This study constructs a time series of real GDP in Germany for the period 1500–1850 using an indirect output estimation technique that relies on wages, prices, and sectoral employment. It thereby contributes to a growing body of partial national account reconstructions for western European economies during the pre-statistical era.Footnote ¹ Given its territorial extension and population, Germany was already one of the largest economies in the western part of the European mainland during the early modern period. Hence, a GDP projection back to 1500, however tentative it may be, has the potential to shed light on two major research issues in economic history.

The first issue relates to the nature and the forces underlying the reversal of fortunes in early modern Europe. Whereas central and northern Italy entered into a long phase of economic decline after about 1400, the Northern Netherlands and, after the middle of the seventeenth century, Britain experienced a rise in real GDP per capita, producing an intra-European (little) divergence in real income. Human capital accumulation, patterns of family organization, Atlantic trade, and institutions placing constraints on rulers and securing inclusive markets have been proposed as factors contributing to this reversal of fortunes (Acemoglu, Johnson, and Robinson Reference Acemoglu, Johnson and Robinson2005; de Moor and van Zanden 2010; Broadberry et al. Reference Broadberry, Campbell, Klein, Overton and van Leeuwen2015, pp. 374–83; de Pleijt and van Zanden 2016). Recent work on the growth experiences of Spain and Portugal has refined our knowledge concerning the timing and the forces underlying early modern divergence (Álvarez-Nogal and Prados de la Escosura Reference Álvarez-Nogal and Prados de la Escosura2013; Palma and Reis Reference Palma and Reis2019; Prados de la Escosura, Álvarez-Nogal, and Santiago-Caballero Reference Prados de la Escosura, Álvarez-Nogal and Santiago-Caballero2020). The present study contributes to this literature by showing that Germany experienced a massive decline in real GDP p. c. during the sixteenth century, which is consistent with a reversal of fortunes from inland regions to economies involved in transcontinental trade at the beginning of the modern era.

The second research field that this investigation addresses relates to the transition from a Malthusian regime to modern economic growth. Earlier studies, among them Abel (Reference Abel1980) and Rostow (Reference Rostow1956), have depicted Germany as being characterized by Malthusian stagnation right until the middle of the nineteenth century, when a rapid take-off into sustained economic growth took place. The present investigation contributes to more recent literature, which argues that the development of modern economies had early modern roots (van Zanden Reference van Zanden2002; Broadberry et al. Reference Broadberry, Campbell, Klein, Overton and van Leeuwen2015, ch. 10). Specifically, I relate the long-term trajectory of the German economy to the stylized sequence of growth regimes advocated by Galor (Reference Galor, Aghion and Steven2005, Reference Galor2011, chs. 2 and 5; Galor and Weil Reference Galor and Weil2000) based on unified growth theory. From this perspective, the new evidence suggests that Germany’s transition from a Malthusian regime to modern growth was a long-drawn-out process starting in the second half of the seventeenth century and coming to an end only in the last two decades of the nineteenth century.

The study starts with a description of the indirect method to construct central aggregates of the output side of the national accounts and continues with a presentation of the data required to apply this method. Brief presentations of the resulting series follow, together with an overview of sensitivity tests. The final section before the conclusion places the results in a wider research context to produce a stylized account of economic growth in Germany during the first three-and-a-half centuries of the modern era.

THE INDIRECT OUTPUT ESTIMATION APPROACH

Reconstructions of the national accounts of England and Holland for the pre-statistical era have focused on a reconstruction of output-side GDP (van Zanden and van Leeuwen Reference van Zanden and van Leeuwen2012; Broadberry et al. Reference Broadberry, Campbell, Klein, Overton and van Leeuwen2015). Data sources for preindustrial Germany are insufficient to follow this approach. Instead, I rely on an indirect technique to estimate output-side GDP or aggregate value added based on wages, prices, and sectoral employment. It was originally developed to estimate agricultural output by Crafts (Reference Crafts1985, pp. 39–41) and applied to an analysis of growth and labor productivity in preindustrial European agriculture by Allen (Reference Allen2000, pp. 13–14). Subsequent works have extended it to estimate aggregate GDP. The procedure is as follows.

Net agricultural output is given by

(1) $${Q_{At}} = {r_t}{c_t}{N_t},$$

where Q _At is agricultural output, N _t total population, c _t real food consumption per capita, and r _t the ratio of food consumption to food production, all at time t. r _t is thus an indicator of the balance of external trade in agricultural products.

Real food consumption per capita is estimated using a demand equation:

(2) $${c_t} = aP\,_{Ft}^e\,I_t^g\,P_{NFt}^b,\,\,\,\,{\rm{s}}{\rm{.t}}{\rm{.}}\,\,\,e{\rm{ + }}g + b = 0,$$

where a is a scaling factor, P _Ft the real price of foodstuffs, I _t real income per head, and P _NFt the real price of consumer goods apart from food, all in year t. e, g, and b are the own price, income, and cross-price elasticities of food demand. Substituting Equation (2) into Equation (1) yields

(3) $${Q_{At}} = a{r_t}\,{N_t}\,P\,_{Ft}^e\,I_t^g\,P_{NFt}^b.$$

To estimate agricultural output (Q _At ), I use data on population (N), income (I), prices of food (P _F ), and non-agricultural products (P _NF ) and will make assumptions about the elasticities (e, g, b) and the ratio of food consumption to food production r. The scaling factor a is chosen so as to fix the level of Q _At to value added in agriculture in the year when direct estimates for agriculture production begin.

With agricultural output and population known, a simple measure for average labor productivity in agriculture, ALPA is

(4) $$ALPA = {Q_{At}}/{L_{At}},$$

with L _A denoting employment in agriculture.

To calculate an index of real GDP, the majority of the literature divides food consumption per capita by the share of agriculture in total employment (Q _At /[L _At /L _t ]); examples include Malanima (Reference Malanima2011, p. 185) and Palma and Reis (Reference Palma and Reis2019, p. 496). This procedure assumes that labor productivity in the agricultural and non-agricultural sectors is identical. The strong shifts in relative prices that will be documented in the next section suggest that this assumption is too restrictive. Therefore, I follow Álvarez-Nogal and Prados de la Escosura (Reference Álvarez-Nogal and Prados de la Escosura2013, pp. 13, 16; see also Prados de la Escosura, Álvarez-Nogal, and Santiago-Caballero Reference Prados de la Escosura, Álvarez-Nogal and Santiago-Caballero2020, p. 14) and proxy value added of industry and services with non-agricultural employment L _NAt .

