John F. Kennedy School of Government Harvard University Faculty Research Working Papers Series

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1 John F. Kennedy School of Governmen Harvard Universiy Faculy Research Working apers Series Commodiy Money Inflaion: Theory and Evidence from France in Joseph Zeira February 22 RW2-8 The views expressed in he KSG Faculy Research Working aper Series are hose of he auhor(s) and do no necessarily reflec hose of he John F. Kennedy School of Governmen or Harvard Universiy. All works posed here are owned and copyrighed by he auhor(s). apers may be downloaded for personal use only.

2 Commodiy Money Inflaion: Theory and Evidence from France in Nahan Sussman The Hebrew Universiy of Jerusalem Joseph Zeira The Hebrew Universiy of Jerusalem, Harvard Universiy and CER February 22 Absrac This paper presens a heory of inflaion in commodiy money and suppors i by evidence from inflaionary episodes in France during he foureenh and fifeenh cenuries. The paper shows ha commodiy money can be inflaed similarly o fia money hrough repeaed debasemens, which ac like devaluaions. Furhermore, as wih fia money, demand for commodiy money falls wih inflaion. Unlike fia money, a high raes of inflaion demand for commodiy money becomes insensiive o inflaion, since commodiy money has inrinsic value in addiion o is ransacions value. Finally, we show ha an anicipaed sabilizaion reduces demand for commodiy money, which is opposie o he effec of anicipaed sandard sabilizaion on demand for fia money. JEL Classificaion: E3, N3 Keywords: Inflaion, commodiy money, debasemens, seignorage, sabilizaion. Mailing Address: Joseph Zeira Kennedy School of Governmen Harvard Universiy 79 JFK Sree Cambridge, MA 238 USA joseph_zeira@ksg.harvard.edu

3 Commodiy Money Inflaion: Theory and Evidence from France in Inroducion This paper describes and analyzes inflaion in an economy wih commodiy money. The resuls are derived from a simple model of commodiy money and are suppored by hisorical daa on money and prices in Medieval France, in he years We show ha here is much similariy beween inflaion of commodiy money and ha of fia money. Firs, commodiy money can be inflaed by debasing he currency and inflaion can be quie high. Second, he demand for commodiy money falls as inflaion rises. We also find wo dissimilariies beween he wo ypes of money. The firs is ha due o he inrinsic value of commodiy money, he demand for i becomes insensiive o inflaion when he rae of inflaion is high. The second dissimilariy is ha under commodiy money he demand for money falls wih anicipaion for sabilizaion, while i increases under fia money. The paper firs shows how repeaed debasemens lead o inflaion, which can be raher high. In each new debasemen he ruler issues a new coin wih a lower conen of he precious commodiy, which is silver in our hisorical example. When he new coin eners ino circulaion, he quaniy of money increases and prices rise. The ruler gains from such debasemen since he collecs seignorage from coins mined and remined. The main inuiion behind his resul is basically Gresham s Law. The new coin, which has Some fia money inflaions and sabilizaions were accompanied by issuance of new fia noes, hus resembling more our commodiy money model, bu hese cases were rare.

4 less silver conen, drives ou some of he older coins, which conain much more silver. Agens gain from remining he old coins despie he loss of seignorage. An implici assumpion here is ha coins circulaed by ale raher han by weigh. This assumpion was recenly quesioned in Rolnick, Velde and Weber (996), bu we find ha i is srongly suppored by our empirical resuls. The paper hen analyzes demand for commodiy money. Inflaion erodes he value of money and operaes as a ax on money holdings. Hence, if he public expecs higher inflaion he demand for money is reduced. Bu losses o holders of commodiy money are a bounded funcion of he inflaion rae, due o he alernaive use of commodiy money, which can be used o creae new coins by remining. Furhermore, when inflaion is sufficienly high, so ha all coins are remined, he demand for commodiy money becomes insensiive o he rae of inflaion. The firs main resul of he paper is herefore ha demand for money is negaively relaed o inflaion, bu a high raes of inflaion i becomes insensiive o i. Nex he paper discusses he effec of anicipaed sabilizaion. Noe ha under fia money anicipaion of sabilizaion reduces fuure expeced coss of holding money and herefore increases he demand for money. Under commodiy money sabilizaion requires issuing new coins wih higher conen of silver, since he process of inflaion has previously reduced he silver conen of coins o very low levels. This is indeed how many inflaionary episodes ended during he hisorical period we examine. Hence, in sabilizaion old coins become eiher compleely useless or go hrough silver exracion, which is quie cosly. Hence, sabilizaion is cosly for money holders, and anicipaion of 2

5 such sabilizaion reduces he demand for money raher han increases i. This is he second main resul of he paper. The empirical par of he paper examines hese wo predicions of he model. Alhough we do no have direc observaions on he demand for money in medieval France, we do have daa on mining volumes by he royal mins and our model enables us o relae he wo variables. Our empirical analysis indeed shows ha he negaive effec of he rae of inflaion on he demand for money is srong a low raes of inflaion and disappears a high raes of inflaion. We also find suppor o he oher resul of he paper, ha anicipaion of sabilizaion reduces he demand for money. We esimae he probabiliy of sabilizaion under raional learning and show ha his probabiliy has a negaive effec on he demand for money. I is imporan o noe ha his finding also supplies some evidence for raional Bayesian learning, which is ineresing as well. This paper, herefore, exends he exising lieraure on commodiy money and connecs i o he mainsream lieraure on money and inflaion. Recen imporan conribuions o he heory of commodiy money are Li (995), Sargen and Smih (997), and Velde, Weber and Wrigh (997). While hese papers develop he basic heory of commodiy money and of a one-ime debasemen, our paper offers hree imporan addiions o his lieraure. Firs, i exends he analysis o a siuaion of repeaed debasemens, namely of inflaion, which o our bes knowledge has never been done before. Second, i derives esable quaniaive predicions on he demand for money during inflaion. Tha leads o our hird conribuion o he lieraure, namely an empirical analysis of mining during inflaion, which suppors he main resuls of our model. 2 On 2 Exending he analysis o issues of inflaion comes a he cos of simplificaion. Insead of using search or cash-in-advance models as he above papers, we use a simpler model wih money in he uiliy funcion. 3

