Risk, Returns, and Multinational Production

Risk, Returns, and Multinational Production Abstract This paper starts by unveiling a new empirical regularity: multinational corporations systematically tend to exhibit higher stock market returns and earnings yields than non-multinational firms. Within non-multinationals, exporters tend to exhibit higher earnings yields and returns than firms selling only in their domestic market. To explain this pattern, we develop a real option value model where firms are heterogeneous in productivity, and have to decide whether and how to sell in a foreign market where demand is risky. Firms can serve the foreign market through trade or foreign direct investment, thus becoming multinationals. Multinational firms are more exposed to risk: following a negative shock, they are reluctant to exit the foreign market because they would forgo the sunk cost that they paid to start investing abroad. We calibrate the model to match U.S. export and FDI dynamics, and use it to explain cross-sectional differences in earnings yields and returns. 1 1 Introduction Multinational firms tend to exhibit higher stock market returns and earnings yields than non-multinational firms. Among non-multinationals, exporters tend to exhibit higher returns and earnings yields than firms selling only in their domestic market. Many studies in the new trade literature have documented features distinguishing firms that sell into foreign markets from firms that do not: exporters and multinational firms tend to be larger, more productive, to employ more workers, and sell more products than firms selling only domestically.1 However, none of this literature has addressed the question of whether the international status of the firm matters for its investors. Similarly, in the financial literature, explanations of the cross section of returns disregarded the role of the international status of the firm.2 In this paper we attempt to fill this gap in the literature. We develop a real option value model where firms’ heterogeneity, aggregate uncertainty and sunk costs provide the missing link between firms’ international status and their returns on the stock market. The fact that exporters and multinational firms give higher yields and returns than domestic firms does not constitute an anomaly per se. It just indicates that these firms are “riskier” than firms that do not serve foreign markets: if this was not the case, rational agents would not hold shares of domestic firms in equilibrium. The purpose of our structural model is to identify a plausible channel that delivers differential exposure to risk of firms with different “international status”. The mechanism of the model is simple: suppose a firm decides to enter a foreign markets where aggregate demand is subject to fluctuations, and entry involves a sunk cost. In “good times”, when prospects of growth make entry profitable, a firm may decide to pay the sunk cost and enter. If – after entry – the shock reverses, the firm will be reluctant to exit immediately because of the sunk cost it paid to enter, and may prefer to bear losses for a while, hoping for better times to come again. If sunk costs of establishing a foreign affiliate are larger than the sunk costs of starting to export, then the exposure to demand fluctuations and possible negative profits will be higher for multinational firms than for exporters, and will command a higher return in equilibrium. The choice of whether to serve the foreign market and how (via export or foreign invest1 2 See, among others, Bernard, Jensen, and Schott (2009). One notable exception is Fatemi (1984). 2 ment, henceforth FDI) is endogenous, and we model it following the literature on heterogeneous firms, namely the influential contribution by Helpman, Melitz, and Yeaple (2004). Exports are characterized by low sunk costs and high variable costs, due to the necessity of shipping goods every period, while FDI entails high sunk costs of setting up a plant and starting production abroad, but low variable costs, since there is no physical separation between production and sales. The model in Helpman, Melitz, and Yeaple (2004) is static, hence the value of a firm coincides with its profits, and earnings yields are constant across firms. A dynamic but deterministic model, or a dynamic and stochastic model with idiosyncratic shocks, share the same feature, with earnings-to-price ratios simply given by the discount rate. The same is true for the returns, which are given by the earning yields plus the expected change in the valuation of the firm (this last term being zero). To generate heterogeneity in these variables across firms, we extend the basic Helpman, Melitz, and Yeaple (2004) framework to a dynamic and stochastic environment characterized by persistent shocks, using Dixit (1989) as a benchmark to model entry decision under uncertainty. Firms choose whether to export or invest abroad based on their productivity and on prospects of growth of foreign demand. Larger sunk costs of investment compared to export imply that multinational firms’ behavior displays more persistence than exporters’ behavior, and multinationals may experience larger losses if the economy is hit by a negative shock. How does this behavior generate heterogeneity in earnings yields and returns? Sunk costs of exports and FDI can be interpreted as the premia to be paid to exercise the option of entering the foreign market. The value of this option is an important component of the valuation of the firm. Hence profit flow and firm value are not proportional due to this extra component: the option value of entering/exiting the market, which differs across firms. To generate heterogeneity in stock market returns, we model risk-averse consumers who own shares of the firms, and discount future consumption streams with a stochastic discount factor dependent on the aggregate shocks. Firms’ heterogeneity and endogenous status choices imply that different firms will differ in the covariance of their earnings yields with the aggregate uncertainty, which affects consumers’ marginal utility. As a result, the model endogenously determines cross-sectional differences in earnings-to-price ratios and returns, and provides a complementary explanation for the cross section of returns exploiting the production side from an international point of view. The solution of the model delivers a series of