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Article Excerpt
Economic analysis of spectrum policy focuses on government revenues derived via competitive bidding for licenses. Auctions generating high bids are identified as "successful" and those with lower receipts as "fiascoes." Yet spectrum policies that create rents impose social costs. Most obviously, rules favoring monopoly predictably increase license values but reduce welfare. This article attempts to shift analytical focus to efficiency in output markets. In performance metrics derived by comparing 28 mobile telephone markets, countries allocating greater bandwidth to licensed operators and achieving more competitive market structures are estimated to realize efficiencies that generally dominate those associated with license sales. Policies intended to increase auction receipts (e.g., reserve prices and subsidies for weak bidders) should be evaluated in this light.
1. Introduction
* Competitive bidding to assign wireless licenses constitutes a substantial policy advance.
Following their suggestion by Leo Herzel (1951) and Ronald Coase (1959), auctions were finally adopted by New Zealand in 1989 (Crandall, 1998), India in 1991 (Jain, 2001), and the United States in 1993 (McMillan, 1994). At least 25 other countries have instituted license auctions in recent years (Hazlett, 2008b).
The argument for using the "price system" to allocate wireless licenses is premised on three types of economic efficiencies:
(i) elimination of rent dissipation associated with "comparative hearings" or "beauty contest" awards (Kwerel and Felker, 1985);
(ii) assignment of licenses to the most productive suppliers, saving the costs of secondary market reassignments (Cramton, 2002);
(iii) generation of public revenues, displacing taxes; the consensus estimate is that $0.33 in social cost is saved for every tax dollar saved (Cramton, 2001; Klemperer, 2002b). (1)
A healthy literature on the implementation of wireless auctions has emerged. (2) Revenues raised by government auctions are seen both as indicators of auction design efficiency and as appropriated surplus that increases social welfare by offsetting activity-distorting taxes. Consequently, auction success is typically measured by license receipts. (3)
In evaluating alternative bidding mechanisms, Paul Klemperer has written: "What really matters in auction design are the same issues that any industry regulator would recognize as key concerns: discouraging collusive, entry-deterring and predatory behavior.... By contrast, most of the extensive auction literature ... is of second-order importance for practical auction design" (Klemperer, 2002b, emphasis in original). (4)
This approach, "just good undergraduate industrial organization" (Klemperer, 2002b), is unassailable. But an essential analytical conflict is left intact: auction rules that alter market structure or operator performance produce welfare effects, and these spillovers may not be systematically incorporated. For instance, arguments are often advanced to improve license auctions by imposing reserve prices, (5) extending credits to "weak bidders," (6) or restricting the number of licenses (to increase scarcity value). (7) In addition, the social discount rate is ignored in auction processes that delay productive use of frequencies for months or years.
The problem is put into perspective with some simple estimates of social value. Empirical research undertaken a decade ago found the annual consumer surplus associated with U.S. cellular telephone licenses (issued in the 1980s) at least 10 times as large as annual producers' surplus (Hausman, 1997; Rosston, 2001). Today, U.S. wireless phone market data yield an annual consumer surplus estimate of at least $150 billion. (8) The total revenue obtained from selling all wireless licenses (not just for mobile telephony) is just $53 billion. (9) Given that the latter is a present value and the former an annual flow, these data suggest that the ratio (CS to PS) is much above an order of magnitude.
Policies undertaken to improve license revenues, then, focus on a small fraction of the economic value at stake. Rules that increase auction bids but risk collateral damage--say, by reducing operator efficiency or market competitiveness--generate potential costs not properly evaluated by reference to rent extraction alone. This is true even when revenues raised by license auctions do, ceteris paribus, increase welfare.
We offer an extension of the Klemperer critique. Economists should not only consider market structure effects within auctions but should incorporate consumer welfare effects from wireless output markets whenever alternative auction rules influence not only public rent extraction but retail prices.
