Reconstruction of the Spanish Money Supply, 1492-1810

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 monetary 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. This monetary expansion can account for most of the price level rise in early modern Spain. In its absence, Spain would have required substantial deflation to accommodate its early modern output gains.


Introduction
This paper presents new times series for the Spanish money supply in the early modern period . 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. 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.
While this paper focuses 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 the majority of Spain's price level rise between 1492 and 1810. Absent its monetary windfall, Spain would have had to deflate its price level by more than half to accommodate its population driven output growth.
The remainder of this paper is structured as follows: Section 2 provides an overview of the monetary system in early modern Spain. Section 3 presents the methodology and the money supply estimate, followed by validation exercises and comparisons to alternative stock estimates. Section 4 uses the new money supply seriees to analyze Spain's early modern price level rise. Section 5 concludes.

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, as well as 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., forthcoming). 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 parity). 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 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, ch. XIV provides 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;Sindreu, 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 Sindreu (2016, p.366), only 6% of Spanish silver arrivals in the 18th century were minted in Seville.
economy's production function as intermediate inputs for the production of other goods (e.g. silverware). Thus, when the commodity market value of precious metals rose above its mint parity, an arbitrage profit could be realized by melting down coins and selling the metal on the commodity market. The primary function of precious metals, however, was monetary. 5 In fact, almost all of Spanish America's mining output was directly minted in American mints (Céspedes del Castillo, 1996;Irigoin, 2018). As a consequence, the vast majority of precious metals from Spanish America arrived in Spain as coins (Sindreu, 2016;Costa et al., 2013, p.63).

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 in-and 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 Velde, 2013). 6 The initial stock (M 1492 ), in-and outflows (in k , out k ) and depreciation determine the money supply (M t ): 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 5 Spanish precious metals were partly channelled into the commodity markets of other European countries (Nogues-Marco, 2011). This trade, however, did not simply arbitrage between precious metals in minted and un-minted form, but also between domestic and foreign denominations. The commodity market price of a precious metal was primarily underpinned by its local mint parity. Deviations between mint parity and commodity market price thus typically reflected international arbitrage opportunities, e.g. when the same amount of silver could buy more goods in France than in Spain.
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 (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 (esp. 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. 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 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 . 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 3,600 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. The upper bound value grounds in Jacob's initial European stock value of 1,749 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 7 While the gold and silver production data allow us to calculate separate gold-and 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 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 tonne values whose average forms the baseline estimate's initial value.

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 (Schurz, 1939;Borah, 1954;Chuan, 1969;Bonialian, 2012) (Appendix A.4). Second, we account for the amount of precious metals that stayed in the Americas (Walton, 1994;Barrett, 1990, 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, 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 shortrun, 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 short-and long-run, we implement a linear diffusion process that lasts for 10 years -a time span long enough to encompass short-term adjustment dynamics.
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, 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 , 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 Most salvaging operations were concluded within one year. Only in a few cases did salvaging operations extend beyond one year, e.g. when access to the treasure was complicated by bad weather.
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.
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 this part corresponds to the European precious metal outflow-to-stock ratio, out EU t /M EU t ⇡ 0.79% (Attman, 1986;de Vries, 2003). 17 We treat European precious metal arrivals from non-Spanish colonies, i.e. gold inflows from Africa and from Portuguese Brazil, analogously to European production 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 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 where in AM !ESP k and in EU !ESP 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, pacif ic k denotes precious metals leaving America through the Pacific, loss k salv 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 out EU k /M EU k is the fraction of the European precious metal stock that leaves Europe every year. EU denotes the sample average of Spain's 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.
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,  puts this share at two thirds. Another estimate for 1688 by  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%. 19 The one-year lag reflects the time delay between the mining of precious metals in America and their shipping to Spain.
European GDP share, which we calculate based on the 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 EU 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 o k . 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 in-and outflow sequences, in k and out k , into equation 1 we obtain the money supply estimate for Spain. Figure 1 depicts the resulting baseline estimate as a solid black line. Gray-shaded probability intervals show how the money supply estimate is affected by data uncertainty in the input variables (Appendix A.1). Dotted lines highlight the 95% probability region. 21 According to the baseline estimate, the Spanish money supply increased 15-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 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 equation 2). 21 Downward drops in the money stock series represent transportation losses, some of which are quickly reversed due to salvaging in the subsequent year. 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. 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 28-fold, implying an average annual money growth rate between 0.7% and 1%. Figure 1 depicts the money supply series at an annual frequency. 22 While part of the underlying data is annual (American production, transportation losses), other input variables entail linear interpolations over several decades (European production, the Pacific flows, Spanish outflows). 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.

