Auction Design and Auction Outcomes

We study the impact of auction design on the final prices paid by telecommunications operators for the past two decades across the world. Our empirical strategy combines information about competition in the local market, the level of adoption and a wide range of socio-economic indicators. Using a micro dataset of almost every mobile spectrum auction performed so far – both regional and national – we show that auction design affects final prices paid. Two combinations of lot pricing and package rules (SMRA with augmented switching and CCA with core pricing) result in auctions with systematically higher normalized returns. Further, the past history of spectrum awards appears to affect prices paid in subsequent auctions. Previous ownership of commercial lots is linked with higher prices paid per lot which varies across national and regional licences. We discuss the mechanisms of cost minimization and foreclosure faced by operators in different regulatory environments. Our findings have implications for policy-makers and regulators.


Introduction.
Auctions are mechanisms that help allocate resources to those that can use them most valuably. Numerous economic transactions are conducted through auctions including treasury bills, foreign exchange, assets under privatization, mineral and spectrum rights among others (Klemperer, 1999;Binmore andKlemperer, 2001, Salant, 2014). The types of goods auctioned help shape the overall allocation mechanism and the specific rules of the process. For example spectrum rights represent contracts on rivalrous and scarce natural resources where normally no other operator can use the same band or airwaves 3 for a specified period of time. In cases where scarce goods under public control are auctioned, regulators and antitrust agencies try to prevent collusive, predatory and entry-deterring behaviours while maximizing the social gains.
Auction design, rules and regulatory requirements have been central to the political debate for decades. The rapid adoption of mobile communications and digital technologies has rendered a previously underutilized natural resource good -the electromagnetic spectrum -a commodity of major importance. To this end a range of spectrum allocation processes have been used by policy makers in an attempt to maximize the economic and social returns to the local and national economies. The literature suggests that various allocation methods, from administrative awards through beauty contests to alternative auction designs, lead to different levels of normalized social returns to the resource in question (Cramton, 2012 4 ).
Despite the progress in developing auction mechanisms, auction design "is not 'one size fits all' and must be sensitive to the details of the context" (Klemperer, 2001). The "context" represents the specific market structure and potential, the regulatory constraints and the overall economic environment in which firms operate. In the recent history of spectrum auctions researchers observed various types of imperfect outcomes both because of the methods used (the actual design of the process) as well as the understanding of the context. Common methodological oversights include the oversupply of licences compared to the local market needs (Swiss and Italian 3G auctions, 2000) 5 , the lack of control for collusion (tacit or otherwise) among operators (like bid signaling in FCC auctions; Crampton and Schwarz, 2002;Bajari and Yeo, 2009) and high reserve prices for single or packaged lots that end up unsold (Indian auction 2016, for 700MHz, 900MHz and 2.4GHz) 6 . An auction may result in suboptimal social returns in other cases. Illustrative examples are the UK 7 and German 3G auctions in the early 2000s where operators overestimated the value of each lot and paid orders of magnitude more than other operators in similar socioeconomic contexts (Klemperer, 2002b). Some argue that elevated costs of entry in mobile services may have an impact on investment for coverage and quality of connections, and lead to higher prices and subsequently lower adoption rates. As we show in section 3 this finding has often been disputed. 3 In a given region or country 4 http://econ.ohio-state.edu/seminar/papers/120831_TBA.pdf 5 This can be attributed to one operator pulling out before the auction or not participating at all. 6 This ended with only 10% of the envisaged revenues due to very high reserve prices by the regulator. 7 http://news.bbc.co.uk/2/hi/business/727831.stm Are auctions always better than other allocation processes like structured negotiations or "beauty contests"? This is a question that we intend to approach empirically in this paper. In the literature of government security sales the key aspects that affect an auction's results are market thickness, i.e. the guarantee that there is a large pool of bidders for the auctioned lots, and low entry costs (Klemperer, 2001). There have been several experiments with different kinds of auctions that yielded inconclusive results 8 especially with respect to the issue of market power as an impediment to efficient outcomes. While auction design is mainly occupied with the allocation process and its "context" the structural imperfections related to market power of various actors within existing markets (like a dominant position or a new entrant) may also affect the final outcomes. (Morey, 2001 -EEI) Spectrum auctions have gradually displaced beauty contests as the primary mechanism for assigning high value spectrum, especially for mobile communications. Such auctions combine complexity with far-reaching economic impacts, and have stimulated many of the theoretical developments in the past decade. As a result of this activity we now have records of hundreds of spectrum auctions throughout the world. This makes it possible to address some empirical questions about spectrum auction design and auction outcomes. This paper is a first attempt -to our knowledge -of this kind. We address two key questions: First whether auction design influences the outcome in terms of revenue derived, measured by a standard nominal metric of $ per MHz per unit of population (in the coverage area). And second whether the amount paid for spectrum by an operator is linked to that operator's legacy spectrum holdings.
To address these questions we use a micro-dataset of more than 10,000 lots covering 85 countries and 371 auctions for the period 1994-2015. We find that any auction design is preferable to administrative awards, first come/first serve awards and beauty contests in terms of the normalized returns. Moreover sealed bid auctions, simultaneous multiple round auctions (SMRA) and combinatorial clock auctions (CCA) are the key designs used so far. Apart from the overall format some specific components of the design have a significant impact on the final price paid. These include the pricing rules (core pricing, "pay what you bid", "highest loser", etc), the flexibility to choose among combinations of lots (packaged bids) and the switching of spectrum blocks. The leading combinations in terms of the normalized returns are SMRA auctions with augmented switching and the CCA with core pricing. There is substantial heterogeneity across regional and national licences while local socioeconomic conditions help explain a substantial proportion of the residual effects.
We further look into the market power in a given region and its link to the final prices paid. We reconstruct the panel to account for all mergers and acquisitions in the telecommunications industry over the past decades and test the importance of an operator's customer base, its status as incumbent or entrant and the local regulations concerning dominant firms. Our results show that structural imperfections in local markets combined with local regulations have a major impact on normalized returns.
The paper is organised as follows. Section 2 describes our data sources and econometric approach. Section 3 gives our answer to the first question above, together with a brief attempt to set it in the broader context of spectrum management. Section 4 addresses the second question in a similar framework. Section 5 summarises and concludes.