predictions relating firms’ productivity 3 and the realization of the shocks to the pattern of trade and FDI dynamics. First, more productive firms need smaller positive shocks to enter a foreign market, and larger negative shocks to exit. Second, a larger positive shock is needed to induce a domestic firm to become multinational with respect to the one needed to become an exporter. Third, a larger negative shock is needed to induce a multinational to exit the market with respect to the one needed to induce an exporter to exit. The model is consistent with qualitative features of the data on trade and FDI dynamics, like the imperfect sorting of productivity into international statuses, and the fact that also relatively large firms exhibit changes of status. We calibrate the theory to match these facts quantitatively, and with the parameterized model we compute moments of the financial variables from simulated data. We show that the model is able to generate the rankings of earnings yields and returns, which were not targeted in the calibration. Why are we interested in the cross section of returns and earnings yields? Historically, average returns vary across stocks. Fama and French (1996) is a comprehensive description of the cross-sectional picture of returns. In this paper we address the risk-return trade-off regarding multinational and non-multinational firms. We focus on cash flow dynamics of the firm and how these are determined by endogenous decisions and exogenous risk. Multinational firms are exposed to foreign demand risk for longer due to the higher persistence in their status. This risk must be rewarded by a higher asset returns in equilibrium. Investors will be willing to hold these companies if the returns are high enough to compensate for the risk. We find that this risk is not fully captured by the multifactor model in Fama and French (1993). The existing financial literature that focuses on cross-sectional differences in earningsto-price ratios and returns abstracts from the international organization of the firm. Various attempts to explain cross sectional differences in expected returns are based either on different specifications of preferences, or on the presence of persistent shocks to the endowments, or both.3 We contribute to the financial literature by endogenizing the exposure of cashflows to these types of shocks. Exposure is directly linked to the decision of when and how to serve the foreign market, which is ultimately driven by the interaction between productivity and cost structure. 3 Yogo (2006) and Piazzesi, Schneider, and Tuzel (2007) are examples of non-separable goods in the utility function. Campbell and Cochrane (1999) use internal habits specifications. Bansal and Yaron (2004) and Hansen, Heaton, and Li (2008) use recursive preferences with persistent shocks to the endowment. 4 Our work is related to the literature on trade and FDI under uncertainty, mainly to Rob and Vettas (2003), Russ (2007), and Ramondo and Rappoport (2008). Rob and Vettas (2003) developed a model of trade and FDI with uncertain demand growth. In their framework FDI is irreversible, so it can generate excess capacity, but has lower marginal cost compared to export. The authors show that uncertainty implies existence of an interior solution where export and FDI coexist. Besides the different focus of the exercise, our work generalizes their model to one with many heterogeneous firms and a more general process for demand growth. Russ (2007) also formulates a problem of foreign investment under uncertainty to study the response of FDI to exchange rate fluctuations. Her model features firm heterogeneity, but does not allow trade as a way to serve foreign markets. Ramondo and Rappoport (2008) introduce idiosyncratic and aggregate shocks in a model where firms can locate plants both domestically and abroad. Multinational production allows firms to match domestic productivity and foreign shocks, and works as a mechanism for risk sharing. Our framework allows for risk sharing and diversification in addition to the risk exposure driven by the combination of aggregate shocks and sunk costs. We allow for country-specific shocks with various correlation patterns. Moreover, we model both trade and multinational production as different modes of dealing with uncertainty in foreign markets. This paper is also related to a growing body of literature on trade dynamics with sunk costs. Particularly, Alessandria and Choi (2007) and Irarrazabal and Opromolla (2009) model entry and exit into the export market in a world with idiosyncratic productivity shocks and sunk costs. Our model is closer to the framework in Irarrazabal and Opromolla (2009) for the use of the real option value analogy in solving the firm’s optimization problem. While Irarrazabal and Opromolla (2009) concentrate their attention on the impact of idiosyncratic productivity shocks for firm dynamics, we model aggregate demand shocks that affect firms differently only through their endogenous choice of international status. Alessandria and Choi (2007) study the impact of firms’ shocks and sunk costs on the business cycle. While the objective of our exercise is different from their paper, we follow their calibration methodology. Both papers analyze the decision to export, but do not consider the possibility of FDI sales. Roberts and Tybout (1997) and Das, Roberts, and Tybout (2007) address empirically the issue of market participation for export. Our model has similar predictions for both exports and FDI sales, and can be calibrated using information from trade and FDI data. In general, we contribute to the trade dynamics literature both 5 empirically and theoretically: we document features of trade and FDI dynamics for large firms, and we incorporate in the model the mode of entry (i.e., the decision between export and FDI sales). While individual elements of our framework are found in other work, to our knowledge this paper is the first to propose a dynamic industry equilibrium model where risk affects firms’ international strategies and their financial variables in the stock market. The remainder of the paper is organized as follows. Section 2 presents empirical evidence establishing the ranking in earnings-to-price ratios and returns according to the firms’ international status. Sections 3 and 4 develop the model and illustrate its analytical properties. Section 5 brings the model to the data: we parameterize the model using aggregate trade and FDI data and report the quantitative results on the earnings yields and returns predicted by the calibrated version of the model. Section 6 is devoted to robustness checks, and Section 7 concludes. 