Economists typically assume that people know the price of all goods at all times, but this is more true for some goods than others. While commodities like crude oil and rough rice have a single price determined by trades in public exchanges, prices are a bit less transparent for consumer goods. After all, do you know the various prices for Heinz 57 at stores in your county? Still, comparison shopping and price-based marketing campaigns (Tide detergent: Now only $4.99!) keep it so that people have a good sense of the price of consumer goods.

Prices are much more opaque for goods sold on the black market, where there cannot be an Uber for migrant farm workers, futures contracts for smuggled assault rifles, or subway ads pushing low-cost LSD. This makes PriceofWeed.com a particularly interesting source of data to explore. Since 2010, over 300,000 people have anonymously submitted the price, quantity, quality, and location of their marijuana deals, shining a light into one black market. Using this data, you can calculate the average price of weed in each US state–as Forbes did back in early 2015–to conclude that, as you’d expect, states that have legalized marijuana (e.g., Colorado, Washington, Oregon), have lower prices.

The dataset is much richer than that, though. PriceofWeed.com also collects information about the quality of the marijuana being purchased, whether high-quality dank or low-quality schwag. Using that information, you can map prices for high-, medium-, and low-quality marijuana.

Average Price ($/oz.) of Marijuana in U.S., 2013-2015

States with lower marijuana prices are displayed in darker shades of green here. The color scale of this map automatically adjusts based on the price range for each quality level so that the map always highlights relative price differences across states; by contrast, using a fixed color scale would have illustrated an obvious characteristic of the data: low-quality weed costs less than high-quality weed.

The map shows that while states where marijuana is currently legalized–Colorado, Oregon, Washington, and Alaska–all have notably low prices for high-quality weed, their prices for medium-quality weed aren’t much lower than other states. Additionally, for whatever reason, the Midwest appears to be the bastion of cheap, low-quality weed.

In addition to the quality of the marijuana purchased, the dataset also includes the date when marijuana transactions occurred. Using that, we can explore how prices have varied over the time when this data was collected, December 2013-July 2015. (Going forward, we’ll only look at high-quality marijuana prices, both because there are more reported transactions for high-quality marijuana and because, hey, go big or go home.)

Monthly Price ($/oz.) of Marijuana in U.S., 2013-2015

While Western states maintain the low prices that they have at the beginning of this time period, other states’ prices start out higher but gradually decline over time. This observation begs a question: Does the West Coast function as one integrated market for marijuana, with price changes in one state immediately trickling over to their neighbors? Or are there other groups of states–perhaps in different regions or with similar policy structures (e.g., legalized medical marijuana)–that experience similar price shifts?

To begin to answer these questions, let’s first take a deeper look at the data for individual states. (Want to analyze the data yourself or see how I produced these charts? Check out my Jupyter Notebook on GitHub.)

State-Level Marijuana Prices

If you went out to buy high-quality weed today, which states would give you the biggest bang for your buck? Unsurprisingly, it’s the states that have legalized marijuana.

states_final_prices_ranked

Oregon has the lowest price ($202.21 per oz.) with Washington and Colorado close behind. California has the lowest price among states where marijuana isn’t legal, presumably due to presence of growing operating in NorCal and the state’s booming medical marijuana business. Although Alaskans voted to legalize marijuana in February 2015, their most recent price for high-quality weed was $293.50/oz., perhaps owing to the short time for markets to adjust or the fact that everything is expensive in The Last Frontier.

At the other end of the scale, North Dakota has the most expensive marijuana at $383.87/oz, followed, surprisingly, by the stereotypically head shop-filled, Ben & Jerry’s-spawning commonwealth of Vermont.

There is some evidence that a state’s price influences the price of neighboring states, as Nevada, Utah, New Mexico, and Montana all have low prices–and all are close to the states with the lowest prices. That said, many of Colorado’s neighbors–e.g., Wyoming, Nebraska, Kansas, and Oklahoma–have relatively high prices. Overall, it’s quite difficult to see a clear pattern in the prices, as any possible theory (e.g., prices seems to be high in New England) have clear counterexamples (e.g., Rhode Island and Maine, where low prices give their residents are strong incentive to engage in (illegal, it should be noted) arbitrage).

Rather than comparing prices levels between states, what if we looked at the price changes in states between 2013 and 2015? As the animated map suggested, the states that saw the steepest declines in marijuana prices weren’t the states that recently legalized marijuana.

states_beginning_to_end_perc_change

Wyoming saw the sharpest decline in marijuana prices, dropping 11.9% from $355.90/oz. in December 2013 to $313.72/oz. in July 2015. Minnesota, North Dakota, South Dakota, and Arkansas all saw prices drop by more than 7.5% during this time. Meanwhile, only three states–Colorado, Alaska, and Kentucky–saw prices increase, an interesting finding since both Colorado and Alaska have legalized marijuana.

Considering all of this data, it seems like American marijuana prices are converging. States with initially high prices (e.g., North and South Dakota) saw steep declines in prices, whereas states with lower initial prices (e.g., Colorado, Washington) saw prices decrease by a small amount, if at all.

To test this idea with a small amount of rigor, let’s look at a simple regression of a state’s average month-over-month percent change in marijuana prices on the price of marijuana at the beginning of this time period.

states_initial_prices_versus_average_change

The fitted line here shows a statistically significant relationship: higher initial marijuana prices are associated with larger month-over-month decreases in marijuana prices.

Although North Dakota–the dot at ($416, -.29%)–saw large prices decreases, this regression tells us that we shouldn’t be too surprised by the .29% average monthly price reduction given the state’s initially high price level. Instead, we should be surprised by states like Oregon ($213, -.19%) and Montana ($280, -.28%) which had much larger month-over-month price decreases than you would expect given their lower initial prices.