6 he hisorical side our paper is relaed o various hisorical accouns of debasemens. I is mos closely relaed o Sussman (993), which describes he same hisorical episode, bu also o oher sudies of debasemen, mosly in early periods of modern Europe. 3 The paper is organized as follows. I begins wih hisorical background in Secion 2. Secions 3-6 provide he heory of commodiy money inflaion, where Secion 3 oulines he model, secion 4 analyses mining and prices, Secion 5 presens inflaion dynamics, and Secion 6 sudies he effec of expeced sabilizaion. Secion 7 describes he daa and Secion 8 presens he empirical analysis. Secion 9 concludes. 2. Hisorical background During he French economic and commercial expansion of he hireenh cenury, here was a growing demand for a common medium of exchange o faciliae commercial ransacions. Tha developmen coincided wih rulers effors o reaffirm heir sovereigny by conrolling he currency and raising seignorage revenues. They achieved hese objecives by esablishing a sysem of mins, which charged seignorage for coining privae bullion ino royal coins. By he end of he hireenh cenury hese mins were gradually replacing privae mins. The royal min sysem expanded hroughou he foureenh cenury and by 45 here were 24 mins operaing in France, requiring a relaively sophisicaed mechanism of monioring min masers. I involved incenives, like paying min masers some percenage of he coins sruck, direc supervision by royal officials, and also inspecion in aris of random samples of coins sen from mins. As a furher reflecion of he influence 3 See Bordo (986) for a survey, Gould (97) for he Tudor debasemen, Kindleberger (99) for debasemens during he 3 years war; Miskimin (984) for France; Moomura (994) for Spain and amuk 4

7 and conrol of he cenral arisian adminisraion, he regional min accouns were wrien in he French of he cour, whereas all oher local fiscal accouns were wrien in Lain or local dialecs. This relaively well-organized and well-moniored min sysem gave he crown an insrumen capable of effecively carrying ou is moneary policy. Mins combined pure silver wih base alloys o produce an alloy of a given fineness (percenage of silver) and hen cu i ino coins. The coins face value was no samped on hem bu raher assigned by he crown. The prevailing accouning sysem in France was he ournois sysem, based on he denier ournois, he penny of Tours. In his sysem welve deniers equaled one sou, and weny sous made up one livre. The livre ournois was used as a numeraire by which all commodiies, silver and gold included, were valued. Royal mins produced hree ypes of coins: ) full bodied gold coins of denominaions greaer han one livre, 2) silver coins of fifeen, en (he mos popular), five and hree deniers, 3) pey coins, conaining less silver, of wo, one and half denier. The objecives of medieval moneary auhoriies were similar o hose of heir modern successors. In ordinary imes he moneary auhoriy was concerned wih responding o flucuaions in marke prices of precious meals and wih problems arising from wear and ear of coins in circulaion. I also addressed oher concerns such as monioring mins, combaing counerfei and mainaining he qualiy of royal coins hrough legislaive and enforcemen measures. In periods of fiscal crisis he crown had an addiional objecive, namely o raise inflaion ax. This was achieved by debasing he currency. A debasemen was an ac by he moneary auhoriy of lowering he silver conen of he livre ournois, usually by issuing a new coin wih he same face value, bu wih smaller conen of silver. Thus, (997) for he Ooman Empire. 5

8 debasemens generaed inflaion by increasing he nominal value of bullion, in a similar way o modern exchange rae devaluaions. The debasemens increased he demand for nominal money, which was me by increased money supply hrough mining of new silver bullion and of older coins and hus increased he crown s seignorage revenues. Such periods of repeaed debasemens were very common during he hundred years war. During such episodes fineness fell o very low levels and many episodes ended in sabilizaions, when he crown sopped he process and issued new coins of high fineness, which became he only legal ender. These episodes of debasemens and sabilizaions are he opic of his paper. We nex describe money creaion. In ordinary imes money supply was generaed primarily hrough mining of privae bullion. The moneary auhoriy offered o exchange, a he min price, any amoun of bullion in reurn for royal coins. The min price was he amoun of coins mined from one uni of bullion ne of seignorage and min s profis. Besides mining fresh bullion, he min would also remin older coins ino new ones. In ordinary imes people preferred no o remin old coins o avoid seignorage losses, unless he old coins were damaged. Bu here were wo siuaions in which such exchange ook place. The firs one was following a debasemen. Then, by remining coins of high fineness ino coins of lower fineness, bu of he same face value, people could increase heir money holdings, even afer deducion of seignorage. Thus, debasemens riggered much remining. The second siuaion was sabilizaion, where people were forced o remin heir old coins, as only he new coins were legal. To describe such an exchange, o coins wih higher fineness, we use a differen erm, recoinage, since i involved a differen echnology. While regular remining only 6

