1.1 Related literature

Only recently has the literature started to use structural models of demand and supply for differentiated products to study different aspects of Airbnb (^{Farronato and Fradkin, 2022}; ^{Farhoodi, 2021}; ^{Calder-Wang, 2021}). However, these are about Airbnb in the U.S., and the differences between professionals and nonprofessional hosts have yet to be studied. The closest to us is ^{Farhoodi (2021)}, who studied the distribution of benefits among neighborhoods in the Chicago Airbnb market, finding that higher-income neighborhoods benefit the most from access to the platform and that a tax on platform users has redistributive effects. Our research contributes to this growing literature using structural methods to study markets for short-term rentals by offering a stylized structural framework to study the differences be-tween professional and nonprofessional hosts, and doing so in a Latin American city.

^{Chen and Xie (2023)} is the only other paper previous to us investigating the roles of professional and nonprofessional hosts in the Airbnb market using econometric techniques. They used a quasi-experimental design, exploiting a policy change in San Francisco and New York that caps the number of properties a host can manage. This provides indirect empirical evidence of substitution between properties managed by professional and nonprofessional hosts. On the other hand, there is a large number of papers providing descriptive evidence on the professionalization of Airbnb hosts; in addition to those cited in the Introduction, ^{Abrate et al. (2022)} and ^{Ki and Lee (2019)} documented the complex pricing strategies followed by professional hosts as compared to nonprofessional ones. By implementing structural econometric techniques, we offer an alternative approach to studying the relevant economic differences between professional and nonprofessional Airbnb hosts, some of which (such as costs and margins) are difficult to recover otherwise.

Regarding Airbnb in Mexico City, only a few studies have been conducted so far. ^{López Tamayo and Ramírez Álvarez (2021)} con-ducted a hedonic price analysis for Airbnb in Mexico City, finding positive determinants of price such as the maximum number of guests allowed, number of bedrooms, number of bathrooms, number of amenities, and professional host, as well as negative determinants such as crime in the accommodation area. ^{Ruiz-Correa et al. (2019)} and ^{Madrigal Montes de Oca et al. (2018)} approached the issue of Airbnb in Mexico City from an Urban Studies perspective. Banco de Mexico (2021) examined the evolution of the Airbnb market in Mexico City. We provide a state-of-the-art framework to estimate unobservable economic primitives in the industry, and a first set of estimates speaking to the differences between Airbnb hosts in Mexico City. Moreover, the proposed structural framework can be further refined to provide insights into the effect of different public policies.

We follow the literature on estimating models of product differentiation initiated by ^{Berry et al. (1995)} to address several methodological challenges. We estimate several logit and random coefficients (RC) demand models using the standard nonlinear IV technique with modern differentiation instruments of ^{Gandhi and Houde (2019)} to account for price endogeneity. To deal with the significant heterogeneity in Airbnb listings in a computationally tractable way, we adopt an aggregation method developed by ^{Farronato and Fradkin (2022)}. Finally, many listed properties are not rented on a given day, which translates into the well-known zero market share problem (^{Dube et al., 2021}). Our results are robust to the two most common ways of handling products with zero market share in these types of models, excluding observations with zero market share and imputing to them a positive market share value close to zero (^{Gandhi et al., 2023}).

2.1 Data

We use a private microdata set provided by AirDNA, a short-term rental intelligence firm, containing data for the 16 alcaldías in Mexico City during 2019, scraped from the Airbnb portal.³ It records the final status (not booked, booked, unavailable) and corresponding rental price (in US dollars) for each posted accommodation and date. Additionally, it offers detailed information about each accommodation, including exact location (latitude and longitude), number of bedrooms, bathrooms, number of photos posted, internet access, and whether the accommodation is an entire home/apartment or a shared/private room, whether it is offered by a “superhost”, and amenities offered, among others. A major drawback of this data is that it does not contain any demographic or other guests’ characteristics, which makes it difficult to identify taste variation.

