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Abstract The Foreign Corrupt Practices Act (FCPA) prohibits U.S.-related firms from making bribes abroad. We analyze the FCPA’s effects in a model of competition between a U.S. and foreign firm for contracts in a host country. If the FCPA only applies to the U.S. firm, it reduces that firm’s competitiveness and either increases bribery by the foreign firm or reduces overall investment. If the FCPA also applies to foreign firms, it reduces total bribery, and in host countries with high corruption levels, it increases total investment. The model suggests that the FCPA will deter bribery and stimulate investment while not disadvantaging U.S. firms if its enforcement is aimed at firms who engaged in bribery in highly corrupt countries and whose main competitors are also subject to the FCPA. “It’s a horrible law and should be changed (...) It puts us at a huge disadvantage.” –Donald Trump speaking on the U.S. Foreign Corrupt Practices Act (CNBC, 2012) 1. Introduction Corruption has been shown to reduce economic growth, investment activity, and international trade (for a survey of empirical evidence, see Dreher and Herzfeld, 2005). In an effort to reduce corruption, the U.S. government has levied billions of dollars in penalties over the last several years for violations of the Foreign Corrupt Practices Act (“FCPA”) of 1977, a broad U.S. law that criminalizes the payment of bribes by U.S. citizens and corporations to government officials anywhere in the world. FCPA enforcement actions have been taken against many of the world’s largest and most well-known companies, including IBM, General Electric, Ralph Lauren, Pfizer, and Chevron (https://www.sec.gov/spotlight/fcpa/fcpa-cases.shtml). In this article, we address the following questions: how does the FCPA affect the competitiveness, bribery activity, and investments of U.S. firms, and how do the answers depend on whom the U.S. firms are competing against and in which countries they are competing? To answer these questions, we use a contest model of competition between a multinational firm headquartered in the U.S. (the U.S. firm) and its foreign competitor (the non-U.S. firm) for a government contract in a host country. Firms can increase their chances of winning the contract through two activities, productive investment and bribery. The relative weight that the contest official places on bribery is a proxy for the extent of corruption in the host country. In this context, we ask: When does the FCPA disadvantage U.S. firms? Does the FCPA achieve its goal of reducing bribery? Does it have an impact on productive investments made by the U.S. firm and its competitor? The answers depend critically on whether the competing firm has U.S. ties. When the competing firm has no ties to the U.S., the FCPA only applies to the U.S. firm.1 In this case, the FCPA always puts the U.S. firm at a disadvantage, reducing its probability of winning the contract. The FCPA reduces bribery by the U.S. firm. However, it increases bribery by the competing firm if the U.S. firm is the favorite to win the contest, and it reduces productive investment by both firms if the U.S. firm is not the favorite to win. It increases total bribery effort if the U.S. firm is sufficiently dominant in the productive activity and the level of corruption in the host country is sufficiently high. In sum, with enforcement limited to U.S. firms, the FCPA not only harms the competitiveness of U.S. firms but may also fail in achieving its primary objective of reducing bribery or will have the negative externality of reducing productive investment. On the other hand, when the competing firm has ties to the U.S. (see footnote 1), the FCPA applies to both firms. In this case, the FCPA favors the firm with the absolute disadvantage in bribery. It reduces total bribery efforts by the firms. If one of the firms has the absolute advantage in both bribery and investment, then the FCPA balances the contest and increases both firms’ investment efforts. If no firm has an absolute advantage in both bribery and investment, then the effect of the FCPA on investment efforts depends on the level of corruption in the host country. The FCPA increases both firms’ investment efforts if the firm that has the absolute advantage in bribery is the favorite to win the contest, which is the case when the level of corruption in the host country is high. On the other hand, the FCPA reduces both firms’ investment efforts if the firm with the absolute disadvantage in bribery is the favorite to win, which is the case if the corruption level in the host country is low. In sum, with symmetric enforcement limited to activity in host countries with high corruption levels, the FCPA does not a priori harm the competitiveness of U.S. firms and both reduce bribery and increases productive investment. Broadly, the model suggests that the FCPA can reduce bribery and increase investment while maintaining U.S. competitiveness if it is enforced against firms who engaged in bribery in countries with high levels of corruption and whose main competitors are also subject to the FCPA. Analyzing FCPA cases from 2012 to 2018, we find that the overwhelming majority of the cases have concerned activity in host countries with high corruption levels as measured by corruption perception indices. Moreover, we find a significant proportion of cases against foreign multinational companies with cooperation from foreign governments. In fact, total fines in FCPA cases against foreign multinationals exceeded total fines in FCPA cases against U.S. multinationals by over |${\$}$|4 billion over the period 2016–18. An additional analysis of the main competitors of the firms that were prosecuted in these FCPA cases reveals that the overwhelming majority of these competitors are traded on U.S. financial markets and are therefore also subject to the FCPA. This may reflect a smart policy by U.S. prosecutors to prosecute mainly in situations where most firms are subject to the FCPA. The article is organized as follows. Section 2 discusses our paper’s contributions in relation to existing literature. Section 3 develops and solves the theoretical model. Section 4 analyzes the effects of the FCPA in the case where it only applies to U.S. firms. Section 5 analyzes the case where the FCPA applies to U.S. and foreign firms. Section 6 analyzes recent FCPA cases to determine whether in practice FCPA actions have been taken mainly against U.S. firms and mainly in highly corrupt host countries. Section 7 discusses extensions of the model to the case of a constant elasticity of substitution (CES) contest success function (CSF) and to the case of more than two firms. Section 8 concludes. 