We hasten to note that Paul Klemperer has correctly diagnosed the temptation to favor monopoly rent creation over competitive output markets. Klemperer (2002b) comments on a proposal by Italian regulators (not, in fact, implemented) to eliminate a 3G (10) license (and the competitor it would empower) in order to raise auction revenues: "[T]he approach was fundamentally flawed ... it is putting the cart before the horse to create an unnecessarily concentrated mobile-phone market to make an auction look good" (Klemperer, 2002b). (11)
In contrast, however, Klemperer endorses the policy implemented in 3G license auctions held in Belgium and Greece in 2001. Both countries appear to have raised incremental revenue by imposing reserve prices. The result was that each country sold three wireless licenses, with a fourth unsold. Klemperer credits the authorities for producing receipts of about 45 Euros per person, a rent extraction generating some public financing efficiency. Excluded from the analysis, however, is the fact that each unsold license was allocated approximately 35 MHz of bandwidth, (12) and that this frequency space could have been productively employed by a fourth network (if a willing entrant had come forth at a license price of between and 45 Euros per capita (13)) or divvied up among the three incumbent networks to expand capacity. (14)
After calibrating an empirical model measuring the relationship between frequencies allocated to cellular service and retail prices, we find that the welfare cost of withholding spectrum via reserve prices likely exceeded public gains from the revenues raised in either Belgium or Greece. This is one frequently encountered example of how policies prescribed for license assignments alter market structure. The problem arises when the auction analysis does not then incorporate attendant welfare effects. We offer a critique of analytical partitioning that is asymmetrically broached.
Our empirical analysis focuses on wireless telephone service in 28 countries, of which 19 employ auctions to assign licenses. After adjusting for cross-sectional differences in demand and supply, we find that larger quantities of spectrum, as well as more intense competitiveness (measured by the Herfindahl-Hirschman Index), are strongly associated with lower prices. We then use the coefficient estimates from our model to perform simulations quantifying retail market effects associated with various policy changes. In general, auction rules intended to increase license rent extraction by restricting spectrum access are not welfare enhancing. Restricting the use of spectrum inputs is a relatively expensive way to raise public funds.
This article is organized as follows. In Section 2, we describe our empirical model and report regression results. Section 3 uses these estimates to simulate welfare effects of policy choices made in the design of license auctions. Section 4 offers a conclusion.
2. The relationship between spectrum and retail prices
A simple model. Consider a market where N firms will be producing a homogeneous mobile telephone service, with output levels given by [q.sub.i] where i identifies the firm. We assume there is no initial incumbent. Aggregate output is given [[summation].sub.i] [q.sub.i] = Q. The market price associated with this output is defined by the inverse demand function p(Q).
Firm i has a cost function assumed to adopt the form
[C.sub.i]([q.sub.i]) = c([K.sub.i], [S.sub.i])[q.sub.i]. (1)
This implies constant marginal cost given a particular level of capital, [K.sub.i], and the amount of spectrum, [S.sub.i], allocated to the license awarded firm i. When quantity decisions are made, capital and spectrum are fixed and the prices paid for these resources are sunk. In order to focus the analysis on spectrum allocation policies, we assume symmetric investments ([K.sub.i] = K for all i). Marginal cost is decreasing in capital and spectrum, and these two inputs are substitutes (engineering cost models indicate that for a given level of service, as the amount of spectrum [MHz] increases, capital cost per subscriber falls [Reed, 1992]).
In what follows we assume Cournot competition. We denote market share as [s.sub.i] = [q.sub.i]/Q, and price elasticity of demand as [epsilon](Q). The spectrum allotted to a given license can be written as [S.sub.i] = [[phi].sub.i]S, < [[phi].sub.i] [less than or equal to] 1, where S is the total amount of spectrum assigned to wireless services. In such a context it is easy to show that a mark-up equation is defined by (15)
p(Q) = [[1 + HHI/[epsilon](Q)].sup.-1] [N.summation over (i=1)] [s.sub.i]c(K, [[phi].sub.i]S). (2)
We interpret the equilibrium mark-up equation (2) as one where the supply depends on the elasticity of demand [epsilon](Q), the level of investment (K), the amount of allocated spectrum (S), and the Herfindahl-Hirschman Index (HHI).