2 Motivating Evidence In this section we document an empirical regularity distinguishing firms that sell only in their domestic market from exporters and multinational firms. Multinational firms tend to exhibit significantly higher earnings yields and returns than exporters, and exporters in turn have higher earnings yields and returns than firms selling only in their domestic market. Our sample consists of US-based manufacturing firms in the Compustat Segments database, and tracks about 5,300 firms from 1979 to 2006. We define a firm to be a multinational (MN) if it reports the existence of a foreign geographical segment associated with positive sales. Similarly, we define a firm to be an exporter if it reports a positive level of export sales.4,5 According to this definition, on average, 34.81% of firms sell only 4 Multinational and exporter dummies are constructed based on Compustat geographic and operating segments data. According to the Statement of Financial Accounting Standards (FAS) No. 131, “segments are components of an enterprise about which separate financial information is available”. Firms must report information about profits, revenues and assets for each segment. For geographical segments, this information includes revenues perceived and assets held in foreign countries. The FAS is not explicit in defining an ownership threshold for reporting, but the existence of accounting standards for the segments themselves leads us to think that the parent (U.S.-based) firm must have a control stake in the foreign entity. Moreover, one of the Financial Accounting Standards Board (FASB)’s roles is to “require significant disclosures about the separate operating segments of an entity’s business so that investors can evaluate the differing risks in the diverse operations”. Appendix A contains a summary of the FAS Statement, and more details about the construction of the sample. 5 6% of firms in the sample report both positive exports and FDI sales. We classify these firms as 6 Table 1: Summary Statistics. Domestic Exporters Multinationals 274.18 301.03 1562.39 export sales (millions $) 0 32.25 127.36 FDI sales (millions $) 0 0 937.52 number of employees (thousands) 1.71 2.43 12.27 capital/labor ratio (millons $ per worker) 0.11 0.05 0.06 book value per share ($) 5.26 6.78 9.43 market capitalization (billions $) 0.16 0.16 1.82 book/market 0.68 0.73 0.61 earnings per share ($) 0.23 0.5 0.88 share price ($) 8.38 10.31 17.47 annual return 0.06 0.1 0.11 number of firms 2580 2164 2667 domestic sales (millions $) in the U.S. market, 29.2% also export to foreign countries, and the remaining 35.99% have positive levels of FDI sales.6 Table 1 reports descriptive statistics of the sample we use. In line with the numbers reported by other papers, exporters and multinationals have a size advantage with respect to domestic firms, both in terms of sales and number of employees. Particularly, the size advantage of multinationals is extremely large: on average, multinational firms hire about five times more workers than exporters, and have sales about eight times larger. Consistently with previous evidence, export sales are a small percentage (10%) of exporters’ total sales.7 The novel facts that Table 1 highlights are that the same ordered differences hold for financial variables like book value, earnings, share prices, and returns. Differences in earnings and market prices do not cancel out: at the contrary, also earnings yields (or earnings-to-price ratios) are ordered. Figure 1 shows earnings-to-price ratios multinationals, based on the criterium that the existence of FDI sales is sufficient to make them subject to the risk of owning a plant in a foreign market. For robustness, however, we run all the regressions contained in this section also excluding those firms from the sample. The results are unchanged. 6 Notice that the shares of firms belonging to each group are very different from what reported in other papers that use different data. Particularly, the share of multinational firms is disproportionately large. This is due to the fact that Compustat collects data for publicly listed firms only, which tend to be the largest firms in the population. 7 Bernard et al. (2003) report an average ratio of export over total sales of 10% for a sample of manufacturing firms in the OECD countries. 7 0.14 MN EXP D 0.12 0.1 0.08 0.06 0.04 0.02 0 −0.02 −0.04 1980 1985 1990 1995 2000 2005 Figure 1: Earnings-to-price ratios, portfolios of firms in each group. over time for three portfolios of firms. Each portfolio is composed by firms with the same international status (only domestic sales, exporters, multinationals).8 The solid line represents earnings-to-price ratios of multinational firms, the dashed line the ones of exporters, and the dash-dotted line the ones of firms selling only domestically. Multinational firms exhibit higher earnings-to-price ratios than non-multinational firms, consistently over the entire time period. Similarly, exporters exhibit higher earnings-to-price ratios than firms selling only in their domestic market. The average earnings-to-price ratios for the three groups are 4.85% for multinational firms, 4.1% for exporters, and 2.25% for firms selling only domestically. Figure 1 plots the raw data, but the ordering is robust to controlling for the effect of other variables related to size and industry. To separate the effects of the international status from other firm characteristics, the left panel of Table 2 displays the results of the 8 The portfolios are constructed as follows. For each firm i, determine its status S (S = D, EXP, M N ) at the end of year t − 1, and collect data on earnings (eit ) and market capitalization (pit ) in year t. Portfolio earnings EtS and portfolio value PtS are constructed as equally weighted averages of individual values: EtS = 1 X i et NtS i∈S , PtS = 1 X i pt , ∀ S NtS i∈S where NtS denotes the number of firms in status S at time t. Portfolio earnings yields are given by EtS /PtS . 