License Quotas and the Inefficient Regulation of Sin Goods:Evidence from the Washington Recreational Marijuana Market∗

Danna Thomas†

January 15, 2018

Abstract

This paper studies the welfare impacts of license quotas in markets for “sin goods.” Licensequotas not only affect market structure and reduce total sales, their implementation also createsallocative costs. Retail licenses are often restricted by geography, meaning licenses are not neces-sarily allotted to areas where they are most valuable. Furthermore, licenses may be distributedto firms randomly; hence, the most profitable potential entrants are not necessarily license re-cipients. A difficulty in studying license quotas is finding credible counterfactuals of unrestrictedentry. Therefore, I first develop a three stage model that endogenizes firm entry decisions andincorporates spatial demand. I then estimate the model using a new firm-level data set from theWashington recreational marijuana market and use data on the participants in a marijuana retaillicense lottery to simulate counterfactual entry patterns. I find that allowing firms to enter freelyat Washington’s current marijuana tax rate increases total surplus by 21.5% relative to a baselinesimulation of Washington’s license quota regime. Geographic misallocation and random allocationof licenses account for 6.6% and 65.9% of this difference, respectively. Moreover, I study tax poli-cies that directly control for the marginal damages of marijuana consumption. Free entry withtax rates that keep the quantity of marijuana or THC consumed equal to baseline consumptionincreases welfare by 6.9% and 11.7%, respectively. While free entry with a non-uniform sales taxconsistent with Washington’s geographic license restrictions increases efficiency by over 7%.

∗I am grateful to my advisors Katherine Ho, Francois Gerard, and Tobias Salz for their guidance. This paperbenefited from conversations with Michael Riordan, Chris Conlon, Wojciech Kopczuk, and Zach Brown. Lin Tian, JingZhou, and Nandita Krishnaswamy also provided helpful comments. I also thank Brian Yauger, Jerry Derevyanny, andLogan Bowers for all their helpful insight into the inner workings of the Washington recreational marijuana market. Allmistakes are my own.†Columbia University, dkt2109@columbia.edu

1 Introduction

To mitigate negative externalities from the consumption of “sin goods” (e.g. tobacco products,

alcohol, marijuana, etc.), states commonly restrict entry into retail markets for the offending goods

via license quotas. Table 1 describes some of these quota policies. License quotas limit competition,

increasing firms’ market power. However, retail license quotas carry welfare implications aside from

those due to decreased competition. The license quota, much like a traditional quantity quota,

prevents many productive transactions.

The distribution of licenses also creates allocative costs. License quotas are typically implemented

by imposing a maximum number of entrants in each county or municipality based on the jurisdiction’s

population. This means jurisdictions of equal size have an equal number of available licenses though

jurisdictions may have heterogeneous marginal social benefit from a store. Hence, licenses are not

necessarily allocated to cities where they are most valuable, creating allocative inefficiency. Further,

retail licenses in these markets are often distributed randomly (e.g. by lottery). In the absence of

an efficient secondary market for licenses, as may be the case in markets such as marijuana, this

creates another source of allocative cost: the most efficient stores are not necessarily the ones that

receive licenses. These costs due to allocative inefficiency are seldom studied empirically but could

be economically significant.

Therefore, this paper not only explores the competitive effects of restricted entry but also inves-

tigates the empirical importance of the welfare costs caused by license quota policies. A challenge

in studying license quotas is finding credible counterfactuals of unrestricted entry. Therefore, I take

a structural approach, developing a three-stage model that endogenizes firms’ entry decisions and

estimating the model using data from the Washington recreational marijuana market, a setting with

several institutional features favorable to estimating counterfactuals. I then simulate entry patterns

under free entry with taxation and compare the results to a simulated baseline with restricted entry.

Taxes discourage entry through reduced profitability. However, unlike current license quota regimes,

firms will continue to enter until the jurisdiction’s marginal benefit of a firm equals the marginal cost,

and the most efficient firms will enter.

In the three-stage model firms decide whether to enter a market where the government has re-

stricted entry with a license quota, incurring a fixed cost of entry. Upon entry, firms realize demand

and choose prices, playing a Nash-pricing game. Demand takes a nested logit specification, with con-

sumers choosing firms then products, and incorporates disutility from travel to firms. Detailed data

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Table 1: Examples of License Quotas in Retail Markets

State/Locality Retailer Number of LicenseLicenses Distribution

Washington marijuana (2015) 334 state-wide lottery

Pennslyvania medical 27 state-wide points-basedmarijuana application process

San Francisco, CA tobacco 49 per supervisory district first-come, first-served

California liquor 1 per 2,500 people in county lottery

Massachusetts liquor 1 per 5,000 people in city/town first-come, first-served

Florida liquor 1 per 7,500 people in county lottery

Arizona liquor 1 per 10,000 people in county lottery

from the Washington recreational marijuana market on prices, quantities, and product characteristics

merged with demographic data allows me to estimate the demand system. The data also includes

wholesale costs which I use along with the Nash pricing equation to estimate a non-parametric dis-

tribution of costs. I then combine costs and demand to compute variable profits.

Estimating fixed costs involves using the logic of revealed preferences to infer the profitability

of firms. If n firms enter, then n firms are profitable, and firm n + 1 is not (Bresnahan and Reiss,

1991a). However, if there is a binding license quota, the profitability of firm n+ 1 cannot be inferred

(Schaumans and Verboven, 2008; Ferrari and Verboven, 2010). The Washington marijuana market,

though, has jurisdictions where retail license quotas do not bind, allowing me to draw the necessary

assumptions about profits to estimate fixed costs. Nonetheless, as is common in games of entry, a

multiplicity of equilibria exist, complicating the point identification of fixed costs. I, therefore, find

bounds on fixed costs using the moment inequalities methodology outlined in Pakes et al. (2015) and

Pakes (2010).

With the model and estimates in hand, I simulate counterfactual entry in those jurisdictions with

binding license quotas. A particularly difficult aspect of simulating entry in a model that incorporates

spatial demand is where to locate the simulated market entrants as it involves determining where firms

would have located if entry was not restricted. However, the Washington recreational marijuana

market provides me with plausible locations. After marijuana legalization, Washington regulators

opened an application window for retail licenses. Potential entrants needed to provide prospective

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addresses on these license applications. For those jurisdictions with more applicants than available

licenses, the state distributed licenses via a lottery. I use addresses from applications not chosen in

the lottery to serve as counterfactual locations.

The first counterfactual exercise eliminates the license quota and simulates free entry, allowing

all profitable firms to enter. At Washington’s current marijuana tax rate of t = 0.37, I find that

the number of entrants increases by 60%—ninety-five additional firms; hence, license quotas severely

constrain firm entry in this market. Unrestricted entry also boosts total surplus by $23 million relative

to the baseline—an increase of 21.5%. This difference in surplus is because (1) less marijuana is sold

due to the license quota, and (2) licenses are not allocated efficiently under the quota regime.

To study the importance of allocative inefficiency, I decompose the difference in surplus between

the free entry simulation and the baseline. First, I simulate the outcome of a statewide license auction

without geographic license restrictions. By holding the number of licenses fixed to the baseline number

of total entrants, but not restricting the licenses by jurisdiction, or randomly distributing licenses,

this counterfactual measures the effect of the quota without allocative costs. Next, I generate the

outcome of a within-jurisdiction auction, keeping the number of licenses within each jurisdiction

equal to the jurisdiction’s baseline number of entrants. This captures the change in surplus due to

the misallocation of licenses over geography without capturing the cost of the license lottery.

The reduction in quantity sold due to the quota is responsible for 27.5% of the difference in surplus

between free entry and the baseline, and geographic license restrictions explains around 6.6%. The

allocation of retail licenses via lottery is the largest source of inefficiency, accounting for about 65.9%

of the loss in total surplus. Hence, allocative costs comprise over 70% of the efficiency loss due to

Washington’s license quota policy.

As governments may use license quotas as tools to mitigate externalities, I also study policies

that directly control for the marginal damages of marijuana consumption. To do this, I simulate free

entry while increasing the sales tax rate which deters entry and reduces consumption without creating

allocative costs. With free entry and a sales tax of t = 0.765, the amount of marijuana consumed is

the same as the quantity consumed in the baseline. Because there is no allocative inefficiency, total

surplus is 6.9% higher than in Washington’s license quota regime. The amount of THC consumed

remains equal to baseline consumption at t = 0.66 with total surplus increasing by almost 12%.

Because geographic license restrictions could be a way to account for hetergenous marginal dam-

ages across the state—meaning there is no misallocation of licenses across geography, I also simulate

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free entry with a marijuana sales tax that varies across jurisdictions and is consistent with each juris-

diction’s license quota. This non-uniform sales tax produces a total surplus is 6.3% higher than the

baseline, highlighting the efficiency loss from allocating licenses randomly further.

This paper contributes to the literature on allocative costs. The theoretical literature is extensive

and discusses allocative costs in a variety of contexts (Deacon and Sonstelie, 1989; Bulow and Klem-

perer, 2012; Viscusi, Harrington, and Vernon, Viscusi et al.). However, the empirical importance

of allocative inefficiency is understudied, and to my knowledge no paper in the empirical literature

discusses retail license allocation. Notably, Glaeser and Luttmer (2003) studies misallocation due to

rent control policies. Davis and Kilian (2011) and Luttmer (2007) explore price ceilings in the U.S.

natural gas market and the labor market, respectively, and Frech and Lee (1987) analyze the welfare

cost of queuing during U.S. gasoline shortages in the 1970s. Further, these papers do not discuss

imperfect competition nor do they study allocative costs due to quantity regulation in markets with

negative externalities.

The size of allocative costs is particularly important in markets with negative externalities where

policy makers must choose between instruments such as taxation or quotas. Hence, this paper is also

related to the theoretical literature comparing corrective taxation to quantity regulation in mitigating

externalities (Weitzman, 1974; Kaplow and Shavell, 2002; Glaeser and Shleifer, 2001; Baumol and

Oates, 1971). An extensive discussion of this literature in the context of pollution abatement is

offered in Bovenberg and Goulder (2002).

My findings are also related to the industrial organization literature on firm entry and competition

(Bresnahan and Reiss, 1991b; Berry, 1992; Berry and Waldfogel, 1999; Seim, 2006; Mazzeo, 2002).

