1. Introduction
For a long time, economists and economic historians have analysed living standards from the past. Starting with Allen (Reference Allen2001), several studies have estimated welfare ratios for a large number of countries. By doing so, it has been possible to determine the capacity of families to cover their basic needs, the differences in living standards across countries and their evolution over time.
To estimate welfare ratios, it is necessary to make a number of assumptions. Allen (Reference Allen2001) relied on the consumption habits of modern London to make assumptions about the food basket in several European cities. He also assumed that only one man worked per family and that he did so for 250 days per year. Allen (Reference Allen2009) subsequently made some adjustments to the earlier (2001) basket in order to obtain a subsistence basket. Bread was replaced by a cheaper cereal and the amounts of meat and other expensive items were reduced; the assumptions regarding the number of people who worked per family and the number of workdays remained unchanged.
For many years, most studies used Allen's methodology (2009) to estimate welfare ratios. Recently, however, some of the traditional assumptions have been questioned. Some criticisms refer to the food basket.Footnote 1 López and Piquero (Reference López and Piquero2021), for instance, questioned the exclusion of bread from the basket of Spain, arguing that bread was an important part of the diets of Spanish families.Footnote 2 Meanwhile, Humphries (Reference Humphries2023) and Horrell (Reference Horrell2023) were of the opinion that the living costs should change in response to changing consumption habits. Rather than assuming a fixed basket, as Allen did, Humphries used board and lodging costs as a measure of living costs in order to include changing habits in England, whereas Horrell constructed a chained-Laspeyres price index in England based on changing expenditure patterns.
Consumption habits have largely been used to make assumptions about the subsistence food basket. However, using historical diets to estimate welfare ratios may be problematic. First, historical diets could have provided a deficient amount of some nutrients and an excessive amount of others. Consequently, it is necessary to adjust the historical diets to obtain a subsistence basket.Footnote 3 Second, if the subsistence baskets (corresponding to historical diets) were different across cities or over time, the resulting welfare ratios may not be comparable. For instance, using a different basket may not be appropriate if income or tastes influenced consumption habits.Footnote 4 In addition, using the same basket may not be appropriate if relative prices were different.Footnote 5
Linear programming, a common optimisation method, can also be used to select the subsistence basket (Allen, Reference Allen2017, Reference Allen2020; Zegarra, Reference Zegarra2021, Reference Zegarra2022). Linear programming relies on information on prices, the chemical composition of foods and nutritional requirements to find the lowest-cost food basket. Linear programming has several advantages compared to the use of consumption habits. First, whereas historical diets need to be adjusted to obtain a subsistence basket, no adjustment of the lowest-cost basket is necessary. In addition, unlike historical diets, the lowest-cost basket is not affected by income or tastes. Instead, it is affected by the prices of goods, the chemical composition of foods and nutritional requirements. Finally, the method allows for substitution in response to changes in relative prices.Footnote 6
Several studies have relied on linear programming to estimate welfare ratios. Allen (Reference Allen2017) used linear programming to determine poverty lines in the 21st century. Later, other studies used linear programming to determine food baskets and welfare ratios prior to 1900 in London and other European cities (Allen, Reference Allen2020; Zegarra, Reference Zegarra2022).Footnote 7 However, there are still many countries for which no linear programming model has been estimated to find the lowest-cost basket and calculate welfare ratios. For instance, no study has used a linear programming model for Spain.
Three studies have estimated welfare ratios for pre-1800 Spain (Allen, Reference Allen2001; Allen et al., Reference Allen, Murphy and Schneider2012; López and Piquero, Reference López and Piquero2021). According to Allen (Reference Allen2001), the respectability welfare ratio in Spain in the 1600-1800 period was around the same as in France, Germany and Italy, but below that of Northern Europe. Allen's estimations suggest that the divergence in welfare ratios between Northern Europe and Spain started in the 16th century.Footnote 8 Later, Allen et al. (Reference Allen, Murphy and Schneider2012) estimated subsistence welfare ratios for several countries, including Spain, using a cheaper food basket.Footnote 9 An important finding of this study is that Toledo and Valencia had lower ratios than London in the period 1525-1800. More recently, López and Piquero (Reference López and Piquero2021) found new welfare ratios for Spain. According to their estimates, Madrid had similar welfare ratios to Northern Europe in the 17th century. Over time, however, the welfare ratio in Spain declined. Unlike the estimates of Allen and Allen et al., those of López and Piquero suggest that the divergence in welfare ratios between Northern Europe and Spain only started in the 18th century.
The three studies used historical consumption habits to estimate welfare ratios. By relying on historical diets, the resulting welfare ratios measure the capacity of families to cover their consumption habits. However, these ratios do not necessarily measure the capacity of families to cover their basic needs; it is possible that there were alternative food baskets that provided nutrients at a lower cost and were available for people at the time. In order to determine the basket that provided the necessary nutrients at the lowest possible cost, it is possible to use linear programming.
