A
Okay welcome to the cannabis data science meetup March 17 2021
21. Visit Can-Lytics if you want more information and you want to contribute to open source
research on cannabis analytics. Today, I thought it would be interesting to look at the rates
of return on capital in the cannabis industry. Last week, we looked at the real wage that
workers can be expected to be paid. So this week, it would be interesting to look at the
other input, which is capital. If you look at an article by Poulsen from 2013, it would
be interesting to look at the current rate of capital. He expects that there are high
rents from capital because you have a semi-legal market. So the states consider it legal, the
federal government still considers it illegal, which results in a high rate of capital because
large banks and investors are often hesitant to lend to cannabis businesses. So when you
start a business, you may need to take out loans. And then investors also want to get
rate of return on their loans. So it's interesting to know what the rate of return is in the
cannabis industry because you may expect it to be high. So we're going to use a similar
production function as we used last week. However, we're going to use an even simpler
production function. So first, we're going to take the simplest model and we're just
going to assume that cannabis sold in a given period, yt, is a function of the number of
plants, kt. And it's augmented by technology and there's a random element. And so that'll
be epsilon, or random shop. So of course, the actual production of cannabis is more
complicated than just cultivating plants and turning that into revenue. However, we're
going to abstract just to create the simplest model and then you can expand on it to make
it more realistic. So if you plot these variables against each other, we can start to see some
positive trends. So if you plot retail revenue against cultivated retail plants, you do see
the positive trend like we would expect. And there may or may not be diminishing marginal
returns. What that simply says is you would expect that the more plants you cultivate,
you're going to get less and less revenue for each additional plant. So as you grow
more plants, the overall cannabis becomes less valuable. And so the average price per
output decreases and you're only going to be able to get so much revenue from the additional
plants cultivated. What's interesting to note is that there seems to be a lot steeper. It
seems that diminishing marginal returns have taken place in the medical cannabis market.
So if you just look at the comparison, you can see that there's between 300 and 350,000
retail plants cultivated. And the timeframe on this is 2014 through 2016. At the same
period, retail plants went from 50,000 to 450,000. So you see high returns in the beginning
and as the market matures, like in the medical industry, the medical markets, you get diminishing
marginal returns. So we're interested in estimating alpha. And we expect that it should be between
zero and one. So we can take the production function from earlier and we can simply take
the log of both sides. And then you can estimate it using a linear regression. Once we estimate
it, the competitive rate of return is equal to the marginal product of capital. So if
you take the derivative...
Are you still there Charles?
Yes. Yeah, you froze up.
Okay. So I must... Well, that's why we're recording. So anyways, we're back now.
So where was I when things cut off?
So let's see, you're taking the log of both sides and you were going to estimate alpha.
And then it was just right after that.
Okay. So we take the log of both sides and then we want to calculate the marginal product
of capital. So capital is KT. Right? So that's our number of plants.
And so we want to estimate alpha. So if we take the log of both sides, we can run a linear
regression of the log of sales. Great. So we've got the log of sales and then this is
going to be a constant.
So your slides aren't showing now.
Okay.
Okay. Yeah.
Okay. So we're back. Okay. So just to kind of get back into things.
Okay. So just sort of to do a recap here after sort of that bumpy transition. Okay. So we've
got the total amount of cannabis sold and that's YT. And that's going to be a function
of the number of plants, KT. So we've got our production function.
We take the log of both sides and we get log of cannabis, log of sales equals a constant
plus alpha log of plants. So we can estimate this with the linear regression. And then
given alpha, we can find the marginal product of capital.