Frechette et al. (2016) study entry restrictions in the New York City taxi market albeit in a dynamic

model with a focus on search frictions. Most closely related to this paper is Schaumans and Verboven

(2008) which uses a model and empirical approach similar to Mazzeo (2002) to study license quotas in

the pharmacy market in Belgium though the study does not focus on the misallocation of licenses but

rather on the competitive effects of restricted entry. My empirical approach is also closely related to

papers in the product positioning literature, including Wollman (2016), Nosko (2010), and Eizenberg

(2014). More broadly this paper contributes to the industrial organization literature related to entry

and regulation in markets with negative externalities, such as Seim and Waldfogel (2013) which studies

the liquor market in Pennsylvania, providing additional insight into the consequences of restrictions

on firm entry.

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This study also contributes to the growing literature in marijuana taxation and policy. Though

the drug remains illegal at the federal level, in recent years states have increasingly liberalized their

marijuana laws in order to generate tax revenue and save resources on marijuana law enforcement.

Many states have adopted some form of medical marijuana and/or marijuana decriminalization laws.

Moreover, as of 2017, Washington, Colorado, Maine, California, Oregon, Massachusetts, Nevada,

Alaska, and the District of Columbia have all legalized recreational marijuana. In 2016 recreational

marijuana generated over $1.8 billion in sales,1 and Washington itself realized over $264 million in

tax revenue. Hence, studying marijuana reforms and the policies and outcomes of early recreational

marijuana adopters and remains an important area of research.

Many papers in the marijuana literature focus on crime and public health rather than on marijuana

demand and market structure regulations in the legalized marijuana. For example, recent papers

study the impact of decriminalization on crime (Adda et al., 2014) and the relationship between

medical marijuana legalization and adverse outcomes such as traffic accidents and increased teen usage

(Anderson et al., 2013, 2015). Marie and Zolitz (2017) studies the impact of recreational marijuana

legalization in the Netherlands on university academic performance. Literature that studies marijuana

demand includes Jacobi and Sovinsky (2016), which uses data from surveys of black market usage

to estimate the impact of legalization on demand. This paper instead focuses on marijuana demand

in legalized recreational markets. Most closely related to this study is Hansen et al. (2017) which

uses a sales tax reform in the Washington recreational marijuana as a natural experiment to estimate

the elasticity of demand and study sales tax pass through, finding an elasticity of -0.81. This is in

contrast to the market elasticity of -1.83 implied by my model.

The remainder of the paper is structured as follows. Section II describes the important institu-

tional features and background of the Washington marijuana market, and Section III discusses the

data in detail. Section IV sets out the two-stage model of entry. Section V discusses estimation

strategies and results. Section VI details the counterfactual experiments, and Section VII concludes.

2 Background

After legalizing marijuana Washington established retail license quotas within counties and munic-

ipalities. In many areas the number of firms that wished to enter far exceeded the quota. Therefore,1See “Exclusive: U.S. marijuana sales could rise 35% in 2017, hit $17B annually by 2021” Marijuana Business Daily.

Last modified May 17,2017. https://mjbizdaily.com/exclusive-u-s-marijuana-sales-rise-35-2017-hit-17b-annually-2021/

5

Washington held a lottery to distribute retail licenses and required all lottery entrants submit prospec-

tive store addresses. In this section I detail Washington’s marijuana legalization law, the distribution

of retail licenses, and other important institutional details.

2.1 Initiative-502: Washington’s Marijuana Legalization Law

Though medical marijuana was available in Washington state, medical marijuana dispensaries were

unregulated, untaxed, and only for patients with doctors’ recommendations. Therefore, on November

6, 2012, Washington state voters approved Initiative-502 (called I-502), legalizing recreational mar-

ijuana “for [all] persons twenty-one years of age and older.”2 I-502 created several regulations with

the aim of “bring[ing] [marijuana] under a tightly regulated, state-licensed system similar to that for

controlling hard alcohol” and “generat[ing] new state and local tax revenue.”34

First, I-502 established three types of licenses: producer, processor, and retailer. Producers are

marijuana farmers while processors include a broad set of businesses that convert marijuana plants

into products such as joints, marijuana cookies, and marijuana vapor products. Additionally, the

law limited vertical integration, banning integration between retailers and upstream firms though not

between producers and processors.

I-502 also established a marijuana sales tax. While the law originally mandated that a 25% sales

tax be assessed at each step in the marijuana supply chain, this encouraged vertical integration to

reduce firms’ tax burden. Hence, in July 2015 the Washington legislature changed the tax structure

to a 37% sales tax levied at the retailer level. Hansen et al. (2017) studies this reform in depth.

Further, the law called for the state to establish licensing restrictions and quotas. The Washington

Liquor Cannabis Board (WLCB) did not limit the number of producer or processor licenses, but

it created a state-wide cap of 334 retail licenses. The WLCB then organized the state into 124

jurisdictions—incorporated cities and rural county areas—and established a license quota within

each jurisdiction. To decide how many stores to license in each jurisdiction, the state first determined

the number of licenses allowed within counties using a complex formula that involves “minimiz[ing]

a proxy for the average distance from a user [within the county] to the closest store.”5 Then the2Initiative 502, 2013 Wash. Sess. Laws, p 29.3Ibid4Other goals stated in the law include “tak[ing] marijuana out of the hands of illegal drug organizations” and

“allow[ing] law enforcement resources to be focused on violent and property crimes.”5Caulkins, Jonathan P. and Linden Dahlkemper, ”Retail Store Allocation,” BOTEC Analysis Corporation, Jun. 28,

2013, available from Washington Liquor Cannabis Board.

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available licenses were divided across the county’s incorporated cities according to the proportion

of the county’s population located in the city. The county’s rural areas were assigned licenses not

allocated to cities.

For example, the WLCB assigned Spokane County a retail license quota of eighteen. The city of

Spokane has forty-four percent of Spokane County’s population and, hence, had a retail license quota

of eight. Spokane Valley, with has sixteen percent of the county’s population, was assigned a license

quota of three with the remaining licenses assigned to Spokane County’s rural areas. Note that this

license quota rule maps into a uniform quantity restriction of stores within counties. In Spokane

County, there was one license per 26,187 people in a municipality.

2.2 The Retail License Lottery

To acquire a retailer license, potential entrants applied to the WLCB which opened a thirty day

window for applications in November 2013. Submitting an application carried a $250 dollar fee, and

the license fee was $1,000. The information on these applications was made publicly available on the

WLCB’s website. Moreover, license applications also had to contain a potential store address in order

for regulators to determine if the site complied with various location restrictions outlined in I-502.

Stores were not allowed to be located within 1000 feet of a “school, playground, ... child care center,

public park, public transit center, or library.”6 Though license application addresses were not binding,

in practice, retailers typically entered at or near the address listed on their license application. Forty-

seven percent of entrants locate in the exact location listed. Another twenty-eight percent of retailers

locate within one-third of a mile of the application address.

In forty-nine jurisdictions the number of retail license applicants was less than or equal to the

number of available licenses. In these areas there were in total seventy-seven available licenses with

only forty-eight applicants, so all applicants can receive licenses. However, in seventy-five jurisdictions

there were more applicants than available licenses—257 available licenses with 1125 license applicants.

Seattle alone had 191 applicants for only twenty-one licenses.

Therefore, the WLCB held a series of license lotteries in April 2014 to distribute licenses in

jurisdictions with binding license constraints. In each lottery the applicants were assigned a number6These location restrictions were in addition to local zoning ordinances. Additionally, firms struggle to find locations

due to the reluctance of landlords to lease to marijuana businesses due to its federal illegality. In an interview a retailerdetailed the difficulties of finding a location, describing himself as “lucky” to find a good location. Figure A.15 displaysa map of marijuana retailer location constraints for the city of Bellevue, WA after accounting for local zoning ordinancesand state-mandated entry barriers.

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Figure 1: Jurisdictions

1 to n, where n is the number of lottery participants. If the applicant’s number was less than the

number of allowed entrants, that applicant “won” a license and could enter the market.7 Those with

multiple retail license applications were limited to winning no more than three licenses and no more

than one-third of all licenses in a jurisdiction.8 The state made the results of the lottery public on

May 2, 2014.

2.3 Sales in Washington State

Recreational marijuana sales in Washington began July 8, 2014. Figure 2 displays gross sales and

the number of firms in the market from August 2014 to April 2016. Few firms enter to start: in

August 2014, thirty-one retailers had around $450,000 in total sales. Entry may have been slowed7Lottery winners tend to become entrants. Seventy percent of lottery winners enter the market. Of the winners that

did not enter, 50% did not enter due to local ordinances banning marijuana sales. The rest of the firms do not enterafter winning may have failed subsequent background checks after the lottery though I cannot account for these firms.

8Even though the lottery fee is not particularly costly, 47% of lottery applicants only submit one application. Ninety-nine percent submit three or fewer applications. Given that a firm submitted multiple applications, 52% did not submitthese applications in the same jurisdiction. This provides evidence that firms did not systematically submit multipleapplications to increase the odds of winning the lottery.

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by local ordinances such as zoning, moratoria, or prohibition. However, firms rapidly enter over the

next year growing to over $30 million in monthly sales in the fall of 2015.

In 2016 Washington folded the medical marijuana market into the recreational market. Existing

medical dispensaries were forced either to obtain recreational retailer licenses or close. In Figure 2

the beginning of this merger is seen in the uptick in sales and entry in March 2016. To accommodate

these additional firms, the state increased the license quota from 334 to 556, doubling the number of

licenses available in cities like Seattle.

Figure 2: Number of Firms and Gross Sales (July 2014-April 2016)

Notes: The red vertical lines indicates the period of the data used in estimation.

2.4 Comparison to Colorado

Though Washington and Colorado legalized recreational marijuana around the same time, Wash-

ington’s policy of restricted entry differed drastically from Colorado free entry regime. Colorado,

which began recreational marijuana sales in January 2014, also enacted a different tax structure with

a 10% sales tax along with a 15% wholesale tax. Table 2 compares the number of licensees in selected

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Table 2: Number of Recreational Dispensary Licenses (December 2015)

Population Marijuana Lottery People(2013) Dispensaries Applicants per Store

Panel A: Washington

Seattle 652,405 18 191 36,245Bellevue 133,992 3 19 44,664Auburn 74,860 1 5 76,860Olympia 48,338 2 9 24,169

Panel B: Colorado

Denver 649,495 159 - 4,085Boulder 103,166 19 - 5,430Pueblo 108,249 11 - 9,840

Wheat Ridge 30,920 4 - 7,730

Source: Colorado Department of Revenue

cities of various sizes in Washington and Colorado in of December 2015. Notably, while Seattle and

Denver are similar sizes, in December 2015, Seattle had 141 fewer stores, evidence that Washington’s

license quota is suppressing the number of retailers greatly.