Data and econometric approach
The dataset used in this study is a thorough collection of spectrum auctions in the past decades. It includes 85 countries over 1994-2015 and 13,059 lots from 41 frequency bands and their combinations. The data come from the DotEcon database 9 and manual collection process by the authors. A full description of the variables can be found in Table A.1 of the Appendix. As a normalized metric of the final prices paid we use the natural logarithm of the price of a lot divided by the MHz of spectrum and the population covered ($/MHz/pop). We compare different auction designs, pricing and other rules based on this normalized metric. Figure 1 compares the generic auction formats and shows that SMRA-like and multi-round clock-like auctions designs often return higher normalized revenues. We further show ( Figure A1) that packaged bids have higher chances of increasing the final price paid (normalized) and also that not allowing block switching will lead to similar outcomes ( Figure A2). Our empirical specification models the normalized (log) price of a lot k (i.e. the price per MHz and population covered) sold at a country i at time t as a function of the auction specific parameters as well as a range of local competition and regional socioeconomic conditions. Our baseline empirical specification is: 9 A leading consultancy firm.
where !"# ! is the auction format [SMRA-like, Clock-like, Sealed bid, other], pricing rule, and auction description. !" is a vector of lot and locational and economic characteristics characteristics. ! is a dummy variable to control for unobserved timeinvariant country effects and ! is a dummy variable for unobserved year effects. In order to increase the granularity of the auction designs we further look into eight award class descriptions 10 : Apart from the normalized price effects on the auction design we also embark on a dynamic analysis of how conditional ownership and operator status influence the final prices paid that we observe. For this purpose we look at each country's auctions and cumulate the frequencies held by each operator. This needs to account for all the ownership and naming changes over time 11 .
In this process we introduce three new metrics: !"# is a binary variable for operators that have no ownership of spectrum, !"# is the % ownership of any spectrum in the previous period and !"# !"! the average % spectrum ownership in all previous periods. We also add a control variable for sub 1GHz frequencies ! . This is based on all (measured in MHz) spectrum held from any previous auction and the fraction each operator won. !"# and !"# !"! take values from 0 to 1. With these changes Eq.
(2) now becomes: Introducing the memory it becomes: 10 Award class descriptions include: First come first serve, Beauty contest, Beauty contest with financial bid criterion, Auction-unknown, Auction-other, One-shop sealed bid auction, Standard clock auction, Standard SMRA auction, Standard SMRA auction with augmented switching, Standard CCA with core pricing and Unknown. 11 Operators can change names, merge (within countries) or become part of another group.
Therefore there is a temporal evolution of operators and groups, i.e. Panafon Greece becomes Vodafone in 2001 (part of Vodafone group). This means that Panafon as an operator remains the same (same id) but group changes from sole company (Panafon_id) to group (Vodafone group).
And with full memory it becomes: To capture the actual dynamics of the % ownership we add the first and second order polynomial terms of the full memory, so that it becomes 12 : Bands for popular technologies (2G, 3G, 4G) are often more expensive compared to other spectrum parts. For this on top of the frequency-level controls already included we present the findings of this analysis for each cluster separately (for 2G, 3G and 4G and then for all other frequencies).