2. Related Literature Our article contributes to the economics literature on corruption. From the outset, corruption and bribery have been considered forms of rent-seeking in the economics literature (Krueger, 1974; Posner, 1975; Tullock, 1980; Baye et al., 1993; Lambsdorff, 2002). We model bribery in an extension of the standard Tullock contest model that allows for players to engage in more than one activity, and we distinguish bribery from other activities in that it is illegal and potentially subject to fines. In our model, bribery is potentially harmful in that it can unbalance contests in favor of firms that are better at bribery and thereby reduce productive investment. Our article also contributes more specifically to the law and economics literature on bribery. For an excellent review, see Rose-Ackerman (2010). Polinsky and Shavell (2001) and Garoupa and Klerman (2004, 2010) analyze optimal law enforcement given the central problem that public enforcement creates incentives for bribery and thus undermines deterrence. Basu et al. (2014) find that it may be optimal to punish bribers and bribees asymmetrically to reduce collusion and preserve the incentives of agents to report bribery. They model the choices of a representative firm, and focus on the bribe choice. We model the interplay between competing firms and consider both the choices of productive investment and bribery. We model competition in both investment and bribery using a Cobb–Douglas CSF.2Arbatskaya and Mialon (2010) provide an axiomatization of this type of CSF for multi-activity contests. Classic axioms, including an independence from irrelevant alternatives property, yield the general logit form for the CSF and an additional homogeneity axiom, whereby an equiproportionate change in both players’ efforts in an activity does not affect players’ success probabilities, yields the logit form with production functions of the Cobb–Douglas type. Arbatskaya and Mialon (2012) employ this type of CSF to analyze dynamic multi-activity contests, where players can make both short-run and long-run investments. Haan and Schoonbeek (2003) and Melkonyan (2013) employ this type of CSF to analyze hybrid contests where players can make expenditures borne by both winners and losers as well as expenditures born only by winners. To our knowledge, our article is the first to provide a formal theoretical analysis of the effects of the FCPA on the bribery and investment activities of U.S. and foreign firms. Several papers have empirically analyzed the effects of the FCPA on U.S. competitiveness and business activity. Overall, the results have been mixed. Hines (1995) finds a reduction in business activity by U.S. firms in bribery-prone countries following the 1977 enactment of the FCPA, arguing that the FCPA weakened the competitiveness of U.S. firms without reducing the importance of bribery in these countries. Wei (2000) finds that U.S. investors did not invest less in corrupt countries than did investors from other Organisation for Economic Cooperation and Development countries following the FCPA enactment. Lippitt (2013) finds no significant relationship between U.S. foreign direct investment growth and prosecuted FCPA violations, while Graham and Stroup (2016) find a reduction in the number of acquisitions by U.S. firms of targets headquartered in foreign countries following FCPA enforcement actions. Our theoretical analysis shows that the FCPA may reduce or not affect the competitiveness of U.S. firms and may decrease or increase investment by U.S. firms, depending on whether or not their rivals are also subject to the FCPA and depending on the levels of corruption in the host countries, which may help explain mixed results of prior empirical studies. Future empirical studies may want to control for, and explore interactions with, measures of corruption in host countries and of the extent to which rivals of prosecuted firms were also subject to the FCPA. Moreover, relationships between FCPA enforcement and U.S. competitiveness and investment may have changed over time. While early FCPA prosecutions, as covered by Hines (1995), involved mainly U.S.-based firms, our analysis of more recent FCPA cases shows that many of the prosecuted firms are non-U.S. based and that a majority of the rivals of U.S.-based prosecuted firms trade stock in U.S. financial markets and are therefore also subject to the FCPA. So while the FCPA may have been associated with reduced U.S. competitiveness and investment in the early period, those relationships may no longer hold in the more recent period. 3. Basic Model Consider two firms competing for a contract allocated by a government official in a host country. The value of the contract to each firm is normalized to one. Firm 1 is the U.S. firm, and firm 2 is a foreign firm that may or may not have ties with the U.S. The firms can influence the outcome of the contest by engaging in productive investment and in bribery. Denote by |$x_{i}\in \mathbb{R} _{+}$| and |$y_{i}\in \mathbb{R} _{+}$| efforts of player |$i\in\{1,2\}$| in productive investment and in bribery, respectively. Both activities increase a firm’s chances of winning the contest. We assume that firm |$i$|’s probability of winning (called CSF) has the logit representation |$p_{i}\left( x_{1},x_{2},y_{1},y_{2}\right) =f\left( x_{i},y_{i}\right) /\left(\,f\left( x_{1},y_{1}\right) +f\left( x_{2},y_{2}\right) \right) $| with an influence production function of Cobb–Douglas type |$f\left( x_{i},y_{i}\right) =x_{i}^{1-\beta} y_{i}^{\beta}$|, where |$\beta\in\left( 0,1\right) $| is the (relative) weight placed on bribery in the CSF and is a measure of the level of corruption in the host country, which is a function of the host country’s political institutions.3 The marginal cost of productive investment for firm |$i$| is |$c_{i}>0$|. The marginal cost of bribery is increasing in fines on firms that are subject to the FCPA. We analyze two regimes, one where the FCPA applies only to the firm 1 (U.S. firm) and one where the FCPA applies to both firms. In the first regime, the marginal cost of bribery is |$d_{1}\left( t\right) =d_{1}+t$| for firm 1 and |$d_{2}(t)=d_{2}$| for firm 2. In the second regime, the marginal cost of bribery is |$d_{i}\left( t\right) =d_{i}+t$| for both firms since they are both subject to fines under the FCPA in this regime. The term |$t>0$| captures the expected sanction for being subject to the FCPA. Firm |$i$|’s payoff in the contest is then: $$\begin{equation} \Pi_{i}(x_{1},x_{2}\mathbf{,}y_{1},y_{2})=\frac{x_{i}^{1-\beta}y_{i}^{\beta} }{x_{1}^{1-\beta}y_{1}^{\beta}+x_{2}^{1-\beta}y_{2}^{\beta}}-c_{i}x_{i} -d_{i}\left( t\right) y_{i}\text{.