3 Data

My primary data sets include marijuana sales data and license lottery results, both of which are

available by request through the Washington Liquor Cannabis Board. The WLCB data is detailed

and comprehensive. In addition to prices and quantities sold, it includes measures of wholesale cost

and marijuana potency. In this section I describe the WLCB data and how I use it to construct the

data used in estimation. I also discuss additional data sources on consumer location, demographics,

and medical marijuana.

3.1 WLCB Traceability Data

My main data source is from the WLCB Traceability System. To ensure that marijuana is not

“leaking” outside the state, Washington regulators mandate that firms submit a log of their trans-

actions via the Traceability System. Hence, the Traceability data can track the supply chain of

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Table 3: Summary Statistics

Panel A: Market Characteristics

number of stores 190number of products 3141number of months 6median monthly sales per store $145,172

Panel B: Product Data

Inhalables Usables Edibles

mean price $27.01 $15.41 $14.80std. deviation price 5.55 2.97 2.85mean cost $11.07 $6.75 $6.10std. deviation cost 2.03 1.60 1.10median THC content 65.93 20.58 6.99median CBD content 1.61 .32 .5

Panel C: Tract Characteristics

average distance to closest store 5.17 mi.minimum 0.03 mi.maximum 71.64 mi.median population density 2443.57% ≥ 35 54.3%

marijuana from “seed-to-sale,” providing a comprehensive look at Washington’s recreational mari-

juana market.

I use the Traceability System’s dispensing data which provides a complete record of retail sales

since July 2014.9 Each observation contains the firm, month, year, product name, product description,

product category, prices, and quantities sold. I drop all refunds and transactions with prices less

than $1.00 as these typically indicate employee samples or mistakes by retailers uploading the data.

Importantly, the data also includes an inventory identifier that I use to match products to wholesale

cost data.

To construct the wholesale cost data, I use data on firm-to-firm transfers. Firm transfer data

includes the inventory identifier, the amount of inventory sold by the producer/processor to the

retailer, and the unit price. I assume the unit price is the wholesale cost of the product. I also drop

any cost data with prices less than $1.00 which may indicate samples from wholesalers to retailers9This data was also used in Hansen et al. (2017).

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Figure 3: Percentage Sales by Product Category

or mistakes in logging the transactions. The Traceability data also includes the firms’ geographic

coordinates and marijuana potency reports. Each producer/processor is required to submit a sample

of his/her products to a state-sanctioned lab for potency testing. Therefore, I merge in lab reports

on tetrahydrocannabidiol (THC) and cannabidiol (CBD) content by product.10

Retailers sell an extensive range of products. Product categories include usable marijuana (e.g.

flower, bud), edibles (cannabis-infused cookies, gummies, etc.), inhalables (resin, hash, vaping prod-

ucts, etc.), topicals (e.g. marijuana-infused lotions), cannabis-infused drinks, and marijuana-tobacco

mixes. Figure 3 displays the percentage of total sales in 2015 attributed to each product category. In

fact, retailers on average sold 270 different products each month in 2015, and just within the usable

marijuana category, retailers on average sold 90 different cannabis strains per month.

Because using individual products would complicate estimation by creating extremely small shares,

I aggregate the data at the product category-month level for estimation, constructing the weighted10THC is the primary psychoactive component of marijuana that produces the “high” sought by recreational marijuana

users. CBD is another psychoactive constituent of marijuana which may mitigate the effects of THC (Bhattacharyyaet al., 2010). High CBD content marijuana is commonly used for medical marijuana.

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average price, wholesale cost, and median THC and CBD content for each product-store pair by

month. I also use only the top three product types—usable marijuana, inhalables and edibles—as

the market shares of topicals, drinks, and mixes are extremely small. Further, the top three product

types are sold by all firms and comprise over 96.5% of sales in Washington.11

I also limit the data to July 2015-December 2015 to avoid using data on the early recreational

market. As seen in Figure 2, in the early period after legalization, firms are entering rapidly, and

sales are quickly increasing. Using early post-legalization data would be inconsistent with a static

entry model which assumes the market is in long-run equilibrium. Further, I drop data from a firm’s

first month of sales if they are not in the market for the full month. I also exclude data after 2015

due to the entry of medical dispensaries into the recreational marijuana market at the beginning of

2016.12

Panel A and B of Table 3 displays summary statistics of the demand data. After cleaning and

collapsing the data, I have 3,141 products for 190 individual stores over six months. Further, each

store sells usable marijuana, inhalables, and edibles. Inhalables tend to have the highest prices, and

costs and extremely high potency. Edibles, in constrast, are very low potency products though their

prices and costs are similar to usable marijuana products.

3.2 Additional WLCB Data

Additional data from the WLCB includes each jurisdictions’ license quotas and lottery results.

The lottery data includes the application number, firm tradename, and potential addresses for all

1,173 lottery entrants. Some applications list the same address, so I drop duplicate addresses. I

also drop addresses from jurisdictions with local ordinances banning retailers leaving 746 locations.

I geocode the remaining address data using Texas A&M University GeoServices, and I match the

lottery data to existing retailers.

3.3 Census Data

I proxy for consumer location by using population-weighted Washington census tract centroids

from the U.S. Census Bureau. I combine this data with geocoded lottery addresses and retailer data

to calculate the distances from census tracts to existing retailers and lottery losers. Panel C of Table11For 98% of stores, these products count for over 90% of all sales.12Discussions with industry professions revealed that the decision to allow medical dispensaries to enter the recreational

market was an unexpected policy change.

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3 summarizes the distance from a tract centroid to its closest existing retailer. Stores are relatively

close to consumers—the average distance to the nearest store is less than 5.5 miles.

Furthermore, I merge the location information with demographic data and additional geographic

data found in the Census TIGER/Line shapefiles with American Community Survey (2010-2014). I

compute the total population of adults over the age of twenty-one, and as Azofeifa et al. (2016) show

that most marijuana users are below the age of 35, I also calculate the percentage of adults over the

age of thirty-five and the population density of each census tract to include in the demand model.

In addition to Census data from Washington, I also use data from Idaho and Oregon census tracts

that are within thirty-five miles of the Washington border in order to incorporate cross-border shop-

ping into demand. Figure 4 shows the drop in gross sales experienced by retailers within thirty-five

miles of the Washington-Oregon border after Oregon legalized recreational marijuana in September

2015, providing evidence that some consumers may travel to Washington from Idaho and Oregon to

purchase marijuana.

Figure 4: Change in Gross Sales for Retailers Close to the Border

Notes: Oregon legalized recreational marijuana in July 2015. The horizontal red line indicates the date when Oregonallowed existing medical marijuana stores to sell to customers regardless of whether they held medical marijuana cards.

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3.4 Medical Marijuana Data

Because medical dispensaries were not regulated by the WLCB during my period of study, medical

marijuana dispensing data is not available. Nonetheless, I proxy for the existence of medical marijuana

stores using the number of medical dispensaries within ten miles of a census tract. In the demand

model, I include this information in consumers’ outside option. I obtain this address information

from the web.

A concern is that medical marijuana is a close substitute for recreational marijuana and not

including medical marijuana dispensaries will understate the amount of competition in the market.

Many untaxed and unregulated medical dispensaries and collective gardens were operating both

before and after the passage of I-502. However, my discussions with recreational retailers revealed

that I-502 retailers did not consider medical dispensaries direct competitors. Reasons included the

substantive differences in products and stores, the fact that customers did not need to obtain a

doctor’s recommendation, and the additional legitimacy provided by being state-sanctioned.

4 A Three Stage Model of Entry

I develop a three stage model that endogenizes firms’ entry decisions. The model’s timing is as

follows:

Stage 1a (Entry) – Firms make simultaneous decisions to enter a license lottery in a juris-

diction where the government has set a quota of n firms. The information set includes all

own-characteristics, characteristics of potential entrants, and license quotas.

Stage 1b (Lotto) – If there are more than n applicants, the government chooses n entrants

randomly.

Stage 2 – Firms select prices by playing a Nash-pricing game.

Stage 3 – Demand and profits are realized.

The model is solved by backwards induction; therefore, exposition of the model begins with the stage

3.

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4.1 Stage 3: Demand

I modify the nested logit model detailed in Berry (1994), incorporating the distance from con-

sumers to firms as a product characteristics as in Davis (2006) and Houde (2012). A consumer—

defined as a person over the age of twenty-one—is located at an address h ∈ H—a population-weighted

census tract centroid. He purchases one unit of a marijuana good (j, f) in month t by first selecting

a firm f in his general proximity and then j from f ’s product set, Jf .1314 Each firm’s product set

consists of three goods: usable marijuana, inhalables, and edibles.

Formally, a consumer’s choice set is

Bh = {(j, f) | dhf ≤ rh}

where dhf is the Euclidean distance from h to f , and rh is the maximum distance a consumer at h

will travel.15

Consumption of (j, f) yields utility

uhjf = α(1 + t)pjf + xjfβ + ξjf︸ ︷︷ ︸δjf

+g(dhf , τ) + γhf + (1− σ)εhjf︸ ︷︷ ︸εhjf

. (1)

The function g(dhf , τ) measures travel cost. As in Holmes (2011) and Zheng (2016), g(dhf , τ) interacts

distance with population density, Ph, to capture the additional cost of travel in more populous areas.

g(dhf , τ) = τ1dhf + τ2dhf · log(Ph) (2)

Additionally, pjf is the price. εhjf is an i.i.d. extreme value taste shock where γhf is the idiosyncratic

firm shock, and εhjf is the product-level shock. xjf is a vector of observed characteristics which

includes THC and CBD concentration, and ξjf is the unobserved product characteristic. As prod-

uct characteristics are assumed not to be endogenous, I assume unobserved and observed product

characteristics have independent distributions Fx and Fξ which are i.i.d. across products.

