Commodiy Money Inflaion: Theory and Evidence from France in 350-436 Nahan Sussman The Hebrew Universiy of Jerusalem Joseph Zeira The Hebrew Universiy of Jerusalem and CEPR Augus 2000 Absrac This paper presens a heory of inflaion in an economy wih commodiy money and suppors i by evidence from he 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 devaluaion. Furhermore, as wih fia money, demand for commodiy money falls wih inflaion. Unlike fia money, a high raes of inflaion he demand for commodiy money becomes insensiive o inflaion, since commodiy money has inrinsic value in addiion o ransacions, and hus losses from inflaion are bounded. Finally, we show ha an anicipaed sabilizaion reduces he demand for commodiy money, which is opposie o he effec of an anicipaed sandard sabilizaion on he demand for fia money. All he resuls of he model are suppored by he daa. JEL Classificaion: E3, N3 Keywords: Inflaion, commodiy money, debasemens, seignorage, sabilizaion. Mailing Address: Nahan Sussman Deparmen of Economics Hebrew Universiy of Jerusalem M. Scopus Jerusalem 9905 Israel E-mail: msussman@mscc.huji.ac.il
Commodiy Money Inflaion: Theory and Evidence from France in 350-436. Inroducion This paper describes and analyzes inflaion in an economy wih commodiy money, and compares i wih fia money inflaion. 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 350-436. 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, is inflaionary losses are bounded. As a resul, when he rae inflaion is high, he demand for money becomes insensiive o inflaion. 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. The 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 ha he unis of commodiy money are coins and no silver, and coins can have differen conens of silver and hus differen values. We herefore assume ha coins circulae by ale raher han by
weigh. This assumpion is suppored by our daa from France in 350-436. The daa show ha debasemens were frequen and subsanial, ha raes of inflaion were quie high and someimes even very high, and ha he volumes of mining and remining and of seignorage during debasemens were subsanial. The paper hen analyzes he 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 bounded when inflaion is high. This is due o he alernaive use of commodiy money, which can be used o creae new coins by remining, and even be convered, alhough a some cos, o silver. As a resul, he demand for commodiy money in high inflaion becomes insensiive o he rae of inflaion. Alhough we do no have observaions on he demand for money in medieval France, we do have daa on mining volumes by he royal mins. The model enables us o relae he demand for money o he volume of mining, in various sages of he inflaionary process. This enables us o perform empirical ess of he predicion of he model. 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 much weaker a high raes of inflaion. Nex we discuss he effec of an anicipaed sabilizaion. A sandard sabilizaion of fia money inflaion consiss mainly of sopping moneary expansion. Hence, anicipaing such 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 Rolnick, Velde and Weber (996) quesion his assumpion and claim ha coins did no circulae by ale. We discuss his issue exensively in he paper. 2
has previously reduced he silver conen of older coins by oo much. During he hisorical period we examine, many inflaionary episodes ended wih sabilizaions and always he silver conen of coins increased a sabilizaion. Hence, in sabilizaion old coins become eiher compleely useless or go hrough silver exracion, which is a very cosly aciviy. Hence, sabilizaion is cosly for money holders, and anicipaion of such sabilizaion reduces he demand for money raher han increases i. This resul is also suppored by he daa from French mins. We find ha he demand for money decreased prior o major anicipaed sabilizaions. We esimae he probabiliy of sabilizaion under raional learning and show ha his probabiliy had a negaive effec on he demand for money. I is imporan o noe ha his finding is relaed no only o our heory of inflaion, bu is also evidence for raional learning by he public on he probabiliy of sabilizaion, which is an ineresing resul in iself. This paper 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). These papers analyze he heory of commodiy money, of he ypes of coins in circulaion and of debasemens. 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 urns from issues such as Gresham s Law o he more applied and more quaniaive issue of 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 Our paper is also relaed o 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 model wih uiliy from money. 3
oher hisorical accouns of debasemens. The closes is Sussman (993) which deals wih he same hisorical episode, bu here are many oher hisorical episodes of inflaing commodiy money by debasemen, no only in France. A number of sudies examine similar episodes in early periods of modern Europe. 3 The paper is organized as follows. I begins wih hisorical background, hen discusses he heory, and finally presens he empirical resuls. Secion 2 describes he hisorical episode and he debasemen process. Secions 3-6 presen he heory of commodiy money inflaion. Secion 3 oulines he model, secion 4 analyses mining and prices, Secion 5 sudies inflaion dynamics under debasemens, and Secion 6 sudies he effec of expeced sabilizaion. Secion 7 presens he daa and descripive saisics, and Secion 8 describes he mehod and presens he resuls of 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 mins ha 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 3 See Bordo (986) for a survey, Gould (970) for he Tudor debasemen, Kindleberger (99) for debasemens during he 30 years war; Miskimin (984) for France; Moomura (994) for Spain and 4
