International Protection of Consumer Data

We study the international protection of consumer data in a model where data usage benefits firms at the expense of their customers. We show that a multinational firm does not balance this trade-off efficiently if its data usage lacks (full) transparency or if consumers’ privacy preference differs across countries. Unilateral data regulation by each country addresses the moral-hazard problem associated with opacity, but may nevertheless reduce global welfare due to cross-country externalities that distort output and data usage. The regulations may also cause excessive investment in data localization, even though localization mitigates the externalities. Our findings highlight the need for international coordination - though not necessarily uniformity - on regulations about data usage and protection.


INTRODUCTION
A central concern in the digital economy is how to protect consumer data. Digital technologies and the Internet have enabled firms to collect, transmit, and use consumer data for a variety of purposes, ranging from targeted advertising and price discrimination to the design of tailor-made products, bringing new revenue streams to firms. A recent survey estimated that the value of the global data market reached $26 billion in 2019 with an annual growth rate of more than 20%. 1 However, consumers may suffer from the collection and usage of their data by firms, possibly from loss of privacy, unwanted advertising, higher prices due to price discrimination, and security fraud. It was estimated that displayed advertising alone accounted for 18%-79% of data costs for mobile plan users in the United States in 2016. 2 According to government reports, companies use big data for differential pricing that can harm consumers and potentially could require regulation. 3 Moreover, a survey in 2016 showed that 15.4 million U.S. consumers suffered from identity theft and fraud with a total loss of about $16 billion during that year. 4 Because consumers' demand for a firm's product depends on how the firm treats their personal information, the firm may take actions to (partially) respond to consumers' concerns about data protection by, for example, investing in data safety and obtaining consumers' consent for data collection and usage. The economics and legal literature, discussed below, has investigated the various ways in which firms may utilize consumer data, their incentives and ability to protect data, and data protection regulation. However, there has been little formal analysis of the usage and protection of data when firms sell products in multiple 1 https://www.onaudience.com/files/OnAudience.com_Global_Data_Market_Size_2017-2019.pdf.
The estimation only included the direct value of consumer data transactions. The indirect value from using consumer data was much higher. For example, the value of digital display advertising in 2019 was about $120 billion. 2 https://www.techdirt.com/articles/20160317/09274333934/why-are-people-using-ad-blockers-ads-can-regulations, what will be the equilibrium non-cooperative standards and how would such regulations affect global welfare? What is the scope for coordinated regulatory approaches that might improve welfare? We conduct an economic analysis of these issues in this paper.
We consider a multinational firm selling a digitally-enabled product in two countries. The firm obtains personal data when consumers purchase the product and can profitably utilize the data through, for example, data sales, price discrimination, or targeted advertising. In our base model, the firm chooses a common level of data usage in the two countries. A larger usage level generates higher data revenue but also greater disutility to consumers.
We assume that the firm's choice of data usage has two components, one observable to consumers before product purchase and another that is not. This is a convenient way of modeling the transparency of-or the firm's ability to commit publicly to-data usage.
The firm also sets (possibly different) prices in the two countries, whereas consumers will consider, in addition to price, their utility from the product and disutility from the firm's data usage when making purchasing decisions.
If the firm's chosen data-usage level were fully observable to consumers before purchase, and if additionally consumers in the two countries had the same preference for privacy, the firm would fully internalize consumer disutility in selecting its desired data usage, which would coincide with the global optimum. However, the equilibrium choice of data usage often departs from the efficient level (from the global perspective) for two reasons. First, when consumers cannot fully observe how and to what extent their data will be used, the firm suffers from the moral-hazard problem of expanding data use beyond the efficient level. 8 Second, when consumers in one country have larger disutility from data usage than those in the other country, the firm is unable to balance properly the revenue from data usage and consumer disutility, even if it could commit to any level of usage common to both countries. The firm's use of data can then be inefficiently excessive or deficient, depending on the property of demand curvature. Moreover, increasing the transparency of the firm's data usage can have a non-monotonic impact on global welfare, possibly first increasing and 8 In equilibrium, however, consumers correctly anticipate the firm's choice and thus have a lower willingness to pay for the product. 3 International Protection of Consumer Data then decreasing.
We further consider the possibility that the two countries can regulate the use or protection of consumer data by unilaterally imposing caps on data-usage levels. We show that such caps enable the firm to commit to lower data usage and can therefore improve global welfare, but the regulations could also exacerbate equilibrium distortions. In particular, a country with a larger consumer disutility for data usage would not internalize the negative impact of a more restrictive regulation on output and data usage in the other country. We demonstrate that equilibrium data regulations increase global welfare when transparency of data usage is low and consumer privacy concerns are not too different across countries, but can reduce welfare otherwise; and we show how the welfare effects of regulations may also depend on demand curvature properties. Furthermore, we provide conditions under which international coordination of data-protection regimes may or may not achieve (full) global efficiency.
A firm can sometimes invest in data localization, which allows it to choose a data usage level specific to a country, avoiding the mingling of data across countries. The firm can benefit from this option, but in equilibrium, it does not internalize the full benefits of data localization and therefore its private incentive to make the investment can be inefficiently low. While unilateral data-usage regulations strengthen the firm's incentives to invest in localization, it is also possible that they cause (inefficiently) excessive investment and reduce welfare in equilibrium.
Overall, our analysis reveals that unilateral data regulations can either raise or reduce global welfare, depending on the transparency level of data usage, the cross-country difference in privacy preference, and the properties of demand for the product. The analysis shows that there can be substantial gains from international coordination in data regulations, though a uniform level of data usage need not be globally optimal.
Our paper contributes to the literature on personal data and consumer privacy (see the review by Acquisti, Taylor The rest of the paper is organized as follows. Section 2 presents our baseline model. Section 3 characterizes the market equilibrium and compares the equilibrium data usage chosen by the firm with the efficient level. Section 4 incorporates data regulations into the model and examines equilibrium regulations that are unilaterally chosen by each country.
Section 5 considers the possibility that the firm can invest in data localization, and examines the effects of data regulation in this context. Section 6 discusses some additional extensions.

