Annex

1. Regression results from the average treatment effect estimation

Note: Superscripts ***, ** and * represent significance levels of 0.1, 0.05 and 0.01 respectively.

Specification
Variable(1)(2)(3)(4)
CCFTAijt0.061***0.135***0.115***0.061***
(0.020)(0.005)(0.005)(0.020)
Tijkt0.005***-0.010**0.018***0.007***
(0.002)(0.004)(0.004)(0.002)
ln GDPit0.788***0.523***0.507***0.788***
(0.006)(0.006)(0.006)(0.006)
ln GDPjt0.258***0.541***0.653***0.258***
(0.018)(0.019)(0.018)(0.018)
ln pcgji-0.179***-0.584***-0.692***-0.179***
(0.019)(0.020)(0.020)(0.019)
ftait-0.058***-0.048***-0.052***-0.058***
(0.009)(0.009)(0.009)(0.010)
ln imrikt0.244***0.201***0.200***0.244***
(0.001)(0.001)(0.001)(0.001)
ln popit0.390***1.032***1.214***0.390***
(0.036)(0.041)(0.041)(0.036)
Tariff standardizationNoNoYesYes
Parametric weighingNoYesYesNo
Non-parametric matchingNoNoNoYes
Panel set-upYesYesYesYes

Source: Author s own calculation

2. Deriving the Margins

Following from Hummels and Klenow (2005), consider there are h = 1,...,H countries in the world. Each country produces many types of goods and all of them can be exported. Assume that the set of goods produced and exported by country h at time t is

Upper case I superscript lower case h subscript lower case t is a strict subset of set one, two, three, and so on.

For each

Lower case i is an element of upper case I superscript lower case h subscript lower case t.

the quantity of good i is

Lower case q superscript lower case h subscript lower case it is larger than zero.

and thus the vector of each type of good produced in country h at time t is

Lower case q superscript lower case h subscript lower case t is larger than zero.

There are some goods that common to countries h and j, which we name as common goods set, It. Next we further assume the production function in country h follows a CES transformation function with aggregate resources

 Upper case L superscript lower case h subscript lower case t is larger than zero.

then the total outputs of country h equals,

Upper case L superscript lower case h subscript lower case t equals to function of lower case q superscript lower case h subscript lower case t and upper case I superscript lower case h subscript lower case t, also equals to open bracket the summation on lower case i that belongs to upper case I superscript lower case h subscript lower case t of lower case a subscript lower case i times lower case q superscript lower case h subscript lower case it to the power of the fraction of omega plus one t

where ω > 0 is the elasticity of transformation between goods.

The ratio of two CES functions across two countries h and j at time t is the product of the price index of the common goods,

Lower case p superscript lower case h subscript lower case t is larger than zero, when lower case I equals to lower case h or lower case j.

to both countries

Upper case I subscript lower case t is equivalent to open bracket the intersection of upper case I superscript lower case h subscript lower case t and upper case I superscript lower case j subscript lower case t close bracket, and does not equal to empty set.

 multiplied by the terms that indicate the revenue share of the non-common goods.

Product on lower case i that belongs to upper case I subscript lower case t of open bracket the ratio of lower case p superscript lower case h subscript lower case it to lower case p superscript lower case j subscript lower case it close bracket all to the power of function lower case w subscript lower case it of upper case I subscript lower case t multiplied to open parenthesis the ratio of function lambda superscript lower case h subscript lower case t of upper case I subscript lower case t an

Here,

Lower case w subscript lower case it open bracket upper case I subscript lower case t close bracket.

are weights calculated using the revenue shares of countries h and j .

Function lower case w subscript lower case it of upper case I subscript lower case t equals to the fraction with numerator equals to the difference of function lower case s superscript lower case h subscript lower case it of upper case I subscript lower case t and function lower case s superscript lower case j subscript lower case it of upper case I subscript lower case t divided by the difference of natural logarithm of function lower case s superscript lower case h subscript lower case it of u

The weights sum to unity over the common goods set It.

