Reconstruction of the Spanish money supply, 1492–1810

Explorations in Economic History 81 (2021) 101401 Contents lists available at ScienceDirect Explorations in Economic History journal homepage: www.elsevier.com/locate/eeh Shorter Article Reconstruction of the Spanish money supply, 1492–1810 ☆ Yao Chen a , Nuno Palma b , c , d , Felix Ward e , f , ∗ a Erasmus School of Economics, Erasmus University Rotterdam, The Netherlands b Department of Economics, University of Manchester, United Kingdom c Instituto de Ciências Sociais, Universidade de Lisboa, Portugal d Centre for Economic Policy Research, London, United Kingdom e Erasmus School of Economics, Erasmus University Rotterdam, Burgemeester Oudlaan 50, 3062 PA Rotterdam, The Netherlands f Tinbergen Institute, The Netherlands a r t i c l e i n f o JEL classification: E31 E51 N13 Keywords: Early modern period Equation of exchange Quantity theory of money a b s t r a c t How did the Spanish money supply evolve in the aftermath of the discovery of large amounts of precious metals in Spanish America? We synthesize the available data on the mining of precious metals and their international flow to estimate the money supply for Spain from 1492 to 1810. Our estimate suggests that the Spanish money supply increased more than ten-fold. Viewed through the equation of exchange this money supply increase can account for most of the price level rise in early modern Spain. 1. Introduction This paper presents new times series for the Spanish money supply in the early modern period (1492–1810). This period has been interesting to economic historians and monetary economists alike. The influx of vast amounts of precious metals from Spain’s American colonies, together with a rising price level, gave birth to early formulations of the quantity theory of money at the School of Salamanca. Today, research into the economic consequences of the inflow of American precious metals into Europe continues ( Brzezinski et al., 2019; Palma, 2019, 2021 ). We hope that the money supply estimate we provide in this paper generates new inroads for the quantitative analysis of this unique period in monetary history. To estimate the Spanish money supply, we combine the available information on initial stocks with data on global mining output and international precious metal flows. The available information comprises data on the mining of precious metals in America and Europe, American retention of precious metals, precious metal flows across the Atlantic and Pacific (including transport losses), money outflows from Spain and Europe, and numismatic evidence on the wear of coins, as well as melt losses associated with their minting. To the best of our knowledge, we are the first to combine this information to obtain a money supply series for Spain in the early modern period. Throughout, we account for uncertainty about the underlying data by using stochastic simulations that translate data uncertainty into a probability distribution for the Spanish money supply. Our estimate suggests that the Spanish money supply, measured in tonnes of silver equivalent, increased more than ten-fold between 1492 and 1810. ☆We thank K ı vanç Karaman, Nicholas J. Mayhew, and Pilar Nogues-Marco, François R. Velde, as well as participants at various seminars and conferences for helpful comments. We are grateful to Carlos Álvarez-Nogal, K ı vanç Karaman, Leandro Prados de la Escosura, and Pilar Nogues-Marco for sharing their data with us. Any remaining errors are our own. Nuno Palma acknowledges financial support from Fundação para a Ciência e a Tecnologia (CEECIND/04197/2017). Replication data and codes are available at https://doi.org/10.3886/E139761V2 ( Chen et al., 2021 ). ∗ Corresponding author. E-mail addresses: [email protected] (Y. Chen), [email protected] (N. Palma), [email protected] (F. Ward). https://doi.org/10.1016/j.eeh.2021.101401 Received 8 May 2020; Received in revised form 21 April 2021; Accepted 29 April 2021 Available online 7 May 2021 0014-4983/© 2021 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ ) Y. Chen, N. Palma and F. Ward Explorations in Economic History 81 (2021) 101401 While we focus on calculating the Spanish money supply, we also take a first look at what the new series implies for a long-standing question in monetary history: to what extent does money growth account for rising prices in the early modern period? We confirm that money growth accounts for most of Spain’s price level rise between 1492 and 1810. 2. Money and precious metal inflows in early modern Spain Coin in early modern Spain was commodity money. Silver was the most important monetary metal, although gold was used for coins of high denomination. 1 Coins made of precious metals were more widely accepted than banknotes or bills of exchange ( Nightingale, 1990 ). In continental European countries, precious metal coins typically accounted for more than half of the money supply as late as 1860 ( Flandreau, 2004 , p.3). For Spain in particular, gold and silver still made up around 85% of the money supply in 1875 ( Tortella et al., 2013 , p.78). Our analysis therefore focuses on the narrow monetary aggregate consisting of gold and silver coins, which we interchangeably name “money ”in the following. 2 Spain’s money supply was heavily influenced by the inflow of silver and gold from America ( Desaulty et al., 2011 ). Annual Atlantic inflows were large, and primarily consisted of remittances, transfers of incomes from abroad, and capital inflows. Less than a third of precious metal inflows constituted payment for Spanish exports (based on total export values from Phillips, 1990 , p.82). In terms of their functionality, liquidity, and acceptance as a means of payment, precious metal coins are comparable to narrow money aggregates today. In contrast to today’s cash, early modern commodity money was not supplied by central banks, but minted by a mint on request of its customers. Precious metal mines were owned and run by private entrepreneurs ( Elliott, 2006 , p.93), and 85% to 95% of precious metal remittances from the Spanish American colonies were privately owned ( García-Baquero González, 2003 ; Costa et al., 2013 ). 3 The government, however, owned the Imperial mints, set mint fees, decided upon which denominations to issue, and set the rate at which precious metals were exchanged for coin (the mint price). 4 Commodity money possesses a higher intrinsic value than fiat money. This is because the same precious metals that are used to produce commodity money can also enter the economy’s production function as intermediate inputs for the production of other goods such as silverware ( Mayhew, 2012 ). Thus, when the commodity market value of precious metals rose above its mint price, an arbitrage profit could be realized by melting down coins and selling the metal on the commodity market. The primary function of American precious metals, however, was monetary. Regulation required all precious metals arriving from America to be brought to the Casa de Contratación. Private owners could pick up their silver from there, but had to submit a certificate of coinage from a mint of their choice within six months ( Hamilton, 1934 , pp.25, 29). 5 At least from the 18th century onwards, most of Spanish America’s mining output was directly minted in American mints ( Céspedes del Castillo, 1996; Irigoin, 2020 ), and thus the vast majority of precious metals from Spanish America arrived in Spain as coins ( Costa et al., 2013; de Paula, 2016 , p.63). 3. Money supply estimate 3.1. General methodology We calculate the Spanish money supply by combining an estimate of the Spanish money stock in 1492 with data on Spanish precious metal inand outflows. To correct for the wear of coins we apply an annual depreciation rate of 0.24%. This value lies at the center of the 0.2% to 0.28% range that numismatic research has established for the depreciation of coins through wear ( Mayhew, 1 Copper also played a monetary role in the form of small change. The prominence of copper money fluctuated over time ( Motomura, 1994; Sargent and Velde, 2002 ). Only for a few decades after 1617 did copper coins make up a substantial share of the Spanish money stock ( Velde and Weber, 2000a ). Appendix B.3 summarizes the available quantitative information on the Spanish copper coin supply. 2 Spain at the time was a composite monarchy under the same ruler. The dominant polities were Castile and Aragon. Our money supply estimate does not distinguish between different coins that existed in different parts of Spain ( Mateu y Llopis, 1946 , pp.253–274 provide an overview in this regard). Instead, we focus on the total money supply of Spain as a geographic entity in its modern borders. 3 Only in the late 18th century did the Royal Treasury’s share of precious metal remittances increase above 20%. 4 Spain’s early modern network of mints was distributed across many cities (Burgos, Coruña, Cuenca, Granada, Segovia, Seville, Toledo, Valladolid). Total mint output, however, was highly concentrated in Seville ( Mateu y Llopis, 1942; de Paula, 2016 ), which accounted for around 80% of all coinage in the first half of the 17th century ( Motomura, 1997 ). Spanish mints became less active over time, as silver was increasingly minted in America. According to de Paula (2016 , p.366), only 6% of Spanish silver arrivals in the 18th century were minted in Seville. 5 For a precious metal flow to circumvent this regulation it had to be unregistered, i.e. smuggled. Unregistered inflows became important on the back of unregistered production between 1640 and 1720 (see Appendix A.3 ). In those decades, it is more likely that part of the precious metal inflow from America entered Spain for non-monetary use. Our stochastic simulation is informative about the extent to which this could influence the money stock estimate. This is because it accounts for the 1640–1720 rise in uncertainty surrounding unregistered production, which translates into rising uncertainty about Spanish inflows from America. To the extent that the amount of unregistered inflows was linked to the non-monetary use of metals, uncertainty about the former reflects uncertainty about the latter. As a consequence, the lower percentiles of the money stock probability distribution also delimit the effect that an increased non-monetary use of American precious metals could have on Spain’s money stock estimate. 2 Y. Chen, N. Palma and F. Ward Explorations in Economic History 81 (2021) 101401 1974; Velde, 2013 ). 6 The initial stock ( 𝑀 1492 ), inand outflows ( 𝑖𝑛 𝑘 , 𝑜𝑢𝑡 𝑘 ) and depreciation determine the money supply ( 𝑀 𝑡 ): 𝑀 𝑡 = 𝑀 1492 (1 − 0 . 24%) ( 𝑡 −1492) + 𝑡 ∑ 𝑘 =1493 [ (𝑖𝑛 𝑘 − 𝑜𝑢𝑡 𝑘 )(1 − 0 . 24%) ( 𝑡 − 𝑘 ) ] . (1) The money stock we calculate comprises gold and silver coins. It, therefore, is subject to a valuation effect deriving from gold-silver rate fluctuations. In early modern Spain, the price of gold vis-à-vis silver increased. As a consequence, the stock of gold coins expressed in silver equivalents increased. To account for this effect, we first calculate gold and silver stocks separately. 