Learning to Set Prices

Abstract

The authors empirically examine how firms learn to set prices in a new market. The 2012 privatization of off-premises liquor sales in Washington State created a unique opportunity to observe retailers learning to set prices from the beginning of the learning process. Tracking this market as it evolved through time, the authors find that firms indeed learn to set more profitable prices, that these prices increasingly reflect demand fundamentals, and that prices ultimately converge to levels consistent with (static) profit maximization. The authors further demonstrate that initial pricing mistakes are largest for products whose demand conditions differ the most from those of previously privatized markets, that retailers with previous experience in the category are initially better informed, and that learning is faster for products with more precise sales information. These findings indicate that firm behavior converges to rational models of firm conduct, but such convergence takes time to unfold and plays out differently for different firms. These patterns suggest the important roles of firms’ learning and heterogeneous firm capabilities.

Keywords

pricing strategy structural learning entrant behavior alcoholic beverage markets

Pricing is a big question mark, for everyone entering the spirits business in Washington. … [BevMo! CEO Alan Johnson says,] “I sure don't know what we’ll charge the consumer. There is going to be a lot of scrambling.”

—Gregutt (2012)

In classical models of imperfect competition, firms are relentless in their pursuit of profit, infinite in their capacity for computation, and fully informed of underlying economic primitives. The resulting long-run equilibria are well defined but often leave little scope for managerial ability or persistent economic profit. A more behavioralist viewpoint has consistently challenged whether firms in fact reach this efficient ideal (Simon 1955) and emphasized a more central role of firms’ heterogeneous capabilities and persistent competitive advantage (Goldfarb and Xiao 2011; Teece, Pisano, and Shuen 1997). Recent empirical evidence reveals heterogeneous firm performance and large departures from optimality (Arcidiacono et al. 2020; Hortaçsu et al. 2019). Learning models, which maintain the pursuit of optimality but provide a concrete role for information acquisition and process heterogeneity (for a survey, see Aguirregabiria and Jeon [2020]), represent a promising middle ground between these competing viewpoints, illuminating the pathways by which equilibria arise and highlighting sources of at least transitory advantage. But do firms in fact learn and converge to optimal practices? If so, what market features must they infer to get there? And are there meaningful differences in how, and how quickly, they reach the optimum?

Addressing these questions requires empirically characterizing the learning process without assuming whether or how firms actually learn. To do so, we focus on a setting—new category pricing in an established retail channel—that includes both the necessary variation to detect learning and rich enough observable information to characterize optimal behavior (and identify departures from it). In particular, we examine the newly privatized Washington State retail liquor market, where firm prices, market outcomes, and strong proxies for costs can be observed from the market's inception, when firms had incomplete information. Tracking this market as it evolved through time, we demonstrate that firms make significant pricing mistakes upon entry but eventually learn to set profit-maximizing prices; the broad features of the learning process are also consistent with canonical learning models. Our descriptive approach yields new evidence about how firms learn and what they uncover. We find that, though all firms eventually converge to optimal pricing behavior, firm differences in the learning process provide substantial short-term profit advantages over competitors. Notably, these advantages are tied to previous experience, a potential source of dynamic capability. We further find that these information gains accrue from learning nuanced features of consumer demand (e.g., a heterogenous distribution of tastes), a more complex target than is tackled in the firm learning literature (but consistent with its intent).

Our research objectives require an empirical strategy that avoids placing strong assumptions on the form and structure of the underlying learning process. At a basic level, we seek to characterize the empirical relationship between the underlying market conditions (the object of firms’ potential learning) and the individual prices charged (the clearest reflection of their changing beliefs), without specifying ex ante the exact parameter(s) targeted by learning or the mechanism by which such learning takes place. To address this challenge, we exploit institutional features of the Washington liquor market to rule out confounding effects outside of learning. Leveraging both rich demand data and strong proxies of costs, we employ a multistage approach in which the least restrictive assumptions are imposed at each step.

We begin our analysis by documenting that prices display sizable and heterogeneous movements in the first two years after privatization and remain stable thereafter. These transitory, nonstationary price movements are consistent with a wide range of learning models, all of which imply systematic changes in firm behavior due to learning. We also find that the prices of different products (and product types), relative to other states, adjust in different directions, suggesting that firms are learning about the particular tastes of Washington consumers.

We next present two novel pieces of evidence consistent with firm learning about demand. Both build on the notion that learning should manifest through an initial, but eventually vanishing, nonstationarity in the joint distribution between prices and information about demand conditions. First, we show that prices for a given product respond to lagged demand shocks of the product and that the rate of response to these shocks declines steadily over time. We further demonstrate via simulation that this pattern is consistent with both canonical Bayesian (Ching 2010; Hitsch 2006) and adaptive (Doraszelski, Lewis, and Pakes 2018) learning models, in that firms continue learning from the new information contained in sales until they accumulate sufficient experience to adequately infer demand. Second, we show that prices gradually adjust to capture the underlying demand fundamentals—prices increase for products that are popular in Washington and decrease for less popular products. Simulations establish that this pattern is also consistent with Bayesian or adaptive learning: firms learn about demand, identifying products that customers are willing to pay more (or less) for and setting higher (or lower) prices correspondingly. These analyses also reveal that most of the learning occurs early in the sample period. Later in the sample period, firms do not systematically adjust their strategies, suggesting that learning has ceased.

We then present more direct evidence that firm learning in fact converges to optimal practice. Aghion et al. (1991) prove that adequate¹ learning can occur under relatively mild conditions, although it is not universally guaranteed. How long learning takes and whether firms, in practice, reach optimality are empirical questions. Our approach to answering both is to first recover consumer demand (the “target” of learning) and then evaluate whether firms’ eventual pricing behavior converges to the short-run maximum given this target. To do so, we employ a flexible random coefficient demand model (Berry, Levinsohn, and Pakes 1995) that includes aggregate and micro-level moments to pin down substitution patterns. We find that the resulting parameter estimates and implications regarding preferences accord well with existing evidence on demand in related liquor markets (Conlon and Rao 2019; Miravete, Seim, and Thurk 2018).

We then impose two conditions regarding observed steady-state behavior, namely that firms have reached full information by the last half year of our sample (four years into the new market) and, once at full information, prices are set to maximize static profits. These conditions allow us to recover firms’ marginal costs. The external validity of these conditions is demonstrated by showing that prices stabilize and that the costs implied by these prices (under static profit maximization) closely match our best-available proxies: state-owned retailers’ wholesale prices in Washington before the privatization and in neighboring Oregon over several periods. The finding that prices have converged to the optimum suggests that systematic departures from this optimum are indeed transitory and eventually eliminated by learning.

We next use the structural model estimates to simulate a counterfactual benchmark against which to contrast observed firm behavior. This exercise allows us to compute the gap between full-information and limited-information prices and quantify the economic importance of learning. We hereafter refer to prices’ deviations from the optimum as “mistakes,” noting that they might be actual pricing mistakes due to limited information or might represent retailers’ strategic experimentation to acquire information.² We find that, at the median, prices in the first quarter are 9% above the full-information optimum and that these mistakes lead to 9.3% lower profit. However, retailers are quick to learn: they adjust prices and close one-third of the profit gap within a quarter and another one-third within the next six quarters.

We finish with some descriptive evidence on the nature of firms’ pricing mistakes and the underlying learning process, framing the discussion within the context of canonical learning models. In particular, Bayesian learning implies an optimal weighting of prior beliefs and new information, with weights tied to each component's information precision (inverse variance). As a result, the Bayesian firm will lean on the prior when it is more precise (e.g., when the firm has more experience) and will lean on the signal when it is more precise. Consistent with this prediction, we demonstrate that the learning rate (the rate at which firms correct pricing mistakes) decreases with firms’ accumulated experience in Washington, decreases with their experience in other markets prior to entering Washington, and increases with the precision of new information from realized sales quantities. Together with the finding that retailers achieve optimality, we find that the Bayesian learning framework (Ching 2010; Hitsch 2006) presents a credible depiction of retailer price adjustments in this new market.

Our evidence also highlights two important aspects of learning in this market. First, firm differences in learning can support short-term profit advantages, and such learning appears to transfer between contexts (different markets where demand primitives differ). This provides additional empirical support for the profit impact of dynamic capabilities and firm heterogeneity (Goldfarb and Xiao 2011; Teece, Pisano, and Shuen 1997). Second, in this context at least, firms appear capable of learning a fairly high-dimensional target, namely the distribution of consumer tastes for different product types. This finding suggests a high degree of managerial sophistication and capability. In particular, it implies a more sophisticated process than either descriptive pricing research (Noble and Gruca 1999) or adaptive learning models suggest, and a more complex target than canonical Bayesian learning models presume (likely reflecting model tractability).

Our article contributes most directly to a recent firm learning literature aimed at relaxing the rational expectations assumption and the Bayesian requirement that firms weight information optimally. Jeon (2020) examines firm investment decisions in the container shipping industry, where firms adaptively learn about the level of demand from historical data. Without assuming that firms use optimal information weights, she finds that an adaptive learning model that overweights recent information best explains firm behavior. Doraszelski, Lewis, and Pakes (2018) study firm learning about demand and equilibrium competitor behavior. They estimate a model where firms adaptively learn about demand (firms estimate demand with all available information) and learn about competitor actions using fictitious play. Covert (2015) finds that firms in the hydraulic fracturing industry overweight their own information, compared with public information from other firms. Li and Ching (2021) study how Prosper, an online lending platform, adapts to changes in the marketplace. They consider a class of data-selection algorithms (where one uses recent data to learn adaptively about the market primitives) and find that one algorithm best explains Prosper's actions. Our empirical strategy differs from these papers in that we aim to describe how firms learn without assuming the learning mechanism (and, as a result, without estimating a learning model). Instead, we measure learning through the evolution of the covariance between prices and demand primitives.³ Even in the absence of a learning model, we demonstrate that how prices converge to the optimum is most consistent with canonical Bayesian updating.