}\end{equation}$$(1) Firm |$1$| (the U.S. firm) has an absolute advantage in the productive activity if |$c_{1}<c_{2}$|; an absolute advantage in bribery if |$d_{1}(t)<d_{2}(t)$|; and a comparative advantage in the productive activity if |$c_{1}/c_{2}<d_{1}(t)/d_{2}(t)$|. Let |$A=A\left( t\right) =\frac{d_{1}(t)/d_{2}(t)}{c_{1}/c_{2}}$| be the measure of firm 2’s comparative advantage in bribery. We call |$\Theta=\Theta\left( t\right) \equiv\left( c_{1}/c_{2}\right) ^{1-\beta}\left( d_{1}(t)/d_{2}(t)\right) ^{\beta}$| firm |$2$|’s overall (relative) strength. Firm 1 is stronger overall if |$\Theta<1$| and is weaker overall if |$\Theta>1 $|. We first characterize the equilibrium efforts of the contest |$\left( x_{1}^{\ast},x_{2}^{\ast},y_{1}^{\ast},y_{2}^{\ast}\right) $| and conditions for firm |$i$| to be the favorite to win the contest (|$p_{i}^{\ast}>1/2$|). Proofs of all results are in the Appendix. Lemma 1 (i) In the unique equilibrium |$\left( x_{1}^{\ast} ,x_{2}^{\ast},y_{1}^{\ast},y_{2}^{\ast}\right) $| of the contest, firms’ efforts are |$x_{i}^{\ast}=\frac{1-\beta}{c_{i}}\Lambda$| and |$y_{i}^{\ast}=\frac{\beta}{d_{i}(t)}\Lambda$|, where |$\Theta=\left( \frac{c_{1}}{c_{2}}\right) ^{1-\beta}\left( \frac{d_{1}(t)}{d_{2} (t)}\right) ^{\beta}$| for |$t\geq0$| is firm |$2$|’s overall (relative) strength and |$\Lambda=\Theta\left( 1+\Theta\right) ^{-2}$| is the balance of power in the contest; |$i=1,2$|. (ii) The U.S. firm’s probability of winning is |$p_{1}^{\ast }=\left( 1+\Theta\right) ^{-1}$|. The U.S. firm is the favorite to win the contest (|$p_{1}^{\ast}>1/2$|) whenever it is stronger overall, |$\Theta<1$|, i.e. when it has an absolute advantage in both activities, or only in productive investment and the corruption level is sufficiently low (|$\beta<\overline{\beta}\equiv\log\left( \frac{c_{2}}{c_{1}}\right) /\left( \log\left( \frac{c_{2}}{c_{1}}\right) -\log\left( \frac{d_{2} (t)}{d_{1}(t)}\right) \right) \in\left( 0,1\right) $|), or only in bribery and the corruption level is sufficiently high (|$\beta>\overline {\beta}$|). The firms’ payoffs are |$\Pi_{1}^{\ast}=\left( p_{1}^{\ast }\right) ^{2}=\left( 1+\Theta\right) ^{-2}$| and |$\Pi_{2}^{\ast }=\left( 1-p_{1}^{\ast}\right) ^{2}=\left( 1+1/\Theta\right) ^{-2}$|, and the total industry payoff is |$\Pi^{\ast}=\Pi_{1}^{\ast}+\Pi_{2}^{\ast }=1-2\Lambda$|. According to Lemma 1(i), the equilibrium efforts depend on the balance of power in the contest, |$\Lambda$|, which in turn depends on the overall strength of the U.S. firm: |$\Lambda=\Theta\left( 1+\Theta\right) ^{-2}\in(0,1/4]$|. When the contest is fully balanced (|$\Theta=1$|), the level of rent dissipation reaches its maximum of 50% because the total expenditures are |$ \sum_{i=1,2} \left( c_{i}x_{i}^{\ast}+d_{i}(t)y_{i}^{\ast}\right) =2\Lambda$| and |$\Lambda=1/4$| when |$\Theta=1$|. Lemma 1(ii) states the U.S. firm’s probability of winning is |$p_{1}^{\ast}=\left( 1+\Theta\right) ^{-1}$|. It follows that if the U.S. firm is stronger overall (|$\Theta<1$|), then it is the favorite to win the contest (|$p_{1}^{\ast}>1/2$|), and if it is weaker overall (|$\Theta >1$|), then it is the underdog (|$p_{1}^{\ast}<1/2$|). Quite intuitively, for the U.S. firm to be the favorite, it must either have an absolute advantage in both activities, or only in one activity but with sufficient weight being placed on that activity in the influence production function. Finally, firms’ payoffs are increasing in their probability of winning, and the industry payoff is decreasing in the balance of power |$\Lambda$|. 4. When FCPA Only Applies to U.S. Firm We first consider the case where firm 1 (the U.S. firm) is competing against a firm that is not subject to FCPA enforcement because it does not have U.S. ties. In this case, instead of costs |$d_{1}$| and |$d_{2}$| per unit of bribery effort, the firms have costs |$d_{1}+t$| and |$d_{2}$|. FCPA enforcement then only increases the cost of bribery for firm 1. Proposition 1 Suppose there is a marginal increase in the cost of bribery only for the U.S. firm under the FCPA. Then, the U.S. firm’s bribery effort (|$y_{1}^{\ast}$|) decreases. When the U.S. firm is the favorite to win the contest (|$\Theta<1$|), both firms’ investment efforts and the bribery effort of firm 2 (|$x_{1}^{\ast}$|, |$x_{2}^{\ast}$|, and |$y_{2}^{\ast}$|) increase, and otherwise they decrease. Total bribery effort (|$Y^{\ast}=y_{1}^{\ast}+y_{2}^{\ast}$|) increases if and only if |$\Theta<1$|, |$\beta>\widehat{\beta}\in (0,1)$|, and |$\frac{c_{1}}{c_{2}}<\widehat{\frac{c_{1}}{c_{2}}} $|, where $$\begin{align}&\widehat{\beta}=\left( 1+\frac{d_{1}+t}{d_{2}}\right) ^{-1}\text{ {and} }\notag\\&\widehat{\frac{c_{1}}{c_{2}}}=\left( \frac{\beta\left( 1+\frac{d_{1} +t}{d_{2}}\right) -1}{\beta\left( 1+\frac{d_{1}+t}{d_{2}}\right) +1}\right) ^{\frac{1}{1-\beta}}\left( \frac{d_{1}+t}{d_{2}}\right) ^{-\frac{\beta}{1-\beta}}\text{.}\end{align}$$(2) The U.S. firm is disadvantaged in that its probability of winning and payoff decrease, while the non-U.S. firm is always better off. When the FCPA only applies to the U.S. firm, it unambiguously reduces the U.S. firm’s probability of winning the contest and the U.S. firm’s bribery effort. Its effects on the non-U.S. firm’s bribery effort and on both firms’ investment efforts depend on whether or not the U.S. firm is the overall favorite in the contest (|$\Theta<1$|). Intuitively, if the U.S. firm is the overall favorite in the contest, then increasing the U.S. firm’s marginal cost of bribery through FCPA enforcement balances the contest, thereby increasing the non-U.S. firm’s bribery effort and both firms’ investment efforts. On the other hand, if the U.S. firm is not the overall favorite in the contest, then increasing the U.S. firm’s marginal cost of bribery through FCPA enforcement unbalances the contest, thereby decreasing the non-U.S. firm’s bribery effort and both firms’ investment efforts. By part (ii) of Lemma 1, the U.S. firm is the favorite if it has an absolute advantage in both activities, or only in bribery but the corruption level in the host country (|$\beta$|) is sufficiently high, or only in productive investment but the corruption level is sufficiently low. Thus, when the FCPA only applies to the U.S. firm, it either increases bribery by the foreign firm or reduces both firms’ investment efforts. Moreover, Proposition 1 shows that it increases total bribery effort if the level of corruption in the host country is sufficiently high and the U.S. firm is sufficiently dominant in the productive activity (|$c_{1}/c_{2}$| is sufficiently low). 