7 Before adding them up, we convert the gold stock into contemporary silver equivalents using the Spanish Empire’s official gold-silver rate ( Cross, 1983 , p.400). 8 The data that enters the calculation of the Spanish money supply comes with a considerable degree of uncertainty. To account for this, we use stochastic simulations to accompany each point estimate of the Spanish money supply with a probability distribution. The setup of the stochastic simulation in accordance with the type and degree of data uncertainty we face is provided in Appendix A.1 . Initial stock As the baseline estimate for Spain’s initial money stock we use the mid-point of a range of initial stock estimates. The bounds of this range are demarcated by the estimates of Velde and Weber (2000b) and Jacob (1831) . The discussion of initial stock estimates in Appendix A.2 shows how the values proposed by these authors emerge as the lower and upper bounds of plausible stock estimates at the eve of the early modern period. According to Velde and Weber the global precious metal stock in 1492 amounted to 3600 tonnes of silver and 297 tonnes of gold. 9 We calculate the Spanish part of this according to Spain’s share of global economic activity ( Bolt et al., 2018 ). Adding gold to the silver stock at Spain’s official silver-gold rate results in 228 tonnes of silver equivalent. This is the lower bound value for Spain’s initial money supply. Jacob’s initial European stock value of 1749 tonnes of silver equivalent. According to Spain’s share of European economic activity this translates into 565 tonnes of silver equivalent. 10 The mid-point of the 228 to 565 tonne range – 396 tonnes of silver equivalent –serves as the baseline estimate for Spain’s initial money stock. 11 Inflows The precious metal inflow series for Spain starts from the mining output data for Spain’s American colonies ( TePaske, 2010 ) ( Appendix A.3 ). We transform this production data in the following way to arrive at Spanish precious metal inflows from America. First, we subtract the amount of precious metals that went directly from America to Asia ( Bonialian, 2012; Borah, 1954; Chuan, 1969; Schurz, 1939 ) ( Appendix A.4 ). Second, we account for the amount of precious metals that stayed in the Americas ( Barrett, 1990; Irigoin, 2009; Walton, 1994 , p.245). 12 Third, we account for the loss of precious metals in maritime disasters and pirate attacks ( Appendix A.5 ). Such losses could be large. In our sample they amounted to almost 5% of all American production ( Potter, 1972 , 6 Note that several other publications have chosen a 1% depreciation rate ( Motomura, 1997; Velde and Weber, 2000b ). The value of 1%, however, accounts for more varieties of precious metal loss than pure wear, e.g. transport losses and trade deficits ( Mayhew, 1974; Patterson, 1972 ). Here, we focus on depreciation through wear, because our money stock measure separately accounts for trade-related precious metal outflows and transport losses. Undisclosed hoards are another reason for the disappearance of part of the money supply. Such hoards typically arise from emergency situations (especially wars) in which owners are unable to subsequently recover their hoard – either because they were permanently displaced, or because they did not survive the emergency. For example, early modern English hoards often stem from the English Civil War ( Mayhew, 1995 ), and French hoards from the early years of the French Revolution ( Velde, 2013 ). With the exception of Napoleon’s Peninsular War after 1808, no similarly far-reaching conflict unfolded on Spanish territory. This lowered Spanish hoard owners’ prospect of permanent displacement and unexpected death, and thus the incidence of undisclosed hoards in early modern Spain. 7 While the gold and silver production data allow us to calculate separate goldand silver inflows, we have to make assumptions about how various other flows (outflows, transport losses, and diffusion flows) were divided between gold and silver. We assume the allotments corresponded to the production shares. This ensures that the gold-silver composition of the Spanish money stock stays in line with mining output. This is broadly consistent with the observation that Spain’s monetary system remained a bimetallic one throughout the early modern period, which implies that imbalances in the outflow of gold and silver must have been limited. We set the initial gold-silver share in accordance with the data by Velde and Weber (2000b) . 8 The Spanish Empire’s official gold-silver rate was periodically adjusted to keep it in line with market rates across Europe. This is a necessary requirement to prevent the collapse of a bimetallic monetary system into a monometallic one according to the prediction made by Gresham’s Law. 9 Throughout the paper “tonnes ” refers to metric tonnes. 10 Given Spain’s population level at the time, this translates into 106.6 grams of silver per person. The European countries upon which Spain’s European GDP share is based include Belgium, Finland, France, Germany, Greece, Italy, the Netherlands, Poland, Portugal, Spain, Sweden, Switzerland, and England. 11 The use of GDP-shares as indicative of precious metal shares has some theoretical appeal. Assuming that purchasing power held in the long-run and that velocities did not differ substantially across countries, it follows from the equation of exchange, 𝑀𝑉 = 𝑃 𝑌 , that the international money stock distribution behaves according to real GDP-shares. The stochastic simulation that generates the money supply distribution allows for deviations from this theoretical baseline ( Appendix A.1 ). As a consequence, the 95% probability interval for 1492 ranges from 185 to 676 tonnes, which goes beyond the 228 and 565 t values whose average forms the baseline estimate’s initial value. 12 Barrett (1990 , p.245) estimates that 15% of American precious metal production was either retained in America or lost in transport. In our sample, transport losses amount to a bit less than 4% of American production. This implies a 11% retention rate for American precious metals. Similarly, data from the mint in Mexican City in the 1770s shows that 75% of its output was exported to Spain, whereas the remaining 25% either stayed in America or went over the Pacific to Manila ( Walton, 1994 , p.181). In the 1770s around 7% of American metals went over the Pacific, 3 Y. Chen, N. Palma and F. Ward Explorations in Economic History 81 (2021) 101401 p.xix). Assuming that salvaged precious metals entered the European economy with a delay of one year, we add the amount of last year’s salvaged precious metals to the American inflow measure. 13 Transportation losses were initially borne by Spanish merchants. 14 Thus, in the short-run, transportation losses first impacted the Spanish money supply. Over time, however, transportation losses probably diffused across borders: Spain’s precious metal exports decreased, and its precious metal imports increased in the aftermath of a transportation loss. This type of diffusion is a standard feature of international monetary models, such as Hume’s price-specie flow model ( Hume, 1752 ), or the monetary approach to the balance of payments ( Flynn, 1978; Frenkel and Johnson, 2013 ). We assume that in the long-run, Spain bore precious metal losses in proportion to its world GDP share. For the interim between shortand long-run, we implement a linear diffusion process that lasts for 10 years –a time span long enough to encompass short-term adjustment dynamics. While Spanish America was the most important supplier of precious metals in the early modern period, mines in other regions continued to turn out non-negligible quantities of gold and silver. For example, silver mining in Europe experienced a boom in the early 1500s. 15 Part of this non-Spanish precious metal output diffused into Spain. To account for this, we calculate the part of Central and Eastern European production that flowed into Spain according to Spain’s share of European GDP, and add it to Spanish inflows. 16 First, however, we subtract that part of the European production that did not diffuse within Europe but flowed to the rest of the world. We assume that newly produced European metals were subject to the same outflow rate as all other European precious metals. Thus, we set the fraction of the European production that flowed to the rest of the world ( 𝜅𝐸𝑈,𝑜𝑢𝑡 ) equal to the European precious metal outflow-to-stock ratio, 𝜅𝐸𝑈,𝑜𝑢𝑡 = 𝑜𝑢𝑡 𝐸𝑈 𝑡 ∕ 𝑀 𝐸𝑈 𝑡 ≈0.79% ( Attman, 1986; de Vries, 2003 ). 17 We treat European precious metal arrivals from non-Spanish trading outposts and colonies, i.e. gold inflows from Africa and from Portuguese Brazil, analogously to European production ( Morineau, 1985; TePaske, 2010 ). 18 During the minting of coins, so-called melt losses consume part of the metal. Therefore, we remove one-time melt losses of 𝜆= 0 . 52% from the production data to arrive at coin output ( Mayhew, 1974 , p.3). All in all, we calculate Spanish precious metal inflows as 𝑖𝑛 𝑘 = 𝑝𝑟𝑜𝑑 𝐸𝑆𝑃 𝑘 −1 (1 − 𝑟𝑒𝑡𝑒𝑛𝑡 𝑘 )(1 − 𝜆) − 𝑝𝑎𝑐𝑖𝑓𝑖𝑐 𝑘 − 𝑙𝑜𝑠𝑠 𝑘 + 𝑠𝑎𝑙𝑣 𝑘 −1 ⏟⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏟⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏟ ≡𝑖𝑛 𝐴𝑀→𝐸𝑆𝑃 𝑘 + 𝑑𝑖𝑓 𝑓 𝑢𝑠𝑒 𝑘 + 𝜒𝐸𝑈 (𝑝𝑟𝑜𝑑 𝐸𝑈 𝑘 + 𝑖𝑛 𝑅𝑂𝑊 →𝐸𝑈 𝑘 )(1 − 𝜆) (1 − 𝜅𝐸𝑈,𝑜𝑢𝑡 𝑘 ) ⏟⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏟⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏟ ≡𝑖𝑛 𝐸 𝑈→𝐸 𝑆𝑃 𝑘 , (2) leaving an American retention rate of 18%. Up to 1780 we use the average of 11% and 18% as the American retention rate. Starting in the 1780s the U.S. began to absorb an important fraction of American silver, as it inserted itself as a key intermediary in the trade networks linking Spanish America, with the Pacific and Atlantic economies. The U.S. cemented its role as a conduit for Spanish American silver during the Napoleonic wars. U.S. silver import data available for the 1820s suggest the U.S. imported on average 6.8 million pesos per year ( Irigoin, 2009 , Appendix I), whereas Spanish American production amounted to 26.2 million pesos per year on average between 1780 and 1810. The ratio of these two quantities amounts to 27% of Spanish American silver production. Adding the 27% U.S. absorption to the pre-1780s retention rate of 14.5% yields a 40.5% American retention rate. Between 1780 and the beginning of the Napoleonic wars in 1803 our final American retention rate linearly interpolates between these two figures. 13 Instances when ships sank in very shallow waters and their treasure could be salvaged so quickly that it reached Spain without much delay are not included in the loss series. For example, the 1711 Nueva España fleet’s treasure was quickly salvaged in this way ( Marx, 1987 , p.353), as was the treasure of Farfan’s Tierra Firme Armada, which in 1555 stranded on Zahara beach, south of Cádiz ( Potter, 1972 , p.340). Only when salvaging operations dragged on for several months do we include losses into the loss series, and subsequently salvaged precious metals into the salvage series. We are aware of two events where salvaging operations lasted for more than one year. First, the salvaging of the 1715 loss continued until 1718, but returns to later salvaging operations rapidly diminished ( Peterson, 1975 , p.369). Second, the 1656 event, where repeated salvaging operations recovered part of the treasure, until shifting sands finally prevented further salvaging ( Marx, 1987 , p.316). Shifting sands were a more general problem that restricted the time horizon during which the lost treasure could be salvaged even if the ship sank in shallow waters. Marx (1987 , p.424) mentions the San José shipwreck of 1631 in this regard. Thus, a 1-year lag due to salvaging was the most common scenario for the losses we consider. We make no attempt at adjusting for the more protracted salvaging operations associated with the 1656 and 1715 losses. 