Our initial microdata set consisted of 6,471,668 observations corresponding to daily accommodations offered in Airbnb in Mexico City for the year 2019 (for the economy of language hereafter, we refer to one of these accommodation-date observations as a listing). We conducted the following data cleaning process: First, we removed 2,682 listings with a zero price. Subsequently, we eliminated 1,228,841 listings from 7,448 available accommodations that were never rented during 2019. Of the remaining 5,240,145 listings, shared rooms and hotel rooms represent small percentages (1.83% and 1.57% respectively, see Table 1), so we focus our analysis on private rooms and entire homes/apartments exclusively.

Additionally, to prevent biases and enhance the accuracy of our estimates, for each accommodation type and alcaldía, we filtered out all listings with prices above 99% or below 1% of the prices of booked listings during 2019.

Our final sample contains 4,844,410 listings, of which 40.72% correspond to booked ones. This information pertains to 24,956 unique accommodations scattered across the 16 alcaldías of Mexico City. The alcaldías with the most significant number of total listings, as well as booked and non-booked listings, are Cuauhtemoc, Miguel Hidalgo, and Benito Jua´rez (see Table A.1).

Finally, in our demand models, we assume guests’ outside option is booking a room in the traditional lodging sector.⁴ We obtain data on monthly average daily hotel room occupancy from DataTur, a tool implemented by the Mexican Secretary of Tourism to monitor hotel occupancy. Table 2 compares these averages with Airbnb’s average daily occupancy calculated by us from our final sample described in the previous paragraphs. It shows that in terms of the monthly average of daily occupancy (resp. available accommodations), Airbnb rentals represent between 16% and 20% (resp. 20% and 31%) of the occupancy (resp. availability) in Mexico City’s traditional sector.

2.2 Preliminary analysis

The 24,956 accommodations belong to 14,788 hosts. We classify these hosts as professional or not according to the number of accommodations they manage on the platform. In the body of the paper, we adopt the single-unit/multi-unit definition of nonprofessional and professional hosts, largely adopted in the literature.⁵ In Appendix A.4, we review the robustness of our results to more nuanced definitions of what it means to be a professional host, also based on the number and type of properties.

Of the 14,788 hosts, 26.93% were classified as professional hosts who can manage between 2 and 77 accommodations, amounting to 56.70% of the accommodations posted on Airbnb in Mexico City during 2019. More specifically, 55.22% of professional hosts offer exactly two accommodations, and 20.02% offer exactly three accommodations. On the other hand, Table 3 presents the annual number of listings by type of host. Professional hosts offered 58.22% of the listings and 64.60% of the booked listings.

Finally, Table 4 shows descriptive evidence regarding price variation among accommodations posted on the platform. We regress prices at the listing level (i.e., accommodation-date) on reservation status, host type, accommodation type, alcaldía, and date fixed effects. The alcaldías with the highest prices are Miguel Hidalgo, Cuauhtemoc, and Cuajimalpa. Booked listings are $6.70 less expensive than non-booked ones. Listings offered by professional hosts are $6.24 costlier than those from nonprofessional hosts. Lastly, private rooms are $42.28 cheaper than entire homes/apartments.

Motivated by these preliminary findings suggesting there might be differences between professional and nonprofessional hosts, the rest of the paper is dedicated to building and estimating models of demand and supply of differentiated products for the Airbnb market in Mexico City. As a preliminary step, the following section addresses an issue that arises due to the nature of Airbnb.

3.1 The stylized choice problem

Within this stylized framework, the choice set faced by every consumer looking for accommodation on a given date is the subset of the 116 representative products offering accommodation on that date, plus an outside option of booking a hotel room outside the platform. The demand for a given representative product for a given date is the count of accommodations belonging to the corresponding category that were booked for that date. We estimate the size of the out-side option with the corresponding monthly average of daily occupied hotel rooms (Table 2).