Agricultural output Q _At , non-agricultural employment L _NAt , and sectoral prices—agricultural prices P _At and a price index for industry and services P _It Footnote ² —serve to compute a Fisher ideal index of real output-side GDP at factor cost. This methodological choice follows Diewert (Reference Diewert1992) and the System of National Accounts (European Commission et al. 2009, ch. 15). In a preliminary step, not only agricultural output, but also the volume index of non-agricultural output proxied by non-agricultural employment is calibrated so that current price values added (P _At Q _At and P _It L _NAt , respectively) in the year when direct estimates become available equal observed values. I use the averages from 1856–1860 for calibration.

The Fisher quantity index (QI _F ) is the geometric average of the Laspeyres (QI _L ) and the Paasche indices (QI _P ):

(5) $$QI{}_{Lt,t + 1} = {{{P_{At}}{Q_{At + 1}} + {P_{It}}{L_{NA + 1}}} \over {{P_{At}}{Q_{At}} + {P_{It}}{L_{NAt}}}}$$

(6) $$QI{}_{Pt,t + 1} = {{{P_{At + 1}}{Q_{At + 1}} + {P_{It + 1}}{L_{NAt + 1}}} \over {{P_{At + 1}}{Q_{At}} + {P_{It + 1}}{L_{NAt}}}}$$

(7) $$QI{}_{Ft,t + 1} = {(Q{I_{Lt,t + 1}}Q{I_{Pt,t + 1}})^{1/2}}$$

QI _Ft,t+1 is the rate of change of aggregate output from year t to t + 1. Multiplying values for consecutive years yields a chain index that can be normalized to any year.

The prior literature suggests that the indirect approach to estimating output-side GDP yields valid results under some conditions. The application to England by Nuvolari and Ricci (2013) suggests lower rates of real GDP growth in the long run than found by Broadberry et al. (Reference Broadberry, Campbell, Klein, Overton and van Leeuwen2015). The use of day wages to proxy income appears to be the main reason why the indirect method underestimates economic growth relative to a direct output estimate, as the number of days worked increased over the early modern period (Broadberry et al. Reference Broadberry, Campbell, Klein, Overton and van Leeuwen2015, pp. 257–65).

For Spain, Prados de la Escosura, Álvarez-Nogal, and Santiago-Caballero (Reference Prados de la Escosura, Álvarez-Nogal and Santiago-Caballero2020, pp. 10–13) compare the estimate of agricultural output using the demand approach with an aggregate index of tithe returns for major agricultural products. The two series move broadly in parallel, which suggests that they present the long-term trajectory of agricultural output in the correct way. For Germany, Pfister and Kopsidis (Reference Pfister and Kopsidis2015, p. 284 and Online Appendix) combine the indirect approach with contemporary harvest statistics for 1792–1812 and 1815–1830 to study agricultural output in Saxony, the most important early industrial region of Germany. The fit between estimated and observed food production is poor during the first sub-period, when war-related events disrupted markets, so that prices (and possibly wages) did not reflect conditions of supply and demand. By contrast, the fit is satisfactory for the post-war period, but by no means perfect. Results also show that the indirect approach is best capable to track output in basic food crops, that is, rye, wheat, and potatoes, excluding barley and oats.

The bottom line of these cross-checks is that the indirect approach produces valid results on economic growth in the mid-term, albeit with a considerable margin of error. In the short run, estimates strongly depend on fluctuations in prices of basic food grains, which introduces spurious volatility already in the estimate of agricultural output. Thus, preference should be given to smoothed values or trend growth rates.

SOURCES, ASSUMPTIONS, AND DATA DEFINITIONS

This section describes the sources, key assumptions and the data definitions underlying the variables and parameters required to implement the indirect output estimation approach. All relevant data series can be found in Online Appendix 3.

The primary geographical unity of study is the overlap between the Holy Roman Empire in the borders of 1792 and the territory of the nation state formed in 1871 (see Figure 1; Fertig et al. Reference Fertig, Christian Schlöder, Langfeldt and Pfister2018, pp. 8–9; Pfister and Fertig Reference Pfister and Fertig2020, p. 1151). Relative to the borders of the present-day Federal Republic of Germany, this aggregate of “historical Germany” additionally includes Eastern Pomerania, Silesia, and the small territory of the German-speaking Community of Belgium. By contrast, South Schleswig is excluded. Choice of this geographical frame of reference is mainly guided by data availability: The territory thus defined is covered by early statistical compilations reaching back into the eighteenth century and by a German-language historiography on preindustrial population and urban development.

Figure 1 MAP OF AREA STUDIED

Note: White lines: present-day territorial borders; broken grey line: overlap of Holy Roman Empire in 1792 and the nation state of 1871; squares: consumer price index and wage data; circles: wage data only; asterisk: additional price data.

Source: This study.

For prices and wages, which mostly relate to individual towns, I also draw on information for Strasbourg (until 1681 only) and Gdansk, which are both located outside the area defined as historical Germany but for which sources are particularly rich. Gdansk was a member of the Hanseatic League until the seventeenth century, but became an autonomous community within the kingdom of Poland from the middle of the fifteenth century. In 1793, it was integrated into the Prussian state that had acquired the town’s hinterland in successive steps from the early sixteenth century. Strasbourg was an independent city within the Holy Roman Empire until it was taken over by the French king in 1681.

One may duly ask whether historical Germany, as defined previously, constitutes a meaningful unit of analysis given poor market integration in most inland areas before the railway age. In particular, it has been argued that bullion and money markets in the Holy Roman Empire were highly fragmented (Gerhard and Engel Reference Gerhard and Engel2006, pp. 43–44). This point is relevant because the wage and price series relate to values in grams of silver as the common denominator to aggregate local information into national series. With non-integrated bullion and money markets, this procedure would be invalid. Reassuringly, however, gold-silver price ratios in Cologne and Vienna were cointegrated from 1480 to 1790, suggesting some degree of bullion market integration (Pfister Reference Pfister2017, pp. 706–7). The existence of currency unions and, from 1566, of a common currency regime support this conclusion (Boerner and Volckart Reference Boerner and Volckart2011; Cunz 2002, pp. 197–290).