14 By regulation, only Spanish merchants were allowed to engage in transatlantic business with the Spanish colonies ( Nogues-Marco, 2011 , p.6). Thus, although much of the precious metals arriving in Spain subsequently diffused throughout Europe, they first passed through a Spanish entity that was the initial owner. 15 Mining in Spain itself, however, came to a halt after the discovery of the far richer mines of America. 16 Up to 1600, the European production data comes from Nef (1941) , whereas afterwards it comes from Soetbeer (1879) . The data consists of bidecennial observations. We sum the linearly interpolated production data from all European regions to arrive at European precious metal production. We base our stock estimate on precious metal production data, rather than on official Spanish arrival data or mint output data for the following reasons: First, Spanish arrival data is less reliable ( Appendix A.3 ), and data for the first 150 years on American minting is scarce. In addition, mint output data contains re-coinages, which leads to a double counting problem. 17 The calculation of the European stock, 𝑀 𝐸𝑈 𝑡 , is described in Appendix B.1 . 18 In contrast to American production, a significant fraction of European production and African inflows was not minted into coins. For the 16th and 17th centuries, Jacob (1831) suggests that 20% was manufactured into ornaments or utensils. For the late 18th century, especially after 1780, Jacob (1831) puts this share at two thirds. Another estimate for 1688 by King (1696) puts it at 38.7%. To account for this non-monetary use of precious metals, we subtract 20% of European production and African inflows up to 1688. Between 1688 and 1780, we subtract 38.7%, and after 1780 we subtract 67%. 4 Y. Chen, N. Palma and F. Ward Explorations in Economic History 81 (2021) 101401 Fig. 1. Spanish money supply Notes: Lightest gray shade: 1/99th percentiles. Thereafter from light to dark gray: 5/95th to 45/55th percentiles. Dotted lines highlight 95% probability interval. Distribution based on 10,000 draws from the input variable distribution. Centered 11-year moving average, neglecting missing observations at the borders. where 𝑖𝑛 𝐴𝑀→𝐸𝑆𝑃 𝑘 and 𝑖𝑛 𝐸 𝑈→𝐸 𝑆𝑃 𝑘 are the summary terms for Spanish money inflows from America and Europe, respectively. 𝑝𝑟𝑜𝑑 𝐸𝑆𝑃 𝑘 −1 is the Spanish-American production, 19 𝑟𝑒𝑡𝑒𝑛𝑡 𝑘 is the American precious metal retention rate, 𝑝𝑎𝑐𝑖𝑓𝑖𝑐 𝑘 denotes precious metals leaving America through the Pacific, 𝑙 𝑜𝑠𝑠 𝑘 − 𝑠𝑎𝑙 𝑣 𝑘 −1 are Atlantic transportation losses less previous year’s salvaged treasure, 𝑑𝑖𝑓 𝑓 𝑢𝑠𝑒 𝑘 is the transportation loss diffusion term, 𝑝𝑟𝑜𝑑 𝐸𝑈 𝑘 is the European precious metal production, 𝑖𝑛 𝑅𝑂𝑊 →𝐸𝑈 𝑘 are other (non-Spanish) European precious metal arrivals, and 𝜅𝐸𝑈,𝑜𝑢𝑡 is the fraction of the European precious metal production that leaves Europe every year. 𝜒𝐸𝑈 denotes the sample average of Spain’s European GDP share, which we calculate based on the real purchasing power adjusted GDP data from Bolt et al. (2018) . Spain’s European GDP share fluctuates between 13% and 18%, with the sample average 𝜒𝐸𝑈 equalling 15%. Outflows Data on Spanish money outflows is relatively scarce. Attman (1986) and Walton (1994) provide the most comprehensive compilations in this regard. Their data indicates that the Spanish outflow ratio ( 𝑜 𝑘 ) –the fraction of Spanish money inflows from America, which left Spain – hovered slightly above 90% for much of the 17th century. In the late 17th century, this share increased to 100%. Only in the late 18th century did inflows systematically exceed outflows once again. 20 During severe military conflicts, outflows could temporarily exceed inflows from America, which was the case during the height of the Dutch War for Independence and the War of Spanish Succession. We are unaware of any source for Spanish precious metal outflows before the late 16th century. Therefore, at the beginning of our sample, we work with a 91% outflow rate, which is representative of Spanish outflows in the 17th and late 18th centuries outside of periods of severe military conflict. We use linearly interpolated values to bridge gaps in the Spanish outflow rate. The resulting series is displayed in Appendix A.6 , together with the individual observations from Attman and Walton that underpin it. Based on the outflow ratio, 𝑜 𝑘 , we calculate Spanish money outflows as 𝑜𝑢𝑡 𝑘 = ( 𝑖𝑛 𝐴𝑀→𝐸𝑆𝑃 𝑘 + 𝑙𝑜𝑠𝑠 𝑘 − 𝑠𝑎𝑙𝑣 𝑘 −1 ) 𝑜 𝑘 , i.e. as a fraction of Spanish money inflows from America excluding transportation losses. This renders the outflows consistent with the previously introduced diffusion assumption. It is important to note that this series is painted with a broad brush and conveys no information about short-run variations in Spanish money outflows. It is, however, consistent with the trends lined out by the available data. Money supply By plugging the inand outflow sequences, 𝑖𝑛 𝑘 and 𝑜𝑢𝑡 𝑘 , into Eq. 1 we obtain the money supply estimate for Spain. Fig. 1 depicts the centered 11-year moving average of the resulting baseline estimate as a solid black line. Gray-shaded probability intervals show 19 The one-year lag reflects the time delay between the mining of precious metals in America and their and their entering of the monetary circulation in Spain. 20 Outflows in the following are expressed as a fraction of Spanish inflows from America. This normalization does not imply that all the precious metals that left Spain were necessarily of American origin. Where Attman (1986) and Walton (1994) state an absolute Spanish outflow value without accompanying inflow, we divide this value by our inflow measure ( 𝑖𝑛 𝐴𝑀→𝐸𝑆𝑃 𝑘 from Eq. 2 ). 5 Y. Chen, N. Palma and F. Ward Explorations in Economic History 81 (2021) 101401 how the money supply estimate is affected by data uncertainty in the input variables ( Appendix A.1 ). Dotted lines highlight the 95% probability region. According to the baseline estimate, the Spanish money stock increased from around 400 tonnes in 1492 to around 6400 tonnes in 1810. For much of the sample period the upper and lower bounds of the 95% probability region cover a ± 30% range around this level. At the beginning of the sample this range is wider, ± 50%, reflecting the larger uncertainty about the initial stock level. By the late 1500s the influence of the initial stock uncertainty has faded and the 95% bounds converge to the ± 30% range. According to the baseline estimate, the Spanish money supply increased 16-fold between 1492 and 1810. The corresponding increases for the upper and lower bounds of the 95% interval are 13-fold and 22-fold, respectively. To account for the possibility that money supply sequences begin near the lower bound of the distribution in 1492, and end near the upper bound of the distribution in 1810 we also calculate the 95% probability interval for Spain’s early modern money supply increase. It ranges from ten-fold to 30-fold, implying an average annual money growth rate between 0.7% and 1.1%. Fig. 1 depicts the money supply series as an 11-year moving average. 21 As a consequence, the series’ low frequency variation is more reliable than its annual variation. Focusing only on the former, the Spanish money supply appears to have grown around a linear trend, with temporary stagnations occurring at the turns of the 17th and 18th centuries. 3.2. Validation In this section we present several validation checks for the Spanish money supply estimate we propose. We begin by checking whether the velocity implied by the baseline estimate is plausible. We calculate velocity by dividing the Spanish nominal GDP series from Álvarez-Nogal and Prados de la Escosura (2013) by our baseline money supply estimate. The resulting velocity averages 2.6, and ranges from 1.3 to 4.8. This is of similar magnitude as other velocity estimates for the early modern period. According to Mayhew (2013) , velocity in England ranged from 2.2 to 8.7, whereas Palma (2018) locates it between 3.5 and 8.8. For the year 1526, Lindert (1985) proposes an English velocity range of 2.4 to 6.2; our Spanish velocity value for that year is 2.6. Another way to validate the money supply estimate is to compare its 1810 end-point with money supply estimates for the 19th century. For 1875, Tortella et al. (2013 , p.78) report a Spanish money stock amounting to 7265 tonnes of silver equivalent. Our baseline estimate for 1810 is 6607 tonnes. This implies a modest money stock growth of 10% in the 65 years after 1810 (0.15% per year). This is consistent with global events. While silver inflows reached record levels in 1810, they collapsed afterwards ( Tutino, 2018 , p.244). This was due to British control of the Atlantic, the loss of Spanish control over its American colonies, and drastic declines in American silver production ( Walton, 1994 , p.196). In the turmoil following New Spain’s (Mexico’s) independence, its silver mining output remained at around half its 1810 level until 1840 ( Tutino, 2017 , p.175). On top of this, American retention rates increased as American populations grew quickly in the 19th century. 22 Against this backdrop, the 95% interval’s lower bound of 4285 tonnes for 1810 should be considered too low, because it implies that the Spanish coin stock grew at a similar rate after the independence of its American colonies as before. The actual 1810 money stock value is likely to lie closer to the baseline estimate. 23 3.3. Comparison to other money stock estimates How does our money supply estimate compare to other money supply estimates that have been proposed in the literature? For early modern Spain, two alternative approaches to estimating the money stock exist. The first approach approximates stocks by cumulating mint output over a period of time. The second approach counts mint output at a specific point in time –the late 18th century recoinage. This section discusses both these approaches. Spooner (1972 , pp.305-9), and later Challis (1978 , pp.234-8), approximate a country’s money stock by cumulating its mint output over 30 years. For Spain, this approach is more problematic than for other countries because it exported a large share of its mint output. Spanish mint output, thus, did not necessarily add to the Spanish money supply. Against this backdrop, it is perhaps not surprising that a 30-year cumulation of the gold and silver coin output of Spanish mints during the early 1600s results in an almost twice as high value as our baseline estimate ( Motomura, 1997 ). 