The role of Iceberg Costs in GTAP and NQT Models

In GTAP, there is a technology change variable. It operates directly on the quantity of trade – either enhancing it (trade facilitation) or eroding it (iceberg melt) (this is Professor Thomas Hertel's words when we exchanged some thoughts on this in emails); on the other hand, there is a variable representing cost index for international transportation which reflects the cost of the input into the transport activity itself.  This index is indirectly impacted by a transportation margin calculated as the CIF price over the custom import value (a. Custom import value (CIV) is defined as the price actually paid for the merchandise excluding import duties, freight, insurance, and other charges incurred in the importing of merchandise to its destination; b. This is because, in GTAP, higher transportation margin leads to larger share of margin in total costs of getting goods from source to origin.). It operates similarly as the Samuelsonian iceberg equaling CIF over FOB prices.

The GTAP technical document explains that there seems to be a relationship of this margin with the role of geographic distance by looking at its value (lower likely means geographically closer), and for example, some pairs of bilateral regions such as the US and Canada and US and others, but this leaves a mystery for other pairs such as with New Zealand and Japan that are not explained alone by distance. It shows that there is a strong evidence of the relationship between this margin and importance of distance for some goods, such as live animals.

The following is the import demand equation in GTAP derived in percent change form:

    qxs(i,r,s)
        = -ams(i,r,s) + qim(i,s)
        - ESUBM(i) * [pms(i,r,s) - ams(i,r,s) - pim(i,s)];

• qxs is export sales of commodity i from r to region s
• ams is the iceberg cost (or technology change) variable
• qim is aggregate imports of i in region s
• ESUBM is region-generic elasticity of substitution among imports of i in Armington structure
• pms is domestic price for good i supplied from r to region s
• pim is market price of composite import i in region r

​(In GTAP syntax, lowercase letters mean percent change of a variable, uppercase letters represent parameters or data both read from files, green color means endogenous variable, and red means exogenous variable that is “shockable”).

pms(i,r,s) = tm(i,s) + tms(i,r,s) + pcif(i,r,s);

• Both “tm”s are tariff shocks, one is source-generic, the other is by source-destination
• pcif is CIF price

The following equation links export and import prices for commodities:

• FOBSHR is the FOB share (goods price at FOB) of total import values
• TRNSHR is the transport share (transportation costs of the goods) of total import values
• pfob is FOB price
• ptrans is the transport margin or cost index for transport of i from r to s

In my view, the iceberg can be  melt twice  based on the equations above: one is counterfactually operated through “ams” which is an iceberg shock (directly on quantity) that is equivalent to either a de facto positive or negative productivity shock (i.e., importers ask less or more than what they receive); the other is operated through “ptrans” indirectly impacted by the data that GTAP collected from COMTRADE/Census which seems to have already explained some of the geographic variations (both natural and artificial). For example, a longer distance between bilateral pairs would suggest higher value of transportation margin and ptrans therefore higher pcif and pms which impedes bilateral trade. See the same import demand equation below but with - ESUBM(i) * [pms(i,r,s) highlighted.

    qxs(i,r,s)
        = -ams(i,r,s) + qim(i,s)
        - ESUBM(i) * [pms(i,r,s) - ams(i,r,s) - pim(i,s)];

​Again, ESUBM are the region-generic elasticities of substitution among imports of goods i, which are positive. Note that this equation has some gravity sense (in the sense that the change of bilateral trade flows on the LHS is explained by some variables and variables on the RHS). The role of distance and other variations reflected by geographic locations are absorbed by pms through the transportation margin, but the role of elasticity of trade costs with respect to distance and other factors such as border frictions (as in NQT literature) is disappeared.