Consumers may choose not to purchase marijuana from a recreational retailer. The utility from13Purchasing one good per visit is consistent with the data. Cash register level data shows that one good is typically

bought per transaction. (See Figure A.14.) However, because I do not observe customer level data, I cannot accountfor multiple visits by a customer in one month.

14I suppress the subscript t for clarity.15The market definition differs by consumer with rh as the minimum radius that guarantees that each address in a

county-city has at least three firms in its product set. Table A1 list the radii for each county-city pair.

16

the outside option is

uh0 = ΠDh + γh0 + εh0 (3)

where γh0 is normalized to zero. Dh is a vector of address characteristics which includes the percentage

of h’s population over the age of thirty-five and the number of medical marijuana stores within ten

miles of h in Dh.16

Consumers at h maximize their utility, choosing to purchase (j, f) with probability

shjf = shjf |f · shf ,

the product of the probability of selecting j given f and the probability of selecting f . These proba-

bilities have the standard logit forms

shjf |f = exp (δjf/(1− σ))∑j′∈Jf

exp(δj′f/(1− σ)

) (4)

shft = exp(g(dhf , τ) + (1− σ)IVf )exp(ΠDh) +

∑f ′ exp(g(dhf ′ , τ) + (1− σ)IVf ′)

(5)

with inclusive value

IVf = ln

∑j′∈Jf

exp(δj′f/(1− σ)

) .Total demand at h for (j, f) is the product of the choice probability and Mh, the number of consumers

at h. Hence, total demand is

Qjf =∑h∈Hf

shjf ·Mh. (6)

where the set Hf = {h|f ∈ Bh}, the tracts that have firm f in their choice set.

4.2 Stage 2: Pricing

Firms’ second stage decision is to set prices. Because Washington state limits the number of retail

licenses a firm can obtain, I assume a firm is single store enterprise that chooses its prices to maximize16Azofeifa et al. (2016) analyzes survey responses in the National Survey of Drug Usage and Health and finds that

people under thirty-five are primary users of marijuana. The study also finds that males are the most prevalent usersof marijuana; however, I cannot identify coefficients on gender as census tracts are all roughly fifty percent male.

17

its variable profit function

rf =∑j∈Jf

(pjf − cjf ) ·Qjf (7)

where cjf is the firm f ’s marginal costs of product j. In addition, I assume marginal costs have an

additive form:

cjf = cjf + ωjf . (8)

cjf and ωjf are observed and unobserved marginal costs, respectively. Observed variable costs are

the wholesale prices seen in the data while unobserved marginal cost include the cost of shelving and

stocking products. Like product characteristics, observed and unobserved costs also have independent

distributions—Fc and Fω—which are i.i.d. across products. The first order conditions of firm f are

∂rf∂pjf

= Qjf +∑j′∈Jf

(pj′f − cj′f ) · ∂Qj′f

∂pjf= 0 ∀j ∈ Jf .

Further, the firm’s FOCs have the following matrix form:

pf − cf + ∆−1f Qf = 0. (9)

where ∆ is a matrix of cross-price derivatives, ∆j′,j = −∂Qj′f∂pjf

.

4.3 Stage 1a: Decision to Enter the Lottery

In the first stage a set of potential firms f ∈ Fm with information sets If choose whether to apply

for a retail license in a jurisdiction m. The product and cost characteristics of the firm are exogenous.

I assume that own-characteristics and potential competitors’ characteristics are included in the firm’s

information set. Jurisdictions and firm locations are also exogenous, consistent with the fact that

many marijuana store owners are local businessmen, and that firm location is tightly constrained due

to legal barriers. Furthermore, as addresses on lottery applications are public knowledge, I assume

firm location and potential competitors’ locations are included in the information set.

The government has restricted the number of licenses—and, hence, entrants—to nm licenses in

each jurisdiction. This license cap and the firms who apply for licenses, nf are known to all f . If entry

18

is constrained, nf > nm, the government chooses license recipients randomly while if nf ≤ nm, all

applicants are granted retail licenses. I assume that if f is a license recipient, f enters in jurisdiction

m.

Firms know their own product sets Jf and predict which other firms will enter the lottery though

the identities of these firms are selected by the lottery. I assume firms make their lottery entry decision

based on expected profits given the other firms who enter subsequently with the lottery. Moreover,

firms enter only if expected profits are weakly greater than zero whatever the subset of competitors

after the lottery. This implies the following inequality:

E(πf (df , d−f ; θ) | If ) ≥ 0. (10)

The profit function πf (df , d−f ; θ) has the form

πf (df , d−f ; θ) = rf (df , d−f ; θ)− F (11)

where rf (·) is equation 7, the variable profit function .

To capture higher fixed costs in urban areas, I model fixed costs as follows:

F = η1 + η2I(urbanf ). (12)

I(urban) equals one if the firm is in a urban area to capture any additional costs associated locating

in an urban area. To define urban versus rural, I use the U.S. Census definition of an “urbanized

area” which is a geographic area with “50,000 or more people.”17

5 Estimation

Estimation mirrors the logic of the backwards induction solution of the model: I estimate demand

and marginal costs yielding a measure of variable profits. I then use the estimates for variable profits

to find the fixed cost of entry.17See ”2010 Census Urban and Rural Classification and Urban Area Criteria,” United States Census Bureau,

https://www.census.gov/geo/reference/ua/urban-rural-2010.html.

19

5.1 Demand Estimation

Because unobserved product characteristics are likely correlated with prices, Berry (1994) outlines

a procedure to estimate the nested logit model which uses two-stage least squares to correct for price

endogeneity. However, because the dispensing data is available at the firm level rather than the block

group level, meaning I observe Qjf and not shjf , I cannot use the simple logarithmic transformation

seen in Berry (1994) to invert the shares and obtain an expression for ξjf as a function of observable

data. Therefore, to instrument for price, I invert the shares numerically and estimate the model as in

Berry et al. (1995) (BLP). Grigolon and Verboven (2014) shows that inverting shares in the nested

logit model requires modifying the BLP fixed point contraction mapping:

δkjf = δk−1jf + log(Sjf )− (1− σ) log(Sjf (δk−1)). (13)

Not including the (1−σ) factor means that (13) is not a contraction mapping unless σ is close to zero.

Grigolon and Verboven (2014) also shows that the (1− σ) factor dampens the convergence speed of

the contraction mapping particularly as σ → 1.

Hence, instead of using the nested fixed point algorithm outlined in BLP, I use the Mathematical

Programming with Equilibrium Constraints (MPEC) estimation method detailed in Su and Judd

(2012) and Dube et al. (2012). Estimation involves minimizing the GMM objective function subject

to the constraint that observed market shares equal the analytical shares:

minθ

ξ′ZWZ ′ξ

s.t. sob = s(θ)1−σ

where θ = (α, β, σ, τ,Π, ξ)′. The MPEC algorithm estimates ξ as a parameter rather than using the

fixed point algorithm to compute the implied ξ. I use these estimates of ξ to recover the distribution

of unobserved product characteristics Fξ.

The matrix Z is a vector of instruments that is correlated with prices and satisfies the exclu-

sion restriction E(ξjf |zjf ) = 0. Because the data includes wholesale costs, I can include cost in Z,

alleviating concerns about weak instruments (Gandhi and Houde, 2016). Further, as observed prod-

uct characteristics are assumed to be independent from ξjf , product characteristics are also valid

instruments. Moreover, the distribution of costs and product characteristics are independent across

products; hence, average wholesale cost and product characteristics of other goods in Jf are in Z. I

20

also include the population-weighted average tract characteristics and BLP instruments—mean costs

and product characteristics of expected competitors.

5.2 Demand Results

Table 4 reports the demand estimates. Column (1) reports the estimates from my preferred

specification which uses demographic data from Washington census tracts.18 Most coefficients are

the expected signs: consumers like products with high concentrations of THC but dislike price and

travel. The coefficient on CBD concentration is a negative, consistent with the idea that CBD

concentration may be more valuable to medical marijuana consumers than recreational marijuana

consumers.

The first panel of Table 5 reports the implied prices elasticities of demand by quantile using

specification (1). Most elasticities of usable marijuana fall in the interval [−3,−2] with only 25% of

the demand elasticities falling under -2.92. Inhalables are highly elastic with most elasticities falling in

[−6,−4.5]. Out of all 3,141 product-firm pairs only one implied elasticity is greater than -1, meaning

firms are not pricing along the inelastic portion of the demand curve.

Using Traceability data, Hansen et al. (2017) estimates an average market elasticity of demand of

−0.85 for one gram of usable marijuana. My reported demand elasticities are for each firm-product

pair. To reconcile these estimates, I calculate the total market demand for marijuana products and

increase prices by one percent. I estimate a demand elasticity of -1.83. Closer to my firm-level

analysis, Hansen et al. (2017) also estimates the elasticity of demand across firms within cities,

finding an elasticity of −0.81. However, the study cannot reject that the elasticity of demand is -1,

and, therefore, cannot reject “that firms are making profit-maximizing decisions.”

Figure 5 and the second panel of Table 5 report travel cost by quantile. At the median population

density—about 2,300 people per square mile—the travel costs are around $0.74 a mile. Though census

tracts in the bottom two percent of population density—less than five people per square mile—glean

positive utility from travel, the estimates seem sensible when compared with the median travel cost

of $0.98 per mile found in Seim and Waldfogel (2013) on alcohol markets, $0.32 per mile in Davis

(2006) on movie theaters. Houde (2012) predicts that a customer will pay $0.90 per minute to avoid

shopping for twenty liters of gasoline.

Column (3) of Table 4 presents estimates using data from block groups. Block groups cover a18As a check on the robustness of these estimates, I report additional results varying the radius defining the consumers’

choice set in Table A2.