THE BASELINE MODEL
There are two countries, Home (H) and Foreign (F ). A multinational firm, located in H, sells a (digitally-enabled) product at prices p H and p F respectively in the two countries. We normalize the firm's production cost to 0. A consumer in each country demands one unit of the product and derives a value u, which is a random draw from a probability distribution g (u) > 0 with cumulative density G (u) on the support [u,ū] , where 0 ≤ u <ū ≤ ∞. The mass of consumers is λ in country H and 1 − λ in country F, with λ ∈ (0, 1) .
The transaction of the product brings data about consumers to the firm. The firm can use the data as a second source of revenue, possibly selling the data to a third party or using the data to increase profit from its other products; but consumers have disutility from their personal data being used. We assume that the firm's data-usage level from each consumer 10 The issue of international policy harmonization has been studied in other contexts, such as patent policies (Grossman and Lai, 2004), technical product standards (Chen and Mattoo, 2008), and tax competition to attract multinational firms (Keen and Konrad, 2013). Such models reflect tradeoffs among multiple welfare objectives in inherently distorted markets. Our focus on data use versus privacy costs is novel in this area.
6 Yongmin Chen, Xinyu Hua, Keith E. Maskus (who purchases the product) is where x 1 can be observed by consumers before purchase but x 2 cannot, with x i ∈ [0, 1] for i = 1, 2, whereas θ ∈ [0, 1] is exogenous and commonly known. A higher θ reflects more transparency of data usage or a higher ability of the firm to publicly commit to the data-usage level. 11 This formulation of data usage is aligned with a variety of economic settings. First, it captures the idea that, in serving consumers, the firm can collect various types of information about a consumer, ranging from personal identification (e.g., name, age, occupation, address) to the consumer's transaction and consumption data (e.g., search history, purchase habit, consumption frequency, post-sale service needs). The firm can make public that it will collect and use some of the data, denoted by x 1 , which could include information that is required for the transaction and post-sale services, but it may (intentionally or unintentionally) conceal the collection and use of other information, denoted by x 2 , which may include for instance consumer search and purchase patterns. 12 A higher value of x 1 or x 2 indicates that the firm collects more information about consumers. The formulation can also reflect the extent to which consumer data may be utilized, with x 1 and x 2 representing respectively data usage that the firm may or may not be able to commit to before consumers purchase the product. Furthermore, we may consider x as the inverse of the firm's effort in protecting consumer data, so that a higher x corresponds to less data protection and lower effort cost, with x 1 and x 2 corresponding to protection levels that the firm may or may not be able to commit to.
As discussed above, the firm's revenue will naturally increase in data usage x. Specifically, 11 We take θ as a given parameter in our model. As it will become clear later, if the firm were able to choose or influence the value of θ, it could benefit from committing to a higher level of θ. 12 This is related to the idea of "incomplete contracts". The consumer, or even the firm, may not foresee all possible types of consumer information that may be profitably utilized. Hence, no commitment about the use of such information can be made before the product is purchased, even though all parties expect such use to occur.

International Protection of Consumer Data
Electronic copy available at: https://ssrn.com/abstract=3688295 we assume that the firm's data-usage revenue from each consumer is r(x), where r (0) = 0 = r (1), r (0) is sufficiently high, r (x) > 0 for x < 1, and r (x) < 0. When Q H and Q F consumers in countries H and F , respectively, purchase the product, the firm's total revenue from data usage is (Q H +Q F )r(x), where Q H and Q F are determined endogenously.
Consumers in the two countries may differ in their preference for privacy, and their disutility increases in the data-usage level x. Specifically, a consumer who purchases the product in country H or F suffers disutility x or τ x, respectively, where τ > 0 measures the relative consumer preference for privacy or the difference in consumers' disutility for data usage between the two countries: When τ = 1, consumers in the two countries have the same preference for privacy, whereas τ > 1 or τ < 1 indicates, respectively, that consumers in F have a stronger or weaker preference than those in H. To summarize, each consumer's gross value in purchasing the product is u − x in H and u − τ x in F.
We assume that it is optimal for the firm to sell in both countries, which would be true if the expected value of u is relatively high. A strategy of the firm specifies its choices of x 1 and x 2 , as well as its prices p H and p F in countries H and F, respectively. A consumer with value u in country j, seeing x 1 and p j for j = H, L, chooses whether to purchase the product under her belief about x 2 . We study the perfect Bayesian equilibrium of the game, in which the firm's strategy is optimal given consumers' purchasing strategy, consumers' purchasing strategies are optimal given the firm's strategy and their belief about x (or x 2 ), and consumers' belief is consistent with the firm's strategy.
Note that in this baseline model, the firm sells a standard product with a common datausage level in the two countries. A firm may choose separate levels of data usage in different countries by investing in data localization, and we shall examine the firm's incentives to do so in Section 5.