Our article is also closely related to the Bayesian firm learning literature (Ching 2010; Hitsch 2006; Huang, Luo, and Xia 2019), which structurally characterizes firms’ dynamic entry, exit, and pricing decisions with Bayesian learning. Our finding, that firms’ learning about demand is broadly consistent with Bayesian updating, provides support for these models. However, whereas this literature characterizes firm learning about product (or product-category) quality, our empirical finding presents a case where firms must learn about nuanced segmentation patterns of the demand function.⁴

Broadly, our research also speaks to the literature on pricing practices. Several previous studies use surveys and interviews to learn how managers make pricing decisions (see, e.g., Kaplan, Dirlan, and Lanzillotti 1958; Noble and Gruca 1999) and find that managers rely on suboptimal heuristics such as “cost-plus” pricing. Consistent with this view, a collection of recent empirical evidence suggest bounded rational pricing by supermarkets (Arcidiacono et al. 2020; DellaVigna and Gentzkow 2019) and other firms (Hortaçsu et al. 2019). Our findings demonstrate that (at least in our context) supermarkets can learn to set optimal prices, but the process takes time and is heterogeneous across firms.

Finally, our article connects to recent literature on the regulation and privatization of the liquor industry per se. Conlon and Rao (2019) and Miravete, Seim, and Thurk (2018, 2020) examine the impact of tax policy and market structure on upstream competition, optimal taxation, and consumer welfare, respectively. Aguirregabiria, Ershov, and Suzuki (2016) study regulation and tax regimes in the Ontario wine market. Seo (2016) and Illanes and Moshary (2018) leverage Washington State's liquor privatization to study, respectively, the value of one-stop shopping and the impact of market structure on prices and product variety.

The rest of the article is organized as follows. In “Context, Data, and Sample Construction,” we describe the institutional background, data sources, and sample construction. “Learning About Demand: Descriptive Evidence” provides descriptive statistics about price movements in the privatized market and presents key reduced-form evidence of retailer learning. In “Model: Demand and Costs,” we employ a structural model to infer demand and recover costs. In “Empirical Characterization of the Learning Process,” we use the structural estimates to evaluate the optimality of firm behavior, explore the moderators of the learning process, and discuss what they reveal about the learning mechanism and firm capabilities. Finally, we conclude with suggestions for further research.

Context, Data, and Sample Construction

The 2012 privatization of off-premises liquor sales in Washington State provides a unique opportunity to observe how retailers learn to set prices from the point at which that learning process begins. The liquor category itself is not new to the market, which both limits the scope of confounding factors, such as consumers’ learning about their own preferences (as would occur with the introduction of entirely new products) or manufacturers’ uncertainty about product quality, and provides a sharper focus for our analysis. In this section, we provide institutional background on the Washington liquor market both before and after the privatization, and then we describe the data we assemble to examine the learning process.

Institutional Setting

Given the strong association with negative health and societal outcomes, the production and distribution of distilled spirits in the United States have been strictly regulated since the repeal of prohibition in 1933. The regulation of retail sales generally takes one of two forms. In “control” states, sales take place directly through a monopoly of state-owned outlets, sometimes referred to as “package stores.” To raise tax revenue and reduce consumption, most control states impose a large and fixed markup over cost in setting shelf prices, levying additional taxes per volume of ethanol. In “license” states, the government grants individual firms the right to sell alcohol in their own retail outlets. While shelf prices are generally left to the discretion of these independent firms, most states impose an ad valorem tax on revenue and a specific excise tax on ethanol to reduce consumption and collect revenue.

Before June 2012, Washington was a liquor control state with a fixed retail markup of 51.9% and a specific tax of $3.77 per liter. Following the passage of Initiative 1183, the state-owned chain was replaced by privately owned retailers, licensed by the state. The new policy prioritized the issuance of retail liquor licenses for “existing grocery premises licensed to sell beer and/or wine,” and further stipulated that retail licenses only be issued to outlets with at least 10,000 square feet of floor space. The initiative also mandated a retailer licensing fee of 17% of liquor revenue and an increase in retail off-premises sales taxes from 10% to 20.5%. In addition to these ad valorem taxes, the specific tax remained at $3.77 per liter.

As in other states, Washington adheres to a three-tier alcohol distribution system, in which manufacturers may sell to retailers only through licensed distributors. The new policy in Washington affects only retail distribution and does not alter the distributor side of the market. In addition, the new policy only affects liquor (i.e., distilled spirits), as licensed retail wine and beer sales were already permitted under existing law.

The focus on licensing existing grocery premises motivates our use of the Nielsen Retail Measurement Services (RMS) data set for our empirical analysis, as this database provides good coverage of the grocery, drug, and mass merchandise channels that constitute the grocery market. Moreover, the fact that these retail channels are already mature and well established also partly mitigates concerns regarding changes in market structure. We further leverage two additional institutional details in constructing our data set and carrying out our empirical analyses. First, liquor products are visibly distinguished and marketed by category. The main liquor categories include whiskey, gin, rum, tequila, and vodka. Because very little substitution exists across product categories, pricing is generally done on a category-by-category basis (Conlon and Rao 2019). Therefore, to maintain tractability and allow for flexible substitution across products within a category, we focus on a single liquor category: whiskey products. Whiskey is the largest category by sales volume and includes a rich variety of products that are differentiated both horizontally (e.g., bourbon, Scotch/Irish, and Canadian) and vertically (Johnnie Walker Red vs. Blue).⁵ Second, as has been shown to be the case with most consumer packaged goods (DellaVigna and Gentzkow 2019; Hitsch, Hortaçsu, and Lin 2021), Washington State retailers set uniform prices across stores, within each product, at a given point in time. In our structural analysis, we will exploit this regularity when inferring costs from observed pricing behavior. Further documentation of these patterns is provided in Web Appendix A.

Data

As noted, our primary data source is the Nielsen RMS data set. We focus on the whiskey category in Washington State, primarily from June 2012 (the month of privatization) until the last quarter of 2016.

For some analyses, we supplement the Nielsen data from Washington State with auxiliary information from other states or data sources. First, in some descriptive analyses, we compare Washington to other license states in which retailers have up to several decades of experience with private retail grocery liquor sales. The Nielsen data include 15 such states or jurisdictions (in descending order of total liquor sales volume): California, Arizona, Louisiana, New Mexico, Nevada, Texas, Nebraska, South Dakota, Wyoming, Colorado, Delaware, Arkansas, Maryland, North Dakota, and the District of Columbia. Second, we use posted (control-state) retail prices from Washington and Oregon to help estimate and validate the wholesale prices inferred from our structural analysis. State-run outlets in Washington before privatization and in Oregon throughout the entire sample period followed fixed markup policies (with Oregon markup fixed at 104%), allowing us to directly calculate wholesale prices (retailer costs) from their posted shelf prices. Finally, we also use Nielsen consumer panel data between December 2009 and December 2016 to examine consumer behavior in greater detail and to construct micro-moments (Petrin 2002) for use in the structural demand estimation.

Sample Construction

We apply three filters in constructing our sample. First, as noted, we narrow our focus to a category within liquor, the broad whiskey category. This category is sizable, has little substitution with other categories (e.g., vodka, tequila), and offers the most product diversity, including distinct whiskey types such as single-malt and blended scotch, Canadian whiskey, American bourbon and rye, and American whiskey. This filter simplifies our analysis and allows us to focus on firms’ learning. This filter yields a data set containing 724 unique Universal Product Codes (UPCs) and 635 unique product names (some products are available in multiple sizes), with a sample size of 6,288,941 observations at the UPC-retailer-store-week level in Washington State.

Second, we restrict our attention to a stable set of stores during our sample period to avoid store entry and exit unrelated to the liquor category (during which prices may be poorly measured or nonrepresentative because of stockouts or closeout sales). We select stores that sell a positive quantity in at least 95% of all weeks. This filter selects 561 of 625 stores and removes 5.9% of the observations from the overall sample.

Third, we filter out products that enter and exit during the period to focus on “core assortments,” which contain the bulk of liquor revenues and profits. Within a given retailer, we select those products that first appear before December 2012, last appear after March 2016, and remain present for at least 25 weeks. This filter selects 276 of 724 UPCs and eliminates newly introduced products, discontinued products, and products that are only occasionally or seasonally offered. Although it might appear that we eliminate many UPCs in this step, the products we drop account for only 15.8% of the observations and 11.4% of the total revenue from the previous filter. We discuss the choice of focusing on these core products in more detail in Web Appendix B.2. After these sample selection steps, our sample contains 4,985,621 observations, from 276 products, six retailers, and 561 stores. In Web Appendix B we present further sample adjustments to facilitate our structural analysis. Specifically, there we simplify to focus on (1) the most popular size, 750 mL bottles, (2) products with high-enough sales to ensure precise market share measurements, and, for the supply side analysis, (3) the period of stable demand for the three largest retailers, which represent 80% of sales revenue (see Web Appendix B for further rationale and details).

Learning About Demand: Descriptive Evidence

In this section, we present our initial descriptive evidence of firm learning. We begin by outlining a conceptual framework that characterizes firm learning about demand. This conceptual framework yields three testable predictions, focusing on key features of the joint distribution of prices and quantities and how these sample features transition over time. We empirically examine these predictions in Washington after privatization and present novel empirical evidence of firm learning about demand.

We first show that prices do in fact change within the first two years after privatization and then stabilize, and that the directions and magnitudes of these changes differ across products. These patterns are consistent with retailers learning demand conditions in the early period, and with this learning eventually ceasing. Second, we demonstrate that prices immediately begin reacting to realized quantity shocks as retailers start selling liquor in Washington, but that, over time, they adjust less and less to these shocks. Third, we show that the price of a product increasingly reflects its demand fundamentals (e.g., whether the product is especially popular or caters to a price-insensitive customer segment). This evidence suggests that retailers steadily acquire information about demand fundamentals, and the prices they set increasingly reflect their refined information. We also present placebo tests that replicate these descriptive exercises in other states in which retailers sold liquor for many years prior to 2012, and demonstrate that these comparison states do not exhibit such evidence of learning.

