Abstract
There is a long history of governmental efforts to protect personal privacy and strong debates about the merits of such policies. A central element of privacy is the ability to control the dissemination of personally identifiable data to private parties. Posner, Stigler, and others have argued that privacy comes at the expense of allocative efficiency. Others have argued that privacy issues are readily resolved by proper allocation of property rights to control information. Our principal findings challenge both views. We find: (a) privacy can be efficient even when there is no “taste” for privacy per se, and (b) to be effective, a privacy policy may need to ban information transmission or use rather than simply assign individuals control rights to their personally identifiable data.
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Notes
A distinct conception of privacy is autonomy, both from the state (e.g., the right to choose to have an abortion) and from annoyance by other private parties (e.g., the ability to be free of telemarketing calls). For an early discussion by an economist of privacy as autonomy, see Hirshleifer (1980).
Even this trend is not new. Concerns about increasing surveillance and data processing led to the amendment of the California State Constitution in the early 1970s to include an explicit right to privacy.
See, e.g. ``Greeting Big Brother with Open Arms,” New York Times, January 17, 2004, B9.
See Smith (2003) for a recent summary of federal legislation.
Another situation in which privacy concerns arise is one in which the individual wishes to prevent a trading partner from intentionally or unintentionally sharing information with a third party (e.g., the sale of mailing lists or the failure to take adequate measures to secure a database of credit card numbers). Of course, the two cases are linked when the third party obtaining the information is also one of the individual's trading partners. For a recent analysis of thirdparty sharing, see Kahn et al. (2000). See also Calzolari and Pavan (2004), who establish conditions under which privacy is a equilibrium outcome but do not examine whether such outcomes are efficient, and work cited therein.
See Taylor (2004) for a recent analysis along these lines.
This does not, however, imply that protecting privacy will promote efficiency. Depending on the elasticity of demand for information, implementing a privacy policy that raises the cost of collecting information might actually worsen the inefficiency by leading to higher levels of socially unproductive expenditures.
This effect of privacy is implicit in the lemons model of Akerlof (1970) lemons model of asymmetric information. It can also be viewed as an extreme form of the first mechanism identified by Posner and Stigler.
We observe that, in order to understand the full effects of privacy policies, one must also examine other potential market responses to privacy, such as insurance suppliers' relying on employerpurchased plans to reduce selfselection. Wathieu (2002) examines the roles of intermediaries (e.g., employers) who possess finer information about customers (e.g., insurees) than product or service producers (e.g., insurance companies).
Stigler (1980) at 630–631.
Murphy (1996) at 2382.
For a seminal analysis of the effects of ex post contracting on ex ante incentives, see Williamson (1975).
The structure of the argument is isomorphic to the logic of granting patents and other intellectual property rights.
Curiously, despite reaching his overall conclusion that privacy is harmful, Stigler (1980) also observes that disclosure can discourage efficient investment in obtaining information. He apparently failed to notice that this fact can be construed as an argument that privacy protection can be efficiency enhancing.
For a recent analysis in a related context, see Kahn et al. (2000).
This argument is an application of the general theory of the second best (Lipsey and Lancaster, 1956).
For example, Shapiro and Varian (1997, pp 29 and 30) argue that:
The right way to think about privacy, in our opinion, is that it is an externality problem. I may be adversely affected by the way people use information about me and there may be no way that I can easily convey my preferences to these parties. The solution to this externality problem is to assign property rights in information about individuals to those individuals. They can then contract with other parties, such as direct mail distributors, about how they might use the information.
See, e.g., Hermalin and Katz (2006) for a discussion.
See, e.g., Posner (1981) at 405.
Observe that we are assuming that the value of transacting with a given household is independent of a firm's transactions with other households.
See, for instance, Varian (1997).
In what follows, we could invoke the revelation principle, but the discussion in terms of general mechanisms better shows the logic of the argument.
For an early application of this type of unraveling argument in a monopoly context, see, e.g., Grossman (1981).
Kahn et al. (2000) appear to obtain a conflicting result. However, as they themselves note, the assignment of property rights affects the equilibrium outcome in their model because of restrictions they place on the scope of contracts that can be written.
That is, \(\frac{{f_2 (\theta )}}{{f_0 (\theta )}}\) increasing implies \(\frac{{f_0 (\theta )}}{{f_1 (\theta )}}\) is increasing as well.