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 6.5, and ranges from 3.3 to 12. This is in line with other velocity estimates for the early modern period. According to Palma (2018), velocity in 22 England ranged from 3.5 to 8.8, whereas Mayhew (1995) locates it between 2.2 and 8.7.
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 7,265 tonnes of silver equivalent. Our baseline estimate for 1810 is 6,391 tonnes. This implies a modest money stock growth of 14% in the 65 years after 1810 (0.2% 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. 23 Against this backdrop, the 95% interval's lower bound of 4,153 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. 24

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 23 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.
24 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 2,214 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. This can explain the low stock value for 1830, which implies the implausibly high velocity of 20 according to the 1830 GDP estimate by Álvarez-Nogal and Prados de la Escosura (2013). 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). 25 Motomura himself notes that a substantial part of the coins minted during this period left Spain to finance military operations in the Low Countries. 26 However, the more persistent economic reason behind the export of Spanish coins was their status as an internationally accepted means of payment ). As such, Spanish pesos were used by various European trading companies for their East Asia trade. 27 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 an implausibly high velocity of 36.
In sum, in contrast to previous stock estimates, our money supply series implies 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.

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? 28 According to the monetarist view, rising price levels were primarily a consequence of rising money stocks, brought about the the influx of precious metals from America (Hamilton, , 1947Fisher, 1989;Mayhew, 1995). 29 Another view highlights the role of an accelerating money velocity (Miskimin, 1975;Lindert, 1985;Goldstone, 1984: 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 positions in the money vs. velocity debate are conveniently summarized through the following formulation of the equation of exchange: where P t denotes the price level, M t the money stock, V t its velocity, and Y t stands for real output. We can use equation 3 to decompose Spain's price level rise into the contributions of money, velocity, and real output. To quantitatively assess the importance of each of these we use the importance measure I(·): where small letters denote the natural logarithm of the respective variable, and indicates 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, To apply the accounting machinery lined out in equations 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. 30 We generate the 11-year moving average of the annual GDP series by Álvarez-Nogal and Prados de la Escosura. 31 We then 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 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.
29 European prices modestly rose prior the the arrival of large quantities of American precious metals. This has been attributed to an increase in production of European silver mines (Munro, 2003). 30 Other goods price indices for early modern Spain have been compiled by Allen (2001), Munro (2008), and Losa and Zarauz (2020). Although the underlying price series differ somewhat in their regional coverage, sample period, and goods basket composition, their aggregate behavior is very similar, yielding very similar decomposition results. 31 In particular, we use their baseline estimate III.
The following decomposition result reflects data uncertainty in the money supply series through 95% probability intervals. 10,000 random draws from the money supply distribution at the beginning and end of the sample generate the distribution of importance measures, I(·), upon which the probability intervals are based. These intervals do not reflect uncertainty in the output and price series, which are the point-estimates taken from the literature.
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 5.7 and real GDP by a factor of 2.7. This was largely accommodated by a 15-fold increase in money. To balance the equation of exchange a 3% increase in velocity sufficed.
The second row of Table 1 reports the counterfactual price level changes implied by scenarios in which either money, velocity, or output stayed at its initial 1492 level. According to this measure, the Spanish price level in 1810 would have been 38% of its 1492 level, had money not increased between 1492 and 1810. In other words, prices would have had to fall by 62% to accommodate Spain's early modern output gains. Put in terms of the importance measure described in equation 4, the money supply increase explains 72% of Spain's price level increase. 32 The 95% probability interval of this importance measure stretches from 60% to 73%. 33 Money growth thus appears to explain the majority of Spain's early modern price level rise.
The conclusion that money growth mattered most is supported by the second counterfactual, presented in column four of Table 1. It shows that even if velocity had stayed constant at its initial level of 8.5, prices would have risen by a factor of 5.5 -not too far from the actual price increase of 5.67. Thus, even in the absence of the small change in velocity, the increase in money accounts for an increase in prices that resembles the actually observed price level rise. In terms of the importance measure 4 the 3% increase in velocity accounts for only 1% of the change in prices. The 95% probability interval for this measure stretches from 0% to 14%.
Finally, column five shows that the 15-fold increase in money, together with the 3% 32 Note that long-run real output growth may have been influenced by the repeated monetary injections. Palma (2019), for example, argues that early modern money inflows rendered Spain's economy chronically uncompetitive, and real output increases would thus have been larger in the absence of the continuous arrival of American precious metals. In the presence of this long-run monetary non-neutrality an even larger price decline would have been required to accommodate the larger counterfactual output increase. 33 The interval is asymmetric around the baseline estimate because the importance measure is a nonlinear 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. increase in velocity would have implied a 15.5-fold increase in prices had real GDP not grown 2.7-fold. Clearly, output growth took substantial pressure off the price level (Nicolini and Ramos, 2010). As a consequence, the contribution of output growth to the price level change is substantial -27% according to the importance measure defined in equation 4.
In sum, the results support money-based explanations of the early modern price level rise in Spain Fisher, 1989). 34 Velocity hardly changed, and thus mattered comparatively little for the price level rise over the whole sample. 35