Our case for learning turns on the claim that firms gradually acquire new knowledge about demand, and this new information is reflected in the changing prices we observe. It is therefore important to rule out the possibility that demand (or the environment) itself is changing, so that firms might instead be reacting to these changing conditions. If the environment exhibits ongoing nonstationarities, the price adjustments we observe could reflect firms’ rational expectations adjusting to reflect these changes, rather than (initially) biased perceptions adapting through learning. To evaluate this possibility, we provide evidence that consumer tastes are not changing, that the competitive landscape and upstream (distributor) behavior are stable, and that most other retailer strategies remain relatively fixed over this period.

Conceptual Model

To fix ideas, we first present a simple conceptual model that motivates our initial set of testable implications. This is not the structural model we later estimate, but rather a stylized representation intended to highlight the key intuitions. Consider a single firm that produces J products, with each product $j$ facing stable demand given by the linear function

q_{jt} = β_{j} + α_{j} p_{jt} + ξ_{jt},

(1)

in which each product has its own intercept

β_{j}

and price sensitivity parameter

α_{j}

. The product-specific intercept captures each product's popularity in the new market, and the product-specific price sensitivity captures the different customer segments that each product caters to. Implicitly, there is no substitution between products (in this stylized abstraction), and prices are set independently based on the firm's belief about each product's demand. We further assume that the demand shock

ξ_{jt}

is realized after prices are set and that the marginal cost of each product is a constant

c_{j}

The firm forms beliefs about demand parameters $(β_{j}, α_{j})$ , which are denoted $F_{jt}$ . After prices are set, $ξ_{jt}$ is realized, and the firm observes the total quantity $q_{jt}$ at the end of the period (but does not observe the parameters of the demand function directly). Throughout the article, we remain agnostic about how the firm updates its information set $F_{jt}$ , other than assuming that all firms eventually learn fully about demand (this is in line with Aghion et al. [1991] in that, if the demand function is smooth or analytic, both of which are satisfied here, adequate learning is guaranteed). In Web Appendix C, we develop a special case where the firm updates its beliefs $F_{jt}$ in a Bayesian manner (where it optimally incorporates all past information) and sets static-optimal prices given its belief. We also demonstrate that model predictions are similar in two alternative cases, where the firm (1) estimates demand adaptively using all available data, without a prior (as in Doraszelski, Lewis, and Pakes 2018), and (2) updates $F_{jt}$ in a Bayesian manner while also conducting price experiments.

To be clear, we do not assume that firms employ any particular form of learning in our empirical analysis. However, these numerical examples provide a point of reference to complement and motivate our empirical findings.

Price Changes After the Privatization of Liquor Sales

Our first hypothesis is that, if firms learn about demand in the new market, one should expect the distribution of prices to adjust in a nonstationary manner. It is straightforward to show that our conceptual model would exhibit such a pattern. We now examine how the average Washington whiskey price changes upon privatization and over time. To facilitate comparison to other states, we focus on 65 popular 750 mL products that are available both before and after privatization and compute the average sticker (pretax) prices using time-invariant quantity weights. Panel A of Figure 1 shows a sharp, 41% increase in the average price upon market privatization, followed by a gradual decrease in the next two years that eventually stabilizes to a mild time trend.

Figure 1.

Price changes over time and between Washington and other states.

Next, we examine whether such price changes differ across products. To account for possible (mild) cost changes we focus our analysis on the ratio of the average price of each product (product-retailer-half year) in Washington to the average across the other 15 states, ${\tilde{p}}_{jrt} = {\bar{p}}_{jrt}^{WA} / {\bar{p}}_{jt}^{other}$ , normalizing this ratio by its initial value, $({\tilde{p}}_{jrt} - {\tilde{p}}_{jr t_{0}}) / {\tilde{p}}_{jr t_{0}}$ , to facilitate comparison across products and retailers. We plot quantiles of these normalized prices over time in the right panel of Figure 1. We find that the bulk of the Washington price changes relative to those of other states occur in the first two years after privatization. During this period, not only does the median price go down by more than 5%, but there is a large dispersion in how prices change for individual products. Consistent with learning about demand, the systematic departure of Washington prices from other states’ prices occurs soon after the new market opens, and observed price changes are heterogeneous across products.

Price Response to Lagged Demand Shocks

Our second testable hypothesis is that, if retailers learn about stable demand through the information contained in sales quantity shocks, they will initially adjust prices in the direction of demand shocks, but cease doing so once they are sufficiently informed. We first illustrate how this prediction plays out in the simulated environment of our conceptual model, where the firm updates its beliefs $F_{jt}$ in a Bayesian manner (the specifics of this learning process, and alternative learning processes, are detailed in Web Appendix C).

Using this conceptual model, we now show that prices respond to the firm's unexpected lagged quantity $q_{jt - 1} - E (q_{jt - 1} | p_{jt - 1}, F_{jt - 1})$ , with the response diminishing over time. Initially, the demand function is uncertain to the firm. If the realized quantity is higher than expected, the firm will attribute part of this realization to a signal of higher-than-anticipated product quality (higher $β_{j}$ ) or a less price-sensitive customer base (higher $α_{j}$ ) than previously expected and, thus, update its beliefs and raise the product's price. If the realized quantity is lower than expected, the firm should adjust its beliefs, and the price, in the opposite direction. However, as demand uncertainty resolves through learning, the firm will eventually attribute all of the unexpected quantity realization to the idiosyncratic demand shock $ξ_{jt}$ .

We demonstrate this intuition in Figure 2, Panel A. If the firm learns about demand over time, prices (reflective of firm beliefs) respond positively to the unexpected quantity. In addition, as uncertainty is resolved over time, prices eventually stop responding to unexpected quantity. The ideal testable implication would examine realized quantities relative to the firm's expected quantities (as previously), but in reality firm beliefs are unobserved to the researcher (without further strong assumptions). Thus, Panel B of Figure 2 uses the same Bayesian learning example to demonstrate that simply regressing changes in price on changes in lagged quantity will yield a similar pattern, albeit with attenuated regression coefficients (as lagged quantity is effectively a noisy signal of the ideal measure).⁶

Figure 2.

Price adjustments and lagged unexpected quantity: simulation under Bayesian learning.

Turning now to the actual data, we now present evidence of firm learning in line with the intuition in Figure 2, Panel B (where we proxy the firm's unexpected sales quantity with past quantity shocks). We demonstrate that past quantity shocks indeed have significant initial informational content for Washington retailers and that this information effect is eventually exhausted. To document these patterns, we estimate a linear model of how the current price is correlated with the lagged sales quantity, conditional on various controls and fixed effects. Denoting j as a product, $r$ as a retailer, and $t$ as a month, we estimate a linear model of the current price on one-month lagged quantity, controlling for current quantity and lagged prices:

\log (p_{jrt}) = β_{τ} \log (q_{jrt - 1}) + ρ \log (p_{jrt - 1}) + α^{- 1} \log (q_{jrt}) + ψ_{jr} + ϕ_{t} + η_{jrt} .

(2)

Our key parameter of interest is the sensitivity of the current price to

\log (q_{jrt - 1})

, the units sold for product

j

by retailer

r

in the previous month,

t - 1

. We allow

β_{τ}

to take a different value for each half year. Our controls capture stable product-retailer characteristics (

ψ_{jr}

), common variations within a month (

ϕ_{t}

), serial correlation in prices (

ρ

), and the inverse demand elasticity (

α^{- 1}

). For estimation, we take first differences within each product-retailer and employ the standard instrumental variable approach from the dynamic linear model literature (Arellano and Bond 1991).⁷

Figure 3 plots the estimates of $β_{τ}$ and corresponding confidence intervals. We find that in Washington, prices respond to the previous month's sales quantity positively and significantly in the early periods. We also find that the effect decreases over time until it is less than a third of the initial response. Thus, retail prices incorporate past sales shocks, but decreasingly so. This finding is consistent with retailers learning about demand by incorporating information contained in realized sales quantities. This pattern for Washington State stands in sharp contrast to what we find for the states where retailers already have extensive experience in the liquor market. In these states, the responsiveness to sales shocks is much smaller, centered close to zero, with most coefficients statistically insignificant. Thus, for retailers with greater experience, prices do not respond to past sales shocks.

Figure 3.

The response of current price to lagged quantity.

Prices’ Correlation with Demand Fundamentals

Our third testable hypothesis is that, if firms start with incorrect beliefs about demand but learn over time, these beliefs and the prices they set based on them should increasingly reflect (true) demand fundamentals. Relative to a given prior belief, prices for products that have (surprisingly) high demand will tend to rise to reflect that higher demand, and prices for (surprisingly) low-demand products will fall. The end result is that the prices charged and quantities sold should become increasingly correlated as retailers learn about demand. Thus, learning should be reflected in a clear pattern of increasing covariation between prices and the underlying demand fundamentals.

In the conceptual model of Equation 1, the static optimal price given belief $F_{jt}$ is $p_{jt} = - \frac{E (β_{j} | F_{jt})}{2 E (α_{j} | F_{jt})} + \frac{c_{j}}{2}$ , a simple function of the firm's belief about demand ( $E [(β_{j}, α_{j}) | F_{jt}]$ ). If retailers initially set prices based on noisy beliefs over the demand primitives, their initial prices will only partly reflect these constructs. However, if their beliefs in fact converge toward the truth via learning, $E [(β_{j}, α_{j}) | F_{jt}] \to (β_{j}, α_{j})$ , observed prices will increasingly capture these demand primitives. Our second numerical exercise illustrates that, in a case where the retailer learns about the linear demand function via Bayesian updating, observed prices will become increasingly correlated with the optimal markup $- \frac{β_{j}}{2 α_{j}}$ (eventually reaching the limit of 1). If the researcher knows demand primitives and can compute optimal prices, the way prices converge to optimal prices (or markups) provides a direct test of learning, as demonstrated in Figure 4, Panel A.

Figure 4.

Price and demand fundamentals: simulation under Bayesian learning.

The conventional approach is to estimate the demand primitives and evaluate the extent to which prices capture these primitives. We present a new descriptive test that does not rely on ex ante demand estimates. The idea is to estimate the cross-sectional relationship (i.e., ignoring the product fixed effects) between prices and sales quantity in each period and evaluate how this estimated relationship changes over time. For example, with the linear demand in Equation 1, a cross-sectional regression would group product-specific quality and price sensitivity into the error term:

q_{jt} = {\bar{β}}_{t} + {\bar{α}}_{t} p_{jt} + \underset{error term, correlated with price}{\underset{⏟}{β_{j} - {\bar{β}}_{t} + (α_{j} - {\bar{α}}_{t}) p_{jt} + ξ_{jt}}} .

