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Mismeasurement of DistanceEffects: The Role of Internal Location of Production** **

**One sentence summary**: The overestimation of distance effects in gravity studies is an aggregation problem due to ignoring the internal location of production, which can be fixed by a corrective distance index based on the dispersion of economic activity within the exporter country and its remoteness from the rest of the world.

The corresponding paper by Hakan Yilmazkuday has been published at Review of International Economics.

**Abstract**

The estimated effects of distance
in empirical international trade regressions are unrealistically high. Using
state-and-sector level U.S. exports data, this paper shows analytically and
proves empirically that ignoring the internal location of production (of
international exports), which leads to the overestimation of distance effects
by about twofold, is a possible explanation. This overestimation is mostly
attributed to the mismeasurement of the distance elasticity of trade costs when
internal locations of production are ignored. A corrective distance index is
proposed to avoid such mismeasurements and is shown to work well for the median
sector. The results are robust to the consideration of alternative estimation methodologies
and data sets.

**Non-technical Summary**

The concept of "trade
costs" has been one of the keys to understanding welfare-reducing barriers
to international trade. Anderson and van Wincoop (2004) broadly define it by
considering its components such as transportation costs (including time-to-ship),
policy barriers, information costs, contract enforcement costs, costs
associated with the use of different currencies, legal and regulatory costs,
and local distribution costs. When it comes to the measurement of these
components, though, the data are either limited or nonexistent. To bypass the
data problem, the common (and successful) empirical practice in the literature
has been to use the geographical location of source and destination countries
and thus geographical distance as a proxy to capture the effects of many
components of trade costs introduced above. This practice has come at the cost
of unrealistically high/overloaded estimated ad-valorem tax equivalents of
distance effects, considered under the title of "distance puzzle";
e.g., in their meta-analysis based on 1,466 estimates in the literature,
Disdier and Head (2008) have shown that the absolute value of the coefficient
in front of (log) distance estimates in gravity-type regressions have a mean of
0.91 and a median of 0.87. While these high distance effects can be
investigated under the magnitude dimension of the distance puzzle, their
persistence over time constitutes the time dimension of the puzzle.

In this paper, we focus on the
magnitude dimension of the distance puzzle. To understand the severity of
magnitude dimension better, consider the ad-valorem tax equivalents of distance
effects. Under the assumption of constant elasticity of substitution (CES)
utility functions, the estimated coefficient in front of (log) distance (i.e.,
the distance elasticity of trade) is the multiplication of the elasticity of
substitution and the distance elasticity of trade costs. Following the
empirical literature on international trade, if we consider the fact that the
elasticity of substitution estimates are as low as 3, the mean/median distance
elasticity of trade costs in Disdier and Head (2008) is implied about 0.3,
which corresponds to ad-valorem tax equivalents of distance effects as much as
694% when distance (between source and destination) is about 1,000 miles. In
the context of the time dimension of the puzzle, although the literature has
attempted to explain and reduce the severity of these effects through several
data sets and methodologies, there are no studies to our knowledge that
particularly focus on the magnitude dimension of the distance puzzle.

Accordingly, the contribution of
this paper is twofold. First, we attempt to understand the magnitude of
distance effects by considering their possible mismeasurement, which we call
the Mismeasurement of Distance Effects (MDE). Second, we propose a corrective
distance index that can be used to avoid MDE.

In particular, based on a simple
model, we analytically show that the estimated effects of distance would be
mismeasured if the internal location of production (of international exports)
is ignored in the estimation. The magnitude and the direction of MDE, however,
depends on the estimated variables (e.g., source prices), parameters (e.g.,
elasticity of substitution, distance elasticity of trade costs, taste parameters),
and distance data (e.g., the spatial distribution of production). Accordingly,
to determine such details empirically, we estimate the implications of our
model under two data sets of the U.S. exports at the 3-digit NAICS sector
level, one considering the location of production at the state level (i.e., the
estimation using state-and-sector level U.S. exports data), the other one
ignoring the location of production (i.e., the estimation using only
sector-level U.S. exports data). The results show that the median (across
sectors) distance elasticity of trade is estimated around 0.17 with
state-and-sector level exports data, while it is around 0.50 when only sector
level exports data are used.

In order to depict the role of
MDE on the ad-valorem tax equivalents of distance effects, under the assumption
of CES utility functions, we further decompose the estimated coefficient in
front of distance (i.e., the distance elasticity of trade) into the elasticity
of substitution and the distance elasticity of trade costs. Such a
decomposition, however, depends on the identification of the elasticity of
substitution which requires an additional set of information; we follow
Yilmazkuday (2012) by using data on state-and-sector level production (for the
U.S.) to identify the elasticity of substitution across varieties (each
produced in a different U.S. state) of each sector, and by using data on sector
level production (for the U.S.) to identify the elasticity of substitution
across products of different sectors (produced in the U.S.). In the estimation
process, while the former is used to identify the distance elasticity of trade
costs when state-and-sector level exports data are used, the latter is used to
identify the distance elasticity of trade costs when only sector level exports
data are used. This identification strategy is similar to the approach used by
Anderson and van Wincoop (2003) who connect CES utility functions to
gravity-type estimations; however, this paper is different from theirs, since
they use an ad hoc measure of the elasticity of substitution for
identification, while we estimate it using production-side data. The results
show that the median (across sectors) distance elasticity of trade costs is
estimated around 0.05 with state-and-sector level exports data, while it is
around 0.15 when only sector level exports data are used. In order to have a
better idea about the difference between the distance elasticity of trade costs
estimates of 0.05 and 0.15, consider the corresponding ad-valorem tax
equivalents of distance effects: when distance measure is 1,000 miles, 0.05
corresponds to 41%, and 0.15 corresponds to 182%.

Finally, by considering the
appropriate aggregations, we calculate the overall MDE when the internal
location of production is ignored. The results show that the distance effects
estimated by sector level data are on average about double the distance effects
estimated by state-and-sector level data; therefore, distance effects are
overestimated when sector level data are employed. These results are robust to
the consideration of alternative estimation methodologies and data sets.

When we formally investigate the
source of MDE, it is evident that the lion's share belongs to the
mismeasurement of the distance elasticity of trade costs and ignoring
preferences of individuals in the destination countries (among products
produced in different locations within the U.S.). Across 3-digit NAICS sectors,
we also show that MDE decreases as the elasticity of substitution (across the
products of U.S. states) increases.

Therefore, MDE is mostly due to
aggregation issues where the underlying micro details are still coming from the
internal location of production (i.e., disaggregated data). However, such
disaggregated data are not available all the time. Accordingly, we propose a
solution to avoid mismeasurement of distance effects through the estimation of
distance elasticity of trade costs. Under certain conditions, we analytically
show that the mismeasurement can be avoided by using a corrective distance
index created by using internal distance measures (i.e., the dispersion of
economic activity) and international distance measures (i.e., the remoteness of
the source country from the rest of the world). We employ this index and show
that it works well to avoid MDE (i.e., the magnitude dimension of the distance
puzzle) for the median sector.

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