MARKET EQUILIBRIUM
In equilibrium, consumers have correct beliefs about the data-usage level x chosen by the firm. Given their belief about x and the observed prices (p H , p F ) , a consumer in country 8 H will purchase the product if u − x − p H ≥ 0 while a consumer in country F will do so if Thus, the probability for a consumer in H or F to buy the product is, respectively: Accordingly, the total outputs in H and F are respectively λq H and (1 − λ) q F . For each unit of output, the firm receives two streams of revenue: the price of the product and the data-usage revenue r(x). Hence, the firm's profit as a function of (p H , p F ) under given x is Denote the inverse hazard rate of the consumer-value distribution by Throughout the paper, we shall maintain the assumption where part (i) is the familiar monotonic hazard-rate condition that is satisfied by many wellknown distributions, and part (ii) will rule out the corner solution where the equilibrium price is equal to u − x in H or u − τ x in F. We define p H + x and p F + τ x as the "effective prices" for consumers respectively in countries H and F , which include the purchase prices and the disutility from losing privacy. Since 1 − G (p H + x) (or 1 − G (p F + τ x)) is the demand of a consumer in country H (or F ), part (i) can be alternatively interpreted as a firm's demand in each country being logconcave. Moreover, denoting demand per consumer where α (p) is the curvature and η (p) the price elasticity of D (p) . At the profit-maximizing p, α η equals the curvature of the inverse demand function, and demand is convex or concave if, respectively, m (p)+1 ≥ 0 or ≤ 0 (Chen and Schwartz, 2015). Hence, m (u)+1 measures the curvature of demand in each country, and its property will determine how a change in x affects the firm's optimal price, or the firm's trade off between the revenues from product sales and data usage. The following lemma characterizes the equilibrium prices given x.
Lemma 1 (Equilibrium Prices) Given x, the equilibrium prices in the two countries uniquely with equilibrium outputs λq * Lemma 1 implies that, given data usage x, the firm has a lower price of the product but a higher " effective price" (and accordingly, a lower expected output per consumer) in the country where consumers have larger disutility from losing privacy. Furthermore, when the per-consumer revenue from data usage, r(x), increases, the firm's optimal prices will decrease. This is because when the revenue from data usage is higher, the firm has incentives to generate a larger output-hence also more consumer data-by reducing prices.
From condition (4), we can derive ∂p * H ∂r and ∂p * F ∂r , which measure the impacts of an exogenous increase of data-usage revenue (for a given level x) on product prices, and we call their absolute values the rates of revenue substitution: The rate of revenue substitution reflects the firm's tradeoff between revenues from direct product sales and the use of consumer data. Note that the revenue substitution rates are constant, decreasing, or increasing in x, respectively if m (u) is linear, concave, or convex (equivalently, if the demand curvature m (u) + 1 is constant, decreasing, or increasing).
An increase in data revenue can have different impacts on product prices in the two countries, depending on the relative preference for privacy, τ , and the change (rate) of demand curvature in each country, m (u). For illustration, consider the case with τ > 1 and m (u) > 0. Since τ > 1, country F has a stronger preference for privacy and, as shown in Lemma 1, the effective price is higher in F than in H: p * F + τ x > p * H + x. Given m (u) > 0, the demand curvature at the equilibrium price is thus larger in country F than in country H. When r rises, both p * F and p * H fall, but for the same price decrease there is more output expansion in F than in H because demand is more convex (or less concave) in F . Therefore, when τ > 1 and m (u) > 0, an increase in r would result in a large decrease in p * F than in p * H , so that the revenue substitution rate in H is smaller than that in F , ρ H r < ρ F r . 13 The following lemma confirms this intuition and compares the revenue substitution rates in the other cases as well.
Lemma 2 (Revenue Substitution Rates) An exogenous increase of r has a smaller impact Next, we examine how the choice of data usage x affects the output and profit in each country. Suppose that the firm could commit to any data-usage level. From condition (4), we can derive the impacts of a marginal increase of x on product prices: Using condition (5), we can rewrite (6) and (7) as Recall that p * H + x and p * F + τ x are the effective prices for consumers in the two countries. So, ρ H x +1 and ρ F x +τ are marginal effective prices of data usage in H and F , respectively. We can also consider r(x) − x and r(x) − τ x as the "net benefits" of data usage per consumer, which include the firm's data-usage revenue and each consumer's disutility from losing privacy. Thus, r (x) − 1 and r (x) − τ represent the marginal net benefit of data usage, in H and F respectively. Condition (8) says that the marginal effective price of data usage in each country equals, in absolute value, the revenue substitution rate multiplied by the marginal net benefit of data usage in the country. Because r (x) can be higher than max {1, τ } for small x and lower than min {1, τ } for high x, ρ H x + 1 and ρ F x + 1 can be either positive or negative.
Note that the equilibrium output in each country, in F , decreases in the effective price. Then condition (8) implies that a marginal increase of data usage x increases (or decreases) the output in country H when r (x) > 1 (or when r (x) < 1). Similarly, a marginal increase of data usage x increases (or decreases) the output in country F when r (x) > τ (or when r (x) < τ ). Intuitively, an increase of data usage increases consumer disutility, which reduces the output; but the increase of data usage also raises the firm's data-usage revenue, which motivates the firm to increase the output by reducing product prices. The next result summarizes the nonmonotonic impacts of data usage on outputs.
Lemma 3 (Output Changes) The equilibrium output in each country first increases and then decreases in x, with the maximal output in country H and in country F achieved respectively when r (x) = 1 and when r (x) = τ .
In choosing x, the firm needs to consider the trade-offs between the data-usage revenue and consumer disutility from losing privacy, as well as the non-monotonic impacts on the outputs. The firm's equilibrium profit as a function of x is given by Utilizing the envelop theorem and condition (4), we have Hence, increasing data usage strictly raises firm profits if r (x) > max{1, τ } and strictly reduces firm profits if r (x) < min{1, τ }. Intuitively, when r (x) < min{1, τ }, the marginal revenue of data usage is lower than the marginal disutility of privacy loss in both countries, and the opposite is true when the marginal revenue of data usage is higher than the marginal disutility in one country but lower in the other country, in which case the firm's optimal data-usage must balance these two conflicting effects. We shall maintain the assumption that π (x) is single-peaked, which is ensured if r (x) is sufficiently concave.
Suppose that the firm could commit to any data-usage level. Define the (unconstrained) profit-maximizing level as x = arg max x π (x). Then x satisfies is the marginal net benefit of data usage in country H (or in country F ). Thus, for profit maximization, the firm desires to set x such that the output-weighted marginal net benefits of data usage are equalized (in absolute value) for the two countries.
While x maximizes the firm's profit, the equilibrium data usage may differ from x due to the firm's inability to commit to x 2 . Denoting the equilibrium data usage by x * , we have: The equilibrium data usage x * weakly decreases in the transparency level θ: θ and x 2 = 1.
In equilibrium we must have x 2 = 1, as consumers cannot observe x 2 and it is optimal for the firm to choose the highest possible x 2 to increase data-usage revenue. If data usage is sufficiently transparent (θ ≥ 1 − x), the firm can commit to the (unconstrained) profit-maximizing usage level, x * = x, whereas if data usage is not sufficiently transparent , the firm chooses a usage level higher than x. 14 Global Welfare Benchmark 14 Thus, if the firm were able to commit to any transparency level, it would have the incentives to choose 13

