# Thought experiments that exact hat algebra can and cannot compute

Among other things, I’m teaching the Eaton-Kortum (2002) model and “exact hat algebra” to my PhD class tomorrow. Last year, my slides said “this model’s counterfactual predictions can be obtained without knowing all parameter values by a procedure that we now call ‘exact hat algebra’.” Not anymore. Only some of its counterfactual predictions can be attained via that technique.

As I reviewed in a 2018 blog post, when considering a counterfactual change in trade costs (and no change in exogenous productivities nor population sizes), the exact-hat-algebra calculation requires only the trade elasticity and initial trade flows in order to solve for the endogenous proportionate wage changes associated with any choice of exogenous proportionate trade-cost changes.

In Section 6.1 of Eaton and Kortum (2002), the authors consider two counterfactual scenarios that speak to the gains from trade. The first raises trade costs to their autarkic levels (“dni goes to infinity”). The second eliminates trade costs (“dni goes to one”). Exact hat algebra can be used to compute the first counterfactual; see Costinot and Rodriguez-Clare (2014) for a now-familiar exposition or footnote 42 in EK (setting α = β = 1). The second counterfactual cannot be computed by exact hat algebra.

One cannot compute the “zero-gravity” counterfactual of Eaton and Kortum (2002) using exact hat algebra because this would require one to know the initial levels of trade costs. To compute the proportionate change in trade costs associated with the dni=1 counterfactual, one would need to know the values of the “factual” dni. The exact hat algebra procedure doesn’t identify these values. Exact hat algebra allows one to compute proportionate changes in endogenous prices in an underidentified model by leveraging implicit combinations of parameter values that rationalize the observed initial equilibrium without separately identifying them.

Exact hat algebra requires only the trade elasticity and the initial trade matrix (including expenditures on domestically produced goods). That’s not enough to identify the model’s parameters. (If these moments alone sufficed to identify bilateral trade costs, the Head-Ries index that only computes their geometric mean wouldn’t be necessary.) Thus, one can only use exact hat algebra to compute outcomes for counterfactual scenarios that don’t require full knowledge of the model’s parameter values. One can express the autarky counterfactual in proportionate changes (“d-hat is infinity”), but one cannot define the proportionate change in trade costs for the “zero-gravity” counterfactual without knowing the initial levels of trade costs. There are some thought experiments that exact hat algebra cannot compute.

Update (5 Oct): My comment about the contrast between the two counterfactuals in section 6.1 of Eaton and Kortum (2002) turns out to be closely related to the main message of Waugh and Ravikumar (2016). They and Eaton, Kortum, Neiman (2016) both show ways to compute the frictionless or “zero-gravity” equilibria when using additional data (namely, prices or price deflators). See also footnote 7 of Sposi, Santacreu, Ravikumar (2019), which is attached to the sentence “Note that reductions of trade costs (dij − 1) require knowing the initial value of dij.”

# Do customs duties compound non-tariff trade costs? Not in the US

For mathematical convenience, economists often assume iceberg trade costs when doing quantitative work. When tackling questions of trade policy, analysts must distinguish trade costs from import taxes. For the same reason that multiplicative iceberg trade costs are tractable, in these exercises it is easiest to model trade costs as the product of non-policy trade costs and ad valorem tariffs. For example, when studying NAFTA, Caliendo and Parro (2015) use the following formulation:

Caliendo and Parro (REStud, 2015), equation (3)

This assumption’s modeling convenience is obvious, but do tariff duties actually compound other trade costs? The answer depends on the importing country. Here’s Amy Porges, a trade attorney, answering the query on Quora:

Tariff rates in most countries are levied on the basis of CIF value (and then the CIF value + duties is used as the basis for border adjustments for VAT or indirect taxes). CIF value, as Mik Neville explains, includes freight cost. As a result, a 5% tariff rate results in a higher total amount of tariffs on goods that have higher freight costs (e.g. are shipped from more distant countries).

The US is one of the few countries where tariffs are applied on the basis of FOB value. Why? Article I, section 9 of the US Constitution provides that “No Preference shall be given by any Regulation of Commerce or Revenue to the Ports of one State over those of another”, and this has been interpreted as requiring that the net tariff must be the same at every port. If a widget is loaded in Hamburg and shipped to NY, its CIF price will be different than if it were shipped to New Orleans or San Francisco. However the FOB price of the widget shipped from Hamburg will be the same regardless of destination.