8 following firm-level regression: MN EXP (e/p)it = α + γ1 Dit + γ2 Dit + γ3 βiM KT + γ4 Xit + δN AICS + δt + εit . (1) M N and The dependent variable (e/p)it is the earnings-to-price ratio of firm i in year t. Dit EXP are multinational and exporter dummies, respectively, β M KT is the market beta of Dit i the primary security of firm i,9 Xit is a set of controls, including capital/labor ratio, sales per employee (our measure of productivity), book-to-market ratio, total revenues and market capitalization (measures of size). δN AICS and δt are 4-digit industry and year fixed effects, respectively, and εit is an orthogonal error term. The coefficients associated to exporters and MN dummies are positive and significant. Moreover, the coefficient associated to multinationality is significantly larger than the one associated to export status, identifying a further difference between these two groups. We reject the null hypothesis that the two dummies’ coefficients are the same, confirming the difference in earnings yields of multinational firms versus exporters. While Table 2 only contains sales per employee and total revenues as additional controls, we run the regression also adding capital intensity and market capitalization.10 The purpose of adding the market betas is to control for aggregate market risk and to highlight the contribution of the international status to the magnitude of earnings yields once market risk is accounted for. Similarly, measures of size (revenues, market capitalization) and book-to-market ratio are meant to control for other potential sources of risk. Earnings-to-price ratios carry information about returns on the firms’ stocks. The right panel of Table 2 reports the results of a regression analogous to (1), but with annual firmlevel returns as the dependent variable.11 The coefficients on the multinational and exporter dummies are positive and significant, which confirms that firms selling in foreign markets tend to have higher returns than firms selling only domestically. The coefficient on the multinational dummy is significantly higher than the one on the exporter dummy, indicating even larger excess returns for multinational 9 The market betas have been computed by running a regression of individual security returns on the market aggregate returns (NYSE, AMEX, and Nasdaq) for the entire sample period. 10 In the data capital intensity appears to be highly correlated with sales per employee, while market capitalization is highly correlated with total revenues. For this reason, we run the regression with all the combinations of the two controls that are not strongly correlated with each other. The results are basically identical across specifications. 11 We identify firm-level returns with the returns of the firm’s common equity. Data on returns are taken from CRSP. 9 Table 2: Earnings-to-Price and Returns Regressions. Firm-level regressions of earnings-to-price ratios and stock returns on multinational and exporter dummies, market betas and other controls, with year and industry fixed effects. Standard errors clustered by firm and status. (Top and bottom one percent of earnings-to-price sample excluded, top and bottom five percent of returns sample excluded. All dollar values are expressed in billions). (1) MN dummy EXP dummy Earnings-to-Price (2) (3) total revenue Prob > F : H0 : MN=EXP No. of obs. R2 (3) 0.092 0.093 0.098 0.05 0.05 0.046 (0.005)∗∗∗ (0.005)∗∗∗ (0.005)∗∗∗ (0.005)∗∗∗ (0.005)∗∗∗ 0.061 0.062 0.062 0.035 0.035 0.037 (0.006)∗∗∗ (0.006)∗∗∗ (0.006)∗∗∗ (0.006)∗∗∗ (0.006)∗∗∗ (0.006)∗∗∗ -0.004 -0.004 0.008 0.005 (0.001)∗∗∗ (0.001)∗∗∗ (0.002)∗∗∗ (0.002)∗∗∗ 5.23e-05 5.24e-05 5.24e-05 5.24e-05 4.95e-05 4.77e-05 (2.92e-05)∗ (2.99e-05)∗ (2.99e-05)∗ (3.9e-05)∗ (2.97e-05)∗ (2.88e-05) 8.68e-07 8.38e-07 8.02e-07 4.77e-07 6.07e-07 3.36e-07 (4.04e-07)∗∗ (4.07e-07)∗∗ (4.03e-07)∗∗ (3.07e-07) (3.27e-07)∗ (2.65e-07) book/market constant Returns (2) (0.005)∗∗∗ β M KT sales per emp. (1) -0.001 -0.104 (0.007) (0.011)∗∗∗ -0.095 -0.094 -0.093 0.021 0.007 0.081 (0.005)∗∗∗ (0.006)∗∗∗ (-0.007)∗∗∗ (0.005)∗∗∗ (0.005) (0.01)∗∗∗ 0 0 0 0 0 0.06 47691 0.073 45979 0.073 45979 0.072 47547 0.134 45975 0.134 45858 0.161 firms. The ranking holds controlling for market risk, sales per employee, total revenues, and book-to-market.12 Any cross-sectional differences in returns generated by exposure to aggregate risk is captured by cross sectional differences in their market betas. Hence, the significant coefficients on the multinational and exporter dummies identify a separate source of risk. After an exploration of earnings-to-price and returns across the three groups of firms, it seems natural to explore the source of higher returns. Higher returns do not constitute a puzzle by themselves; they simply indicate that multinational firms are riskier. From a CAPM point of view, higher returns must be explained by higher betas, or co-movements 12 The discussion about the correlations across controls in footnote 10 still applies. 10 with the aggregate risks. Beyond the one-factor CAPM model, Fama and French (1993) introduced a multifactor extension to the original CAPM. Fama and French (1993) argue that a unique source of risk is not able to explain the cross section of returns. Instead, a three-factor model explains a higher fraction of the variation in expected returns. Higher returns must be explained by higher exposure to either of these three factors: market excess returns, high-minus-low book-to-market, or small-minus-big portfolio.13 Each of the three factors is assumed to mimic a macroeconomic aggregate risk. Therefore, any asset is represented as a linear combination of the three Fama-French factors. Columns (1)-(3) in Table 3 show the results of running one time-series Fama-French regression for each of the three portfolios of firms characterized by the same international status.14 The risk to which multinationals and exporters are exposed, and the corresponding higher returns that they provide to investors, are not explained by the three existing FamaFrench factors. On the contrary, we find that the market betas are lower than those of domestic firms. Multinationals and exporters’ exposure to the HML factor, related to the value premium, is also significantly lower than the exposure of domestic firms to the same factor. In columns (4)-(6) we enlarge the set of factors by considering the excess returns on an “international market” portfolio that serves as a market benchmark for firms with foreign operations. Data on the excess returns on this global market portfolio