Risk, Returns, and Multinational Production Chapter 3

Table 9: Baseline versus Higher Risk Aversion. Summary statistics of earnings yields, value changes and returns computed from simulated data, baseline scenario and counterfactual scenario (γ = 30). All values are in percentage terms. Earnings Yields Baseline Value Change Returns Earnings Yields γ = 30 Value Change Returns DOM EXP 0.909 0.978 0.009 0.081 0.916 1.057 0.413 0.454 0.127 0.107 0.54 0.559 MN 1.217 0.078 1.3 0.647 0.088 0.736 7 Conclusions This paper started by presenting a novel fact distinguishing multinational firms from exporters and from firms selling only in their domestic market. Multinational corporations tend to exhibit higher earnings yields and returns than non-multinational firms. Within non-multinationals, exporters tend to have higher earnings yields than firms selling only in their domestic market. To explain this fact, we presented a real option value model where firms choose optimally whether to produce only domestically, export, or serve the foreign market through FDI. In equilibrium, firms are imperfectly sorted into the three statuses according to their productivity and to the realization of the shocks. The option value of changing status introduces a systematic deviation between a firm’s profits and its valuation, which generates heterogeneity in earnings yields. The endogenous choice of international status generates heterogeneity in the covariance of profit flows with aggregate shocks, which affects the returns required by risk-averse stockholders. While being consistent with a number of facts about trade and FDI dynamics, the model provides a complementary explanation for the cross section of returns by exploiting the production side from an international point of view. Firms selling in foreign markets are more exposed to aggregate risk. If these firms exit after a negative shock, they forgo the sunk cost that they paid to enter. This generates status persistence, and the possibility of negative profits. Moreover, exiting is a more expensive strategy for multinationals than for exporters, who paid a lower premium; hence, exporters are less exposed and less risky: the difference in sunk costs generates a difference in exposure and in excess returns between exporters and multinational firms. The solution of the model delivers a series of predictions relating firm productivity and 38 the realizations of the shocks to the pattern of status changes. We calibrate the model to match quantitatively relevant moments related to firm dynamics and selection into export/FDI. With the parameterized model we compute moments of the financial variables from simulated data. We show that in addition to matching fairly well the overall aggregate dynamics of trade and FDI, the model is also able to reproduce the ordering in earnings yields and returns that we observe in the data. We see this paper as the first step in a novel research agenda linking trade and FDI dynamics to asset pricing. Interesting extensions include a firm-level analysis of the dynamics of financial variables at the times of status changes, and the study of differential exit patterns of exporters versus multinational firms. We think this is a promising avenue for research in finance and international trade that we plan to pursue in future work. Appendix A Accounting Standards and Data Selection The empirical analysis contained in this paper is based on