This assumption rules out the possibility that marginal information rents fall as x _{θ} increases. If the marginal rents fell sufficiently fast, the monopolist's problem would not be concave and multiple equilibria might exist, making comparative statics difficult.
The restriction to thirddegree price discrimination when individual consumers have downward sloping demand curves is as an example of the price rigidities discussed in the introduction.
For instance, suppose there are three types, with types 1 and 3 plentiful (especially type 1), while type2 households are relatively rare and have demands close to those of type1 households. Under privacy, it could be profitmaximizing to bunch types 1 and 2 at the same x > 0. Now consider the partition in which 1 is alone and 2 and 3 are together. Now the monopolist could prefer to shut out type 2. That is, partitioning in this way leads to type 2's consumption going down.
Assumption (c) and condition (ii) are satisfied, for example, by a Poisson distribution with mean less than \(1 + \sqrt 3\).
For example, an emerchant could require consumers to sign up and provide personal information before being allowed to shop.
The adverse selection structure is similar to a used car market in which workers are the sellers of used cars and employers are potential buyers of used cars as studied in Akerlof's (1970) seminal article.
Levin (2001) has shown that a particular form of improved information (discussed below) can raise or lower efficiency when θ is continuously distributed.
Because vθ_{1} < θ_{2}, there is also a perverse Nash equilibrium in which employers expect workers of ability θ_{2} not to seek employment and, thus, employers never bid above νθ_{1}. However, this is not Bayesian perfect under the market structure assumed here. If an employer deviated and offered a wage of θ_{2} + ɛ, ɛ an arbitrarily small positive number, then all workers would be willing to be employed by that firm and the deviating employer would earn positive expected profit for sufficiently small ɛ because νθ_{A} (g) − θ_{2} > 0.
Straightforward calculations reveal that the sign of the change is equal to the sign of 1 − 2g _{2}.
If health status is a perfect indicator of ability, then the norevelation equilibrium doesn't exist.
A wellknown necessary condition for efficiency is that total output rises, but this is not easily computed a priori.
One rationale for this approach is that allowing price discrimination weakly raises a producer's profits, and this may generate increased investments in plant or R&D that benefit consumers in the long run. Of course, letting all firms in an industry engage in price discrimination might lower their profits. And there is no general theorem stating that the additional R&D is always worth more to consumers than its cost.
The relevant aspects of Topkis's Monotonicity Theorem can be summarized as follows: Let X be a lattice and Y be a partially ordered set (a property clearly satisfied by the interval [0,1]). Let \(\phi (x,y):X \times Y \to \Re\) be supermodular in x for any given y and let that function exhibit decreasing differences in x and y. Then, if y ≤ y′, the join (pointwise maximum) of the x that maximizes φ(x, y) and the x′ that maximizes φ(x, y′) maximizes φ(x, y).
Calculations for parts (b) and (c) available from the authors upon request.
We ignore the pathological cases in which the largest solution is a tangency or there is no largest solution because there are infinitely many solutions. ν < 2 and F _{σ}(θ) weakly concave are sufficient to rule out such cases.
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Acknowledgment
The authors would like to thank Thomas Davidoff, Giancarlo Spagnolo, Jean Tirole, Hal Varian, Michael Waldman, and Luc Wathieu, as well as participants in the 2004 “Quantitative Marketing and Economics Conference” and 2004 “Conference on the Economics of Electronics Communications Markets,” for helpful discussions of these issues. We are particularly grateful to an anonymous referee. An earlier version of this paper was titled “Is Privacy Efficient? The Economics of Privacy as Secrecy.”
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Appendix
Appendix
We begin by describing the general form of the problem faced by the profitmaximizing monopolist considered in the text. The incentive compatibility and individual rationality constraints associated with the seller's program are
and
respectively. It is well known, that the seller's profit maximization program reduces to:
where \(F_\sigma (\theta ) \equiv \sum\nolimits_{i = 1}^\theta {f_\sigma (i)}\).^{Footnote 41} The marginal benefit to the monopolist of increasing x _{θ} is thus proportional to
(we need not worry about the definition of b _{ K } _{+1}(·) because 1 − F _{σ}(K)=0). The firm increases x _{θ} as long as (A2) is positive, unless the \(x_{\theta + 1} \ge x_\theta\) constraint binds.
Define f _{λ}(·) ≡ (1 −λ)f _{ m }(·) + λf _{ n }(·), and define F _{λ}(·) analogously. Observe that, if f _{ m }(θ) / f _{ n }(θ) is monotonic in θ, then so too is f _{λ}(θ) / f _{ n }(θ). Define
where x ≡ (x _{1}, …, x _{ K }). Let X be the subset of ℜ^{K} such that \(x_{\theta + 1} \ge x_\theta \ge 0\quad\)for all \(\theta \in \{ 1, \ldots K  1\}\).
Lemma A.1.
Suppose that, for all \(x < x_\theta ^w\), \(b_{\theta + 1} (x)  b_\theta (x)\) is nondecreasing in x for all \(\theta \in \{ 1,2,\ldots,K  1\}\). Then V(x, λ) and X have the following properties:

(a)
V(·, λ) is supermodular for all λ.

(b)
V(·, λ) has a unique maximizer in X for all λ.

(c)
V(·,·) has decreasing first differences if f _{ n } (θ) / f _{ m } (θ) is increasing in θ.

(d)
X is a lattice.
Proof:

(a)
By Topkis's Characterization Theorem (Milgrom and Roberts, 1990), property (a) is implied by the fact that \(\frac{{\partial ^2 V}}{{\partial x_\theta \partial x_{\hat \theta } }} \ge 0\quad\)for \(\theta \ne \hat \theta\).

(b)
V(·, λ) attains a maximum over X because V(·, λ) is continuous and bounded and there would be no loss of generality in limiting its domain to \(X \cap [0,x_K^w ]^K\), which is closed and bounded. \(b_\theta (x)\) is decreasing and \(b_{\theta + 1} (x)  b_\theta (x)\) nondecreasing in x for all \(\theta \in \{ 1,2,\ldots ,K  1\}\). Thus, V(·, λ) is concave. Given that X is convex, the maximizer of V(·, λ) is unique.

(c)
The additive separability of V(x, λ) with respect to the components of x implies it is sufficient to show decreasing differences with respect to a single x _{θ}, which can be shown by demonstrating that the crosspartial derivative of V with respect to λ and x _{θ},
$$ \frac{{(F_n  F_m )f_\lambda + (1  F_\lambda )(f_n  f_m )}}{{f_\lambda ^2 }}(b_{\theta + 1}  b_\theta ), $$(A3)is negative, where arguments have been suppressed for readability. Straightforward algebra reveals that the sign of (A3) equals the sign of F _{ n }(θ) − F _{ m }(θ). As is well known, f _{ n }(θ) / f _{ m }(θ) increasing in θ implies that F _{ m }(θ) > F _{ n }(θ) for all θ < K, which establishes (c).

