### Price Elasticity of Demand in Railway Trasportation in the 1880’s: Another Application of Instrumental Variable Regression

Data set can be found at http://www.aw-bc.com/stock_watson; analysis is based on ” A Study of Cartel Stability:  The Joint Executive Committe, 1880-1886″ Professor Robert Porter from The Bell Journal of Economics

During the 1880’s rail transportation of grain from the Midwest to eastern cities in the United States was controlled by a cartel known as the Joint Executive Committee (JEC).  Like many cartels, including OPEC, the JEC was bound by agreement, but its members often cheated on shipment/price quotas that were set up in order to advance individual gain.  One can exploit the variation in supply resulting from the periodic collapse of the JEC cartel to estimate the elasticity of demand for rail transport of grain.  Indirectly, this estimate will have implications on the effectiveness of cartel pricing in the 1880’s in extracting monopoly rent from its clients.

Description of Variables

week = the week of observation in the sample; week 1 = 1/1/1880 to 1/7/1880 and week 328 is the final week

price = weekly index of price of shipping a ton of grain by rail

ice = 1 if Great Lakes are impassable because of ice, 0 other wise

cartel = 1 if cartel is operative, 0 otherwise

quantity = total tonnage of grain shipped per week

seas1-seas13=thirteen monthly binary variables each approximately 4 weeks long

Descriptive Statistics

The average indexed price of transportation was .24 dollars.  The cartel was operative about 61% of the time during the time of observation.  The average amount of tonnage shipped per week was 25,384 reaching as high as 76,407 and as low as 4,810.  Ice made transportation across the great lakes impossible about 42.6% between 1880 and 1860 which is the period of observation.

OLS Regression Estimate of Elasticity

As we can see from the regression results above, the elasticity of demand for rail transportation of grain is approximately .64.  The problem with this estimate is that price and quantity are jointly determined with price, thus we can have an econometric specification problem.  Using cartel as an instrument for price is a nice solution to this problem.  The variable cartel is highly correlated with price proving it to be a strong instrument.  There variable cartel should not be correlated with the error term in the demand equation.  These two conditions of the variable cartel make it a relevant and exogenous instrument that can be used to deal with the simultaneous determination of price and quantity and should yield a better estimate of elasticity.

Test for Cartel as a Weak Instrument

IV Regression Estimate of Price Elasticity

As one can see from the regression above, the elasticity of demand for rail transportation of grain is .87 which is inelastic.  This means that the pricing of rail transportation in the period from 1880 to 1886 was not optimal if the cartel was acting rationally.  Cartels band together to act as one, essentially a monopoly, monopolies operate in the elastic range.  That is, monopolies charge higher prices until the percentage change in quantity demanded falls by a greater amount than the percentage change in price.  The JEC railway cartel could have extracted higher profits if it had charged higher prices when it operating in the grain transportation business.