9 required adding cheap meal o coins, recoinage required exracion of silver from old coins o increase fineness and should have been more cosly. Indeed we find hisorical evidence o such coss. For example, afer he debasemen cycles of and of 36 debased coins were purchased by mins a much lower prices han bullion of he same amoun of silver. The difference in price was %-5%. 4 Our descripion above of remining during debasemens implies ha coins of various levels of fineness circulaed ogeher a he same face value. Remining reduced he scope of his phenomenon, bu as long as people did no remin all heir old coins, here were sill some ypes of coins in circulaion. Could people disinguish beween hese differen coins? The answer is no, since his informaion was cosly. In order o find fineness one needed o assay he coins, which was an exper s job. There is ample hisorical evidence on moneychangers in Medieval Europe, who specialized in coin evaluaion and exchange. They were usually exper goldsmihs, eiher governmen agens or privae enrepreneurs. Changers manuals were professional books, which described in deail he procedures for essaying and evaluaing coins. Surviving archival documens, like changers accoun books, inform us abou heir operaions. These accouns show ha changers were fully aware of he debasemen process since hey caalogued, in deail, he coins from he various issues and deermined heir exchange raes. I is herefore plausible ha changers were amongs he firs o observe debasemens of coinage and ha hey aced as middlemen beween he public and he min. Cosly informaion can explain boh how differen coins could circulae ogeher on he one hand and how people could know which coins o remin on he oher hand. If informaion is cosly i is purchased only when he benefi is sufficienly high. Thus 4 See De Saulcy (879), p. 352,

10 individuals did no go o an exper before each ransacion a he markeplace and hence coins circulaed by ale in he goods markes. Bu people did go o an exper afer a debasemen o check which coins o remin. Indeed our hisorical daa shows ha he bulk of remining usually ook place during he firs days afer each debasemen. The main period of debasemen explored in his paper is during he Hundred Years War. This war beween England and France, which began in he 33s and lased wih inervals unil 452, placed a heavy burden on governmen finance. The fiscal resources of he French monarchy were designed o cover is regular expenses. Financing a war required addiional resources on a grand scale. The French crown resored o seignorage revenues by debasing he royal coinage primarily because seignorage was par of he radiional feudal righs of he king. As such, he crown did no require he consen of he represenaive assemblies for levying his ax, while oher axes were always conesed, hard o obain and required exensive and lenghy bargaining o secure. Moreover, he collecion coss involving seignorage revenues were small and he flow of funds o he reasury imely. The exen of debasemen depended on he (mis)forunes of war and on he poliical bargaining power of he king. The Hundred Years War winessed wo periods of exensive debasemens: and The firs was associaed wih he oubreak of he war, he major French defeas a Crecy and oiiers (when King Jean II was capured by he English and held for ransom) and he onse of he Black Deah. The second period followed he defea a Agincour and he civil war beween he Armagnac and Burgundian facions. 8

11 3. The Model Consider a small open economy in a discree ime framework. There is an aggregae consumpion good in he economy. Each individual produces uni of he consumpion good during each period of ime. We furher assume ha he individual canno consume his own produc bu only producion of ohers. Hence, each individual has o rade in order o consume. We furher assume ha rading akes place in small quaniies and hus each individual rades many imes during a single period of ime. We assume ha here are wo asses in he economy, silver (in he form of bullion) and money (coins). Boh silver and he consumpion good are assumed o be inernaionally radable, and hus have a fixed relaive price, which is assumed o be. Silver can be raded over ime as well. Lending and borrowing of silver is done in he world s capial marke a a world ineres rae, which is assumed o be fixed and equal o r. The second asse is money, which comes in he form of coins, which conain silver. Money is non-raded inernaionally, bu is he only legal ender wihin he economy. The price of silver and of he physical good in erms of money is. There is a coninuum of size one of consumers wih infinie life horizons. They derive uiliy from consumpion and from money holdings, since hey need his money o carry ou heir many ransacions during he period. This model herefore follows he radiion of money in he uiliy funcion, which began wih Sidrauski (967), and has been recenly adaped o an open economy in Obsfeld and Rogoff (996, Ch. 8). For he sake of simpliciy consumers are assumed o be risk neural. Uiliy of individuals in ime is: () m U = ( ρ ) c v, = 9

12 where m is he amoun of money (coins) held by he individual a he beginning of period and v is a sandard concave uiliy funcion. For he sake of simpliciy we assume ha he subjecive discoun rae is equal o he world ineres rae, i.e. ρ = r. Money is issued by mins, which offer Q coins for uni of silver in period. We call Q he min price. The fineness, namely he proporion of silver in coins issued in period is f. We assume ha all coins have he same weigh, and normalize i o be, namely he same weigh as one uni of silver. 5 The overall amoun of coins ha can be made of one uni of silver is /f, bu consumers who bring silver for mining ge fewer coins, since he governmen exracs seignorage a a rae s. Hence: (2) Q = ( s ). f In his paper we consider debasemens, namely increases of Q by governmen, hrough reducion of fineness. More precisely, we consider episodes of repeaed debasemens over a long period of ime, during which he min price rises coninuously. Mins issue new coins in exchange of bullion, and in exchange of old coins, by remining during debasemens, or by recoinage during sabilizaions. As discussed in Secion 2, recoinage is more cosly. We herefore assume ha remining is cosless (excep for seignorage), while recoinage coss x per one uni of exraced silver. We nex lay ou he informaional and iming assumpions of he model. Each period opens wih an announcemen of a debasemen (or a sabilizaion). Then mins operae a he beginning of he period, while rade in goods, which requires money, akes place only laer. We assume ha all coins look alike for ordinary folks and canno be disinguished wihou help of expers, who are called money changers. Such help is