monioring mechanism. A min maser operaed each local min. The cenral adminisraion encouraged he min maser o produce coins by paying him a given percenage of he coins he sruck. I also appoined royal officials o monior he various aciviies of his economic enerprise. Moreover, i required he min o submi random samples of coins for inspecion in Paris. As a furher reflecion of he influence and cenral conrol of he Parisian 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 meal wih base alloys o produce an alloy of a given fineness and hen cu i ino coins. The coins' face value, denominaed according o prevailing uni of accoun, 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 he numeraire in he French economy by which all commodiies, silver and gold included, were valued. Royal mins produced he following hree ypes of coins: ) full bodied gold coins of denominaions greaer han one livre usually, 2) silver coins of 50 o 00 percen fineness valued a fifeen, en (he mos popular), five and hree deniers, and 3) pey coins, conaining less han 20 percen silver, valued a wo, one and one half denier. The money supply was generaed primarily hrough mining of privae bullion. The moneary auhoriy offered o exchange, a he min price, any amoun of bullion (or foreign coins) in reurn for royal coins. Besides mining fresh bullion, he min Pamuk (997) for he Ooman empire. 5
would also remin older coins. Remining occurred boh in periods of debasemens and during currency reforms. 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. As a resul people could make arbirage profis from remining heir old coins ino new ones, even if some of he coins are paid o he ruler as seignorage. Also, recoinage was carried ou, usually by decree, during currency reforms. These reforms ook place afer periods of repeaed debasemens or in response o he physical deerioraion of he currency. We herefore refer o hem in he paper in he more modern erm sabilizaion. The objecives of medieval moneary auhoriies were similar o hose of heir modern successors. Ordinarily, he moneary auhoriy was concerned wih managing he money supply by responding o flucuaions in marke prices of precious meals, and by dealing wih problems arising from wear and ear of coins in circulaion. I also addressed oher concerns such as monioring he 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 increase seignorage revenues. This was achieved by debasing he currency, usually by reducing he conen of silver in he new coins issued. Hence, debasemens generaed inflaion by increasing he nominal value of bullion, as in modern devaluaions. I also increased he money supply hrough greaer mining and remining. During a prolonged period of debasemens, remining increased significanly, as he min price rose frequenly and induced remining of older coins. This provided he crown wih seignorage revenues a imes when inflaionary expecaions reduced he incenive o sell fresh bullion o he min. 6
One issue ha emerges here is he circulaion ogeher of coins wih various levels of fineness. Remining reduced he scope of his phenomenon bu as long as people did no remin all heir coins, bu only hose wih highes conen of silver, here was more han one coin in circulaion. Could people disinguish beween hese differen coins? The answer is ha hey could, bu only by help of expers, namely his informaion was cosly. While increases in face value or weigh of coins were ransparen, changes in fineness were difficul o deec, as no informaion was released o he public wheher he change in min price was due o change in fineness or o seignorage rae or o boh. In order o find fineness one needed o assay he coins, which was an exper s job. We have hisorical evidence o he exisence of moneychangers in medieval Europe, who specialized in coin evaluaion and exchange. They were usually exper goldsmihs, eiher governmen agens or privae enrepreneurs. Surviving archival documens inform us abou heir operaions. "Changers manuals," ha served as professional exbooks, describe in deail he procedures for essaying and evaluaing coins. Changers accoun books shed ligh on heir acual aciviy and indirecly on coin circulaion in he regions hey operaed in. Surviving accouns show ha he changers were fully aware of he debasemen process since hey caalogued, in deail, he coins from he various issues and deermined heir exchange raes wih foreign and wih full bodied older coins. I is herefore plausible ha changers were amongs he firs o observe debasemen 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 7