We assume demand for wireless telephony to be a function of the price of wireless service (p), income level (Y), and the price of alternative telephone services (F). (16) In principle, we can posit a constant elasticity of demand function for wireless telephony such that
Q = [lambda][Y.sup.[delta]][F.sup.[rho]][p.sup.[epsilon]]. (3)
* Empirical estimation. The empirical implementation of our model is based on the estimation of a system formed by an empirical mark-up equation, motivated by the variables in equation (2), and an expanded log-log version of the demand function given by equation (3). Both include nonlinear terms. The benchmark system is given by:
Empirical mark-up equation:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)
Empirical demand equation:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (5)
where i denotes the country and t the period, and ln stands for natural logarithm. Variables are defined as follows:
RPM Revenue per minute in constant 2000 US$ for mobile voice services.
Q Output, measured as total minutes of use per month (totmin) in millions.
HHI Herfindahl-Hirschman Index in the market (0-10,000).
Spectrum Aggregate bandwidth available for mobile phone service by all operators in the market. Measured in MHz.
Density A proxy for capital cost. Measured as mean inhabitants/square kin.
Auction Dummy variable = 1 if wireless licenses awarded via auction; elsewise.
NotCPP Dummy variable = 1 if the market not using calling party pays rule.
GDPpc Gross Domestic Product per capita in constant 2000 US$.
Fixprice Mean price of 3 minute local fixed network peak period call in constant 2000 US$.
Data, primarily from Merrill Lynch (2003), are quarterly from 1999I through 2003II for wireless telephone markets in 28 countries. Retail prices are proxied by mean revenue per minute of use for voice services (excluding data). (17) The time series were incomplete for some countries, yielding unbalanced panel data. A detailed description of the sample is given in Appendix A. Summary statistics are displayed in Table 1.
(4) and (5) represent a system of equations in the endogenous variables ln(RPM) and ln(TOTMIN). Given a sample of countries and quarterly data, we initially ran a fixed-effects model to control for factors specific to the countries, such as population size and institutional differences. One problem encountered was that the variable Fixprice took the value zero in several countries (e.g., USA). To control for this truncation we introduced a dummy variable, dumfix, which takes the value of unity if the fixed line price is zero, and is otherwise equal to zero. Omitting Fixprice, we then included a variable defined as (1 - dumfix) * ln(Fixprice) as a regressor we labeled Alfixprice. Given that dumfix did not change within countries during the sample period, it was absorbed in the fixed-effects component. Likewise, the variables Auction and NotCPP dummies did not change over time for given countries, so in a standard fixed-effects model their role would be missed. Another issue involved the Herfindahl-Hirschman Index, which should not be considered exogenous. When additional spectrum is allocated, it is expected to negatively impact market concentration. We will return to this problem momentarily.
The estimation procedure adopted involves three stages. In the first, we perform a "within" transformation for unbalanced panel data. Then we run a standard 3SLS regression for the system of equations (4) (5) considering as endogenous variables ln(RPM), ln(TOTMIN), and ln(HHI). In the second, we use the residuals of the first stage to capture the effect of time-invariant variables (NotCPP and Auction dummies in our database), generating pseudo-fixed effects. In the third, we again perform a 3SLS procedure to estimate the system with the variables in levels, including the pseudo-fixed effects and time-invariant explanatory variables. The details are given in Appendix B. A summary of final results for different specifications of the model is given in Table 2. The upper part of the table corresponds to the mark-up equation and the lower to the demand equation. Results for the preferred specification (model 6) are given in the last column and are referred to here. (18) The model selection process is described in Appendix B.
The use here of fixed-effects panel data estimation could be challenged on various grounds. On the one hand, a totally pooled model is the simplest approach. Following Baltagi (2001), a direct application of an F-test (separately applied for the demand and mark-up equations) permits us to reject, at a 1% confidence level, the null hypothesis that the fixed effects are all the same. (19) On the other hand, differences among countries could not be constrained to intercept terms and may make slopes "country specific." The size of our panel is of insufficient scale to statistically reject this hypothesis. (20) We assume, as is often done, that a fixed-effects model is reasonable, supporting the assumption while improving the efficiency of our estimations by employing a pseudo-fixed-effects approach. This permits us to measure the effect of time invariant variables.
The pseudo-fixed-effects model constrains the interpretation of coefficient estimates driven primarily by cross-country variation. The slope estimates relied on to evaluate policy counterfactuals are produced with an embedded assumption that, after controlling for explanatory variables that include fixed effects and time-invariant variables, incremental impacts on equilibrium output (associated with, say, spectrum allocation changes)...
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