21

Table 4: Demand Parameter Estimates

(1) (2) (3) (4) (5)

price -0.14659∗∗∗ -0.14444∗∗∗ -0.14698∗∗∗ -0.18484∗∗∗ -0.14747∗∗∗(0.00714) (0.00726) (0.00722) (0.00834) (0.00710)

distance 0.03144∗ -0.12777 0.04019∗∗ 0.06960∗∗∗ 0.01005(0.01639) (0.10602) (0.01869) (0.01512) (0.00808)

distance * ln(pop. density) -0.01810∗∗ 0.00644 -0.01512∗∗ -0.01925∗ -0.01996∗∗(0.00786) (0.01751) (0.00679) (0.01037) (0.00795)

% THC 0.03725∗∗∗ 0.03648∗∗∗ 0.03743∗∗∗ 0.05168∗∗∗ 0.03906∗∗∗(0.00248) (0.00251) (0.00250) (0.00303) (0.00251)

% CBD -0.20300∗∗∗ -0.19629∗∗∗ -0.19800∗∗∗ -0.21423∗∗∗ -0.24146∗∗∗(0.03348) (0.03437) (0.03365) (0.03732) (0.03264)

% population ≥ 35 0.02533∗∗∗ 0.01214∗ 0.02959∗∗∗ 0.04221∗∗∗ 0.04407∗∗∗(0.00539) (0.00656) (0.00604) (0.00627) (0.00602)

number of medical stores 0.02809∗∗∗(0.00879)

σ0.13624∗∗ 0.18925∗∗∗ 0.12782∗∗ 0.27775∗∗∗ 0.24027∗∗∗(0.05309) (0.05714) (0.05440) (0.03732) (0.03776)

N 3141 3141 3141 2412 3141

states WA WA WA interior WA WA, OR, IDcensus tract/block group tract tract block group tract tract

Note: Standard errors are reported in parenthesis. ∗∗∗ indicates p < 0.01. ∗∗ indicates p < 0.05, and∗ indicates p < 0.1.

smaller area and may offer a more precise proxy for consumer location. Using census tracts could

overstate/understate distance to the firm relative to the smaller block group. The parameter results

are largely unchanged, though parameter estimates on the travel cost functions are slightly different,

implying lower travel costs. The distribution of the implied elasticities and travel costs for block

groups are reported in Table A3.

The specification reported in Column (2) includes the number medical marijuana firms within ten

miles of the census tract in the outside option. Increasing the number of medical dispensaries within

10 miles of a block group makes the outside option more attractive. However, the addition of medical

marijuana stores makes the distance parameters insignificant and switch signs.

While columns (1)-(3) include estimates using only data from geographic tracts in the state of

Washington, the last two columns in Table 4 account for cross-border shopping. Not accounting for

22

Figure 5: Travel Costs by Quantile of Population Density

Table 5: Implied Elasticities and Travel Costs by Quantile

Panel A: Implied Price Elasticities

Usable Edibles Inhalables

25% -2.92016 -3.32763 -6.0930350% -2.54836 -2.89659 -5.3894375% -2.22119 -2.50839 -4.75936

% |εp,d| < 1 0.0001% 0 0

Panel B: Travel Costs ($)

25% $0.5309450% $0.7410475% $0.82367

23

Figure 6: Tracts Used to Account for Cross-Border Shopping

(a) Excluding Border Census Tracts

(b) Including Border Census Tracts

Notes: Census tract shapefiles are obtained from the U.S. Census Bureau (2015).

24

border-crossing could overstate the size of border firms’ market shares, biasing estimates. Therefore,

I report estimates from additional specifications that account for census tracts near the Washington

state border.

Column (4) uses the interior Washington tracts, excluding tracts and stores less than thirty-five

miles from the border. Column (5) include tracts from Oregon and Idaho within thirty-five miles

of the Washigton state border. Figure 6 displays maps of the tracts used in column (4) and (5),

respectively. The coefficient estimates on price and THC are robust particularly when using census

tracts from Oregon and Idaho. I report travel costs along with implied elasticities in Table A4.

Unsurprisingly, adding cross-border shoppers from Idaho and Oregon increases travel cost to $0.99

for the median population density of 2,557 people per square mile.

5.3 Marginal Cost Estimation and Results

Rather than use the Nash-pricing condition—equation (9)—to create additional moments for

demand estimation, I use the pricing equation and the demand estimates to back out unobserved

marginal costs. A similar idea is pursued in Wollman (2016) which uses the pricing equation and

demand estimates to estimate observed marginal cost parameters via least squares and then obtain

unobserved cost. I, however, have observed wholesale costs in the data and can use a non-parametric

approach. Plugging (8) into (9) and rearranging the equation to isolate ω yields an expression of

unobserved marginal costs as a function of prices, shares, observed costs and the demand model

parameters:

ωf = pf − cf −∆−1f (θ)Qf . (14)

Hence, inserting the estimated parameters θ into (14) recovers an estimate of the distribution of

unobserved marginal costs—Fω.

Figure 7 shows distribution of unobserved marginal costs by product. In particular, unobserved

marginal costs are generally positive, and I do not calculate that the sum of observed and unobserved

marginal cost is negative. Table 6 describes the distribution of unobserved and unobserved marginal

cost by quantile. Unobserved marginal costs for edibles and usable marijuana are generally in the

interval [0 5] in comparison to observed costs which fall in the interval [5 7]. Unobserved costs of

inhalables tend to be higher, falling in the interval [5 15]. Figure 8 displays the distribution of the ratio

of unobserved to observed marginal costs, providing a better picture of the magnitude of unobserved

25

versus observed marginal costs. This ratio generally falls in the interval [0,1] in all product categories,

meaning that unobserved costs do not account for a majority of variable costs. A discussion of the

relationship between ω and firm characteristics is in Section A.5.

With cost estimates in hand, I can calculate the implied price-cost markups. Table 8 reports

the price-cost margins by quantile. The median markup on usable marijuana is 68%, slightly higher

though still in line with reports of markups of from 54-67% for one gram of usable marijuana in

Washington for 2015.19

5.4 Fixed Cost Estimation - Moment Inequalities

As generally is the case in games of entry with heterogeneous players, the entry game likely

does not yield a unique equilibrium (Bresnahan and Reiss, 1991a). However, rather than specify an

equilibrium selection mechanism or make additional assumptions to guarantee point identification of

the fixed cost parameters, I use the moment inequalities methodology outlined in Pakes et al. (2015)

(PPHI) and Pakes (2010) to bound identify fixed costs.

Fixed costs are typically identified using a revealed preference argument: If n firms enter, it

must be the case that n firms are profitable, but the n + 1th firm is not (Bresnahan and Reiss,

1991b). However, as Grigolon and Verboven (2014) points out, if entry is constrained by a cap, firm

n+ 1’s profits are ambiguous. Therefore, I split my set of jurisdictions according to whether entry is

constrained. Let M0 = {m | nf ≤ nm}, the set of jurisdictions without binding license constraints,

and analogously, defineM1 = {m | nf > nm}, the set of jurisdictions with binding license constraints.

If the license cap does not bind, I assume all firms with positive expected profit entered. No

additional firms can enter m profitably else there would be nf + 1 license applicants. Therefore,

E(πnf +1(dnf +1, d−f ; θ) | Inf +1,M0) < 0. (15)

To simulate inequality (15), I assume that firm nf + 1 in opens in the population-weighted centroid

of the jurisdiction. If m ∈ M1, I can make no assumptions about the nf + 1th entrant though I can

assume that each entrant had positive expected profits,

E(πf (df , d−f ; θ) | If ,M1) ≥ 0. (16)19See McVey, Eli. “Chart: Retail marijuana markups in Washington state continue to dip.” Marijuana Business Daily.

Last modified February 13,2017. https://mjbizdaily.com/chart-retail-marijuana-markups-in-washington-state-continue-to-dip/

26

(a) Edibles (b) Inhalables

(c) Usable Marijuana

Figure 7: Conditional Distribution of Unobserved Marginal Cost (ω)

27

(a) Edibles (b) Inhalables

(c) Usable Marijuana

Figure 8: Ratio of Unobserved to Observed Marginal Cost (ω/c)

28

Table 6: Distribution of Observed and Unobserved Costs by Quantile

Observed Unobserved

Panel A: Usable ($)

25% $5.66 $0.9750% $6.44 $2.2075% $7.52 $3.62

Panel B: Edible ($)

25% $5.19 $1.2250% $6.07 $2.6575% $7.00 $4.24

Panel C: Inhalable ($)

25% $10.07 $7.1850% $11.49 $9.8175% $12.76 $12.96

Table 7: Correlation Between Unobserved and Observed Marginal Cost

Correlation Coefficient

Usable 0.3154Edible 0.4878Inhalable 0.2042

Table 8: Implied Price-Cost Markup(p−cp

)by Quantile

Usable Edibles Inhalables

25% 0.55699 0.51754 0.2282350% 0.68393 0.65105 0.2737875% 0.86808 0.84353 0.32029

29

Additionally, I can rewrite the expected profit function as a function of the demand and marginal

cost estimates, observed cost and characteristics distributions from the data, and an error.

E(πf (df , d−f ; θ) | If ) = πf (df , d−f ; θ, Fx, Fc, Fξ, Fω) + νf (17)

= rf (df , d−f ; θ, Fx, Fc, Fξ, Fω)− η1 − η2 · I(ruralf ) + νf (18)

νf is an expectational error E(νf | If ) = 0, and (η1, η2) are parameters to be estimated.20

The empirical analog of (16) for rural jurisdictions is

1F 0

1

∑f0

1∈F01

rf (df , d−f ; θ)− η1 > 0 (19)

where F01 is the set of firms in rural jurisdictions with binding license quotas, and F 0

1 = |F01 |. Likewise,

the empirical analog of (15) for rural jurisdictions is

1F 0

0

∑f0

0∈F00

rnf +1(dnf +1, d−f ; θ)− η1 ≤ 0. (20)

F00 is the set of firms in rural jurisdictions with without binding license quotas, and F 0

0 = |F00 |.

Therefore, the fixed cost bounds for rural jurisdictions are

1F 0

0

∑f0

0∈F00

rnf +1(dnf +1, d−f ; θ) ≤ η1 <1F 0

1

∑f0

1∈F01

rf (df , d−f ; θ) (21)

Defining the sample moments analogously for rural areas, I obtain the bounds

1F 1

0

∑f1

0∈F10

rnf +1(dnf +1, d−f ; θ) ≤ η1 + η2 <1F 1

1

∑f1

1∈F11

rf (df , d−f ; θ). (22)

Additional details on estimation such as the estimation algorithm are presented in Section A.7.1.

5.5 Fixed Cost Results

The estimates for the fixed cost parameters are reported in Table 9. The estimates imply that

urban retailers have fixed costs between $54,390 and $118,757 while rural retailers have fixed costs

between $15,170 and $34,945. These are consistent with discussions with industry professionals who20PPHI allows for a structural error term. However, I do not assume a structural error. Therefore, all heterogeneity

in fixed costs comes from whether retailers are rural or urban.