5. When FCPA Applies to Both Firms We now consider the case where firm 1 (the U.S. firm) is competing against a firm that is also subject to FCPA enforcement because it has U.S. ties. In this case, instead of costs |$d_{1}$| and |$d_{2}$| per unit of effort, firms have costs |$d_{1}+t$| and |$d_{2}+t$|. FCPA enforcement then increases both firms’ cost of bribery by a common amount. Proposition 2 Suppose there is a common marginal increase in the cost of bribery for the U.S. firm and its competitor under the FCPA. Then, the total bribery effort (|$Y^{\ast}=y_{1}^{\ast}+y_{2}^{\ast} $|) decreases. If the firm with the absolute advantage in bribery is the favorite to win the contest (|$d_{1}<d_{2}$| and |$\Theta<1$| or |$d_{1}>d_{2}$| and |$\Theta>1$|), then the firms’ investment efforts (|$x_{1}^{\ast}$| and |$x_{2}^{\ast}$|) increase, and otherwise they decrease. A firm’s probability of winning the contest and payoff increase if and only if it has an absolute disadvantage in bribery (|$d_{i}>d_{j}$|); |$i\neq j=1,2$|. A common marginal increase in the cost of bribery for both firms under the FCPA favors the firm with an absolute disadvantage in bribery. It unambiguously reduces total bribery efforts since it increases the penalty for bribery across both firms. However, the effect on the firms’ investment efforts depends on which firm is the favorite to win the contest. Intuitively, when the firm with the absolute advantage in bribery is the favorite to win the contest, then the FCPA reduces the favorite’s advantage, thereby balancing the contest and increasing both firms’ investment efforts. On the other hand, when the firm with the absolute advantage in bribery is not the favorite to win the contest, then the FCPA increases the favorite’s advantage, thereby unbalancing the contest and reducing both firms’ investment efforts. By part (ii) of Lemma 1, the firm with the absolute advantage in bribery is the favorite if it also has an absolute advantage in productive investment or if it does not have an absolute advantage in productive investment but the level of corruption in the host country is sufficiently high. Thus, if the FCPA applies to both firms, then it reduces bribery total efforts; and if its enforcement is targeted to activity in host countries with high levels of corruption, then it also increases productive investment by both firms, while not a priori harming the competitiveness of the U.S. firm. 6. Analysis of Recent FCPA Cases Proposition 1 shows that if the FCPA is only applied to U.S. firms, then it harms the competitiveness of U.S. firms and either increases bribery by competing foreign firms or reduces productive investments by both U.S. and foreign firms. In this case, Donald Trump’s statement that the FCPA puts U.S. firms at a disadvantage (see the introductory quote) is found to be correct. However, Proposition 2 shows that if the FCPA is applied to both U.S. and foreign firms and in host countries where corruption levels are high, then it reduces bribery and increases investment without a priori harming U.S. competitiveness. Therefore, two key empirical questions are whether the FCPA is mainly applied to U.S. firms or is applied to both U.S. and foreign firms and whether or not FCPA actions are predominantly in host countries with high levels of corruption in practice. Table 1 provides a summary of FCPA enforcement actions over the period 2012–18, which includes 46 FCPA actions against US-based firms and 30 FCPA actions against non-U.S.-based firms. Table 1. FCPA Enforcement Actions, 2012-2018 . 2012 . 2013 . 2014 . 2015 . 2016 . 2017 . 2018 . U.S. firms No. of actions: 5 5 7 6 13 4 7 Total fines: |${\$}$|103,200,000 |${\$}$|106,582,000 |${\$}$|691,400,000 |${\$}$|69,700,000 |${\$}$|433,415,000 |${\$}$|78,200,000 |${\$}$|93,800,000 Ave. host CPI: 37.4 33.1 36.7 39 36.5 33.1 34.5 Non-U.S. firms No. of actions: 4 3 0 2 11 3 7 Total fines: |${\$}$|68,300,000 |${\$}$|652,500,000 - |${\$}$|44,000,000 |${\$}$|2,558,200,000 |${\$}$|1,008,000,000 |${\$}$|1,981,950,000 Ave. host CPI: 41 39.5 - 40.5 34.2 43 42.2 . 2012 . 2013 . 2014 . 2015 . 2016 . 2017 . 2018 . U.S. firms No. of actions: 5 5 7 6 13 4 7 Total fines: |${\$}$|103,200,000 |${\$}$|106,582,000 |${\$}$|691,400,000 |${\$}$|69,700,000 |${\$}$|433,415,000 |${\$}$|78,200,000 |${\$}$|93,800,000 Ave. host CPI: 37.4 33.1 36.7 39 36.5 33.1 34.5 Non-U.S. firms No. of actions: 4 3 0 2 11 3 7 Total fines: |${\$}$|68,300,000 |${\$}$|652,500,000 - |${\$}$|44,000,000 |${\$}$|2,558,200,000 |${\$}$|1,008,000,000 |${\$}$|1,981,950,000 Ave. host CPI: 41 39.5 - 40.5 34.2 43 42.2 Notes: Information on FCPA enforcement actions are from the U.S. Securities and Exchange Commission (https://www.sec.gov/spotlight/fcpa/fcpa-cases.shtml, last accessed February 22, 2020). The CPI is the Corruption Perceptions Index from Transparancy International (www.transparency.org/research/cpi/overview, last accessed February 22, 2020), where a CPI of 0 is “highly corrupt” and 100 is “very clean.” Average host CPI is the average CPI across host countries in FCPA enforcement actions. Open in new tab Table 1. FCPA Enforcement Actions, 2012-2018 . 2012 . 2013 . 2014 . 2015 . 2016 . 2017 . 2018 . U.S. firms No. of actions: 5 5 7 6 13 4 7 Total fines: |${\$}$|103,200,000 |${\$}$|106,582,000 |${\$}$|691,400,000 |${\$}$|69,700,000 |${\$}$|433,415,000 |${\$}$|78,200,000 |${\$}$|93,800,000 Ave. host CPI: 37.4 33.1 36.7 39 36.5 33.1 34.5 Non-U.S. firms No. of actions: 4 3 0 2 11 3 7 Total fines: |${\$}$|68,300,000 |${\$}$|652,500,000 - |${\$}$|44,000,000 |${\$}$|2,558,200,000 |${\$}$|1,008,000,000 |${\$}$|1,981,950,000 Ave. host CPI: 41 39.5 - 40.5 34.2 43 42.2 . 2012 . 2013 . 2014 . 2015 . 2016 . 2017 . 2018 . U.S. firms No. of actions: 5 5 7 6 13 4 7 Total fines: |${\$}$|103,200,000 |${\$}$|106,582,000 |${\$}$|691,400,000 |${\$}$|69,700,000 |${\$}$|433,415,000 |${\$}$|78,200,000 |${\$}$|93,800,000 Ave. host CPI: 37.4 33.1 36.7 39 36.5 33.1 34.5 Non-U.S. firms No. of actions: 4 3 0 2 11 3 7 Total fines: |${\$}$|68,300,000 |${\$}$|652,500,000 - |${\$}$|44,000,000 |${\$}$|2,558,200,000 |${\$}$|1,008,000,000 |${\$}$|1,981,950,000 Ave. host CPI: 41 39.5 - 40.5 34.2 43 42.2 Notes: Information on FCPA enforcement actions are from the U.S. Securities and Exchange Commission (https://www.sec.gov/spotlight/fcpa/fcpa-cases.shtml, last accessed February 22, 2020). The CPI is the Corruption Perceptions Index from Transparancy International (www.transparency.org/research/cpi/overview, last accessed February 22, 2020), where a CPI of 0 is “highly corrupt” and 100 is “very clean.” Average host CPI is the average CPI across host countries in FCPA enforcement actions. Open in new tab The table reveals that FCPA enforcement actions have mainly been in host countries with high levels of corruption. The average corruption perception index (CPI) across host countries in FCPA enforcement actions is below 50, where a CPI of 0 is “highly corrupt” and a CPI of 100 is “very clean.” The table also reveals that FCPA enforcement actions have quite often been taken against foreign firms as well as U.S. firms. Over the last 2 years, total FCPA fines on foreign firms exceeded that