(d)
X is a lattice if the meet (pointwise minimum) and join (pointwise maximum) of any two elements of X are in X. Suppose the join of x ^{1} and x ^{2} was not in X for two elements x ^{1} and x ^{2} of X. Then there must exist a θ such that \(\max \{ x_\theta ^1 ,x_\theta ^2 \} > \max \{ x_{\theta + 1}^1 ,x_{\theta + 1}^2 \}\), which is impossible given that \(x_\theta ^i < x_{\theta + 1}^i\) for i=1, 2. The proof that the meet is in X is similar.
Lemma A.2.
Let z be the value of x ∈ X that maximizes V(x, λ). Then z uniquely maximizes Π(x, λ) subject to x ∈ X, where
Proof:
In maximizing either V or Π, there are K − 1 constraints of the form \(x_{\theta + 1}  x_\theta \ge 0\). Form the Lagrangian
where μ_{0} is the Lagrange multiplier on the restriction that sales be nonnegative and μ_{ K } ≡ 0. Making the change of variables \(\alpha _\theta = \mu _\theta  \mu _{\theta  1}\), the Lagrangean is
We have a solution if there exist x and \(\{ \alpha _\theta \}\) such that
and
We can similarly write the Lagrangean for the V problem as
The problem is unchanged if we scale each Lagrange multiplier by defining \(\hat \alpha _\theta \equiv \tilde \alpha _\theta f_\lambda (\theta )\). We then have a solution for the V problem if there exist x and \(\{ \hat \alpha _\theta \}\) such that
and
Multiplying (A5) by f _{λ}(θ), we see that, if x and \(\{ \hat \alpha _\theta \}\) are a solution to (A5), then they also satisfy (A4). V and Π are both concave (the proof of the latter parallels the proof that V is concave) and X is convex. Hence, both V and Π have unique maximizers in X. Therefore the x and \(\{ \hat \alpha _\theta \}\) that solve the V problem are the unique solution to the Π problem.
Proof of Proposition 3:
(a) When σ=q is good news, f _{ q }(θ) / f _{0}(θ) is strictly increasing. Define f _{λ}(·) ≡ (1−λ)f _{0}(·) + λf _{ q }(·). By Lemma A.2, we need only compare the consumption allocation that maximizes V(x, 0) to the one that maximizes V(x, 1). Denote the former by x ^{0} and the latter by x ^{q}. By Lemma A.1, Topkis's Monotonicity Theorem (Milgrom and Roberts, 1990) implies that the pointwise maximum of x ^{0} and x ^{q} also maximizes V(x, 0).^{Footnote 42} Because V(x, 0) has a unique maximizer (Lemma A.1), the pointwise maximum of x ^{0} and x ^{q} equals x ^{0}; that is, \(x_\theta ^0 \ge x_\theta ^q\) for all θ. As discussed in the text, there is no distortion at the top: \(x_K^0 = x_K^q = x_K^w\). Because there is no negative consumption, \(x_\theta ^0 = 0\) implies \(x_\theta ^q = 0\). To conclude our proof of part (a) we need to show that \(x_\theta ^0 > 0\) implies \(x_\theta ^0 > x_\theta ^q\) for θ < K. Suppose, counterfactually, that there exists at least one θ < K such that \(x_\theta ^0 = x_\theta ^q > 0\). Consider the smallest such θ, \(\tilde \theta\). Because \(\tilde \theta\) is the smallest such θ, it must be that \(\smash{x_{\tilde \theta }^q > x_{\tilde \theta  1}^q }\) (without loss of generality, we can use the convention \(\smash{ x_0^\sigma = 0 }\) should \(\tilde \theta = 1\)). The fact that the \(x_{\tilde \theta }^q \ge x_{\tilde \theta  1}^q\) constraint is not binding implies that
As is well known, if f _{σ}(θ) / f _{σ} ^{′}(θ) is increasing, then
Hence,
This expression implies that the constraint that \(x_{\tilde \theta }^0 \le x_{\tilde \theta + 1}^0\) is binding when σ=0 (if not, then it would be profitable to increase \(x_{\tilde \theta }^0\), contradicting the optimality of x ^{0}). Given x ^{0} ≥ x ^{q} , \(x_{\tilde \theta }^q = x_{\tilde \theta }^0 = x_{\tilde \theta + 1}^0\) implies \(x_{\tilde \theta }^q = x_{\tilde \theta + 1}^q\). Moreover, this argument can repeated inductively so that if \(x_{\tilde \theta }^0 = x_{\tilde \theta + i}^0\) for i=1, …, I, then \(x_{\tilde \theta }^q = x_{\tilde \theta + i}^q ( = x_{\tilde \theta }^0 )\) for i=1, …, I. Because it is never optimal to set \(x_\theta > x_\theta ^w\), we know \(\tilde \theta + I < K\); that is, there is a type \(\tilde \theta + I + 1\) such that \(x_{\tilde \theta }^0 = \cdots = x_{\tilde \theta + I}^0 < x_{\tilde \theta + I + 1}^0\). Substituting the constraint \(x_{\tilde \theta }^q = \cdots = x_{\tilde \theta + I}^q\) in the maximization of V(x, 1) (recall λ=1 corresponds to σ=q), the firstorder condition with respect to \(x_{\tilde \theta }^q\) implies
where the second line follows from (A6) and the fact that \(\smash{ x_{\tilde \theta }^0 < x_{\tilde \theta + I + 1}^0 }\). But this implies that it would be feasible to increase profits when σ=0 by raising \(\smash{ x_{\tilde \theta }^0 =\cdots = x_{\tilde \theta + I}^0 }\), which contradicts the optimality of x ^{0}. Hence, by contradiction, we've established the rest of part (a).
Part (b) has the identical proof, except that, now,f _{λ}(·) ≡ λf _{0}(·) + (1−λ)f _{ q }(·).
Proof of Proposition 4:
Let –s be the common slope. Let b _{2}(x) − b _{1}(x)=δ, where δ > 0. If x _{1} is an interior solution, then it follows from (A2) that
where H _{σ}=f _{σ}(2) / f _{σ}(1). An interior solution exists only if and only if \(\beta > \delta H_\sigma\). The resulting deadweight loss triangle per lowtype is \({\textstyle{s \over 2}}(x_1^w  x_1 )^2\).
Consider each case in turn:

(a)
If \(\beta \le \delta H_0\), then \(x_1 = 0\) under privacy and the deadweight loss is maximized. If β > min{δH _{1}, δH _{2}}, then \(x_1 > 0\) for one subpopulation absent privacy, and privacy is less efficient.

(b)
When β > max{δH _{1}, δH _{2}}, direct calculations show that privacy reduces deadweight loss.^{Footnote 43}

(c)
The percapita deadweight loss under dissemination tends to 0 as the sorting of household types becomes perfect and thus dissemination is then more efficient than privacy. Instances in which the information improvement lowers total surplus can be constructed by making use of (b) and the continuity of average deadweight loss with respect to the proportion of low types, and considering values of max{δH _{1}, δH _{2}}that are just above \(\beta\).
Proof of Proposition 5:
As a preliminary, observe that, if (A2) is strictly increasing in θ for all x, then the associated order constraint (i.e., \(x_{\theta + 1} \ge x_\theta\)) is not binding and \(x_\theta\) is found by setting (A2) to zero and solving. Therefore, if (A2) is strictly increasing in θ for two distinct values of σ, say m and n, and if
then \(x_\theta\) is greater when σ=m than when σ=n.
By assumptions (b) and (c), (A2) is strictly increasing in θ for all x when σ=0 (recall \(b_\theta (x)\) is strictly increasing in θ).
Suppose types are partitioned into J blocks, and let S _{ j } denote the maximal element in block j. Index the blocks so that \(1 \le S_1 < \cdots < S_J = K\). Let σ=j be that value of the indicator variable that indicates that a household with that realization of σ is in the j ^{th} block.
Under condition (i), any type in block i is lower than any type in block j if i < j. Observe that f _{σ}(θ) is equal to \(f_0 (\theta ){\textstyle{{N_0 } \over {N_\sigma }}}\) if θ is in the σ^{th} block and 0 otherwise. Hence,
for θ in the σ^{th} block. The inequality is strict for all blocks except block J. As noted before, there is no distortion for the top type within any population or subpopulation; hence, each type S enjoys efficient consumption. Except for S _{ J }, this represents a strict increase in efficiency. For S _{ J } (i.e., K), there is no change in efficiency. For the other types, recall that the marginal profit function is proportional to
From (A7), a switch from σ=0 (i.e., privacy) to σ ∈ {1, … , J}, cannot lower the marginal profit function and, for σ ∈ {1, … , J−1}, it strictly increases it. Hence, the consumption of these types increases, at least weakly. Because at least some types consume an amount strictly more efficient under the partition than under privacy, while no type consumes an amount that is less efficient, the result follows when condition (i) is satisfied.
Now assume condition (ii) is met. As above, the consumption of types {S _{1}, …, S _{ J } _{1}} is efficient and, thus, more efficient than under privacy. The consumption level of S _{ J }=K is equally efficient with or without privacy. Consider a type θ that is not the maximal type within its block. Let type θ+k be the next higher type within that block. If k=1 for all such types, then we have an ordered partition and the previous analysis applies. Restrict attention to the case k ≥ 2. Now the marginal profit function is proportional to
which, by (A7) and the fact that k ≥ 2, is weakly greater than
If we can show that term is greater than