24 Motomura himself notes that a substantial part of the coins minted during this period left Spain to finance military operations in the Low Countries. 25 However, the more persistent economic reason 21 Table D.1 in the Appendix tabulates the 11-year moving average series. Table D.2 shows the underlying annual series. 22 More generally, in the 19th century, for many countries the amount of precious metals they attracted increasingly fell short of output growth. Partly this gave rise to deflation, partly this was compensated by the 19th century growth in non-metallic forms of money, such as bank notes and bank deposits. 23 Carreras de Odriozola and Tafunell Sambola (2006 , p.678), based on unpublished work by Tortella (n.d.) , present another estimate for the Spanish stock of gold and silver coins in 1830 that amounts to 2214 tonnes of silver equivalent. The 1830 stock estimate is a mint output-based backward extension of stock estimates for the second half of the 19th century. As such, it is affected by the same problem as other mint output-based estimates of the Spanish money stock: As suppliers of an internationally accepted means of payment, Spanish mints produced more coins than were absorbed by the Spanish money stock, with the excess being exported. Thus, subtracting several decades of Spanish mint output to extend the Spanish money stock series backwards probably severely underestimates earlier stocks, as is pointed out by Tortella (n.d.) himself. 24 Motomura (1997 , Table 1, columns 5–6) separately reports minted gold and minted silver. We use the Spanish Empire’s official gold-silver rate to convert gold weights into silver equivalent ( Cross, 1983 , p.400). 25 The period after 1617 also witnessed a sharp increase in the issuance of copper money, which raises additional doubts about the applicability of the 30-year rule for the early 17th century ( Appendix B.3 ). 6 Y. Chen, N. Palma and F. Ward Explorations in Economic History 81 (2021) 101401 behind the export of Spanish coins was their status as an internationally accepted means of payment ( Irigoin, 2009 ). As such, Spanish pesos were used by various European trading companies for their East Asia trade. 26 Tortella (n.d.) presents a stock estimate for 1775 which is equivalent to 563 tonnes of silver. This estimate is based on Spanish mint output during the Empire-wide recoinage of 1772 to 1778. It is important to notice that the recoinage was not compulsory for private holders ( Hamilton, 1947 , p.66). As a consequence, not all money was re-coined. For example, in the viceroyalties of New Spain (Mexico) and New Granada (Colombia) only between 28% and 50% of the local money stock was recoined ( Moreno, 2014 ). This can explain why Tortella’s stock value for 1775 lies substantially below our baseline value. The 1775 GDP estimate by Álvarez-Nogal and Prados de la Escosura (2013) provides another reason to prefer a higher money stock estimate for this year. The value of 563 tonnes implies a rather high velocity of 14.5. In sum, in contrast to previous stock estimates, our money supply series implies more plausible velocities. Furthermore, our money supply series connects initial stock estimates for 1492 to the more reliable stock estimates for the second half of the 19th century. It does so based on a meticulous synthesis of the available data on the mining and international flow of monetary metals in the early modern period. 4. What accounts for the early modern price level rise? We can use our money supply series to throw new light on a long-standing debate in monetary history: to which extent does money growth account for the early modern rise in European price levels? 27 According to the monetarist view, rising price levels were primarily a consequence of rising money stocks, brought about by the influx of precious metals from America ( Fisher, 1989; Hamilton, 1934; 1947; Mayhew, 1995 ). 28 Another view highlights the role of an accelerating money velocity ( Goldstone, 1984; 1991; Lindert, 1985; Miskimin, 1975 ): early modern increases in urbanization rates facilitated a larger number of economic transactions in any given time period –i.e. money velocity increased, pushing up the price level. The money vs. velocity debate is commonly viewed through the lens provided by the equation of exchange : 𝑃 𝑡 = 𝑀 𝑡 𝑉 𝑡 ∕ 𝑌 𝑡 , (3) where 𝑃 𝑡 denotes the price level, 𝑀 𝑡 the money stock, 𝑉 𝑡 its velocity, and 𝑌 𝑡 stands for real output. While the equation of exchange is silent on the causal relationship of its constituent series, we can use identity 3 to account for Spain’s price level rise in terms of money growth, velocity changes, and real output growth. To this end we use the importance measure 𝐼( ⋅) : 𝐼( 𝑖 𝑡 ) = |Δ𝑖 𝑡 | |Δ𝑚 𝑡 |+ |Δ𝑣 𝑡 |+ |Δ𝑦 𝑡 |, 𝑖 𝑡 ∈{ 𝑚 𝑡 , 𝑣 𝑡 , 𝑦 𝑡 } , (4) where small letters denote the natural logarithm of the respective variable, and Δindicates changes over time. This importance measure assigns positive percentage contributions to 𝑚 𝑡 , 𝑣 𝑡 , and 𝑦 𝑡 , and ensures that they sum to unity, 𝐼( 𝑚 𝑡 ) + 𝐼( 𝑣 𝑡 ) + 𝐼( 𝑦 𝑡 ) = 100% . 29 To apply the accounting machinery lined out in Eqs. 3 and 4 , we need data on prices, real output, money and velocity. Current best-practice estimates on the former two come from Álvarez-Nogal and Prados de la Escosura (2013) . Their data, in combination with the new money supply estimate, allow us to back out velocity from the equation of exchange. We use the 11-year moving average GDP series by Álvarez-Nogal and Prados de la Escosura. We generate the equivalent moving average for all other variables to avoid putting too much weight on individual annual observations at the beginning and end of the sample. This is particularly relevant for prices, which experienced double-digit growth rate gyrations after the onset of the Napoleonic Wars. The following decomposition results reflects data uncertainty in the series for money, real GDP, and prices through 95% probability intervals for the importance measures, 𝐼( ⋅) . In particular, 10,000 random draws from the money supply distribution at the beginning and end of the sample reflect uncertainty in the money supply series. Analogously, we account for uncertainty in real 26 As silver was increasingly minted in American mints, Spanish mints became less active over time. According to de Paula (2016 , p.366), only 6% of Spain’s 18th century silver arrivals from America were minted in Seville –Spain’s primary mint ( Mateu y Llopis, 1942 , p.51). Consequently, the 30-year sums of the Sevillian mint output data compiled by de Paula (2016) begin to lie substantially below the baseline stock estimate in the late 17th and 18th centuries. 27 Here, we focus on the increase in silver prices, abstracting from changes in the silver value of the contemporary Spanish unit of account (UOA) –the Maravedí ( Karaman et al., 2020; Pamuk, 2001 ). UOA prices rose more than silver prices due to debasements. The question whether early modern price inflation in Spain is accounted for by changes in the quantity of money or its velocity is more directly addressed by dropping the variable “silver per unit of account ”from the analysis. The equation of exchange is easily translated from UOA units into silver units, because “silver per unit of account ” enters on both sides –multiplying the price level 𝑃 𝑡 , and the money stock 𝑀 𝑡 . Dividing the equation of exchange by the silver content of one UOA thus allows us to abstract from changes in the silver value of the UOA. 28 European prices modestly rose prior the arrival of large quantities of American precious metals. This has been attributed to an increase in production of European silver mines ( Munro, 2003 ). 29 As the equation of exchange is silent on the causal relationship between its four constituent variables, the importance measure results are consistent with different explanations for how money, velocity, real output, and prices are causally related to one another. For example, according to the quantity theory of money, the causal link runs from 𝑚 𝑡 to 𝑝 𝑡 , for given 𝑣 𝑡 and 𝑦 𝑡 . Palma (2019) , however, argues that early modern money inflows rendered Spain’s economy chronically uncompetitive, i.e. some of the importance of 𝑦 𝑡 is causally attributed to 𝑚 𝑡 . Although the importance measure 𝐼( ⋅) does not provide conclusive evidence in this regard, it does constitute a moment that is more readily matched by some theories than others. 7 Y. Chen, N. Palma and F. Ward Explorations in Economic History 81 (2021) 101401 Table 1 Equation of exchange decomposition. Variable 𝑖 Prices ( 𝑃) Money ( 𝑀) Velocity ( 𝑉 ) Real GDP ( 𝑌 ) Actual change x 4.95 x 15.67 x 0.89 x 2.80 Importance 𝐼( ⋅) 70% 3% 26% [62%, 71%] [0%, 14%] [21%, 30%] Notes: The percentage contributions may not add up to exactly 100% due to rounding. 95% probability interval in brackets. output growth through random draws from uniform distributions at the beginning and end of the sample period. The range of these two uniform distributions is set according to the min-max range spanned by the three GDP estimates that Álvarez-Nogal and Prados de la Escosura (2013) provide for the years 1492 and 1810. Finally, to account for uncertainty about Spain’s early modern price level, we use the alternative price indices that have been compiled by Allen (2001) , Munro (2008) and Losa and Zarauz (2020) . 30 Unfortunately, these different price series lack overlap for the years 1492 and 1810. Therefore, instead of using min-max ranges for these two years, we multiply the 1492 and 1810 price level values by Álvarez-Nogal and Prados de la Escosura with normally distributed error scalars with mean 1 and standard deviation 8%. This mirrors the average percentage deviation of the three alternative price series from the price series by Álvarez-Nogal and Prados de la Escosura across all overlapping years. To which extent can Spain’s money growth account for its early modern price level rise? Table 1 shows the decomposition results. The first row reports the actual changes in prices, money, velocity, and real GDP. Prices increased by a factor of 4.95 and real GDP by a factor of 2.8. This was accommodated by a 15.6-fold increase in money, whereas velocity fell by 11%. Put in terms of the importance measure described in Eq. 4 , the money supply increase accounts for 70% of Spain’s price level increase. The 95% probability interval of this importance measure stretches from 62% to 71%. 31 By contrast, the 11% decrease in velocity accounts for only 3% of the change in prices (95% interval: 0% to 14%). The 2.8-fold real GDP increase took substantial pressure off the price level ( Nicolini and Ramos, 2010 ). Correspondingly, real GDP growth accounts for 26% of the change in prices (95% interval: 21% to 30%). Money growth thus accounts for more of Spain’s early modern price level rise than velocity. In sum, the results are consistent with money-based accounts of the early modern price level rise in Spain ( Fisher, 1989; Hamilton, 1934 ). 32 Spanish money velocity ends the early modern period at a level similar from where it began and consequently accounts for comparatively little of the price level rise over the whole sample. 