annual, firm-level data. We limit the present study to the universe of publicly traded, US based, manufacturing firms included in the Standard & Poors Compustat Segments Database.1 Compustat data is comprised of key components from annual regulatory filings. Information on firms’ foreign operations is included in the Segments Data. Segments data categorize a firm’s operations along a particular business division and report sales, asset, and other information based on these groups.2 The Financial Accounting Standards Board (FASB), in its Statement No. 131, sets the standards for the way in which public businesses report information about operating segments in their annual financial statements. Operating segments are defined by the FASB as “components of an enterprise about which separate financial information is available that is evaluated regularly by the chief operating decision maker in deciding how to allocate resources and in assessing performance”. FAS 131 establishes standards for the way firms should disclose data about products and services, geographic areas, and major customers. The FAS 131 determines that firms should 1 2 The NAICS code for manufacturing firms contain the 2 digit prefix 31, 32, or 33. The four segment classifications are business, geographic, operating, and state. 39 report data about revenues derived from the firm’s products or services, countries in which they earn revenues and hold assets, and about major customers regardless of whether that information is used in making operating decisions. However, the statement does not require firms to disclose the information on all the different segment types if it is not prepared for internal use and reporting would be impracticable. Therefore, the firms decide how to report the data, disaggregated in several different ways: either by product, geography, legal entity, or by customer, but they do not necessarily have to report all of them. This method is referred to as the management approach. The statement establishes a minimum threshold to report separately information about an operating segment: either revenues of the segment are 10% or more of the combined revenue of all operating segments, or profits or losses are 10% or more of the combined reported profit or losses, or its assets are 10% or more of the combined assets of all operating segments. Hence, if a given firm considers best practice to aggregate the information upstream to the management level by customer, it may elect not to disclose geographical segments information. That contrasts with the previous FAS No. 14, superseded by FAS No. 131 in 1998, in which firms were required that the financial statements of a business include information about the enterprise’s operations in different industries, its foreign operations by geographical area and export sales, and its major customers. According to the new FAS 131, when an enterprise reports the existence of a geographical segment, it must report revenues and holdings of long-lived assets. This information may or may not be disaggregated by individual foreign country. In a sense, the new regulation goes towards a major disaggregation of the information, provided that it does not contrast with the normal management of the firm. Faced with the potential measurements problems associated with the loose reporting requirements of the Compustat Segments, we had two options to select our dataset: 1) include in the dataset