So that's the marginal product of capital. And so that's simply the derivative of the
production function with respect to alpha. And so that would be how productive your capital
is going to be. And then we're going to subtract off depreciation. And for this simple example,
we're going to assume zero depreciation. So in reality, there is depreciation. So once
again, this is the simplest model. And so, and then this is just the simplest way that
you could estimate the rate of return on capital. And just to go ahead and look at the empirical
literature so we can go ahead and get our Bayesian prior. We saw in Poulsen's paper
that the interest rates are typically between 7 and 15%. And so that was from Poulsen's
research. And so we want to look at data that we have and see if we can estimate a marginal
product of capital. So let's go ahead and jump into that and do just that. So I'm going
to share with you the data resources. So here is the Colorado Department of Revenue
annual updates. And so you also have them quarterly as well. And so for these particular
updates, they're simply PDF documents with tables of data. So here you have the number
of stores. You have the occupational license data. You have the number of plants. You have
retail. This is retail plants. But then you also have flowers sold per month. And then
you get down here to break down for the different product types. And then you also have total
sales. So we'll be utilizing that as well. So we're not given the rate of return, but
we're given just these raw data points. And we're going to figure it out. And for future
research, it may be worth looking into the testing data here. So it could be worthwhile
to compare what's going on in the Colorado testing market versus Washington. But these
are the data sources. So they're a little tricky. You have to sort of essentially copy
and paste out of these tables. And I've done that here. And I've currently got through
data through December of 2016. But as you can see, there is data through October of
2020. So for future exercise, and I'll be adding this to the Cannabis Data Science GitHub
repository, but we can essentially get the latest data and calculate the rate of return
up through 2020. However, for this exercise, we'll simply calculate it through 2016, since
that's the data that I've already compiled. So let's go ahead and just jump right into
that. I will be using Spyder in Python. Of course, you can use your favorite programming
language and text editor. However, I find Spyder simple and easy to use. It's not glamorous,
but easy to use. So to do this, we only need three Python packages. We just need numpy,
stdc, stdc and stdc. Next, after importing the packages, you can import the data. And
so I'll just be importing this spreadsheet here, which I'll make available on the GitHub
repository after the presentation. Once you've read in the data, of course, number one rule,
look at the data. So you've got some observations or columns. Essentially, we just have date.
I grabbed the number of licenses for future work. Then we can do number of plants, cultivations
and revenue. These are variables that will be useful. However, as you saw in the reports,
there are many more variables that you could grab to do further analysis. So we've read
in the data. Now, if you go back to our model, we need to calculate the log of sales and
the log of capital. So we can use numpy, np.log and go ahead and create the log of retail
revenue and the log of retail plants. And now we can do a simple ordinary least squares
regression of the log of sales, yt, on a constant, which will be the log of technology, a, in
addition to the log of capital, which is retail plants. So we can go ahead and fit this model
in. What's interesting to observe is for such a bare bones model. So we've got 36 observations.
You do have a decent R squared. So we are explaining a lot of the variation and retail
plants. It's significant to the 5% level. So like I said, there's this model, it's got
its flaws, but there does seem to be correlation between the number of plants grown and the
amount of capital. One should note that obviously, cannabis grown in time t is not sold in time
t. So it may be more realistic to estimate an autoregressive regression, where you would
estimate yt sales on kt minus one, kt minus two, perhaps all the way up to kt minus six
or more. That would simply mean that sales today are dependent on the plants grown six
months ago, or one month ago, or three months ago. So it would be an interesting analysis
to add multiple lagged capital variables and see if that has a more significant effect.
But that's research for the future. So in our regression, if you go back to our presentation,
you see that we're looking for alpha. So we're looking for the coefficient on log t. And
so in that case, that's going to be 0.67. So we can go ahead and grab alpha. And now
that we know alpha, we can now calculate the rate of return on capital, which will be alpha
times kt to the alpha minus one. And we're assuming depreciation is zero. So we can program
that in SPDR. So here we have alpha times kt, which is retail plants, to the alpha minus
one. And I'm multiplying this by 100 because I would like to display r as a percentage.
And remember, r is the real rate of return of capital. And so let's estimate that, and
then we'll talk a little about that. Rule number one about data, look at the data. So
here we have what we have estimated to be the real rate of return of capital in the
cannabis market in Colorado from 2014 to 2016. So what we're essentially estimating is we're
saying that an investor would expect a rate of return of 2.6% in 2014 to about 1% in 2016.
In 2015. And that would be at time t. So that would be their monthly rate of return. So
they would like to get a 2% to 1% rate of return per month. And then this would be if
everything was entirely efficient. But as Olson noted, he observed that interest rates
were typically between 7 and 15%. So this model doesn't take into consideration risk.