33 5. Conclusion This paper presents a new long-run estimate of the Spanish money supply between 1492 and 1810. The flood of precious metal inflows from America make this period a uniquely interesting episode for monetary historians to study. We arrive at an estimate of the Spanish money supply by combining data on the early modern production of precious metals and their international flow, with data on initial money stocks. The estimate suggests that Spain’s money supply grew at an annual rate between 0.7% and 1.1%. Viewed through the lens of the equation of exchange, the resulting money supply increase accounts for most of Spain’s early modern price level rise. Appendix A. Data A1. Uncertainty bands Economic data for the early modern period comes with uncertainty. We use stochastic simulations to generate a probability distribution for the Spanish money stock that reflects this uncertainty. More concretely, for uncertain input variables we specify a 30 The price series differ somewhat in their regional coverage, sample period, and goods basket composition, but their aggregate behavior is very similar to the index by Álvarez-Nogal and Prados de la Escosura (2013) . 31 The interval is asymmetric around the baseline estimate because the importance measure is a non-linear function of the money stock. In particular, the importance measure’s use of absolute values implies that equally sized increases and decreases in velocity obtain the same importance weight. Starting from a minimum weight of close to 0%, velocity’s importance can only go up. This is the case regardless of whether more money growth implies less velocity growth or whether less money growth implies more velocity growth. This asymmetry is inherited by the probability intervals of the other variables’ importance measures. 32 Appendix C.1 explores the robustness of this finding with respect to the initial money stock. Only for an initial stock that exceeds the baseline initial stock value of 396 tonnes by 580% does the contribution of velocity begin to dominate the contribution of money growth –a tall order to overcome. 33 This leaves open the possibility that velocity changes mattered over shorter horizons, but that these velocity changes were subsequently reversed. In fact, the claim by Goldstone (1984) that an increase in velocity accounted for early modern price increases in the 16th and early 17th centuries, was accompanied by his claim that velocity decreases played an important role in Europe’s subsequent 17th century deflations ( Goldstone, 1991 ). Appendix C.3 shows subsample decomposition results that are consistent with Goldstone’s velocity view for the case of Spain’s deflation between 1651 and 1750. 8 Y. Chen, N. Palma and F. Ward Explorations in Economic History 81 (2021) 101401 Table A.1 Input variable distributions. Input variable Distribution Parameterization Notes/Sources Initial stock ( 𝑀 1492 ) Uniform  ( 𝑚𝑖𝑛, max ) see text and Section A.2 Flows: Pacific flow Uniform  ( 𝑚𝑖𝑛 𝑡 , 𝑚𝑎𝑥 𝑡 ) see Table A.3 European outflow ( 𝑜𝑢𝑡 𝐸𝑈 𝑘 ) x Normal (1 , 0 . 08 2 ) Attman (1986) ; Barrett (1990) ; de Vries (2003) Spanish outflow rate ( 𝑜𝑢𝑡 𝐸𝑆𝑃 𝑘 ) + Normal (0 , 0 . 05 2 ) see text and Section A.6 Transport losses ( 𝑙𝑜𝑠𝑠 𝑘 ) x Normal (1 , 0 . 07 2 ) Mangas (1989) Production: American production ( 𝑝𝑟𝑜𝑑 𝐸𝑆𝑃 ∕ 𝑃 𝑅𝑇 𝑘 ) x Normal (1 , 𝜎2 𝑡 ) see text and Section A.3 European production ( 𝑝𝑟𝑜𝑑 𝐸𝑈 𝑘 ) x Normal (1 , 0 . 1 2 ) see text African inflows ( 𝑖𝑛 𝐴𝐹 𝑅 →𝐸𝑈 𝑘 ) x Normal (1 , 0 . 1 2 ) see text Other: Depreciation Uniform  (0 . 20% , 0 . 28%) Mayhew (1974) (annualized) American retention rate + Uniform  (−0 . 035 , 0 . 035) see text Mint rate + Uniform  (−0 . 15 , 0 . 15) see text Spain’s European GDP share 1 + Uniform  (−0 . 025 , 0 . 025) see text Spain’s European GDP share 2 + Uniform  (−0 . 05 , 0 . 05) Bonfatti et al. (2020) Notes: x: multiply with error scalar. + : add error term. probability distribution that reflects the type and degree of uncertainty we face in the data sources. We then repeatedly calculate the Spanish money stock based on random draws from the input variables’ distribution. 34 The result is a time-varying distribution of the Spanish money stock that reflects data uncertainty. This approach also allows us to report probability intervals for all our results. An overview of the distribution of input variables can be gleaned from Table A.1 . The rest of this section discusses the specification of this distribution. We account for uncertainty about the initial money stock by defining a min-max range that corresponds to the range of initial stock estimates in the literature. Section A.2 summarizes and discusses these estimates. The initial stock values by Velde and Weber (2000b) and Jacob (1831) emerge as lower and upper bounds that delimit the set of plausible initial stock values. The upper bound value of 565 tonnes exceeds the lower bound value of 228 by around 250%. We take random draws from an accordingly delimited uniform distribution to reflect initial stock uncertainty. To account for uncertainty in Pacific flows we use period-specific range estimates for how many million pesos were carried by the Manila galleons. Range estimates are wide, with upper bounds commonly exceeding lower bounds by 100%. Section A.4 discusses the underlying data, and Table A.3 lists the period-specific ranges. Absent prior information about how Pacific flows are distributed within these ranges, we draw from period-specific uniform distributions. Draws are conducted independently for each of the sub-periods. To reflect the uncertainty in precious metal outflows from Europe we randomly draw an error scalar from a normal distribution whose standard deviation reflects the dispersion seen in the literature. Our baseline series for European outflows uses data from Attman (1986) and de Vries (2003) . In particular, we use Attman’s estimates for precious metal flows across the Baltic and Levant, and de Vries’ revision of direct flows to East Asia via the Cape route. Barrett (1990) has also compiled a European outflow series. 35 Barrett’s series is very similar to the series proposed by de Vries and Attman up to the mid 18th century. After that, Barrett’s series misses the Cape route flows of several European trading companies, and thus underestimates the direct flow from Europe to East Asia. The standard deviation of the discrepancy between Attman’s outflow series for Europe and our baseline outflow series is 7.6%. With respect to Barrett’s outflow series the equivalent figure up to the mid 18th century, when Barretts series begins to systematically underestimate Cape route flows, is 8%. We therefore set the standard deviation of the normally distributed scalar to 8% of our baseline outflow figure. Error terms are drawn independently for each observation, i.e. 25-year periods. To the Spanish outflow rate, we add a normally distributed error term with a 5 percentage point standard deviation. This captures the large uncertainty surrounding the Spanish outflow data. More concretely, the standard deviation of the difference between our baseline outflow rate series ( Fig. A.5 ) and the individual outflow observations provided by Walton (1994) and Attman (1986) is 4.7 percentage points. The available data is laid out in Section A.6 . The error term is drawn independently for each observation, i.e. each of the constituent sub-periods displayed in Table A.5 . The calculation of interpolated values then proceeds based on the current set of random draws for each sub-period. Transportation loss data are subject to uncertainty because of unregistered shipments. Private treasure flows were taxed upon arrival in Spain and thus there existed an incentive for smuggling. The data collected by Mangas (1989 , p.316) and Morineau (1985 , pp.242 and 375) suggests that, on average, smuggling amounted to 30% of registered shipments in the 16th century, 67% in the 17th century, and 47% in the 18th century. The standard deviation in the smuggling rate amounts to 7 percentage points (based on 27 observations for the 17th century from Mangas (1989) ). We therefore multiply the smuggling rate for each transportation loss with 34 We take 10,000 draws from the joint distribution of input variables. This is sufficient to ensure that the resulting money stock distribution has converged. Draws are independent across input variables. A stochastic simulation that incorporates additional covariance across input variables is discussed in Appendix C.2 . 35 The European outflow series compiled by Morineau (1985) neglects precious metal flows across the Baltic, and thus is systematically too low ( Attman, 1986 , p.75). 9 Y. Chen, N. Palma and F. Ward Explorations in Economic History 81 (2021) 101401 A5. Transportation losses Table A.4 Atlantic transportation losses: sources. Year Source Silver equivalent Notes 1502 Walton (1994 , pp.14–15), Morineau (1985 , p.242) 10,955 kg 300,000 pesos in gold sunken 1537 Walton (1994 , p.24) 18,258 kg around 500,000 pesos captured 1550 Potter (1972 , pp.215,299) 8,079 kg more than 300,000 pesos sunken 1554 Walton (1994 , p.61) 73,031 kg almost 3 million pesos in treasure sunken, about half salvaged 1555 Potter (1972 , p.160), Bonifacio (2010) 12,780 kg 500,000 pesos sunken 1563 Earle (2007 , pp.9ff.), Bonifacio (2010) 24,430 kg around 1 million pesos sunken 1567 Walton (1994 , p.61) 109,547 kg more than 4 million pesos sunken; salvaging failed 1591 Walton (1994 , p.83) 255,610 kg 10 million pesos sunken; about 3/4 salvaged 1605 Walton (1994 , pp.83–84) 204,488 kg 8 million pesos sunken; salvaging failed 1621 Marx (1987 , p.302.) 382 kg around 15,000 pesos in treasure sunken; most of it salvaged 1622 Potter (1972 , pp.215ff.), Marx (1987 , pp.200ff.) 188,951 kg more than 7 million pesos in treasure sunken; partly salvaged 1623 Marx (1987 , p.202) 76,345 kg about 3 million pesos sunken 1624 Mangas (1989 , p.318) 51,122 kg 2 million pesos sunken 1628 Potter (1972 , p.160), Marx (1987 , p.248) 30,538 kg around 1.2 million pesos sunken, largely salvaged 1628 Venema (2010 , p.213) 80,660 kg 177,000 pounds of silver and 66 pounds of gold captured 1631 Marx (1987 , p.424) 58,169 kg more than 2 million pesos sunken; 1 million pesos salvaged 1631 Marx (1987 , p.249) 150,241 kg more than 5.5 million pesos sunken; very little salvaged 1634 Sandz and Marx (2001 , p.129) 7,635 kg around 300,000 pesos in treasure sunken, partly salvaged 1641 Mangas (1989 , p.318) 76,683 kg 3 million pesos sunken 1654 Earle (2007 , p.83) 255,610 kg 10 million pesos sunken; 3.5 million pesos recovered 1656 Potter (1972 , p.432) 173,815 kg 2 million pesos captured; around 5 million pesos sunken 1656 Walton (1994 , pp.128, 140) 127,805 kg 5 million pesos sunken, 2.5 million pesos salvaged 1682 Bueno (1996 , p.84) 153,366 kg 6 million pesos sunken 1698 www.todoavante.es 161,540 kg around 6.5 million pesos sunken, 6 million pesos salvaged 1702 Kamen (1966) 7,350 kg around 80,000 pesos captured and sunken by British and Dutch 1708 Phillips (2007 , pp.46,181), Sedgwick (1970) 1 286,283 kg 11 million pesos sunken and 200,000 pesos captured 1715 Marx (1987 , p.431) 309,972 kg 12 million pesos sunken; around 5 million salvaged 1730 Walton (1994 , p.166) 139,556 kg more than 5.5 million pesos sunken; partly salvaged 1733 Fine (2006 , p.153) 311,908 kg around 12.5 million pesos sunken; almost all salvaged 1750 Putley (2000) , Amrhein (2007 , ch.1) 2 10,321 kg 272,000 pesos sunken; 14,467 pesos salvaged; 144,000 pesos captured 1752 Marx (1987 , p.443) 49,620 kg 2 million pesos sunken, mostly salvaged 1753 Marx (1987 , p.443) 38,134 kg 1.5 million pesos sunken 1762 Gentleman’s and Magazine (1763 , p.528) 62,895 kg around 2.5 million pesos captured 1786 Potter (1972 , pp.349ff.) 185,716 kg 7.5 million pesos sunken, mostly salvaged 1800 Bravo (2010) 51,264 kg around 2 million pesos sunken; partly salvaged 1802 Sandz and Marx (2001 , p.218) 13,742 kg around 0.5 million pesos sunken 1804 Cobbett (1804 , p.663) 113,084 kg 1.5 million pesos sunken; 3 million pesos captured Notes: 1 URL: http://www.historyofparliamentonline.org/volume/1715-1754/member/wager-sir-charles-1666-1743#footnoteref3_g4iwhgx . 