high. Thus 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. The main period of fiscal crisis and debasemen we explore in his paper is during he Hundred Years War. The war beween England and France, which began in he 330s and lased wih inervals unil 452, placed a heavy burden on governmen finance. The fiscal resources a he disposal 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 raising seignorage revenues by means of 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. 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: 337-360 and 48-436. The firs was associaed wih he oubreak of he war, he major French defeas a Crecy and Poiiers (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. 3. The Model Consider a small open economy in a discree ime framework. There are hree goods in he economy. The firs is an aggregae consumpion good. I is produced by labor 8
only and each uni of labor produces uni of he physical good during each period. The consumpion good is assumed o be radable. The second good is silver in he form of bullion, which are also inernaionally raded. Silver can be len or borrowed in he world s capial marke a a world ineres rae, which is assumed o be fixed and equal o r. Inernaional price of he consumpion good in erms of silver is. The hird good is money 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 in erms of money is denoed P. Money is issued by mins, who offer Q coins for uni of silver in period. We call Q he min price. The proporion of silver in coins, which are issued in period, is f, which we call fineness. We assume ha all coins have he same weigh h, where is he weigh of one uni of silver. 4 The overall amoun of coins ha can be made of one uni of silver is /hf, bu consumers who bring silver for mining ge fewer coins, since he governmen exracs seignorage from any mining by he min. We denoe he rae of seignorage in period by s. Hence: () Q = ( s ). hf In his paper we consider siuaions where Q is increased by he governmen, by reducion of fineness. Such an increase is called debasemen. More precisely, we consider siuaions of repeaed debasemens for a long period of ime, during which he min price rises significanly. Mins issue new coins in exchange no only of silver bullions, bu also in exchange of old coins. Here we should disinguish beween wo cases. The firs case occurs during debasemens, where he coins brough o he min are urned o coins 4 Hisorically no all coins had he same weigh, bu we assume i for he sake of simpliciy. 9
wih lower fineness. We call his remining. The second case occurs in a sabilizaion, which follows a long period of successive debasemens. In his case coins are urned ino coins wih higher fineness, and we call i recoinage. Of course, he wo ypes of exchange require differen echnologies, as remining only requires adding cheap meal o coins, while recoinage requires exracion of silver from old coins before issuing new ones. Hence, recoinage is more cosly han remining. We formally assume ha recoinage coss x per one uni of exraced silver. We nex lay ou he informaional assumpions of he model. Firs, we assume, for he sake of racabiliy, ha mins operae a he beginning of each period before rade in goods akes place, namely before paymens by money are made. Our main assumpion is ha all coins look alike for ordinary folks and canno be disinguished wihou help of expers, who are called money changers. Such help is 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 chooses one ime in each period o evaluae his coins. We also assume ha during a period many ransacions ake place and coins circulae many imes. As a resul individuals canno keep rack of he composiion of coins hey use and hold. Hence, heir opimal sraegy is o check coins a he beginning of each period, in order o decide which coins should be remined, which coins should be urned ino silver and which should be kep in circulaion. During he period, when goods are coninuously raded, he se of coins changes, he informaion is los and all coins look alike. Hence, as a resul of 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. 0
We would like o furher discuss our informaional assumpion ha coins wih differen fineness could no be disinguished in ordinary daily ransacions, bu only by money changers. In oher words coins circulaed by ale and no by weigh, or no by inrinsic value. This is a raher srong assumpion, as poined by Rolnick, Velde and Weber (996), since i means ha agens repeaedly remin heir old coins and hus lose seignorage on hese coins. We have hree hisorical findings ha suppor his assumpion. The firs is he evidence on inflaion in commodiy prices during debasemen episodes, as documened in Sussman (993). This means ha coins were used as numeraire in heir face value, and commodiies were no priced by silver, even in imes of repeaed debasemens. The second finding is ha he volume of mining and remining was high during periods of debasemens, as shown laer in he paper, and so was he volume of seignorage. Since i is no likely ha mins coined only new bullion, i is reasonable ha much of heir aciviy was remining. The laer conclusion is also suppored by evidence from coin hoards of he ime. These show ha during sable periods he public held a variey of coins from many vinages, bu hoards from periods of debasemens conain mosly he newes vinages and almos no old coins. This is evidence for circulaion by ale and no by weigh, since agens would no mind holding old coins if hey had circulaed by weigh. We nex describe individuals in he model economy. There is a coninuum of size one of consumers wih infinie life horizon. Each supplies one uni of labor in each period and hus produces uni of good. For he sake of simpliciy hey are assumed o be risk neural. They derive uiliy from consumpion and from money holdings. This model herefore follows he radiion of money in he uiliy funcion, which began wih Sidrauski (967), and follows he open economy version in Obsfeld and Rogoff (996, Ch. 8). Uiliy of individuals in ime 0 is:
(2) m U = ( + ρ ) c + v, = 0 P where m is he amoun of money (coins) held by he individual a he beginning of period, afer all ransacions a he min are compleed, and v is concave. For he sake of simpliciy we assume ha he subjecive discoun rae is equal o he ineres rae, i.e. ρ = r. The governmen imposes no axes and finances is aciviy by seignorage only. In each period i ses boh fineness f and a seignorage rae s from mining new coins and uses he seignorage revenues o finance is expendiures. We assume ha hese expendiures are impors from abroad and hence he governmen mus exrac he silver from he revenues domesic coins. The silver value of hese revenues is herefore: g = hs n f (-x) where n is he amoun of mining and remining, namely of producion of new coins. An alernaive assumpion, ha he governmen uses is seignorage revenues for domesic purchases raher han impors would no change he main resuls of he paper. Hisorically, he crown used seignorage income for boh ypes of purchases, bu we need o se some assumpions in order o close he model. 5 Finally, he governmen can also sabilize he currency. A sabilizaion consiss of replacing he old coins wih new ones, which have higher fineness, namely reduce he min price Q and fix i a he new lower level hereafer. We assume ha all markes are perfecly compeiive and ha expecaions are raional. We firs analyze a process of debasemens and inflaion, assuming all fuure policies o be fully known in advance. In he nex sage we add a possible sabilizaion and allow for uncerainy wih respec o he iming of he sabilizaion, which ends he process of debasemens. 2
4. Mining Decisions and Prices We begin our analysis of equilibrium dynamics by looking a mining, remining and exracion decisions of agens. Remember ha his decision is aken in he beginning of he period, afer he consumer akes he sock of money o he exper and learns wha coins he has. Firs, as long as he price of silver, which is also he price of he consumpion good P, is less han he min price Q, here is incenive for more mining and he quaniy of money increases. Second, remining occurs for all coins wih sufficienly high fineness, namely if i can increase he number of coins. Formally, all coins wih fineness f such ha f (3) hfq = ( s ) f are remined. Noe ha fineness is non-increasing over ime, namely f f for all, and he inequaliy is sric when a debasemen occurs. Hence, all coins from periods prior o τ(), where f τ ()(-s ) < f and f τ ()-(-s ) f, are remined in, and f τ () is he highes fineness held by agens. Consumers can also bring coins o he min o exchange wih silver, as long as he value of exraced silver exceeds he number of coins used. Hence, hey exrac he silver from coins of fineness f u if (4) P hf u. x The supply of money can herefore be described by a sep funcion, as in figure. The amoun of money m,r is he amoun afer remining and before bullion mining or exracion ake place. This amoun does no depend on he price P, since remining does no depend on price, as seen in equaion (3). The demand for money is he 5 The crown indeed lised in is accouns he silver value of is seignorage revenues. 3
demand of consumers only, as he governmen impors only. The demand for money is proporional o he price level P and is presened in Figure by a ray from he origin. The equilibrium, which deermines he equilibrium price level and he equilibrium quaniy of money is deermined by he inersecion of he supply sep funcion and he demand for money. The equilibrium price mus, herefore, be wihin he following range: (5) P Q = ( s ). hf x hf Figure presens hree possible equilibria. If he demand for money is small, as in D, coins are ransformed o silver by exracion and m =m. If he demand for money is large, as in D, bullions are mined ino coins and m =m. If he demand for money is D, here is neiher silver exracion nor silver mining and m =m,r. 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, since he equilibrium price exceeds he min price. Thus, repeaed debasemens lead o inflaion, which is analyzed in he nex secion. 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 Q. 4
5. Debasemens and Inflaion In his secion we consider he case of repeaed debasemens a a fixed rae π. Consider he following moneary policy: he governmen collecs seignorage a a fixed rae, namely s = s, and i debases he currency every period a a fixed rae π, i.e. Q f (6) = = + π Q f for all. 6 If he rae of debasemen is fixed, here is a fixed number of ypes of coins in circulaion, which we denoe by T. Every period a new coin is inroduced and he oldes coin is remined. T is bounded by he following inequaliies, which are derived from (3): T (7) ( + π ) ( s) <. + π We nex show ha afer a few debasemens he price P becomes equal o he min price Q. To see his noe ha he moneary dynamics are: T (8) m = m + n T [( + π ) ( s) ] + Qe, where n is he amoun of coins mined in ime and e is he amoun of bullion mined ino coins in. If here is no mining of new bullion, we ge from (8): m T m [( + π ) ( s)] 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 hence afer a few debasemens here mus be mining of new 6 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. 5