(3)

When the firm sets profit-maximizing prices that incorporate some (though not necessarily all) information about the demand primitives, one should expect prices to reflect underlying product quality or positioning (Trajtenberg 1989), and, as a result, estimates that rely on cross-sectional variation in price and quantity between products will yield a price-sensitivity parameter estimate that is biased upward. In addition, as the firm learns about demand, its beliefs should reflect the true demand fundamentals more strongly, intensifying the price-endogeneity bias in the cross-sectional regression. Therefore, if firms learn about demand over time, the full extent of bias will not show up right away, but will progressively develop as prices gradually incorporate the demand fundamentals. When learning is complete, this correlation should stabilize, as will the estimates of these (now fully biased) coefficients. Conversely, if learning does not occur, this correlation should instead be stable from the start. In the simulated example where the firm learns via Bayesian updating, we report the estimated

{\hat{\bar{α}}}_{t}

over time. Figure 4, Panel B, shows that these estimates reflect an increasing endogeneity bias (the true average price sensitivity is −.5) and closely track the pattern in Figure 4, Panel A, where the researcher observes the true demand (and optimal markups).

We now implement this test in our empirical context. Using data at the product-retailer-week level, we regress quantity on price, estimating the price coefficient ${\bar{α}}_{τ}$ for each six-month time window ( $τ$ ), while controlling for retailer-week fixed effects but not product fixed effects. Thus, following the classic omitted-variable bias formula, the estimated price coefficient ${\hat{\bar{α}}}_{τ}$ will be the true slope of demand plus any bias due to the way prices capture unobserved demand primitives.⁸ We report the estimated $α_{τ}$ values and corresponding standard errors for the Washington sample in Figure 5. We also examine retailers in other states as a placebo test, but with one change to account for including multiple states: we include retailer-state-week fixed effects.

Figure 5.

Coefficient estimates of $α_{τ}$ from Equation 3.

In Washington, we find that retail prices show increasing correlation with demand primitives, reflected by the way ${\hat{α}}_{t}$ increases from 2012 to 2015. If the underlying price sensitivities are stable over time, this finding suggests that retailers set prices with more and more information about demand, so that the price sensitivities are biased more and more toward zero. In addition, ${\hat{α}}_{t}$ stabilizes in the second half of the sample, suggesting that most of the learning occurs in the first two years after the market opens and that, after this initial period, there is no systematic learning that changes how prices reflect demand fundamentals. In contrast to the finding in Washington, we find that other states’ ${\hat{α}}_{t}$ values are stable over the full time period, consistent with experienced retailers in the existing liquor markets being fully informed (i.e., no longer learning about demand in systematic ways).

A slightly different explanation of this finding is that retailers strategically experiment with prices to acquire information. These experiments add noise to prices and result in the initial ${\hat{α}}_{t}$ being less biased. As retailers become more informed about demand, they experimentally vary prices less, resulting in a larger bias in ${\hat{α}}_{t}$ for the later periods. As discussed previously, this article does not distinguish whether retailers learn by passively observing demand or by engaging in strategic experimentation to acquire information. Both types of learning are consistent with this evidence.

Throughout this section, we have demonstrated that Washington liquor prices evolve in a nonstationary fashion, are positively correlated with realized sales shocks, and increasingly reflect sales levels for each product. We have also demonstrated that these patterns occur in Washington but not in other states, and mainly in the first two years after the start of the new market. These patterns collectively suggest that retailers learn about demand and adjust their prices accordingly in the new Washington market.

Alternative Explanations to Learning About Demand

We claimed at the outset that the most probable source of the nonstationary movements in prices we observe in Washington State is retailers’ initial uncertainty over stable demand primitives. We turn now to justifying this assumption. Of primary concern is the possibility that other features of the environment could be changing at the same time, and thus confounding the main evidence of learning—that the joint distribution of price and quantities exhibit nonstationary movements in the early periods after privatization in Washington. In this section, we consider four such confounds, namely: (1) changes in consumer demand, (2) changes in the competitive market structure, (3) changes in distributors’ behavior, and (4) changes in other retailer strategies. We account for the impact of cost changes later (see “Wholesale Prices [Retailers’ Marginal Costs]”). Here, we provide evidence that these alternative mechanisms are not of first-order importance in our setting. This section outlines the main findings, with Web Appendix B providing further detail.

Stable consumer demand and store traffic

First, it is important to rule out systematic changes in consumer behavior after privatization. On the one hand, if consumers gradually learn about the set of products or search for low-price products, they might appear to be increasingly price sensitive over time. In this case, the observed price adjustments might be responses to changes in consumers’ price sensitivities, instead of responses to firms’ having better information about demand. To address this possibility, we estimate a simple log-log demand curve with a rich set of fixed effects. We find little changes in the slope of demand before and after 2014, suggesting that consumers’ price sensitivity remains stable. We also examine whether demand levels are different over time, using our later structural estimates. We find little variation over time both in the demand intercepts and in the variance of demand shocks. We present details of these analyses in Web Appendix B.1.

On the other hand, optimal liquor pricing might be dynamic if consumer demand is inertial (Dubé, Hitsch, and Rossi 2010), or if consumers take advantage of sales to stockpile liquor (Erdem, Imai, and Keane 2003; Hendel and Nevo 2006), or if liquor prices affect persistent consumer store traffic. Using Nielsen Homescan panel data, we find no evidence of first-order state dependence (see Web Appendix Table W.8), little evidence in support of consumer stockpiling (see Web Appendix Table W.1), and no evidence that some retailers’ carrying liquor in 2012 affects consumer store traffic (see Web Appendix Table W.3). These findings suggest that optimal prices should maximize static liquor-category profit for each retailer.

No retail competition in liquor sales

Next, it is important to examine the extent of competition in the Washington retail liquor market and potential changes in the competitive market structure. If retailers face intense competition in the liquor market, they might be learning about competitor behavior instead of consumer demand. We begin by demonstrating that liquor customers are part of the installed grocery customer base (instead of a stand-alone market). We further show in Web Appendix B.3 that the demand for a given product has negligible substitution between local retailers—consistent with the finding by Illanes and Moshary (2018) that local retail market structure does not affect Washington liquor prices. This evidence suggests that competition between chains is not a salient aspect of pricing in the liquor market. We proceed by assuming that retailers are aware of this fact from the start and do not use price setting to learn about competitor behavior (or in response to it).

Passive distributors

Third, one might wonder whether liquor distributors change their behavior after the retail privatization. Whereas we do not have data on actual wholesale contracts, we conducted a series of interviews to better understand the degree of coordination and strategic interaction along the vertical channel. The complex nature of the three-tier system and its challenges for upstream information flow, in particular, came up repeatedly in these interviews. A common theme was the passive nature of the middle tier (distributors), which apparently follow simple pass-through strategies that follow the lead of the (more informed) manufacturers. For example, one respondent characterized the distributors as “not very economic or demand driven.”

We further examine the impact of the Washington State wholesale liquor market's privatization in January 2012 (Senate Bill 5942). We explore how this change in the upstream affects the state retailer's wholesale prices up to the point of retail privatization. If distributors actively set wholesale prices based on market conditions, observed wholesale prices should exhibit a discrete jump after the distribution system is privatized and competing distributors enter the market. We demonstrate in Web Appendix Figure W.14 that the average wholesale price ticks up by about 2% in 2012 (compared with 2011), a modest change compared with the 41% retail price jump at the point of retail privatization. We interpret the result as consistent with our interviews, in which practitioners describe distributors as passive.

Other retailer strategies: Promotion, features, displays, and assortment

Finally, retailers might change other strategies as they learn about consumer demand. We document a lack of systematic changes in price promotion strategies during the sample period (see Web Appendix B.2), suggesting that the observed systematic changes in prices mainly come from regular prices. We also show that feature promotion strategies remain stable, although retailers put fewer products on display in the second half of the sample. Nonetheless, our estimated demand suggests that features and displays play a minor role in explaining consumer demand. Further, as discussed previously, we focus on 276 “core” assortments in the empirical analysis, which are sold throughout the sample period and account for 88.6% of retailer revenue. Therefore, although retailers do adjust assortments over time, the changes pertain primarily to low-revenue products that have a limited influence on retailer pricing and profitability.

Model: Demand and Costs

Having presented several pieces of model-free evidence that prices are updated in a manner that increasingly reflects stable underlying demand primitives, but eventually settles into a stable process, we now propose a structural model of consumer and firm behavior. The goal of this modeling framework is to both provide additional evidence of firm learning and quantify its economic importance, as well as to further illuminate the mechanisms by which learning occurs and the moderators of its success. We start by proposing a model of consumer demand, which we use to recover the primitive components of consumer preferences that firms are purportedly learning about. Importantly, estimating the demand system characterizes the target of learning and does not require a model of firm behavior.

We then propose a benchmark supply model of how firms should behave under full information. We leverage this model and the fact that prices appear to converge by the end of the sample period to infer the implied costs that those firms must be facing. In doing so, we assume that firms are fully informed rational maximizers at the end of our observation period (but not necessarily earlier). We later validate this assumption by comparing the implied costs to the best available proxies. We find that these measures accord closely. This close correspondence indicates that firms eventually learn to set prices (nearly) optimally. Having concluded that firms indeed learn to price, we then turn, in the two remaining sections, to quantifying the economic importance of learning, exploring how the initial stock and later flow of information shapes the learning process, and identifying the key features of demand about which firms appeared to be most miscalibrated.

The Demand for Liquor

We assume that demand for liquor is characterized by a standard random coefficient logit model, and we estimate its parameters via established nested fixed point methods that incorporate micro-moments to identify heterogeneous demand parameters (Berry, Levinsohn, and Pakes 1995; Nevo 2001; Petrin 2002). We allow preferences to be heterogeneous along two dimensions. First, to accommodate consumers’ self-selecting into a broad range of vertically differentiated whiskey products, we allow for heterogeneity in the price coefficient (operating partly through consumer income). Second, since the whiskey category comprises several distinct whiskey types (e.g., scotch whiskey, American bourbon and American whiskey, and Canadian whiskey) that are clearly targeted to different demographic groups, we allow the tastes for these whiskey types to also vary by income.

