Dispensary density and sales

Please find replication materials (code and data) reproducing all figures and statements made in this blogpost at this link.

One perennial theme on Brookline’s Townwide Discussion Facebook page is the NETA cannabis dispensary, with a vocal group of perhaps 10 people (in the Facebook group, the underlying constituency must be larger)  raising concerns about nuisance (most often being public urination and public consumption) and traffic. It’s not hard to imagine how having 2500-3000 people coming to a business near your house comes with some problems.

Inevitably, somebody comments that opening more stores will alleviate the problem. NETA, right now the only store in Brookline, absorbs traffic from a huge area in Metro Boston, because so many big, nearby municipalities (Boston, Cambridge, Somerville, Watertown, etc) do not have any stores.

But intriguingly, many folks have responded that opening new stores will not help, and that more stores actually increases sales per store. E.g. one poster responds with “The data says otherwise. Here’s a study showing that cannabis turnover per retail outlet increases as the number of outlets grows.” The study referenced is actually a short report made by a group opposing a once-proposed marijuana dispensary in Brookline’s St. Mary’s neighborhood (the group charmingly called itself “The Coalition to Save St. Mary’s Neighborhood”). The evidence for the claim that more stores increases sales per store comes from two plots. First, plotting the trend in sales per dispensary in Washington state and superimposing the trend in store openings; both appear to be increasing during the first six months of recreational sales (July 2014 to December 2014). Second, plotting the sales at Cannabis City, Seattle’s first marijuana store, and superimposing the trend in store openings. Both appear to be increasing.

This counterintuitive claim (it is not obvious why the opening of competitor Store B would increase demand at Store A) piqued my curiosity, so I downloaded the monthly sales data per store from the state of Washington and tried to investigate.  I merged these data with publicly available business information for licensed cannabis establishments to get store locations. And directly comparing store openings with monthly sales per store, I find evidence for the much more boring story that more stores means less sales per store. Looking at the city of Seattle (one confusing thing in the St Mary’s report is conflating Seattle with the state of Washington), sales per store is inversely correlated with stores open. (The outlier at the bottom left is the first month, July 2014; sales did not start until the middle of that month and were hindered by a product shortage.)


And sales at Seattle’s first Dispensary — Cannabis City — decline considerably as other stores in the city open.


One can also plot sales at the first shop in Seattle over time. As more stores open (the numbers above each bar are the stores open in Seattle that month), sales at Cannabis City stabilize and then decline. It’s important to remember that the first month is an outlier in part because sales did not begin until July 8th, and the store closed, having run out of stock, just three days later. If not for the product shortage, sales during the first month would have been much higher.


The relationship between store openings and sales per store can also be estimated formally using an econometric model. I estimated three statistical regression models at the city-month level of monthly sales per store on number of stores, with fixed-effects for city (holding time-invariant city-specific factors constant) and month-year (ie., July 2014, August 2014, …, October 2017, holding constant time-varying shocks that affect all cities). Using this framework, I first estimate how monthly sales per store within a city change when an additional store opens in that city. The result, Model 1 in the table below, is that opening an additional store in a city is associated with decreased sales per store of $7100, and statistically different from zero (p < 0.001). Model 2 takes the natural logarithm of sales to estimate the percent change in sales per store when one additional store opens, finding that an additional store is associated with about a 6% decline in sales per store. Third, I directly estimate the elasticity of sales per store on store openings, by taking the natural logarithm of both the dependent and independent variables. This approach usefully captures the fact that an additional store will have greater impact when fewer stores are open and less impact when more stores are open. In the two-way fixed effects model, the estimated elasticity of price per store on store openings is about -0.46, indicating that a 1% increase in stores is associated with a -0.46% decrease in sales per store. This means that a 10% increase in stores is associated with a 4.3% decrease in sales per store:

> 100*(1 - exp(-0.458629*log(1.1)))
[1] 4.277041

And a doubling of stores (a 100% increase) brings a 27.2% decrease in sales per store.

> 100*(1 - exp(-0.458629*log(2)))
[1] 27.23226
Statistical models of store openings on sales per store
Dependent variable:
Sales per Store log(Sales per Store)
Interpretation: Model 1: Dollars Model 2: % Change Model 3: Elasticity
Δ Stores -7,100*** -0.06***
Standard Error (1,877) (0.02)
Δ log(Stores) -0.46***
Standard Error (0.10)
Observations 3,227 3,227 3,227
Adjusted R2 0.83 0.71 0.71
City Fixed Effects Yes Yes Yes
Time Fixed Effects Yes Yes Yes
Note: *p<0.1; **p<0.05; ***p<0.01


A couple of notes on the St Mary’s report. Its plots use two y-axes, which is usually not a good sign, since these are hard to interpret and often deceptive (see also). The report also truncates the months displayed in a cherrypicked way (e.g. in the first figure plotting sales at the first shop in Seattle, sales decline considerably in the month following the last month shown). That figure is also not transparent about the number of stores that are open. The plot says there was 1 cannabis store open in July 2014 and 18 in August 2014. The City of Seattle did not have 18 stores open in August 2014. Cannabis City remained the only store open in August (in September, just 1 additional store reported sales in Seattle; in October, 4 stores reported sales). Why is there this discrepancy? The report says it is using all the stores in the state: “Volume in that third month of operation, September 2014, was FIVE TIMES the volume the entire first month, even though the state had gone from one legal store to 47.” This is misleading; it is hard to imagine that stores on the border with Canada are competing with those in Seattle.

But the report is not faithfully representing the number of stores operating statewide, either, because 13 stores in Washington reported recreational marijuana sales in July 2014, not one. Cannabis City wasn’t even the biggest retailer in July — there were 5 stores with more sales that month; two in Vancouver, Washington on the Oregon border, two in Bellingham, Washington near Canada, and one in Prosser, Washington. So is the plot of the city or the state? Beyond this, the numbers for store openings I obtain from publicly available sales data on Washington’s LCB website (see replication materials) are not consistent with what is in the St Mary’s report. In August, I count 24 stores with nonzero sales, not 18 as in the St Mary’s report. While the sales totals for Cannabis City are the same between our two analyses, we count a much different number of stores. Their report does not link to any data source, so it is difficult to clarify the origin of this discrepancy. What is incontrovertible is that Cannabis City was not the only recreational marijuana store operating in Washington in July 2014, so the St Mary’s report misleads in saying that just one store was open in July 2014.


One final point. The claim that sales increase with more stores is supported by plots of an increasing trend in sales over six months alongside a trend of increasing store openings during this period. This overlooks some important time-varying contextual factors (i.e., confounders). Due to a weak harvest and early-industry regulatory issues, Washington did not have enough recreational marijuana to sell when stores first opened, so store shelves sat empty (here’s another article about this), artificially depressing sales during the first months. As mentioned, Cannabis City, Seattle’s first store, closed after three days because it ran out of products. As the supply chain matured, we would expect more sales to occur, because there was previously a product shortage. This is important context that was missed entirely by the simple plots in the St Mary’s report. The two-way fixed effects approach is useful because it directly models such time-varying shocks.

I have posted all replication data and code reproducing these plots and statements for free access here.