2 Loss associated with the ship “El Salvador ” corrected to 240,000 pesos; correction confirmed with the author. Where sources refer to officially registered silver transports only, we add an estimate of the smuggled silver as follows: 30% for the 16th century (average from Morineau, 1985 , p.242), 67% for the 17th century from Mangas (1989 , p.316) or Morineau (1985 , p.242), and 46% for the 18th century (including the years up to 1810) from Morineau (1985 , p.375). Silver/peso conversion rates: 1 peso = 25.561 g (1492–1727), 24.809 g (1728–1785), 24.245 g (1786–1810). 16 Y. Chen, N. Palma and F. Ward Explorations in Economic History 81 (2021) 101401 A6. Outflows This section gives an overview of the Spanish outflow data. Table A.5 shows Spanish money outflows as a fraction of inflows from Spanish America –the Spanish outflow rate. Fig. A.5 displays the linearly interpolated series together with the individual observations from Attman and Walton. Table A.5 Spanish outflows (% of American inflows). Years Source Outflow rate Notes 1492–1588 91% Representative outflow ratio for normal periods in 17th and 18th centuries 1589–1599 Walton (1994 , p.86) 𝑎 107% Height of the Dutch War for Independence 1600 91% Representative outflow ratio for normal periods in 17th century 1601–1640 intrpl 1641–1642 Attman (1986 , p.36) 𝑎 & Walton (1994 , pp.86,145) 𝑎 91% 1643–1667 intrpl 1668–1670 Attman (1986 , p.40) 92% 1671–1699 intrpl 1700 Attman (1986 , p.30) 100% 1701–1713 Attman (1986 , p.30) & Walton (1994 , p.156) 106% War of Spanish Succession 1714–1750 Attman (1986 , p.30) 100% 1751–1769 intrpl 1770–1779 Walton (1994 , p.181) 100% 1780–1789 Attman (1986 , pp.30,32) 91.5% 1790–1810 91.5% continuation/extrapolation Notes: intrpl – linear interpolation. 𝑎 Source states an absolute Spanish outflow value without accompanying inflow. Where sources state an absolute Spanish outflow value without accompanying inflow, we divided this value by our inflow series ( 𝑖𝑛 𝐴𝑀→𝐸𝑆𝑃 𝑘 from Eq. 2 ). Fig. A.5. Spanish outflows (% of American inflows). Appendix B. Alternative money stock estimates In this section we briefly introduce two alternative money stock measures, that act as a robustness check for our baseline estimate. The first alternative estimate is the European in/out based estimate, for which we calculate the Spanish money stock as a share of the European money stock. We do so in two steps. First, we calculate the European precious metal stock by combining an estimate of the initial European stock in 1492 with data on Europe’s precious metal inflows, outflows, and production. Second, we calculate the Spanish share of European precious metals after 1492 according to Spain’s average share of European GDP. This allows us to 17 Y. Chen, N. Palma and F. Ward Explorations in Economic History 81 (2021) 101401 Fig. B.1. Money stock measures (11-year moving averages). replace the sparse Spanish outflow data with the more abundant European outflow data. The European in/out based estimate of the Spanish money stock is depicted as the dashed gray line in Fig. B.1 . Overall, the European in/out based estimate exhibits trends and low frequency variations that are similar to the baseline estimate. The second alternative estimate is the Asian absorption estimate. In contrast to the previous two money stock estimates, the Asian absorption estimate dispenses with the need for data on Pacific precious metal flows, as well as Spanish and European outflows. Instead, it relies on an estimate of the quantity of precious metals that eventually wound up in Asia. The latter is often expressed as a fraction of the American precious metal production –the so-called Asian absorption rate. Based on this absorption rate, we obtain an estimate of the European money stock. We then proceed in the same way as for the European in/out based estimate. Estimates of the Asian absorption center around 50%. 42 To reflect the uncertainty around these estimates, we calculate a range of stock estimates assuming the Asian absorption rate was at least 33%, but no more than 66%. The result is shown as the gray area in Fig. B.1 . 43 The short-dashed gray line indicates the center of this range, which corresponds to a 50% Asian absorption rate. Reassuringly, the European in/out based estimate, as well as the Asian absorption estimate are very similar to the baseline estimate. The largest discrepancy occurs in the 18th century, where the Spanish outflow data suggests a hemorrhaging of Spanish silver that is not captured by the two alternative estimates. Unsurprisingly, the two alternative estimates also miss the Spain-specific increase in money outflows during the Dutch War of Independence and the War of Spanish Succession. The following sections describe the construction of the European in/out and Asian absorption estimates in greater detail. B1. European in/out estimate Initial stock For the initial European precious metal stock estimate we rely on the same sources as for the baseline series. If we take the European share of the Velde and Weber (2000b) estimate of the global precious metal stock according to the European-to-World GDP ratio around 1500 ( Bolt et al., 2018 ) ( ≈23%) we obtain a value of 1510 tonnes of silver equivalents – 823 tonnes of silver and 68 tonnes of gold. 44 This constitutes the lower bound of our initial stock range for Europe. The highest plausible initial value is 3749 tonnes of silver equivalents ( Jacob, 1831 ). The mid-point of the 1510 to 3749 ton range – 2630 tonnes –serves as our initial European stock estimate. 42 Irigoin (2009 , p.207) provides an overview of references in this regard. 43 The 33% absorption rate scenario starts with the upper bound initial precious metal value, whereas the 66% absorption rate starts with the lower bound initial value. 44 The European GDP figure includes Belgium, Finland, France, Germany, Greece, Italy, the Netherlands, Poland, Portugal, Spain, Sweden, Switzerland, and England. We linearly interpolate the underlying population and real purchasing power adjusted per capita GDP series from Bolt et al. (2018) . 18 Y. Chen, N. Palma and F. Ward Explorations in Economic History 81 (2021) 101401 Inflows The European inflow measure differs from the Spanish one in the following ways: First, to arrive at total European precious metal inflows, we add non-Spanish European precious metal arrivals, 𝑖𝑛 𝑅𝑂𝑊 →𝐸𝑈 𝑘 , and the complete European precious metal production, 𝑝𝑟𝑜𝑑 𝐸𝑈 𝑘 , instead of only a fraction. Second, we need to replace the Spanish transport loss measure, 𝑙𝑜𝑠𝑠 𝑘 , with the European transport loss measure, 𝑙𝑜𝑠𝑠 𝐸𝑈 𝑘 . The difference between the two equals piracy losses, 𝑝𝑖𝑟 𝑘 , which constituted only a redistribution of precious metal inflows within Europe – away from Spain to the pirates’ home country. Finally, we remove the diffusion term, 𝑑𝑖𝑓𝑓 𝑘 , from the European inflow equation. 45 The resulting European precious metal inflow is 𝑖𝑛 𝐸𝑈 𝑘 = 𝑝𝑟𝑜𝑑 𝐸𝑆𝑃 𝑘 −1 (1 − 𝑟𝑒𝑡𝑒𝑛𝑡 𝑘 )(1 − 0 . 52%) − 𝑝𝑎𝑐𝑖𝑓𝑖𝑐 𝑘 − 𝑙𝑜𝑠𝑠 𝐸𝑈 𝑘 + 𝑠𝑎𝑙𝑣 𝑘 −1 ⏟⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏟⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏟ ≡𝑖𝑛 𝐴𝑀→𝐸𝑈 𝑘 + ( 𝑝𝑟𝑜𝑑 𝐸𝑈 𝑘 + 𝑖𝑛 𝑅𝑂𝑊 →𝐸𝑈 𝑘 )(1 − 0 . 52%) , (B.1) where 𝑙 𝑜𝑠𝑠 𝐸𝑈 𝑘 = 𝑙 𝑜𝑠𝑠 𝑘 − 𝑝𝑖𝑟 𝑘 , and all other terms are defined as for the baseline estimate (see Eq. 2 ). Outflows We combine the European inflow data with European outflow data from Attman (1986) and de Vries (2003) . In particular, we use Attman’s estimates for precious metal flows across the Baltic and Levant, and de Vries’ revision of direct flows to East Asia via the Cape route. This outflow data consists of 25-year averages. It is thus available at a higher frequency than the Spanish outflow data that we use for the baseline estimate. Money stock Based on the initial European stock and the European inand outflow data we calculate the European precious metal stock, 𝑀 𝐸𝑈 𝑡 , according to Eq. 1 . We then calculate an intermediary measure for the Spanish money supply according to Spain’s share of European GDP:  𝑀 Euro pean in ∕ out 𝑡 = 𝜒EU 𝑀 EU 𝑡 , (B.2) where 𝜒𝐸𝑈 denotes Spain’s average share of European GDP over the period 1492 to 1810. We need to make some Spain-specific adjustments to the intermediary stock measure,  𝑀 Euro pean in ∕ out 𝑡 , to arrive at the final European in/out based measure for the Spanish money supply. First, we subtract piracy related money losses, 𝑝𝑖𝑟 𝑘 , because they constituted losses to the Spanish money stock that are not reflected in the European stock measure, 𝑀 𝐸𝑈 𝑡 . Second, we correct for the rescaling of the non-piracy related transportation losses in Eq. B.2 , recognizing that the entire loss was initially born by Spain ( Nogues-Marco, 2011 , p.6). The same logic applies to salvaged precious metals. These two adjustments are summarized in the following term: 𝑎𝑑 𝑗 𝑖𝑛𝑓𝑙𝑜𝑤,𝐸𝑈 𝑘 = − 𝑝𝑖𝑟 𝑘 − (𝑙 𝑜𝑠𝑠 𝐸𝑈 𝑘 − 𝑠𝑎𝑙 𝑣 𝑘 −1 )(1 − 𝜒𝐸𝑈 ). (B.3) Next, we account for the diffusion of Atlantic transportation losses over time. In contrast to the baseline money supply estimate, however, we only need to adjust for the money loss diffusion within Europe. The European diffusion to the rest of the world is already accounted for in European outflows. Accordingly, we assume that, in the long-run, Spain bore precious metal losses in proportion to its European GDP share. We apply the same linear diffusion process as for the baseline estimate to transition from the initial Spanish money loss value to the long-run value. The European in/out based estimate of the Spanish money stock, 𝑀 Euro pean in ∕ out 𝑡 , is obtained by subtracting the cumulative sum of the above two adjustments from the intermediary measure, taking into account that the adjustment terms need to be subjected to the same annual depreciation rate: 𝑀 Euro pean in ∕ out 𝑡 =  𝑀 Euro pean in ∕ out 𝑡 + 𝑡 ∑ 𝑘 =1493 (ad 𝑗 inflow , EU 𝑘 + dif 𝑓 EU 𝑘 )( 1 − 0 . 24% ) 𝑡 − 𝑘 . (B.4) B2. Asian absorption estimate Initial stock The Asian absorption estimate starts from the same initial value range as the European in/out based estimate: The low value of 1510 tonnes of silver equivalent initiates the lower bound of the Asian absorption range estimate. The lower bound Asian absorption estimate is then calculated based on a high Asian absorption rate of 66%. The high value of 3749 tonnes initiates the upper bound estimate, which uses the low Asian absorption rate of 33%. Finally, the mid-point Asian absorption estimate of the Spanish money stock starts at the mid-point of the 1510 to 3749 t range, i.e. 2630 tonnes. 