only those firms that reported the existence of operating segments and drop all the others, or 2) include all firms in Compustat and impute as Domestic the status for those firms that did not report the existence of operating segments. The data analysis reported in Section 2 corresponds to the first selection criterium, which we prefer, because it generates a cleaner, albeit smaller, dataset. For robustness, we run all the regressions also using the dataset constructed with the second selection criterium, and the results on the ranking of earnings yields and returns are unchanged. 40 The relevant segment for our classification of firms by status division is the geographic segment. 96% of the firms that reported the existence of operating segments also report the existence of a geographic segment. Segments that report only domestic sales are classified as domestic, those that report positive export sales are classified as exporters, and those that report positive foreign sales are classified as multinational firms. For the remaining firms, we aggregate data from the business segment and assume the firm’s operations are entirely domestic. However, due to reporting errors, misclassifications, and multiple classifications, a few notes are required. As is typical when a data point is unreliable, unreported, or otherwise a break from the traditional definition, the provider will report codes in place of an interpretable value. Compustat employs a similar methodology. In these instances we assume the segment to be of negligible importance and consider associated sales and exports to be null. As mentioned above our implementation of segment data relies entirely on the classification provided in the data. However, in a few instances sales for the non-domestic segments indicate the market of operation as the United States. In these cases we assume the reported classification was in error and re-classify the segment as domestic. The data is then aggregated by firm-year. For many firms this aggregation requires combining multiple segments and may result in competing classifications for a firm in a particular year. In these instances we classify the firm by the most “globally engaged” reported segment (for example domestic firms with exports are classified as exporters, while exporters with foreign sales are considered multinational). Once firms have been appropriately classified by their international status we are able to observe the dynamics of this classification. Examining a firm’s international classification over time reveals what we believe to be reporting errors. These cases are characterized by a one-year “downward” status change, which results in a return to the original status. We believe this transient status change is a result of inaccurate segment reporting. As such we re-classify the observation to ensure continuity in the series. However, the opposite is not true: when a firm enters into an international market only to return to a less advanced geographic segment the following year, that firm retains the reported classification. The logic for this is evident - it is far easier to omit classification in a given year than to report segment details that were nonexistent. 