13 cosly. To simplify hings we assume he following cos srucure: in each period an individual can obain one evaluaion of his coins for free, bu addiional evaluaions are infiniely cosly. As a resul, an individual evaluaes coins only once each period. As assumed above, many ransacions ake place during a single period and coins circulae many imes, so ha individuals canno keep rack of he coin composiion of heir money. Hence, he opimal sraegy is o check heir coins a he beginning of he period, o decide which coins o remin, which coins o urn ino silver and which coins o keep in circulaion. During he period, when goods are coninuously raded, he se of coins changes and he iniial informaion is los, since all coins look alike. Hence, due o he law of large numbers, by he end of each period he composiion of coins held by each individual is he same as he economy-wide composiion. The governmen imposes no axes and finances is aciviy by seignorage only. In each period i ses boh fineness f and he seignorage rae s from mining new coins and uses he seignorage revenues o finance is expendiures. We assume ha he governmen spends hese revenues on impors raher han domesically. This assumpion is made for racabiliy only, and he alernaive assumpion, ha seignorage revenues are used domesically, would no change he main resuls of he model. 6 Finally, if he governmen decides o sabilize he currency, i issues new coins wih higher fineness. In oher words, i reduces he min price Q and fixes i a he new lower level hereafer. We furher assume ha all markes are perfecly compeiive and ha expecaions are raional. We firs analyze debasemens and inflaion ha coninue forever, wihou any sabilizaion. In he nex sage we add sabilizaions o he analysis. The public 5 Hisorically no all coins had he same weigh. This is of course only a simplifying assumpion.

14 anicipaes sabilizaion a he end of he debasemens process, bu does no know is exac iming. 4. Mining Decisions and he Supply of Money We begin he analysis of equilibrium dynamics by looking a he decisions made in he beginning of he period, afer he consumer learns of he composiion of his coins from he exper. Firs, he consumer mins silver ino coins as long as he price of silver is less han or equal o he min price Q. Second, he consumer remins all coins wih sufficienly high fineness, such ha remining can increase he number of coins. Formally, he consumer remins all coins wih fineness f such ha f (3) fq = ( s ). f Since fineness is non-increasing over ime, namely f u f u for every ime u, only he older coins wih higher fineness are remined. Hence, for every here is a former period τ(), such ha coins older han i are remined and f τ () is he highes fineness held. This hreshold period is defined by: f τ() < /Q and f τ()- /Q. Finally, consumers can also urn coins ino silver, if he value of exraced silver exceeds he number of coins used. Hence, silver is exraced from coins of fineness f u if (4) f u. x The supply of money can herefore be described by a sep funcion, as in Figure, which has he price on he verical axis and he quaniy of money M on he horizonal 6 Hisorically, he crown used seignorage income for boh domesic purchases and impors. Ineresingly, i lised he silver value of is seignorage revenues in is accouns. 2

15 axis. The amoun of money M,r is he hisorically given amoun of coins from las period afer remining, bu before bullion mining or silver exracion. This amoun does no depend on he price, since remining does no depend on price, as shown by equaion (3). The demand for money is he demand of consumers only, as he governmen impors only. The demand for money is proporional o he price level and is presened in Figure by a ray from he origin. The equilibrium, which deermines boh he equilibrium price level and he equilibrium quaniy of money, is given by he inersecion of he supply sep funcion and he demand for money. The equilibrium price mus, herefore, be wihin he following range: (5) Q = ( s ). f x f Figure presens hree possible equilibria. If he demand for money is small, as in D, coins are ransformed o silver by exracion. If he demand for money is as in D, here is neiher silver exracion nor silver mining and M =M,r. In boh cases he price of silver exceeds he min price Q. If he demand for money is large, as in D, bullions are mined ino coins and he price is equal o he min price. Consider nex he effec of debasemen on equilibrium. A debasemen inroduces a new coin wih lower fineness. Hence i raises Q and shifs some of he supply curve upward. If he new fineness is low enough, so ha f falls below f τ(-) (-s ), here is remining, which shifs he whole supply curve o he righ as well, as i makes he upper sep in he supply curve wider. Hence, a debasemen ends o raise he price. Clearly, here can be a debasemen, which leaves he price unchanged, if here is no remining and if he previous price exceeds he new min price. Bu if debasemens are repeaed, hey finally raise prices. Thus, repeaed debasemens cause inflaion. 3

16 When he auhoriies declare sabilizaion, all coins mus be remined and hence he supply of money becomes infiniely elasic a he new min price Q. As a resul, he equilibrium price, in he case of sabilizaion, is equal o he min price. 5. Debasemens and Inflaion In his secion we consider he case of repeaed debasemens a a fixed rae π. Assume ha he moneary policy he governmen pursues is he following: he rae of seigniorage is fixed over ime, namely s = s, and he governmen debases he currency every period a a fixed rae π. 7 Formally: Q f (6) = = π. Q f If he rae of debasemen is fixed, he number of coins in circulaion is fixed and we denoe i by T. Every period a new coin is inroduced and he oldes coin is remined, namely τ ( ) = T for every. T is he unique ineger which saisfies he following inequaliies, which are derived from (3): T (7) ( π ) ( s) <. π We nex show ha afer a few debasemens he price becomes equal o he min price Q. To see his noe ha he moneary dynamics are: ~ T (8) M = M N [( ) ( s) ] Q e, where N ~ π is he amoun of coins remined in ime and e is he amoun of bullion mined T ino coins in. Hence, if here is no mining of new bullion M M [( π ) ( )] s 4