on U.S. firms by about |${\$}$|3 billion. The 2016–18 cases included a |${\$}$|519 million fine on the Israeli pharmaceutical company, Teva; a |${\$}$|795 million fine on the Dutch telecom, Vimpelcom; a |${\$}$|965 million fine on the Swedish telecom, Telia; and a |${\$}$|1.78 billion fine against the Brazilian petrochemical giant, Petrobras. In practice, enforcement actions by the U.S. Securities and Exchange Commission (SEC) and U.S. Department of Justice against foreign firms are facilitated by cooperation from the governments of the home countries of these foreign firms. The fact that an increasing number of FCPA cases with blockbuster fines have been mounted against foreign firms may indicate increasing international cooperation in anti-bribery efforts. For example, in the 2016 case against Vimpelcom for violations of the FCPA to obtain business in Uzbekistan, the SEC received cooperation from government prosecution and anti-bribery agencies in the Netherlands, Norway, Sweden, Switzerland, and Latvia (https://www.sec.gov/news/pressrelease/2016-34.html). Most large foreign multi-national companies have shares that trade in U.S. markets and are therefore also subject to the FCPA. Although FCPA rulings do not provide direct information on who were the competitors of the prosecuted firms in bids for contracts where bribery was alleged, we can obtain some indirect evidence on the extent to which firms that were prosecuted under the FCPA faced competitors who were also subject to the FCPA. We know that, at a minimum, any firm that is based in the United States or trades on U.S. financial markets is subject to the FCPA. For each of the 46 FCPA prosecutions of U.S.-based firms and 30 FCPA prosecutions of non-U.S.-based firms from 2012 to 2018, we identified the top competitors of the prosecuted firm from the Hoovers database (www.hoovers.com), which lists up to three top competitors for every company covered by its database. Using Google’s knowledge graph for a company, we then determined whether each of the top competitors were (1) U.S.-based; (2) traded on U.S. financial markets, in particular, the NYSE, NASDAQ, or OTC Markets; or (3) non-U.S.-based and not traded on those U.S. financial markets. In total, our sample, which is available upon request in Supplementary Appendix A, consists of 135 top competitors for the 46 U.S.-based prosecuted firms and 87 top competitors for the 30 non-U.S.-based prosecuted firms over the period 2012–18. We find that only 4 of the 135 top competitors of the U.S.-based prosecuted firms, and only 5 of the 87 top competitors of the non-U.S.-based prosecuted firms, are non-U.S.-based and do not trade on the U.S. financial markets. Thus, it appears that the overwhelming majority of top competitors of firms prosecuted under the FCPA were also subject to the FCPA. This provides evidence that we are more likely to be in the theoretical case of Proposition 2 in our model, where all firms are subject to the FCPA and the FCPA is likely to have the benefits of reducing bribery and increasing productive investment while not disadvantaging U.S. firms. As a check on the validity of our measure of being subject to the FCPA, we also determined whether the non-U.S.-based firms that were prosecuted under the FCPA were traded on the U.S. financial markets. We find that every non-U.S.-based prosecuted firm was traded on the NYSE, NASDAQ, or OTC Markets at the time of infraction. The fact that the overwhelming majority of top competitors of firms that were prosecuted under the FCPA were also subject to the FCPA might reflect a smart policy by U.S. prosecutors to prosecute mostly in situations where all competitors are subject to the FCPA (and in countries where corruption levels are high). That way, as is shown in Proposition 2 in our model, one can reduce bribery and increase productive investment without systematically disadvantaging U.S. firms. The SEC’s current resource guide to the FCPA (U.S. Securities and Exchange Commission, 2012) is consistent with such a prosecutorial policy, emphasizing not only “a level playing field for honest businesses” (p. 2), but also “a fair playing field for U.S. companies doing business abroad” (p. 4). 7. Extensions We now discuss extensions of the model to the case of a CSF with CES and to the case of more than two firms. 7.1. CES Contest Success Function In Supplementary Appendix B, we show that the results of the article generalize to the CES influence production function, allowing the elasticity of substitution |$\sigma$| between productive effort and bribery to vary from 1 under the Cobb–Douglas influence production function (|$\sigma\rightarrow1$|), all the way to the case of perfect substitutes (|$\sigma\rightarrow\infty$|). With the CES function, we have an additional effect present: the share effect. The overall outcome of a policy that increases the marginal cost of bribery on firms’ efforts then depends on three effects: (1) the direct effect (it is more costly to engage in bribery); (2) the balance of power effect (the fines change the relative power of player 1 and the balance of power/competitiveness of the contest), and (3) the share effect (as bribery becomes more costly for a player, the player changes its share of expenditures allocated to it). With the CES function, we find (in Proposition 1B) that levying a fine for bribery only on the U.S. firm would always reduce bribery by the U.S. firm. The negative effect is stronger here. As before, the direct effect of costlier bribery dominates the balance of power effect, but there is an additional negative share effect. As bribery becomes relatively costlier for the U.S. firm to engage in, the U.S. firm spends a smaller share of its expenditures on bribery, substituting toward a relatively cheaper productive activity. The strategic effect on the rival remains the same as for the Cobb–Douglas function: the weaker rival increases both productive and bribery efforts. What happens to the productive effort of the U.S. firm depends on the degree of substitution between activities. While it is still true that the productive effort of the U.S. firm increases if the U.S. firm is the overall favorite (|$\Theta<1$|), it may increase even if the U.S. firm is not the favorite, provided the elasticity of substitution |$\sigma$| between productive effort and bribery is sufficiently high. This is quite intuitive. All else equal, a firm would show a larger substitution response to a change in relative costs of inputs when it is easy to substitute between activities. We also extend the results of Proposition 2 to the class of CES influence production functions with |$\sigma>1$|. We show that, as in Proposition 2, whether the U.S. is favored by the FCPA enforcement depends on the ratio of firms’ costs of bribery. While