International Protection of Consumer Data
We next consider the data-usage level that would maximize global welfare and examine how welfare may change with transparency. 15 We assume that the firm can still choose its profit-maximizing prices in the two countries. Global welfare from the two countries as a function of x is Then: Using (1), (4) and (5), we can rewrite (13) as where we recall Denote the globally efficient data usage by Comparing (11) and (15), the result below shows that x o can be higher or lower than its (unconstrained) profit-maximizing counterpart x.
Lemma 4 (Efficient versus Profit-maximizing Data Usage) The profit-maximizing data us- privately-optimal data usage can diverge from the efficient level. To see the intuition, rewrite (14) as is the corresponding impact in country F . The changes in consumer surplus depend on the revenue substitution rates (ρ H r and ρ F r ) and the output-weighted marginal net benefits of data usage in H and in F .
Consider the scenario where τ > 1 and m (u) > 0. Lemma 2 shows that, in this case, the revenue substitution rate in country H is lower than that in country F (ρ H r < ρ F r ), due to the more convex demand at the equilibrium price in country F . Since τ > 1, the privately-desired data usage x satisfies 1 < r ( x) < τ . As indicated by condition (11), for a small increase in x from x, the output-weighted marginal net benefit of x in H equals the absolute value of the output-weighted marginal net benefit of x in F . Thus, condition (16) implies that the increase of consumer surplus in H is smaller than the decrease of consumer surplus in F . Intuitively, the marginal change of data usage would cause a larger impact on consumer surplus in the country with a larger price change. The small increase of data usage also changes firm profit, which however is a second-order effect. Therefore, the increase of data usage reduces global welfare. Similar intuition can be obtained when τ < 1 and m (u) > 0. To summarize, the firm's optimal data usage exceeds the globally efficient level when τ = 1 and the demand curvature is increasing (i.e., m(u) is convex).
By contrast, the firm's optimal data usage is below the global optimum when τ = 1 and the demand curvature is decreasing (i.e. m(u) is concave). For illustration, suppose that τ > 1 and m (u) < 0. As shown in Lemma 2, the revenue substitution rate in country H is larger than that in country F (ρ H r > ρ F r ), due to the more convex demand at the equilibrium price in country H. Accordingly, for a small increase of data usage from x, the When data usage is not transparent enough (i.e. θ is small), the equilibrium data-usage level is greater than the global optimum even if the firm's most desired x coincides with the efficient level ( x = x o ), due to the firm's moral hazard. More transparency mitigates the moral hazard problem and enables the firm to commit to a lower data-usage level. The welfare impact, however, depends on the cross-country difference in privacy preference, τ , and how the demand curvature, m (u) , changes. As shown in Lemma 4, the firm's privatelydesired data usage, x, is higher than the globally efficient level when τ = 1 and demand curvature m (u) + 1 is increasing (or m (u) is convex). Even if the firm can commit to any data-usage level, or there is no problem of transparency, the firm still over-uses consumer data compared to what is (globally) efficient. In this case, more transparency (i.e. a larger θ) weakly increases global welfare but cannot achieve the global optimum.
Interestingly, it is also possible that welfare is non-monotonic in the transparency para-  Welfare increases in θ for θ < 0.620 and becomes constant for θ ≥ 0.620.
The finding in Proposition 2 that more transparency of data usage can reduce welfare is intriguing. Many countries have regulations aimed at improving transparency by requiring firms to disclose data usage or data protection. While increases in transparency are often considered as welfare-improving, our result indicates that their welfare impact is more nuanced and may have unintended consequences.