Moreover, cities in the spatial aggregate under study shared both a common trajectory of product prices over time and highly symmetric shocks (Pfister Reference Pfister2017, p. 710). Finally, capital markets in what is termed here as historical Germany plus the Southern and Northern Netherlands were better integrated than those in more developed central and northern Italy (Chilosi, Schulze, and Volckart Reference Chilosi, Schulze and Volckart2018). In sum, the territory studied here shared a common experience in a sufficient number of economically relevant aspects to make it a meaningful object of analysis.

Total Population

Figure 2 shows the evolution of population size. For the nineteenth century, information rests on a reconstruction based on official statistics (Fertig et al. Reference Fertig, Christian Schlöder, Langfeldt and Pfister2018). The series for 1730–1815 combines censuses from individual German territories with published parish registers relating to some 140 parishes (Pfister and Fertig Reference Pfister and Fertig2010, pp. 9–10, 13–30). In 1690–1730, evidence is largely confined to parish registers, and the consistency of the estimates of population and vital events is less clear. This is why the values for this period are shown as a broken line. The point estimates for 1500–1650 are from Christian Pfister (Reference Pfister and Scribner1996, pp. 38–43), adjusted for the territory as shown in Figure 1 (Pfister and Fertig Reference Pfister and Fertig2010, p. 5). To arrive at an annual series, I fill in gaps before 1690 with exponential interpolation.

Figure 2 POPULATION (MILLION)

Sources: 1500–1650 Pfister and Fertig (Reference Pfister and Fertig2010, p. 5); 1690–1870 Pfister and Fertig (Reference Pfister and Fertig2020, Online Appendix B).

The resulting series indicates the following demographic development: Population grew by about 0.4–0.5 percent annually both in the sixteenth and the eighteenth centuries. By contrast, the period of the Thirty Years’ War (1618–1648) saw a massive demographic downturn by some 40 percent. War-related mobility facilitated the spread of epidemic diseases, particularly plague, and disrupted agricultural production. Food crises were further aggravated by requisitions and looting of troops. Finally, after the turn of the nineteenth century, population growth accelerated to an annual rate of 0.8 percent.

Sectoral Employment

L _NAt , the index of employment outside agriculture, is approximated by the urbanization rate (U _t /N _t ) and the share of the non-agricultural population in the rural population (sNAR _t ):

(8) $${L_{NAt}} = \left[ {{U_t}/{N_t} + sNA{R_t}\left( {1 - {U_t}/{N_t}} \right)} \right]{N_t}$$

The procedure assumes a constant labor force participation rate. Figure 3 shows the urbanization rate and the estimated share of the non-agricultural labor force in total employment, that is, L _NAt /L _t .

Figure 3 URBANIZATION RATE AND SHARE OF NON-AGRICULTURAL EMPLOYMENT (PERCENT)

Sources: Urbanization rate: Pfister (Reference Pfister2020b, pp. 15, 27–29); share of non-agricultural employment: this study.

Data for urban population come from a compilation covering communities with more than 5,000 inhabitants located in the territory as defined in Figure 1. Values between census years were calculated with exponential interpolation, and the trajectory of the population of the towns with information for both the early and the middle of the seventeenth century served to extrapolate figures for towns for which information is sparse before 1700 (Pfister Reference Pfister2020b).

The modest fall in the urbanization rate from 1500 to 1560 indicates that Figure 2 may overstate population growth during this period. However, the urbanization rate is usually considered to vary with income per capita, and the real wage also declined during this period (see Figure 6), which renders a concomitant decrease in the urbanization rate plausible. In sum, Figure 3 suggests that after an initial decline, the urbanization rate stagnated at a level slightly below 10 percent during the early modern period. Sustained urbanization set in only after the turn of the nineteenth century.

The series for the share of the non-agricultural population in the rural population (sNAR) relies on point estimates for 1780 and 1810 and assumes a constant value for 1500–1650. The estimates for 1780 and 1810 rest on Weiss’s (1993) figures for Saxony, which are calibrated to the national level (Table 1). To clarify the following discussion, “Rural craftsmen” designate handicraft activities serving a local clientele, such as construction workers, shoemakers, bakers, and so on; “proto-industry” refers to regional export industries, which consisted mainly of linen, worsted, and cotton manufacture.

Table 1 Non-agricultural rural population in Saxony and Germany (percent of work-force)

Sources: Columns (1) and (2): Weiss (Reference Weiss1993, pp. 104, 108); Columns (3) to (5): this study

Weiss also gives the number of rural craftsmen per thousand inhabitants; for 1780, the figure was 38. This value can be compared with information for other German territories. Schultz (Reference Schultz1981, pp. 36–37) provides figures for 18 regions that are part of Germany as defined in Figure 1; the mean year is 1790. The average craftsmen-population ratio was 32.4 per thousand, that is, 15 percent inferior to the value for Saxony in 1780. For Germany as a whole, Kaufhold (Reference Kaufhold and Abel1978, pp. 37–39) places the ratio of master artisans to the total population at 36.4 per thousand around 1800. Because Saxony’s countryside was arguably the most commercially developed region in Germany in the late eighteenth and early nineteenth centuries, it is plausible that rural craftsmen were more numerous there than elsewhere. Thus, I deflate the share of craftsmen in the labor force in Saxony by 10 percent to estimate the corresponding figure for Germany as a whole.

The development of export-oriented regional proto-industries added a significant segment to the occupational structure of many rural areas in the course of the early modern era (Kaufhold Reference Kaufhold and Pohl1986; Ogilvie 1996). By the early nineteenth century, rural export industries existed, notably in Saxony, Silesia, parts of the Rhineland and Westphalia, the Upper Palatinate, Eastern Swabia, and Württemberg (Kaufhold Reference Kaufhold and Pohl1986). In c. 1815/16, all these regions made up between one-third to two-fifths of the German population (Pfister Reference Pfister1994, pp. 19–23). Consequently, I estimate the national mean for the non-agricultural population apart from crafts to be 33 percent of the share recorded for Saxony (Column (4) in Table 1). The sum of the share of rural craftsmen and of proto-industrial workers yields a tentative estimate of the share of non-agricultural employment in the countryside for 1790 and 1810 (Column (5) in Table 1).