Here’s a similar explanation from Neville Peterson LLP.

On page 460 of The Law and Policy of the World Trade Organization, we learn that Canada and Japan also take this approach.

Pursuant to Article 8.2, each Member is free either to include or to exclude from the customs value of imported goods: (1) the cost of transport to the port or place of importation; (2) loading, unloading, and handling charges associated with the transport to the port of place or importation; and (3) the cost of insurance. Note in this respect that most Members take the CIF price as the basis for determining the customs value, while Members such as the United States, Japan and Canada take the (lower) FOB price.

While multiplicative separability is a convenient modeling technique, in practice ad valorem tariff rates don’t multiply other trade costs for two of the three NAFTA members.

# What’s an “iceberg commuting cost”?

In the recent quantitative spatial economics literature, the phrase “iceberg commuting cost” appears somewhat often. The phrase primarily appears in papers coauthored by Stephen Redding (ARSW 2015, RR 2017, MRR 2018, HRS 2018), but it’s also been adopted by other authors (Fratto 2018, Gaigne et al 2018, Matt Turner’s lecture notes). However, none of these papers explicitly explains the meaning of the phrase. Why are we calling these commuting costs “iceberg”?

The phrase was imported from international economics, where the concept of “iceberg transport costs” is widely used. That idea is also explicitly defined. Alan Deardorff’s glossary says:

A cost of transporting a good that uses up some fraction of the good itself, rather than other resources. By analogy with floating an iceberg, costless except for the part of the iceberg that melts. Far from realistic, but a tractable way of modeling transport costs since it impacts no other market. Due to Samuelson (1954).

Two bits of trivia that aren’t very relevant to the rest of the post: these should be called “grain transport costs” because von Thunen introduced the idea with oxen-pulled grain carts more than a century before Samuelson (1954) and basic physics means there are actually economies of scale in shipping ice.

Why do we use the iceberg assumption? As Deardorff highlights, it lets us skip modeling the transportation sector. By assumption, the same production function that produces the good also produces its delivery to customers. For better or worse, that means that international or long-distance transactions don’t affect factor demands or transport prices by being international or long-distance per se (Matsuyama 2007). This is one way of keeping trade models simple. Per Gene Grossman: “few would consider the ‘iceberg’ formulation of shipping costs as anything more than a useful trick for models with constant demand elasticities.”

In urban economics, saying that commuting costs take the “iceberg” form means that the model abstracts from transportation infrastructure and the transport sector. Commuters “pay” commuting costs by suffering lower utility. There is no supplier of transportation services that earns any revenues. (Given that most US roads are unpriced, this isn’t much of an abstraction.) But, just as folding transportation services into the goods-producing firm’s production function has consequences for trade models, saying that commuting enters the utility function directly has consequences for the economic content of urban models.

Given that these models do not feature a labor-leisure tradeoff, there is an equivalence between utility costs and time costs. As described by Ahfeldt, Redding, Sturm, and Wolf (2015): “Although we model commuting costs in terms of utility, there is an isomorphic formulation in terms of a reduction in effective units of labor, because the iceberg commuting cost enters the indirect utility function (5) below multiplicatively.” If the cost of commuting is mostly about the opportunity cost of time, then this modeling device captures it reasonably well in a model with homogeneous workers.

If workers are heterogeneous in their hourly wages, then their opportunity costs of time differ. Higher-wage workers have higher opportunity costs of time. In the classic model of locational choice (see Kevin Murphy’s lecture), this causes higher-wage workers to be more willing to pay for residential locations that give them shorter commutes. In the typical quantitative spatial model, however, preferences are Cobb-Douglas over housing and a tradable good. As a result, even with heterogeneous agents, the utility-cost and time-cost formulations of commuting costs are equivalent.

But what if commuting costs are paid with money? In addition to more time on the road, driving a greater distance involves burning more fuel. (Actually, in these models, it typically involves burning more of the numeraire good.) This is not equivalent to the utility formulation, because the cost of a tank of gas is not a constant proportion of one’s income. Moreover, if the car itself costs money, then lower-wage workers might take the bus. The monetary costs of accessing different commuting technologies can have big consequences for urban form, as suggested by LeRoy and Sonstelie (1983), Glaeser, Kahn, and Rappaport’s “Why do the poor live in cities?” and Nick Tsivanidis’s paper on bus-rapid transit in Bogota. The iceberg formulation of commuting costs cannot tackle these issues.

