∗0.147(0.022)∗∗0.108(0.013)∗∗-0.348(0.100)∗∗-0.635(0.064)∗∗0.788(0.009)∗∗
46868
0.932
0.202
(0.008)∗∗

(3)
LSDV

(4)
LSDV IV

0.070(0.016)∗∗-0.446(0.118)∗∗0.029(0.017)+-0.579(0.141)∗∗

0.747(0.107)∗∗
N
49916
35411
2
R
0.802
0.940
ρ̂
0.241
(0.104)∗
UnderId χ2
15.863p-val(0.003)
Weak Id χ2
4.135
p-val
(0.003)
Over Id χ2
0.921
p-val
(0.820)Notes: This table uses size-adjusted trade as dependent variable to reproduce the results from Table 3 of the main text.
All results are obtained with exporter-time and importer-time
fixed effects, whose estimates are omitted for brevity. The dependent variable in each specification is the log of nominal bilateral trade. Column (1) reports standard (long run) gravity
estimates. The estimates from column (2) are obtained withlagged trade added as a covariate. Column (3) reproduces
the results from column (2) but with pair fixed effects, thus
implementing the LSDV estimator. Column (4) implements
an IV LSDV estimation. Robust standard errors are reported
in parentheses + p < 0.10, ∗ p < .05, ∗∗ p < .01. See text for
further details.

76

0.614
(0.011)∗∗
46868
0.939
0.371
(0.011)∗∗

Table 13: SR Gravity & Efficiency, International Trade Data Only

LN DIST
CNTG
CLNY
LANG
FTA

(1)
Standard-1.210(0.040)∗∗-0.082(0.192)0.452(0.163)∗∗0.761(0.104)∗∗0.420(0.063)∗∗-1.204(0.336)∗∗(2)
LagTrade-0.272(0.014)∗∗-0.006(0.042)0.098(0.037)∗∗0.155(0.023)∗∗0.116(0.014)∗∗-0.304(0.098)∗∗0.772(0.008)∗∗
45932
0.955
0.217
(0.000)∗∗

(3)
LSDV

0.023
(0.018)-0.458LN TARIFF(0.162)∗∗
L.ln trade
0.889(0.174)∗∗
N
48928
34697
R2
0.879
0.957
ρ̂
0.105
(0.165)
UnderId χ2
10.190p-val(0.070)
Weak Id χ2
1.720
p-val
(0.143)
Over Id χ2
6.875
p-val
(0.143)
Notes: This table uses international trade only as the dependent variable to reproduce the results from Table 3 of themain text. All results are obtained with exporter-time andimporter-time fixed effects, whose estimates are omitted forbrevity. The dependent variable in each specification is thelog of nominal bilateral trade. Column (1) reports standard(long run) gravity estimates. The estimates from column (2)are obtained with lagged trade added as a covariate. Column(3) reproduces the results from column (2) but with pair fixed
effects, thus implementing the LSDV estimator. Column (4)implements an IV LSDV estimation. Robust standard errors
are reported in parentheses + p < 0.10, ∗ p < .05, ∗∗ p < .01.
See text for further details.

77

0.067
(0.017)∗∗-0.439(0.118)∗∗0.613(0.011)∗∗
45932
0.960
0.373
(0.011)∗∗(4)LSDV IV

Table 14: SR Gravity & Efficiency, Arellano-Bond(1)
All Years-0.856(0.064)∗∗0.020(0.117)0.324(0.100)∗∗0.544(0.077)∗∗0.248(0.038)∗∗-0.927(0.228)∗∗-2.352(0.268)∗∗0.254(0.045)∗∗46868
168.99(0.025)-10.268(0.000)1.302(0.193)(2)
3-Year Intervals
LN DIST-0.460(0.194)∗CNTG
0.024(0.101)
CLNY
0.162(0.111)LANG
0.277(0.141)∗FTA
0.184(0.047)∗∗
LN TARIFF-0.694(0.340)∗INTL BRDR-1.140(0.578)∗
0.603
L.LN TRADE(0.161)∗∗
N
15551
2
Over Id χ
17.530p-val(0.041)AR(1)-4.5142
χ p-val(0.000)
AR(2)
2.293
2
χ p-val(0.022)AR(3)-0.476
χ2 p-val(0.634)
Notes: This table reports results fromthe structural investment approach to test
SR gravity theory with the Arellano-Bondestimator.
All estimates are obtainedwith exporter-time and importer-time fixed
effects, whose estimates are omitted forbrevity. The dependent variable in eachspecification is the log of nominal bilateral
trade. Column (1) implements the ArellanoBond estimator with data for all years. Column (2) uses 3-year interval data. Robust
standard errors are reported in parentheses+ p < 0.10, ∗ p < .05, ∗∗ p < .01. See text
for further details.