Weiss (Reference Weiss1993) also provides estimates of non-agricultural employment in rural Saxony at 30 to 40 year intervals back until 1565. However, before 1660 they are in the range of 5 to 13 percent, which is implausibly low. Allen (Reference Allen2000, pp. 6–8) assumption that about 20 percent of the rural labor force in England and France was employed outside agriculture around 1500 is probably too high for Germany. Schultz (Reference Schultz1981, pp. 36–37) reports ratios of rural craftsmen to population below 30 per thousand for several regions as late as the end of the eighteenth century. If multiplied by a household size of 5, such values are consistent with a share of rural crafts in the labor force of some 15 percent at best. Therefore, I set the value for sNAR at 1500 to 15 percent and left it constant at that level until 1650.

To obtain an annual index of L _NAt from 1500 to 1810 using Equation (8), I interpolate values between key years in the population series, the urbanization rate, and Column (5) of Table 1 using exponential interpolation. The same method serves to interpolate values between 1810 and 1849, when census information becomes available (Hoffmann Reference Hoffmann1965, pp. 204–6). The result is shown in Figure 3 (grey graph: L _NAt /L _t ).

For the sixteenth century, the series quantifies the idea that the development of new textile districts did not compensate for the relative stagnation of the large linen and fustian complex of Swabia and the massive decline of copper and silver refining in central Europe (Kiessling Reference Kiessling1998, pp. 49–54; Westermann Reference Westermann1986, pp. 196–201). The disruption of markets during the Thirty Years’ War most likely caused a continuation of this trend. The steady increase of the share of employment outside agriculture after the mid-seventeenth century mirrors two stylized facts stressed by the existing literature. On the one hand, regional export industries, or proto-industries, experienced a sustained expansion. The annual rate of increase of non-agricultural employment in 1700–1791—0.8 percent—is at the same order of magnitude as the one of fragmentary series of regional textile production during varying subperiods of the eighteenth century: linen, mostly from Silesia (0.8 percent), worsted from Württemberg (0.7–0.8 percent), and cotton manufacture (1.0 percent; Kaufhold Reference Kaufhold and Pohl1986, pp. 173, 186; Pfister Reference Pfister2015, pp. 202–8). On the other hand, regardless of whether a region engaged in the production of manufactures for export or not, crafts serving a local clientele comprised a growing fraction of the rural work force (Schremmer Reference Schremmer1972). In 1800, the estimated employment share of the non-agricultural sectors is 34 percent. This value tends towards the lower end of earlier estimates given by Henning (Reference Henning and Fischer1971, p. 115; 38 percent), Kaufhold (Reference Kaufhold and Pohl1983, pp. 24, 31; 33 percent), and Dipper (Reference Dipper1991, p. 98; 37.5 percent).

Prices and the Consumer Price Index (CPI)

The analysis of prices follows the methodology defined by Allen (Reference Allen2001). Thus, the CPI is the annual cost of a basket with fixed quantities of 11 goods—six foodstuffs and five non-food items—in grams of silver. Data refer to the 12 towns shown in Figure 1 and are aggregated to a national CPI (Pfister Reference Pfister2017, pp. 703–09, Supporting Information S2, pp. 1–11).

In the framework of the Allen methodology, the real price of food P _F (Equation (2)) is simply the share of foodstuffs in the total cost of the consumer basket, which forms the CPI, and the real price of non-foods P _NF equals 1 – P _F . Figure 4 shows the trajectory of the share of food in the CPI. Values fluctuate within a narrow band of 0.75 to 0.85. The cost of food rose relative to the cost of the whole consumer basket from 1500 to about 1625 and increased again in the last quarter of the seventeenth century. From the beginning of the eighteenth century, the share of food in the CPI fell, interrupted by spikes connected with well-known subsistence crises, notably those in 1771/72, 1817, and 1846/47.

Figure 4 SHARE OF FOOD IN TOTAL COST OF CONSUMER BASKET (PERCENT)

Sources: Own computation based on price data underlying consumer price indices of 12 towns as shown in Figure 1; on the method of aggregation, see Online Appendices A1.1 and A1.2.

Since foodstuffs are land-intensive products and non-foods include manufactures, whose production is labor-intensive, the long-term comovement of the share of food in the CPI with population (Figure 2) during the sixteenth and seventeenth centuries reflects the relationship between factor proportions and the relative price of products with a differing composition of factor inputs. However, after about 1700, this relationship broke down; the share of food in the CPI fell despite continued demographic expansion. Closer inspection of the non-food category reveals contrasting trajectories of the prices of textiles and energy (firewood and charcoal), which can be attributed to their differing input structures. Figure 5 shows the price of these two goods relative to the price of rye. The relative price of textiles fell from the fifteenth to the eighteenth century, that is, for several centuries before the industrial revolution mechanized textile manufacture. Textiles are a labor-intensive product, whereas rye is a land-intensive good. Thus, the decline in the price of textiles relative to rye reflects the change of factor proportions, that is, the decline of the land-labor ratio, as a consequence of secular population growth. The demographic depression in the wake of the Thirty Years’ War brought only a temporary reversal of this trend. The small magnitude of the effect of the demographic depression of the seventeenth century can be attributed to the fact that the price of textiles relative to rye was not only driven by factor proportions but also by differential productivity growth, perhaps mainly as a result of an improvement in business techniques in the non-agricultural sectors. Whereas one meter of linen twill cost the equivalent of 1.9 working days of an unskilled urban laborer in 1603/07, the price had shrunk to the equivalent of 0.6 days in 1708/12 (wage as in Figure 6). Note that the relative price of industrial products (Online Appendix A1.6) follows almost the same trajectory as that of textiles. Similar trends have been found for other European countries (Álvarez-Nogal and Prados de la Escosura Reference Álvarez-Nogal and Prados de la Escosura2013, p. 15; Broadberry et al. Reference Broadberry, Campbell, Klein, Overton and van Leeuwen2015, p. 193).