REGULATIONS ON DATA USAGE
In recent years, countries have been enacting regulations on the use and protection of data. Compared to consumers, regulators are in a better position to monitor and verify data usages. In this section, we turn to the question of how regulations may impact data usage and global welfare. We assume that regulators in countries H and F independently and simultaneously set caps on data usage, σ H and σ F , so that the firm is required to choose x ≤ σ H and x ≤ σ F in the respective countries. 16 Although the firm is unable to announce its choice of x to consumers before they purchase the product, a regulator can find out the firm's choice of x ex post and can therefore implement the regulation (possibly with a high penalty for violations).
Consumer surplus in H or in F is, respectively, We assume that the regulatory objective of each country is to maximize its total surplus.
That is, the regulator in H aims to maximize the sum of consumer surplus in H and firm 16 Notice that even if the firm transmits consumer data in F back to H, it still needs to follow regulations set by F when using the data. Notice also that regulations with usage caps are different from policies aiming to improve transparency of data usage (i.e. increasing θ). As shown in Section 3, when θ = 1, the firm chooses the profit-maximizing usage x. In contrast, under the usage caps, the firm has to choose x ≤ min{σH , σF }.
profits in both countries (as the firm is located in H), whereas the regulator in F aims to maximize only consumer surplus in F . Notice that where we recall q * . Therefore, provided that the constraint x ≤ σ H is binding, country H will impose the cap σ H such that which implies r (σ F ) = τ .
When consumers in country F have a stronger preference for privacy (τ > 1), conditions (21) and (22) imply that F imposes a more stringent regulation than H, that is, Similarly, when consumers in country H have a stronger preference for privacy (τ < 1), H imposes a more stringent restriction on data usage with σ F > σ H . The firm will need to comply with the lower of the two caps in order to sell in both countries. We show below that, as long as τ = 1, the firm has to follow the lower cap which, however, is below the efficient data-usage x o that maximizes global welfare. 17  However, as shown in Proposition 2, when demand curvature is decreasing (m (u) < 0) and data usage is highly transparent (θ > 1 − x o ), the firm will find it optimal (and can commit) to choose a data-usage level that is lower than the efficient level (x * < x o ). In this case, a uniform cap on data usage cannot lead to the efficient level x o .

21
International Protection of Consumer Data

DATA LOCALIZATION
It is possible that a firm can choose a different level of data usage in a different country by making certain investments, for example, setting up local servers to store and process data.
This section allows for this possibility. In subsection 5.1, we examine the firm's incentives to make the "localization" investment, in the absence of data regulation. In subsection 5.2, we further analyze the welfare effects of data-usage regulations unilaterally imposed by the two countries that may change the firm's incentives to invest in localization. 18

Localization without Data Regulation
Suppose that there is no data regulation, and the firm may invest a fixed amount k > 0 which enables it to choose data-usage levels x H and x F separately in countries H and F .
If the firm invests k, then similar to the analysis in Section 3, the firm's optimal prices p l H and p l F satisfy where the superscript l denotes for localization. The firm's profit (excluding investment costs k) as a function of (x H , x F ) is where q l H (x) ≡ 1 − G p l H + x H and q l F (x) ≡ 1 − G p l F + τ x F . One can show that the profit-maximizing data-usage levels, denoted as ( x H , x F ), satisfy That is, with data localization, the firm desires to choose usage levels that are also efficient for each market, because it fully internalizes consumers' disutility from losing privacy. 18 We have also considered an alternative form of regulation that directly requires the firm to invest in localization. The welfare effects of such localization requirements, if feasible, are similar to the results in subsection 5.2 where data-usage regulations indirectly impact the firm's incentive to invest in localization.
Recall that, without data localization, the firm's most desired data-usage, x, satisfies min{1, τ } < r ( x) < max{1, τ } when τ = 1. We thus have the following comparison Hence, the firm may invest in data localization only if consumers in the two countries differ in their preferences for privacy (τ = 1). While Given Lemma 6 and Proposition 1, when the transparency of data usage is low (θ ≤ 1 − max{ x H , x F }), the equilibrium data usage is the same whether the firm invests in localization or not. When data usage is highly transparent (θ ≥ 1 − min{ x H , x F }), the profit difference between localization and no localization, π( x H , x F )−π( x), does not depend on the transparency parameter θ. We further show in the appendix that, for τ = 1 and the , the profit difference between localization and no localization, π(x * H , x * F ; θ) − π(x * ; θ), strictly increases in θ. The relationship between the profit difference caused by localization and the transparency parameter θ can be understood intuitively as follows. Data localization is costly but allows the firm to choose different usage levels in the two countries, which raises firm profit.
When data usage is not very transparent (i.e. under severe moral hazard problems), the equilibrium choices of data usage with and without localization both tend to be high. In