If no individual accommodation belonging to a specific category is offered on a given date, we drop that particular representative product from the corresponding date’s choice set. Relatedly, there are dates when no accommodation belonging to a given category is rented despite having available accommodations, resulting in a zero market share, which might create some issues in the estimation of the demand models. We implement the two most widespread ways of dealing with this issue (see section 4.3 for a detailed discussion).

On the supply side, representative products offered by nonprofessionals are assumed to be provided by single-product hosts. In contrast, the representative products offered by professionals are assumed to be supplied by a multi-product host who maximizes joint profits.

Our framework, though highly stylized, still captures crucial features of the market for short-term rentals while keeping the estimation issues mentioned at the beginning of this section under control. Specifically, our model captures daily demand and price fluctuations; it still captures variation in quality, location, and type of accommodations offered by professional and nonprofessional hosts, and complex substitution patterns; as well as the multi-product nature of professional hosts’ portfolio, which enables economies of scope and internalization of within portfolio substitution effects.

Naturally, this stylized aggregation abstracted some aspects of the Airbnb market for short rentals. The most critical elements lost by our modeling choices (on top of the choice set endogeneity) are the variation across professional hosts’ portfolios and an even more extensive product heterogeneity, which we leave for future research.

4.1 Models of demand

We model consumer demand using logit and mixed logit (a.k.a. random coefficients) models. On a given date, guests demand one out of a subset of the 116 categories offered by professional hosts (who offer more than one accommodation type) and nonprofessional hosts (who offer only one accommodation type) or the outside option of renting a hotel room in the traditional lodging sector.¹¹ Next, we formalize these ideas.

Logit: Guest n chooses an accommodation belonging to category j∈Jt , where Jt is the set of categories available in day t on the platform. The utility guest n receive from an accommodation in category j, with observed features xj→ and price pjt , including the tax rate τj on day t is:

β→ and α characterize consumers’ preferences for accommodations’ observed attributes. ξjt captures preferences for unobserved features that do not vary among guests. εnjt corresponds to preferences for unobserved aspects that do vary among guests. As usual, we assume that εnjt are i.i.d. Gumbel. For simplicity, we denote δjt=β'xj→→-αlog⁡(pjt(1+τj))+ξjt to represent the average utility. There is an outside option (such as renting a hotel room outside the platform) whose utility we normalize to 0 in any day t. Thus, the probability of a guest choosing the accommodation in category j for day t is:

Mixed logit: Also known as the random coefficients model, it is the most popular extension of the logit model in demand estimation because of its flexibility to accommodate heterogeneity in tastes among consumers, which allows flexible substitution patterns (^{Berry and Haile, 2021}; ^{Einav and Levin, 2010}; ^{Gandhi and Nevo, 2021}). In relation to the baseline model, the choice problem for guest n remains unchanged: to choose j∈Jt However, the random utility model in equation (1) becomes now:

With β_n a random vector and α_n a random variable such that βnk(βk-,σk2) for the kth characteristic, mutually independent, and αn(α-,σp2) , independent from each component of βn→ . As before, these coefficients characterize the guest n’s preferences for accommodations’ observed attributes. Also, as before, ξjt captures preferences for un-observed features that do not vary among guests, and εnjt captures unobserved taste variation among guests, assumed to be distributed i.i.d. Gumbel.

It is useful to separate the average and individual taste shocks.

Rewrite (3) as,

where δjt=∑kβk-xjk-α-log⁡pjt+ξjt is the part of utility which varies across alternatives but not consumers. On the other hand, μnjt=∑kσkνnkxjk-νnpσplog⁡pjt is the part of utility varying across consumers, with νnk,k=1,…,dim(xj→) and νnp mutually independent normal standard taste shocks. Thus, the unconditional probability of a guest choosing the accommodation in category j for day t is now:

With F a multivariated standard normal distribution with dimension dim (x_j) + 1.