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%. 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. A. Data

A.1. 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 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. 4 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.4 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) andde 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. 5 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 ( Figure 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.6. 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 each transportation loss (incl. average smuggling rates) with a normally distributed scalar that is centered around 1 and has a standard deviation of 7%. We draw this scalar independently for each loss event.
The main source of uncertainty about the American precious metal output pertains to the amount of unregistered production that took place. Section A.3 provides a detailed discussion of this subject and the available data. To account for the uncertainty introduced by unregistered production, we multiply the American production data (incl. average estimates for illicit production) with a normally distributed error scalar, whose standard deviation mirrors the dispersion between different production series. In particular, we set the error scalar's standard deviation to 10% for the periods prior to 1640 and after 1720. Between 1640 and 1720 we apply a higher standard deviation of 15% to reflect the higher degree of uncertainty surrounding the amount of unregistered production during this time period. These period-specific standard deviations reflect the discrepancy between the production series by Humboldt (1811), which includes illicit production, and our baseline production series, which adds an estimate of illicit production to the comprehensive official production data by TePaske (2010) (see Figure A.1). Error scalar draws are independent across the three sub-periods, 1492 to 1639, 1640 to 1720, and 1721 to 1810.
With regard to the European precious metal production the estimates by Soetbeer (1879) have been taken over by much of the subsequent literature (Ridgway, 1929;Merrill, 1930;Velde and Weber, 2000b). Only the pre-1600 data has been substantially revised upwards by Nef (1941). However, this lack in variance in the literature cannot be interpreted as the absence of uncertainty about European production figures. We therefore multiply the European production data with an error scalar that has a standard deviation of 10% and a mean of 1. The error scalar is drawn independently for each 20-year period observation by Soetbeer and Nef. We follow the same approach for the African precious metal inflows by .
We reflect uncertainty about the depreciation rate of money due to the wear and tear by a uniform distribution with limits set according to the 0.2% to 0.28% range described by . Our estimate of the American retention rate up to 1780 is 14.5%. This fraction is an average based on observations by Barrett (1990) and Walton (1994). Barrett estimates that 15% of the American precious metal production either stayed in America, or was lost in transport. We subtract transportation losses from the 15% figure to arrive at American retention. Thus the American retention rate inherits uncertainty from transportation losses, and the American precious metal production series. The other observation comes from the mint in Mexico City. In the 1770s it exported 75% of its mint output to Spain (Walton, 1994, p.181). The remaining 25% either went over the Pacific or stayed in America. We subtract the contemporary Pacific flow rate of around 7% from the 25% figure to arrive at American retention. To the extent that the exact Pacific flow is uncertain, the American retention rate inherits this uncertainty. In addition, we add a uniformly distributed random error term from the +/-3.5 percentage point range to the American retention rate. This 7 percentage point range spans the difference between the 11% retention rate estimate based on Barrett (15% minus a 4% average transportation loss), and the 18% rate based on the Mexican mint data (= 25% minus a 7% mid-point pacific flow estimate). For each calculation run, the error term is drawn once for the entire retention rate series from 1492 to 1810.
The uncertainty surrounding the rate at which the European precious metal production and African arrivals were minted is reflected in a uniformly distributed error term that ranges from -15 to +15 percentage points. This large variance is warranted because the mid-point estimates by  and  are at best educated guesses. Thus, for the period from 1492 to 1687 the share of unminted metals is equally likely to be any number between 5% and 35%. For 1688 to 1779 the range is 24% to 54%, and from 1780 onwards it is 52% to 82%. Finally, the use of Spain's share of European GDP in the money supply estimate is associated with two types of uncertainty. First, there is data uncertainty about the exact value of Spain's European GDP share in the early modern period. The data by Bolt and van Zanden (2013) imply an average share of 15%. However, shares vary between 13% and 17.5% depending on time period and underlying source. The stochastic simulation reflects this uncertainty by adding a uniformly distributed error term from the +/-2.5% range to Spain's 15% average GDP share.
The second type of uncertainty pertains to the extent to which Spain's European GDP share is representative of intra-European precious metal diffusion. This is because the money supply estimation assumes that intra-European precious metal diffusion from the rest of Europe into Spain corresponds to Spain's European GDP share. 6 To cover the uncertainty associated with this assumption we add a second error term to Spain's average GDP share of 15%. We opt for a uniformly distributed error term whose support spans the +/-33% range around the 15% baseline. This treats the GDP share of 15% as equally representative of precious metal diffusion shares in the 10% to 20% range. The choice of this range is motivated by Bonfatti et al. (2020) according to which the money holdingsto-income ratio of Europe's most monetized economies tended to be no more than two times the money holdings-to-income ratio of Europe's least monetized economies. The two error terms for Spain's European GDP share are drawn once for the whole sample. Spain's initial stock estimate inherits this error term to the extent that it uses Spain's European GDP share to translate European stocks into Spanish stocks.