are obtained from Kenneth French’s data library on international indexes.15 The coefficients on the international market betas are not significant. If the exposure to the three factors does not explain the higher reward that multinational stocks provide, it must be reflected in the pricing errors of the model. In fact, the alpha of the portfolio of multinational firms is significantly higher than the one of the exporters’ portfolio, which in turn is higher than the alpha of the portfolio of domestic firms. The results are unchanged when we include among 13 The small-minus-big (SMB) and high-minus-low (HML) factors are constructed upon 6 portfolios formed on size and book-to-market. The portfolios are the intersection of 2 portfolios formed on size (small and big) and 3 portfolios formed on book equity to market equity (from higher to lower: value, neutral, and growth.) This generates 6 portfolios: small-value, small-neutral, small-growth, big-value, big-neutral, and big-growth. SMB is the average returns on the three small portfolios minus the average returns on the three big portfolios. HML is the average return on the two value portfolios minus the average return on the two growth portfolios. The third factor, the excess return on the market, is the value-weighted return on all NYSE, AMEX, and NASDAQ stocks minus the one-month Treasury bill rate. For more details see Fama and French (1993). 14 Every year portfolios are formed by equally-weighting firms belonging to each of the three categories (see footnote 8). We run the Fama-French regressions also at the firm-status level: the results are consistent with the ones of the portfolio regressions, albeit noisier due to the even smaller number of observations. 15 http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/Data Library/int index port formed.html. 11 the regressors the returns on the global market portfolio. GRS tests on the null hypothesis that the alphas are jointly equal to zero strongly reject the hypothesis. Table 3: Portfolio Regressions. Time-series coefficient estimates of Fama-French 3-factor regressions for the three equally-weighted portfolios based on international status. Portfolio annual excess returns are regressed on the three Fama-French factors (market excess return, Small Minus Big, and High Minus Low) for specification (1)-(3). In Columns (4)-(6) we add excess returns from an international index portfolio. The α coefficients capture the pricing errors of the three-factor model. (1) DOM Rmkt RSM B RHM L (2) EXP (3) MN (6) MN 0.695 0.611 0.671 0.693 0.636 0.66 (0.075)∗∗∗ (0.071)∗∗∗ (0.084)∗∗∗ (0.09)∗∗∗ (0.086)∗∗∗ 0.735 0.744 0.529 0.735 0.74 0.531 (0.081)∗∗∗ (0.087)∗∗∗ (0.083)∗∗∗ (0.083)∗∗∗ (0.089)∗∗∗ (0.085)∗∗∗ 0.267 0.172 0.188 0.267 0.171 0.189 (0.069)∗∗∗ (0.074)∗∗ (0.07)∗∗ (0.07)∗∗∗ (0.075)∗∗ (0.071)∗∗ 0.002 -0.031 0.015 (0.056) (0.06) (0.058) -0.079 -0.029 -0.02 -0.079 -0.028 -0.02 (0.013)∗∗∗ (0.014)∗∗ (0.013) (0.013)∗∗∗ (0.0144)∗ (0.013) Prob > F : H0 : αDOM = αEXP = αM N = 0 Obs. R2 (5) EXP (0.07)∗∗∗ RIN T α (4) DOM 28 0.903 28 0.878 0 28 0.87 0 28 0.903 28 0.879 28 0.87 Tables 2 and 3 consistently convey the message that the three groups of firms differ significantly in their financial variables, and that these differences cannot be accounted for either by differences in productivity and size or by traditional risk-factor explanations. The exposure to a global index does not explain the differences in returns either. The excess return of multinational firms is not explained by the common factors widely used in the finance literature. Our goal is to understand what is the underlying risk driver that generates multinationals returns in excess of those of exporters or domestic firms. In the next section we develop a dynamic structural model in which productivity differences determine the selection of firms into the three statuses, and the presence of aggregate shocks and sunk costs gives rise to the observed pattern in their financial variables. 12 3 Model 3.1 Preferences and Technology The economy is composed of two countries, Home and Foreign. Variables related to consumers and firms from the foreign country are marked with an asterisk (*). In both countries, agents are infinitely lived, and have preferences defined by: U= Z ∞ e−ϑt 0 Q(t)1−γ dt 1−γ where θ > 0 is the subjective discount factor, and γ > 1 denotes risk aversion. Q is a CES aggregate of differentiated varieties: Q(t) = Z 1−1/η qi (t) η/(η−1) di where η > 1 denotes the elasticity of substitution across varieties. Agents maximize U subject to their budget constraint. Labor supply is perfectly inelastic. Income is given by the wage plus the profit shares derived from ownership of firms incorporated in the country where the agents live. In each country, aggregate consumption of the differentiated good is hit by random shocks. Q and Q∗ evolve according to geometric Brownian motions: dQ Q dQ∗ Q∗ = µdt + σdz (2) = µ∗ dt + σ ∗ dz ∗ (3) where µ, µ∗ ≥ 0, σ, σ ∗ > 0 and dz, dz ∗ are the increments of two standard Wiener processes with correlation ρ ∈ [−1, 1]: dz = dW (4) dz ∗ = ρdW + p 1 − ρ2 dW 2 . (5) dW is the increment of a standard Wiener process, hence E(dz) = E(dz ∗ ) = 0, and E(dz 2 ) = E(d(z ∗ )2 ) = dt, E(dzdz ∗ ) = ρ. Agents are risk averse. Separability of the intratemporal utility function implies that 13 agents in each country discount future utility with stochastic discount factors described by the following geometric Brownian motions: dM M dM ∗ M∗ = −rdt − σM dz (6) ∗ = −r ∗ dt − σM dz ∗ (7) ∗ = γσ ∗ ) and dz, where r = ϑ + γµ (r ∗ = ϑ + γµ∗ ) is the risk-free rate, σM = γσ (σM dz ∗ are the increments of the Brownian motions ruling the evolution of Q and Q∗ .16 For convergence of the risk-adjusted expected values, we will assume that r > µ + σσM and ∗ and r ∗ > µ + ρσσ ∗ ). r > µ∗ + ρσ ∗ σM (and similarly r ∗ > µ∗ + σ ∗ σM M Labor is the only factor of production. Each country is populated by a continuum of firms of total mass n (n∗ ), which operate under a monopolistically competitive market structure. Each firm produces a differentiated variety with a linear technology defined by a unit labor requirement a, which is a random draw from a distribution G(a) (G∗ (a)). a indicates the number of units of labor that a firm employs in order to produce one unit of a differentiated variety. Differentiated varieties qi are tradeable; hence, a firm may sell its own variety only in