“Information Frictions and the Law of One Price,” C. Steinwender (2014)

Well, I suppose there is no surprise that I really enjoyed this paper by Claudia Steinwender, a PhD candidate from LSE. The paper’s characteristics are basically my catnip: one of the great inventions in history, a policy question relevant to the present day, and a nice model to explain what is going on. The question she asks is how informational differences affect the welfare gains from trade. In the present day, the topic comes up over and over again, from the importance of cell phones to village farmers to the welfare impact of public versus closed financial exchanges.

Steinwender examines the completion of the transatlantic telegraph in July 1866. A number of attempts over a decade had been made in constructing this link; the fact that the 1866 line was stable was something of a surprise. Its completion lowered the time necessary to transmit information about local cotton prices in New York (from which much of the supply was sent) and Liverpool (where much of the cotton was bought; see Chapter 15 of Das Kapital for a nice empirical description of the cotton industry at this time). Before the telegraph, steam ships took 7 to 21 days, depending on weather conditions, to traverse the Pond. In a reduced form estimate, the mean price difference in each port, and the volatility of the price difference, fell; price shocks in Liverpool saw immediate responses in shipments from America, and the prices there; exports increases and become more volatile; and similar effects were seen from shocks to ship speed before the telegraph, or temporary technical problems with the line after July 1866. These facts come from amazingly well documented data in New York and UK newspapers.

Those facts are all well and good, but how to explain them, and how to interpret them? It is not at all obvious that information in trade with a durable good should matter. If you ship too much one day, then just store it and ship less in the next period, right? But note the reduced form evidence: it is not just that prices harmonize, but that total shipments increase. What is going on? Without the telegraph, the expected price tomorrow in Liverpool from the perspective of New York sellers is less variable (the conditional expectation conditions on less information about the underlying demand shock, since only the two-week-old autocorrelated demand shock data brought by steamship is available). When high demand in Liverpool is underestimated, then, exports are lower in the era before the telegraph. On the other hand, a low demand shock and a very low demand shock in Liverpool both lead to zero exports, since exporting is unprofitable. Hence, ignoring storage, better information increases the variance of perceived demand, with asymmetric effects from high and low demand shocks, leading to higher overall exports. Storage should moderate the volatility of exports, but not entirely, since a period of many consecutive high demand shocks will eventually exhaust the storage in Liverpool. That is, the lower bound on stored cotton at zero means that even optimal cotton storage does not fully harmonize prices in the presence of information frictions.

Steinwender confirms that intuition by solving for the equilibrium with storage numerically; this is actually a pretty gutsy move, since the numerical estimates are quantitatively quite different than what was observed in the data. Nonetheless, I think she is correct that we are fine interpreting these as qualitative comparative statics from an abstract model rather than trying to interpret their magnitude in any way. (Although I should note, it is not clear to me that we cannot sign the relevant comparative statics just because the model with storage cannot be solved analytically in its entirety…)

The welfare impact of information frictions with storage can be bounded below in a very simple way. If demand is overestimated in New York, then too much is exported, and though some of this cotton is stored, the lower bound at zero for storage means that the price in Liverpool is still too high. If demand in underestimated in New York, then too little is exported, and though some stored cotton might be sold, the lower bound on storage means that the price in Liverpool is still too low. A lower bound on the deadweight loss from those effects can be computed simply by knowing the price difference between the UK and the US and the slopes of the demand and supply curves; in the case of the telegraph, this deadweight loss is on the order of 8% of the value of US cotton exports to the UK, or equivalent to the DWL from a 6% tax on cotton. That is large. I am curious about the impact of this telegraph on US vis-a-vis Indian or Egyptian cotton imports, the main Civil War substitutes; information differences must distort the direction of trade in addition to its magnitude.

January 2014 working paper (No IDEAS version).

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