23
International Protection of Consumer Data this case, localization does not change the usage levels by much and therefore the profit difference is small. In contrast, when data usage becomes more transparent, the firm has more "flexibility" in committing to usage levels. In this case, localization facilitates larger changes of usage levels and, accordingly, causes a greater change in profit. In other words, the benefit of data localization to the firm is greater when data usage is more transparent. 19 Define Then the earlier analysis implies that, given any k < k 1 (τ ), there exists a unique value θ l such that The unregulated firm invests in localization if and only if k < k 1 (τ ) and θ > θ l .
Since as Suppose that τ > 1. If θ ≤ 1 − x H , then Proposition 1 and Lemma 6 imply that the equilibrium data-usage levels remain the same no matter whether the firm invests in localization or not (x * H = x * F = x * ), in which case the firm's decision of not investing in localization is efficient.
If θ > 1 − x H , then localization changes the equilibrium data-usage levels such that Recall that x H and x F maximize both welfare and consumer surplus respectively in country H and F . Therefore, the welfare gain from 19 As shown in Lemma 3, ( xH , xF ) maximize the outputs in the two countries. Under localization, more transparency causes the firm's data-usage levels to be closer to ( xH , xF ) and therefore raises the outputs in both countries.

24
Yongmin Chen, Xinyu Hua, Keith E. Maskus localization is strictly larger than the profit increase (excluding costs k): The same results can be obtained when τ < 1. Thus, if the investment cost k is smaller than the welfare gain but larger than the profit increase, the localization incentive by the firm is inefficiently low. The following proposition summarizes the (unregulated) firm's localization incentives.

Localization with Data Regulation
Now suppose that regulators in both countries independently and simultaneously impose data-usage caps (σ l H in H and σ l F in F ) and, after observing the regulations, the firm chooses whether to invest in localization (as well as makes corresponding price and datausage decisions). The regulator in each country sets a usage cap, correctly anticipating the cap set in the other country and potential responses from the firm in equilibrium. There can be two possible types of equilibria: one in which the firm does not invest in localization and another in which the firm does. If the firm does not invest in localization, it has to follow the lower of the two caps in the two countries: x ≤ min{σ l H , σ l F }. If the firm invests in localization, however, it can choose different usage levels in the two countries such that x H ≤ σ l H and x F ≤ σ l F . As we have shown, if consumers in the two countries have the same preference for privacy (τ = 1), the data-usage level x o maximizes both firm profit and welfare in each country. In

25
International Protection of Consumer Data this case, the countries will impose caps σ l H = σ l F = x o , and the firm does not invest in localization. We shall thus focus on the cases where τ > 1 or τ < 1 below.
Suppose first that τ > 1; that is, consumers in country F have a stronger preference for privacy. In this case, there always exists an equilibrium in which H imposes σ l H = x H and F imposes σ l F = x F , whether or not the firm will respond with localization. We show that neither country has the incentive to deviate from its cap at the proposed equilibrium. Recall that x F < x H when τ > 1. Given σ l H = x H , x F maximizes the surplus in F whether or not the firm invests in localization. Thus, σ l F = x F is optimal for F and it has no incentive to deviate. Now consider the incentive of H. If the firm invests in localization and chooses x H in H and x F in F , the welfare for H (sum of the consumer surplus in H and the firm's profit in two countries) will be maximized. Therefore, anticipating localization, H has no incentive to deviate from the cap σ l H = x H . If the firm does not invest in localization, the constraint x H ≤ σ l H is not binding and the firm would choose data usage x F < x H in both countries. Still, H cannot benefit from any deviation to set a binding cap below x F , because any binding cap by H, say σ < x F , would result in data-usage level σ in H, lowering welfare for H. Suppose next that τ < 1, that is, consumers in H have a stronger preference for privacy.
Unlike the case with τ > 1, here the optimal cap in H depends on whether the firm will choose localization. We focus on the equilibrium where the regulators impose σ l H = x H and σ l F = x F respectively, while the firm will invest in localization, where x F > x H with τ < 1. 20 Given σ l H = x H and σ l F = x F , if the firm does not invest in localization, the equilibrium data usage is min{ x H , x F } and profit is π(min{ x H , x F }); if the firm invests in localization, the data-usage levels are x H in H and x F in F, resulting in profit (excluding costs k) 20 Notice that, given τ < 1, σ l H = xH and σ l F = xF cannot be supported in any equilibrium where the firm does not invest in localization, as H can then deviate to a cap slightly larger than xH , which would not change the firm's localization decision but raise welfare for H.

26
Yongmin Chen, Xinyu Hua, Keith E. Maskus Then, given σ l H = x H and σ l F = x F , the firm invests in localization if and only if k < k 2 (τ ). In the appendix, we show that k 2 (τ ) increases in τ when τ > 1 and decreases in τ when τ < 1. Intuitively, without localization, when the cross-country difference in privacy preference (|τ − 1|) is larger, there would be a larger difference between the firm's privately-desired data-usage and the lower of the caps imposed in the two countries. Accordingly, the profit difference caused by localization becomes greater.
In contrast, under regulations σ l H = x H and σ l F = x F , the firm invests in localization if and only if k < k 2 (τ ). That is, data regulations strengthen the firm's incentives to invest in localization, because localization allows the firm to follow the different data-usage caps in the two countries instead of complying with the lower of the two caps.
When localization is feasible, will data regulations enhance or reduce global welfare? If the Importantly, a uniform data-usage regulation is generally not optimal, even when countries can coordinate their regulations. Uniformity in the regulation of data usage for each country does not allow for the flexibility desirable under preference diversity across countries, and it cannot realize the potential gains when the firm can choose the efficient data usages through localization or when coordinated regulations can impose optimally differentiated data-usage caps in different countries.