17 and he erm in brackes is smaller han π according o (7). Hence, if here is no mining of new silver, he quaniy of money grows a a rae lower han π. This canno las long and afer a few debasemens here mus be mining of new silver. Noe ha silver is mined only if he equilibrium price equals he min price, as shown in Figure, and hence: (9) = Q, and his equaliy holds from hen on. The inuiion behind his resul is simple. Since he governmen uses he silver i ges as seignorage ouside he economy, i reduces he silver conens of coins coninuously. Hence, consumers need o min new bullion, which hey would no have done had he price of silver exceeded he min price. 8 In he res of he secion we focus on he seady sae equilibrium. As shown above he rae of inflaion a he seady sae is π and he price equals he min price. There are wo main cases. In he firs here is more han one ype of coins in circulaion, i.e. T>. In his case remining is parial. In he second case he rae of inflaion is so high ha here is only one coin in circulaion, i.e. T=. In his case all former coins are remined. 5.. Debasemens wih arial Remining We nex describe he seady sae disribuion of coins when T is greaer han. 9 The quaniy of coins of fineness f -u for all u T- is he quaniy of coins mined in period -u, and is equal o 7 Hisorically, he debasemen episodes consised no only of reducion in fineness, bu ofen of increased seignorage raes as well. In he heoreical par of he paper we rea inflaion and seignorage raes as independen. We reurn o his issue in he empirical par of he paper in Secion 8. 8 We should sress here ha if he governmen uses is seignorage revenues domesically he equilibrium price migh no always equal o he min price, bu he main resuls of he model remain inac. 9 I can be shown ha he disribuion of coins converges o his seady sae disribuion. 5

18 () π N u = M ( π ) T π ( π ) u. Noe ha his disribuion of coins is economy-wide, bu also holds for any individual by end of rading period, due o high circulaion of coins. The individual maximizes uiliy () wih respec o he budge consrains. Le us denoe he opimal value of uiliy by V. Due o saionariy, he opimal value depends only on he amouns of asses inheried from he pas. Since he coin composiion by he end of each period is he same for all individuals, due o he law of large numbers, only he overall amoun of money maers. Hence: () =, m V V b. Hence, he Bellman equaion is (2) m m m V b =, max c v V b,. r The budge consrains are as follows. The amoun of silver changes according o (3) b b ( r e, = ) where e is he amoun of bullion mined. The consumer s quaniy of money changes hrough mining, remining and hrough ransacions. Hence: T (4) m ( w) m wm ( π ) ( s) ( c e, = ) where w is he share of coins of highes fineness, which are being remined, and is equal according o () o (5) π w =. T ( π ) Subsiuing (3) and (4) ino he Bellman equaion (2) we ge: 6

19 (6) ( ) =, ) ( ) ( ) ( max, m b V r m v s w w m m b r b m b V T π. Hence, he firs order condiions are: (7) =, m b V r b wih respec o silver and: (8) =, m b V r m v m wih respec o real balances. Shifing (6) one period ahead we can calculae he marginal opimal value wih respec o silver and real balances: V r b = and: [ ] π π π = = ) ( ) ( ) ( ) ( s w w s w w T T m V. Hence he demand for money is deermined by he following condiion, which holds for any period : (9) ) ( ) ( ) ( = T T s r m v π π π π. Equaion (9) describes he demand for money. The lef hand side is he marginal uiliy from holding money, while he righ hand side is he marginal cos of holding money. I is a weighed average of he loss due o inflaion o he coins, which are no remined, and a smaller loss for he coins ha are o be remined nex period. Since he 7

20 demand for money is endogenous in his economy, equaion (9) deermines he seady sae amoun of real balances: M = m. The equilibrium real balances herefore depend boh on he rae of inflaion and on he rae of seignorage. Furhermore, he number of coins in circulaion T is an endogenous variable, which depends on hese wo variables as well. In order o find how real balances depend on π and s in he reduced form, consider he rae of debasemens, a which he number of coins swiches from T o T. This rae is deermined by: T ( π ) ( s) =. A his rae he marginal coss of boh ypes of coins are equal. A his rae of debasemen equilibrium real balances are (2) M v =. ( r)( π ) We, herefore, conclude ha real balances depend negaively on he rae of inflaion as long as more han one ype of coins circulaes. Ineresingly, demand for money does no depend on seignorage. While our heory predics he equilibrium sock of money, our daa from Medieval France consiss of flows of mining. Luckily, our model enables us o easily calculae he flow of mining, which depends on he amoun of money and on he disribuion of coins. The amoun of real mining N/ is: (2) N π π ( π ) = T M. From his equaion we see ha inflaion affecs mining in hree channels. Firs, he overall demand for money M/ falls wih inflaion. Second, higher inflaion reduces he value of old coins more rapidly and ha increases mining as shown in he firs erm in 8

21 he RHS of (2). This exers a posiive effec of inflaion on mining. Third, higher inflaion reduces he number of coin ypes in circulaion T and ha also affecs mining posiively. In order o consider he hree effecs ogeher, consider again he rae of inflaion a which he number of coins falls from T o T. A his rae mining is (22) N = π s π M. Hence, inflaion affecs mining in wo ways: posiively by reducing he number of ypes of coins in circulaion and negaively by reducing he demand for money. The overall effec depends on he elasiciy of he demand for money wih respec o π. In our empirical analysis we es for he effec of inflaion on he amoun of real mining. If he effec we find is negaive, i clearly shows ha real balances are negaively relaed o he rae of inflaion Debasemens wih Full Remining We nex urn o he case where inflaion is so high, ha all old coins are remined and here is only one coin in circulaion, i.e. T=. This case holds when (23) ( π )( s) >. Soluion of he opimal uiliy is similar o ha in secion 5., hough simpler, since all coins are remined and w=. In his case he equilibrium amoun of money is given by: (24) M v r s =. r Hence, he demand for money a a high rae of debasemens does no depend on he rae of inflaion bu on he rae of seignorage only. This is a very surprising resul, and i is unique for inflaion in commodiy money. More precisely, i is a resul of he inrinsic value of coins, namely of heir silver conen, 9

