The More We Die, The More We Sell? A Simple Test of the Home-Market Effect Online Appendix Arnaud Costinot Dave Donaldson MIT, CEPR, and NBER MIT, CEPR, and NBER Margaret Kyle Heidi Williams Mines ParisTech and CEPR MIT and NBER December 28, 2018 1 Contents A Theoretical Appendix3 A.1 Multinational Enterprises (Section III.1)..........................3 A.2 Log-Linearization (Section III.2)...............................3 A.3 Beyond Perfect Competition (Section III.3).........................6 A.3.1 Monopolistic Competition..............................6 A.3.2 Variable Markups...................................7 A.3.3 Endogenous Innovation...............................8 A.3.4 Price Regulations...................................9 A.4 Bilateral Sales (Section VI.1)................................. 12 B Empirical Appendix 12 B.1 Rich versus Poor Countries................................. 12 B.2 Additional Empirical Results................................ 13 B.3 Benchmarking IMS MIDAS data.............................. 13 B.3.1 Benchmarking to the OECD HealthStat Data................... 13 B.3.2 Benchmarking to the MEPS Data.......................... 14 B.4 ATC to GBD Mapping.................................... 15 2 A Theoretical Appendix A.1 Multinational Enterprises (Section III.1) In this appendix, we illustrate how to incorporate multinational production into our basic envi- ronment. Following Ramondo and Rodríguez-Clare(2013), suppose that each firm headquartered in country i that sells drugs targeting disease n in country j 6= i can choose the country l in which its production takes place. If l = i, then the firm exports, if l = j, it engages in horizontal FDI, and if l 6= i, j, it engages in platform FDI. Like in Ramondo and Rodríguez-Clare(2013), we assume that firm-level production functions exhibit constant returns to scale, but we further allow for external economies of scale at the level of the headquarter country for each disease. Formally, at each production site l, we assume that the marginal cost of a firm from country i serving country j is constant and given by n n n n cij(l) = c(si /hi )kij(l), (A.1) n n where c(si /hi ) captures the extent of economies of scale, which depends on the total supply of n n n tech n ship drugs targeting disease n in country i, and kij(l) = cil(til ) (tlj ) captures the costs of inputs n for firms from country i producing drugs targeting disease n in country l, cil, the potential frictions n tech associated with replicating Home’s technology in country l, (til ) , as well as the trade costs n ship associated with shipping goods from country l to country j, (tlj ) . The previous specification allows, for instance, firms from country i to combine imported inputs from their country with local factors of production in country l. In equilibrium, all firms from country i will serve country n j from the location l that minimizes their unit costs cij(l) across all l and charge an equilibrium price, n n pij = minfcij(l)g. (A.2) l n n n n n Now set pi ≡ c(si /hi ) and tij = minlfkij(l)g. By construction, equation (4) holds with s(·) = c−1(·), whereas equation (5) derives from equations (A.1) and (A.2). A.2 Log-Linearization (Section III.2) In this appendix, we derive equation (7) by log-linearizing our model around a symmetric equi- n n n n librium with qj = 1 for all j and n; hi = 1 for all i and n; tii = 1 for all i and n and tij = t for all n and i 6= j. We let D, d, and x denote aggregate drug consumption, the per disease expenditure on domestic drugs, and the per disease expenditure on drugs from any other country, respectively, in the symmetric equilibrium. In turn, we let l = d/(d + (I − 1)x) denote the share of expenditure on domestic drugs, with I the total number of countries. In the symmetric equilibrium, l is also equal to the share of revenue on the domestic market. Finally, without loss of generality, we nor- n malize all drug prices, pi , to one in the symmetric equilibrium and we let Pdis and Pagg denote the 3 n common values of Pj and Pj across all disease-destination pairs and