Figure 5 PRICES OF ENERGY, TEXTILES, AND INDUSTRIAL PRODUCTS RELATIVE TO RYE (INDICES, 1600=100; FIVE-YEAR CENTERED AVARAGES)

Sources: This study, see Online Appendices A1.3–6.

Forestry is similar in land intensity to agriculture, so we should not expect the relative price of energy to rye to fluctuate in parallel with population. In conformity with this expectation, the energy to rye price ratio was trendless from the fifteenth to the seventeenth centuries. After 1700, however, the relative price of energy embarked on a rising trend, which is consistent with the expansion of non-agricultural employment from around this time (Figure 3); because metal manufacture and processing constituted an important segment of Germany’s industry already around this time, (proto-)industrial growth increased the energy intensity of the economy. The energy to rye price ratio experienced a peak during the agrarian price depression of the 1820s and fell thereafter, possibly as a response to the beginning substitution of biomass with coal.

Income: Day Wages and Land Rent

The real day wage of unskilled male urban building laborers shown in Figure 6 is a first potential proxy for income (I in Equation (2)). Comparison with Figure 2 suggests that until about 1800, real wages fell when the population expanded and rose when the population contracted. This reflects the negative association between population and material welfare in pre-industrial economies (Clark Reference Clark2007, p. 20). After 1800, this relationship ended since the acceleration of population growth went together with real wage stability at a level that was significantly higher than in the late eighteenth century.

For three main reasons, the real day wage of male construction workers in towns may not accurately reflect household income. First, they may not be representative of the wage income of the whole population. This possibility can be explored using evidence relating to three wage gaps: the rural-urban gap, the gender gap, and the skill premium (Pfister Reference Pfister2019). Wages of agricultural workers and unskilled urban building laborers were apparently close to par in many regions and their ratio remained broadly stable or declined very slowly (at an annual rate of –0.1 percent at most) between 1500 and the onset of rapid industrialization in the 1840s (for Strasbourg until 1700 see also Geloso (Reference Geloso2018, p. 519): journalier annual/ouvrier summer). Within agriculture, the gender gap widened between the second quarter of the sixteenth to the early seventeenth centuries, but this phenomenon may have been limited to the vicinity of towns, where guilds progressively excluded women from skilled occupations. From the middle of the seventeenth to the early nineteenth centuries, the gender gap seems to have remained stable. The widening of the gender gap in the century preceding the Thirty Years’ War was paralleled by an increase in the skill premium, that is, the ratio of the wage of master artisans and journeymen to the wage of unskilled laborers in urban construction. However, this trend came to a halt around 1600, and by the 1630s, the skill premium had fallen back to the level prevailing in the second quarter of the sixteenth century, at which it stayed until the second half of the nineteenth century. At the bottom line, since likely trends move in opposite directions, there is no reason to conclude that the wage of unskilled urban building laborers grossly misrepresents the evolution of labor incomes of German households.

Second, the real day wage may not adequately capture annual income because the number of days worked per year may have changed. Given the current state of research, we do not know the duration of the working year before the late nineteenth century. Therefore, a sensitivity test will explore the effect of a potential increase in the work effort per employee on the results (Table 4).

Third, income from factors of production other than labor may have followed a different path than real wages. This holds in particular for the land rent. Figure 6 includes the rent-wage ratio, where land rent refers to the lease price per hectare in grams of silver on five estates in Westphalia back to 1558. In 1540–1558, data refer to Pomerania, spliced with the Westphalia series using the average in 1560–1569. With a given area of arable land, population growth leads to factor substitution: Land is cultivated more intensively, so that the real land rent increases, whereas the decline in the land-labor ratio leads to a reduction in the real wage. Consequently, the rate of technical substitution (the number of days one needs to work in order to substitute one hectare of land and maintain output constant; right scale in Figure 6) rises, implying that the real wage and the rent-wage ratio moved in the opposite direction, and the real land rent compensated partly for fluctuations in the real wage. Figure 6 is fully consistent with this line of reasoning as far as the pre-1800 period is concerned. At the same time, however, with largely constant land resources population growth diminishes the average share of the individual household in the aggregate land rent. With diminishing returns, the effect of population growth to dilute the endowment of labor with fixed resources surpassed the intensification effect (see the discussion of Table 2).

Table 2 PROXIMATE SOURCES OF GROWTH OF REAL GDP PER CAPITA (RATES OF CHANGE IN PERCENT)

Notes: Values are based on centered five-year averages (1500 refers to 1500–04). Weight of agriculture is geometric mean of share in current price output in t ₀ and t ₁.

Source: This study.

Against this background, I construct an index of aggregate real income as follows. Land rent is the series underlying the rent-wage ratio in Figure 6. Because land endowment per unit of labor changed over time, I adjust nominal rent with the ratio of the proportion of arable in total surface to population. Bork et al. (Reference Bork, Helga Bork, Faust and Piorr1998, p. 161) provide point estimates of the proportion of arable in total surface for the 1520s (0.38), c. 1610 (0.41), the 1650s (0.32), 1780s (0.39), and 1870s (0.40). These figures probably underestimate the expansion of the arable during the modern era (Bracht and Pfister Reference Bracht and Pfister2020, pp. 264–65); later in the study, I shall explore the sensitivity of the results with respect to this likely error. I compute values for the intervening years using exponential interpolation. Adjusted nominal land rent and day wage indices, each normalized to 1850, are weighted according to the factor shares prevailing in 1851–1859, which imply weights of 0.2 and 0.8, respectively (Pfister Reference Pfister2020a, Online Appendix 2). Aggregate nominal income is deflated with the CPI (Pfister Reference Pfister2017, Supporting Information S3). Before 1540, estimated income rests solely on the real day wage of unskilled urban laborers.

OUTPUT AND LABOR PRODUCTIVITY IN AGRICULTURE

Figure 7 plugs the data described earlier into Equations (2) to (4) to derive estimates of food consumption per capita and average labor productivity in agriculture. Because relative prices between foodstuffs and non-food products changed little (Figure 4), estimated food consumption is mostly driven by income, particularly the real wage (Figure 6).