in the Cobb–Douglas case (Proposition 2), the U.S. firm is favored if and only if it has an absolute disadvantage in bribery, in the CES case (Proposition 2B), the U.S. firm is favored if and only if it has a sufficient absolute disadvantage in bribery. With this adjustment, the other results are the same. For example, total bribery effort always goes down when all firms are subject to FCPA enforcement, as in the Cobb–Douglas case. This is intuitive, since FCPA enforcement has an additional share effect tending to reduce bribery efforts in the CES case, which is not present in the Cobb–Douglas case. 7.2. More than Two Firms In Supplementary Appendix C, we extend the model to the case of |$n$| firms, including |$k\geq1$| U.S. firms with same costs and |$n-k\geq1$| foreign firms with same costs. We find that the main insights of the article are the same, with a few additional points. As in the case of two firms, FCPA enforcement changes the costs of bribery. This generates a negative direct effect on the equilibrium bribery effort by a targeted firm and a change in the balance of power from a firm’s perspective, which can generate an additional positive or negative effect on the firm’s bribery effort. In the case of two firms, if one firm gains due to FCPA enforcement (in terms of overall strength, probability of winning, and payoff), the other one loses, and the contest balances or unbalances for both. With three or more firms, it is possible for the contest to balance for some firms and unbalance for others, and for some firms to gain and others to lose. However, the underlying forces at play are the same as in the case of two firms. In Lemma 1C, we show that the equilibrium with |$n$| firms is very similar to that with two firms except that now conditions have to be placed on players’ costs to ensure that in the equilibrium all firms choose positive efforts and have a positive probability of winning. The comparative statics results also extend intuitively to the case of |$n$| firms. A firm’s bribery effort tends to decrease as its bribery cost increases. This happens under a broad set of conditions, including when the contest is unbalancing for the firm (in which case both the direct and balance of power effects are negative) or when the contest is balancing for a firm but the negative direct effect dominates the positive balance of power effect. It is possible, both in the case of two and more than two firms, for a firm to increase its bribery effort after experiencing an increase in its cost of bribery (because other firms face even larger relative increases in costs of bribery). A firm not subject to the FCPA increases its bribery effort whenever the contest balances for the firm. Proposition 1C documents these findings. We know from Proposition 1 that when the U.S. firms are subject to the FCPA, but the foreign firms are not, the U.S. firms are disadvantaged, and the foreign firms are better off. This is true for any number of the U.S. and foreign firms. If a U.S. firm is not dominant, then disadvantaging it unbalances the contest for the U.S. firm and leads it to decrease all its efforts. If a foreign firm is dominant, then favoring it unbalances the contest for the foreign firm and decreases all its efforts. The opposite is true when a foreign firm is not dominant. Finally, if a U.S. firm is dominant, then disadvantaging it balances the contest for the U.S. firm and leads it to increase its productive investment, but its bribery effort decreases because the negative direct effect of higher bribery cost dominates the positive balance of power effect. Proposition 2C is an extension of Proposition 2 to the case where all firms are subject to the FCPA. We find that both in the case of two and the case of more than two firms, a firm’s bribery effort decreases unless the firm is not dominant firm and has an absolute disadvantage in bribery, in which case its bribery effort may decrease or increase. Here is some intuition for why in the case of a dominant firm the direct effect on bribery effort dominates the balancing effect, but it may not be the case for a non-dominant firm. When a targeted firm is dominant, then for the contest to be balancing for the firm, it has to face a disproportional burden of the FCPA enforcement. Given the dominant firm is hit harder than others, the direct effect always dominates the balance of power effect. In contrast, for the contest to be balancing for a non-dominant firm, it needs to experience a relatively small change in the cost of bribery. This allows the direct effect to be smaller than the balance of power effect for a non-dominant firm. We also show that while the total bribery effort may decrease or increase in the case of U.S. firms being targeted by the FCPA enforcement (as in Proposition 1), the total bribery effort decreases in simulations when all firms are subject to the FCPA (as in Proposition 2). In the case two firms, we could prove this analytically. This is hard to prove for any number of firms because it involves comparisons of sizes of the direct and balance of power effects for different firms. Instead, we ran 100,000 paired simulations to find whether the total bribery effort always decreases for a common increase in bribery costs. We chose random costs for three firms and computed the equilibrium. Then, we added a random positive number to each cost and compared the new equilibrium to the old one, if both were interior. Out of 100,000 paired trials, none is found to show an increase in total bribery after FCPA enforcement. That is, total bribery always decreased for a common increase in bribery costs. 8. Conclusion We developed a model to analyze the effects of the FCPA on competitiveness, bribery, and productive investment. Our results show that if the FCPA is applied only to U.S. firms, then it harms the competitiveness of U.S. firms and either increases bribery by non-U.S. firms or reduces productive investment by both U.S. and non-U.S. firms. However, if the FCPA is applied to both U.S. and non-U.S. firms and targets activity in host countries with high corruption levels, then it does not a priori harm the competitiveness of U.S. firms, and it reduces total bribery and increases productive investment by both U.S. and non-U.S. firms. Analyzing FCPA cases from 2012 to 2018, we find that the overwhelming majority of prosecutions have been against firms who engaged in bribery in host countries with high corruption levels and whose main competitors are traded in U.S. financial markets and therefore also subject to the FCPA. In our model, we assume that the degree of corruption in the host country (|$\beta$|) is exogenous and not affected by the FCPA. With international cooperation in anti-bribery efforts, it might be possible to reduce the demand