We estimate liquor demand at the level of retailer $r$ , three-digit zip code (market) $m$ , and month $t$ . Consumer $i$ comes to the retailer to buy groceries and derives utility from purchasing whiskey product $j$ :

u_{ijrmt} = γ_{ki} + α_{i} p_{jrmt} + x_{jrmt} β + δ_{jrm} + λ_{rt} + ξ_{jrmt} + ε_{ijrmt} .

(4)

In this equation,

γ_{ki}

represents whiskey type

k

and household

i

specific intercept, where

k

takes 1 (American bourbon and rye), 2 (Canadian whiskey), or 3 (Irish whiskey and scotch). The baseline type is American whiskey (e.g., Jack Daniels).⁹ The parameter

α_{i}

represents household-specific price coefficients. These parameters capture heterogeneity in the tastes for liquor types and sensitivities to prices across households. The variables

x_{jrmt}

indicate if the product is on feature and/or display, not on feature/display, or the feature/display status is unknown. Next,

δ_{jrm}

are product-retailer and retailer-market fixed effects capturing tastes for different products, which could differ across shoppers frequenting different retailers or residing in different markets, and

λ_{rt} = λ_{ry}^{1} + λ_{t}^{2}

are retailer-year and month fixed effects, which capture changes over time in the demand for liquor in grocery stores. Finally,

ξ_{jrmt}

captures unobserved characteristics or demand shocks, and

ε_{ijrmt}

are type 1 extreme value utility shocks. If the consumer does not buy any liquor in the given trip, the consumer’s utility is normalized to

u_{i 0 rmt} = ε_{i 0 rmt}

The consumer chooses among products from a given retailer, that is, from the choice set $J_{rmt}$ . This choice set includes products from the focal retailer only, in line with our supporting evidence that consumers do not substitute between local retailers (thus, retailers effectively act as monopolists over their own store traffic). Given this structure, the market share within a retailer-market is an integral of logit choice probabilities over the included random coefficients,¹⁰

\begin{aligned} s_{jrmt} = \int s_{ijrmt} dF (α_{i}, γ_{i}) \\ = \int \frac{\exp (γ_{ki} + α_{i} p_{jrmt} + x_{jrmt} β + δ_{jrm} + λ_{rt} + ξ_{jrmt})}{1 + \sum_{j^{'} \in J_{rmt}} \exp (γ_{k^{'} i} + α_{i} p_{j^{'} rmt} + x_{j^{'} rmt} β + δ_{j^{'} rm} + λ_{rt} + ξ_{j^{'} rmt})} \\ \times dF (α_{i}, γ_{i}) \end{aligned} .

(5)

As noted previously, a key feature of the whiskey category is sharp (horizontal and vertical) differentiation by spirit type. To capture this aspect in the model, we parameterize the household's preferences toward whiskey type

k

as a function of log household income,¹¹

γ_{ki} = γ_{k} \log (y_{i}),

(6)

noting that the average whiskey-type-level intercept is absorbed by the included product intercepts. We parameterize the price coefficient as a function of log household income and an independent normal random draw

ν_{i}

α_{i} = α_{0} + α_{1} \log (y_{i}) + α_{ν} ν_{i} .

(7)

Identification

Price coefficient

We estimate model parameters by a set of moments enforcing that demand shocks $ξ_{jrmt}$ are conditional mean zero, given instruments $z_{jrmt}$ (including nonprice covariates, fixed effects, and excluded instruments for price and random coefficients):

E [ξ_{jrmt} | z_{jrmt}] = 0.

(8)

Price endogeneity might arise for a number of reasons, including measurement error (which arises from the aggregation of prices over weeks and stores) and price setting based on the unobserved characteristics,

ξ_{jrmt}

. Previously, we argued and demonstrated that learning creates a pattern of increasing covariations between prices and the unobserved characteristics as retailers learn the demand primitives. Thus, we need instruments that exclude both potential correlated measurement errors and the shocks and unobserved qualities that firms learn about. We construct price instruments similar to those used by Conlon and Rao (2019) and Miravete, Seim, and Thurk (2018) to address these concerns. For each product carried by each retailer, we construct average prices of the product carried by all other retailers and across all states other than Washington, and use them as the instrument for retail prices in Washington. The prices in other states likely capture common wholesale price variations across states but do not correlate with either demand shocks or the learning occurring in Washington (after controlling for the fixed effects previously noted). One example of wholesale price comovement is that prices of scotch whiskey move with the USD-GBP exchange rate, as illustrated in Web Appendix Figure W.13. Furthermore, to the extent that measurement errors arise from aggregating prices across weeks and stores, the instruments constructed from other retailers’ prices should have independent measurement errors.

Random coefficients

We identify the random coefficients by combining the instruments suggested by Berry, Levinsohn, and Pakes (1995) with additional micro-moments that inform substitution patterns (Petrin 2002) that are inspired by the constraints used by Conlon and Rao (2019). First, we count the number of products available in each retailer-market-month. Variations in the market shares of the focal product in response to changes in the number of products can help identify the disproportionate substitution to other products versus to the outside option captured by type-intercepts $γ_{ki}$ .

Second, we construct five sets of micro-moments, using the Homescan panel data, to help identify how the type intercept and price coefficient vary with log income. Specifically, we divide annual household income (in thousand dollars) into three bins $I_{b}$ : [0, 42.5], (42.5, 85], (85, $\infty$ ). For Washington households in Homescan who visit the six focal retailers, these three income bins create three roughly equal-sized groups.

Next, for each income bin, we compute three moments: the average probability of buying liquor among retailer visits, the average price paid among liquor purchases, and the share of the three major whiskey categories among purchases. For each set of parameters $θ$ , we match the model moments to the sample analogs. The first set of moments match the average probability of choosing the inside good:

{\bar{S}}_{rmt}^{b} = \frac{1}{N_{b}} \sum_{i \in I_{b}} \sum_{j \in J_{rmt}} s_{ijrmt} (θ) .

(9)

The second set of moments match the average price paid conditional on purchase of liquor:

{\bar{p}}_{rmt}^{b} = \frac{1}{N_{b}} \sum_{i \in I_{b}} \frac{\sum_{j \in J_{rmt}} p_{jrmt} \times s_{ijrmt} (θ)}{\sum_{j \in J_{rmt}} s_{ijrmt} (θ)} .

(10)

The third to fifth set of moments match the share of bourbon (and rye), Canadian whiskey, and scotch (and Irish whiskey) among liquor purchases:

{\bar{s}}_{rmt}^{k, b} = \frac{1}{N_{b}} \sum_{i \in I_{b}} \frac{\sum_{j \in k} s_{ijrmt} (θ)}{\sum_{j \in J_{rmt}} s_{ijrmt} (θ)} .

(11)

In the preceding equations,

N_{b}

is the number of income draws falling into bin

b

k

is the product type (1, 2, or 3), and

j \in k

represents product

j

falling into type

k

. As in Petrin (2002), we match the observed overall and type-level purchase probabilities and purchase prices to the simulated ones, yielding our micro-moments.

Estimation Results

Table 1 reports parameter estimates for the mean and standard deviation of price coefficients. We control for product-retailer, retailer-market, retailer-year, and month fixed effects but do not report their coefficients in the table. For comparison, we also estimate the model without household-level coefficients and without micro-moments as in Berry (1994).

Table 1.

Demand Parameter Estimates.

	Main Spec.	Berry (1994)	Price (First Stage)
Price ( $α_{0}$ )	−.833 (.002)	−.171 (.015)
Price × log(income) ( $α_{1}$ )	.121 (.002)
Std. dev. of price coef. ( $σ_{ν}$ )	.053 (.014)
Bourbon/rye × log(income) ( $γ_{1}$ )	−.301 (.116)
Canadian × log(income) ( $γ_{2}$ )	.773 (.100)
Irish/scotch × log(income) ( $γ_{3}$ )	.011 (.414)
Feature or display	.154 (.014)	.145 (.013)	−.278 (.037)
Missing feature/display	.239 (.004)	.237 (.009)	−.096 (.025)
Average price in other states			.104 (.005)
Number of products			−.004 (.003)
Product-retailer and retailer-market FE ( $δ_{jrm}$ )	X	X	X
Retailer-year and month FE ( $λ_{rt}$ )	X	X	X
Number of observations	174,299	174,299	174,299
R-squared (linear part)	.839	.821	.971

Notes: This table reports parameter estimates of the demand side. The first column reports estimates and standard error of the main specification. The second column reports estimates of a Berry (1994) logit model. The third column reports the first stage for price in the Berry (1994) logit model. The F-statistic for the two excluded instruments is 268.85. FE = fixed effects.

In the random coefficient logit model (“Main Spec.” column in Table 1), we find considerable heterogeneity in price sensitivities and in category utility (i.e., the intercept). The 5th percentile price sensitivity is −.432, and the 95th percentile is −.194; the former is more than twice the magnitude of the latter. Part of this heterogeneity is driven by income, indicating that high-income consumers are less price sensitive. Consistent with Conlon and Rao (2019), we also find that high-income consumers derive lower utility from the liquor category despite being less price sensitive.

We measure the in-sample fit of the model using the R-squared for the mean utility projection, which is inverted via the Berry, Levinsohn, and Pakes (1995) contraction mapping on observed market shares given the nonlinear coefficients. We find that the model fits the data well, explaining 84% of the share variation.

Implied elasticities

We next compute implied elasticities using our demand estimates. In Table 2, we present the own- and cross-elasticity matrix for six products sold by retailer 32 in June 2016. We find that elasticities increase in magnitude with price: the implied price elasticities of these example products range between −1.98 and −4.53.

Table 2.

Example of Implied Elasticities and Markups.