30

Figure 9: Fixed Cost Confidence Intervals (in $10,000’s)

Notes: The blue dots indicate trial points in the parameter space where I could not reject the null hypothesis that θo

is the true parameter vector. The orange dots indicate the estimated parameter set.

Table 9: Fixed Cost Parameter Estimates

lower bound upper bound

constant $15,170.66 $34,945.1895% CI $1,794 $58,922

I(urban) $39,220.07 $83,812.9395% CI -$31,473 $204,918

31

estimated that retailers in urban areas must earn around $100,000 per month to break even while

stores in rural areas can make substantially less and stay in business ($10,000-$30,000 per month).

Recent reports in the industry estimate the median annual operating costs of recreational marijuana

dispensaries to be $600,000.21

Standard errors are calculated using the asymptotic version of the Generalized Moment Section

test detailed in Andrews and Soares (2010). Additional details on calculating standard errors are

presented in Section A.7.2. Table 9 displays the projections of the 95% confidence set. However,

more informative is Figure 9 which displays the full confidence set. The confidence set is large,

unsurprising due to the small number of firms and jurisdictions. Moreover, I cannot rule out that the

parameter value for η2 is less than zero. However, as Figure 9 shows, if η2 < 0, η1 tends to be large.

Therefore, total fixed costs are always positive in the 95% confidence set. Nonetheless, I cannot reject

that urban fixed costs are less than rural fixed costs.

6 Counterfactuals

In this section I explain the computation of my counterfactual simulations and discuss the results. I

begin by exploring a policy of free entry. Free entry improves surplus relative to a baseline simulation

of Washington’s license quota policy. I then break down the sources of this gain to explore the

role of allocative efficiency by simulating the outcome of license auctions. The surplus generated

by a statewide license auction that distributes the same number of licenses as the license quota

does not have allocative costs due to either geographic license restrictions or the lottery while a

within-jurisdiction license auction that distributes the same number of licenses in a county/city incurs

allocative costs due to geographic misallocation but not due to randomization. Thus, the differences

in surplus generated by each of these simulations allow me to discuss the importance of each source

of inefficiency caused by Washington’s license quota policy.

I also discuss additional counterfactuals that directly control for the marginal damages of mari-

juana consumption. To do this, I back out the tax rates that hold marijuana/THC consumption fixed

to baseline consumption. As taxes with free entry neither restrict over geography nor keeps the most

efficient firms from entering, these policies control for negative externalities without creating alloca-

tive costs. I also explore efficiency improving tax policies assuming heterogenous marginal damages21See McVey, Eli. “Chart of the Week: Profitability in the Cannabis Industry.” Marijuana Business Daily. Last

modified May 9,2016. https://mjbizdaily.com/chart-of-the-week-profitability-in-the-cannabis-industry/

32

across geography, backing out the implied non-uniform tax schedule consistent with Washington’s

current regime of license quotas.

6.1 Unrestricted Entry Counterfactual

In the model firms entered the lottery with knowledge of the license quota and the fact that

competition will be reduced. Hence, without the quota I cannot assume that all who entered the

lottery would enter the market. In the unrestricted entry scenario, I assume that all lottery entrants

in the data are potential entrants in the free entry game and use the associated lottery addresses as

their locations. (I draw from the empirical distributions of Fx, Fη, Fc, and Fω to simulate the firm

characteristics of lottery losers.) As before, firms are still endowed with their locations, products,

and costs, and these are known to all competitors. However, now there is no lottery randomization.

Firms enter if expected profits are positive:

E(π(di, d−i, θ)|If ) ≥ 0.

6.1.1 Computing Counterfactual Entry

Multiple equilibria are almost certain in an entry game with heterogeneous firms. Therefore, to

compute counterfactual entry with tax t, I adopt an iterative best response process similar to Wollman

(2016).22 I begin by assuming all n potential entrants have entered, d = 1, and specifying an order in

which firms make their decisions, ordering by profitability. Assuming a tax of t, I play a Nash-pricing

game with all n firms. I then allow firm 1 to play its best response: enter or not enter. The firms in

the market then replay the Nash-pricing game. Next, firm 2 plays its best response given the actions

of the other players, and the Nash-pricing game is replayed based on firm 2’s choice. This continues

until I go through each firm in the order. I repeat this process until I converge to a solution where

all entrants have positive expected profits, and no firm has a profitable deviation.

6.1.2 Computing Baseline Entry

In the unrestricted entry game described in Section , firms know their competitors and competitors’

characteristics, and there is no lottery randomization. Hence, under free entry there is no ex-post

regret. However, due expectational error, firms in the entry model described in Section 4.3 and may22Lee and Pakes (2009) also discuss the equilibrium selection, suggesting learning processes which “select out” equi-

libria.

33

experience ex-post regret. To bring consistency between the two simulations, I compute the baseline

simulation by first randomly ordering firms within each jurisdiction as described in Section 2.2. I

then take the first n firms in each jurisdiction as the lottery winners. All lottery winners enter the

market. If a firm experiences ex-post regret, I remove that firm and replace it with the next firm in

the lottery ordering. I do this until all firms have positive profits. Guaranteeing that all firms in the

baseline simulation have no ex-post regret increases the magnitude of total surplus, consumer surplus,

producer surplus, and tax revenue though fixed costs are constant. This biases the results away from

finding inefficiency due to license allocation and, thus, does not greatly impact the interpretation of

the results.

6.1.3 Decomposing the Sources of Welfare Loss

The unrestricted entry counterfactual simulates the outcome in Washington sans distortions from

the license quota policy. The distortions from the quota comes from a few sources. First, less

marijuana is sold due to fewer stores, a similar effect to quantity cap. Moreover, the geographic

distribution of licenses does not account for the heterogeneous marginal benefits to stores across

geography. Finally, the licenses are allocated randomly, ensuring that the most efficient stores are

not necessarily the ones that receive licenses. I detail the steps I use to decompose these sources of

surplus loss below.

To capture the loss from restricting the number of total entrants statewide, I simulate the results

of a statewide license auction. I first assume firms pay a lump sum amount $L for a license. Using

the iterative best response process discussed in Section 6.1.1, I compute the entry game outcome at

t = 0.37 with lump sum payment $L and increase this lump sum until the number of entrants is equal

to the number of entrants in the baseline. By utilizing a lump-sum payment and not restricting license

by jurisdiction, this counterfactual does not have allocative costs among firms due to randomization

or misallocation across geography.

To isolate the cost due to the geographic misallocation of licenses, I compute the outcome of license

auctions within each jurisdiction. This counterfactual proceeds similarly to the simulation discussed

in the previous paragraph. However, I allow the lump sum license payment to vary by jurisdiction

and increase the payments until the number of firms within the jurisdiction is equal to the baseline.

Restricting the licenses across jurisdictions creates allocative costs across geography. However, there

is no cost due to randomization. Because the total number of firms is equal to the total number of

34

firms in the baseline, this simulation captures the loss from both geographic misallocation and the

restricted number of entrants.

Therefore, the difference in surplus between the unrestricted entry simulation and the statewide

auction reflects the loss due to restricting the number of entrants. The change in surplus between

the statewide license auction and the within-jurisdiction auctions measures the loss from geographic

misallocation. As the baseline simulation captures all the distortions from the license quota policy,

the loss in surplus between the jurisdiction-specific auctions and the baseline is accounted for by

randomization.

6.1.4 Results

As presented in Panel B of 11, the free entry increases total surplus almost $23 million—a 21.5%

increase relative to the baseline. The results are also denoted by the point labeled “Free Entry” on

Figures 10 and 11 while baseline surplus measures are labeled “Base” in the figures. The vertical

distance between Points “Free Entry” and “Base” represents the increase in the surplus measures.

Producer surplus increases by 32.6%. Consumer surplus increases by 18.7% driven by the fact that

stores are closer to consumers and increased competition creates lower prices.

The number of firms increases from 165 to 260. The map in Figure 12 displays the differences in

the number of firms between the baseline and free entry with t = 0.37. Urban areas such as Seattle,

Tacoma, and Vancouver are the most affected with the city of Seattle gaining 12 additional stores

under free entry. Additional maps showing the changes in the distribution of stores between free and

restricted entry are in Figure A.16 of the Appendix.

Table 10 displays the change in average markups due to the increased competition. The average

markups decrease for all product categories relative to baseline. The most popular product category,

usable marijuana, experiences the smallest decline in price while the average markup for edibles falls

by over 5%.

Free entry along with a statewide license “auction” increases total surplus 15.6% relative to the

baseline The full results of the simulation are reported in Panel C of 11 and denoted by “Statewide”

in Figures 10 and 11. Consumer surplus improves 12% as firms are both located in better areas and

prices are lower. Further, while the number of firms is equal to the baseline, firms are more efficient;

hence, producer surplus is 21.6% higher.

The within-jurisdiction license “auction” increases total surplus 13.9% relative to the baseline.

35

The results are reported in Panel D of 11 and denoted by “Jurisdiction” in Figures 10 and 11. Even

though the number of firms within each jurisdiction is constant, prices are still lower than in baseline.

Hence, consumers by more marijuana products, and consumer surplus increases by 10.9%. Producer

surplus is also 17.5% higher.

The cost from restricting the number of total entrants statewide, shown graphically as the vertical

distance between “Free Entry” and “Statewide” in Figure 10, comprises 27.5% of the $23 million

difference in surplus. Allocative costs constitute the remainder of the difference–over 70%. The

distance between “Statewide” and “Jurisdiction” in Figure 10 represents the cost due to geographic

misallocation, 6.6% of the change in total surplus, and the gap between “Jurisdiction” and “Baseline”

depicts the efficiency cost attributable to randomly distributing licenses to potential entrants. This

distance is the largest, representing 65.9% of the total cost.

6.2 Controlling for Marginal Damages of Consumption

Previous research in both economics and health show that marijuana causes short and long-term

cognitive impairment, impairs short-term motor function, is associated with paranoia and psychosis,

and adversely effects adolescent brain development and school performance (Crean et al., 2011; Marie

and Zolitz, 2017; Prashad and Filbey, 2017; Volkow et al., 2014). Therefore, policy makers may

institute license quotas because they care more about limiting the amount of marijuana consumed

and by extension the marginal damages of consumption.