22 in addiion o heir ransacion value. When inflaion is high, holders of commodiy money can avoid he inflaion ax by remining. In doing so hey reduce heir losses o seignorage only. As a resul heir demand becomes insensiive o he inflaion rae. The rae of inflaion a which individuals begin o remin all heir coins and a which he demand for money depends only on he rae of seignorage only is (25) π s * = s. When inflaion exceeds π* and full remining prevails, he real amoun of mining is equal o real balances, since all coins are new. Hence, a raes of inflaion above π* he amoun of mining also depends on seignorage only and no on he rae of inflaion. 6. Debasemens and Sabilizaion In secion 5 we describe a debasemen process ha goes on forever. While his is a helpful simplificaion, i is no very realisic. Rulers could no debase heir currency forever by bringing fineness as close as possible o zero, since a very low levels fineness becomes pracically indisinguishable from zero and commodiy money loses is value. Indeed, our hisorical records show ha periods of repeaed debasemen, which reduced fineness o very low levels, ended in sabilizaions. Since such sabilizaion was anicipaed i affeced he demand for money. This effec is he opic of his secion. As in Secion 5 we assume ha here is a fixed rae of debasemen π and a fixed rae of seignorage s. We furher assume ha he rae of debasemen is high so ha agens remin all coins every period. Le z denoe he probabiliy in period ha sabilizaion occurs nex period. Laer on, we make his probabiliy endogenous as well. 2

23 Before solving he model we show ha in his case he price is equal o he min price as well, if he rae of seignorage is sufficienly high. Noe ha if here is no mining of new bullion, money supply grows by a rae, which is much lower han he rae of debasemen π. Hence, even if he demand for real balances falls as sabilizaion becomes more anicipaed, i canno decline o zero. We herefore conclude ha here is mining of new bullion and he equilibrium price equals he min price. ) )( ( s π Hence, he rae of inflaion is equal o π. We solve he model recursively, firs calculaing opimal uiliy from sabilizaion on, and hen calculaing opimal uiliy before sabilizaion, during he debasemen process. If sabilizaion occurs in period, opimal uiliy V depends on he accumulaed amouns of silver and real balances, and is equal o S (26) *) ( * ) )( ( ) (, l v r r l x s m r b r r m b V S = where l* is he amoun of real balances afer sabilizaion, which is deermined by r r l v = *) (. Nex denoe by V he opimal value of uiliy prior o sabilizaion in period. The Bellman equaion is (27) = S m b V r z m b V r z m v c m b V,, max, under he consrain: (28) m b r b s m c = ) ( ) )( ( π. Noe ha even if he price is higher han he min price he qualiaive resuls of he model remain inac. 2

24 Before we derive he firs order condiions, noe ha due o he envelope heorem, he parial derivaives of V are V b = r and V m = ( π )( s) = s. The firs order condiion of he Bellman equaion wih respec o silver b is herefore redundan. The firs order condiion wih respec o money is: (29) m v z z r s ( s) xz = ( s)( x) ( s) =. r r r Hence, he demand for money depends boh on he rae of seignorage and on he probabiliy of sabilizaion. This probabiliy has a negaive effec on he demand for money. Noe ha his effec depends on x being posiive, namely i depends on he cos of silver exracion being posiive. Hence, he probabiliy of sabilizaion has a negaive effec on he demand for money since agens wish o minimize he cos of recoinage, of convering debased coins ino good coins. We nex ry o describe how he probabiliy of sabilizaion evolves over ime, using a Bayesian learning process under very simple assumpions. Assume ha he public only knows ha he process of debasemen canno go on o zero fineness, and here is a minimum level of fineness f*. Hence, if he economy is expeced o reach his fineness in period T*, and here has been no sabilizaion unil, he probabiliy of sabilizaion is uniform, and is equal o (3) z =. T * Fineness falls a a rae π, and hence T* can be deduced from This is herefore only a simplifying assumpion. 22

25 f * = f T f π ( T* ) * = ( ) We herefore ge ha he probabiliy of sabilizaion is. (3) z = T * log( π ) = log f log f. * The probabiliy of sabilizaion, herefore, depends negaively on fineness. The lower fineness is, he higher is he probabiliy ha he process of debasemens ends soon. This probabiliy also depends posiively on he rae of debasemen. Finally noe ha since only one coin circulaes, he amoun of mining is equal o he amoun of money: N = M = m. Hence, mining depends negaively on he rae of seignorage and negaively on he probabiliy of sabilizaion. As debasemen coninues, anicipaion of sabilizaion rises, and hence mining is reduced. This is also an explanaion o he puzzle raised by Rolnick, Velde and Weber (996), who find he amoun of mining o be oo small given he raes of inflaion in such siuaions. 7. Daa and Descripive Saisics The daa used in his paper is derived from original min accouns found in he naional French archives and in he regional archive of he Isere a Grenoble. eriodical min accouns were submied o he cenral moneary adminisraion in aris. They conain informaion on he ype and quaniy of coins mined, on coss, seignorage revenues and ne profis of min. Due o losses, fires and wars he exen of coverage of hese documens is incomplee, bu we were able o assemble a daa se ha covers he main periods of debasemens during he 35s and in from 2 mins of varying imporance and locaion. The full lis of mins and daes of accouns is in he Appendix. 23

26 I is imporan o noe ha he daa does no come in fixed periods of ime bu raher in periods wih varying lenghs, since he frequency of submiing min accouns o he audiors in aris was no uniform. The accouns lenghs vary from one day o fifeen monhs, he average lengh being one monh. Accouns lenghs varied boh across mins and over ime. Under normal circumsances accouns were submied annually or semiannually. However, during debasemens, hey were submied more frequenly. This is due o igher conrol over mins in such periods, and also because mins had o submi accouns following changes in any of he characerisics of he coinage. During debasemen hese changes were more frequen. A furher complicaion arises from he fac ha royal orders reached mins wih varying delays, due o disances beween mins and aris, due o difficuly of ravel in war zones and due o necessiy o someimes pass hrough provincial adminisraive ceners. Alhough he daa are in varying lenghs of ime, hey cover coninuous periods of ime for he 2 mins and enable us o calculae he main variables and how hey evolve over ime. The daa are pooled and allow us o es our wo main hypoheses. The relevan variables are min prices, from which we derive raes of debasemens or raes of inflaion, seignorage raes, and amouns of mining. Daa on amouns of mining are in unis of silver mined. I is equal o real mining in he model, since: N = N Q = N f s. The righ hand side is he amoun of silver mined (including seignorage), which is repored in he accouns. As for he inflaion variable, we have calculaed wo inflaion raes. One is a rae of inflaion for each accoun, namely he rae of change since las For greaer deail see Sussman (997). 24