Similarly, even though transportation infrastructure is surely more capital-intensive than much of the economy, we cannot speak to that issue when we parsimoniously model transport as simply coming out of people’s utility.

“Iceberg commuting cost” is a short, three-word phrase. I hope the 600+ words above suggest what it might mean.

# What economic activities are “tradable”?

I’ve had a couple conversations with graduate students in recent months about classifying industries or occupations by their tradability, so here’s a blog post reviewing some of the relevant literature.

A number of papers emphasize predictions that differ for tradable and non-tradable activities. Perhaps the most famous is Atif Mian and Amir Sufi’s Econometrica article showing that counties with a larger decline in housing net worth experienced a larger decline in non-tradable employment.

Mian and Sufi define industries’ tradability by two different means, one yielding a discrete measure and the other continuous variation:

The first method defines retail- and restaurant-related industries as non-tradable, and industries that show up in global trade data as tradable. Our second method is based on the idea that industries that rely on national demand will tend to be geographically concentrated, while industries relying on local demand will be more uniformly distributed. An industry’s geographical concentration index across the country therefore serves as an index of “tradability.”

Inferring tradability is hard. Since surveys of domestic transactions like the Commodity Flow Survey don’t gather data on the services sector, measures like “average shipment distance by industry” (Table 5a of the 2012 CFS) are only available for manufacturing, mining, and agricultural industries. Antoine Gervais and Brad Jensen have also pursued the idea of using industries’ geography concentration to reveal their tradability, allowing them to compare the level of trade costs in manufacturing and services. One shortcoming of this strategy is that the geographic concentration of economic activity likely reflects both sectoral variation in tradability and sectoral variation in the strength of agglomeration forces. That may be one reason that Mian and Sufi discretize the concentration measure, categorizing “the top and bottom quartile of industries by geographical concentration as tradable and non-tradable, respectively.”

We might also want to speak to the tradability of various occupations. Ariel Burstein, Gordon Hanson, Lin Tian, and Jonathan Vogel’s recent paper on the labor-market consequences of immigration varying with occupations’ tradability is a nice example. They use “the Blinder and Krueger (2013) measure of `offshorability’, which is based on professional coders’ assessments of the ease with which each occupation could be offshored” (p.20). When they look at industries (Appendix G), they use an approach similar to that of Mian and Sufi.

Are there other measure of tradability in the literature?

# Atkin & Donaldson – Who’s Getting Globalized? The Size and Nature of Intranational Trade Costs

David Atkin and Dave Donaldson are presenting this paper tomorrow afternoon at the NBER summer institute:

This paper uses a newly collected dataset on the prices of narrowly defined goods  across many dispersed locations within multiple developing countries to address the  question, How large are the costs that separate households in developing countries from the  global economy? Guided by a flexible model of oligopolistic intermediation with variable mark-ups, our analysis proceeds in four steps. first, we measure total intranational trade costs (ie marginal costs of trading plus mark-ups on trading) using price gaps over space within countries—but we do so only among pairs of locations that  are actually trading a good by drawing on unique data on the location of production  of each good. Second, we estimate, separately by location and commodity, the passthrough rate between the price at the location of production and the prices paid by inland consumers of the good. Our estimates imply that incomplete pass-through—and therefore, intermediaries’ market power—is a commonplace, and that pass-through is especially low in remote locations. Third, we argue that our estimates of total trade costs (Step 1) and pass-through rates (Step 2) are sufficient to infer the primitive effect  of distance on the marginal costs of trading; after correcting for the fact that mark-ups  vary systematically across space we find that marginal costs are affected by distance  more strongly than typically estimated. finally, we show that, in our model, the estimated pass-through rate (Step 2) is a sufficient statistic to identify the shares of social  surplus (ie the gains from trade) accruing to inland consumers, oligopolistic intermediaries, and deadweight loss; applying this result we find that intermediaries in  remote locations capture a considerable share of the surplus created by intranational  trade.

You can listen to a podcast of Donaldson presenting a much earlier version of this work from the International Growth Centre. He does a really nice job of summarizing the issues involved in inferring trade costs from price data.