The counterfactuals above restricted entry, controlling for marginal damages of consumption by

decreasing the number of stores. Here, I study counterfactuals that directly control for the externality

using taxation without restricting entry. Sales taxes decrease the profitability of stores, deterring firm

entry, and discourage consumption. However, unlike with Washington’s license quota, firms can enter

where they are most valuable, and firms are not randomly chosen, meaning the most efficient will enter.

Moreover, a common justification for legalizing marijuana is alleviating ailing state budgets through

a marijuana sales tax. License quotas, rather, restrict consumption without collecting revenue.

6.2.1 Controlling for Quantity Consumed

Assuming that the marginal damages of consumption are constant across products and geography

and no consumer leakage into the black market, setting taxes in an unrestricted entry regime so

that the quantity sold is the same as the baseline quantity sold should keep the marginal damages

36

Figure 10: Total Surplus

Notes: The figure displays surplus versus the tax rate. The baseline is normalized to 1.

37

Figure 11: Counterfactual Results

(a) Consumer Surplus (b) Producer Surplus

(c) Tax Revenue (d) Average Producer Price

(e) Average Consumer Price

Notes: The figure displays surplus or average prices versus the tax rate. The baseline welfare is normalized to 1.Statewide and Jurisdiction auction simulations are not labeled in the average price charts for clarity because prices arewithin $0.03 of the free entry price.

38

Figure 12: Change in Number of Firms

Table 10: Change in Average Markups and Demand

Free Entry Baseline % Change

Panel A: Markups

Usables 0.45522 0.45621 -0.219%Inhalables 0.27101 0.27607 -1.835%Edibles 0.45694 0.48273 -5.343%

Panel B: Quantity Sold

Usables 3,292,106 2,323,975 41.658%Inhalables 1,067,880 801,255 33.276%Edibles 388,347 316,626 22.652%

39

Table 11: Counterfactual Results

Total Consumer Producer Tax Fixed Numberof

Firms

Quantity(10,000s)

THC(10,000s)Surplus Surplus Surplus Revenue Cost

($10,000s) ($10,000s) ($10,000s) ($10,000s) ($10,000s)

Panel A: Baseline with t = 0.37Results 10,616.146 6,999.341 2,276.417 2,169.038 828.650 165 344.186 103.784

Panel B: Free Entry with t = 0.37Results 12,894.988 8,304.740 3,018.438 2,910.310 1,338.500 260 474.833 142.591% of Baseline 1.215 1.187 1.326 1.342 1.615 1.576 1.380 1.374

Panel C: Free Entry with t = 0.37 and Statewide AuctionResults 12,269.209 7,837.572 2,768.411 2,625.625 962.400 165 427.317 129.813% of Baseline 1.156 1.120 1.216 1.211 1.161 1.000 1.242 1.251

Panel D: Free Entry with t = 0.37 and Jurisdiction-wide AuctionResults 12,096.619 7,759.728 2,666.921 2,487.920 817.950 165 405.478 124.312% of Baseline 1.139 1.109 1.172 1.147 0.987 1.000 1.178 1.198

Panel E: Free Entry with t = 0.765 (Constant Quantity)Results 11,346.846 6,849.183 1,703.086 3,618.276 823.700 162 344.236 91.163% of Baseline 1.069 0.979 0.748 1.668 0.994 0.982 1.000 0.878

Panel F: Free Entry with t = 0.660 (Constant THC)Results 11,856.869 7,218.689 1,994.723 3,599.356 955.900 187 379.598 103.762% of Baseline 1.117 1.031 0.876 1.659 1.154 1.133 1.103 1.000

Panel G: Free Entry with Non-Uniform TaxResults 11,371.957 7,040.674 2,060.642 3,083.242 812.600 165 352.095 97.346% of Baseline 1.071 1.006 0.905 1.421 0.981 1.000 1.023 0.938

of consumption fixed across policy regimes. Panel E of Table 11 and Point Q in Figures 10 and 11

display the results of a free entry counterfactual at t = 0.765, the tax rate that holds the quantity

consumed fixed to the baseline.

Despite the tax rate being more than twice that of the baseline, total welfare in the unrestricted

entry simulation is almost 7% higher than in the baseline because there are no allocative costs from

the license quota policy. Producer surplus is around 75% of the baseline producer surplus, largely

driven down due to depressed producer prices after the tax. As seen in Figure 11d and 11e, incidence

40

of the tax falls largely on producers rather than consumers. Unsurprisingly, consumer surplus is

roughly equal to the baseline as consumers are buying the same amount of marijuana. As is visible

from Figure 11c, t = 0.765 is close to the revenue maximizing tax rate, and tax revenue is 67% higher

than the baseline tax receipts, implying that the state forgoes substantial amounts of tax revenue by

using license quotas. The high sales tax rate also depresses entry to 162 firms, close to the baseline

number of entrants which controls for other possible costs related to the number of entrants such as

enforcement costs or neighborhood-level externalities.

6.2.2 Controlling for THC Consumed

Marginal damages of consumption may not be the same across products. As Table 3 displays,

potency varies across product categories. Volkow et al. (2014) shows that increases in THC potency

over time are associated with increased marijuana-related emergency room visits and motor vehicle

accidents. Hence, policy makers may be interested in not controlling for the amount of marijuana

consumed but the amount of THC consumed. Therefore, I find the tax rate that instead keeps the

quantity of THC consumed constant. Panel F of Table 11 and Point THC in Figures 10 and 11

display the results of a counterfactual at t = 0.66, the tax rate that holds the quantity of THC

consumed equal to the baseline.

Similar to the counterfactual discussed above, though the tax rate is almost twice the baseline

sales tax rate, allowing for free entry increases total welfare by 11.7% relative to the baseline. The

number of firms increases to 187, but despite the increased number of firms, producer surplus is

roughly 87% of the baseline. Markups are again driven down by high sales taxes. Further, though

THC consumption is constant, the quantity of marijuana consumed is 10% higher than in the baseline

simulation. The higher taxes cause consumers to substitute out of expensive THC-rich inhalables and

into the comparatively less potent and cheaper usable marijuana and edibles.

6.3 Heterogenous Marginal Damages

If the marginal damages of consumption are not constant across jurisdictions, Washington could

be using license quotas to account for heterogeneous damages, mitigating allocative costs due to

misallocation of licenses across geography.23 However, allocative inefficiency would still exist due to

the lottery distribution licenses.23As discussed in the introduction, license quotas often take the form of uniform quantity restriction. Therefore, it is

not likely that states are accounting for heterogeneous marginal damages.

41

Therefore, I compute counterfactual free entry under the non-uniform sales tax implied by license

quota. To back out the non-uniform tax, I use the iterative best response process discussed in Section

6.1.1 but raise sales taxes differentially across jurisdictions until the number of firms within each

jurisdiction equals the jurisdiction’s baseline number of firms. The simulation results are reported in

Panel G of 11 and is denoted by Point MD on Figures 10 and 11. In Figure 11, the t-coordinate is the

average tax rate paid, t = 0.6522, and Figure 13 displays the implied tax rate for each jurisdiction.

Counterfactual quantity sold is only 2.3% more than the baseline quantity, and THC consumption

is actually 6.2% less than baseline THC consumption, meaning that the non-uniform tax achieves

a similar level of marginal damages as the baseline. However, free entry improves welfare by 7.1%

because entrants are not chosen randomly. The free entry regime also yields 42% more tax revenue

revenue.

Washington may be unable to implement a non-uniform tax (perhaps due to concerns over fairness

or equity). However, the within-jurisdiction auction counterfactual discussed in Section 6.1.3 would

also control for heterogenous marginal damages across geography while allowing the most efficient

firms to enter, improving total surplus by almost 14%. However, consumption would also be 17.8%

higher than in the baseline.

7 Conclusion

I study the welfare impacts of common license quotas policies in the context of the Washington

recreational marijuana market. I focus not only on the welfare effects of restricted entry and reduced

sales but also on the allocative costs of license quotas, contributing to the relatively small empirical

literature measuring allocative inefficiency. To do this, I use detailed firm-level marijuana sales data

to estimate a three-stage model of firm entry and spatial. I then use a novel dataset on entrants in

Washington’s recreational marijuana license lottery to estimate counterfactual entry patterns.

I demonstrate the empirical importance of allocative inefficiency in the Washington marijuana

market, finding that allocative inefficiency accounts for almost 70% of the welfare loss in counterfactual

simulations comparing free entry to Washington’s current policy regime of license quotas. Geographic

misallocation and random allocation of licenses account for 7.9% and 65.9% of this loss, respectively.

I also study policies that directly control for the marginal damages of marijuana consumption. A free

entry regime with t = 0.765 keeps the quantity of marijuana consumed equal to baseline but increases

welfare by 6.9% while free entry with t = 0.66 keeps the quantity of THC consumed equal to baseline

42

Figure 13: Heterogenous Sales Taxes

Notes: Map displays the non-uniform sales tax rate for each jurisdiction implied by the current policy of license quotas.

consumption but increases welfare by almost 12%. Further, assuming that license quotas are used

to account for heterogeneous marginal damages across geography, a non-uniform sales tax consistent

increases efficiency relative to the baseline by over 6%.

The magnitude of the efficiency loss and forgone tax revenue invites the question of why state

and local governments distribute licenses for “sin goods” in this manner. Possible explanations of the

license quota in itself include the limiting enforcement costs. The WLCB budget for FY2016 was 34

million dollars with 18 million allocated toward licensing and enforcement of liquor and marijuana,

a budget which is dwarfed by the increase in tax revenues in the counterfactuals. Concerns about

fairness or rent seeking could also play into distribution of licenses by lottery.

License quotas may be instruments used to control for more localized negative externalities though

quotas are not usually implemented at the neighborhood level. Thomas and Tian (2017) uses the

Washington retail license lottery as an instrument to measure the impact of marijuana dispensaries on

property values. However, research on the impact of legalized marijuana dispensaries on neighborhood

43

outcomes such as crime and hospital visits remains an fruitful area for future research.

I also leave to future research the impact of retail license quotas on upstream firms. While pro-

ducers and processors can enter the market freely in the Washington recreational marijuana market,

retailer entry restricted. Hence, producers and processors drive down their prices to compete for

highly limited shelf space in stores. Increasing the number of retailers relieves pressure on upstream

firms; hence, upstream firms may increase wholesale prices, causing an increase in retailer costs.

