Cross Section of Nevada Slot Regions

Applying the aggregated Nevada time series model to the individual regions provides confirmation of the same general findings in the previous post.  We are also able to group regions by qualitative findings.

The following table suggest one possible interpretation using three qualitative groups.

The R^2 value is the amount of variation explained by our linear model.  Accordingly, within each group, I rank by the region’s R^2.  The higher the R^2, the better our model explained the actual data of the region.  The first thing to note is that the grouping is a pretty good indication of average explained variation.  So, what are the characteristics of each group?

Group 1:  All of these regions have characteristics that match the aggregated model.  All show a long run tightening hold of on average between 1 – 2.5 hundredths of a % per month.

Each member of Group 1 has a monthly oscillating pattern that can be described by two months of data. The average holds are pretty tight.  Finally all show a significant loosening in December.

Group 2:  Reno and Elko stand apart as they have on average a looser hold than their Group 1 counterparts, and show no long run change in monthly hold.  Instead of an oscillating pattern, movements in hold tend to reiterate themselves.  The December loosening is milder in these regions.

Group 3:  NSLT and Mesquite are the only regions that show a tightening in December.  This is most likely the result of the bad fit of the model.  With them SSLT shows a long run loosening in hold.  Their various other coefficients do not lead to any obvious interpretation.  The lack of competition in these regions (relative to the bigger gambling destinations) probably leads to different strategies, exposure to shocks and small sample problems.  An ARCH type model looks like it would be a better fit.

Importantly, the regions when analyzed under the aggregated model do not dispute recession hold tightening.  In fact most of the regional models, even Mesquite, show higher than average tightening during that time. Under the lens of the tightening hypothesis, Mesquite’s peculiarities are likely brought on by the recession.

As far as statistical methodology, there are still places I may have tripped.  Efficient estimators of the variance structure should be explored.  Also, since I ran the regressions one at a time, I could run a panel regression for better estimates.

Evidence of Tightening During the Recession

I will show results from the R statistical language that will solidify some observations we can make about aggregate Nevada slot holds over time.  (Again the data covers the years 2004 - 2014 and comes from  http://gaming.unlv.edu/reports/nv_slot_hold.pdf).  Essentially what we want to do is figure out a regular pattern, subtract that and see what remains unexplained.

The blue line above is the average monthly hold in Nevada that I've talked about before.  The orange line is a standard time series estimate which we will take to be our model.  This estimated model “explains” roughly 70% of the variation of the data (as measured by adjusted R^2).  There are a few things we learn about the data in building this model.

First, a model looking backwards only two months works pretty well as far as capturing the oscillating pattern we see in the market overall.  If the data were weekly, I’d expect to see a relevant period of more than 4 but less than 10 weeks.

Second, there is a linear trend over time of increasing tightness: if you were to draw a straight line through the data, it would have an upward slant.

Third, December is a time of loosening: this explains the periodic low points about 12 months apart. 

Removing any of these three factors greatly reduces the explanatory power of the model.  But incorporating all of them into a one equation model gives us a powerful explanatory tool.  It may be a useful prediction tool as well, but that won’t be my focus here.  In the chart below I plot the errors of the model.

A model with no biases would look random and wouldn't have any discernible patterns.  This is mostly the case for our model except for the period corresponding to the recession, during which we see that the model systematically underestimates the tightening of slot machines.  This I think is strong first pass verification that there is something to investigate as far as concerns the dynamics between Players and Casinos during the recession.  Indeed, the "great tightening" was more than business as usual.

In my opinion this model is mostly useful for capturing descriptive qualities of the market and not necessarily useful for determining whether demand or supply side factors are the cause.  To further this line of analysis, I would apply the same form of model to the individual regions, and see if it retains its explanatory power.  The resulting cross section of variation will give us a lot of clues about why the patterns emerge.

After that, the goal will be to use economically fundamental variables, like income, profit and expenditures of the Players and Casinos, to explain a system of equations governing this list of variables as well as hold.

Supply, Demand and Estimation

The Nevada Gaming Control Board in its Gaming Revenue Reports provides monthly hold data for slot machines (http://gaming.nv.gov/index.aspx?page=149). Hold data is the aggregate of what is payed out to Players divided by what they pay to play. From this, the long run trends in holds can be established.  For example consider Dr. David G Schwartz’ claim that holds have tightened by 13.54% between 2004 and 2014 in the following report: http://gaming.unlv.edu/reports/nv_slot_hold.pdf.  

In the above chart I have placed aggregate monthly data versus a linear trend beginning in January of 2004.  It illustrates Schwartz’ claims, but how useful is this data for evaluating hypotheses like a “great contraction” corresponding to the 2007-2010 economic turmoil?  It turns out it is not so obvious how to interpret this kind of data, and the reason is that each month we are observing the intersection of both an aggregate demand and an aggregate supply function.

A rise in hold from one period to the next could for example mean that on average Players have chosen to play tighter games, or could be that other things equal, the Casino has tightened the average return of its machines.  The reality, we should all realize, is we are seeing layers of strategy from both parties.

So what is it that we need?  First steps might involve analyzing the data by region, which reveals that the Casinos and Players differ in their strategies, region to region.  For example, Elko seems to have tightened during the recession, whereas Mesquite seems to have tinkered less than they did prior to the recession.  One single model is unlikely to explain all the data, and each region can be explained by multiple models.

I bet Players, Casino operators and salesmen in the regions could tell me a lot about what happened during this time.  But given the difficulty of finding all of the relevant information, we have to settle for models which, using what information we have, prescribe behaviors to the Players and Casinos.  Given these assumptions, we then see what the data has to say.  Fortunately we will have lots of models to choose from, and each model chosen should teach us something new.

As a start, I would want to know the change in employment (both aggregate and by region) for each month.  We could use it as a predictor for the change in hold, and this would probably be the best way to gauge the effect of a typical Player’s income.  However, in the regions of interest, the Casinos are also major suppliers of jobs, so the employment data will also give partial information about the financials of the Casinos. It stands to reason that a Casino's financial situation determines in part their slot floor strategy. It is up to the researcher then to make assumptions when interpreting the results (in this example determining the effect of employment on hold through supply and demand channels).

Cleaning the data using time series methods is another step I would likely take.  This would filter out noise from seasonal patterns like Casino purchase timings or the Christmas season, and also long run trends.  But even though time series methods help us get a clearer picture, they implicitly make assumptions about the behavior of Players and Casinos.  Really there isn't a way to do the empirical work without making economic assumptions.  To me this means that we must use our training, experience and imaginations to come up with models that have meaningful predictions, and then test them against the data.