A.2. Initial stock
The earliest known estimate of the European precious metal stock comes from economic statistician . King puts the total stock of precious metals at 45 million pound sterling. According to his data for the late 1600s, 61.3% of that was in minted form. This translates into 3,073 tonnes of minted silver equivalent. Unfortunately, King does provide no information on how he arrived at his initial stock figure.
Other estimates of precious metal stocks for 1492 can be categorized into three groups: production-based estimates, equation-based estimates, and secondary-literature values. Among the first group are Jacob (1831) and Velde and Weber (2000b). Jacob puts the initial European stock at 33,674,256 pound sterling (3,749 tonnes of silver equivalent). He arrives at this quantity based on a Roman money stock figure put forth by Sueton for the time of Vespasian's reign. This figure is then depreciated at an annual rate of 1/360 up to the early 9th century, at which point the resumption of European precious metal production is assumed to exactly offset any further depreciation up to the early modern period.
The timing of these assumptions has been broadly confirmed by McConnell et al. (2018) based on traces of antique lead pollution that are recognizable in Greenland ice cores today. However, the depreciation rate of 1/360 has been criticized as too low, because it only reflects the wear and tear of coins in normal times (Chevalier, 1847, pp. 68-69). This neglects, among others, transportation losses and lost hoards. When these are taken into account, money stocks depreciated at a faster rate (MacCulloch, 1855(MacCulloch, [1846, p.1054). For this reason, Velde and Weber (2000b) apply a higher depreciation rate of 1% to arrive at a global precious metal stock through the cumulation of precious metal production. This 1% depreciation rate is endorsed by Patterson (1972) as a plausible catch-all rate of depreciation. Velde and Weber arrive at a global stock of 6,897 tonnes of silver equivalent in 1492.
The second group of initial stock estimates uses additional assumptions to back out initial stocks. Braudel and Spooner (1967) assume that in 1500 and in 1660 the value of the European gold stock equals the value of the European silver stock. Combining this assumption with a European net-inflow of 181 tonnes of gold and 16,886 tonnes of silver between these two years and a gold silver ratio of 10.5 in 1500 and 14.5 in 1660 they obtain initial European stocks for gold, G 1500 , and silver, S 1500 , as the solution to the following two equations: The arbitrariness inherent in this approach has been pointed out by many authors, including Braudel and Spooner themselves. The assumption that the value of the gold stock equals the value of the silver stock lacks grounding in economic theory Glassman and Redish, 1985;Palma, 2019). In addition, the resulting initial stock value of 74,854 tonnes of silver equivalent is so high that it defies the available production side data.  points out that accumulating this stock would have required all European mines to operate at their peak 16th century capacity since antiquity, and even then a zero depreciation and outflow assumption would be needed to reach such a high stock level for 1492.  Glassman and Redish (1985) Europe 3,542 t average of Del Mar (1877b) and King (1696)  Europe 15,000 t erroneous translation of Hume (1752); unclear conversion rate Notes: Stock figures refer to metric tonnes of silver equivalent. Tonne figure from Del Mar (1877b) deviates from Jacob (1831) because the former source apparently converts the latter's pound sterling value into a USD value, using a late 19th century USD-GBP exchange rate.