for bribes as well as its supply in the host countries—effectively changing the culture of corruption in these countries. Specifically, fines could be applied not only to international firms for engaging in bribery but also to government officials in the host countries for accepting bribes. Investigating the optimal mix of fines on international firms and on government officials in host countries for engaging in corruption is an interesting avenue for future research. Acknowledgement We are grateful to Kai Konrad and Thomas Remington for helpful comments and to Lila Siwakoti, Tanner Lewis, Shefain Islam, and Ryuta Oku for research assistance. Appendix Proof of Lemma 1. (i) We look for the equilibrium |$\left( x_{1}^{\ast},x_{2}^{\ast},y_{1}^{\ast},y_{2}^{\ast}\right) $| in the two-activity contest with marginal costs |$c_{i}$| and |$d_{i}(t)$|, |$i=1,2$|. The optimal interior solution for firm |$i$| is found by first deriving the cost function |$C_{i}^{\ast}(z_{i})$| as |$\min\left\{ c_{i}x_{i}+d_{i} (t)y_{i}\right\} $| subject to the constraint |$f\!\left( x_{i},y_{i}\right) =z_{i}$| and then solving the reduced contest with the derived cost function and payoffs |$\pi_{i}(z_{1},z_{2})=\dfrac{z_{i}}{z_{1}+z_{2}}-C_{i}^{\ast }(z_{i})$|. The cost function associated with the Cobb-Douglas type production function |$f\!\left( x_{i},y_{i}\right) $| is |$C_{i}^{\ast}(z_{i})=m_{i}z_{i}$|, where |$m_{i}=\frac{c_{i}^{1-\beta}d_{i}^{\beta}\left( t\right) }{\left( 1-\beta\right) ^{1-\beta}\beta^{\beta}}$|. The conditional demand of firm |$i$| is |$x_{i}^{\ast}=\partial C_{i}^{\ast}/\partial c_{i}=\frac{1-\beta}{c_{i} }m_{i}z_{i}$| for productive investment and |$y_{i}^{\ast}=\partial C_{i}^{\ast }(z_{i})/\partial d_{i}=\frac{\beta}{d_{i}(t)}m_{i}z_{i}$| for bribery. The first-order conditions for firms 1 and 2 yield |$z_{2}\left( z_{1} +z_{2}\right) ^{-2}=m_{1}$| and |$z_{1}\left( z_{1}+z_{2}\right) ^{-2}=m_{2} $|. Using notations |$\Theta=\frac{m_{1}}{m_{2}}=\left( \frac{c_{1}}{c_{2} }\right) ^{1-\beta}\left( \frac{d_{1}\left( t\right) }{d_{2}\left( t\right) }\right) ^{\beta}$| and |$\Lambda=\Theta\left( 1+\Theta\right) ^{-2}$|, we find that |$z_{2}/z_{1}=\Theta$| and then solve for |$m_{1}z_{1} =m_{2}z_{2}=\Theta\left( 1+\Theta\right) ^{-2}$|. Thus, firm |$i$|’s efforts are |$x_{i}^{\ast}=\frac{1-\beta}{c_{i}}\Lambda$| and |$y_{i}^{\ast}=\frac{\beta }{d_{i}\left( t\right) }\Lambda$|. Firm |$1$|’s probability of winning is then |$p_{1}^{\ast}=\left( 1+\Theta\right) ^{-1}$|. (ii) We next derive conditions for |$\Theta<1$| and |$\Theta>1$|. First, suppose |$\frac{c_{1}}{c_{2}}=\frac{d_{1}\left( t\right) }{d_{2}\left( t\right) }$|. Then, |$\Theta=\frac{c_{1}}{c_{2}}=\frac{d_{1}\left( t\right) }{d_{2}\left( t\right) }$|; |$\Theta<1$| when |$\frac{c_{1}}{c_{2}}=\frac{d_{1}\left( t\right) }{d_{2}\left( t\right) }<1$|; and |$\Theta>1$| when |$\frac{c_{1} }{c_{2}}=\frac{d_{1}\left( t\right) }{d_{2}\left( t\right) }>1$|. Next, consider |$A=A\left( t\right) =\frac{d_{1}(t)/d_{2}(t)}{c_{1}/c_{2}}\neq1$|. Suppose the U.S. firm has an absolute advantage in both activities, that is, |$\frac{c_{1}}{c_{2}}<\frac{d_{1}\left( t\right) }{d_{2}\left( t\right) }\leq1$| or |$\frac{d_{1}\left( t\right) }{d_{2}\left( t\right) } <\frac{c_{1}}{c_{2}}\leq1$| holds. Then, |$\Theta<1$|. Suppose the U.S. firm has an absolute disadvantage in both activities, that is, |$1\leq\frac{c_{1}} {c_{2}}<\frac{d_{1}\left( t\right) }{d_{2}\left( t\right) }$| or |$1\leq\frac{d_{1}\left( t\right) }{d_{2}\left( t\right) }<\frac{c_{1} }{c_{2}}$| holds. Then, |$\Theta>1$|. Finally, suppose |$\frac{c_{1}}{c_{2} }<1<\frac{d_{1}\left( t\right) }{d_{2}\left( t\right) }$| or |$\frac {d_{1}\left( t\right) }{d_{2}\left( t\right) }<1<\frac{c_{1}}{c_{2}}$|. Since |$\Theta=\frac{c_{1}}{c_{2}}A^{\beta}$| is monotonic in |$\beta$|, there exists a unique |$\overline{\beta}$| such that |$\Theta=1$|. Solving equation |$\Theta=1 $| for |$\beta$|, we find that |$\overline{\beta}=\frac{\log\left( \frac{c_{2}}{c_{1}}\right) }{\log A\left( t\right) }\in(0,1)$|. If |$\frac{c_{1}}{c_{2}}<1<\frac{d_{1}\left( t\right) }{d_{2}\left( t\right) }$|, then |$A>1$|; |$\Theta$| is exponentially increasing in |$\beta$|; and |$\Theta<1$| for |$\beta<\overline{\beta}$| and |$\Theta>1$| for |$\beta >\overline{\beta}$|. If |$\frac{d_{1}\left( t\right) }{d_{2}\left( t\right) }<1<\frac{c_{1}}{c_{2}}$|, then |$A<1$|; |$\Theta$| is exponentially decreasing in |$\beta$|, and |$\Theta<1 $| for |$\beta>\overline{\beta}$| and |$\Theta>1$| for |$\beta<\overline{\beta}$|. The total expenditures of each player are |$c_{i}x_{i}^{\ast}+d_{i} (t)y_{i}^{\ast}=\Lambda$| and payoffs are |$\Pi_{1}^{\ast}=p_{1}^{\ast} -\Lambda=\left( 1+\Theta\right) ^{-2}=\left( p_{1}^{\ast}\right) ^{2} $| and |$\Pi_{2}^{\ast}=p_{2}^{\ast}-\Lambda=\left( 1+1/\Theta\right) ^{-2}=\left( 1-p_{1}^{\ast}\right) ^{2}$|, and the total industry payoff is |$\Pi^{\ast}=\Pi_{1}^{\ast}+\Pi_{2}^{\ast}=1-2\Lambda$|. Q.E.D. □ Proof of Proposition 1. Consider |$d_{1}(t)=d_{1}+t$| and |$d_{2}(t)=d_{2}$|. From Lemma 1, |$x_{i}^{\ast}=\frac{1-\beta}{c_{i}}\Lambda$|, |$y_{1}^{\ast}=\frac{\beta}{d_{1}+t}\Lambda$|, and |$y_{2}^{\ast}=\frac{\beta }{d_{2}}\Lambda$|, where |$\Lambda=\Theta\left( 1+\Theta\right) ^{-2} $| and |$\Theta=\left( \frac{c_{1}}{c_{2}}\right) ^{1-\beta}\left( \frac{d_{1} +t}{d_{2}}\right) ^{\beta}$| for |$t\geq0$|; |$i=1,2$|. First, we show that |$\frac{dy_{1}^{\ast}}{dt}<0$|. Indeed |$\frac{1}{y_{1}^{\ast}}\frac{dy_{1} ^{\ast}}{dt}=\frac{d\Lambda}{dt}\frac{1}{\Lambda}-\frac{1}{d_{1}+t}<0$| holds because |$\frac{d\Lambda}{dt}=\frac{\partial\Lambda}{\partial\Theta} \frac{\partial\Theta}{\partial t}$|, |$\frac{\partial\Lambda}{\partial\Theta }=\frac{1-\Theta}{\left( 1+\Theta\right) ^{3}}$|, and |$\frac{\partial\Theta }{\partial t}=\beta\Theta\frac{1}{d_{1}+t}$| implies that |$\frac{d\Lambda} {dt}\frac{1}{\Lambda}=\beta\frac{1-\Theta}{1+\Theta}\frac{1}{d_{1}+t}<\frac {1}{d_{1}+t}$|. Next, |$sign\left( \frac{dy_{2}^{\ast}}{dt}\right) =sign\left( \frac{dx_{i}^{\ast}}{dt}\right) =sign\left( \frac{d\Lambda} {dt}\right) =sign\left( 1-\Theta\right) $|; |$i=1,2$|. Hence, |$\frac {dy_{2}^{\ast}}{dt}>0$| and |$\frac{dx_{i}^{\ast}}{dt}>0 $| if |$\Theta<1$|, and |$\frac{dy_{2}^{\ast}}{dt}<0$| and |$\frac{dx_{i}^{\ast}}{dt}<0$| if |$\Theta>1 $|. Total bribery effort |$Y^{\ast}=y_{1}^{\ast}+y_{2}^{\ast}$| can be written as |$Y^{\ast}=\beta\left( \frac{1}{d_{1}+t}+\frac{1}{d_{2}}\right) \Lambda$|. Total differentiation of |$Y^{\ast}$| yields |$\frac{dY^{\ast}}{dt}=\frac {\beta\Lambda}{\left( d_{1}+t\right) ^{2}}\left( -1+\beta\left( 1+\frac{d_{1}+t}{d_{2}}\right) \frac{1-\Theta}{1+\Theta}\right) $| since |$\frac{d\Lambda}{dt}\frac{1}{\Lambda}=\beta\frac{1-\Theta}{1+\Theta}\frac {1}{d_{1}+t}$|. Hence, |$\frac{dY^{\ast}}{dt}<0$| if and only if $$\begin{equation}\beta\left( 1+\frac{d_{1}+t}{d_{2}}\right) \frac{1-\Theta}{1+\Theta}<1\text{.