In this article, I use a linear programming model to determine the lowest-cost food baskets and estimate welfare ratios in Toledo and Barcelona between 1600 and 1800. Some restrictions on the intake of several nutrients were imposed as part of the model. Food baskets were allowed to vary across cities and change over time. The cost of fuel, clothing, housing and other basic products was also added to estimate the total living cost. The welfare ratios were then calculated as the ratio between family income and the total living cost.
I used primary and secondary sources. Much of the information on prices and wages in Toledo and Barcelona comes from Hamilton (Reference Hamilton1934, Reference Hamilton1947), the records of the Faithful Executors (Juzgado de Ejecutores) of Toledo and Feliu (Reference Feliu1991). I complemented these sources with other sources.Footnote 10 In addition, I obtained information about the chemical composition of foods from McCance and Widdowson (Reference Mccance and Widdowson1946) and Paul and Southgate (Reference Paul and Southgate1978) and nutritional requirements from FAO (1985) and Rao (Reference Rao2009).
According to my estimates, the welfare ratio in Toledo was usually above the ratio in Barcelona. In particular, the welfare ratio of a family of four members (two adults and two children) in Toledo was above 1.0 between 1600 and 1750, but below 1.0 in the period from 1750 to 1800, whereas in Barcelona the ratio ranged between 0.75 and 1.2 between 1600 and 1800. Families faced more difficulties to cover their basic expenses in Barcelona than in Toledo until the late 18th century. The estimates of this study differ from other studies. The welfare ratios in Spain estimated in this study are higher than the ratios of Allen (Reference Allen2001), far lower than those of Allen et al. (Reference Allen, Murphy and Schneider2012), and slightly lower than those of López and Piquero (Reference López and Piquero2021). On the other hand, the estimations suggest that Spain had lower welfare ratios than Northern Europe between 1600 and 1800, especially after 1625. This study supports some of the findings of Allen (Reference Allen2001) and Allen et al. (Reference Allen, Murphy and Schneider2012), in particular the idea that Spain had lower welfare ratios than Northern Europe before the Industrial Revolution; however, the differences in welfare ratios between Northern Europe and Spain in the early 17th century were not as large as those found by those two studies. In addition, this study contradicts the argument of López and Piquero, who stated that the divergence between Spain and Northern Europe only started in the 18th century.
This article contributes to the literature on living standards in Spain. The main contribution is methodological; I use a different methodology to estimate welfare ratios compared to previous studies for Spain. Whereas previous studies estimated the capacity of families to cover their consumption habits, I estimated the capacity of families to cover their basic needs. In addition, the article contributes to the literature by showing that there were important differences in welfare ratios within Spain through the period of analysis, as well as between Northern Europe and Spain.
2. The literature
Two decades ago, Allen (Reference Allen2001) estimated welfare ratios for a large number of European cities. Allen relied on a food basket composed of bread, legumes, meat, eggs, butter, cheese and beer or wine. He did not consider this basket to be a subsistence basket. In fact, Allen (Reference Allen2009) indicated that this basket was a respectability one. In addition to the food basket, Allen (Reference Allen2001) also included fuel, linen, lamp oil, candles and soap in the subsistence basket. The cost of subsistence of a family was calculated as three times the cost of subsistence of an adult man. In addition, housing costs were assumed to represent 5 per cent of other costs.
According to Allen (Reference Allen2001), the respectability welfare ratios in Toledo and Valencia were usually below 1.0 in the 1600-1800 period (Table 1). The welfare ratios in Northern Europe were above those in the rest of Europe, including Spain. London had higher ratios than Toledo, Valencia, Paris, Leipzig, Vienna and other European cities. In the 16th century, welfare ratios in Northern Europe were already higher than in Spain. The differences in welfare ratios increased over time.
Table 1. Welfare ratios in Europe
NC, New Castile; Val, Valencia; Lnd, London; Ams, Amsterdam; Par, Paris; Lpz, Leipzig.
Previous studies.
Notes: The table reports the welfare ratios of Allen (Reference Allen2001), Allen (Reference Allen2009), Allen et al. (Reference Allen, Murphy and Schneider2012) and López and Piquero (Reference López and Piquero2021) for New Castile and Valencia. In the case of New Castile, the figures refer to Toledo (Allen, Reference Allen2001; Allen et al., Reference Allen, Murphy and Schneider2012) or Madrid (López and Piquero, Reference López and Piquero2021). Allen (Reference Allen2009) and Allen et al. (Reference Allen, Murphy and Schneider2012) used the same method (including the composition of the food basket) to compute welfare ratios. The table also reports the relative ratios of welfare ratios of New Castile and Valencia with respect to other European cities. These relative welfare ratios are calculated as the welfare ratio of one city divided by the welfare ratio of another city. The welfare ratios of Allen (Reference Allen2001) were obtained from https://gpih.ucdavis.edu/Datafilelist.htm. The welfare ratios of López and Piquero (Reference López and Piquero2021) were obtained from https://addi.ehu.es/handle/10810/40426?show=full. The original ratios of Allen et al. (Reference Allen, Murphy and Schneider2012) for Toledo, Valencia, London and Amsterdam are reported in the appendix of the study; I estimated the ratios in Paris and Leipzig using the same prices and wages as Allen (Reference Allen2001).