8
The estimate by Gallatin (1830) uses a value of American precious metal inflows of 800 million USD until 1596 and a 3.5-fold increase in goods prices, P , to derive a 1492 precious metal stock, M 1492 , for Europe of around 300 million USD (evaluated in 1830 USD). While Gallatin does not explicitly state how he deducts the latter from the former, his writing suggests that he assumes the real money stock, M/P , to be constant: Solving this equation for M 1492 yields the proposed initial stock value around 300 million USD, translating into around 7,800 tonnes of silver equivalent. While this value is substantially smaller than the one obtained by Braudel and Spooner (1967) and thus conforms more closely to production side estimates, its grounding in economic theory is similarly weak.
To explore the assumptions involved, first consider the equation of exchange for Europe: MV = P Y . A constant real money stock involves a constant ratio of real output over velocity, Y/V . This is hard to justify even when assuming a stable velocity, V , and a Malthusian constancy of real output per capita. This is because Europe experienced population growth of around 30% in the 16th century, which increased real output, Y . Second, the proposed stock addition of 800 million USD/20,000 tonnes of silver equivalent neither takes cumulated European production nor cumulated European outflows into account. According to our estimates the former amounts to 6,200 tonnes, and the latter to 5,300 tonnes. In addition there was a small inflow from Africa, amounting to around 820 tonnes. Finally, the proposed American inflow value of 20,000 tonnes exceeds our best estimate of 8,700 tonnes by more than 100%. When we revise the Gallatin estimate by these factors -population growth, European outflows, European production, African inflows, and lower cumulated inflows from America -we arrive at a revised initial European stock estimate of 3,228 tonnes -a value not far from Jacob's production side estimate.
Next, there exists a secondary literature on precious metal stock estimates for Europe at the eve of the early modern period. Del Mar (1877b, p.40) states a value of 167 million USD, which is a USD-translation of Jacob (1831) at a USD-pound sterling exchange rate of 4.96 (see Del Mar, 1877a, pp.71ff.). 7 Glassman and Redish (1985) average the initial stock estimates by  and Del Mar (1877b) to initialize their European stock. By construction, their estimate thus lies within our preferred initial stock range. The initial European stock value used by Morineau (1985, p.571) -60 million pound sterling/15,000 tonnes -is a curiosity: First, it is based on a French translation of Hume (1752), but, as has been pointed out by Stengers (2004), the value of 60 million pound sterling is not contained in Hume's original work. It has been introduced by a loose French translation. Second, equating 60 million pound sterling into 15,000 tonnes of silver equivalent implies an inexplicable conversion rate of 250 grams of silver per pound sterling. For these reasons it is hard to justify the 15,000 tonne figure.
Hume's original text states that an annual precious metal inflow from America to Europe amounting to 6 million per year would probably have doubled the initial European money stock within ten years (6 million times ten years equals 60 million). 8 Importantly, Hume's original text does not specify the unit, and "million" might well refer to Spanish pieces of eight (pesos), which would bring it line with inflow data for the early 16th century. Even at the time of Hume's writing, in the mid-18th century, an inflow value of 6 million pound sterling is too high. European precious metal inflows from America only reached that level around 1800. The peso interpretation of Hume would yield an initial European stock of around 1,500 tonnes of silver equivalent -a value in the vicinity of that implied by Velde and Weber (2000b). The pound sterling interpretation of Hume's figures yields a silver weight of around 6,500 tonnes -somewhat below the number yielded by the equation-based approach of Gallatin (1830).
In sum, the literature provides various estimates of initial precious metal stocks around 1500. Our preferred estimates are the production-based ones. Although they require heroic assumptions, their methodological basis is in principle sound. The productionbased estimates receives additional support from two sides: First, the revised initial stock springing from the real money stock assumption of Gallatin (1830) falls within the range spanned by the two production-based estimates. Second, the production-based estimates furthermore align with the stock estimates proposed by  and the peso-interpretation of Hume (1752) -the two earliest authorities on the matter.