Product	Price	% Margin	Elasticity
Product	Price	% Margin	1	2	3	4	5	6
1	8.01	.448	−1.978	.007	.007	.007	.007	.007
2	11.50	.353	.002	−2.550	.002	.002	.002	.002
3	14.53	.307	.017	.020	−2.955	.024	.025	.029
4	21.29	.234	.003	.004	.004	−3.963	.006	.007
5	26.76	.207	.004	.005	.006	.008	−4.551	.010
6	29.08	.211	.002	.003	.004	.005	.006	−4.526

Notes: Elasticity and implied markup for six products (chosen because of the differences in prices), sold by retailer 32 in June 2016. The elasticity table shows, for example, that a 10% decrease in the price of product 1 will increase its sales by 19.78% and decrease the sales of product 2 by .07%.

Across all retailers and products, we find that the average elasticity at the observed prices is −4.00. For products below a $15 average price, the average elasticity is −2.59. For products above $15, the elasticity is −4.79. These numbers are similar to those reported by Miravete, Seim, and Thurk (2018), who find elasticities in the Pennsylvania liquor market to be −2.9 for “cheap” products and −4.9 for “expensive” products. Intuitively, this pattern arises from the fact that consumers who are less sensitive to price (and thus are the main customers for high-end liquor) value the liquor category lower as a whole and thus have limited willingness to pay.

Thus far, we have not assumed anything about what firms know or how they behave. We have simply recovered the parameters that govern the demand system (about which the firms may be incompletely informed). We next leverage a model of firm pricing behavior to further explore the role and nature of learning.

Wholesale Prices (Retailers’ Marginal Costs)

We now present a supply-side model to recover wholesale prices (retailer marginal costs). The goal of this exercise is twofold. The first goal is to provide an indirect test of long-run optimality by comparing the marginal costs implied by the model to our best available proxies. The second goal is to measure the economic impact of firm learning, identify the moderators of learning, and evaluate what demand fundamentals retailers learn about.

This process has two distinct steps. In the first step, we assume the optimality of firm pricing behavior in the last six months of our observation window, when we previously identified learning as appearing to be complete.¹² From this step, we obtain cross-sectional variation in the implied retailer-product wholesale prices. The second step imposes a transition process for the wholesale prices and leverages data from Oregon to model the time path of wholesale price changes back to the beginning of the privatization period. We now discuss each step in turn.

Recovering wholesale prices after the learning period (under optimality)

To recover wholesale prices, we assume that retailers are fully informed about demand in the last six months of the sample. During this period, the fully informed retailer r sets prices for its products based on demand primitives,¹³ with the restriction that the price must be set uniformly for each product across all markets in Washington. Specifically, the retailer, as a multiproduct and multimarket monopolist, chooses the vector of prices, $p_{rt}$ , to maximize the total profit in month $t$ ,

π_{rt} (p_{rt}) = \sum_{j \in J_{rmt}} \sum_{m \in M_{r}} ((1 - f) p_{jrt} - c_{jrt}) \times {\tilde{s}}_{jrmt} (p_{rt}) \times h_{rmt},

(12)

where

{\tilde{s}}_{jrmt}

denotes the model-predicted market shares (using an AR(1) process for the demand shock; see note 13),

M_{r}

is the set of markets (three-digit zip code) in which it operates,

h_{rmt}

is the size of market

m

in month

t

for the retailer (which is local population times the retailer's share of grocery revenue in the market),

c_{jrt}

is the marginal cost for product

j

t

, and

f = .17

is the share of gross revenue levied by the state, which is included in the list price. This profit maximization problem leads to the first-order condition such that for all

j

p_{rt} = \frac{c_{rt}}{1 - f} - (Δ_{rmt})^{- 1} \sum_{m} {\tilde{s}}_{rmt} (p_{rt}) \times h_{rmt},

(13)

where the

j

j^{'}

th element of

Δ_{rmt}

\frac{\partial (\sum_{m} {\tilde{s}}_{jrmt} h_{rmt})}{\partial p_{j^{'} rt}}

We impose this optimality condition only for the last six months of the sample and calculate the implied markups $(Δ_{rmt})^{- 1} {\tilde{s}}_{rmt}$ over “effective cost” $c_{rt} / (1 - f)$ based on demand estimates. We use these markups to back out both wholesale prices $c_{rt} = {c_{jrt}}_{j \in J_{rt}}$ and margins as $(1 - f) (Δ_{rmt})^{- 1} {\tilde{s}}_{rmt}$ divided by price (see Table 2 for examples). For example, for product 3, the retailer sets the price at $14.53 and gains 30.7% of the price as gross margin. These estimated margins indicate that retailers set lower percentage margins for high-priced products. This particular, but well-known, feature of liquor demand arises from the increasing elasticities in price.

Inferring wholesale prices over the learning period (before optimality)

We now infer wholesale prices while the retailer is still learning (i.e., from before the six-month window that we assume is optimal). Our approach has three key elements: we recover and employ the final (cross-sectional) average costs, we assume a cost transition process, and we then leverage Oregon prices to estimate the changes in wholesale prices. The underlying cost function we assume takes the following form:

\log (c_{jrt}) = {\bar{c}}_{jr} + τ_{k (j) y (t)} + ω_{jrt} .

(14)

The log wholesale price is composed of a component that is constant over time but varies across products and retailers (

{\bar{c}}_{jr}

), a component that captures common type-year variation (

τ_{k (j) y (t)}

), and an unobserved mean-zero cost shock,

ω_{jrt}

.¹⁴

Allowing for type-year cost variation captures differences in exchange-rate movements. For example, Canadian dollars depreciated during the sample period (whereas the British pound and the euro remained stable), potentially leading to different import-price changes for Canadian whiskey. Moreover, Equation 14 assumes that wholesale-price changes are common between Washington and Oregon. To provide support for this assumption, Figure 6 takes a fixed set of products and compares their average prices (de-meaned) between the Washington state retailer (before June 2012), the Oregon state retailer, and other liquor-privatized states in the RMS data. The average price series in different markets track each other closely.

Figure 6.

Percentage retail price change: comparison across states.

The recovered wholesale prices have large dispersion across different products; however, such dispersion is expected given the large degree of vertical segmentation in the category. For 2016, the 5th percentile of wholesale prices (among product-retailer pairs) is $4.09, the median is $12.23, and the 95th percentile is $31.38. More details are presented in the Web Appendix.

Empirical Characterization of the Learning Process

In this section, we use our estimates to empirically characterize firms’ pricing strategies during the learning phase. We examine whether learning is completed during the sample period and, if so, how much prices and profits differ between the initial, limited-information state and the eventual, full-information one. The goal of this exercise is to examine the extent of deviation from the full-information optimum and whether this deviation is transitory or persistent. We first conclude that prices are in line with full-information behavior by the end of the sample period by verifying that model-implied marginal costs (assuming optimal behavior by the end of the sample period) are consistent with our best-available proxy. Then, we show that initial prices are systematically different from the optimum, leading to an average 9.3% gap between realized and optimal profit at the outset. Systematic, suboptimal pricing is present and economically important, but also transitory, as a result of learning.

Having established that prices eventually converge to full-information behavior, we next examine how prices evolve from the initial, limited information state to the eventual, full-information one. We present descriptive evidence that firms’ initial behavior and learning rates are consistent with the predictions of classical learning models: learning occurs more quickly for products for which sales are more informative and for firms that are less informed about the market. In both cases, the marginal impact of additional learning is higher, in line with canonical (Bayesian or adaptive) learning models.

Finally, we attempt to pin down the object of firm learning and further unpack how firms leverage previous experience and earlier market conditions to shape the learning process. In particular, we demonstrate that learning in this context focuses on Washington consumers’ taste distribution, which differs systematically from other, previously privatized states. We further show that all retailers make similar initial mistakes consistent with their using other states’ consumer behavior as exemplars for the Washington market. However, the firm with direct experience in other markets initially outperformed those that did not. This evidence suggests that, instead of simply copying other states’ prices (which would not have suited the Washington market), the retailer was able to more quickly infer the unique aspects of Washington demand. In other words, this retailer seems to have been solving a fairly nuanced (and counterfactual) inference problem.

Throughout this section, we focus on the three grocery retailers that remained stable throughout our observation period—retailers 158, 182, and 32—and that account for 80.7% of revenues. Retailers 152 and 182 operate only in states where liquor cannot be sold in grocery stores, meaning that they had no direct experience with this category. Retailer 32, in contrast, had extensive experience selling liquor in the other states in which it operates, before starting the sale of liquor in Washington.

Evidence That Retailers Have Learned to Set Optimal Prices

Our wholesale price recovery imposes that retailers are fully informed and set static-optimal prices in the final six months of the sample period (four years after their entry into the market). In theory, a monopolist retailer will eventually learn about demand if the inference problem is bounded and sufficiently well-behaved (Aghion et al. 1991).¹⁵ In the empirical literature, this assumption is often either imposed explicitly (Doraszelski, Lewis, and Pakes 2018) or implied by the specific learning process invoked (Ching 2010; Hitsch 2006). Thus far, we have demonstrated that learning reaches a stable rest point after a couple of years, consistent with the conclusion that learning is complete by the end of the sample period. We now empirically validate this claim, establishing a central component of our conjectures regarding learning: Upon reaching this rest point, retailers have learned to price optimally.

We compare our wholesale price estimates ${\bar{c}}_{jrt}$ to two sets of direct measures, ${\tilde{c}}_{jt}$ , recovered from publicly available posted prices under state regulated fixed-markup regimes. Washington State imposed a fixed 51.9% markup before privatization, and Oregon imposed a 104% markup, which we use to compute ${\tilde{c}}_{jt}$ (for each state, over different time periods) from posted retail prices. If Washington private retailers face similar wholesale prices as the (pre-privatization) state-owned chains, full-information optimal pricing implies that ${\bar{c}}_{jrt}$ —estimated under the assumption that learning is complete by the end of the sample period—should be similar to both proxies ${\tilde{c}}_{jt}$ . However, because manufacturers should respond to the change in retail markups from the pre-privatization fixed-markup rule to the post-privatization flexible rule, ${\tilde{c}}_{jt}$ should not be the same as ${\bar{c}}_{jrt}$ . In particular, Miravete, Seim, and Thurk (2020) characterize manufacturer and retailer pricing decisions and show that retail and (manufacturer-set) wholesale markups are strategic substitutes, and thus one should expect lower (higher) wholesale prices for products where retail markups increase (decrease) the most. Thus, in comparing the wholesale prices, we seek to find consistency between pre-privatization and implied wholesale prices, up to a rotation.