silver. Noe ha silver is mined only if he equilibrium price equals he min price, as shown in Figure, and hence: (9) P = 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. 7 In he res of he secion we focus on he seady sae equilibrium. As we have seen he rae of inflaion a he seady sae is π and he price is equal o he min price. We differeniae beween wo 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 high so here is only one coin in circulaion, i.e. T=. In his case all former coins are remined. 5.. Debasemens wih Parial Remining We nex describe he seady sae disribuion of ypes of coins when he number of ypes T is greaer han. 8 The quaniy of coins of fineness f -u for all 0 u T- is he quaniy of coins mined in period -u, and is equal o (0) = u u ( + π ) T n m π + π ( + π ), where m is he aggregae amoun of money, which we derive nex. Noe ha he disribuion of coins as described in (0) is boh economy-wide and also holds for any individual by end of rading period, due o high circulaion of coins. 7 We should sress here ha even if he governmen uses is seignorage revenues wihin he counry and as a resul he equilibrium price is no always equal o he min price, he main resuls of he model do no change a all. 8 I can be shown ha he disribuion of coins converges o his seady sae disribuion. 6
The individual maximizes uiliy (2) wih respec o he budge consrains. We nex calculae he marginal benefi and marginal cos of holding money in order o find he demand for money. The marginal uiliy of real money balances is v m / P ). ( In calculaing he marginal cos of money he individual akes ino consideraion ha some coins will remain in circulaion in nex period and some will be remined, hus having differen raes of reurn. Since he individual has no conrol over he disribuion of coins he will hold by end of period, he can only calculae he expeced marginal cos of holding money, based on he disribuion (0). The marginal real cos of holding coins, ha will no be remined nex period, is due o inflaion and loss of ineres, namely: (). + r + π The marginal cos of holding coins, which will be remined nex period, is lower, since remining increases he number of coins, and is equal o: (2) T ( + π ) ( s), + r + π which is smaller han () due o (7). Given he disribuion of coin ypes (0) we ge ha he expeced marginal cos of money is: T ( + π ) + π ( s) (3) T. + r + π ( + π ) Equaing he marginal cos and marginal benefi of money yields he equilibrium real balances in he economy, since only consumers hold money: T m ( + π ) + π ( s) (4) v = T. P + r + π ( + π ) This equaion shows ha in equilibrium real balances (he demand for money) depend boh on he rae of inflaion and on he rae of seignorage. Furhermore, he number of 7
coins in circulaion T is an endogenous variable, which depends on hese wo variables as well. In order o see how real balances depend on π and s in he reduced form, consider he raes of debasemen, a which he number of coins changes and T falls from T+ o T. This rae is deermined by he condiion: ( + π ) ( s) =. A his rae he marginal coss of all ypes of coins are equal and given by (). Hence, he equilibrium real balances are described by: (5) m v P r + π + rπ =. ( + 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. While equaions (4) and (5) deermine he equilibrium sock of money, our daa from Medieval France consiss only of flows of mining, as repored by he various mins. Luckily, our model enables us o easily find he flow of mining, which depends on he demand for money and on he disribuion of coin ypes. The amoun of mining n is herefore given by: (6) n P π + π ( + π ) = T m P. From his equaion we see ha inflaion affecs mining in hree channels. Firs, he overall demand for money m/p 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 he RHS of (6). 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 equal o: 8
(7) n P π m = s + π P. 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. Mining is negaively affeced by π if his elasiciy is greaer han /(+π). 9 Mining is also affec by he rae of seignorage, which has a negaive effec. 5.2. Debasemens wih Full Remining We nex examine he case where inflaion is so high, ha all he old coins are remined and here is only one coin in circulaion, i.e. T=. This case holds when (8) ( + π )( s) >. In his case he marginal cos of money is given by (2), since all coins are remined, and is equal o: s. + r Equaing he marginal cos wih he marginal benefi of money yields: (9) m v P r + s =. + r Hence, he demand for money in his case 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, in addiion o heir ransacion value. When he rae of inflaion is high, holders of commodiy money can avoid some of he inflaion ax by remining. In 9 In our hisorical episode he effec of inflaion on mining is negaive, as shown in Secion 8. 9