44

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49

Appendix

A.1 Number of Products Purchased Per Transaction

Figure A.14: Percentage of Transactions with X Number of Products Purchased

A.2 Radii Defining Choice Sets

The tables describe the radius defining each consumer’s choice set located within the city or

county. The radius for each county applies to the county’s rural areas unless a suburb is specified in

the parenthesis.

50

Table A1: Radii Defining Consumer Choice Sets

City radius (rh)

Auburn 12Bainbridge Island (King County) 10Bainbridge Island (Pierce County) 10Battle Ground 9Bellevue 11Bellingham 6Bonney Lake 6Bothell 9Bremerton (King County) 4Bremerton (Snohomish) 3Burien 4Burlington 5Centralia 13East Wenatchee 9Ellensburg 5Federal Way 5Ferndale 9Goldendale 7Kelso 9Kennewick 2Kent 44Kirkland 9Lacey 5Lake Stevens 6Lakewood 7Longview 7Lynden 5Maple Valley 4Marysville 13Mercer Island 9Mill Creek 5Monroe 4Moses Lake 11Mukilteo 4Oak Harbor 5Omak 5Port Angeles 44Port Townsend 6Quincy 10Renton 6Richland 5Sammamish 49SeaTac 10Seattle 6Sedro-Woolley 4Sequim 9Shelton 13Spokane 4Spokane Valley 5Sunnyside 6Tukwila 6Tumwater 4University Place 5Vancouver 5Walla Walla 9Wenatchee 17Yakima 58

County (suburb) radius (rh)

Adams County 57Asotin County 28Benton County 62Benton County (Kennewick—Pasco) 52Chelan County 31Clallam County 59Clallam County (Port Angeles) 14Clallam County (Sequim) 14Clark County 18Clark County (Portland) 20Columbia County 45Cowlitz County 22Cowlitz County (Longview) 9Douglas County 38Franklin County 50Franklin County (Kennewick–Pasco) 44Grant County 44Grays Harbor County 33Island County 15Island County (Seattle) 10Jefferson County 30Jefferson County (Bremerton) 18King County 24King County (Bremerton) 9King County (Seattle) 14Kitsap County 13Kitsap County (Bremerton) 16Kitsap County (Seattle) 8Kittitas County 33Klickitat County 35Lewis County 50Mason County 23Okanogan County 48Pacific County 45Pend Oreille County 54Pierce County 24Pierce County (Seattle) 17San Juan County 27Skagit County 31Skamania County 44Skamania County (Portland) 23Snohomish County 26Snohomish County (Marysville) 13Snohomish County (Seattle) 13Spokane County 20Spokane County (Spokane) 12Stevens County 30Thurston County 21Thurston County (Olympia–Lacey) 11Walla Walla County 72Walla Walla County (Kennewick–Pasco) 68Whatcom County 28Whatcom County(Bellingham) 11Whitman County 69Yakima County 35Yakima County (Yakima) 7

51

A.3 Demand Estimation Robustness Checks

To vary consumer’s choice set, I set the radius in each county/metropolitan area so that every

census tract within the county/metro has at least X number of firms in it’s choice set. For example,

in Seattle the radius that insures that each consumer has at least 5 firms in its choice set is 5 miles.

Table A2: Demand Parameter Estimates Varying Consumer Choice Sets

(1) (2) (3)

price -0.14681∗∗∗ -0.14516∗∗∗ -0.14521∗∗∗(0.00719) (0.00710) (0.00721)

distance 0.02700∗∗ 0.04841∗∗∗ 0.05109∗∗∗(0.01098) (0.00949) (0.00867)

distance * ln(pop. density) -0.01437∗∗ -0.02475∗∗∗ -0.02570∗∗∗(0.00535) (0.00684) (0.00686)

% THC 0.03746∗∗∗ 0.03694∗∗∗ 0.03699∗∗∗(0.00249) (0.00244) (0.00246)

% CBD -0.20237∗∗∗ -0.19350∗∗∗ -0.19258∗∗∗(0.03479) (0.03373) (0.03376)

% population ≥ 35 0.03641∗∗∗ 0.01431∗∗ 0.01470∗(0.00487) (0.00710) (0.00771)

σ0.16296∗∗∗ 1.6972e-07 1.0294e-07(0.04497) (0.03971) (0.04126)

N 3141 3141 3141

minimum # of firms 5 firms 10 firms 12 firms

Note: Standard errors are reported in parenthesis. ∗∗∗ indicates p <0.01. ∗∗ indicates p < 0.05, and ∗ indicates p < 0.1.

52

A.4 Implied Elasticities and Travel Costs (Block Group)

Table A3: Implied Elasticities and Travel Costs by Quantile

Panel A: Implied Elasticities

Usable Edibles Inhalables

25% -2.96693 -3.33686 -6.1116950% -2.57834 -2.90534 -5.4053175% -2.24873 -2.51649 -4.77237

% |εp,d| < 1 0 0 0

Panel B: Travel Costs ($)

25% $0.3798950% $0.5456975% $0.61238

Table A4: Implied Elasticities and Travel Costs by Quantile

Panel A: Implied Elasticities (Usable Only)

Interior WA WA, OR, ID

25% -3.06199 -2.6858750% -2.67966 -2.3158075% -2.33411 -2.01124

% |εp,d| < 1 0 0

Panel B: Travel Costs ($)

Interior WA WA, OR, ID

25% 0.27163 0.7517450% 0.43246 0.9936575% 0.50208 1.08133

53

A.5 Relationship between ω and Firm Characteristics

This section explores the relationship between unobserved marginal costs (ω) estimated in Section

5.3 and firm characteristics. Because I remove the product categories in the data that do not comprise

a large amount of sales statewide (drinks, topicals, etc.), ω may be generated by unmodeled revenue.

Therefore, I regress unobserved marginal costs against unmodeled revenue (i.e. the difference between

firm’s revenue from just the usable, inhalable, and edible categories and the revenue from all products

the firm sells.). After controlling for jurisdiction or firm effects—along with product and time fixed

effects, the coefficient on unmodeled revenue is not significant.

I also check that unobserved marginal costs are not higher in areas without binding license quotas.

Panel C of Table A6 shows the results of a regression of ω on an indicator equal to one if the firm is

in a jurisdiction with binding license quotas. The coefficient on the indicator variable, while positive,

is not significant.

As ω is an inventory storage cost or shelving cost, ω could be correlated with firm size—a larger

store may be harder to stock because according to I-502, products must be strictly managed in the

stores. Products on display or on sale must be contained in locked glass cases or behind the counter

and can only be handled by store personnel, and products must be handled and stored properly to

keep them from perishing. Therefore, I regress ω on measure of firm size. Panel A of Table A6

displays the results of a regression of unobserved variable cost on store revenue. After controlling for

firm fixed effects, stores with larger revenue tend to have larger ω. Further, Panel B shows the results

of a regression of ω on store square footage. Square footage is associated with higher ω, providing

additional evidence that retail space is related to unobserved costs.

Table A5: Regressions of Revenue from Small Products

revenue from small products 0.0000513∗∗∗ 0.0000193 9.87e-06(0.1146998) (7.25e-06) (6.64e-06)

firm FE N N Yjurisdiction FE N Y N

R2 0.5742 0.7019 0.7787N 3141 3141 3141

Note: All regressions include time and product fixed effects. Robuststandard errors are reported in parenthesis. ∗∗∗ indicates p < 0.01. ∗∗indicates p < 0.05, and ∗ indicates p < 0.1.

54

Table A6: Regressions of Unobserved Cost on Firm Characteristics

Panel A: Revenue

revenue 1.48e-06∗∗∗ -2.95e-07 2.44e-06∗∗∗(3.41e-07) (4.07e-07) (1.20e-06)

firm FE N N Yjurisdiction FE N Y N

R2 0.5672 0.7009 0.7793N 3141 3141 3141

Panel B: Square Footage

ln(sqft) 0.0003805(0.0000876 )

firm FE Njurisdiction FE N

R2 0.6144N 786

Panel C: Lottery Jurisdiction

I(lotto) 0.5065206(0.1523993)

firm FE Njurisdiction FE N

R2 0.5641N 3141

Note: All regressions include time and product fixed effects.Robust standard errors are reported in parenthesis. ∗∗∗ in-dicates p < 0.01. ∗∗ indicates p < 0.05, and ∗ indicatesp < 0.1.

55

A.6 Example of Marijuana Zoning

Figure A.15: Bellevue, WA Zoning Map

Notes: Insert sources of shapefiles here.

A.7 Details of Fixed Cost Estimation

A.7.1 Estimation of Parameters

Typically, fixed cost estimation using moment inequalities involves finding the set of parameters

η that satisfy

arg minη

∑k

(min

{mk(ηo)σk(ηo)

, 0})2

where mk are the sample moments. However, because my fixed cost function is linear, the identified

set of fixed costs is the set which solves the following simple programming problem:

maxη

f · η

s.t. m(η) ≥ 0

56

where f = {[1, 0]; [−1, 0]; [0, 1]; [0,−1]}. This programming problem is solved for every vector in f .

m(η) is a vector of sample moments defined in Section 6.1.2:

m(η) =

−(

1F 1

0

∑f1

0∈F10rnf +1(dnf +1, d−f ; θ)

)1F 1

1

∑f1

1∈F11rf (df , d−f ; θ)

−(

1F 0

0

∑f0

0∈F00rnf +1(dnf +1, d−f ; θ)

)1F 0

1

∑f0

1∈F01rf (df , d−f ; θ)

A.7.2 Calculation of Standard Errors

To compute confidence intervals, I form an evenly spaced grid, and within the grid I take a guess

of the parameter values, ηo = (η1, η2). I then find the mean and variance of the sample moments

evaluated at ηo, and compute

Qn(ηo) =∑k

(min

{mk(ηo)σk(ηo)

, 0})2

where mk(η) is moment condition k and σk(η) is the standard error of the sample moment k. The

mean and variance are normally distributed, so I then bootstrap from the empirical distribution of

the Qn. I then accept the points in the confidence set for which Qn(ηo) falls below the ninety-fifth

percentile of the bootstrapped objective function evaluations. For more specific details I refer to

Andrews and Soares (2010) and the Appendix of Dickstein and Morales (2016).

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A.8 Free Entry v. Restricted Entry

(a) Restricted Entry

(b) Free Entry

Figure A.16: Restricted v. Free Entry Results

58