# Don’t go to Shanghai for your Big Mac

Richard Florida says “While it’s commonly thought that globalization has put the world’s global cities on an increasingly level playing field, substantial differences in prices persist”:

What should leap to mind? Trade costs.

The biggest price gap (a ratio of 100) is for a good that is completely non-tradable and varies greatly in quality (bus fare is 7 cents in Mumbai and \$7 in Oslo). A good of relatively uniform quality that is perishable varies quite a bit (Big Mac, from \$2 in Shanhai to \$6 in Oslo). A durable good with a high value-to-weight ratio, the iPad 2, exhibits less variation, a ratio of under two (\$1058 in Buenos Aires and \$548 in Bangkok). So it looks like trade costs are a pretty good explanation for nominal price differences.

That iPad gap may not be as large as it seems. You’ll want to adjust for taxes. The VAT is 21% in Argentina and 7% in Thailand.

How can there still be a ~\$350 price difference when one can probably mail an iPad to most countries for less than a hundred bucks? Shouldn’t arbitrage drive price differences for identical products down to the shipping cost? Not so fast. It turns out it’s quite difficult to arbitrage iPads. Apple tracks its customers and doesn’t allow bulk purchases.

Why is gasoline, a very homogeneous and fungible commodity, \$2 in Amsterdam but only 42 cents in Dubai? Taxes in the former and subsidies in the latter.

In short, these data are a lesson about trade costs. You’ll notice that Richard Florida didn’t title his post “why you should buy a bus ticket in Mumbai instead of Oslo”!

(Relatedly, price comparisons of personal services, as opposed to goods, suggest a lesson about global labor mobility. A one-hour Thai massage costs \$6 in Bangkok and about \$100 in New York City!)

# Can the Port of Long Beach compete with the Panama Canal?

An update on the Panama Canal expansion from the Economist that focuses on the west coast’s reaction:

But what can the California ports do? Floating cargo from Asia to the east coast by boat will always be cheaper, concedes Christopher Lytle, the executive director of the Port of Long Beach. But unloading in Long Beach and taking the train to New York can be faster by a week, he says. So California’s ports must compete on speed, which is increasingly important for time-sensitive goods such as fashion wear or consumer electronics. Let the lawn chairs go and keep the iPads, he reckons.

A lot must happen to keep that advantage in speed, however. One bottleneck is that short truck ride to the railway yard. Not only do the trucks account for much of the port’s air pollution (even though they are dramatically cleaner than just a decade ago), but they clog up stretches of the I-710 freeway, wasting precious time. One of the port’s plans is therefore to build a new, better and closer railway yard…

David Pettit, a lawyer at the National Resources Defence Council and one of those environmentalists who so frustrate Mr Baker, says that he fully understands the threat posed by the canal. But moving the railway yard to another community, and thus polluting it, is not the answer. Better, he says, to put the railway yard right on the docks. That would take up too much space, replies the port. The combatants have only until 2014 to work out their answer and build it.

[HT: Clayton]

# Peru’s “Easy Export” program

Here’s how the World Development Report 2009 summarized a Peruvian trade-facilitation project:

BOX 8.9 Exporting by mail in Peru—connecting small producers to markets

In many countries small enterprises are often excluded from export chains because they operate in villages or small towns or do not have the needed information to export. In Peru a trade-facilitation program called “Easy Export” connects small producers to markets. The key to this program is the most basic of transport networks—the national postal service.

How does it work? An individual or firm takes a package to the nearest post office, which provides free packaging. The sender fills out an export declaration form, and the post office weighs the package and scans the export declaration form. The sender pays the fee for the type of service desired. Goods with values of \$2,000 or less can be exported. The main benefit is that the exporter does not need to use a customs agent, logistics agent, or freight forwarder or to consolidate the merchandise; even the packaging is provided. Firms or individuals need only to go to a post office with a scale and a paper scanner and to use the Internet to complete the export declaration for the tax agency.

Has it made a difference? Within six months of inception, more than 300 firms shipped goods totaling more than \$300,000. Most users are new exporters—microentrepreneurs and small firms, producing jewelry, alpaca and cotton garments, food supplements (natural products), cosmetics, wood art and crafts, shoes and leather, and processed food. And many of them are in the poorest areas of the country.