So risk is likely driving these interest rates well above their real rate of return. Like
last week, we noted that when we added in our uncertainty that we couldn't be quite
so precise in our estimations. So let's do let's add our confidence intervals. So what
is our confidence interval? Well, remember earlier, we estimated alpha to be 0.6777.
Our 95% confidence interval, so we're 95% sure given the data at hand, that alpha given
the model at hand is between 0.6 about 0.61 and about 0.74. So that's our 95% confidence
interval. And so we can calculate our upper and lower alpha. But those those are upper
and lower alpha. So we can calculate our upper and lower interest rates. And we can plot
them. And so now you see our original estimation with interest rates being roughly 2% and dropping
to 1%. Then you see our lower estimation with interest rates being close to 1% and then
dropping quite low to well below 1%. However, our upper bound under confidence interval
is starting around 6 or 5% and then drops down to a little above 3%. Once again, this
is a crude estimation, we're using plants to proxy capital, and we're excluding labor.
So for future work, you can estimate what's called a Cobb-Douglas production function,
where you augment the production function with labor. So a Cobb-Douglas production function,
you can estimate the same model and add another regressor. And that's just going to be beta
log LT. And so that's going to be your labor. And so you can you can estimate a more realistic
function simply by adding the log of labor to our regression. So I'm going to leave that
as a future exercise. And I'll go ahead and do the code and post it to the GitHub repository,
the Candidates Cannabis Data Science repository. So you can check it out there to see the latest
code after the presentation. So we set out to estimate the rate of return on capital.
We knew that because the cannabis industry is still gray in terms of legality, that there
would probably be a high rate of return on capital. However, our model does not factor
in any sort of legality. Our model is simply a function of cannabis sold and plants. We've
got cannabis sold and plants. Of course, we also have technology and then a shock to explain
the random variation. So given this simple model and ignoring the legality, we saw that
there does appear to be diminishing marginal returns as medical plants increases.
Next we estimated the production function, which was simply the log of sales on the log
of capital. For future work, you could add labor. And then we were able to estimate the
actual rate of return of capital. And so here, based on our research, we can actually estimate
the mean rate of return between 2014 and 2016 in Colorado. And so we're seeing it's as low
as 1.2.6%. So just approximation, we'll say 1.25. So the rate of return is, you know,
the real rate of return could be as low as 1.25% per month. So investors in the long
term would be satisfied with a rate of return that low for that amount of production. And
likewise, businesses would be looking at low interest rates for taking out loans for capital
equipment for their cultivations. What we currently see as far as in 2013 is we saw
that the, so this is real, right? And then here we have the actual. And so the actual
rates of return that we observe are between 7 and 15%. So that means risk is explaining
between, you know, six and, you know, about six and 14% of the rate of return in the cannabis
industry. Also, I would like to mention that this is a monthly rate of return. And this
may be an annual rate of return. So it should be, we may want to convert this to APR to
make a good comparison. However, what you could take away from this is that as cannabis
becomes more mainstream and as additional states continue to legalize, so that's what
we've seen since 2016. So from 2016 to the present, 2021, we've seen more states legalize
cannabis, you know, cannabis production and cannabis markets. So, and it will be interesting
to do research to see if cannabis laws and regulations have loosened in the states with
legalized cannabis. Long story short, early on in cannabis markets, we saw high real rates
of return, I mean, high actual rates of return. However, we estimated the real rate of return
would be low. So we would predict that over time, cannabis businesses may see their real
rates of return decrease. So over time, it may become easier and easier for producers,
cultivators to take out loans, whereas investors are currently making large margins because
they're taking on a high amount of risk. So you would expect the margins for investors
will decrease as the risk decreases. And with that, that brings us to the end of the presentation.
And so I'll go ahead and just cut back to the meeting if you have any questions.
No, that was a really good presentation.
Thank you. Yeah. Exactly. So essentially last week, we looked at the labor input. So we
saw, okay, we estimated the real wage for labor, right? Because essentially, that's
what economics is, you know, that's a purpose of economics is sort of estimating the prices
in different markets. So that's actually the labor market. So the wage is the price in
the labor market. And the rate of return is the price in the capital market. So the wage
is what you pay for labor. And the rate of return is what you pay for your capital input.