27 debasemen compounded o annual erms. In our regressions we use an annual rae of inflaion calculaed as he rae of change of he min price in a year a a represenaive min. These are Rouen for he period, and Romans for he period. We firs presen some descripion of French debasemens in he years The firs debasemen period was characerized by repeaed cycles of debasemen and sabilizaions. The period from 337 o 354 winessed 34 mild debasemen cycles wih relaively long periods of sable money (Figure 2). The period from 354 o 36 saw 5 rapid debasemen cycles ha reached hyperinflaionary magniudes in 36 (figure 3). The average rise in he nominal value of silver during such a cycle was 2% and he average duraion of a debasemen cycle was 4 days. The larges debasemen cycle increased silver price by 6% and lased only 6 days. The smalles cycle increased price by 66%. The shores debasemen cycle was 33 days during which he nominal value of silver increased by %. The period from 47 o 422 was characerized by a prolonged process of debasemen during which he nominal value of silver was increased by 35% wihou any aemp o sabilize he currency (figure 4). Milder debasemens (average of 8% per cycle) followed unil 436 (figure 5). The debasemens resuled in subsanial mining and large governmen revenues. While complee daa for all he mins operaing in France is lacking, our daa allows us o assess he quaniaive aspecs of hese episodes. Figure 6 shows min oupus of four major French mins. Toal min oupu for he four mins in 355 was abou 75, marcs of pure silver (2 ons) while he annual average of oal mining in France in nondebasemen years was 5, marcs. The revenues of governmen were also impressive: according o Maurice Rey, he 49 seignorage revenues amouned o six imes ordinary 25

28 royal revenues. Figures 7, 8 and 9 show, respecively, mining levels and seignorage revenues a he mins of Rouen and Monpelier and he Dauphine mins (Cremieu, Mirabel and Romans). The figures illusrae he high share of seignorage revenues ou of oal mining. I is ineresing o compare Rouen (Figure 7) and Monpelier (Figure 8). In 356, following he capure of King Jean by he English a oiiers, he Esaes of Languedoc (souhern France) voed o suspend debasemen whereas he mins of he Norh coninued o debase he currency. In response, min oupus and seignorage revenues in Monpelier sared o decline, while a Rouen hey reached an all ime high. In he heoreical secion of he paper we idenify he price of silver wih commodiy price and hus he rae of inflaion becomes equal o he rae of debasemen. We nex show some supporive evidence. While high qualiy price daa for France are lacking, neverheless, Table reproduces daa from Sussman (993) for he Dauphine, which shows ha grain prices followed he course of min prices whereas he price of gold followed he price of silver. [Inser Table here] 8. Empirical Analysis Our model describes how he demand for commodiy money is relaed o hree main variables: he rae of inflaion, he rae of seignorage and he anicipaed probabiliy of sabilizaion. For lack of daa on quaniy of money we use daa on min oupus insead o es he wo main conclusions of he model. The firs is ha he demand for money falls wih inflaion up o some level and above i becomes insensiive o he rae of inflaion. The second is ha anicipaion of sabilizaion reduces he demand for money. 26

29 Before we describe he empirical analysis we address hree imporan issues. The firs is relaed o he correlaion beween he seignorage rae and he rae of inflaion. While he model reas he wo variables as independen, hisorically hey ended o rise ogeher, in imes of igh fiscal condiions. Bu as our daa shows, he correlaion beween he raes of debasemen and of seignorage is posiive bu no so high, and he correlaions for all mins are less han.5. Hence, we rea hese variables, inflaion and seignorage, as independen explanaory variables in our regression analysis. The second empirical issue is ha lenghs of min accouns varied significanly, as described above. The dependen variable we use is he overall amoun of mining in he accoun period, insead of mining per uni of ime, and we add he lengh of he accoun period o he explanaory variables. This procedure reflecs wha we learn from he records, namely ha mos mining aciviy was concenraed in he beginning of each period, following he debasemen. In any case, we check and find ha using quaniies of mining per uni of ime does no change he resuls by much. The hird and main issue is how o disinguish beween he direc and he indirec effec of inflaion on he demand for money, where he indirec effec is hrough he anicipaed probabiliy of sabilizaion, as shown in equaion (3). We deal wih his issue in wo ways. Firs, we esimae he effec of inflaion on he demand for money during periods, which are relaively far from sabilizaions, so ha he indirec effec hrough anicipaion of sabilizaion is negligible. Second, we esimae he probabiliy of sabilizaion and hen esimae boh he direc effec of he rae of inflaion and he effec of he probabiliy of sabilizaion on mining. We begin our empirical analysis wih esimaions of a basic equaion, of min 27