A.3. American production and European arrivals
Different sources on American precious metal production exist. While they agree about the amount of American precious metal production for the 16th and 18th centuries, they disagree for the 17th century. Sources that account for unregistered precious metal production show substantially higher numbers than sources that focus only on officially registered production (Barrett, 1990). For our calculations, we use the official production data from TePaske (2010), which is the most comprehensive yet compiled. Figure A.1 shows this data and compares it to the production data by Humboldt (1811), who takes unregistered production into account. There is a substantial deviation between these two Given that some of the sources that Humboldt used to construct his production series are unknown today, it is worth considering a second piece of evidence about the quantity of unregistered precious metal production: the amount of American precious metals that was arriving in Europe. This data was regularly published in contemporary Dutch gazettes that have been unearthed by . In the 17th century, the European arrival data at times exceeds the official American production data, suggesting a considerable amount of unregistered production took place in America. Morineau's arrival data and Humboldt's production data reinforce each other in this regard (Barrett, 1990). We therefore adjust the official production data from TePaske for unregistered production.
To account for unregistered precious metal production we add 16.8% to the production series by TePaske -the adjustment factor calculated by Humboldt (1811). From the mid-17th century to the early 18th century the share of unregistered production was higher, reaching up to 50% (TePaske, 2010, pp.311ff.). We thus use a 50% adjustment factor for the period 1640-1720. 9 From 1720, up to the late 18th century we switch back to 9 During this period, the reduced supply of mercury to Mexican amalgamators facilitated an increase in illicit production. More refining was done using smelting, which made it easier to hide the exact amount of silver production from the fiscal authority. Brading and Cross (1972) note that due to the shortage of mercury just under half of Zacatecas's silver was produced using smelting in the years 1685-1705. At Sombrerete, none of the silver was produced using amalgamation. In Peru, although the official production data shows a decline starting in the 1640s, mercury consumption was stable. Thus, Brading and Cross (1972) argue that actual Peruvian production did not peak until 1680. At the most fertile Peruvian mines in Potosi, production was taxed at more than twice the rate levied on other mines. Consequently, the incentive to conceal silver production was higher. The illicit production taking place at Zacatecas, Sombrerete, and Potosi, was substantial relative to the total silver production in America. Together these sites accounted for more than 40% of total official American silver production. The higher 16.8%. Finally, by the late 18th century less and less production escaped registration by the Spanish Empire's reformed bureaucracy. Therefore, from 1780 onwards we set our adjustment factor to 0%. The so-adjusted TePaske series is depicted by the solid black in Figure A.1. It closes much of the 17th century gap between the official production data, and Humboldt's estimate.
The European inflows we calculate based on the American production data should align with the arrival data from . To calculate European arrivals from American production data we subtract Pacific flows, American retention, and transportation losses. Figure A.2 displays the resulting inflow series and compares it to Morineau's arrival data. The solid black line depicts our European inflow series, and the gray markers depict Morineau's arrivals. In addition, the dashed gray line depicts European inflows when calculated on the basis of officially registered production only. The figure shows that accounting for unregistered precious metal production is important for bridging the gap between Morineau's arrival series and European inflows as calculated from American production. While the discrepancy between these two series can still be substantial (esp. from 1650 to 1700), this exercise shows that it is possible to substantially narrow down the range of plausible production and inflow values through the cross-validation of different data sources.
Moving from production data to inflow data, Figure A.3 compares officially registered precious metal inflows with inflows as reported by the Dutch gazettes . In unregistered silver production for the second half of the 17th century also squares well with an increase in unregistered silver shipments to Spain during this period (Mangas, 1989, p.316). Both were symptoms of a general weakening of imperial fiscal control (TePaske, 2010, pp.311). contrast to the production data, these series include Spanish inflows from Spanish America only; Portuguese gold inflows from America are not contained. Officially registered Spanish inflows come from , Fuentes (1980), andGarcía-Baquero (1996), who rely on the official documentation from the Casa de Contratación and individual ship registers.
As is the case with the production data, official inflows fall short of Morineau's unofficial arrival data from the middle of the 17th century onwards, up to the early 18th century. Before that, the official and unofficial data sources are in agreement. After the early 18th century, the official and unofficial data sources converge again (see García-Baquero, 1996, for a detailed comparison).
The shortfall of official inflows vis-á-vis unofficial inflows after 1640 is not solely due to the concomitant increase in unregistered production documented earlier. In addition, it reflects an increase in unregistered transportation, i.e. smuggling across the Atlantic (Mangas, 1989, p.316), and changes in accounting methods for precious metal arrivals TePaske, 2010, p.306) that accompanied the shift of colonial trade from Seville to Cádiz. 10 Thus, while official inflow and production data both suffer from underreporting in the 17th century, the degree of underreporting appears more manageable in the production data. As a consequence, the official production data can constitute a more reliable basis for estimating American precious metal remittances to Spain than the official Spanish inflow data.