41 Another dimension of selecting the data involves which criteria to use to establish the unit of observation and to eliminate outliers. The data span 28 years, from 1979 to 2006,3 but many firms have observations only for a part of this time interval. We impose a lower bound of 6 yearly observation for a firm to be included in our sample. Additionally, we remove extreme observations in each international classification by dropping the top and bottom 1% of earnings-to-price ratios by group and the top and bottom 5% of returns by group. B Derivations and Proofs B.1 Derivation of the Value Functions In this section we present the details of the derivation of the value functions in Section 3. We start by solving for the value function of a firm that is currently selling only in its domestic market. From (12),(13), in the continuation region: πD (a, Q)M ∆t + E[M ∆t · S(a, Q0 )|Q] − S(a, Q) + E[M ∆t · VD (a, Q∗0 )|Q∗ ] − VD (a, Q∗ ) = 0. For ∆t → 0: πD (a, Q)M dt + E[d(M · S(a, Q))] + E[d(M · VD (a, Q∗ ))] = 0. The terms in the expectations can be written as: E[d(M · S)] = E[dM · S + M · dS + dM · dS]   dS dM dS dM + + · = M ·S·E M S M S      dS dM dS = M · S −rdt + E · +E dS M S      dS dM dS = M dt −rS + E · +E dt M dt 3 All variables have been deflated to constant 1984 dollars. 42 (A.1) E[d(M · VD )] = E[dM · VD + M · dVD + dM · dVD ]   dM dVD dM dVD = M · VD · E + · + M VD M VD      dVD dM dVD = M · VD −rdt + E · +E VD M VD      dVD dM dVD = M dt −rVD + E · +E dt M dt (A.2) where the dependence of S on (a, Q) and the dependence of VD on (a, Q∗ ) have been suppressed to ease the notation. Plugging (A.1) and (A.2) into the no-arbitrage condition: πD − rS + E  dS dt  +E  dM dS · M dt  − rVD + E  dVD dt  +E  dM dVD · M dt  = 0. (A.3) By applying Ito’s Lemma and using the expressions for the Brownian motions ruling Q and Q∗ , we can derive expressions for some of the terms in (A.3): 1 1 dS = S 0 dQ + σ 2 Q2 S 00 dt = S 0 [µQdt + σQdz] + σ 2 Q2 S 00 dt 2 2 1 2 2 00 0 E[dS] = µQS dt + σ Q S dt 2 1 1 dVD = VD0 dQ∗ + (σ ∗ )2 (Q∗ )2 VD00 dt = VD0 [µ∗ Q∗ dt + σ ∗ Q∗ dz ∗ ] + (σ ∗ )2 (Q∗ )2 VD00 dt 2 2 1 ∗ 2 ∗ 2 00 ∗ ∗ 0 E[dVD ] = µ Q VD dt + (σ ) (Q ) VD dt . 2 Using these results and the expression for the evolution of M , we can rewrite (A.3) as:    1 dz 1 2 2 00 πD − rS + µQS 0 + σ 2 Q2 S 00 + E (−rdt + σM dz) · µQS 0 + σQS 0 + σ Q S − ... 2 dt 2 1 ...rVD + µ∗ Q∗ VD0 + (σ ∗ )2 (Q∗ )2 VD00 + ... 2    dz ∗ 1 ∗ 2 ∗ 2 00 ...E (−rdt + σM dz) · µ∗ Q∗ VD0 + σ ∗ Q∗ VD0 + (σ ) (Q ) VD =0 dt 2 43 and multiplying every term for dt: 1 πD dt − rSdt + µQS 0 dt + σ 2 Q2 S 00 dt + ... 2    1 2 2 00 0 0 E (−rdt + σM dz) · µQS dt + σQS dz + σ Q S dt − ... 2 1 ...rVD dt + µ∗ Q∗ VD0 dt + (σ ∗ )2 (Q∗ )2 VD00 dt + ...  2  1 ∗ 2 ∗ 2 00 ∗ ∗ 0 ∗ ∗ 0 ∗ ...E (−rdt + σM dz) · µ Q VD dt + σ Q VD dz + (σ ) (Q ) VD dt = 0. 2 (A.4) For the properties of Brownian motions, the terms in expectation can be reduced to:  1 2 2 00 = ... E (−rdt + σM dz) · µQS dt + σQS dz + σ Q S dt 2  1 ... = E − rµQS 0 dt2 − rσQS 0 dtdz − r σ 2 Q2 S 00 dt2 + σM µQS 0 dzdt + ... 2  1 2 2 00 0 2 ...σM σQS dz + σM σ Q S dzdt = ... 2   0 0 ... = σM σQS 0 E(dz 2 ) = ... ... = σσM QS 0 dt and:   ∗ ∗ VD0 dt ∗ ∗ VD0 dz ∗ 1 + (σ ∗ )2 (Q∗ )2 VD00 dt 2  = ... E (−rdt + σM dz) · µ Q +σ Q  1 ... = E −rµ∗ Q∗ VD0 dt2 − rσ ∗ Q∗ VD0 dtdz ∗ − r (σ ∗ )2 (Q∗ )2 VD00 dt2 + σM µ∗ Q∗ VD0 dzdt+ ... 2  1 ∗ 2 ∗ 2 00 ∗ ∗ ∗ 0 ... + σM σ Q VD dzdz + σM (σ ) (Q ) VD dzdt = ... 2 ∗ ∗ 0 ∗ ... = σ σM Q VD E(dzdz ) = ... ... = ρσ ∗ σM Q∗ VD0 dt. So we can rewrite (A.4) as: 1 1 πD − rS + µQS 0 + σ 2 Q2 S 00 + σσM QS 0 − rVD + µ∗ Q∗ VD0 + (σ ∗ )2 (Q∗ )2 VD00 + ρσ ∗ σM Q∗ VD0 = 0 2 2 1 1 πD − rS + (µ + σσM )QS 0 + σ 2 Q2 S 00 − rVD + (µ∗ + ρσ ∗ σM )Q∗ VD0 + (σ ∗ )2 (Q∗ )2 VD00 = 0. 