its domestic market or both in the domestic and in the foreign market.17 Let us now turn to the description of the production costs in the differentiated sector. We assume that there are no fixed costs associated to production for the domestic market, so every firm makes positive profits from domestic sales, and always sells in its domestic market.18 Besides producing for its domestic market, firms can produce also for the foreign country. Production in the foreign market involves fixed operating costs, to be paid every period, and sunk costs of entry. If a firm decides to sell in the foreign market, it can do so 16 The stochastic discount factor is equal to the intertemporal marginal rate of substitution. Marginal utility of consumption is: M = e−ϑt Q(t)−γ . Hence: dQ dM = −ϑdt − γ = −(ϑ + γµ)dt − γσdz. M Q 17 Since consumers own shares of firms incorporated in the country where they live, when firms enter foreign markets, the fluctuations of both domestic and foreign demand have effects on consumers’ incomes via the profit shares. 18 We could have introduced positive fixed costs of domestic production, and modeled the initial decision of entry in the domestic market, like in Helpman, Melitz, and Yeaple (2004) and Irarrazabal and Opromolla (2009). This would have introduced additional complications in solving for firms’ optimal dynamics, without any gains for our empirical analysis. Compustat includes only publicly listed firms, so when a firm enters or exits Compustat we do not have any information about whether the firm is in fact entering or exiting the market. 14 either via exports or via foreign direct investment. We call multinationals those firms that decide to serve the foreign market through FDI sales. We model the choice between trade and FDI along the lines of Helpman, Melitz, and Yeaple (2004): exports entail a relatively small sunk cost of entry, FX , but a per-unit iceberg transportation cost τ to be paid every period.19 Instead, FDI is associated to a larger sunk cost, FI (FI > FX ), but there are no transportation costs to be covered every period, as both production and sales happen in the foreign market.20 Both exports and FDI also entail fixed operating costs to be paid every period, that we denote with fX and fI for exports and FDI, respectively. After entering in the foreign market, a firm can exit at no cost. However, if it decides to re-enter, it will have to pay the sunk cost again.21 Sunk costs and stochastic demand imply that firms decide to enter when their expected profits are well above zero, and are reluctant to exit even in case of losses due to negative shocks. We show that this dynamic behavior, labeled “hysteresis” in the literature (see Dixit and Pindyck (1994)), is more severe for multinational firms than for exporters, due to the larger sunk costs of FDI. Notice also that the cost structure and the nature of uncertainty imply that if a firm decides to enter the foreign market, it will do so either as an exporter or as a multinational firm, but it will never adopt the two strategies at the same time.22 19 τ > 1 units of good need to be shipped for one unit of good to arrive to the destination country. The assumption that FI > FX is key for our results on hysteresis and risk exposure of profit flows. It seems intuitive to us that the costs of starting operations in a new production facility are higher than the costs of establishing an export channel. FDI entails a series of one-time costly activities, like acquiring licenses, dealing with local institutions (often in a foreign language), searching for qualified local labor, arrange relationships with suppliers, and so on. When the investment is greenfield, these costs are added to the cost of actually building a foreign plant. When the investment takes the form of a merger, the firm has to pay the initial acquisition cost. Clearly in both cases foreign plants can be sold, so part of the initial cost may not be sunk. However, all those activities related to starting production in a foreign country are. 21 Roberts and Tybout (1997) report evidence on the fact that previous exporting experience matters as long as firms do not exit the foreign market. They find that the costs of entry for first-time exporters are not statistically different from the costs of entry for second-time exporters, i.e. firms that were once selling in the foreign market, exited, and decided to re-enter. Our assumptions on the structure of sunk costs are motivated by these findings. 22 This feature of the model is the same as in Helpman, Melitz, and Yeaple (2004). Rob and Vettas (2003) obtain the existence of an equilibrium where firms can optimally choose to adopt simultaneously the two strategies because in their model firms choose the amount of the foreign investment, and given the structure of demand there may be the possibility of overinvestment. In their framework, FDI can be adopted to cover certain demand, while exports are used to serve the additional random excess demand without incurring the cost of a larger investment that could be underutilized. In the data we do observe firms that both export and have FDI sales (about 6% of the total). This fact can be rationalized within our framework by having multiproduct firms that choose different strategies for different product lines, or in a multi-country model where firms choose different strategies to enter different countries. Unfortunately, there is not enough information in the Compustat Segments data to check whether any of these is the case. Explaining the 20 15 Hence for a given realization of (Q, Q∗ ), a firm with productivity 1/a must choose its optimal status S (S ∈ {D, X, I}, i.e. domestic, exporter, or multinational), the current selling price pS (a), and an updating rule (how to change the optimal price and status following changes in aggregate demand). The CES aggregation over individual varieties implies that individual pricing rules are independent of (Q, Q∗ ). However, marginal costs of production and optimal pricing rules vary with the status of the firm. Let w, w∗ denote the wages in the home and foreign countries, respectively. We describe here the pricing problem of Home country firms. Prices charged by Foreign country firms are determined in the same way. The marginal cost of domestic production is given by the labor requirement times the domestic wage, M CD = aw. The marginal cost of exporting is augmented by the iceberg transportation cost: M CX = τ aw. When the firm serves the foreign market through FDI, firm-specific productivity is transferred to the foreign country and the firm employs foreign labor: M CI = aw∗ . CES preferences across varieties of the differentiated good imply that η M CS (a). the optimal prices are pS (a) = η−1 Let πD (a; Q), πX (a; Q∗ ) and πI (a; Q∗ ) denote the per-period profits from domestic sales, from exports and from FDI sales abroad, respectively, for a Home country firm with productivity 1/a, given a realization of the aggregate quantity demanded (Q, Q∗ ): πD (a; Q) = B(aw)1−η P η Q (8) πX (a; Q∗ ) = B(τ aw)1−η P ∗η Q∗ − fX (9) πI (a; Q∗ ) = B(aw∗ )1−η P ∗ η Q∗ − fI (10) where B ≡ η −η (η −1)η−1 , and P (P ∗ ) is the aggregate price of the differentiated good in the Home (Foreign) country, that firms take as given while solving their maximization problem. 