A.4. Pacific flows
Several publications provide comprehensive overviews of early modern precious metal flows across the Pacific (Bonialian, 2012;Flynn and Giráldez, 2017). The amount of silver that was allowed to leave America across this route was capped by the "permiso", which between 1593 and 1776 was only slowly raised from 250,000 pesos to 750,000 pesos. While official "permiso"-values suggest Pacific flows only amounted to a modest fraction of American production, actually shipped amounts routinely exceeded the "permiso" many times over (Chuan, 1969;Flynn and Giraldez, 1995).

A.6. Outflows
This section gives an overview of the Spanish outflow data. Table A.6 shows Spanish money outflows as a fraction of inflows from Spanish America -the Spanish outflow rate. Figure A.5 displays the linearly interpolated series together with the individual observations from Attman and Walton. The second alternative estimate is the fixed-flow rate estimate. In contrast to the previous two money stock estimates, the fixed-flow rate 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 productionthe 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 GDP-share based estimate.
Estimates of the Asian absorption center around 50%. 11 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 Figure B.1. 12 The short-dashed gray line indicates the center of this range, which corresponds to a 50% Asian absorption rate.
Reassuringly, the GDP-share based estimate, as well as the fixed-flow rate 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 GDP-share and fixed-flow rate estimates in greater detail. 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 1,510 tonnes of silver equivalents -823 tonnes of silver and 68 tonnes of gold. 13 This constitutes the lower bound of our initial stock range for Europe. The highest plausible initial value is 3,749 tonnes of silver equivalents . The mid-point of the 1,510 to 3,749 ton range -2,630 tonnes -serves as our initial European stock estimate.

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 privateers' home country. Finally, we remove the diffusion term, dif f k , from the European inflow equation. 14 The resulting European precious metal inflow is where loss EU k = loss 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 in-and outflow data we calculate the European precious metal stock, M EU t , according to equation 1. We then calculate an intermediary measure for the Spanish money supply according to Spain's share of European GDP: where EU 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, f M GDP share t , to arrive at the final GDP-share 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 equation 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: 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 longoutflows. 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. 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 GDP-share based estimate of the Spanish money stock, M GDP share 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:

Initial stock
The fixed-flow rate estimate starts from the same initial value range as the GDP-share based estimate: The low value of 1,510 tonnes of silver equivalent initiates the lower bound of the fixed-flow rate range estimate. The lower bound fixed-flow rate estimate is then calculated based on a high Asian absorption rate of 66%. The high value of 3,749 tonnes initiates the upper bound estimate, which uses the low Asian absorption rate of 33%. Finally, the mid-point fixed-flow rate estimate of the Spanish money stock starts at the mid-point of the 1,510 to 3,749 tonne range, i.e. 2,630 tonnes.

Inflows and outflows
The fixed-flow rate 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 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.

B.3. Copper money
Starting in the late 16th century, fiscal pressures arising from persistent warfare led to the issuance of increasing amounts of copper money. Figure 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 95% probability region of the baseline money supply estimate. 15 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  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 in accordance with Gresham's law. However, temporary over-or 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 Figure B.2 may be considered too narrow during the first half of the 17th century.

C.1. 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 tonne 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 2,175 tonnes, at which both items account for 37% of Spain's price level rise. 2,175 tonnes is around 5.5 times our baseline initial estimate of 396 tonnes. Beyond an initial stock value of 2,175 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 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 46% of the price decline. GDP growth of around 30% 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 : Declining Spanish urbanization resulted in a reduction of opportunities for exchange and thus a lower velocity of money.
Finally, panel D displays the decomposition results for the period of reflation, 1751 to 1810. During this period prices rose by more than 200%. Partly this is accounted for by a 36% increase in the money supply. Rising velocity, however, plays a larger role. It explains 55% 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.
How can the contribution of velocity from the mid-17th century onwards be squared with our finding that velocity did not importantly contribute to the Spanish price level rise if we consider the period from 1492 to 1810 as a whole? The answer lies in the frequency domain: Velocity increases in one century were offset by velocity decreases in another. By contrast, money growth was persistent.