45 In contrast to the sparse annual data on Spanish outflows, the European outflow data in principle already reflects the diffusion of Atlantic transport losses through a reduction in European precious metal outflows. In practice, however, the diffusion of Atlantic transportation losses was too small compared to the European stock, and too small compared to the measurement uncertainty in European outflows, to significantly affect the European stock estimate. 19 Y. Chen, N. Palma and F. Ward Explorations in Economic History 81 (2021) 101401 Fig. B.2. Copper money. Inflows and outflows The Asian absorption estimate replaces the Pacific flow data and the European outflow data with an estimate of the quantity of precious metals that eventually wound up in Asia, expressed as a fraction of the American precious metal production. European net-inflows thus become 𝑖𝑛 𝐸𝑈 𝑘 − 𝑜𝑢𝑡 𝐸𝑈 𝑘 = 𝑝𝑟𝑜𝑑 𝐴𝑀 𝑘 −1 (1 − 𝑟𝑒𝑡𝑒𝑛𝑡 𝑘 )(1 − 0 . 52%) − 𝑙𝑜𝑠𝑠 𝐸𝑈 𝑘 + 𝑠𝑎𝑙𝑣 𝑘 −1 ⏟⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏟⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏞⏟ 𝑖𝑛 𝐴𝑀→𝐸𝑈 𝑘 + ( 𝑝𝑟𝑜𝑑 𝐸𝑈 𝑡 + 𝑖𝑛 𝐴𝐹 𝑅 →𝐸𝑈 𝑘 )(1 − 0 . 52%) − 𝑝𝑟𝑜𝑑 𝐴𝑀 𝑘 −1 (1 − 0 . 52%) 𝑎𝑏𝑠𝑜𝑟𝑏 𝑎𝑠𝑖𝑎 . (B.5) where 𝑝𝑟𝑜𝑑 𝐴𝑀 𝑘 −1 is the total American production (i.e. Portuguese American and Spanish American), 𝑖𝑛 𝐴𝐹 𝑅 →𝐸𝑈 𝑘 denotes gold inflows from Africa, and 𝑎𝑏𝑠𝑜𝑟𝑏 𝑎𝑠𝑖𝑎 is the Asian absorption rate. All other terms are defined as before. Money stock We use the net inflow series B.5 to first calculate the European money stock, 𝑀 EU , Asian abso rpti on 𝑡 . Based on this European stock we calculate an intermediate Asian absorption estimate of the Spanish money stock,  𝑀 Asian abso rpti on 𝑡 , according to Spain’s European GDP share. To arrive at the final Asian absorption estimate for Spain, 𝑀 Asian abso rpti on 𝑡 , the intermediary measure undergoes the same set adjustments as the intermediary European in/out measure: 𝑀 Asian abso rpti on 𝑡 =  𝑀 Asian abso rpti on 𝑡 + 𝑡 ∑ 𝑘 =1493 (ad 𝑗 inflow , EU 𝑘 + dif 𝑓 EU 𝑘 )( 1 − 0 . 24% ) 𝑡 − 𝑘 . B3. Copper money Starting in the late 16th century, fiscal pressures arising from persistent warfare led to the issuance of increasing amounts of copper money. Fig. B.2 depicts the accumulating copper money stock from Velde and Weber (2000a) converted into silver equivalents. The solid line uses the market exchange rate between copper and silver coins for this conversion, the dashed line uses the official face value ratio. The gray area depicts the centered 11-year moving average of the 95% probability region for the baseline money supply estimate. 46 46 The original data from Velde and Weber (2000a) , Table 6, Column: “total ”) is provided in units of account (Ducats à 375 Maravedís de vellón). Maravedís de vellón can be converted into tonnes of silver equivalent according to two different conversion rates. First, according to Spain’s official conversion rate of 25.561 g of silver per 272 Maravedí. Using this official conversion rate, however, neglects the fact that, in the market, copper coins traded at a discount vis-à-vis silver coins of identical Maravedí face value. This discount reflected the extent to which market participants were reluctant to accept copper coins for payment. Converting Maravedí de vellón into silver equivalent based on market rates thus results in a lower silver value for the same copper money stock. 20 Y. Chen, N. Palma and F. Ward Explorations in Economic History 81 (2021) 101401 After 1617, when public authorities sanctioned the minting of copper coins, the copper money stock rapidly built up to around half of the value of the gold and silver money supply. Over the subsequent decades, copper money lost its importance and after 1664 it became largely inconsequential as a consequence of the decision to halt copper minting. While copper money existed before and after this period, its role was much diminished outside of the early 17th century ( Velde and Weber, 2000a ). According to Hamilton (1934) and Velde and Weber (2000b) the rise of copper money in the early 1600s primarily altered the composition of the Spanish money stock, not its level. This is because copper coins displaced gold and silver coins, that were driven out of circulation. However, temporary overor underreaction in short-term gold and silver outflows cannot be ruled out. For example, more silver may have left Spain in 1625-27 and 1640-42 when severe flights to silver led to sudden spikes in the market exchange rate between copper and silver coins. More generally, the minting of copper coins adds to the uncertainty about the Spanish money stock for this period. As a consequence, the 95% probability interval depicted in Fig. B.2 may be considered too narrow during the first half of the 17th century. Appendix C. Additional results C1. Robustness to initial stock level Owing to the large influx of precious metals over the early modern period, the initial stock choice for 1492 has only a small influence on the final stock level in 1810. For the decomposition analysis, however, the initial stock is more influential. A doubling in the initial stock implies almost a halving of subsequent money growth. For large enough initial stock values, velocity changes will replace money changes as the most influential accounting item behind Spain’s early modern price level rise. In this section we calculate the initial stock level at which this change in results occurs. To find the threshold initial stock level at which money growth ceases to be the main factor behind Spain’s early modern price level rise, we conduct a grid search over initial stock levels at 25 t intervals. For each initial money stock level we recalculate the percentage contributions of money growth, velocity growth, and real output growth. We find that the velocity growth contribution draws even with money growth at an initial money stock level of 2300 tonnes, at which both items account for 36% of Spain’s price level rise. 2300 tonnes is around 5.8 times our baseline initial estimate of 396 tonnes. Beyond an initial stock value of 2300 tonnes, the contribution of a more than 3.9 fold increase in velocity begins to dominate the contribution of a less than 3.9 fold increase in the money stock. In Section A.2 we have argued that among existing initial stock estimates for Europe all well-grounded ones fall into the 1,519– 3,749 range. Using Spain’s European GDP share of around 15% an initial stock of 2300 tonnes for Spain implies an initial European stock of 15,333 tonnes. While we cannot exclude the possibility that future research comes up with a convincing argument for such a high initial European stock value, 15,333 tonnes sets a high bar for overturning the decomposition finding that money growth was the most important factor behind Spain’s early modern price level rise. Fig. C.1. Percentage point deviation of 95% intervals with and without covariances Notes: Distributions based on 10,000 draws from the input variable distribution. Centered 11-year moving average, neglecting missing observations at the borders. 21 Y. Chen, N. Palma and F. Ward Explorations in Economic History 81 (2021) 101401 C2. Probability interval and covariances Our baseline probability distribution for the Spanish money stock is based on independent random draws from each input variable’s distribution. This section examines the role of dependencies across input variables. After a short description of what we deem to be the most important dependencies, we compare the baseline 95% probability interval with the 95% probability interval that originates from a stochastic simulation that takes cross-input variable dependencies into account. In principle, co-moving input variables can inflate or deflate the uncertainty surrounding the money stock estimate. In our application, however, the most salient dependencies appear to work in favor of a narrower probability distribution for the Spanish money stock. The two input variable covariances we deem most important are i) the covariance between American production volumes and Pacific flows, and ii) the covariance between Spanish inflows and Spanish outflows. First, consider the covariance between American production volumes and Pacific flows, and how it affects the probability distribution for Spain’s money stock. It is plausible to assume that larger American production volumes allowed for larger Pacific flows. A positive covariance between the two variables dampens the volatility of their difference –in this case the amount of precious metals arriving in Spain. Less uncertainty about Spanish inflows in turn translates into less uncertainty about the Spanish money stock. Second, Spanish outflows can be expected to co-move with Spanish inflows: the more money arrives in Spain, the more will leave, e.g. through an increase in Spanish goods imports from the rest of Europe. What does this imply for the uncertainty surrounding the Spanish money stock estimate? The positive covariance between Spanish inand outflows dampens the variation in the Spanish money stock. 47 Note that because Spanish outflows are calculated as a fraction of Spanish inflows the baseline analysis already implicitly takes this dependency into account. 48 Next, we incorporate covariances i) and ii) into a stochastic simulation to generate probability intervals that account for both dependencies. The sample correlation between American production and Pacific flows is 0.25 between 1572 and 1720 –the year when the Pacific route opened and the year when its eventual decline set in. After 1720 Pacific flows decouple from American production volumes. To account for this dependency, we assume that between 1572 and 1720 American production and Pacific flows co-move according to their sample covariance. The covariance between Spanish inflows and outflows is already reflected in the baseline analysis, because outflows are calculated as a fraction of inflows. Although the Spanish outflow rate 𝑜𝑢𝑡 𝐸𝑆𝑃 𝑘 is drawn independently as specified in Table A.1 , the resulting outflow series already exhibits the desired covariance with inflows. Fig. C.1 displays the percentage point deviation between the baseline 95% probability interval and the 95% interval with added covariance. The difference between the two probability intervals is small. The upper band with added covariance lies at most 0.2 percentage points below the baseline upper band. The lower band with added covariance also lies lower, but less so than the upper band. As a consequence, the 95% probability band with added covariance is slightly narrower after 1572, when the Pacific flow starts. C3. Subsample decomposition results While money growth was the dominant influence on the Spanish price level over the period from 1492 to 1810 as a whole, this does not necessarily hold for all sub-periods. The price history of early modern Spain can be separated into three distinct phases: The price revolution (lasting up to 1650), the deflationary period (from 1651 to 1750), and a period of reflation (after 1750). Table C.1 , panels B to D shows the decomposition results for these three sub-periods. For reference, panel A repeats the full sample results from the main text. Panel B shows that money growth accounts for around three quarters of the almost four-fold increase in prices between 1492 and 1650 –the so-called price revolution. During the same period, GDP growth and a decreasing velocity drove a wedge between the 7-fold increase in money supply and the increase in prices. Panel C shows that declining velocity played an important role in the ensuing deflation between 1651 and 1750. It accounts for 40% of the price decline. GDP growth of around 40% also took pressure off prices. As a consequence, a 55% increase in money supply did not translate into inflation during this period. The decomposition result for the post-1650 deflation is thus consistent with a velocity-based explanation ( Goldstone, 1991 ). Finally, panel D displays the decomposition results for the period of reflation, 1751 to 1810. During this period prices rose by almost 200%. Partly this is accounted for by a 42% increase in the money supply. Rising 47 The covariance between Spanish inand outflows is actually a summary covariance, because the inflow series incorporates the random draws from most other input variables (see Eq. 2 in the main text). Accounting for the dependency between Spanish inand outflows thus constitutes a partial remedy for inaccurate covariance assumptions that enter the construction of the Spanish inflow series. For example, excessive Spanish inflows (e.g. brought about by a disregard of the covariance between American production and Pacific flows) can be partially remedied by accounting for a positive covariance between Spanish inand outflows. This is because when excessive Spanish inflows are offset by excessive Spanish outflows, the Spanish money supply estimate becomes less volatile than it would be otherwise. 48 How about other input variable covariances? The logic that applies to Spanish inand outflows in principle also applies to European inand outflows. But European inand outflows play only a minor role in the baseline estimate of Spain’s money stock (see the last term in Eq. 2 in the main text). We thus disregard this dependency. The same holds for the plausible dependencies between European outflows and other input variables, such as European production, and African arrivals. Do there exist potentially important dependencies that could increase the 95% probability interval of the Spanish money stock estimate? For example, a positive correlation between Spanish outflows and Pacific flows, or a negative correlation between American production and Spanish outflows. The practical relevance for such dependencies is less evident than in the previously discussed cases i) and ii). We therefore also do not consider them. 22 Y. Chen, N. Palma and F. Ward Explorations in Economic History 81 (2021) 101401 Table C.1 Equation of exchange decomposition — Sub-periods. Variable 𝑖 Prices ( 𝑃) Money ( 𝑀) Velocity ( 𝑉 ) Real GDP ( 𝑌 ) A: 1492–1810: Full sample Actual change x 4.95 x 15.67 x 0.89 x 2.80 Importance 𝐼( ⋅) 70% 3% 26% [62%, 71%] [0%, 14%] [21%, 30%] B: 1492–1650: Price revolution Actual change x 3.87 x 7.09 x 0.76 x 1.38 Importance 𝐼( ⋅) 76% 11% 13% [66%, 82%] [1%, 24%] [9%, 20%] C: 1651–1750: Deflation Actual change x 0.65 x 1.55 x 0.60 x 1.41 Importance 𝐼( ⋅) 34% 40% 27% [24%, 38%] [34%, 42%] [20%, 42%] D: 1751–1810: Reflation Actual change x 1.94 x 1.42 x 1.89 x 1.38 Importance 𝐼( ⋅) 27% 49% 25% [13%, 42%] [33%, 61%] [24%, 27%] Notes: % decomposition based on log changes. The percentage contributions may not add up to exactly 100% due to rounding. 95% probability interval in brackets. velocity, however, plays a larger role. It explains 49% of the reflation. Accelerating GDP growth towards the end of the early modern period counteracted the dual inflationary pressures arising from a rising money supply and a resurging velocity. Appendix D. Money supply tables Table D.1 Baseline money supply estimate (tonnes; centered 11-year moving average). 1492 411 1543 985 1593 1,722 1643 2,749 1693 3,761 1743 4,418 1793 5,997 1493 414 1544 1,002 1594 1,703 1644 2,798 1694 3,775 1744 4,454 1794 6,050 1494 418 1545 1,019 1595 1,688 1645 2,844 1695 3,788 1745 4,488 1795 6,104 1495 421 1546 1,036 1596 1,676 1646 2,889 1696 3,799 1746 4,521 1796 6,154 1496 425 1547 1,053 1597 1,693 1647 2,931 1697 3,806 1747 4,548 1797 6,205 1497 427 1548 1,072 1598 1,696 1648 2,977 1698 3,812 1748 4,575 1798 6,253 1498 434 1549 1,083 1599 1,704 1649 3,013 1699 3,815 1749 4,600 1799 6,291 1499 440 1550 1,097 1600 1,717 1650 3,024 1700 3,817 1750 4,624 1800 6,329 1500 447 1551 1,112 1601 1,714 1651 3,015 1701 3,818 1751 4,646 1801 6,368 1501 454 1552 1,126 1602 1,716 1652 3,010 1702 3,817 1752 4,668 1802 6,406 1502 461 1553 1,140 1603 1,721 1653 3,003 1703 3,789 1753 4,689 1803 6,444 1503 469 1554 1,154 1604 1,732 1654 2,995 1704 3,776 1754 4,709 1804 6,482 1504 478 1555 1,168 1605 1,745 1655 2,987 1705 3,748 1755 4,730 1805 6,521 1505 486 1556 1,184 1606 1,759 1656 2,979 1706 3,720 1756 4,751 1806 6,534 1506 496 1557 1,199 1607 1,774 1657 2,973 1707 3,693 1757 4,767 1807 6,551 1507 505 1558 1,213 1608 1,790 1658 2,970 1708 3,667 1758 4,787 1808 6,564 1508 516 1559 1,228 1609 1,806 1659 2,969 1709 3,645 1759 4,807 1809 6,578 1509 527 1560 1,250 1610 1,825 1660 2,971 1710 3,599 1760 4,827 1810 6,607 1510 539 1561 1,274 1611 1,844 1661 2,998 1711 3,568 1761 4,847 1511 551 1562 1,288 1612 1,883 1662 3,047 1712 3,542 1762 4,867 1512 563 1563 1,303 1613 1,924 1663 3,093 1713 3,519 1763 4,888 1513 576 1564 1,319 1614 1,966 1664 3,142 1714 3,526 1764 4,909 1514 588 1565 1,336 1615 2,007 1665 3,194 1715 3,537 1765 4,930 1515 601 1566 1,352 1616 2,050 1666 3,248 1716 3,554 1766 4,951 1516 614 1567 1,369 1617 2,075 1667 3,300 1717 3,577 1767 4,972 1517 627 1568 1,386 1618 2,094 1668 3,348 1718 3,605 1768 4,999 1518 640 1569 1,405 1619 2,106 1669 3,393 1719 3,636 1769 5,026 1519 652 1570 1,425 1620 2,117 1670 3,435 1720 3,667 1770 5,053 1520 665 1571 1,446 1621 2,126 1671 3,473 1721 3,726 1771 5,080 1521 678 1572 1,462 1622 2,133 1672 3,507 1722 3,773 1772 5,107 1522 691 1573 1,489 1623 2,129 1673 3,538 1723 3,820 1773 5,134 1523 704 1574 1,516 1624 2,127 1674 3,564 1724 3,861 1774 5,159 1524 717 1575 1,543 1625 2,126 1675 3,587 1725 3,890 1775 5,189 ( continued on next page ) 23 Y. Chen, N. Palma and F. Ward Explorations in Economic History 81 (2021) 101401 Table D.1 ( continued ) 1525 729 1576 1,571 1626 2,121 1676 3,606 1726 3,921 1776 5,222 1526 742 1577 1,599 1627 2,106 1677 3,608 1727 3,948 1777 5,257 1527 754 1578 1,627 1628 2,111 1678 3,609 1728 3,943 1778 5,294 1528 767 1579 1,654 1629 2,125 1679 3,611 1729 3,964 1779 5,333 1529 780 1580 1,680 1630 2,147 1680 3,611 1730 3,984 1780 5,376 1530 794 1581 1,705 1631 2,172 1681 3,611 1731 4,004 1781 5,402 1531 808 1582 1,729 1632 2,202 1682 3,615 1732 4,024 1782 5,447 1532 822 1583 1,752 1633 2,235 1683 3,620 1733 4,044 1783 5,493 1533 836 1584 1,772 1634 2,279 1684 3,626 1734 4,064 1784 5,541 1534 851 1585 1,788 1635 2,322 1685 3,633 1735 4,089 1785 5,592 1535 865 1586 1,777 1636 2,366 1686 3,640 1736 4,126 1786 5,641 1536 879 1587 1,779 1637 2,408 1687 3,647 1737 4,161 1787 5,688 1537 894 1588 1,777 1638 2,469 1688 3,668 1738 4,198 1788 5,736 1538 909 1589 1,772 1639 2,529 1689 3,690 1739 4,264 1789 5,784 1539 924 1590 1,763 1640 2,587 1690 3,713 1740 4,303 1790 5,831 1540 939 1591 1,752 1641 2,644 1691 3,735 1741 4,342 1791 5,879 1541 954 1592 1,738 1642 2,698 1692 3,758 1742 4,380 1792 5,945 Table D.2 Annual money supply estimate (tonnes). 1492 396 1543 981 1593 1,720 1643 2,779 1693 3,780 1743 4,423 1793 5,990 1493 402 1544 997 1594 1,704 1644 2,824 1694 3,797 1744 4,463 1794 6,043 1494 408 1545 1,014 1595 1,690 1645 2,869 1695 3,813 1745 4,503 1795 6,094 1495 414 1546 1,034 1596 1,675 1646 2,913 1696 3,829 1746 4,534 1796 6,150 1496 420 1547 1,054 1597 1,667 1647 2,954 1697 3,845 1747 4,564 1797 6,214 1497 427 1548 1,074 1598 1,658 1648 2,987 1698 3,686 1748 4,594 1798 6,274 1498 434 1549 1,094 1599 1,650 1649 3,021 1699 3,843 1749 4,622 1799 6,334 1499 441 1550 1,106 1600 1,676 1650 3,056 1700 3,846 1750 4,639 1800 6,386 1500 449 1551 1,126 1601 1,706 1651 3,087 1701 3,838 1751 4,666 1801 6,386 1501 457 1552 1,146 1602 1,740 1652 3,115 1702 3,826 1752 4,642 1802 6,447 1502 455 1553 1,164 1603 1,774 1653 3,144 1703 3,823 1753 4,676 1803 6,466 1503 464 1554 1,109 1604 1,806 1654 3,173 1704 3,821 1754 4,700 1804 6,404 1504 473 1555 1,152 1605 1,839 1655 2,948 1705 3,820 1755 4,724 1805 6,464 1505 482 1556 1,171 1606 1,667 1656 2,763 1706 3,820 1756 4,747 1806 6,519 1506 492 1557 1,190 1607 1,693 1657 2,856 1707 3,821 1757 4,771 1807 6,576 1507 502 1558 1,210 1608 1,718 1658 2,879 1708 3,536 1758 4,794 1808 6,630 1508 514 1559 1,228 1609 1,779 1659 2,905 1709 3,538 1759 4,821 1809 6,688 1509 526 1560 1,250 1610 1,801 1660 2,929 1710 3,539 1760 4,848 1810 6,762 1510 537 1561 1,275 1611 1,828 1661 2,966 1711 3,538 1761 4,875 1511 549 1562 1,299 1612 1,868 1662 3,024 1712 3,539 1762 4,839 1512 562 1563 1,299 1613 1,913 1663 3,080 1713 3,542 1763 4,865 1513 575 1564 1,324 1614 1,959 1664 3,135 1714 3,581 1764 4,892 1514 587 1565 1,348 1615 2,006 1665 3,191 1715 3,311 1765 4,918 1515 601 1566 1,417 1616 2,053 1666 3,248 1716 3,485 1766 4,943 1516 614 1567 1,331 1617 2,098 1667 3,305 1717 3,527 1767 4,968 1517 627 1568 1,355 1618 2,141 1668 3,362 1718 3,570 1768 4,999 1518 640 1569 1,384 1619 2,184 1669 3,421 1719 3,615 1769 5,027 1519 653 1570 1,410 1620 2,229 1670 3,478 1720 3,661 1770 5,054 1520 666 1571 1,433 1621 2,271 1671 3,518 1721 3,726 1771 5,081 1521 678 1572 1,455 1622 2,103 1672 3,538 1722 3,786 1772 5,108 1522 691 1573 1,485 1623 2,076 1673 3,557 1723 3,848 1773 5,135 1523 704 1574 1,515 1624 2,051 1674 3,576 1724 3,884 1774 5,162 1524 717 1575 1,544 1625 2,077 1675 3,594 1725 3,922 1775 5,189 1525 729 1576 1,573 1626 2,102 1676 3,610 1726 3,961 1776 5,215 1526 742 1577 1,599 1627 2,129 1677 3,624 1727 4,001 1777 5,242 1527 755 1578 1,628 1628 2,060 1678 3,640 1728 4,041 1778 5,261 1528 767 1579 1,654 1629 2,120 1679 3,654 1729 4,031 1779 5,281 1529 780 1580 1,682 1630 2,173 1680 3,669 1730 3,932 1780 5,349 1530 793 1581 1,711 1631 2,170 1681 3,683 1731 3,995 1781 5,414 1531 804 1582 1,742 1632 2,101 1682 3,543 1732 4,022 1782 5,468 1532 817 1583 1,763 1633 2,164 1683 3,556 1733 3,737 1783 5,515 1533 829 1584 1,781 1634 2,232 1684 3,568 1734 4,074 1784 5,573 1534 849 1585 1,800 1635 2,289 1685 3,580 1735 4,103 1785 5,625 1535 870 1586 1,820 1636 2,355 1686 3,590 1736 4,143 1786 5,485 1536 886 1587 1,842 1637 2,426 1687 3,661 1737 4,182 1787 5,706 1537 896 1588 1,855 1638 2,491 1688 3,683 1738 4,222 1788 5,749 1538 909 1589 1,844 1639 2,547 1689 3,704 1739 4,262 1789 5,793 1539 923 1590 1,829 1640 2,597 1690 3,724 1740 4,303 1790 5,839 1540 937 1591 1,559 1641 2,652 1691 3,744 1741 4,343 1791 5,885 1541 951 1592 1,735 1642 2,631 1692 3,763 1742 4,383 1792 5,936 24 Y. 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