2 2 44 One possible solution of this equation is such that: 1 πD (a, Q) − rS(a, Q) + (µ + σσM )QS 0 (a, Q) + σ 2 Q2 S 00 (a, Q) = 0 2 1 ∗ 2 ∗ 2 00 ∗ ∗ ∗ ∗ 0 ∗ −rVD (a, Q ) + (µ + ρσ σM )Q VD (a, Q ) + (σ ) (Q ) VD (a, Q∗ ) = 0. 2 (A.5) (A.6) We start by deriving the value function S(a, Q), solution of (A.5). Let µ̂ ≡ µ + σσM and recall that πD (a, Q) = B(aw)1−η P η Q ≡ PD (a)Q: 1 −rS + µ̂QS 0 + σ 2 Q2 S 00 = −PD (a)Q. 2 This differential equation admits a solution of the form S(a, Q) = Qχ + cQ, where χ is the solution of the following quadratic equation:   1 2 1 −r + µ̂ − σ χ + σ 2 χ2 = 0 2 2 −r̄s + (ms − 1)χ + χ2 = 0 where ms = 2µ̂ σ2 and r̄s = 2r . σ2 Hence: χ= (1 − ms ) ± p (1 − ms )2 + 4r̄s . 2 Similarly, c is the solution of: −rc + cµ̂ = −PD PD c = . r − µ̂ Hence the value function describing the expected present discounted value of domestic profits takes the form: S(a, Q) = AS (a)Qαs + BS (a)Qβs + PD Q r − µ̂ where αs and βs are the negative and positive value of χ, respectively, and AS (a) and BS (a) are firm-specific parameters to be determined. Since there is no option value associated to domestic profits, we can impose: AS (a) = BS (a) = 0, so that the solution is simply given 45 by the value of profits discounted with the risk-adjusted measure: S(a, Q) = PD Q B(aw)1−η P η Q = . r − µ̂ r − (µ + σσM ) (A.7) In the same way we can derive the value function VD (a, Q∗ ), solution of (A.6). Let µ̃ ≡ µ∗ + ρσ ∗ σM : 1 −rVD + µ̃Q∗ VD0 + (σ ∗ )2 (Q∗ )2 VD00 = 0. 2 This differential equation admits a solution of the form VD (a, Q∗ ) = (Q∗ )ξ , where ξ is the solution of the following quadratic equation:   1 1 −r + µ̃ − (σ ∗ )2 ξ + (σ ∗ )2 ξ 2 = 0 2 2 −r̄ + (m − 1)ξ + ξ 2 = 0 where m = 2µ̃ (σ∗ )2 and r̄ = 2r . (σ∗ )2 Hence: ξ= (1 − m) ± p (1 − m)2 + 4r̄ . 2 The value function describing the expected present discounted value of foreign profits of a domestic firm takes the form: VD (a, Q∗ ) = AD (a)(Q∗ )α + BD (a)(Q∗ )β (A.8) where α and β are the negative and positive value of ξ, respectively. By following the same procedure, we can solve for the expected value of foreign profits of an exporter, VX (a, Q∗ ), and of a multinational, VI (a, Q∗ ): B(τ aw)1−η (P ∗ )η Q∗ fX − r − (µ∗ + ρσ ∗ σM ) r ∗ 1−η ∗ η ∗ B(aw ) (P ) Q fI VI (a, Q∗ ) = AI (a)(Q∗ )α + BI (a)(Q∗ )β + − . r − (µ∗ + ρσ ∗ σM ) r VX (a, Q∗ ) = AX (a)(Q∗ )α + BX (a)(Q∗ )β + 46 (A.9) (A.10) B.2 Proof of Theorem 1: Ordering of the Quantity Thresholds Theorem 1. If FI > FX , fI = fX , and τ w = w∗ , the quantity thresholds Q∗RS (a), for R, S ∈ {D, X, I} and for a given productivity level 1/a, satisfy the following ordering: Q∗IX (a) < Q∗ID (a) < Q∗XD (a) < Q∗DX (a) < Q∗DI (a) < Q∗XI (a). (A.11) Proof: If fX = fI and τ w = w∗ , the operating costs of a firm with productivity 1/a that decides to sell abroad are the same regardless of status, hence the choice of status is uniquely determined by the sunk costs. From Dixit and Pindyck (1994), Chapter 7, we know that entry (exit) thresholds are increasing (decreasing) in both the sunk costs of entry and exit, hence QDI > QDX and QID < QXD . To determine the relative position of QXI , QIX , it is sufficient to notice that the problem of a firm that switches from exports to FDI and viceversa can be written as a problem where FI is the sunk cost of entry and FX is the sunk cost of exit. Hence the switch from export to