This “difference from what you’d expect given initial prices” is known statistically as a residual, the vertical distance between points in the chart above and the fitted regression line. Plotting these residuals for each state lets us find the states that saw prices decrease faster than expected as well as states that, though they saw decreasing prices, didn’t see prices fall as much as would’ve been expected (e.g., West Virginia, where prices decreased by .07%/month but would be expected to decrease by .16%/month given an initial December 2013 price of $361/oz.).

state_percent_change_residuals

Grouping States Together: Cluster Analysis

Should we even expect states’ prices to move together, for high prices in one state to occur at the same time that prices are high in neighboring states? On one hand, the signs for price convergence above suggest that state marijuana markets are connected; states are linked with interstates, after all, and price differences across states incentivize arbitrage. On the other hand, many growers are small enough to sell all of their product locally; plus, it’s a federal felony to transport marijuana across state lines, further dissuading actions that would link prices of neighboring states.

To try to see if there are groups of states where prices do move together, I took a fairly simple approach:

  • Smooth monthly marijuana prices within states using an exponentially-weighted moving average to dampen the influence of transient price shocks
  • Calculate the percent change in marijuana prices within states between each month
  • Apply k-means clustering to group together states that have similar percent changes in prices over time, using a measure called the silhouette to choose the “best” clustering of the data

Using this approach yielded four groups (or clusters) of states:

  1. Colorado and Alaska (Cluster 1)
  2. Minnesota, Missouri, New Hampshire, Rhode Island, South Dakota, and Wyoming (Cluster 2)
  3. Arkansas, Montana, Nebraska, and North Dakota (Cluster 3)
  4. All 38 other states (plus D.C.) (Most States)

To get a baseline understanding of what’s going on within these clusters, let’s average the overall percent change in prices within each cluster.

clusters_overall_perc_change

The cluster with Colorado and Alaska–unsurprisingly, given what we saw earlier–saw prices increase between 2013 and 2015. The other two smaller clusters saw rather large decreases in prices over this time, a 7.6% average decrease for Cluster 2 and a 6.9% decrease for Cluster 3. Most States, meanwhile, saw a 3.3% reduction in prices.

Looking at the average time series for each cluster illuminates what separates Clusters 2 and 3: states in Cluster 3 saw large prices drops earlier than states in Cluster 2.

clusters_time_series_prices

Further supporting the idea of price convergence, Clusters 2, 3, and 4 have more similar prices at the end of the time period than at the beginning.

Let’s compare the time series for states within each cluster to make sure that the k-means clustering actually grouped together states with similar trends over time.

within_cluster_time_trends

Fortunately for us, the patterns basically hold for individual states. Alaska and Colorado both experience no price changes expect for a blip around January 2015 (right before Alaskans voted to legalize marijuana, if that has anything to do with anything). States in Clusters 2 and 3 generally have the early/late timing of price decreases seen in the overall trend. The rest of the states are all over the map but share a slight downward trend overall.

Some Conclusions

So what are we to make of all this? I’d argue that even though the signs of price convergence indicates that the American marijuana market is becoming more integrated, the lack of clear regional groupings of states with similar price changes suggests that there are still significant barriers to operating smoothly across state lines. Arkansas, Montana, Nebraska, and North Dakota all ending up in the same cluster tells me that there isn’t really a common factor (e.g., geography, common policies) driving monthly marijuana prices across states; this grouping is probably the result of random forces and happenstance.

That said, the fact that Wyoming and North Dakota’s large price declines between 2013 and 2015 happened near a pocket of states with low overall prices–e.g., Utah, Idaho, Montana–suggests that states’ prices can influence their neighbors’ prices over a large enough timespan. Any regional price influence needn’t occur within a month, as our analysis above assumed. Instead, low prices could spread from one state to its neighbors over the longer time horizon it likely takes black market dealers to build a network of people to securely transport and sell their illegal (in most states) (for now) product.

Stray Observations

  • Caveat for my mother: I learned about this dataset on Yhat’s blog and figured my economics training would help me say something useful about price trends. You didn’t raise an inveterate stoner, Mom.
  • Caveat for my social scientists: Yes, this entire analysis is contingent on people accurately and honestly reporting their prices to PriceofWeed.com. I used medians where appropriate to remove the influence of outlandish outliers entered by people, but that can’t help if people entered systematically incorrect prices.
  • In case you were also concerned that Vermont’s high July 2015 price was a fluke, I looked up its time series; it seems like marijuana prices have always been above-normal in Vermont.
    vermont_time_series
  • Another reason I only used high-quality marijuana prices for most of the analysis: whoever runs PriceofWeed.com decided to occasionally replace observed prices for low-quality marijuana with sentences like “Who even buys low-quality weed?” and “I feel sorry for these guys.”
  • Technical note: I smoothed the prices before (rather than after) calculating the percent change between months so that I wouldn’t be wasting data. Doing the percent change drops one month from the dataset (Who’s to say whether the first price in the dataset was an increase/decrease from the previous month?), so doing the smoothing earlier takes slightly more information into account.
  • Noted data viz expert Jeffrey Heer has criticized maps like the ones we began with, noting that people are terribly inaccurate at identifying values encoded in color (e.g., lower prices showing up as deeper shades of green). I agree with his critique of these maps (known as choropleth maps), but I wasn’t going for an accurate display of price data in the maps–that was the point of the bar chart; instead, I was going for the visual of the map becoming more and more green as marijuana prices decreased over time.
  • Header image of Highway 420 (aka the High Way) c/o Thomas Hawk