We evaluate the relationship between ${\bar{c}}_{jrt}$ and ${\tilde{c}}_{jt}$ for two distinct sample frames. The first sample is from Washington in the pre-privatization period, and the second is from Oregon for the contemporaneous period.¹⁶ We show in Figure 7 that the estimated wholesale prices are indeed close to those backed out from the Washington data. The median wholesale price is $12.10 in the privatized market, almost identical to the median wholesale price observed in the pre-privatization era at $12.40. In addition, across products, the model-implied and state-observed wholesale prices have a correlation coefficient of .99. Further, visual inspections suggest that the pre-privatization wholesale prices and the corresponding model-implied ones are closely related, with the expected slight rotation. The alternative comparison of implied wholesale prices to observed wholesale prices in Oregon provides similar results (see Web Appendix Figure W.17). The main difference is the degree of rotation, which one would expect to differ given the large difference in fixed markups imposed in each of the two states.

Figure 7.

Comparison between estimated and observed wholesale prices.

An alternative approach is to use the state-observed wholesale prices as a proxy for retailers’ costs. For the subset of 46 products available both before and after the privatization and in Oregon, we take their state wholesale prices as the baseline and add Oregon's whiskey type-year trend (as in Equation 14) to project wholesale prices to the entire sample period. We then compute optimal prices for these products and contrast them with observed prices. Web Appendix Figure W.18 shows a mirror-image result to Figure 7: The observed and model-implied prices track each other closely except for a similar rotation, consistent with manufacturers’ lowering wholesale prices for the high-end products because of their lower retail markup in percentage.

These results provide external validity that the model effectively recovers the wholesale prices that represent the key marginal costs for these retailers. More importantly, we have demonstrated that, after operating in the market for a few years, retailers behave in ways consistent with full-information optimal pricing. The fact that retailers reach optimal pricing outcomes by the end of the observation period places a boundary on the types and extent of behavioral departures from rationality that are at play in this market. In particular, they are at most transitory in nature and generally self-correcting. Having shown that firms learn to price, we turn now to quantifying the economic importance of their learning task.

The Economic Importance of Learning

Measure of limited-information behavior and outcomes

We now quantify the economic importance of learning, contrasting observed pricing decisions with the full-information prices implied by the model. Specifically, we use the structural model to simulate a counterfactual in which retailers have full information about demand and set prices optimally (at all points in time). This counterfactual serves as a benchmark to evaluate how close observed retailer behavior is to optimal decision making under perfect information (at any given point in time). To solve for model-implied optimal prices, we use our supply-side estimates to compute the implied marginal costs, ${\bar{c}}_{jrt}$ . We solve for product-specific optimal prices for each of the three retailers in each month, assuming that each product's price is set uniformly across the state.¹⁷ After obtaining $p_{rt}^{*}$ , we compute the implied total profit for retailer r in month m across all products and markets from the retailer's profit function (Equation 12).

We contrast the fully informed, optimal prices with the observed ones, using the following measure of the percentage price gap:

% price ga p_{jrt} = \frac{p_{jrt}^{*} - p_{jrt}}{p_{jrt}^{*}} .

(15)

Similarly, we also examine the percentage profit gap obtained at observed and model-implied optimal prices,

\frac{\sum_{r} [π_{rt} (p_{rt}^{*}) - π_{rt} (p_{rt})]}{\sum_{r} π_{rt} (p_{rt}^{*})}

, where the profit function

π_{rt} (\cdot)

is evaluated at our estimates of demand and costs.

Quantifying the economic importance of learning

Figure 8 presents, across all retailers and for each quarter,¹⁸ the gap between observed and optimal prices, along with the corresponding gap for total profits. Observed prices in the first quarter differ markedly from the full-information optimal prices, resulting in considerably lower profit for this first period. At the median, prices are 9.3% higher than the optimal level, with large dispersions (quartiles are 0% and 21%). This departure in prices leads to a 9.3% lower profit compared with the optimum, suggesting that retailers’ limited information about the new market is consequential for setting prices: the scope for learning about demand is high.

Figure 8.

Percentage price and profit gaps: pooled across retailers.

The gap between observed and optimal prices decreases steadily over time, with most of the adjustment occurring in the early periods. By the second quarter, the overall price level is much closer to the optimum: the median percentage price gap is 5.8%; quartiles are (−4% and 15%). As a result, the profit gap shrinks to 6.2%—a third of the forgone profits are recovered from learning in the first quarter. By early 2016 (before we assume optimal pricing), the profit gap closes by 7.4 percentage points, which is 80% of the initial gap. This further improvement results less from average price changes and more from the shrinking variation in the price gap distribution, with the price gap interquartile range shrinking to (−2%, 3%) by 2016. This finding suggests that retailers learn about demand and improve pricing, and do so at a quicker rate at the beginning than at the end. The result is a significant improvement in variable profits that, together with the fact that demand is stable over this period, suggests that firm beliefs are initially miscalibrated but gradually refined to reflect the true market conditions.

The Pattern of Learning

Having established that firms are initially misinformed about demand in this new market, but gradually learn from experience, a natural follow-up question is whether the observed learning process follows patterns consistent with predictions from the learning literature (Ching 2010; Hitsch 2006). Our approach is to descriptively characterize the firms’ initial mistakes and learning rates (the initial absolute percentage price gap and the rate at which it declines over time) and examine whether the basic patterns follow those implied by classic learning models.

In particular, we present evidence that is in line with two key prediction of Bayesian learning: Learning occurs at a higher rate (1) when the firm is less informed (in the initial period or with less previous experience) and (2) when the firm obtains stronger information (i.e., observes stronger signals). Further suggestive evidence points to the nature of initial mistakes and the role of knowledge transfer from previous operations in other states to the new Washington market.

Observation 1: Decreasing rate of learning

We first document that learning occurs at the highest rate when firms initially enter the market and that this rate declines as firms become more informed. Figure 8 revealed that prices start far away from the optimum, quickly become much closer to it in the first few quarters, and continue moving toward the optimum at a slower pace.¹⁹ This pattern is consistent with either a canonical Bayesian learning model or an adaptive learning model where firms estimate demand using all available data (e.g., Doraszelski, Lewis, and Pakes 2018): as the firm accumulates information, the marginal contribution of additional signals declines.

Observation 2: Learning rate increases with precision of signals

Our second observation is that the learning rate increases with the precision of demand signals. We define the learning rate as the rate at which prices converge to optimal price levels, using the price gap metric from Equation 15. We measure the extent of initial mistakes and the learning rate for product group $g$ (here, $g$ refers to high- and low-volume products) by estimating the following linear model over the first year of the sample:

| % price gap |_{jrt | j, t \in g} = γ_{0 g} + γ_{1 g} \times t + ν_{jrt},

(16)

where

γ_{0 g}

is the initial absolute percentage price gap and

γ_{1 g}

measures how much this gap shrinks per unit of time.

We examine whether learning occurs at a higher pace for products whose average sales quantity is above the median.²⁰ Average sales volume is a natural proxy for the informativeness of quantity signals because (as we demonstrate in Web Appendix Table W.6) high-volume products are carried by more stores and their demand shocks $ξ_{jmrt}$ exhibit lower variance.

Table 3 demonstrates that the absolute percentage price gap shrinks at almost double the rate for high-volume products than for low-volume products. This evidence suggests that the learning rate increases with the “flow” of new information (which retailers obtain from sales-quantity data), a standard implication of both Bayesian and adaptive learning models. Web Appendix Figure W.20 provides a more detailed picture, documenting how the whole distribution of price gaps changes over time.

Table 3.

Initial Mistakes and Learning Rate Between Time Periods, Retailers, and Product Groups.

	Average Volume		Retailer Experience
	High	Low	Inexperienced	Experienced
Initial absolute percentage price gap	.122 (.001)	.131 (.002)	.145 (.001)	.099 (.001)
Change in price gap per year	−.064 (.002)	−.035 (.003)	−.067 (.003)	−.028 (.003)
Observations	12,199	9,774	13,181	8,792

Notes: This table reports the initial absolute percentage price gap (which is the absolute value of the percentage price gap defined in the section “The Economic Importance of Learning”) and how this price gap decreases per year in the first year of privatization, across products with high and low sales volume and across retailers with different experience. The inexperienced retailers are retailer 158 and 182, the two local retailers that started selling liquor since the privatization in Washington. The experienced retailer is retailer 32, which has sold liquor for a long time in other states. Standard errors are in parentheses.

Observation 3: Initial pricing mistakes reflect Washington's distinct taste distribution

Before diving deeper into the learning process, we discuss the nature of the initial pricing mistakes we observe. We now show suggestive evidence that these initial pricing mistakes are most consistent with retailers having limited information about customer preferences over whiskey types. We arrive at this conclusion in two steps.

First, using the Homescan panel data, we find that Washington's high-income consumers have different preferences over product types, relative to the mainstream preferences observed in other states. Figure 9 demonstrates that, most notably, Washington high-income consumers (top third of the income distribution) are less enamored with bourbon (and rye), as well as scotch (and Irish whiskey), but far more enthusiastic about Canadian whiskey.²¹ We reckon that this pattern could be related to the proximity of Washington to Canada and the distance from the key domestic producing regions (e.g., Kentucky) and their European counterparts. This difference changes the composition of customers who purchase each whiskey type: As a result, bourbon/rye and scotch/Irish whiskey draw more low-income consumers, and Canadian whiskey attracts more high-income consumers.

Figure 9.

Share of purchases by product type and income group.

