The binary variable signifying cartel cooperation within the data set was self reported by the cartel, which raises concerns with regards to its fidelity. An initial timeline plot reveals cooperation deteriorating over time as the cartel resorts to pulling the trigger, competitive levels of output, with greater frequency.
 

The worsening levels of cooperation is noteworthy, but we shouldn't trust the data at first sight. We can check to see if the rest of the data complies with a cartel status. Collusion will lead to a higher prices than would be obtained through competition for a given output, else there would be no incentive to cooperate. This naturally works itself into the hypothesis: 

• H0 Null - On average non-cartel prices are equal to or greater than cartel prices for a given quantity. Equal or less total revenue.
• H1 Alternative  - On average cartel prices are higher than competitive prices for any given level of output. 

A visual check of the data is enough to satisfy a rejection of the null hypothesis, as would a simple linear regression. Non-cartel prices are significantly lower than cartel prices in both statistical and economic sense. Cartel status is associated with roughly a $500 ($11,000 in 2016 prices) increase in weekly revenue. We reject the null hypothesis that Cartel status lacks any change, and if change is associated with lower total revenue.

Qualifier for Cartel Success

A cartel is successful if the members are able to sustain collusion and obtain market power. Market power is the ability to profitably raise price above marginal costs. We unfortunately do not have details on the marginal costs for the cartel members. Rather than trying deduce members costs, we will look at the extreme end of market power to see if the cartel is operating at its fullest potential. The goal of a cartel is to operate in such a fashion as to obtain monopoly rents. In essence, if the cartel is able cooperate to a level that they appear to act as one unified company.

A qualifier of a successful monopoly, or very successful cartel, is that it operates within the elastic range of demand. Within the elastic range of demand, a percentage increase in price is meet with a greater percentage decrease in quantity. Similarly, a percentage decrease in quantity supplied is meet with a lesser percentage increase in market price. In this range any increase to price or reduction in quantity supplied is meet with reduced total revenue for the producers.

While odd at first glance, the counter point makes this clear. Within the inelastic range of demand a monopoly can either increase price, or reduce quantity, resulting in increased total revenue. It is safe to assume increasing price or decreasing output has little significant effect on operating costs, and as such profits increase. Without competition to check them why would a monopoly, much less any other company or collusive group, not seek to increase their profit? 

Therefore the cartel is successful when the Price Elasticity of Demand is greater than 1 in absolute terms, within the elastic range.    | E | > 1

Price Elasticity of Demand

Market Prices and Instruments

The issue with price and quantity data that we posses is that they are determined by a simultaneous equation. Price and quantity are determined by both supply and demand. A change to price and quantity may be result of a change to demand, or it may a result of a change to supply, or it may be both. If we are able to isolate demand, we can determine whether the JEC cartel operated along the elastic or inelastic range of the demand curve. This simultaneous equation poses a problem with OLS regression in teasing out the demand curve. A simple log-log multivariate regression model produces significant results, but neglects the structural problem of endogeneity with suppl and demand.

The simple log-log model shows that the JEC cartel is operating in the inelastic range of demand ( 0 < | PEd | < 1 ) and on average unsuccessful at collusive behavior. However, as mentioned this would be a naive conclusion as the model does not address the endogeneity of price caused by both supply and demand. 

IV Solution - Two Stage Least Squares

In order to tease out the price elasticity of demand we need an instrument that can account for the supply curve.  There are two key qualifications that a instrumental variable must posses.

1. Relevance; The instrument must be correlated with variable in question.
2. Exclusion; The instrument is not correlated with any other determinant of the dependent variable. 

Relevance can be tested, but exclusion only stands on the grounds of a logical argument that often cannot be empirically confirmed. In our case we can make the claim that cartel status has no effect on demand for grain on the Eastern Seaboard.  A New Yorker's increased preference for grain for hot dog buns, due to baseball, is not relevant to whether a cartel members in Chicago are cheating one another. This change in demand should not be confused with a change in quantity demanded. Surely the increased price from constricted supply will result in decreased quantity demanded. But this is movement along the demand curve, as opposed to a shift of the entire demand curve caused by a change in preference.

To test for relevance we can regress price upon cartel status. We find this relationship to be statistically and economically, roughly one standard deviation difference, significant. The previous data checks to see if the self reported cartel variable was reasonable revealed already established this relationship.  We will run several checks on the cartel instrument to see if we can reject it as a valid instrument.

The weak instruments test's null hypothesis is that the instrument, cartel, has a low correlation with the endogenous variable. We significantly reject the hypothesis that cartel is a weak instrument.  Further, we weakly reject the Wu-Hausman hypothesis that the OLS and IV models are equally consistent. If they were equally consistent, it would be more efficient to make use of the OLS model.

Results - Unable to Sustain Cooperation

The IV models reveals a price elasticity of .867, within the inelastic range of the demand curve. The cartel, on average, was not successful in their collusive efforts. It should be noted that if one used an OLS model, ignoring the endogeneity of price, one would incorrectly believe the collusive efforts of the cartel to be less successful.

If we were a JEC cartel member, how is this information useful? Firstly we know that we are leaving money on the table. Our current self governance may not be strong enough to sustain collusion. Secondly, we know that on average weekly total revenue increases by $488.31 when the cartel is colluding. The cartel pulls the trigger, either do to cheating or perceived cheating, on average 38% of the time for a given week of the year. As such, the cartel can dedicate resources up to $15,715 ($348,500 in 2016 dollars) for improving detection and enforcement to sustain collusion. This should be treated as a naive upper bound estimate as the current strategies are approaching the elastic portion of demand. If we believe an analyst can improve collusion by 50%, we should engage them at a cost up to $7,587 per year ($174,241 in 2016 dollars) for their time and needed resources. While this estimate for resource dedication may be a bit simplistic, it is a good starting point to frame a discussion with cartel members.

Of course ideally we, as humans with well intentions, would prefer the cartel member to not exert market power by means of collusion.

 R code is available on Github under the JEC repo.