then we will have shown that marginal profit weakly increases for all nonmaximal types, which completes the proof. A sufficient condition for that relation to hold is that
be decreasing in n. Observe that
where \(\Delta (x) \equiv b_{\theta + n + 1} (x)  b_{\theta + n} (x) > 0\) (because \(x < x_{\theta + n + 1}^w\)) and the inequality follows from assumption (b). Assumption (c) and condition (ii) imply that the term in large parentheses is negative.
Turn now to our labor market example under the assumption that there is a continuum of household abilities. A necessary condition for a wage, \(w_\sigma\), to be an equilibrium is that it equal the average productivity of the households willing to work at that wage, or
A necessary and sufficient condition for equilibrium is that the wage be the highest such wage satisfying Eq. (A8)—otherwise there would exist a wage such that the average productivity of job applicants would be higher than that wage and an employer would find it profitable to deviate by offering that wage. We know that such a value exists because both sides of the equation are continuous and the lefthand side ranges from 0 to ∞ while the righthand side is bounded below by \(\nu\underline \theta\) and above by \(\nu\bar \theta\).^{Footnote 44}
Proof of Proposition 7:
It suffices to show that \(\frac{{f_i (\theta )}}{{f_j (\theta )}}\) monotonically decreasing implies w \(_i < {\it w}_j\). Define \(g_\sigma (\theta ,{\it w}) = \frac{{f_\sigma (\theta )}}{{F_\sigma ({\it w})}}\). By the definitions of \(f_\sigma (\theta )\) and \(F_\sigma (\theta )\),
Moreover, \(\frac{{g_i (\theta ,w)}}{{g_j (\theta ,w)}}\) is monotonically decreasing, so it and θ covary negatively. Hence, their covariance,
is negative for all \(w > \underline \theta\). Therefore,
Both the integral and w are continuous in w, and \(\nu\int_{\underline {\theta } }^{w} {\theta {\textstyle{{f_j (\theta )} \over {F_j (w)}}}d\theta  w}\) goes to −∞ as \(w \to \infty\). Hence, there exists \(w_j > w_i\) such that \(v\int_{\underline {\theta } }^{w_j } {\frac{{\theta f_j (\theta )}}{{F_j (w_j )}}d\theta } = w_j\).
Proof of Proposition 10:
Consider an equilibrium that arises when firms can compel households to reveal the values of their indicator variables. Let \(  t_n (\sigma )\) be the equilibrium wage offered by firm n to any household that has value σ. Because there are no matching benefits, the industry is competitive, and no firm would, in equilibrium, offer a wage that leads it to lose money, it must be that \(t_n (\sigma ) = t_m (\sigma )\) for all n and m. Without loss of generality, order the σs so that \(t(\sigma _i ) \ge t(\sigma _j )\) if i < j. Observe that \(\sigma _1\) is the leastfavored indicator variable because \(u( {\theta ,x(\theta ,t(\sigma _1 )),t(\sigma _1 )} ) \le u( {\theta ,x(\theta ,t(\sigma _j )),t(\sigma _j )})\) for all θ and all j > 1, where \(x\left( {\theta ,t} \right)\) is the bestresponse labor supply decision of a typeθ household when offered t. The result then follows from Proposition 2.
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Hermalin, B.E., Katz, M.L. Privacy, property rights and efficiency: The economics of privacy as secrecy. Quant Market Econ 4, 209–239 (2006). https://doi.org/10.1007/s1112900590047
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DOI: https://doi.org/10.1007/s1112900590047