Putting the news in New York and New Orleans: the impact of information frictions on trade

Abstract

It is notoriously difficult to estimate the impact of information frictions on trade. The 1866 transatlantic telegraph connection has been used to estimate these impacts, but I demonstrate this sample violates the assumptions of an arbitrage model in ways that are likely to bias empirical result. I avoid this bias by constructing a novel dataset that meets all relevant assumptions during the 1848 rollout of the telegraph across the U.S., ultimately estimating the magnitude of the distortions on prices, quantities, and efficiency to be roughly half as large as those found in prior literature.

Appendix

1.1 Data

Most data were collected from historical newspapers, which occasionally had missing, illegible, or qualitative data that proved unusable. As a result, I collect data from multiple newspapers in each location to reduce the number of missing observations. For New Orleans, the Daily Picayune served as the main source of data for prices, exports to New York, and news lags. The New Orleans Commercial Bulletin served as the main source of data for quantities and freight costs and as a secondary source for prices and news lags. The New-Orleans Price-Current was the main source for the rates on bills of exchange to recover interest rates while the Daily Picayune was the secondary source. For New York, The New York Herald served as the only source of data for prices and the primary source for shipping times. The New-York Daily Tribune served as a secondary source for shipping times. Weekly figures for New York storage, receipts, re-exports, and rates on bills of exchange come from the Shipping and Commercial List.

The primary source of transportation speeds comes from The New York Herald, while the secondary source is The New York Daily Tribune. These newspapers list ships that came into port on a given day, where the ships departed from, and the duration of the voyage. Since cargo descriptions were only occasionally available, I recorded the voyage duration of all ships excluding those that did not sail directly to New York and those that were waylaid by maintenance issues.

I obtained non-freight transportation costs such as wharfage, cartage, and insurance from contemporary ledgers that were printed in Boyle (1934) and Entz (1840). To obtain daily interest rates that were incurred when taking out loans for shipping costs, I use the New-Orleans Price-Current to calculate the interest spread between New York bills of exchange with 60-days and zero-day maturities. Over the sample, they average 1.77 percent which is very similar to the 1.5 percent observed in Boyle (1934), but they range from 0.875 to 3.375 percent. The breakdown of costs is provided in Table

Table 9 Transportation costs

9.

1.2 Model

Consider two different information regimes. First, a delayed information (DI) regime in which agents in NO have news from NY up to period $t-1$ and must forecast NY prices in period $t+1$ when their exports can be sold in NY. Let this be represented by information set ${I}_{t-1}^{M}.$ Second, an instantaneous information (II) regime where all agents have news from NY up to period $t$ and must forecast prices for period $t+1$. Let this be represented by information set ${I}_{t}^{M}$. Lastly, let ${\overline{a} }_{D}$ be the average level of demand such that the AR(1) demand process can be rewritten as ${a}_{D,t }-{\overline{a} }_{D}=\rho \left({a}_{D,t-1}-{\overline{a} }_{D}\right)+{e}_{t}$ where ${\overline{a} }_{D}=\frac{\alpha }{1-\rho }$. Then, the following lemmas and proofs are reproduced from Steinwender (2018) for convenience.

Lemma 1

When switching from delayed to instantaneous information, the variance of expected demand increases, ${\text{Var}}\left[{\text{E}}\left[{{\text{a}}}_{{\text{D}},{\text{t}}+1}\mid {{\text{I}}}_{{\text{t}}-1}^{{\text{M}}}\right]\right]<$ ${\text{Var}}\left[{\text{E}}\left[{{\text{a}}}_{{\text{D}},{\text{t}}+1}\mid {{\text{I}}}_{{\text{t}}}^{{\text{M}}}\right]\right]$.

Proof

If the demand shock is ${\text{AR}}(1)$, the variances are:

$${\text{Var}}\left[E\left[{a}_{D,t+1}\mid {I}_{t-1}^{M}\right]\right]={\rho }_{D}^{4}{\text{Var}}\left[{a}_{D,t-1}\right]$$

Note that for a stationary ${\text{AR}}(1)$ process,

$${\text{Var}}\left[E\left[{a}_{D,t+1}\mid {I}_{t}^{M}\right]\right]={\rho }_{D}^{2}{\text{Var}}\left[{a}_{Dt}\right]$$

$${\text{Var}}\left[{a}_{Dt}\right]={\text{Var}}\left[{a}_{D,t-1}\right]$$

For $0 < \rho < 1,$

$${\text{Var}}\left[ {E\left[ {a_{D,t + 1} \left| {I_{t - 1}^{M} } \right.} \right]} \right] < {\text{Var}}\left[ {E\left[ {a_{D,t + 1} \left| {I_{t}^{M} } \right.} \right]} \right]$$