78

Table 15: SR Gravity & Efficiency, PPML Estimations
3-year Interval Data
Data All Years
Standard
SRG
SRG LSDV Standard
SRG
SRG LSDV
(1)
(2)
(3)
(4)
(5)
(6)
LN DIST-0.647-0.073-0.643-0.028(0.065)∗∗ (0.008)∗∗(0.065)∗∗ (0.002)∗∗
CNTG
0.489
0.021
0.491
0.008
(0.148)∗∗(0.018)(0.145)∗∗(0.007)
CLNY-0.049-0.018-0.056-0.007(0.109)(0.021)(0.110)(0.007)
LANG
0.325
0.006
0.346
0.005
∗
∗
(0.139)(0.016)(0.137)(0.006)
FTA
0.142
0.060
0.059
0.126
0.015
0.010
∗∗
∗
∗∗
(0.123)(0.013)(0.024)(0.117)(0.004)(0.008)LN TARIFF-7.4400.524-0.539-7.441
0.166-0.209(1.167)∗∗ (0.150)∗∗(0.138)∗∗(1.091)∗∗ (0.055)∗∗(0.057)∗∗INTL BRDR-2.636-0.124-2.651-0.048(0.154)∗∗ (0.025)∗∗(0.154)∗∗ (0.008)∗∗
0.913
0.691
0.967
0.869
L trade(0.007)∗∗(0.014)∗∗(0.002)∗∗(0.006)∗∗
N
18928
15665
15657
51376
47236
47231
ρ̂
-0.033
0.205
0.031
0.124
(0.007)∗∗(0.015)∗∗(0.002)∗∗(0.006)∗∗
Notes: This table uses the PPML estimator to reproduce some of the results from
Table 3 of the main text. All results are obtained with exporter-time and importertime fixed effects, whose estimates are omitted for brevity. The dependent variable ineach specification is nominal bilateral trade. The estimates from columns (1)-(3) are
obtained with 3-year interval data and the estimates from columns (4)-(6) use data for
all years. Column (1) reports standard (long run) gravity estimates. The estimates fromcolumn (2) are obtained with lagged trade added as a covariate. Column (3) reproduces
the results from column (2) but with pair fixed effects, thus implementing the LSDV
estimator. Columns (4)-(6) reproduce the results from columns (1)-(3). Robust standard
errors are reported in parentheses + p < 0.10, ∗ p < .05, ∗∗ p < .01. See text for further
details.

79

Table 16: SR Gravity & Efficiency, Aggregate WIOD Data
(1)
Standard-1.267(0.055)∗∗0.343(0.112)∗∗0.524(0.134)∗∗-0.034(0.122)0.406(0.081)∗∗-3.553(0.247)∗∗