destinations, respectively. Up to a first-order approximation, for all n and i 6= j, equations (1), (2), and (5) imply n n x n n n ln xij = ln x + ln qj − e (ln pi − ln Pj + ln Pdis + ln tij − ln t) (A.3) D n n n − e (ln Pj − ln Pdis − ln Pj + ln Pagg) + ln Dj − ln D + ln pi + ln tij − ln t. x ≡ −( ( ) ) D ≡ −( ( ) ) with e d ln d z /d ln z z=t/Pdis and e d ln D z /d ln z z=Pdis/Pagg . Taking logs and dif- ferentiating equation (3) around the symmetric equilibrium, we also get 8 ( − x) ¶ ln Pn < 1−l 1 e , if i 6= j, j = I−1 1−led−(1−l)ex n l(1−ed) ¶ ln pij : = 1−led−(1−l)ex , if i j, d ≡ −( ( ) ) with e d ln d z /d ln z z=1/Pdis . Up to a first-order approximation, we therefore have l(1 − ed) 1 − l (1 − ex) ln Pn = ln P + ln pn + (ln pn + ln tn − ln t). j dis d x j − d x ∑ l lj 1 − le − (1 − l)e I 1 1 − le − (1 − l)e l6=j Combining the previous expression with equation (A.3), we obtain 1 − l (1 − ex)(ex − eD) l(1 − ed)(ex − eD) ln xn =k + ln qn + (1 − ex + ) ln pn + ln pn (A.4) ij j j I − 1 1 − led − (1 − l)ex i 1 − led − (1 − l)ex j 1 − l (1 − ex)(ex − eD) 1 − l (1 − ex)(ex − eD) + (ln pn + ln tn) + (1 − ex + ) ln tn, − − d − ( − ) x ∑ l lj − − d − ( − ) x ij I 1 1 le 1 l e l6=i,j I 1 1 le 1 l e with x x (1 − l)(1 − e ) x D D k ≡ ln x + (e − (e − e ) − 1) ln t + e (ln P − ln Pagg) + ln D − ln D. j 1 − led − (1 − l)ex j j For i = j, the same logic implies l(1 − ed)(ed − eD) ln xn =k˜ + ln qn + (1 − ed + ) ln pn (A.5) ii i i 1 − led − (1 − l)ex i 1 − l (1 − ex)(ed − eD) + (ln pn + ln tn), − d x ∑ l li I 1 1 − le − (1 − l)e l6=i with x (1 − l)(1 − e ) d D D k˜ ≡ ln d − (e − e ) ln t + e (ln P − ln Pagg) + ln D − ln D. i 1 − led − (1 − l)ex i i Next, let us compute producer prices around a symmetric equilibrium. Up to a first-order approx- 4 imation, for all i and n, equations (4), (5), and (6) imply (1 − l) (1 + es) ln pn + ln hn = l(ln xn − ln d) + (ln xn − ln x), i i ii − ∑ ij I 1 j6=i s with e ≡ (d ln s(z)/d ln z)z=1. Together with equations (A.4) and (A.5), this implies (ew − eD) (1 − l) (es + ew) ln pn − ln pn = l ln qn + ln qn + xn, i − ∑ l i − ∑ j i I 1 l6=i I 1 j6=i with l2(1 − ed)(ed − eD) (1 − ex)(ex − eD) (1 − l)2 ew ≡ led + (1 − l)ex − − , 1 − led − (1 − l)ex 1 − led − (1 − l)ex I − 1 (1 − l) xn ≡ l(k˜ − ln d) + (k − ln x) − ln hn i i − ∑ j i I 1 j6=i 1 − l (1 − ex)(ed − eD) (1 − l)2 (1 − ex)(ex − eD) + l ln tn + ln tn − − d − ( − ) x ∑ li ( − )2 − d − ( − ) x ∑ ∑ lj I 1 1 le 1 l e l6=i I 1 1 le 1 l e j6=i l6=i,j (1 − l) 1 − l (1 − ex)(ex − eD) + (1 − ex + ) ln tn. − − d x ∑ ij I 1 I 1 1 − le − (1 − l)e j6=i The solution to the previous system is given by (l − 1−l ) xn ln pn = I−1 ln qn + i + zn, (A.6) i s w ew−eD i s w ew−eD e + e + I−1 e + e + I−1 with w D ( 1−l + ew−eD ) n + 1 (e −e ) n I−1 (es+eD)(I−1) ∑j ln qj (es+eD) I−1 ∑l xl zn ≡ . s w ew−eD e + e + I−1 Combining equations (A.4) and (A.6), we obtain, for any n and i 6= j, n n n n n ln xij = dij + d + bM ln qj + bX ln qi + #ij, 5 with x x D d x D x x D ( − x + 1−l (1−e )(e −e ) ) ¯ + (1−e )(e −e ) ¯ + 1−l (1−e )(e −e ) ¯ 1 e I−1 1−led−(1−l)ex xi 1−led−(1−l)ex lxj I−1 1−led−(1−l)ex ∑l6=i,j xl dij ≡ s w ew−eD e + e + I−1 1 − l (1 − ex)(ex − eD) 1 − l (1 − ex)(ex − eD) + (1 − ex + )(ln t ) + (ln t ) + k , − − d − ( − ) x ij − − d − ( − ) x ∑ lj j I 1 1 le 1 l e I 1 1 le 1 l e l6=i,j 1 − l (1 − ex)(ex − eD) 1 − l ew − eD dn ≡ (l − )( ln qn)/(es + ew + ) + (1 − eD)zn, − d x − ∑ l − I 1 1 − le − (1 − l)e I 1 l I 1 d x ( x − D)( l(1−e ) − 1−l (1−e ) )( − 1−l ) e e 1−led−(1−l)ex I−1 1−led−(1−l)ex l I−1 bM ≡ 1 + , s w ew−eD e + e + I−1 x 1−l (1 − e )(l − I−1 ) bX ≡ , s w ew−eD e + e + I−1 x x D d x D x x D ( − x + 1−l (1−e )(e −e ) )( n − ¯ ) + (1−e )(e −e ) ( n − ¯ ) + 1−l (1−e )(e −e ) ( n − ¯ ) 1 e I−1 1−led−(1−l)ex xi xi 1−led−(1−l)ex l xj xj I−1 1−led−(1−l)ex ∑l6=i,j xl xl #n ≡ ij s w ew−eD e + e + I−1 1 − l (1 − ex)(ex − eD) 1 − l (1 − ex)(ex − eD) + (ln tn − (ln t )) + (1 − ex + )(ln tn − (ln t )), − − d − ( − ) x ∑ lj lj − − d − ( − ) x ij ij I 1 1 le 1 l e l6=i,j I 1 1 le 1 l e 1 n where z¯ ≡ #diseases ∑n z denotes the arithmetic average of a given variable z across all diseases.