Border Effects and the Gravity Equation: Consistent Methods for Estimation
| Author | Robert C. Feenstra |
| Published date | 01 November 2002 |
| Date | 01 November 2002 |
| DOI | http://doi.org/10.1111/1467-9485.00244 |
BORDER EFFECTS AND THE GRAVITY
EQUATION: CONSISTENT METHODS FOR
ESTIMATION1
Robert C. Feenstra
ABSTRACT
The CES monopolistic competition model is an especially convenient way to derive the
gravity equation, especially when we allow for transport costs and other trade barriers.
In that case, we need to take account of the overall price indexes in each cou ntry.
We review three methods to do so: using published data on price indexes; using the
computational method of Anderson and van Wincoop; or using country fixed effects
to measure the price indexes. The latter two methods are compared on the dataset
dealingwithtradebetweenandwithinCanada and the US. The fixed effects method
produces consistent estimates of the average border effect across countries, and is
simple to implement, so it might be considered to be the preferred estimation method.
II
NTRODUCTION
In its simplest form, the gravity equation states that the bilateral trade between
two countries is directly proportional to the product of the countries GDP’s.
Thus, larger countries will tend to trade more with each other, and countries that
are more even in their relative sizes will also trade more. This equation performs
extremely well empirically, as has been known since the original work of
Tinbergen (1962). Our goal in this paper is to derive this equation and estimate it
when there are transport costs and other trade barriers across countries, so that
countries have different prices, which turns out to be quite important.
The monopolistic competition model with constant elasticity of substitution
(CES) is an especially convenient way to derive the gravity equation when we
allow for transport costs and other trade barriers. Anderson (1979) was the first
to derive the gravity equation while taking into account these price differences
across countries. Estimating the resulting equation still presents a challenge,
however, and we shall discuss three approaches: the use of prices indexes to
measure the prices effects in the gravity equation, as in Bergstrand (1985, 1989)
Scottish Journal of Political Economy, Vol.49, No. 5, November 2002
#Scottish Economic Society 2002,Publ ishedby Blackwell Publishers Ltd, 108 Cowley Road, Oxford OX4 1JF, UK and
350 Main Street, Malden, MA 02148, USA
491
1This paper draws on chapter 5 from Robert Feenstra, Advanced International Trade: Theory
and Evidence, Princeton University Press (2003).
*University of California, Davis, and National Bureau of Economic Research
and Baier and Bergstrand (2001); the use of estimated border effects to measure
the price effects, as in Anderson and van Wincoop (2001); and the use of fixed
effects for source and destination country to account for the price effects, as in
Harrigan (1996), Hummels (1999), Redding and Venables (2000), Rose and van
Wincoop (2001) and others.
We begin in Section II by reviewing the results of McCallum (1995) for
internal and cross-border trade for Canada and the US. In Section III we derive
the gravity equation when prices differ across countries, and in Section IV
compare the various estimation methods. The method of Anderson and van
Wincoop (2001) will be contrasted with the fixed effects approach on the
Canada– US dataset originally used by McCallum (1995). We will show that the
fixed effects method produces consistent estimates of the average border effect
across countries, and is simple to implement, so it might be considered to be the
preferred estimation method. Further conclusions are given in Section V.
II TRADE WITHIN AND BETWEEN CANADA AND THE US
An application of the gravity model that has stimulated a large amount of
further research came from comparing intra-national trade between Canadian
provinces to international trade between Canadian provinces and US states. This
was the question posed by McCallum (1995), in a study using 1988 data, just
before the Canada– US free trade agreement was signed. He estimated a
conventional gravity model where bilateral trade between Canadian provinces,
or between a Canadian province and US state, should depend on each of their
province or state GDP’s. Specifically, the regression estimated by McCallum is:
ln(Xij þXji)¼þ1ln Yiþ2Yjþ ij þln dij þ"ij;
where ij is an indicator variable that equals unity for trade between two
Canadian provinces and zero otherwise, and dij is the distance between any two
provinces or states. The results from estimating this equation using 1988 data are
shown in column (1) of Table 1. The same regression using 1993 data is shown in
column (2). Note that McCallum’s dataset included trade between Canadian
provinces, and provinces and states, but not trade between the US states. This is
added in column (3) using 1993 data, in which case we also include an indicator
variable that equals one when trade is between two US states and zero otherwise.
The results in columns (1)– (3) show coefficients on provincial or state GDP
close to unity, and a strong negative relationship between distance and trade.
This is no surprise. What is unexpected is the very large coefficient on cross-
provincial trade: ranging from 309 in column (1) to 275 in column (3). Taking
the exponents of these, we obtain the estimates on ‘Canada trade’ shown at the
bottom of the table, indicating the cross-provincial trade is some 22 times larger
than cross-border trade in 1988, and 157 times larger in 1993. These numbers
are extraordinarily high! They are meant to capture any and all factors that
might impede trade between the US and Canada, or what we might call ‘border
effects’. It seems nearly unbelievable, however, that these factors would lead to
16 or 22 times more internal trade in Canada than external trade.
492 ROBERT C. FEENSTRA
#Scottish Economic Society 2002
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