DISCUSSION
To convey our ideas in the most transparent way, we have considered a highly stylized model. The main insights of our analysis will continue to hold in more general settings. Below, we discuss two possible extensions. 21 We choose to spare the readers from the complicated expressions that explicitly characterize the set of parameter values under which regulations reduce welfare in Proposition 5.

Imperfect Enforcement of Regulation
Our baseline model assumes that regulations are perfectly enforced and the firm always complies with both caps on data usage. The insights regarding cross-country externalities remain robust even when regulation enforcement is imperfect. For illustration, suppose that there is no data localization and consider the scenario with τ > 1. Suppose further that regulators in H and F can independently and simultaneously set caps on data usage and regulation enforcement is perfect in H but imperfect in F , with an expected penalty D > 0 if the firm violates the regulation in F . This limited liability reflects the possibility that the violation of regulation is undetected or the firm faces financial constraints.
As shown in Lemma 5, when enforcement is perfect, the optimal caps satisfy r (σ F ) = τ Suppose that the countries maintain the same caps σ H and σ F under imperfect enforcement.
If the firm follows the regulations and choose x = σ F , its profit is π (σ F ). If the firm violates the regulation in country F , it will choose x = min{max{ x, 1 − θ}, σ H }. 22 Therefore, the firm would comply with the regulation in F if and only if When the penalty is large, D ≥ D, the firm complies with the more stringent regulation σ F , which causes negative output and data-usage externalities in country H, the same as in the baseline model. When the penalty is small, D < D, the firm violates the regulation in F . In this case, if 1 − θ > σ H , the firm chooses x = σ H , which mitigates the moral hazard problem and increases welfare in both countries compared to the scenario with no regulation.
Moreover, for a given penalty D, the countries may have incentives to impose caps different from σ H and σ F . For example, if D < D, country F may impose a lessrestrictive cap σ F > σ F to ensure that the firm will comply with the cap in F . If 22 As shown in Proposition 1, the unregulated firm chooses x = max{ x, 1 − θ}. If the firm violates the regulation in F but has to comply with the regulation in H, then its optimal choice of data usage is Such strategic behavior can further reduce global welfare, suggesting one more reason for international coordination on regulations.

Consumer Opt-Out
In recent years, some countries have enacted the "opt-out" policy, which allows consumers to opt out of the collection and use of their personal data by firms. We can incorporate the opt-out policy in our model. Suppose that there is no data localization and data usage transparency is not too low: θ > 1 − min{σ H , σ F }. Recall that consumers only observe Suppose that H allows consumers to opt out of observable data collection and F allows consumers to opt out of observable data collection when Since consumers have a strict preference for privacy, they would indeed opt out when these conditions are met.
In equilibrium, the firm always chooses x 2 = 1, as shown in Section 4. If the firm chooses , then the equilibrium data-usage level satisfies If the firm chooses x 1 > min{σ H ,σ F }−(1−θ) θ , then consumers will opt out, in which case x 1 drops to 0 and the data-usage level becomes x = x 2 = 1 − θ. Since the firm's privatelydesired data-usage x satisfies profit is higher when data usage is min{σ H , σ F } than when it is 1 − θ. Therefore, under the opt-out policy, the firm would choose x = min{σ H , σ F }. Then the welfare impact of the regulations will be the same as in Section 4. Unilateral opt-out policies can cause negative output and data-usage externalities across countries.

CONCLUSION
This paper has conducted an economic analysis of the use and protection of consumer data in an international context. We find that a multinational firm may inefficiently exploit consumer data due to moral hazard or international differences in consumer preference for privacy. Unilateral data regulations imposed by individual countries can impact global welfare positively by solving the moral hazard problem but negatively due to output reductions or data-usage distortions from cross-country externalities. Properties of demand curvature play important roles in determining the net welfare effect. We also show that data regulations can improve welfare when they encourage-but do not cause excessive-investment in data localization. There is significant scope of welfare gains from international coordination in regulations to protect consumer data, though a uniform standard on data usage is generally not warranted.
Proof of Lemma 1. Equilibrium prices p * H and p * F , when they are interior, satisfy the first-order conditions or equivalently, If condition (ii) in Assumption A1 holds, m (p H + x) ≥ p H + r(x) when p H = u − x, and condition (i) then ensures a unique interior solution of p * H > u − x. Similarly, Assumption A1 ensures the unique existence of p * F > u − τ x. Next, if τ = 1, obviously p * H = p * F and q * H = q * F . If τ > 1, suppose to the contrary that p * H ≤ p * F . Then a contradiction. Hence q * H > q * F . The proof for the case of τ < 1 is similar and omitted.
Second, suppose τ = 1 and x o = x (a sufficient condition is m (u) = 0 as shown by Lemma 4). Then similar to Proposition 2, if there is no regulation, Third, suppose τ = 1 and x o > x (a sufficient condition is m (u) < 0 as shown by Lemma 4). Then similar to Proposition 2, if there is no regulation, . That is, without regulation, W (x * ) has an inverted U-shaped relationship with θ. If there is regulation, from Lemma To summarize, when τ = 1 and x o ≥ x (or particularly m (u) ≤ 0), the cut-off μ θ < 1 − x < 1. When τ = 1 and x o < x (or particularly m (u) > 0), in general μ θ may be less than or equal to 1. However, if m (u) is sufficiently small relative to |τ − 1| and θ ≥ 1 − x, then x is sufficiently close to x o while x r is much larger than x o , and hence It remains to identify conditions under which μ θ > 0. Note that, without regulation