Figure 6 REAL WAGE INDEX (1850=100) AND RENT-WAGE RATIO (DAYS PER HECTARE)

Sources: Real day wage of unskilled urban building laborers in 17 towns 1500–1850 from Pfister (Reference Pfister2017) spliced with real wage in industry and urban crafts in 1850 (Pfister Reference Pfister2018). Aggregate rent-wage ratio from Bracht and Pfister (Reference Bracht and Pfister2020, p. 277) divides leasehold rent per hectare in Westphalia by nominal day wage of unskilled urban building laborers, and wages in industry and urban crafts (from 1850). Information on the rent-wage ratio in Pomerania, which refers to ten-year averages, is spliced to the aggregate series in the 1590s (Bracht and Pfister Reference Bracht and Pfister2020, p. 249).

Figure 7 FOOD CONSUMPTION PER CAPITA AND AVERAGE LABOR PRODUCTIVITY IN AGRICULTURE, 1500–1855 (1500=100)

Sources: Own computation based on data described in the text; series in Online Appendix 3.

According to the baseline specification, food consumption per head tended to decrease over the early modern era, albeit not evenly. This finding is consistent with the literature on physical stature, which suggests that the biological standard of living tended to decline in mainland Europe between the early Middle Ages and the nineteenth century (Koepke and Baten Reference Koepke and Baten2005, pp. 75–76; Meinzer, Steckel, and Baten Reference Meinzer, Steckel, Baten and Richard2019, pp. 235–36).

More specifically, Figure 7 suggests four phases.

The first phase relates to the period c. 1500–1650 and is characterized by a long swing. From the 1510s to the early 1570s estimated food consumption per head fell dramatically by about 30 percent, followed by a slower decline until the 1620s and a marked recovery in the 1640s and 1650s. This long swing in food availability inversely parallels the long cycle of demographic expansion during the sixteenth century and contraction during the Thirty Years’ War, which replicates the negative relationship between material welfare and population found for the real wage noted previously.

During a second period, which extends from the late 1640s to the mid-1730s, food consumption per capita remained at a roughly constant level. Until the end of the seventeenth century, however, there was considerable volatility. The high frequency of strong negative shocks can be related to the Maunder Minimum (c. 1645–1715), a period characterized by reduced solar irradiance that led to a series of severe winters and cold springs (Albers and Pfister 2021, p. 472 and Appendix SA5.2). Stability during the initial phase of renewed population growth, particularly after the turn of the eighteenth century, may have been due to the fading of the Maunder Minimum, which went together with a significant rise in average annual temperature and a likely increase in soil productivity.

The third phase, from the mid-1730s to the early nineteenth century, was again characterized by a decrease in estimated food consumption per capita. Like the sixteenth century, this was a period of population growth (Figure 2) and unfavorable climatic conditions: The years 1730–1800 stand out for abnormally high levels of precipitation (Büntgen et al. Reference Büntgen, Valerie Trouet, Hanns Hubert Leuschner, Luterbacher and Esper2010, pp. 1010, 1015). A likely decline in food availability per head was mitigated by the development of food output per agricultural laborer, that is, average labor productivity in agriculture. Despite adverse conditions, it remained roughly constant during the five decades after the 1730s. This took place on the background of a progressive integration of grain markets during the late seventeenth and early eighteenth centuries (Albers and Pfister 2021). Regional studies for Saxony and the lower Rhineland show that regions engaged in export-oriented textile manufacture succeeded in maintaining per-capita supply of food constant, despite an expansion of the regional population (Pfister and Kopsidis Reference Pfister and Kopsidis2015; Kopsidis et al. Reference Kopsidis, Pfister, Scholten and Bracht2017). Demand that stemmed from rising incomes from non-agricultural activities and market integration stimulated at least some degree of agricultural specialization and intensification already in the eighteenth century.

The final phase began after 1817 (the food crisis following the eruption of Mount Tambora in 1815) and was characterized by a sustained increase in average labor productivity in agriculture. As a result, food consumption per head was slightly higher in 1820–1849 than during the 1780s (by about 4 percent), despite a doubling of the rate of population growth relative to the eighteenth century and the rapid expansion of non-agricultural employment. Also note that the average annual temperature in the 1840s and 1850s was on average –0.4 degrees Celsius cooler than during the exceptionally warm 1820s, which must have adversely affected agricultural productivity (Rapp Reference Rapp2000, pp. 138–40). On this background, even a modest increase in food availability per head is remarkable and suggests the beginning of modern agricultural development in the late 1810s.

REAL GDP PER CAPITA

Real output in agriculture (i.e., food consumption per capita multiplied by population), the size of the non-agricultural population (the share displayed in Figure 3 multiplied by population), food prices (Online Appendix A1.2), and prices for industrial products and services (Online Appendix A1.6) serve to construct a chain index of real GDP at factor cost back to 1500 (cf. Equations (5) to (7)). Output in agriculture is spliced to the average of current price value added in this sector in 1856–1860 from Hoffmann (Reference Hoffmann1965, table II/59, pp. 316–19). There is no full reconstruction of the current price output side of German GDP (or net national product (NNP)) prior to 1913. Hence, subtracting current price value added in agriculture from the reflated compromise estimate of NNP at factor cost (Pfister Reference Pfister2020a, Online Appendix 2) in 1856–1860 provides a rough benchmark for current price value added in industry and services. Non-agricultural population, which serves as a proxy for output in industry and services, is calibrated to this value.

The result of these calculations is a quantity index of real GDP based on chaining Fisher quantity indices for adjacent years, which I normalize to 1851 = 1. Figure 8 as well as Online Appendix 3 present annual estimates, but it should be borne in mind that, by construction, short-term fluctuations reflect mainly variations in the harvested quantities of basic vegetable foodstuffs. Therefore, trends over several decades are the most informative; Table 3 presents annual growth rates for select periods.

Figure 8 REAL GDP PER CAPITA, 1500–1855 (INDEX, 1851=1)

Sources: Solid line: this study, see text and Online Appendix 3; broken line (from 1851): compromise estimate from Pfister (Reference Pfister2020a, Online Appendix A2).