Auction design and spectrum auction revenues
One of the long-lasting controversial issues in spectrum management is whether high prices in spectrum auctions have adverse repercussions in communications markets.
To put it in a more challenging way, 'Are spectrum auctions ruining our grandchildren's future? ' (Cave and Valletti, 2000). A major matter of dispute is the extent to which spectrum prices are a sunk cost, so that while expectations of revenues and costs influence bidding in an auction, prices actually paid in that auction have no impact on the subsequent pricing of the spectrum-using service.
The industry generally supports the view that 'high spectrum prices negatively impact consumers and efforts to maximise revenues from spectrum auctions can damage the wider economy (GSMA 2017, p. 3). On the other hand Cambini and Garelli (2017, p.2) conclude on the basis of an empirical investigation using a dataset of firms in 24 countries over ten years that 'spectrum availability and spectrum fees appear to be uncorrelated with mobile operators' revenues, implying that spectrum resources and its value do not have significant impact on industry performance and hence can be considered as sunk expenditures.' The first empirical question to be investigated is whether different auction designs do or do not generate systematically different prices. On the combined assumption of sunk costs and bidder rationality (no winner's curse), there would appear to be no necessary problem with using a design, which raised more cash for the government. For those taking the opposite view, higher prices would entail adverse consequences.
In the case of regional and national lots (column 1) we find that the "Pay your Bid" pricing rule has a strongly positive and significant effect on the normalized metrics of the final outcome of an auction. An almost 50% higher effect is found for second price -highest loser pricing. However once the auction format controls are added (column 3) the effect of the pricing rules dissipates, and final outcomes seem to be driven by the format of the auction instead. The SMRA type of auction variable has the highest effect on final prices paid at 1.223 $/Mhz/pop with multi round clock auctions following at 0.472 $/Mhz/pop and sealed bid auctions at 0.296 $/Mhz/pop. Once the auction format effects are factored in the other parameters of the auction like the use of packaged bids and the switching of blocks change too. The use of packaged bids remains positive across specifications (columns 1 and 3) while the switching of blocks changes sign and becomes positive once the auction formats are added.
Moving to the national lots only (columns 2 and 4), which amount to less than 8% of the lots in the regional category, we observe that the pricing rules remain positive and significant with and without auction format controls. In fact the addition of the "generic" types of auction format is largely insignificant for national lots. The use of packaged bids is also not significant and the use of switching blocks techniques (only relevant in multiple lot and multiple round auctions 13 ) is strongly positive at 0.290  Table 1: Auction formats and rules linked to final prices for national and regional licences 14 The results from columns 1-4 are summarized in Figure    To understand further the link between auction formats and outcomes we break down the auction formats in the three previous categories (SMRA, clock and sealed bid) into 11 award classes that better describe the actual process used in each case. These are found in Table 2 for all licences and national licences separately (columns 1 and 2).
Starting from the first column, we find that beauty contests seem to result in the lowest outcomes with marginal significance (at the 10% level). We get slightly higher results for beauty contests with financial bid criteria -an indication of the importance of these criteria across a range of controls. Moving to the strongly significant results we observe that first come first serve contests are in par with generic types of auctions where we lack the details for their design. The best performance for regional and national competitions (column 1)   The results of Table 2 are relatively aligned across regional and national licences as shown in Figure 3.