Proof of Proposition 4.
(1) We first characterize the firm's localization decisions. Suppose that τ > 1 and θ ∈ (1 − max{ x H , x F }, 1 − min{ x H , x F }). In this case, x H > x F . With localization, firm profit (excluding costs k) is According to Proposition 1, without localization, firm profit is Since max{ x, 1 − θ} ≥ 1 − θ > x F , firm profit in country F is higher under localization. By definition, firm profit in country H is maximized by x H . Therefore, total profit (excluding costs k) is higher under data localization. Now consider two case.
First, suppose θ < 1 − x. The profit difference (excluding costs k) becomes The first term in (34) is independent of θ. The second term, λq * , is the firm's profit in country H when x = 1 − θ. Since x H maximizes firm profit in H and x = 1 − θ < x H , firm profit in country H increases in x or, equivalently, decreases in θ.
Second, suppose θ ≥ 1 − x. The profit difference (excluding costs k) becomes where only the second term (the firm's profit in country F under localization) depends on θ. Since x F maximizes firm profit in F and x = 1 − θ > x F , the second term decreases in x or, equivalently, increases in θ. Accordingly, the profit difference π( increases in θ. To summarize, when τ > 1 and θ ∈ (1 − x H , 1 − x F ), the profit difference between localization and no localization strictly increases in θ. The same result can be obtained when τ < 1 and θ ∈ (1 − x F , 1 − x H ). Thus, given any k < k 1 (τ ) = π( x H , x F ) − π( x), there exists a unique θ l such that π(x * H , x * F ; θ) − π(x * ; θ) > k if and only if θ > θ l . The earlier analysis also implies θ l increases in k.
(2) Now we examine whether the firm's decision about localization is socially efficient or not. Consider three ranges of θ.
First, suppose θ ≤ 1 − max{ x H , x F }. As shown in the text, x * H = x * F = x * = 1 − θ, so that the firm would never invest in localization and this decision is socially efficient.
Second, suppose θ ≥ 1 − min{ x H , x F }. Since min{ x H , x F } < x, θ > 1 − x. Then x * H = x H and x * F = x F with localization, and x * = x without localization. The firm invests in localization if and only if k < k 1 (τ ). Note that When k < k 1 (τ ), the firm invests in localization, which is socially efficient. When k ∈ [k 1 (τ ), W ( x H , x F ) − W ( x)), the firm does not invest in localization while localization raises global welfare. When k > W ( x H , x F ) − W ( x), the firm does not invest in localization and this decision is efficient.
(ii) Suppose τ < 1. Then min{ x H , x F } = x H and k 2 (τ ) = π( x H , x F ) − π( x H ). Note that given x F > x H and 1 − G(p l F ( x F ) + τ x F ) > 1 − G(p * F ( x H ) + τ x H ) from Lemma 3. When τ < 1, the profit difference strictly decreases in τ . The equilibrium characterization then follows from the text. Now we consider the welfare impact of data-usage regulations.
First, suppose τ = 1 and k < k 1 (τ ) < k 2 (τ ). When there is no regulation, the firm invests in localization if and only if θ > θ l ; when there are data regulations, the firm always invests in localization. Therefore, when θ > θ l , the welfare difference between having regulations and not having regulations is When θ ≤ θ l , the welfare difference is [W ( x H , x F ) − k] − W (x * ; θ). Proposition 3 implies that, if m (u) ≥ 0 and there is no localization, global welfare W (x * ; θ) increases in θ for θ ≤ θ l . By the definition of θ l , we have Then by continuity, for any θ ≤ θ l , we have To summarize, given τ = 1 and k < k 1 (τ ) < k 2 (τ ), if m (u) ≥ 0, regulations (weakly) increase welfare for any θ ∈ [0, 1].
Next, suppose m (u) < 0 and k ∈ [k 1 (τ ), k 2 (τ )). Consider the case with τ > 1. We have and, by the envelop theorem, Therefore, if λ is greater than but arbitrarily close to 1, we have Moreover, when τ = 1, x H = x F = x o so that W ( x H , x F ) − W (x o ) = k 2 (τ ). Then by continuity, when λ is sufficiently large, there exists τ > 1 such that for any τ ∈ (1, τ ), we have which further implies that, for θ arbitrarily close to 1 − x o , Similarly, when τ is less than but arbitrarily close to 1, x H is arbitrarily close to x o , so that Therefore, there exists τ < 1 such that for any τ ∈ ( τ , 1), we have which further implies that, for θ arbitrarily close to 1 − x o , W ( x H , x F ) − W (x * ; θ) < k 2 (τ ).

International Protection of Consumer Data
Electronic copy available at: https://ssrn.com/abstract=3688295 The European Commission supports the EUI through the European Union budget. This publication reflects the views only of the author(s), and the Commission cannot be held responsible for any use which may be made of the information contained therein.