Table 3 ANNUAL GROWTH RATES OF REAL GDP PER CAPITA IN EIGHT EUROPEAN COUNTRIES (PERCENT)

Sources: Germany (figures for key years rest on five-year centered averages; the figure for 1500 refers to 1500–04): this study, Online Appendix 3; Central and northern Italy, England/Great Britain, Holland/Netherlands: Broadberry et al. (Reference Broadberry, Campbell, Klein, Overton and van Leeuwen2015, pp. 375–76); Holland 1800: van Zanden and van Leeuwen (Reference van Zanden and van Leeuwen2012, data files); France: Ridolfi and Nuvolari (Reference Ridolfi and Nuvolari2020; data series kindly provided by the authors); Spain (five-year centered averages): Prados de la Escosura, Álvarez-Nogal, and Santiago-Caballero (Reference Prados de la Escosura, Álvarez-Nogal and Santiago-Caballero2020, pp. 45–58); Portugal: Palma and Reis (Reference Palma and Reis2019, p. 500); Sweden: Schön and Krantz (Reference Schön and Krantz2012, p. 546). Apart from the first column, growth rates are based on values for key years.

Comparison of Figures 6 and 8 suggests that at least in some periods, the real wage and real GDP per capita behave differently, and the trajectory of real GDP per capita suggests a more optimistic view of the evolution of material welfare in the long run than the real wage. A similar pattern holds for Britain, and the discrepancy calls for an explanation (Angeles Reference Angeles2008; Broadberry et al. Reference Broadberry, Campbell, Klein, Overton and van Leeuwen2015, ch. 6). Since in the indirect approach, the real wage enters the procedure to estimate GDP as data, the question is mainly about how the indirect method operates with the underlying data series. Table 2 shows rates of change in percent between key years for the main variables entering the estimate of agricultural output (Equation (3)) and the index of real GDP (Equations (5) and (6)): Total real income per head (wage and land rent combined), real output per head in agriculture and in the non-agricultural sectors (Q _A /N and L _NA /N), and the relative price of non-agricultural goods vs. foodstuffs (P _I/P _A). An increase in the relative price of industry and services raises the weight of the rate of change of output in the non-agricultural sectors. A decline has the opposite effect. The last line gives the geometric average of the share of agriculture in current price value added in the two respective key years. It gives a rough impression of the weight of the sectoral growth rates in the growth rate of aggregate GDP (for 1820–1850: 0.389 × 2 + [1 – 0.389] × 17). Given the construction principle of the Fisher ideal index, this procedure does not produce the result with exactitude (mainly in 1700–1800).

Three observations stand out from the data in Table 2. First, the inclusion of land rent—which moved in the opposite direction to the real wage (Figure 6)—dampens fluctuations in income per head, and the fact that income enters the calculation of agricultural output with a weight of 0.5 (Equation (3)) further reduces the variation of the latter relative to the real wage. Specifically, the massive fall of the real land rent in the wake of the Thirty Years’ War, reflecting a reduction of the endowment of land with labor and capital, meant that combined income rose by only 31 percent in the first half of the seventeenth century, compared to a 44 percent increase in the real wage. Consequently, agricultural output per head grew by less than one-third (13 percent) of the rate of increase of the real wage. A reverse effect is visible in the eighteenth century, when the stability of the land rent and the limited responsiveness of food consumption to changes in income mitigated the effect of the fall of the real wage on estimated agricultural output. Changes in the functional distribution of income clearly explain part of the discrepancy between the real wage and real GDP per capita (Angeles Reference Angeles2008, p. 152).

Second, positive rates of change in real GDP per capita after 1650 result primarily from an increase in the output of the non-agricultural sectors, which is proxied by employment outside agriculture. This is because average labor productivity in industry and services was about one-third higher than in agriculture: In 1856–1860 the labor share of the non-agricultural sectors was 47 percent, whereas their share in value added was 64 percent (similar values are obtained from current price estimates for earlier years). This differential in labor productivity contrasts with the small magnitude of the rural-urban gap with respect to day wages (cf. the earlier discussion of wages and income). With homogenous labor and competitive labor markets, the productivity differential must result from differences with respect to the labor effort, that is, the number of days worked (Angeles Reference Angeles2008, pp. 151–52). A likely cause is the lower level of seasonal unemployment in the non-agricultural sector.

Third, the effects of changes in relative prices were apparently minor. The most important case concerns the sixteenth century, when the massive fall in prices in industry and services relative to food prices reduced the power of the relative stability of non-agricultural output to mitigate the impact of the massive fall in agricultural output per head on the estimate of total value added.

Figure 8 and the growth rates in the lower panel of Table 3 suggest three distinct phases of economic growth between the sixteenth and the nineteenth centuries. The first phase extended from the beginning of the period under study until the middle of the seventeenth century. After the 1510s, real GDP per capita fell almost continuously over several decades and reached a nadir sometime between the 1590s to the 1620s at 15 to 20 percent below the initial value. The 1640s and early 1650s saw a substantial recovery; the sensitivity and consistency tests carried out in the next section suggest that the rate of increase of real GDP per capita between the 1620s and the 1650s and 1660s was probably even stronger than suggested by Figure 8 and Table 3. It may well be that during the third quarter of the seventeenth century, real GDP per capita was at a similar level as during the first two decades of the sixteenth century. Thus, material welfare evolved in inverse parallel to the long swing of the population (Figure 2).

The second phase lasted from the third quarter of the seventeenth century to the Revolutionary and Napoleonic Wars (1792–1815) and was characterized by the onset of slow economic growth. During the second half of the seventeenth century, real GDP per capita was trendless, and in 1700–1791, the trend growth rate amounted to 0.1 percent per annum. Expansion of the non-agricultural sectors, where employment was more continuous over the year and natural resource constraints were less binding than in agriculture, was capable of compensating for the decline of the marginal product of labor apparent in the trajectory of the real wage (Figure 6), particularly after the mid-1730s (cf. discussion of Table 2).