FDI is characterized by the same entry cost and a higher exit cost than the change from domestic sales only to export, hence QXI > QDI and QIX < QID . The pure presence of sunk costs implies QXD < QDX , which completes the result. B.3 2 Proof of Theorem 2: Thresholds and Productivity Theorem 2. ∂Q∗RS (a) > 0, f or R, S ∈ {D, X, I}, ∀a. ∂a (A.12) Proof: The proof closely follows Appendix B of Dixit (1989). We show the result for QDX only; the proof for the other thresholds follows exactly the same steps. The value-matching conditions for Q∗DX , Q∗XD are: B(τ aw)1−η P ∗η Q∗DX fX − ∗ ∗ r − (µ + ρσ σM ) r η ∗ 1−η ∗ B(τ aw) P QXD fX + − ∗ ∗ r − (µ + ρσ σM ) r AX Q∗DX α + (BX − BD )Q∗DX β + = FX AX Q∗XD α + (BX − BD )Q∗XD β = 0. 47 Differentiating and using the smooth-pasting conditions: (1 − η)B(τ w)1−η a−η P ∗ η Q∗DX da = 0 r − (µ∗ + ρσ ∗ σM ) (1 − η)B(τ w)1−η a−η P ∗ η Q∗XD da = 0. Q∗XD α dAX + Q∗XD β d(BX − BD ) + r − (µ∗ + ρσ ∗ σM ) Q∗DX α dAX + Q∗DX β d(BX − BD ) + (A.13) (A.14) Dividing (A.13) by Q∗DX and (A.14) by Q∗XD and combining them: dAX = Q∗DX β−1 − Q∗XD β−1 Q∗XD α−1 − Q∗DX α−1 ! d(BX − BD ). (A.15) Plugging (A.15) into (A.13): d(BX − BD ) = Q∗XD α−1 − Q∗DX α−1 Q∗DX β−1 Q∗XD α−1 − Q∗DX α−1 Q∗XD β−1 !   (1 − η)B(τ w)1−η a−η P ∗η · − da r − (µ∗ + ρσ ∗ σM ) (A.16) and plugging (A.16) into (A.15): dAX = Q∗DX β−1 − Q∗XD β−1 Q∗DX β−1 Q∗XD α−1 − Q∗DX α−1 Q∗XD β−1 !   (1 − η)B(τ w)1−η a−η P ∗ η · − da . r − (µ∗ + ρσ ∗ σM ) (A.17) The smooth-pasting condition for Q∗DX is: αAX Q∗DX α−1 + β(BX − BD )Q∗DX β−1 + B(τ aw)1−η P ∗η = 0. r − (µ∗ + ρσ ∗ σM ) Let GDX (·) = VX (·) − VD (·). Differentiating the condition above: G00DX (·)dQ∗DX + αQ∗DX α−1 dAX + βQ∗DX β−1 d(BX − BD ) + (1 − η)B(τ w)1−η a−η P ∗η da = 0. r − (µ∗ + ρσ ∗ σM ) (A.18) Let ∆ ≡ Q∗DX β−1 Q∗XD α−1 − Q∗DX α−1 Q∗XD β−1 . Substituting in the expressions for dAX and d(BX − BD ), equation (A.18) can be rewritten as: −G00 (·)dQ∗DX | {zDX} >0 = (η − 1)B(τ w)1−η a−η P ∗ η da · ... ∆[r − (µ∗ + ρσ ∗ σM )] | {z } >0 h     i ... · α Q∗DX α+β−2 − Q∗DX α−1 Q∗XD β−1 + β Q∗DX α+β−2 − Q∗DX β−1 Q∗XD α−1 + ∆ . 48 In order to show that ∂Q∗DX (a) ∂a > 0, we must show that the last term of the expression above is positive: h     i α Q∗DX α+β−2 − Q∗DX α−1 Q∗XD β−1 + β Q∗DX α+β−2 − Q∗DX β−1 Q∗XD α−1 + ∆ = ... " !   ∗ β−1 !  ∗ α−1   ∗ β−1 # QXD QXD Q∗XD α−1 QXD 1 α 1− +β −1 − + = ... ∗ ∗ ∗ α+β−2 ∗ Q Q Q Q∗DX QDX DX DX DX " !   ∗ 1−β !  ∗ 1−α   ∗ 1−β # QDX QDX Q∗DX 1−α QDX 1 α 1− +β −1 − + . ∗ ∗ ∗ α+β−2 ∗ QXD QXD QXD Q∗XD QDX | {z } >0 

 Q∗DX 1−β + β z 1−α − 1 − z 1−α + z 1−β . Q∗XD > 1 and let φ(z) ≡ α 1 − z and φ0 (z) = (1 − α)(β − 1)(z −α − z −β ) > 0, which proves the result. Let z ≡ φ(1) = 0 C Then 2 Algorithm for the Computation of the Equilibrium In this section we report the algorithm used to compute the equilibrium of the model described in Section 3. At t = 0: 1. Initialize the firms’ distribution into statuses: Ω0 = Ω∗0 = (0, 0) (all firms start by selling in their domestic market only). 2. Compute P0 , P0∗ using the shares of firms in each status from Ω0 , Ω∗0 . 3. Compute the optimal thresholds QRS (0), Q∗RS (0) using P0 , P0∗ as the price indexes. For t = 1, ...T : 4. Draw a realization of (Q(t), Q∗ (t)). 5. Compare (Q(t), Q∗ (t)) with the thresholds QRS (t − 1), Q∗RS (t − 1) and compute the new firm distributions into statuses Ωt , Ω∗t . 6. Compute the equilibrium price indexes Pt , Pt∗ using the shares of firms in each status from Ωt , Ω∗t . 49