doing so hey reduce heir losses o he fixed seignorage only. As a resul hey can hold more money and heir demand becomes insensiive o he inflaion rae. Noe ha his sraegy is no possible under fia money. 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 is (20) π s * = s. When inflaion exceeds π* and full remining prevails, he real amoun of mining is equal o real balances described in (9), since all coins are new. Hence, when inflaion exceeds π* he amoun of mining also depends on he rae of seignorage and no on he rae of inflaion. Secion 8 presens some empirical evidence ha suppors his heoreical resul. 6. Debasemens and Sabilizaion In secion 5 we describe a debasemen process ha goes on forever. This is a helpful bu no very realisic simplificaion. Rulers could no debase he currency forever by bringing fineness as close as possible o zero, since a very low levels fineness becomes indisinguishable from zero and commodiy money loses all is value. This level could no be reached and he public knew i as well. 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. In his secion we add he effec of his anicipaion o he analysis and bring i closer o realiy. We assume as above ha here is a fixed rae of debasemen π and a fixed rae of seignorage s, and ha he rae of debasemen is so high ha agens remin all coins every period. We assume ha he probabiliy of 20
2 sabilizaion is posiive, and denoe his probabiliy in period by z. Laer on, we make his probabiliy endogenous as well. We solve he model in wo sages, afer and before he sabilizaion akes place. We firs calculae he opimal value of uiliy from he sabilizaion on, when he economy reurns o full cerainy and o full price sabiliy. If sabilizaion occurs in period, hen opimal uiliy V S depends on he accumulaed amoun of silver bullion b - and on he amoun of real balances held, and is equal o (2) *) ( * ) )( ( ) (, l v r r l x s P m r b r r P m b V S + + + + + + = where l* is he amoun of real balances afer sabilizaion, which is deermined by (22) r r l v + = *) (. Denoe by V he opimal value of uiliy prior o he sabilizaion in period. Then he Bellman equaion is: (23) + + + + + = + + S P m b V r z P m b V r z P m v c P m b V,, max, under he consrain: (24) P m b r b s P m c + + + + = ) ( ) )( ( π. Before we derive he firs order condiions, noe ha due o he envelope heorem, he parial derivaives of V are (25) ) )( ( and s P P V r V l b + = + = π. The firs order condiions of (23) are, herefore:
z+ z+ (26) = ( + r) + Vb, + r + r which indeed fis (25), and: m z+ z+ P (27) v = ( s)( x) ( + π )( s). P + r + r P Hence, he demand for money falls as he probabiliy of sabilizaion rises. We nex urn o find he rae of inflaion. We prove ha if he seignorage rae is high enough, which has been he case in our hisorical episodes, price equals he min price Q. The equilibrium price is affeced by opposie demand and supply effecs. On he one hand demand for money is reduced as probabiliy of sabilizaion increases. On he oher hand, if here is no mining of new bullion, money supply grows by ( + π )( s) according o (8), which is much lower han he rae of debasemen π. Hence, if he rae of seignorage s is sufficienly high here is always mining of new bullion and he equilibrium price equals he min price. 0 Hence, he rae of inflaion is equal o π. Subsiuing in (27) yields: + (28) m r + s + ( s) xz+ v = P. + 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, since agens wish o minimize he cos of recoinage, of convering debased coins o 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 22
here is a minimum level of fineness f*. 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, namely i is (29) = T * z +. Fineness falls a a rae π, and hence he ime unil T* can be deduced from ( T* ) f * = f T * = f ( + π ). Hence, he probabiliy of sabilizaion is (30) 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. 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 largely from original min accouns found in he naional French archives and in he regional archive of he Isere a Grenoble. These 0 Noe ha wihou his assumpion he price would be higher han he min price bu he qualiaive resuls of he model would remain he same. This is herefore only a simplifying assumpion. For greaer deail see Sussman (997). 23
periodical accouns were submied by he mins o he cenral moneary adminisraion in Paris and conained informaion abou he characerisics of he coins produced, he quaniy mined, he coss, he seignorage revenues and he ne profi of he min. Due o losses, fires and wars he exen of coverage of he documens is no complee. We have daa only for some of he mins and in many cases here are gaps in he daa for cerain years. Nowihsanding, he daa we have allows us o assemble a daa se ha covers he major periods of debasemens during he 350s and beween 45 and 422 from 2 mins of varying imporance and geographical locaions. 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 Paris was no uniform. The accouns cover periods as shor as one day o periods as long as fifeen monhs, and he average lengh of accoun is one monh. Accouning periods varied beween mins and over ime. Under normal circumsances accouns were submied every six monhs or annually. However, during he debasemen period, he accouns were submied more frequenly. This phenomenon reflecs he igher fiscal conrol over he mins, which had o submi he accouns and he profis on a more imely basis. Moreover, he accouns were usually closed, under royal direcive, following changes in any of he characerisics of he coinage. In periods of debasemen he changes were frequen and herefore he accouns cover shorer periods. A furher complicaion arises from he fac ha royal orders reached mins wih varying delays, due o he large disances beween he mins and Paris, due o problems of ravel in war zones and due o necessiy o someimes pass hrough provincial adminisraive ceners. 24