Spectrum prices and ownership
A firm's bidding behaviour in a given spectrum award is influenced both by history, including its own legacy spectrum holdings, and by its expectations of the future concerning both the development of the market place in which it operates and the expected future pattern of spectrum awards. This section is concerned with the impact on bidding of a firm's current holdings, defined by the bands in which the licences are located, the unexpired period of the relevant licences and their expectations of the renewal procedure.
In the proposed framework, firms are often assumed to have two types of motive: -Cost minimisation or efficiency: this sees the firm's demand for its overall access to spectrum as derived from its expectation of its customers' demand for services. The demand for the spectrum in any awards thus depends on its expectation of the overall growth of the relevant downstream markets, its expected share of those markets, its existing endowments of spectrum, the auction price, and other factors such as its access to capital to acquire licences.
-(In the case of dominant firms) a foreclosure motive. This is the phrase used by the US Department of Justice (2014) to describe a particular form of strategic behaviour in spectrum markets -the desire of predominantly large firms to push up the prices which its rivals pay for spectrum. A firm may pursue this strategy of raising its rivals' costs even if its own costs rise. The former 'efficiency' motive will make firms' relative willingness to pay for spectrum in an auction depend on where they currently stand in relation to what they perceive to be the efficient combination of inputs into the production process (including in particular, the efficient combination of spectrum holdings and base stations) over the expected lifetime of the award (taking into account expectations of future awards).
A very crude index of operators' relative shortage of spectrum at the moment of an award is to compare their ratios of spectrum holdings to traffic carried, or -even more crudely -number of subscribers. This metric has a number of obvious difficulties, including the problem of aggregating spectrum holdings in different bands. But it also leaves out expectations. For example, if it is expected the market concentration will increase, then larger operators may expect a greater shortfall than smaller ones (other things equal) and this might 'explain' a positive correlation between willingness to pay in an auction and existing spectrum holdings.
In these circumstances we do not seek to investigate the motives underlying bidding behaviour but to investigate whether there is evidence that the size of a firm's legacy holdings influences its auction bids. Building on Eq.
(3)-(6) we present our findings in Tables 3 and 4. Table 3 shows our first finding, that entrants systematically pay less for the same amount of spectrum compared to established players. The effect is relatively low at 0.044$/MHz/pop for all frequencies and slightly lower for commercial ones. However, the sub 1 GHz spectrum seems to be much higher valued by operators across the world. In commercial frequencies the cost of spectrum below 1 GHz can reach 1.283$/MHz/pop.
(1)  Table 3: Entry, sub 1GHz and award class descriptions linked to final prices for national and regional licences 16 Table 4 introduces the historic ownership of spectrum into the regression framework.
To illustrate the effect, calculations based on Table 4 show that an operator that was awarded 30% of the spectrum auctioned in a previous competition is expected to pay 0.06$/MHz/pop in the next auction. Looking into the full history of auctions -that may include non commercial licences and other types of spectrum -we find that the effect remains strong but drops substantially. The results for the quadratic term suggest that there is a local maximum of spectrum ownership beyond which operators stop imposing further increases of the nominal prices paid (inverted u-curve). Testing with higher level polynomials confirms this observation.
(  In order to understand better the relationship between spectrum ownership (in the previous round) and bidding behavior, we split the countries in two groups: the first one does not have any market-power related regulations on significant market power (SMP, source: ITU ICT eye); the second has explicit market-power regulations. We re-ran the models in Table 4 and plot the resulting u-shaped curves in Figure 4. The results suggest that in cases where market power restrictions exist operators restrict their bidding in auctions, possibly to a level that prevents any sanctions. The situation is different in countries or regions without such restrictions. One possible interpretation of this is that in the absence of SMP restrictions on operators, the likelihood of foreclosure is increasing in the percent of spectrum ownership of each operator.

Conclusion
In this paper we analyse the impact of auction design on final prices paid using a broad dataset of thousands of lots awarded over the period 1994-2015. We identify the key mechanisms that result in the highest returns (SMRA with augmented switching and CCA with core pricing). We further look into the importance of structural market dynamics using the percent of spectrum awarded to each operator in the previous round(s). We find a link between ownership and price paid. A past history of success in spectrum awards has a positive effect on prices paid subsequently. It is possible that the manner in which this effect operates may depend upon local regulations, as our analysis indicates.
This study is a first step in the empirical analysis of auction outcomes at a global scale. We believe that future research based on more granular auction data can shed light not only on auction processes but also on the link between final prices paid in auctions and subsequent market outcomes, such as competitive structures, average revenues per capita, coverage, and new technology adoption levels. The total amount of spectrum available in the award (should be paired plus unpaired) Available Spectrum (Paired, MHz) The amount of paired spectrum available in the award Available Spectrum (Unpaired, MHz) The total amount of unpaired spectrum available in the award

Lotid
Unique identifier for each lots (or, in the case where lot-by-lot data could not be recorded, each winner's winning package) Licence duration The term of the licence in years. This can be expressed as a decimal to reflect nonwhole years. Winner The name of the winner of the licence.