}\tag{A1}\end{equation}$$(A1) This inequality holds if the U.S. firm is the underdog (|$\Theta>1$|). Since |$\frac{1-\Theta}{1+\Theta}<1$|, it also holds for |$\beta\leq\widehat{\beta}$|, where |$\widehat{\beta}=\left( 1+\frac{d_{1}+t}{d_{2}}\right) ^{-1}\in(0,1)$|. Consider |$\beta>\widehat{\beta}$|. Using a continuous function |$g=g(\frac {c_{1}}{c_{2}},\frac{d_{1}+t}{d_{2}},\beta)\equiv\beta\left( 1+\frac{d_{1} +t}{d_{2}}\right) \left( \frac{2}{1+\Theta}-1\right) -1$|, inequality (A1) can be written as |$g(\frac{c_{1}}{c_{2}},\frac{d_{1}+t}{d_{2}},\beta)<0$|. Function |$g$| is strictly decreasing in |$\frac{c_{1}}{c_{2}}$|. As |$\frac{c_{1} }{c_{2}}\rightarrow0$|, we have |$\Theta\rightarrow0$| and |$g\rightarrow \beta\left( 1+\frac{d_{1}+t}{d_{2}}\right) -1>0$|. As |$\frac{c_{1}}{c_{2} }\rightarrow\infty$|, we have |$\Theta\rightarrow\infty$| and |$g\rightarrow -\beta\left( 1+\frac{d_{1}+t}{d_{2}}\right) -1<0$|. Thus, by the Intermediate Value Theorem there exists a unique critical level |$\widehat{\frac{c_{1} }{c_{2}}}\in(0,\infty)$| for the absolute disadvantage of the U.S. firm in the productive activity, such that |$g(\frac{c_{1}}{c_{2}},\frac{d_{1}+t}{d_{2} },\beta)<0$| if |$\frac{c_{1}}{c_{2}}>\widehat{\frac{c_{1}}{c_{2}}}$| and |$g(\frac{c_{1}}{c_{2}},\frac{d_{1}+t}{d_{2}},\beta)>0$| if |$\frac{c_{1}}{c_{2} }<\widehat{\frac{c_{1}}{c_{2}}}$|. Equation |$g=g(\frac{c_{1}}{c_{2}} ,\frac{d_{1}+t}{d_{2}},\beta)=0$| defines this critical level: $$\begin{equation}\widehat{\frac{c_{1}}{c_{2}}}=\left( \frac{\beta\left( 1+\frac{d_{1}+t}{d_{2}}\right) -1}{\beta\left( 1+\frac{d_{1}+t}{d_{2}}\right)+1}\right) ^{\frac{1}{1-\beta}}\left( \frac{d_{1}+t}{d_{2}}\right)^{-\frac{\beta}{1-\beta}}\text{.}\tag{A2}\end{equation}$$(A2) It follows that |$\frac{dY^{\ast}}{dt}>0$| if |$\beta>\widehat{\beta}$| and |$\frac{c_{1}}{c_{2}}<\widehat{\frac{c_{1}}{c_{2}}}$|, and otherwise |$\frac{dY^{\ast}}{dt}<0$|. From Lemma 1, |$p_{1}^{\ast}=\left( 1+\Theta\right) ^{-1}$|, |$\Pi_{1}^{\ast}=\left( 1+\Theta\right) ^{-2}$|, and |$\Pi_{2}^{\ast }=\left( 1+1/\Theta\right) ^{-2}$|. Since |$\frac{\partial\Theta}{\partial t}=\beta\Theta\frac{1}{d_{1}+t}>0$|, we find that |$\frac{dp_{1}^{\ast}}{dt}<0$| and |$\frac{d\Pi_{1}^{\ast}}{dt}<0$|, while |$\frac{dp_{2}^{\ast}}{dt}>0$| and |$\frac{d\Pi_{2}^{\ast}}{dt}>0$|. Q.E.D. □ Proof of Proposition 2. Consider |$d_{1}(t)=d_{1}+t$| and |$d_{2}(t)=d_{2}+t$|. From Lemma 1, |$x_{i}^{\ast}=\frac{1-\beta}{c_{i}}\Lambda$| and |$y_{i}^{\ast}=\frac{\beta}{d_{i}+t}\Lambda$|, where |$\Lambda=\Theta\left( 1+\Theta\right) ^{-2}$| and |$\Theta=\left( \frac{c_{1}}{c_{2}}\right) ^{1-\beta}\left( \frac{d_{1}+t}{d_{2}+t}\right) ^{\beta}$| for |$t\geq0$|; |$i=1,2$|. Then, |$\frac{1}{y_{i}^{\ast}}\frac{dy_{i}^{\ast}}{dt}=\frac{d\Lambda }{dt}\frac{1}{\Lambda}-\frac{1}{d_{i}+t}$|. From |$\frac{d\Lambda}{dt} =\frac{\partial\Lambda}{\partial\Theta}\frac{\partial\Theta}{\partial t}$|, |$\frac{\partial\Lambda}{\partial\Theta}=\frac{1-\Theta}{\left( 1+\Theta \right) ^{3}}$|, and |$\frac{\partial\Theta}{\partial t}=\beta\Theta\frac {d_{2}-d_{1}}{\left( d_{1}+t\right) \left( d_{2}+t\right) }$|, we find that |$\frac{d\Lambda}{dt}\frac{1}{\Lambda}=\beta\frac{1-\Theta}{1+\Theta}\left( \frac{1}{d_{1}+t}-\frac{1}{d_{2}+t}\right) $|. Since |$|\frac{1-\Theta }{1+\Theta}|<1$|, we conclude that |$\frac{d\Lambda}{dt}\frac{1}{\Lambda} <\frac{1}{d_{1}+t}$| if |$\Theta<1$| and |$\frac{d\Lambda}{dt}\frac{1}{\Lambda }<\frac{1}{d_{2}+t}$| if |$\Theta>1$|. Thus, |$\frac{dy_{1}^{\ast}}{dt}<0$| if |$\Theta<1$| (the U.S. firm is the favorite) and |$\frac{dy_{2}^{\ast}}{dt}<0$| if |$\Theta>1$| (the foreign firm is the favorite). Total bribery effort |$Y^{\ast }=y_{1}^{\ast}+y_{2}^{\ast}$| can be written as |$Y^{\ast}=\beta\left( \frac {1}{d_{1}+t}+\frac{1}{d_{2}+t}\right) \Lambda$|. Total differentiation of |$Y^{\ast}$| yields |$\frac{dY^{\ast}}{dt}=\beta\Lambda\left( -\frac{1}{\left( d_{1}+t\right) ^{2}}-\frac{1}{\left( d_{2}+t\right) ^{2}}+\beta \frac{1-\Theta}{1+\Theta}\left( \frac{1}{\left( d_{1}+t\right) ^{2}} -\frac{1}{\left( d_{2}+t\right) ^{2}}\right) \right) $| since |$\frac{d\Lambda}{dt}=\beta\frac{1-\Theta}{1+\Theta}\left( \frac{1}{d_{1} +t}-\frac{1}{d_{2}+t}\right) \Lambda$|. Since |$|\frac{1-\Theta}{1+\Theta}|<1$|, we conclude that |$\frac{dY^{\ast}}{dt}=\frac{dy_{1}^{\ast}}{dt}+\frac {dy_{2}^{\ast}}{dt}<0$|. Next, |$sign\left( \frac{dx_{i}^{\ast}}{dt}\right) =sign\left( \frac{d\Lambda}{dt}\right) =sign(\left( 1-\Theta\right) \left( d_{2}-d_{1}\right) )$| for |$i=1,2$|. Hence, |$\frac{dx_{i}^{\ast}} {dt}>0$| when |$\Theta<1$| and |$d_{1}<d_{2}$| or |$\Theta>1$| and |$d_{1}>d_{2}$|; and |$\frac{dx_{i}^{\ast}}{dt}<0$| if |$\Theta<1$| and |$d_{1}>d_{2}$| or |$\Theta>1$| and |$d_{1}<d_{2}$|. Finally, from |$p_{1}^{\ast}=\left( 1+\Theta\right) ^{-1}$| and |$\frac{\partial\Theta}{\partial t}=\beta\Theta\frac{d_{2}-d_{1}}{\left( d_{1}+t\right) \left( d_{2}+t\right) }$|, we find that |$\frac{dp_{1}^{\ast} }{dt}>0$| and |$\frac{d\Pi_{1}^{\ast}}{dt}>0$| if and only if |$d_{1}>d_{2}$|. Similarly, |$\frac{dp_{2}^{\ast}}{dt}>0$| and |$\frac{d\Pi_{2}^{\ast}}{dt}>0$| if and only if |$d_{2}>d_{1}$|. Q.E.D. □ Footnotes 1. " In addition to applying to all U.S. companies, the FCPA applies to non-U.S. companies that have a U.S. subsidiary or do business in the U.S., issue stock in the U.S., or trade their home country’s stock through American Deposit Receipts that require filing with the U.S. Securities and Exchange Commission. See https://www.law360.com/articles/674583/how-fcpa-applies-to-foreign-private-companies (last accessed February 22, 2020). 2. " A related type of CSF for multi-activity contests was first developed by Epstein and Hefeker (2003). 3. " See Shleifer and Robert (1993), Brunetti and Weder (2003), and Lederman et al. (2005) for theory and evidence that political institutions are important determinants of corruption. For example, evidence indicates that democracies, parliamentary systems, and freedom of the press are each negatively associated with corruption. References Arbatskaya, Maria , and Mialon Hugo M.. 2010 . “ Multi-activity Contests ,” 43 Economic Theory 23 – 43 . Google Scholar Crossref Search ADS WorldCat Arbatskaya, Maria , and Mialon Hugo M.. 2012 . “ Dynamic Multi-activity Contests ,” 114 Scandinavian Journal of Economics 520 – 538 . Google Scholar Crossref Search ADS WorldCat Basu, Karna , Basu Kaushik, and Cordella Tito. 2016 . “ Asymmetric Punishment as an Instrument of Corruption Control ,” 18 Journal of Public Economic Theory 831 – 856 . 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American Law and Economics Review – Oxford University Press
Published: Apr 1, 2020
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