Alhough he daa is in varying lenghs of ime, hey cover coninuos periods of ime for he 2 mins. Hence, hey enable us o calculae he main variables and how hey evolve over ime. The variables ha are relevan for he model are min prices, raes of inflaion, seignorage raes, and amouns of mining. The daa are pooled and allow us o draw some generalizaions and o es he hypohesis derived from our model. We firs presen some descripive feaures of he daa on French debasemens in he years 330-436. The firs debasemen period was characerized by repeaed cycles of debasemen and revaluaion. 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 360 saw 5 rapid debasemen cycles ha reached hyperinflaionary magniudes in 360 (figure 3). The average increase in he nominal value of silver during such a cycle was 200 percen and he average duraion of a debasemen cycle was 400 days. The larges debasemen cycle increased silver price by 600 percen, and lased only 6 days. The smalles cycle increased price by 66 percen. The shores debasemen cycle was 33 days during which he nominal value of silver increased by a 00 percen. The period from 47 o 422 was characerized by a prolonged process of debasemen during which he nominal value of silver was increased by 3500 percen wihou any aemp o sabilize he currency (figure 4), milder debasemens (average of 80 percen per cycle) followed unil 436 (figure 5). This descripion of he dynamics of silver prices in his period shows ha indeed he governmen could inflae commodiy money in high raes. The debasemens resuled in subsanial mining and large governmen revenues. While complee daa for all he mins operaing in France is lacking, he daa we found a he French archives allows us o assess he quaniaive aspecs of 25
hese debasemen episodes. Figure 6 shows he min oupus of four major French mins. The oal min oupu for he four mins in 355 was abou 75,000 marcs of pure silver (20 ons) whereas he annual average of oal mining in France in non debasemen years was 5,000 marcs. The revenues secured by he governmen were also impressive: according o Maurice Rey, he 49 seignorage revenues amouned o six imes ordinary royal revenues. Figures 7, 8 and 9 show, respecively, mining levels and seignorage revenues a he mins of Rouen, 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 he experience of Rouen (Figure 7) and Monpelier and (Figure 8). In 356, following he capure of King Jean by he English a Poiiers, 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. We furher add assumpions ha make he rae of inflaion equal o he rae of debasemen, he rae of increase of min price. I is ineresing o examine wheher hisorical daa can jusify hese assumpions. Unforunaely, high qualiy price daa for France are lacking. Neverheless, reproducing in Table daa repored by Sussman (993) for he Dauphine, we see ha grain prices followed he course of min prices whereas he price of gold followed he price of silver. 8. Empirical Analysis Our model describes how he demand for commodiy money and he amoun of mining are relaed o hree main variables: he rae of inflaion, he rae of seignorage 26
and he anicipaed probabiliy of sabilizaion, and how his relaionship changes a differen levels of inflaion. Since we do no have daa on he quaniies of money bu raher on he amouns of mining, we use his daa o es he main conclusions of he model. Namely we examine how mining depends on he rae of inflaion, on he rae of seignorage and on he probabiliy of sabilizaion. Before we describe he empirical analysis in deail we address he issue of he correlaion beween he seignorage rae and he rae of inflaion. We know from our records ha as inflaion increased so did he rae of seignorage, as he ruler ried o exrac greaer income from debasemens. There is a clear posiive correlaion beween he rae of decline of fineness and he rise in seignorage rae. We have calculaed hese correlaions for various mins and hey are no so high, namely less han 0.5. Hence, he wo variables, inflaion and seignorage are relaed bu can sill be used as explanaory variables in regression analysis. Our empirical analysis has wo pars. In he firs par we examine a basic equaion, of mining as a funcion of he rae of inflaion and he rae of seignorage, and excluding for he meanwhile he probabiliy of sabilizaion. We esimae his basic equaion considering wo cases, ha of low inflaion and parial remining and ha of high inflaion and full remining. Our hypohesis is ha he effec of he rae of inflaion is weaker a higher raes of inflaion. In he second par of he analysis we esimae a measure of he expeced probabiliy of sabilizaion based on he model and add his measure o he mining equaion as a hird variable. Our hypohesis in his case is ha mining is negaively relaed o he probabiliy of sabilizaion. Our regression esimaes are based on a panel of daa pooled from 2 mins ha includes he debasemens episodes described above. As discussed above, due o he varying lenghs of min accouns, he quaniies of mining are from periods of 27