30 oupu as a funcion of he rae of inflaion, he rae of seignorage and he lengh of accoun period, excluding for he meanwhile he probabiliy of sabilizaion. These esimaions are presened in Table 2. According o Regression I he rae of seignorage has a negaive effec on he amoun of mining and he inflaion rae oo has a negaive effec on mining. Noe, ha our model predics ha inflaion has a negaive effec on he demand for money, bu is effec on mining is unclear, as a a higher rae of inflaion fewer coin ypes circulae and a larger proporion of coins is remined. According o Regression I he overall effec in our hisorical episodes was negaive. Tha clearly shows ha he effec of inflaion on he demand for money was negaive, which is he firs main resul of our model. Finally, he effec of ime lengh of accoun is very significanly posiive, as expeced, bu he elasiciy is smaller han, slighly above.5. We inerpre i as a resul of he concenraion of mining a he beginning of he period. I canno be a resul of poenial negaive correlaion beween lengh of accoun period and inflaion, since ha should increase measured elasiciy o above. Regression II in Table 2 is he same equaion as Regression I only wih fixed effecs for mins. The resuls are fairly similar o hose of regression I. 2 [Inser Table 2 here] Regressions III-VI in Table 2 examine wheher he effec of inflaion differs under low and high inflaion raes. 3 According o equaion (25) he hreshold rae of inflaion beween parial and full remining is equal o π* = s/(-s). The rae of seignorage was no fixed during he period we describe, and rose wih inflaion. Since on average i was 2 Random Effec versions o all regressions in Table 2 yield very similar resuls. 3 For selecing sub-samples we use he inflaion rae for each individual min accoun. The inflaion variable in he regression is he annual rae common o all mins. See Secion 7 for precise definiions. 28

31 around /3, he hreshold rae of inflaion should be abou 5%. 4 Regressions III and IV in Table 2 show ha he effec of inflaion is much larger and more significan when inflaion is below 5%. However, a high raes of inflaion he probabiliy of sabilizaion becomes higher, which migh add an indirec effec o inflaion on he demand for money. To reduce his indirec effec Regressions V and VI are limied o periods far from sabilizaion, namely a leas 2 days before any sabilizaion. These regressions fully confirm our main hypohesis: he rae of inflaion has a large negaive effec on he demand for money in Regression V, where inflaion is below 5%, while in Regression VI, when inflaion is above 5% and remining is full, i has no effec on he demand for money. Nex we esimae a measure of he expeced probabiliy of sabilizaion and add i as a fourh explanaory variable o he mining equaion. This probabiliy is esimaed in he following mehod. In every period we know he acual duraion unil sabilizaion, i.e., where is he acual dae of sabilizaion. Expeced duraion unil sabilizaion is equal o (T*-)/2 under he assumpion of uniform disribuion, bu i is also equal o he expecaion of. Hence, we can wrie: T * log f log f * (32) = ε, = ε,. 2 2log( π ) We herefore esimae a regression of he acual ime o sabilizaion on wo explanaory variables: he logarihms of fineness and of he rae of inflaion. This regression is presened in Table 3 and i indeed shows ha he expeced ime o sabilizaion decreases wih inflaion and increases wih fineness. The probabiliy of sabilizaion is exacly equal 4 When inflaion was low he average seignorage rae was 27%, while a high raes of inflaion he seignorage rae was 37% on average and even reached a maximum of 75%! 29

32 o over he expeced ime o sabilizaion. Therefore, he probabiliy of sabilizaion rises wih inflaion and is negaively relaed o fineness. [Inser Table 3 here] We nex add he probabiliy of sabilizaion as an explanaory variable in he mining equaion. In his esimaion we ry o examine ogeher our wo hypoheses, namely ha he demand for money reacs differenly o high and low inflaion and ha i is negaively relaed o he probabiliy of sabilizaion. Table 4 presens hree regressions, wih log of min oupu as he dependen variable, and inflaion, seigniorage, lengh of accoun and he probabiliy of sabilizaion are he dependen variables. All regressions conrol for mins fixed effecs. Regression I replicaes he main resuls presened above: he seignorage rae and inflaion have negaive effecs on mining, while he lengh of he period of accoun has a posiive effec wih elasiciy less han. The new resul is ha he probabiliy of sabilizaion has a significanly negaive effec on mining, namely on he demand for money. The nex wo regressions in Table 4 deal separaely wih periods of inflaion below and above 5%. While he effec of inflaion becomes sronger and more significan a low raes of inflaion, is effec a high raes of inflaion is zero. Anoher ineresing resul is ha he probabiliy of sabilizaion becomes insignifican a low raes of inflaion. This resul is fairly reasonable, as a low inflaion he probabiliy of sabilizaion should be low. [Inser Table 4 here] The regressions in Table 4 herefore give furher suppor o he wo main hypoheses of our model, ha a high raes of inflaion he demand for money becomes 3

33 insensiive o inflaion, and ha he probabiliy of sabilizaion has a significan negaive effec on he demand for money, beyond he effecs of seignorage and inflaion. A his poin, we briefly reurn o he assumpion ha coins canno be disinguished by fineness, namely ha coins are raded by ale and no by weigh. If indeed people have full informaion on he silver conen of coins, hen debasemens would no affec consumer behavior in our model. Consumers would use mosly he old coins and here will be lile demand for he new coins. As a resul he amouns of mining would be zero (or close o zero). Clearly, we will no observe a negaive relaionship beween he rae of debasemen and mining. Thus, he resuls of our empirical analysis provide suppor o our basic assumpion ha coins circulaed by ale and no by weigh. 9. Summary and Conclusions In his paper we show how inflaion and even high inflaion happen under a commodiy money regime. The possibiliy of high inflaion due o debasemens is shown in heory and hen demonsraed by hundred years of frequen debasemens in medieval France. Hence, a commodiy money regime is quie similar o he more modern fia money regime in is abiliy o generae inflaion ax. Despie his basic similariy beween commodiy and fia money, we observe wo main differences beween he wo regimes. Firs, under commodiy money he demand for money falls less a high raes of inflaion, because coins sill reain some inrinsic alernaive value and can be used for remining. The second difference beween he wo regimes is he effec of sabilizaion anicipaions. While under fia money such 3