The third phase began after the Napoleonic Wars and lasted at least until the 1850s. The jump in real GDP per head between 1800 and 1820 by more than 10 percent can be partly ascribed to post-war recovery and short-term changes in climate. Poor availability and quality of data for the war years may also have a negative effect on the accuracy of the growth estimate for this period. The sensitivity and consistency checks carried out in the next section suggest that the likely true level of real GDP around 1820 may have been roughly the same as around 1790. In 1820–1850, economic growth accelerated to 0.3 percent vs. 0.1 percent in 1700–1791. This is all the more noteworthy as the population grew much faster than in the eighteenth century and the favorable weather conditions of the 1820s exerted a negative base effect on the agricultural sector.

In an international comparison, German economic decline during the sixteenth century parallels the experience of central and northern Italy and corroborates the idea of a reversal of fortunes connected with the rise of Atlantic trade, which benefitted the Northern Netherlands and, until the 1560s, Spain (Table 3). The findings of this study also confirm the second half of the seventeenth century as a pivotal period with respect to the divergence between England and mainland Europe. Around 1650, real GDP per head may have been at a similar level in England and Germany. In the subsequent half-century, stagnation in Germany contrasts with a 40 percent increase in England. Further divergence between the two economies set in with the industrial revolution in Britain during the second half of the eighteenth century. At the same time, the stagnation of the German economy during the second half of the seventeenth century also contrasts with small positive growth in other large continental economies, namely, France, central and northern Italy, and Spain. The eighteenth century saw a reversal of this picture: Whereas the German economy expanded slowly, France, central and northern Italy, Portugal, and Sweden experienced stagnation or decline.

SENSITIVITY AND CONSISTENCY TESTS

To explore the sensitivity of the estimate of real GDP per capita with respect to variations in underlying assumptions and particular data series, I developed several alternative indices of real GDP per capita. Online Appendix 2> presents them in detail; this section provides an overview and discusses the implications of the results.

Two tests explore the sensitivity of the GDP series with respect to the assumptions underlying the elasticity of food demand. Assuming constant food consumption per head or weaker income and price elasticity than in the baseline specification has little effect on results from 1570 (lines 1 and 2 in Table A2.1 and Section A2.1). For the first part of the sixteenth century, these two alternative specifications suggest a weaker decline in real GDP per head than the baseline estimate. However, this is not very plausible because the reduction of meat consumption per capita by about 50 percent during the sixteenth century suggests elastic food demand (Pfister Reference Pfister2017, Supporting Information S2, pp. 2–3).

Two further tests combine a plausible assumption concerning the evolution of the number of days worked per year between the early eighteenth and early nineteenth centuries with a tentative construction of factor shares in national income (lines 3 and 4 in Table A2.1 and Sections A2.2–3). Three results stand out: First, assuming an increase in days worked is essential in order to get plausible values for the labor share of national income. Second, income from land must have risen faster than in the baseline specification; otherwise, land shares during the sixteenth century would be implausibly high. Third, to be consistent with a non-negative capital share, GDP levels between 1650 and 1790 must have been 10 to 13 percent higher than suggested by the baseline estimate. I consider the outcome of this consistency test as the most likely alternative course of real GDP per capita between 1500 and 1850. Table 4 presents exponential growth rates between key years.

Table 4 PREFERRED VARIANT: INDEX LEVELS (1851=1) AND GROWTH RATES OF REAL GDP PER CAPITA GROWTH BETWEEN KEY YEARS (PERCENT, BASED ON CENTERED FIVE-YEAR AVERAGES)

Sources: Own computation based on assumption of increasing labor input per head, 1710–1810, and faster growth of land rent than observed; values in 1650, 1700, 1750, and 1790 are augmented by 12 percent. See Online Appendix 2, line 4 in Table A2.1 and Section A2.3.

The remaining sensitivity tests modify the assumptions underlying the estimate of output in the non-agricultural sectors. The first raises the share of non-agricultural employment in the rural labor force in 1500 from 15 to 20 percent. While this value is not very plausible (see the earlier discussion), the test shows that results are sensitive to the assumption of the initial value concerning the non-agricultural rural population (line 5 in Table A2.1 and Section A2.4).

The baseline estimate assumes that labor productivity in industry and services remained constant. However, the massive decline in the price of textiles relative to the price of rye (Figure 5) suggests that labor productivity rose in some non-agricultural activities prior to the onset of industrialization. A further sensitivity test, therefore, uses the coefficient of the unskilled urban day wage and the price of textiles (meter per day) as a simple indicator of labor productivity outside agriculture (line 6 in Table A2.1 and Section A2.5). The modification increases estimated economic growth between 1570 and 1700 and between 1820 and 1850.

The last test follows the majority of the applications of the indirect output estimation approach and constructs an index of real GDP per capita by dividing food consumption per capita by the share of agriculture in total employment (line 7 in Table A2.1 and Section A2.5). As noted in the exposition of the indirect approach, this entails the assumption that labor productivity in the non-agricultural sectors was the same as in agriculture. This variant suggests much smaller rates of economic growth than either the baseline estimate or the test that takes account of the likely increase in labor productivity outside agriculture. This sensitivity test underscores the relevance of making explicit assumptions about labor productivity in industry and services when implementing the indirect approach to output-side GDP reconstructions.

Two conclusions emerge from these sensitivity tests. The plausible variants all imply somewhat higher rates of economic growth than the baseline estimate; the latter clearly errs on the conservative side. Specifically, the tests allowing for a likely increase in labor productivity outside agriculture (number 6 in Table A2.1) and an increase of the labor input per head combined with faster growth of the land rent (number 4 in Table A2.1) both suggest that the likely true level of real GDP per head in 1500–1600 may have been 10–15 percent lower than the baseline estimate. The alternative results displayed in Table 4 imply that growth in 1700–1790 and 1820–1850 was more vigorous than according to the baseline estimate.

Second, growth estimates for major war periods—the Thirty Years’ War and the Revolutionary and Napoleonic Wars—suffer from serious issues probably related to data availability and data quality. Assuming plausible factor shares renders it likely that the recovery of real GDP per capita between the 1620s and 1650s or 1660s was much more vigorous than suggested by the output-side reconstruction, and that real GDP per head in 1820 was virtually the same as around 1790 (Table 4). Consequently, the level of economic activity between the third quarter of the seventeenth century and 1790 may have been 10 to 15 percent higher than suggested by the baseline estimate.