ime of differen lenghs. In order o accoun for ha and o normalize he mining daa we added he lengh of he accoun period as an addiional explanaory variable o he regressions. The resuls of he firs par of he analysis are presened in Table 2. Regressions I and II in his able confirm he main hypohesis of our model, as described by equaion (8). We find ha mining is negaively affeced by boh he seignorage rae and he annual inflaion rae. We hen proceed o es wheher he effecs of inflaion and seignorage differ under low and high inflaion raes. We examine he effec of inflaion on mining a raes below and above 50%. Remember ha according o equaion (23) remining is full above π* = s/(-s). During he period when inflaion was bellow 50% he average seignorage rae was 27% wih a maximum of 50% which roughly corresponds o he inflaion rae calculaed from he model. When inflaion exceeded 50% he seignorage rae was higher a 37% on average and wih a maximum rae of 75%! Indeed, equaions III and IV in Table 2 show ha he effec of inflaion is much larger and more significan han he effec of seignorage in levels of inflaion below 50 percen. However, as shown in equaions V and VI in Table 2, a higher inflaion raes - around 00% - wih complee remining, we find ha he effec of he seignorage rae dominaes ha of inflaion, and ha he effec of inflaion even becomes zero and insignifican. In he second par of our empirical analysis we add a hird explanaory variable, namely he probabiliy of sabilizaion. Following is an explanaion of how his probabiliy is esimaed. 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: 28
T * log f log f * (3) = + 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. The esimaed equaion yields he probabiliy of sabilizaion as a funcion of hese wo variables. This regression is presened in Table 3 and i indeed shows ha he ime o sabilizaion decreases wih inflaion and increases wih fineness. Therefore, he probabiliy of sabilizaion rises wih inflaion and is negaively relaed o fineness. Afer esimaing he probabiliy of sabilizaion as described above, we add his probabiliy as an explanaory variable o he mining equaion. This is presened in Table 4, which shows ha his probabiliy has a significan negaive effec on mining, beyond ha of he seignorage rae and of inflaion. Noe ha his resul is in conras o he effec of expeced sabilizaion in an economy wih fia money, in which anicipaed sabilizaion increases he demand for money. Here i reduces i. As menioned above, his resul can resolve wha Rolnick, Velde and Weber (996) presen as an empirical puzzle. They claim ha he amoun of mining during debasemens is oo small o jusify circulaion by ale. We show ha if we ake ino consideraion he probabiliy of sabilizaion, i can accoun for smaller demand for commodiy money and for less mining during he las phases of debasemen episodes. 9. Summary and Conclusions In his paper we show ha inflaion and even high inflaion is possible under a commodiy money regime. Inflaion can exis in such a regime because people prefer o use coins raher han he commodiy iself. Thus, if he commodiy (silver) conen in coins is reduced coninuously, inflaion occurs. The possibiliy of high inflaion due 29
o debasemens is shown no only in a model, bu also demonsraed by a hundred years of frequen debasemens in medieval France. Therefore he hisorical commodiy money regime was quie similar o he more modern fia money regime and for a similar reason, namely ha people prefer money for ransacions over oher asses. Despie his basic similariy beween commodiy money and fia money, we observe wo main differences beween he wo. Under commodiy money he demand for money falls less when inflaion becomes high. This is because coins sill reain some inrinsic alernaive value and can be used for remining. Anoher imporan difference is wih respec o demand for money when sabilizaion is anicipaed. While under fia money his increases he demand for money, under commodiy money such a sabilizaion requires coin holders o recoin heir money a a subsanial cos, hereby reducing he demand for money when sabilizaion is anicipaed. We es for hese wo resuls using daa found in French archives and are able o corroborae hem. Though we do no have direc daa on he demand for money, bu raher on mining, we show ha mining behaves as indicaed by our model, namely ha i declines wih inflaion in low inflaion environmen and becomes less affeced by inflaion when he raes are high. Furhermore, we are able o show ha mining declines wih he increase in he probabiliy of expeced sabilizaion. Our model, findings and conclusions are no limied o France during he Hundred Years War. There were numerous periods of debasemens in Europe in he early modern period, in he Low Counries, Spain, England, in Ialian ciy saes, in Germany and in he Ooman Empire. Though French daa are perhaps he mos exensive and of he highes qualiy, we believe ha our approach can be used o explain similar episodes in oher counries and over a large period of ime, characerized by he use of commodiy money. 30