Lemma 2

Suppose $\frac{{\overline{{\text{a}}} }_{{\text{D}}}-{\overline{{\text{a}}} }_{{\text{S}}}-\uptau }{{{\text{b}}}_{{\text{S}}}+{{\text{b}}}_{{\text{D}}}}>0$, which means that there are positive exports at the average demand shock. Then, when switching from delayed to instantaneous information:

• (i) Average exports increase

  $$E\left[{x}_{t}^{DI}\right]<E\left[{x}_{t}^{II}\right]$$

• (ii) Conditional on exporting, exports increase

  $$E\left[{x}_{t}^{DI}|{x}_{t}^{DI}>0\right]<E\left[{x}_{t}^{II}|{x}_{t}^{II}>0\right]$$

Proof

Consider the analytical expression for exports, and consider first uncensored exports $\widetilde{x}_{t} : = \frac{{E\left[ {a_{D,t + 1} } \right] - \overline{a}_{S} - \tau }}{{b_{S} + b_{D} }}$. Uncensored exports in both regimes differ only in the way expectations about future demand shocks are formed. In the instantaneous-information regime the information set includes everything up to period $t$, while the information set in the delayed-information regime includes only information up to period $t-1$. By the Law of Iterated Expectations, average uncensored exports are the same in both regimes:

$$E\left[ {\widetilde{x}_{t}^{DI} } \right] = E\left[ {\frac{{E\left[ {a_{D,t + 1} \left| {I_{t - 1}^{M} } \right.} \right] - \overline{a}_{S} - \tau }}{{b_{S} + b_{D} }}} \right] = \frac{{\overline{a}_{D} - \overline{a}_{S} - \tau }}{{b_{S} + b_{D} }} = E\left[ {\frac{{E\left[ {a_{D,t + 1} \left| {I_{t}^{M} } \right.} \right] - \overline{a}_{S} - \tau }}{{b_{S} + b_{D} }}} \right] = E\left[ {\widetilde{x}_{t}^{II} } \right]$$

The variance of uncensored exports is a function of the variance of expected demand shocks, conditional on the respective information set:

$$\begin{array}{cc}& {\text{Var}}\left[{\tilde{x}}_{t}^{DI}\right]=\frac{{\text{Var}}\left[E\left[{a}_{D,t+1}\mid {I}_{t-1}^{M}\right]\right]}{{\left({b}_{S}+{b}_{D}\right)}^{2}}\\ & {\text{Var}}\left[{\tilde{x}}_{t}^{II}\right]=\frac{{\text{Var}}\left[E\left[{a}_{D,t+1}\mid {I}_{t}^{M}\right]\right]}{{\left({b}_{S}+{b}_{D}\right)}^{2}}\end{array}$$

and, using Lemma 1, Var $\left[{\tilde{x}}_{t}^{DI}\right]<{\text{Var}}\left[{\tilde{x}}_{t}^{II}\right]$.

Uncensored exports have the same mean in both information regimes, but the variance of uncensored exports is smaller in the delayed-information regime: $\widetilde{x}_{t}^{II} \sim N\left( {\frac{{\overline{a}_{D} - \overline{a}_{S} - \tau }}{{b_{S} + b_{D} }},\frac{{{\text{Var}}\left( {E_{t} \left[ {a_{D} } \right]} \right)}}{{\left( {b_{S} + b_{D} } \right)^{2} }}} \right)$ and $\widetilde{x}_{t}^{DI} \sim N\left( {\frac{{\overline{a}_{D} - \overline{a}_{S} - \tau }}{{b_{S} + b_{D} }},\frac{{{\text{Var}}\left( {E_{t - 1} \left[ {a_{Dt} } \right]} \right)}}{{\left( {b_{S} + b_{D} } \right)^{2} }}} \right)$. Denoting $\tilde{\mu }:=E\left[{\tilde{x}}_{t}\right]$ and ${\tilde{\sigma }}^{2}:={\text{Var}}\left[{\tilde{x}}_{t}\right]$, average censored exports are given by $E\left[{x}_{t}\right]=\Phi \left(\frac{\tilde{\mu }}{\tilde{\sigma }}\right)\tilde{\mu }+\tilde{\sigma }\phi \left(\frac{\tilde{\mu }}{\tilde{\sigma }}\right)$. A change from $DI$ to $II$ increases the variance of censored exports${\tilde{\sigma }}^{2}$, and this increases average censored exports ${x}_{t}$:

$$\begin{array}{cc}\frac{\partial E\left[{x}_{t}\right]}{\partial \tilde{\sigma }}& =\phi \left(\frac{\tilde{\mu }}{\tilde{\sigma }}\right)\cdot \left(-\frac{\tilde{\mu }}{{\tilde{\sigma }}^{2}}\right)\cdot \tilde{\mu }+\phi \left(\frac{\tilde{\mu }}{\tilde{\sigma }}\right)+\tilde{\sigma }{\phi }^{\mathrm{^{\prime}}}\left(\frac{\tilde{\mu }}{\tilde{\sigma }}\right)\left(-\frac{\tilde{\mu }}{{\tilde{\sigma }}^{2}}\right)\\ & =\phi \left(\frac{\tilde{\mu }}{\tilde{\sigma }}\right)>0\end{array}$$