3.2 Value Functions We solve the model along the lines of Dixit (1989). The state of the economy is described ∗ , ω ∗ )) describes the by the vector Σ = (Q, Q∗ , Ω, Ω∗ ), where Ω = (ωX , ωI ) (Ω∗ = (ωX I distribution of firms from the Home (Foreign) country into the three statuses.23 In the choice of firms to adopt both entry strategies would probably need a differently tailored framework, and is beyond the scope of this paper. 23 ωD = 1 − ωX − ωI . 16 following, we omit the dependence of the value functions on Ω and Ω∗ to ease the notation. Let VS (a, Q, Q∗ ) denote the expected net present value of a Home country firm whose productivity is 1/a, starting in status S (S = D, X, I) when the realization of aggregate demand is (Q, Q∗ ), and following optimal policy. Since there are no fixed costs to sell domestically, all firms are active in their domestic market and make positive profits πD (a; Q) from domestic sales. Domestic activities are not affected by the realization of foreign demand Q∗ . Similarly, the decision of whether to sell in the foreign market is not affected by the realization of domestic demand Q. For this reason, we can express the value function as: VS (a, Q, Q∗ ) = S(a, Q) + VS (a, Q∗ ) (11) where S(a, Q) is the expected present discounted value of profits from domestic sales, which is independent on firm status, and VS (a, Q∗ ) is the expected present discounted value of profits from foreign sales for a firm in status S. Over a generic time interval ∆t, the two components of the value function for a firm that is currently selling only in its domestic market can be expressed as: S(a, Q) = πD (a, Q)M ∆t + E[M ∆t · S(a, Q0 )|Q].  VD (a, Q∗ ) = max E[M ∆t · VD (a, Q∗ 0 )|Q∗ ] ; VX (a, Q∗ ) − FX ; VI (a, Q∗ ) − FI . (12) (13) While (12) simply tracks the evolution of domestic profits, the right hand side of (13) expresses the firm’s possibilities. If it sells only domestically, it gets the continuation value from not changing status, equal to the expected discounted value of the firm conditional on the current realization of foreign demand Q∗ . If it decides to switch to export (FDI) it gets the value of being an exporter, VX (multinational, VI ) minus the sunk cost of entry FX (FI ). Similarly, the present discounted value of profits from foreign sales for an exporter is:  VX (a, Q∗ ) = max πX (a, Q∗ )M ∆t + E[M ∆t · VX (a, Q∗ 0 )|Q∗ ] ; VD (a, Q∗ ) ; VI (a, Q∗ ) − FI (14) and for a multinational:  VI (a, Q∗ ) = max πI (a, Q∗ )M ∆t + E[M ∆t · VI (a, Q∗ 0 )|Q∗ ] ; VD (a, Q∗ ) ; VX (a, Q∗ ) − FX . (15) 17 Notice that the continuation value of an exporter (a multinational) also includes the profit flow from sales in the foreign market πX (a, Q∗ )M ∆t (πI (a, Q∗ )M ∆t). There are no costs of exiting the foreign market: if a firm decides to exit, its value is simply that of a domestic firm: VD (a, Q∗ ). In Appendix B, we show that the solution of the value functions S(a, Q), VS (a, Q∗ ) for S ∈ {D, X, I} takes the form: S(a, Q) = πD (a, Q) r − (µ + σσM ) (16) VD (a, Q∗ ) = AD (a)Q∗ α + BD (a)Q∗ β VX (a, Q∗ ) = AX (a)Q∗ α + BX (a)Q∗ β + VI (a, Q∗ ) = AI (a)Q∗ α + BI (a)Q∗ β (17) B(τ aw)1−η P ∗ η Q∗ (µ∗ + ρσ ∗ σ − fX r r− M) η ∗ ∗ 1−η ∗ fI B(aw ) P Q − + r − (µ∗ + ρσ ∗ σM ) r (18) (19) where α and β are the negative and positive values of ξ:24 ξ= and m = 2(µ∗ +ρσ∗ σM ) , (σ∗ )2 r̄ = (1 − m) ± 2r . (σ∗ )2 p (1 − m)2 + 4r̄ 2 AS (a) and BS (a) (S ∈ {D, X, I}) are firm-specific, time-varying parameters to be determined.25 Notice that since there are no fixed or sunk costs associated to domestic production, there is no option value associated to future domestic profits. The value function S(a, Q) is simply equal to the discounted flow of domestic profits. Conversely, the option value of changing status is a component of the expected present discounted value of foreign profits. In particular, the option value is the only component of the present discounted value of foreign profits for domestic firms. For exporters and multinationals, the value is given by the sum of the discounted foreign profit flow from never changing status plus the option value of changing status. The terms µ + σσM , µ∗ + ρσ ∗ σM in the discount are the riskadjusted drifts, result of taking expectations of the value function under the risk-neutral measure. Equations (17), (18), and (19) describe the value of foreign profits in the firms’ contin24 α < 0, β > 1. Remember that we are not making explicit the dependence of the value functions on the distribution of firms in the three statuses. The parameters AD (a) and BD (a) are time-varying because they also depend on the distribution of firms. 