Now the revenue shares of the non-common goods are,

Function lambda superscript lower case h subscript lower case t of upper case I subscript lower case t equals to the fraction with numerator equals to summation on lower case i that belongs to upper case I subscript t of lower case p superscript lower case h subscript lower case it times lower case q superscript lower case h subscript lower case it, and denominator equals to summation on lower case i that belongs to upper case I superscript lower case h subscript lower case it of lower case p su

And function lambda superscript lower case j subscript lower case t of upper case I subscript t equals to the fraction with numerator equals to summation on lower case i that belongs to upper case I subscript t of lower case p superscript lower case j subscript lower case it times lower case q superscript lower case j subscript lower case it, and denominator equals to summation on lower case i that belongs to upper case I superscript lower case j subscript lower case it of lower case p superscri

Note that the revenue shares are always calculated relative to the common goods set, It . Unless

Upper case I subscript lower case t is equivalent to upper case I superscript lower case h subscript lower case t.

we always have

Lambda superscript lower case h subscript lower case t open bracket upper case I subscript lower case t close bracket is less than or equal to one.

As long as there are goods not in the common goods set that country h produces,

Lambda superscript lower case h subscript lower case t open bracket upper case I subscript lower case t close bracket is less than one.

This means if country h produces certain goods that country j does not produce, then

Lambda superscript lower case h subscript lower case t open bracket upper case I subscript lower case t close bracket.

will be strictly less than 1. In other words, the higher is

Summation on lower case I that belongs to upper case I superscript lower case h subscript lower case t but does not belong to upper case I subscript lower case t of lower case p superscript lower case h I subscript lower case it lower case q superscript lower case h subscript lower case it.

(the total value of the non-common goods country h produces), the lower is the ratio of the revenue shares

Lambda superscript lower case h subscript lower case t open bracket upper case I subscript lower case t close bracket divided by lambda superscript lower case j subscript lower case t open bracket upper case I subscript lower case t close bracket.

Therefore, the inverse of

Lambda superscript lower case h subscript lower case t open bracket upper case I subscript lower case t close bracket divided by lambda superscript lower case j subscript lower case t open bracket upper case I subscript lower case t close bracket.

represents the relative export variety of country h to country j.

Now if we add the world F as reference, then

Upper case I superscript upper case F subscript lower case t.

represents all the varieties that the world produces at time t and considering the pair-wise comparison between country h and country j, we have the extensive margin of the exports from country h to country j equals to,

Upper case EM superscript lower case hj subscript lower case i, export equals to the fraction with numerator equals to summation on lower case i that belongs to upper case I superscript lower case hj subscript t of lower case p superscript upper case F lower case j subscript lower case it times lower case q superscript upper case F lower case j subscript lower case it, and denominator equals to summation on lower case i that belongs to upper case I superscript upper case F lower case j  subscrip

Estimated extensive margin of exports is within the range of 0 to 1, and its value can be interpreted as how much of the exports by country h to country j can be explained by export varieties. It can also be taken as a weighted count of country h's product set relative to the world's product set.

Applying similar logic, we derive the intensive margin of the exports from country h to country j as,

Upper case IM superscript lower case hj subscript lower case i, export equals to the fraction with numerator equals to summation on lower case i that belongs to upper case I superscript lower case hj subscript t of lower case p superscript lower case hj subscript lower case it times lower case q superscript lower case hj subscript lower case it, and denominator equals to summation on lower case i that belongs to upper case I superscript lower case hj subscript t of lower case p superscript upper

The estimated intensive margin of exports is also within the range of 0 to 1, and its value can be interpreted as how much of the exports by country h to country j can be explained by the volume.

The product of the extensive and intensive margins equals to country h's share of exports in country j,

Upper case EM superscript lower case hj subscript I, export times upper case IM superscript lower case hj subscript lower case i, export equals to the fraction with numerator equals to summation on lower case i that belongs to upper case I superscript lower case hj subscript t of lower case p superscript lower case hj subscript lower case it times lower case q superscript lower case hj subscript lower case it, and denominator equals to summation on lower case i that belongs to upper case I super

Essentially, the above equals to the amount of exports from country h to country j divided by the total imports by country j, i.e. the import share of country h in country j.