Truncated exports, i.e., average exports conditional on being positive, $E\left[{x}_{t}\mid {x}_{t}>0\right]=\tilde{\mu }+\tilde{\sigma }\frac{\phi \left(\frac{\tilde{\mu }}{\tilde{\tau }}\right)}{\Phi \left(\frac{\tilde{\mu }}{\tilde{\sigma }}\right)}$ also increase when switching from DI to II:

$$\begin{array}{cc}\frac{\partial E\left[{x}_{t}\mid {x}_{t}>0\right]}{\partial \tilde{\sigma }}& =\frac{\phi \left(\frac{\tilde{\mu }}{\tilde{\tilde{\sigma }}}\right)}{\Phi \left(\frac{\tilde{\mu }}{\tilde{\sigma }}\right)}+\tilde{\sigma }\left(\frac{{\phi }^{\mathrm{^{\prime}}}\left(\frac{\tilde{\mu }}{\tilde{\sigma }}\right)\left(-\frac{\tilde{\mu }}{{\tilde{\sigma }}^{2}}\right)\Phi \left(\frac{\tilde{\mu }}{\tilde{\sigma }}\right)-\phi \left(\frac{\tilde{\mu }}{\tilde{\sigma }}\right)\phi \left(\frac{\tilde{\mu }}{\tilde{\sigma }}\right)\cdot \left(-\frac{\tilde{\mu }}{{\tilde{\sigma }}^{2}}\right)}{\Phi {\left(\frac{\tilde{\mu }}{\tilde{\sigma }}\right)}^{2}}\right)\\ & =\frac{\phi \left(\frac{\tilde{\mu }}{\tilde{\sigma }}\right)}{\Phi \left(\frac{\tilde{\mu }}{\tilde{\sigma }}\right)}+\tilde{\sigma }\left(\frac{\frac{{\tilde{\mu }}^{2}}{{\tilde{\sigma }}^{3}}\Phi \left(\frac{\tilde{\mu }}{\tilde{\sigma }}\right)\phi \left(\frac{\tilde{\mu }}{\tilde{\sigma }}\right)+{\phi }^{2}\left(\frac{\tilde{\mu }}{\tilde{\sigma }}\right)\frac{\tilde{\mu }}{{\tilde{\sigma }}^{2}}}{\Phi {\left(\frac{\tilde{\mu }}{\tilde{\sigma }}\right)}^{2}}\right)>0\end{array}$$

if $\tilde{\mu }>0$, which is assumed for exports to be positive on the average realization of the demand shock.

Note that this proof also holds if there are stochastic supply shocks. Since merchants are in NO, there will be no uncertainty about the realization of supply shocks, so information is not relevant. Supply shocks are relevant only when storage is allowed.

Lemma 3

When switching from delayed to instantaneous information, the variance of the forecast error falls,

$$Var\left[{a}_{D,t+1}-E\left[{a}_{D,t+1}\mid {I}_{t-1}^{M}\right]\right]>Var\left[{a}_{D,t+1}-E\left[{a}_{D,t+1}\mid {I}_{t}^{M}\right]\right]$$

Proof

The variance of the forecast error under the II regime (note this is the same whether conditioning on positive exports or not),

$${\text{Var}}\left[{a}_{D,t+1}-E\left[{a}_{D,t+1}\mid {I}_{t}^{M}\right]\right]={\text{Var}}\left[{\epsilon }_{D,t+1}\right]={\sigma }_{D}^{2}={\text{Var}}\left[{a}_{D,t+1}-E\left[{a}_{D,t+1}\mid {I}_{t}^{M}\right]\mid {x}_{t}^{II}>0\right]$$

while under the DI regime,

$${\text{Var}}\left[{a}_{D,t+1}-E\left[{a}_{D,t+1}\mid {I}_{t-1}^{M}\right]\right]={\text{Var}}\left[{\epsilon }_{D,t+1}+{\rho }_{D}{\epsilon }_{Dt}\right]=\left(1+{\rho }_{D}^{2}\right){\sigma }_{D}^{2}\dots$$

$$={\text{Var}}\left[{a}_{D,t+1}-E\left[{a}_{D,t+1}\mid {I}_{t-1}^{M}\right]\mid {x}_{t}^{DI}>0\right]$$

from which follows

$${\text{Var}}\left[{a}_{D,t+1}-E\left[{a}_{D,t+1}\mid {I}_{t-1}^{M}\right]\right]>{\text{Var}}\left[{a}_{D,t+1}-E\left[{a}_{D,t+1}\mid {I}_{t}^{M}\right]\right]$$

for $0<\rho$. Note that this result also holds strictly for random walk shock processes.