Second, we contrast this difference in customer preferences with retail prices in Washington. If retailers are Bayesian learners with initial beliefs reflecting information from other states, one might expect initial prices not to account for Washington's distinct preference distribution. To validate this conjecture, we provide a simple calibration exercise that measures retailers’ perceived demand and examines how these demand perceptions differ from Washington's actual demand. Firm beliefs are difficult to pin down without further assumptions on pricing behavior. Thus, for this calibration exercise, we assume that retailers are static profit maximizers who set prices to maximize profit conditional on perceived demand (ignoring demand uncertainty). Specifically, we assume that the perceived demand follows the demand model presented in Equations 4–7, up to differences in $γ_{k}$ values—which govern the sorting of customer demographics into different product types. Although the assumption of naive and myopic pricing behavior is strong, it allows us to flexibly recover each retailer's initial perceptions, without specifying how these initial beliefs are formed (e.g., without assuming rational expectation). In Web Appendix E, we document how we calibrate the initial (first-quarter) pricing perceptions to capture how well the initially inaccurate beliefs explain the initial pricing mistakes.²²

The first three columns of Table 4 summarize the difference between perceived and estimated $γ_{k}$ values, by retailer and whiskey type. We find that retailers make sizable and systematic mistakes for bourbon and rye and for Canadian whiskey. Our structural demand model estimate for $γ_{1}$ (for bourbon and rye) is −.30 (see Table 1), implying that Washington high-income consumers do not favor bourbon/rye. In contrast, retailer-perceived $γ_{1}$ values are between 1.36 and 1.65 for all retailers, suggesting that retailers set initial bourbon/rye prices anticipating that a significantly higher fraction of high-income customers favor this whiskey type. Conversely, the perceived $γ_{2}$ parameters (corresponding to Canadian whiskey) are all negative compared with the structural demand estimates, suggesting that all retailers believe that Canadian whiskeys should be targeted to the lower-income segment.

Table 4.

Retailer-Perceived Product Type Preferences and Observed Consumer Type Choice.

	$P e r c e i v e d {\tilde{γ}}_{k} - E s t i m a t e d γ_{k}$			Product Share Difference (Other States $-$ WA)
	Retailer 32	Retailer 158	Retailer 182	Income <$85,000	Income ≥$85,000
Bourbon/rye	1.063	1.242	1.345	.031	.098
Canadian whiskey	−1.689	−1.991	−2.339	−.102	−.171
Irish whiskey/scotch	−.297	.458	.117	.032	.074

Notes: This table shows the difference between retailers’ perceived demand primitives (i.e., those that rationalize initial prices under an optimal static-pricing model) and the estimated ones. The table also contrasts these differences with gaps in product-type shares between other states and Washington. Columns 1–3 present the gap between perceived and estimated type-income interaction term, by type and retailer. For example, the first column shows that retailer 32's initial prices can be rationalized as optimal prices in a market where $γ_{1}$ (for bourbon and rye) is 1.063 higher than the true demand, $γ_{2}$ (for Canadian whiskey) is 1.689 lower, and $γ_{3}$ (for Irish whiskey and scotch) is .297 lower. Columns 4 and 5 are differences in type shares conditional on purchase, calculated from the Homescan data (Figure 9). For example, Column 5 shows that households with at least $85,000 annual income (i.e., the top third of the income distribution) purchase 9.8% more bourbon/rye in other states than in Washington, 17.1% less Canadian whiskey, and 7.4% more Irish whiskey and scotch.

These systematic mistakes are consistent with retailer beliefs initially being substantially biased: away from Washington's true consumer preferences and toward the “typical” preferences of an average U.S. state, although these biases are later corrected through market feedback. Therefore, the initial prior plays an important (and persistent) role in retailers’ pricing strategies during the learning phase, consistent with the predictions from canonical Bayesian learning models (but distinct from adaptive learning, where prior beliefs do not play a role).

Observation 4: Experience helps initial pricing but lowers the initial learning rate

Our final observation is that retailers’ experiences in other markets can impart knowledge about conditions in the Washington market. We contrast initial pricing decisions by retailer 32, which has experience selling liquor in other states, with those made by retailers 158 and 182, which are entirely new to the retail liquor market. We demonstrate that previous experience in other states allows retailer 32 to set better initial prices, while slowing its initial learning.

Because Washington's consumer preference distribution is distinct from other states’, it is possible that direct experience of selling liquor in other states gives the retailer strong, but biased, priors that reflect consumer behavior in other states. It is also possible, however, that the experienced retailer accumulates more nuanced knowledge about consumer preferences by operating in different states, allowing it to better predict Washington's distinct consumer preferences. A third possibility is that all retailers have access to some information about the retail liquor market (e.g., through hiring experienced managers or through market research), with or without having sold liquor in other states.

The previous calibration exercise has demonstrated that all retailers’ perceived consumer preferences are biased in the same direction, yet the experienced retailer 32 has (slightly) smaller biases across all whiskey types, compared with the two inexperienced retailers. This result suggests that all retailers leverage information from other states (despite this information being somewhat misleading about Washington tastes per se), but the experienced retailer exhibits a better initial understanding of the new market itself.

To explore this further, we estimate Equation 16 separately for experienced versus inexperienced retailers to examine how the initial average absolute percentage price gap, as well as its rate of change, differ between the two groups. Table 3 shows that the experienced retailer is better endowed with information about demand and thus sets initial prices closer to the optimum (consistent with this retailer’s better calibration of perceived demand). The average product is priced 10% away from the optimum, and the total profit is 6.3% below the optimum. In contrast, the average product is priced 15% away from the optimum for the inexperienced retailers, with corresponding total profit 13.9% below the optimum. Moreover, despite setting better initial prices, the experienced retailer learns at a lower rate. Absolute percentage price gaps decrease by 2.8 percentage points after the first year, less than half of the inexperienced retailers’ learning rate.

This evidence suggests that retailers’ prior beliefs have a persistent influence on their decision making during the learning phase. Consistent with the prediction of a canonical Bayesian learning model, retailers’ prior beliefs about demand—shaped by previous experience in other markets—play a significant role in their initial pricing decisions and the rate at which they absorb subsequent information. Nevertheless, such experience does not come from operating in a similar market per se, but rather from operating in markets with different primitives (yet still useful in predicting the Washington market).

Discussion

Without imposing a structural learning model, we have presented four empirical observations that characterize the learning process: (1) the learning rate declines over time; (2) the learning rate increases with the precision of new information; (3) the firms’ main learning objective appears to be Washington's distinct customer preference distribution; and (4) the experienced retailer, who has sold liquor in other states, forms priors that are closer to the true demand and are more precise, compared with those of inexperienced retailers.

These observations describe a learning process that is broadly consistent with a canonical Bayesian learning model (Ching 2010; Hitsch 2006): the implied learning rate is governed by the strength of the firm's prior (which is affected by experience from various sources) and the precision of its sales signals. Notably, we document these patterns without assuming a Bayesian model structure. Thus, these observations provide valuable field evidence that supports the relevance of the Bayesian learning framework to firm learning.

However, two aspects of our empirical evidence go beyond the canonical framework. First, firms are apparently learning complex features of the customer preference distribution—a high-dimensional object. Canonical models characterize firm learning about product quality (Hitsch 2006) or category-level quality (Ching 2010), unidimensional objects that greatly facilitate model tractability. Our evidence suggests that the focus of firm learning can be more complex than what has been characterized in existing models. If one were to fully characterize this learning problem for a forward-looking firm, the model would involve the firm strategically setting prices to create data that facilitate future learning. The closest work to this model in marketing is that of Misra, Schwartz, and Abernethy (2019), who present a scalable algorithm that approximates this learning problem. The full solution to the (structural) learning model is a promising area for future research.

Second, the role of firms’ previous experience in other markets suggests that the transfer of firm knowledge is important for understanding learning, namely how priors are formed. In particular, firms demonstrate a capacity to predict outcomes in a new (ex ante counterfactual) environment, consistent with the types of dynamic capabilities emphasized by Teece, Pisano, and Shuen (1997). Understanding precisely how prior beliefs are formed and how knowledge is transferred across markets is outside the scope of current learning models (presumably because of the added model complexity). This area is open for future research.

Conclusion

We have shown that, after privatization, firms in the Washington State liquor market learned to set prices very much in line with classic models of imperfect competition. However, this process took time to unfold and played out differently for different firms, suggesting important roles of both learning and heterogeneous firm capabilities. In our setting, we find that this convergence of pricing strategies to optimal decision making does not require the pressure of direct competition. Instead, firm practices alone appear to create sufficient impetus to develop the sophisticated understanding required to reach optimal pricing policies. Future research could examine the sources and limitations of this drive and whether competition, by adding the complexity of interpreting and anticipating competitive actions, helps or hinders the learning process.

Supplemental Material

sj-pdf-1-mrj-10.1177_00222437211068527 - Supplemental material for Learning to Set Prices

Supplemental material, sj-pdf-1-mrj-10.1177_00222437211068527 for Learning to Set Prices by Yufeng Huang, Paul B. Ellickson and Mitchell J. Lovett in Journal of Marketing Research

Footnotes

Acknowledgments

The authors gratefully acknowledge numerous comments and suggestions from Kristina Brecko, Christopher Conlon, Ulrich Doraszelski, Ronald Goettler, Brett Gordon, Avery Haviv, Jihye Jeon, Przemyslaw Jeziorski, Nitin Mehta, Jeanine Miklos-Thal, Kanishka Misra, Sarah Moshary, Harikesh Nair, Xiliang Lin, Marc Rysman, Greg Shaffer, Kosuke Uetake, Thomas Wollman, Chenyu Yang, and Hongsong Zhang, as well as seminar and conference participants at Carnegie Mellon University, Northwestern University, the 2018 NYU IO Day, the 2017 SHUFE IO Conference, Stanford University, the 2018 Summer Institute in Competitive Strategy Conference, the 2019 Quantitative Marketing and Economics Conference, the University of Chicago, the University of Rochester, and the 2021 University of Texas at Dallas Bass Frontiers of Research in Marketing Science Conference. The authors thank Zhe Hong for excellent research assistance. The analyses are based in part on data from Nielsen Consumer LLC and marketing databases provided through the NielsenIQ data sets at the Kilts Center for Marketing at the University of Chicago Booth School of Business. The conclusions drawn from the NielsenIQ data are the authors’ and do not reflect the views of NielsenIQ. NielsenIQ is not responsible for, had no role in, and was not involved in analyzing and preparing the results reported herein.

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Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Yufeng Huang

Notes

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