3. Theoretical Set-up of Arkolakis et al. (2009)

Consider a traditional Armington (1969) model, there are i = 1,...,n countries, each produces a differentiated good using labour. The labour supply is inelastic and given by Li . There is a representative agent in each country that has the following Dixit-Stigliz utility function,

Upper case U subscript I equals to open bracket summation on I = 1 to lower case n of lower case q subscript ij to the power of sigma minus one over sigma close bracket all to the power of sigma over sigma minus one.

where qij is the quantity of country j's good consumed by country i and

Sigma is larger than one.

is the elasticity of substitution between goods. The associated price index in country j is then given by,

Upper case P subscript j equals to open bracket summation on lower case I equals to one to lower case n of lower case w subscript I tau subscript lower case ij to the power of one minus sigma close bracket all to the power of one over one minus sigma.

where

Lower case w subscript lower case i is larger than zero.

is country i's wage and

Tau subscript lower case ij is larger than or equal to one.

are the trade costs between country i and country j.

When the Dixit-Stigliz utility equation is maximized with respect to the price index, the total imports from country i is then equal to,

Upper case X subscript ij equals to open bracket lower case w subscript lower case i times tau subscript lower case ij divided by upper case P subscript lower case i close bracket all to the power one minus sigma, and times upper case Y subscript lower case ij.

with

Upper case Y subscript lower case ij is equivalent to summation on lower case I from one to lower case n of upper case x subscript lower case ij.

being country j's total expenditure and

Open bracket one minus sigma close bracket is less than zero.

is the partial elasticity of relative imports with respect to the variable trade costs (i.e. the trade elasticity). Also, trade is balanced as

Upper case Y subscript lower case j equals to lower case w subscript lower case j upper case l subscript lower case j.

Assume that there is a shock that affects foreign labour endowment,

Vector upper case L is equivalent to set of upper case l subscript lower case i.

and trade cost,

Vector tau is equivalent to set of tau subscript lower case ij.

but not those of country j's. The change in real income is then,

Total derivative of natural logarithm of upper case w subscript lower case j equals to the negative of summation on lower case i equals to one to lower case n of upper case X subscript lower case ij divided by upper case Y subscript lower case ij times the sum of total derivative of natural logarithm of lower case w subscript lower case I and total derivative of natural logarithm of tau subscript lower case ij, and equals to the negative of summation on lower case i equals to one to lower case n

where λij is the country j's share of expenditure on goods from country i. By simple manipulation, we can see that the change in relative imports would be,

The difference of total derivative of natural logarithm of lambda subscript lower case ij and total derivative of natural logarithm of lambda subscript lower case jj equals to open bracket one minus sigma close bracket times the difference of total derivative of natural logarithm of lower case w subscript lower case i and total derivative of natural logarithm of tau subscript lower case ij.

Combining the last two equations together, i.e. substituting the relative imports equation into the equation for change in real income, we have the change in real income as,

Total derivative of natural logarithm of upper case w subscript lower case j equals to the summation on lower case I equals to one to lower case n of lambda subscript lower case ij times the difference of total derivative of natural logarithm of lambda subscript lower case jj and total derivative of natural logarithm of lambda subscript lower case ij all divided by one minus sigma, and equals to total derivative of natural logarithm of lambda subscript lower case jj divided by one minus sigma.

This gives rise to the final expression for changes in income,

Upper case w circumflex subscript lower case j equals to upper case W prime divided by upper case W, also equals to lambda subscript lower case jj to the power of one over one minus sigma.

The above expression equals to the change of income in the initial equilibrium and the new equilibrium. The interpretation of this result is straight forward; change in real income is dependent on terms of trade changes which in turn are dependent on changes of relative import demand. Thus, the system can be reduced to an expression with two sufficient statistics, λ and σ. Arkolakis et al. (2009) also demonstrate that under various assumptions on preferences, technologies of production and market structures, this expression still holds.