4.2 Supply model

We assume Nash-Bertrand competition. Hosts choose prices to maximize daily profits. The crucial difference between professional and nonprofessional hosts is that the former offer accommodations in diferent categories and maximize the joint daily profit, while nonprofessionals only offer accommodations in a single category. Let JtΩ⊂Jt the set of categories belonging to professional hosts and Jtω⊂Jt the ones belonging to nonprofessional hosts. Let Mt the market size in day t. For the categories of products belonging to professional hosts, we set up a unique decision-maker who faces the following profit maximization problem:

On the other hand, for the representative products belonging to nonprofessional hosts, for each category j∈Jtω , we set up a decision maker who faces the following profit maximization problem:

The market equilibrium for the day t consists of the seller’s prices and consumer’s choices, such that both hosts and guests make the decision that maximizes their profits and utilities, respectively, and that their optimal decisions are consistent with those of others.

4.3 Estimation

We follow the standard procedure for estimating models of demand and supply for differentiated products with aggregate data (^{Berry et al., 1995}). Demand is estimated using the Generalized Method of Moments (GMM) with the moments obtained from the IV orthogonality conditions and the expected market shares. For mixed logit, we leverage state-of-the-art techniques implemented in PyBLP, a freely available Python library developed by leading researchers in empirical IO and increasingly used in the discipline to estimate BLP-type models (^{Conlon and Gortmaker, 2020}). Demand estimates coupled with hosts’ optimality conditions pin down their marginal costs, which are, in turn, used to perform counterfactuals.¹²

4.3.1 Demand

To estimate our logit model, we analytically invert the expressions for the choice probabilities (2) as in ^{Berry (1994)} to obtain an estimate of the δj ’s which are afterward regressed on our variables of interest to obtain the corresponding coefficients for the utility. Specifically, since the mean utility of the outside option is normalized to zero, the expression:

resulting from inverting the logit probabilities pin downs analytically the δjt for each product j and market t (^{Berry, 1994}: 250). These δjt ’s are afterward regressed against product characteristics according to the following specification:

We report the results in the Table 5, column (1).

The previous specification assumes pjt is exogenous. To correct for price endogeneity, we employ the methodology of ^{Berry et al. (1995)}, using differentiation instruments in the spirit of ^{Gandhi and Houde (2019)}.¹³ Once the δjt ’s are obtained from equation (8), moment conditions obtained from the instruments’ orthogonality conditions are used to obtain estimates for β and α using GMM and PyBLP. We report the results in Table 5, column (2).

Finally, for the estimation of the mixed logit, we employ the two-step GMM method as implemented in PyBLP and use differentiation instruments to correct for endogeneity. To estimate the value of the integral in (5), we employ 1000 Halton draws. From integral (5), for any given values of ({σk}k,σp) , the δ→ values such that the predicted share equals the observed market share are calculated, which implies solving a fixed point problem, which is solved using a SQUAREM routine. We report the results in Table 5, column (3).

Zero-valued market shares: It is important to emphasize that certain representative products have no bookings for some dates despite being offered in the market. Such products, therefore, exhibit a market share of zero in those dates, an issue that happens in 778 day-category pairs (out of 40,493 day-category pairs). This is a well-known issue in estimating discrete choice models because it rejects any multinomial choice probabilities (^{Dube et al., 2021}; ^{McFadden, 1974}). In this research, we consider the two most common solutions to this problem, which are either to eliminate observations with a zero market share (hereafter “Drop”) or to impute an extremely small value (hereafter “Imputation”); we use a value of 10^-12 for “Imputation”.

Remarks on data: Recall our final estimation dataset, which con-sists of market shares of the representative products and the outside option for every day in 2019 (section 3). The features of the represenative products are the logarithm of the total amount paid by guests to rent an Airbnb accommodation (“ln (price (1+τ) )”) with τ the lodging tax (3% in 2019) and the price in US dollars of January 2019; the number of amenities in tens (“amenities”);¹⁴ the number of bath-rooms (“bathrooms”); the number of bedrooms (“bedrooms”); the maximum number of guests allowed (“maxguests”); “professional”, a dummy variable indicating whether the host type for a given category has multiple listings on the platform; and “private room”, a dummy variable indicating whether the representative product is a private room or an entire home/apartment. Additionally, we employ fixed effects for the 16 alcaldías of Mexico City and for each day of the year 2019. To create the differentiation instruments, we use “amenities”, “bathrooms”, “bedrooms”, and “maxguests”. To measure the size of the outside option for each day, we used the corresponding monthly average of hotel bookings per day reported in DataTur (see Table 2).