25 18 uation regions. We still need to solve for the updating rule, which in this case consists of thresholds in the realizations of Q∗ that induce firms to change status. Let Q∗RS (a) denote the quantity threshold at which a firm with productivity 1/a switches from status R to status S, for R, S ∈ {D, X, I}.26 In order to find the six quantity thresholds Q∗SR (a) and the six value function parameters AS (a), BS (a), for S ∈ {D, X, I}, we impose the following value-matching and smooth-pasting conditions: VD (a, Q∗DX (a)) = VX (a, Q∗DX (a)) − FX (20) VD (a, Q∗DI (a)) = VI (a, Q∗DI (a)) − FI (21) VX (a, Q∗XD (a)) = VD (a, Q∗XD (a)) (22) VX (a, Q∗XI (a)) = VI (a, Q∗XI (a)) − FI (23) VI (a, Q∗ID (a)) = VD (a, Q∗ID (a)) (24) VI (a, Q∗IX (a)) = VX (a, Q∗IX (a)) − FX (25) VR0 (a, Q∗RS (a)) = VS0 (a, Q∗RS (a)) , f or S, R ∈ {D, X, I}. (26) For each a, equations (20)-(26) are a system of twelve equations in twelve unknowns (the six quantity thresholds Q∗SR (a) and the six parameters AS (a), BS (a), for S, R ∈ {D, X, I}). The system is highly nonlinear, and as such is associated to multiple solutions. To get an economically sensible solution, we follow Dixit (1989) and impose a series of restrictions on the parameters AS (a), BS (a). Since α < 0, β > 1, the terms in Q∗ α (Q∗ β ) are large for low (high) realizations of Q∗ . For low realizations of Q∗ , entry is a remote possibility for a firm selling only in its domestic market, hence the value of the option of entering must be nearly worthless: AD (a) = 0, ∀a. It must then be that BD (a) ≥ 0 to insure non-negativity of VD (a, Q∗ ). Similarly, for high realizations of Q∗ , the option of quitting FDI for another strategy is nearly worthless, hence BI (a) = 0. Moreover, a multinational firm has expected value B(aw ∗ )1−η (P ∗ )η Q∗ r−(µ∗ +ρσ∗ σM ) − frI from the strategy of never changing status, hence the optimal strategy must yield a no lesser value: AI (a) ≥ 0. Finally, an exporter has expected value B(τ aw)1−η (P ∗ )η Q∗ r−(µ∗ +ρσ∗ σM ) − frX from the strategy of never changing status, hence its optimal strategy must yield a no lesser value for any realization 26 The quantity thresholds Q∗RS (a) also depend on the distribution of firm statuses Ω∗ , which affects the equilibrium price index, and are hence time-varying. 19 of Q∗ : AX (a), BX (a) ≥ 0. As a result of these restrictions, the value function of a domestic firm VD is increasing on the entire domain, indicating the fact that, as the realized aggregate demand in the foreign market Q∗ increases, the value of the option of entering the foreign market (either through trade or FDI) increases. The value functions of an exporter and of a multinational (VX and VI respectively) are U-shaped: for low levels of Q∗ , the term with the negative exponent α dominates, and the value is high due to the option of leaving the market. Conversely, for high levels of Q∗ , the value is high due to the profit stream that the firm derives from staying in the market and, for exporters, due to the additional option value of becoming a multinational firm (the term with the positive exponent β). Value functions and quantity thresholds for Foreign country firms are derived in an analogous manner. The system of value-matching and smooth-pasting conditions includes among its variables the aggregate price index P ∗ . P ∗ is an endogenous variable and – as will be clearer in the next section – it depends on the realization of Q∗ . For this reason, one should write each condition taking into account the equilibrium price at that specific realization of Q∗ (i.e., if Q∗ = Q∗DX , then P ∗ = P ∗ (Q∗DX )). However, we appeal to the result developed in Leahy (1993) and Dixit and Pindyck (1994), Chapters 8-9, whereby a firm can ignore the effects of the actions of other firms when solving for the optimal thresholds triggering investment, and use the market equilibrium price P ∗ in all the value-matching and smooth-pasting equations. The intuition behind this results is as follows: the actions of other firms affect the problem of the individual firm via the price index in two ways: more firms entering the foreign market reduce a) the profit flows from foreign sales (export or FDI), and b) the option value of waiting to start selling abroad. It can be shown that these two effects exactly offset each other; hence, taking into account the effect of the actions of other firms on the price index is immaterial for the determination of the thresholds.27 27 Dixit and Pindyck (1994) and Leahy (1993) show this results for a perfectly competitive industry with free entry and CRS production technologies, where the shocks follow a general diffusion process. Leahy (1993) also shows that free entry is unnecessary to obtain the result. Our economy differs from the ones they study in that firms’ technologies exhibit increasing returns to scale and the market structure is monopolistically competitive. However, we argue that the result still applies for the following reasons. The potential problem with increasing returns is that they may induce “too large” investment by the firms. This does not apply to our framework, where firms only decide whether to entry or not, and not the amount to invest. Imperfect competition in turn may invalidate the result if firms display some type of strategic behavior, which is clearly not the case for monopolistic competition with a continuum of firms. 20 3.3 Equilibrium The price indexes in the two countries are the solution of the following system of two equations, where each price index is an aggregate of prices of domestic sales, prices of imports, and prices of FDI sales of multinational firms from the other country: Z  1−η ηaw dG(a) + ... η−1 # "Z  1−η 1−η  Z ηaw ητ aw∗ ∗ ∗ ∗ dG (a) + dG (a) ...n ∗ (Q) η−1 η−1 ωI∗ (Q) ωX 1−η Z  ηaw∗ dG∗ (a) + ... (P ∗ )1−η = n∗ η−1 "Z #   1−η 1−η Z ητ aw ηaw∗ ...n dG(a) + dG(a) η−1 η−1 ωX (Q∗ ) ωI (Q∗ ) P 1−η = n (27) (28) where n (n∗ ) is the mass of firms from the Home (Foreign) country selling differentiated ∗ (Q), ω ∗ (Q) (ω (Q∗ ), ω (Q∗ )) are the shares of these firms that export or varieties, and ωX X I I have multinational sales when the realization of aggregate demand is (Q, Q∗ ). The equations describing aggregate prices depend – via the integration limits – on the distribution of firms into statuses, which in turn depends on the quantity thresholds Q∗RS . On the other hand, quantity thresholds themselves depend on aggregate prices (as evident from the value functions). In solving the firm’s problem, we appeal to the equivalence result shown in Leahy (1993): when finding the quantity thresholds, each firm takes aggregate prices and the firms’ distribution into statuses as given, and does not take into account the effect of its own entry and exit decisions on these variables. This result simplifies considerably the computation of the equilibrium. The computational algorithm is described in Appendix C. Since we abstract from the problem of entry in the domestic market, we take the mass of firms n (n∗ ) as given.28 The initial values of the processes ruling the evolution of the state, Q(0) and Q∗ (0), are also taken as given. 28 Since we do not impose free-entry, we set the masses of firms to n = n∗ = 1, and present the results in terms of shares of the total number of firms. 21