GRAVITY WITH GRAVITAS: The McCallum Gravity Equation

McCallum [1995] estimated the following equation:
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Here %ij is exports from region i to region j, + and +j are gross domestic production in regions i and j, is the distance between regions i and j, and By is a dummy variable equal to one for inter-provincial trade and zero for state-province trade. For the year 1988 McCallum estimated this equation using data for all 10 provinces and for 30 states that account for 90% of U.S.-Canada trade. In this section we will also report results when estimating (1) from the U.S. perspective. In that case the dummy variable is one for interstate trade and zero for state-province trade. We also report results when pooling all data, in which case there are two dummy variables. The first is one for interprovincial trade and zero otherwise, while the second is one for interstate trade and zero otherwise.
The data are discussed in the Data Appendix. Without going into detail here, a couple of comments are useful. The interprovincial and state-province trade data are from different divisions of Statistics Canada, while the interstate trade data are from the Commodity Flow Survey conducted by the Bureau of the Census. We follow McCallum by applying adjustment factors to the original data in order to make them as closely comparable as possible. All results reported below are for the year 1993, for which the interstate data are available. We follow McCallum and others by only using data for 30 states.
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The results from estimating (1) are reported in Table 1. The first three columns report results for respectively (i) state-province and inter-provincial trade, (ii) state-province and inter-state trade, (iii) state-province, inter-provincial and interstate trade. In the latter case there are separate border dummies for within-U.S. trade and within-Canada trade. The final three columns report the same results after imposing unitary coefficients on the GDP variables. This makes comparison with our theoretically based gravity equation results easier because the theory imposes unitary coefficients.
Table 1: McCallum regressions

McCallum Regressions Unitary Income Elasticities
(i) (ii) (iii) (iv) (v) (vi)
Data: CA-CA

CA-US

US-US

CA-US

US-US

CA-CA

CA-US

CA-CA

CA-US

US-US

CA-US

US-US

CA-CA

CA-US

Independent Variable
ln+i 1.22

(0.04)

1.13

(0.03)

1.13

(0.03)

1 1 1
S

n

l

0.98

(0.03)

0.98

(0.02)

0.97

(0.02)

1 1 1
n

l

-1.35

(0.07)

-1.08

(0.04)

-1.11

(0.04)

-1.35

(0.07)

-1.09

(0.04)

-1.12

(0.03)

Dummy — Canada 2.80

(0.12)

2.75

(0.12)

2.63

(0.11)

2.66

(0.12)

Dummy — US 0.41

(0.05)

0.40

(0.05)

0.49

(0.06)

0.48

(0.06)

Border — Canada 16.4

(2.0)

15.7

(1.9)

13.8

(1.6)

14.2

(1.6)

Border — US 1.50

(0.08)

1.49

(0.08)

1.63

(0.09)

1.62

(0.09)

0.76 0.85 0.85 0.53 0.47 0.55
Remoteness Variables Added
Border — Canada 16.3

(2.0)

15.6

(1.9)

14.7

(1.7)

15.0

(1.8)

Border — US 1.38

(0.07)

1.38

(0.07)

1.42

(0.08)

1.42

(0.08)

0.77 0.86 0.86 0.55 0.50 0.57