Region
The region corresponding to the licence Population covered The estimated population covered by the licence Size (MHz) Total amount of spectrum in MHz of the licence (paired plus unpaired spectrum) Paired (MHz) Total amount of paired spectrum in MHz of the licence Unpaired (MHz) Total amount of unpaired spectrum in MHz of the licence Lot price Licence price for the lot awarded. This is the 'headline' price in local currency and does not include any annual fees over the term of the licence plus any other fees e.g. administrative fees Package price Licence price for a package, where it is not possible to split this by lot (e.g. combinatorial auction). This is the 'headline' price in local currency and does not include any annual fees over the term of the licence plus any other fees e.g. administrative fees Lot reserve price The reserve price for the lot awarded. This is in local currency and does not include any annual fees over the term of the licence plus any other fees e.g. administrative fees Package reserve price The reserve price for a package (where applicable). This is in local currency and does not include any annual fees over the term of the licence plus any other fees e.g. administrative fees Payment year The payment year to which the amounts in the following two columns refer two.
Year 0 represents upfront payments.

Amount due
The total estimated payment amount that is due in this payment year for the corresponding lot/package Annualfee The component of the 'amount due' that reflects annual fees, as opposed to the licence fee established in the award process Country area (Sq Km) The  The local currency at the time of the award PPP rate (local currency to USD) Purchasing power parity (PPP) conversion factor is the number of units of a country's currency required to buy the same amount of goods and services in the domestic market that a U.S. dollar would buy in the United States. The reported rate is based on GDP and corresponds to the year of the award. popDensity Population density in specified year urbanPop Population living in urban areas as defined by national statistical offices. It is calculated using World Bank population estimates and urban ratios from the United Nations World Urbanization Prospects. GDPLocalCurrencyReal GDPLocalCurrencyNominal GNILocalCurrencyReal GNILocalCurrencyNominal GDP at purchaser's prices is the sum of gross value added by all resident producers in the economy plus any product taxes and minus any subsidies not included in the value of the products. It is calculated without making deductions for depreciation of fabricated assets or for depletion and degradation of natural resources. The nominal term is based on current prices in local currency, i.e. not inflation adjusted. The real term has been adjusted for inflation using the GDP deflator which is based in different years for different countries. GNI (formerly GNP) is the sum of value added by all resident producers plus any product taxes (less subsidies) not included in the valuation of output plus net receipts of primary income (compensation of employees and property income) from abroad. This data is in local currency, real versus nominal as per GDP terms above. gini Gini index measures the extent to which the distribution of income or consumption expenditure among individuals or households within an economy deviates from a perfectly equal distribution. A Lorenz curve plots the cumulative percentages of total income received against the cumulative number of recipients, starting with the poorest individual or household. The Gini index measures the area between the Lorenz curve and a hypothetical line of absolute equality, expressed as a percentage of the maximum area under the line. Thus a Gini index of 0 represents perfect equality, while an index of 100 implies perfect inequality. inflationConsumerPricesPercent Inflation as measured by the consumer price index reflects the annual percentage change in the cost to the average consumer of acquiring a basket of goods and services that may be fixed or changed at specified intervals, such as yearly. The Laspeyres formula is generally used. inflationGDPDeflatorPercent Inflation as measured by the annual growth rate of the GDP implicit deflator shows the rate of price change in the economy as a whole. The GDP implicit deflator is the ratio of GDP in current local currency to GDP in constant local currency. telephonemainlines Telephone lines are fixed telephone lines that connect a subscriber's terminal equipment to the public switched telephone network and that have a port on a telephone exchange. Integrated services digital network channels ands fixed wireless subscribers are included. mobilesubscribers The number of mobile subscribers fixedBroadbandSubscribers Fixed broadband Internet subscribers are the number of broadband subscribers with a digital subscriber line, cable modem, or other high-speed technology.