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.
Thanks to Jeff Lin (https://twitter.com/jeffrlin/status/1188902334606249984) for reminding me of the LeRoy and Sonstelie paper.
Maarten Bosker and Eltjo Buringh recently have a paper using detailed information on Boston’s nineteenth-century global ice trade-literally ice !- to test the iceberg cost assumption. They show that the cost of shipping the only good that truly melts in transit is not well-proxied by this assumption! Additive cost components account for the largest part of per unit ice(berg) transport costs in practice.