In this point, in this example, we proxied it with plants. So we're basically assuming,
okay, for every X amount of plants you grow, you have to invest a certain amount into capital.
And then when you put together labor and plants, you get output. And so in this case, it's
going to be cannabis sold. And so we're also abstracting out the retail component. Because,
of course, the cultivators are producing the raw flour and plant material, some of which
is then manufactured into manufactured goods and edibles, at which point they're then sold
to the consumers for the actual revenue. So our model abstracted away a large portion
of how the industry actually operates. But it's an abstraction. And so there's a lot
of room for improvement. So I think I'll leave it there. And like I said, I'll make the data
available. And so we can add data up through 2020. So that way we can see how these estimations
evolve over time. And we can maybe even compare our predictions to the actuals. So we looked
at data from 2014 to 2016. And we made some hypotheses. I personally predicted that the
real rate of return is going to continue to decrease. So now we can look at the data and
see what happened.
Okay, yeah, that sounds cool. You know, the other thing I was thinking about was price
of items sold compared to number of licenses.
Exactly. So you can gauge sort of how much each company is taking away at the end of
the day.
Yeah, it is competition increases, price goes down.
Exactly. So we may not have the best measure on price. We could proxy it because we have
essentially we have total revenue in Colorado. Well, we may actually have prices in Washington.
Actually, this could that could actually be a good analysis for Washington. Because you're
right, you could I mean, one way to look at it would just be, I guess, like total amount
of revenue per retailer. And then you could see the market share. In Washington state,
you can actually calculate the actual market share per retailer. And you can make estimations
of the market concentration. In fact, have you heard of the Herfindale? It's HHI, the
Herfindale Hirschman index. And so I may I may present that next week, because it's actually
one of the simpler measures of market concentration you can do. And it's easy to calculate if
you have the right data. And in Washington state, we do. So you simply need to know the
market share per retailer. So market, the retailer, A has shares 0.3, retailer B has
market shares 0.5. And then you actually do the squared. So it's just the sum of all shares
squared. So it would be 0.3 squared plus 0.5 squared plus, you know, 99.2 squared. And
you would see, oh, that's a that's an incredibly concentrated market. Because I forget, I think
I'll need to do a bit of research and tell you more about it next week, because I forget
off the top of my head if the lower numbers or higher numbers represent sharper concentration.
But I want to see higher numbers represent larger, because I feel like the if it's close
to one. But anyways, I may touch on that next week, because that's something that I've been
wanting to look at. And you and it seems they that's your idea as well is, it would be interesting
to look at the concentration in the cannabis markets over time to see if it's becoming
more competitive or more concentrated. Yeah, and we can do it statistically and we can
plot it over time. So that way we could even see month by month, the competitiveness and
it's interesting research, because you could start to find trends and you can maybe find
if if any actions. So if you notice any point in time where there was a big change in the
competitiveness, you may be able to pinpoint the piece of legislation or something that
happened that changed the competitiveness of the market. Yeah, yeah. So I think, of course,
I don't think we have time today. But I think for next week, let's look let's look at just
that because that that's the simplest. That's the simplest measure that I can think of to
look at market concentration. In Washington State, we do have the data. It's in that giant
sales data dump. So it's possible. And it's going to be a good excuse to look at the data.
So that's our philosophy here, correct is look at the data. So I think we've got a good
project for next week. Great. All right, Charles, I think I may just go ahead and wrap up a
little early today. Unless you have anything you want to talk about. Yeah, okay. Well,
I think for today, let's just go ahead and wrap up 10 minutes early. I sort of went through
the presentation quickly. I didn't anticipate moving through it so quickly. So I could have
added a bit more detail. And so like I said, I'll add a bit more detail to the actual GitHub
repository. Just a little technical error. Didn't get it committed before the presentation,
but I'll commit it right after. And then, yeah, and then we'll look at market concentration
next week. And, you know, let me know if you have any questions about this economics. Okay.
Cool. Awesome, Charles. And everyone. So thank you for listening in. And I'll see you this
time next week. See you. Bye. Bye, Charles.