4.3.2 Supply

For each day, to obtain marginal costs that are consistent with market equilibrium, the first-order conditions for professional hosts and for each category of nonprofessional hosts,

are inverted and evaluated using the demand estimates.

5.1 Demand

Table 5 presents our estimations of the different demand specifications, i.e., the logit, logit corrected for endogeneity, and the mixed logit corrected for endogeneity, for both ways of addressing the zero market share problem.

Beginning with the logit model without addressing endogeneity (Table 5, column 1), most coefficients are statistically significant at 95%, and their signs are consistent between the “Drop” and “Imputation” methodologies of handling the zero market share problem (with the exception of “bathrooms” in the “Imputation” method).

Controlling for endogeneity in prices using the IV approach out-lined in the previous section (Table 5, column 2), most of the estimates remain significant at 95% (with the exception of “maxguests” in the “Drop” method) and preserve the directions obtained in the simplest specification. Most coefficients increase in absolute value relative to the estimation, which does not correct the endogeneity issue, emphasizing the importance of correcting the endogeneity issue.

With the inclusion of heterogeneity in consumer preferences using the mixed logit, and correcting for endogeneity (Table 5, column 3), we find that the parameters corresponding to the variance of the random taste shocks are only significant for “bathrooms” in both methodologies and “amenities”, “maxguests”, and the intercept in the imputation methodology. This is not surprising given the lack of demographic or other information varying at the guest level.

In our analysis, the most relevant estimates are those associated with “ln (price (1+τ) )” due to their implications on the price elasticity of demand, which is crucial for the supply model estimations. Values close to 0 would correspond to inelastic demands, which are incompatible with the profit maximization proposed in our supply model. Relative to these coefficients on “ln (price (1+τ) )”, we observe they are consistent across models and ways of handling the zero market share, that they have the expected sign, and the values for logit models for the “Drop” versions are more negative in magnitude compared to their “Imputation” counterparts. For the mixed logit specification, the variances for “ln (price (1+τ) )” are insignificant. The fact that the coefficients on the taste shock parameters are not different from zero offers statistical evidence in favor of the simpler logit model (^{Train, 2009}). Therefore, our preferred specification over-all is the logit with endogeneity, which we use for subsequent analyses.

The discrepancy across models regarding the preferences for the physical characteristics of accommodations (“amenities”, “bathrooms”, “bedrooms”, and “maxguests”) or the insignificance of the estimates suggests that possibly their linear specification in consumer utility is not the most appropriate way to include them. However, since the analyses of the supply and counterfactual primarily depend on the price elasticities of demand, which are consistent across specifications and ways of handling the zero market share problem, we leave this subject matter for future research.

5.2 Supply

For the estimation of the model of the supply, we use the coefficients of our preferred specification for the demand model: logit with endogeneity. Table 6 presents regressions of our estimates of daily marginal costs (c_jt), equilibrium markups (p_jt − c_jt), and price-cost margins (pjt-cjtpjt) against host and accommodation type, alcaldia, and date. The full distributions by host and accommodation (Figure A.3 and Figure A.4).

It is meaningful to note that both methods of addressing the zero market share issue yield similar results, as shown in Table 6.¹⁵ As a result, we will focus on the “Drop” method.