(2)
(3)
(4)
SRG OLS
LSDV
SRG LSDVLN DIST-0.144(0.014)∗∗
CNTG
0.039
(0.017)∗CLNY
0.066(0.025)∗∗LANG-0.009(0.023)
RTA
0.110
0.172
0.112
(0.016)∗∗ (0.062)∗∗(0.051)∗-0.470INTL BRDR(0.045)∗∗
0.870
0.363
L.ln trade∗∗(0.009)(0.022)∗∗
N
14792
12943
14792
12943
2
R
0.890
0.973
0.978
0.982
ρ̂
0.070
0.598
(0.009)∗∗(0.024)∗∗
Notes: This table uses the latest edition of the WIOD data andreproduces the results from Table 3 of the main text. All results
are obtained with exporter-time and importer-time fixed effects,
whose estimates are omitted for brevity. The dependent variable in each specification is the log of nominal bilateral trade.
Column (1) reports standard (long run) gravity estimates. The
estimates from column (2) are obtained with lagged trade added
as a covariate. Columns (3) and (4) reproduce the results fromcolumns (1) and (2) but with pair fixed effects, thus implementing the LSDV estimator. Robust standard errors are reported
in parentheses + p < 0.10, ∗ p < .05, ∗∗ p < .01. See text for
further details.

80

81

FishingAquaculture
SR OLSSR LSDV
(5)
(6)
0.819
0.303
∗∗
(0.010)(0.019)∗∗-0.227(0.019)∗∗0.120(0.029)∗∗0.110(0.034)∗∗-0.054(0.032)+
0.123
0.183
(0.026)∗∗(0.074)∗-0.658(0.070)∗∗
12341
12341
0.956
0.971
0.121
0.663
(0.010)∗∗(0.020)∗MiningQuarrying
SR OLSSR LSDV
(7)
(8)
0.844
0.318
∗∗
(0.011)(0.024)∗∗-0.194(0.019)∗∗0.047(0.024)∗0.098(0.033)∗∗-0.028(0.029)0.098
0.118(0.021)∗∗(0.067)+-0.512(0.059)∗∗
12943
12943
0.965
0.976
0.095
0.647
(0.011)∗∗(0.026)+

Manufacturing
SR OLSSR LSDV
(9)
(10)
0.850
0.327
∗∗
(0.009)(0.021)∗∗-0.180(0.015)∗∗0.046(0.018)∗0.070(0.026)∗∗-0.002(0.024)0.107
0.112(0.017)∗∗(0.051)∗-0.438(0.047)∗∗
12943
12943
0.974
0.983
0.090
0.637
(0.009)∗∗(0.022)∗

Table 17: SR Gravity & Efficiency, Sectoral WIOD Data
ForestryLogging
SR OLSSR LSDV
(3)
(4)
0.841
0.327
∗∗
(0.008)(0.021)∗∗-0.223(0.019)∗∗0.121(0.029)∗∗0.112(0.038)∗∗-0.068(0.033)∗
0.110
0.142
(0.026)∗∗(0.076)+-0.580(0.068)∗∗
12341
12341
0.961
0.974
0.099
0.637
(0.008)∗∗(0.022)+SR OLS(11)
0.870(0.008)∗∗-0.140(0.014)∗∗0.031(0.017)+0.064(0.025)∗∗-0.011(0.024)0.106(0.017)∗∗-0.519(0.046)∗∗
12943
0.972
0.069
(0.008)∗∗

12943
0.981
0.586
(0.022)∗0.111(0.053)∗Services
SR LSDV(12)
0.374(0.020)∗∗Notes: This table reproduces the main results from Table 3 by capitalizing on the sectoral dimension of the latest edition of the WIOD data, as described in the data section.
For brevity, for each sector we focus on reproducing the main specifications with lagged trade and standard gravity variables and with lagged trade and pair fixed effects.
All results are obtained with the OLS estimator and with exporter-time and importer-time fixed effects, whose estimates are omitted for brevity. Robust standard errors arereported in parentheses + p < 0.10, ∗ p < .05, ∗∗ p < .01. See text for further details.

N
R2
ρ̂

INTL BRDR

RTA

LANG

CLNY

CNTG

LN DIST

L.ln trade

CropAnimal
SR OLSSR LSDV
(1)
(2)
0.827
0.288
∗∗
(0.010)(0.021)∗∗-0.227(0.019)∗∗0.098(0.023)∗∗0.069(0.028)∗-0.013(0.027)0.110
0.122(0.022)∗∗(0.066)+-0.597(0.060)∗∗
12943
12943
0.961
0.974
0.113
0.679
(0.010)∗∗(0.022)+