Post-colonial trade between Russia and former Soviet republics: back to big brother?

2.1 The monadic components
The monadic components, m
it
and n
jt
, are the sets of unique attributes that are only 
in the possession of i or j, respectively, at time t explaining the trade flow between 
the pair. The monadic component of any i comprises positive (GDP, y
it
) and nega-
tive (local composite price index of ‘multilateral resistance,’ P
1
−𝜎
it
) attributes, and 
can be written as:
(2)
x
ijt
=
y
it
y
jt
∑
i
y
it
�
𝜏
ijt
P
it
P
jt
�
1
−𝜎
,
(3)
m
it
=
y
it
P
1
−𝜎
it
.
(4)
n
jt
=
y
jt
P
1
−𝜎
jt
.
Economic Change and Restructuring (2021) 54:877–918
887

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1 3
Theoretically speaking, local output, y
it
, is equal to the sum of gross consumption c
ijt
of i’s produce across all countries j (including i) at a price ( p
ijt
) at time t that differs 
from j’s domestic price level by the inclusion of a trade cost ( 𝜏
ijt
):
Region j’s economic size at time t ( y
jt
) is calculated analogously. It is common 
practice in a gravity analysis to proxy economic size using the nominal GDP of the 
country, or by collecting bilateral trade flows by either i or j.
9
An important component of Eq. (
3
) is the multilateral resistance to trade (MRT) 
term, the central contribution of AvW (
2003
). The outward trade resistance of 
exporter region i at time t, P
it
, is price index that takes into account the weighted 
aggregate values of observable traded costs ( ∑
j
𝜏
ijt
) and income share ( ∑
j
𝜃
1
1
−𝜎
jt
, where 
𝜃
jt
=
y
jt
∑
i
y
it
) across all possible import partners and takes the form of CES unit cost 
functions:
Here, 𝜎 is the CES elasticity of substitution between domestic and imported goods. 
The parameter should be larger than one, but exact values may change as preferences 
and trade opportunities change. Some studies try to estimate it (e.g., Chen and Novy 
2012
) or calibrate it (e.g., Balistreri and Hillberry 
2008
) but most studies introduce 
it exogenously by assigning a level to it. The inward trade resistance of region j at 
time t, P
jt
, is derived in similar fashion just by replacing i and j in (
6
). Both inward 
and outward MRT terms are not directly observable, though gravity studies provide 
methods to construct them (see Anderson and Yotov 
2010
).