Regarding host type, compared to nonprofessional hosts, professional hosts’ accommodations have a lower daily cost by $1.76 (p−value < 0.05) and earn $3.67 more (p−value < 0.05) per reserved accommodation, also have 9 percentage points (p − value < 0.05) higher price-cost margin. On the one hand, the lower marginal costs estimated for professional hosts are consistent with the intuition that they might take advantage of economies of scale, scope, and superior management practices, which in turn explains the higher markups professional hosts are able to capture. On the other, it is important to notice that price-cost margins are overall high regardless of host type (the baseline in the most conservative estimation is 38%), which is consistent with the existence of large fixed costs (rent, mort-gage, certain amenities like internet or cable service) and differentiated products.

Compared to renting an entire home/apartment, renting a private room costs $20.72 less (p − value < 0.05) and earns $21.49 less (p − value < 0.05), but has a higher price-cost margin of 0.0301 (p − value < 0.05). Therefore, while more dollars are earned by renting an entire home/apartment, renting by room yields a higher price-cost margin.

Regarding the different alcaldías in Mexico City, Cuauhtemoc, Miguel Hidalgo, and Coyoacán have the highest daily costs but also the highest dollar gains. In contrast, Iztacalco, Iztapalapa, and Gustavo A. Madero have the lowest daily costs but also the lowest markups. Concerning price-cost margins, the highest are those of Tláhuac, Iztacalco, and Iztapalapa, and the lowest are those of Cuajimalpa, Miguel Hidalgo, and Cuauhtemoc.

5.3 Counterfactual exercises

In 2019, guests making a reservation on Airbnb paid a 3% lodging ad valorem tax. As mentioned in the Introduction, governments around the world have implemented differential regulations for professional and nonprofessional hosts, with the former being subject to stricter rules. Consequently, we examine two counterfactual ad valorem tax policies that differentiate professional and nonprofessional hosts, one targeting guests and another targeting hosts.¹⁶

Importantly, the counterfactual exercises were performed for both methodologies addressing the zero market share issue, and similarly to the demand and supply analyses, no major differences were found between the two approaches, which is reassuring. Therefore, as in the case of the supply model, we will focus on the estimates using the “Drop” method.

The first counterfactual examines the effects of a consumption tax, τ , of 5% (additional to the existing 3%) on accommodations belonging to professional hosts only. Table 7 presents the average changes (in percentage) relative to the current equilibrium estimates in subsection 5.2. As expected, the additional tax for booking with professional hosts decreases the price charged by professional hosts (by 1.53%), increases the total amount paid by a guest for staying in a professional host’s property (by 3.24%), and decreases professionals’ market share (by 5.52%). Naturally, markups and price-cost margins for professionals decrease. The market share lost by professionals is only marginally captured by nonprofessional hosts within the platform (0.57%), the remaining being captured by the traditional lodging sector (outside option). Considering the accommodation type, the effects for the entire home/apartment and private rooms are identical in signs, but those for private rooms are larger in absolute magnitude.

The second counterfactual examines the effects of a producer tax, ρ, of 5% of the price of accommodations belonging to professional hosts only. Table 8 presents the average changes (in percentage) relative to the current equilibrium estimates in subsection 5.2. Not surprisingly, the tax on renting imposed on professional hosts increases the price charged by professional hosts (by 3.52%), increases the total amount paid by a guest for staying at a professional host’s property in the same proportion (3.52%), and decreases the market share of professionals (by 5.96%). As expected, markups and price-cost mar-gins for professionals decrease. The market share lost by professionals is only marginally captured by nonprofessional hosts within the plat-form (0.61%), the remaining being captured by the traditional lodging sector (outside option). Considering accommodation type, the effects for entire homes/apartments and private rooms are identical in signs.

Comparing both counterfactual scenarios, from the consumer’s perspective, there is an overall higher cost to rent a property belonging to a professional host when the tax is directed at the host; however, it is important to note that the difference is marginal (0.28%). From the producer’s side, the market share of professional hosts experiences a greater percentage decrease when the tax is imposed on them for renting out an accommodation. However, the overall effect of either tax on a professional’s price-cost margins is a reduction of only about three percentage points relative to the baseline scenario.