Later, Allen (Reference Allen2009) adjusted the food basket, making it cheaper. He replaced bread with cheaper cereals, eliminated eggs, cheese and beer (or wine) and reduced the quantity of legumes and meat in order to reflect the diets of the very poor. The basket provided around 1,940 kcal/day of calories for an adult man. Allen (Reference Allen2009) did not compute welfare ratios for Spain. However, Allen et al. (Reference Allen, Murphy and Schneider2012) used the same assumptions to estimate welfare ratios in Spain.
Allen et al. estimated welfare ratios for Toledo and Valencia, as well as for London and some cities in the Americas. The welfare ratios in Toledo and Valencia were lower than the ratios in London between 1525 and 1800. Therefore, Allen et al. (Reference Allen, Murphy and Schneider2012) reached a similar conclusion to Allen (Reference Allen2001): Spain had lower welfare ratios than London from the 16th century, long before the Industrial Revolution.
López and Piquero (Reference López and Piquero2021) used a different basket to estimate welfare ratios in Madrid and Valencia. For both cities, the new food basket was composed of wheat bread, meat and olive oil. The basket also included legumes in Madrid and rice in Valencia. In addition, the basket provided 2,100 kcal/day of calories for an average person (not for an adult man) and the subsistence cost of a family was calculated as four times the subsistence cost of an average person.
The welfare ratios of López and Piquero were higher than the estimates of Allen (Reference Allen2001) and lower than the ratios of Allen et al. (Reference Allen, Murphy and Schneider2012).Footnote 11 In addition, López and Piquero reached a different conclusion about the divergence of welfare ratios between Northern Europe and Spain compared with previous studies. According to López and Piquero, the differences in welfare ratios between Northern Europe and Spain were not as large as previously shown. In fact, the welfare ratio in Madrid was similar to the ratios in London and Amsterdam until 1700. The welfare ratios in Northern Europe only differed from the ratio in Madrid from the early 18th century.
Allen (Reference Allen2001), Allen et al. (Reference Allen, Murphy and Schneider2012) and López and Piquero (Reference López and Piquero2021) have made important contributions to the study of living standards in Spain. However, some of the assumptions in their studies are questionable. Consider the assumptions regarding the provision of calories. The food baskets of Allen (Reference Allen2001) and Allen et al. (Reference Allen, Murphy and Schneider2012) provided around 1,940 kcal of calories per day. As Humphries (Reference Humphries2013) pointed out, people needed more than 1,940 kcal/day of calories to survive. In response to criticisms, Allen (Reference Allen2014, Reference Allen2015) modified the food basket for the United States and England, including a higher quantity of cereals, thus providing around 2,100 kcal/day for an average person. Spanish men certainly needed far more calories than 1,940 kcal/day for subsistence. Since Spanish men weighed around 60 kg prior to 1900, an adult man of 18-30 years of age would have needed 3,450 kcal per day if he did heavy work (FAO, 1985).Footnote 12 On the other hand, López and Piquero (Reference López and Piquero2021) used a basket of 2,100 kcal/day for an average person. I argue that 2,100 kcal/day were also not enough for subsistence; according to my calculations, an average person in modern Spain required at least 2,384 kcal/day.Footnote 13
For their estimations of welfare ratios in Spain, Allen (Reference Allen2001), Allen et al. (Reference Allen, Murphy and Schneider2012) and López and Piquero (Reference López and Piquero2021) used food baskets that provided certain amounts of calories and proteins. Calories and proteins are important for subsistence. People, however, require a variety of nutrients for a healthy life. People also require minerals, vitamins and fat. The lack of minerals and vitamins may lead to a variety of serious diseases (FAO, 2004).Footnote 14 Based on other studies, I assume that a balanced nutrition required fat, iron, thiamine, niacin, vitamin B12, folate and vitamin C, besides calories and proteins (Allen, Reference Allen2017, Reference Allen2020; Zegarra, Reference Zegarra2020, Reference Zegarra2021, Reference Zegarra2022).
According to my calculations, the baskets of Allen (Reference Allen2001), Allen et al. (Reference Allen, Murphy and Schneider2012) and López and Piquero (Reference López and Piquero2021) did not provide enough quantities of some nutrients. For instance, they did not provide vitamin C. In addition, the baskets of López and Piquero (Reference López and Piquero2021) provided 0.1-0.2 μg/day of vitamin B12, far less than the requirement for an average person. Other studies have estimated welfare ratios for a number of cities in the past assuming that people needed calories, proteins, vitamins and minerals (Allen, Reference Allen2020; Zegarra, Reference Zegarra2020, Reference Zegarra2021, Reference Zegarra2022), but no study has made this assumption for Spain.
It is possible to achieve a greater intake of important nutrients by increasing the consumption of certain items. For instance, increasing the consumption of meat would increase the intake of vitamin B12. Increasing the consumption of vegetables would allow people to meet their requirements of vitamin C. However, it is still not clear which items should be included in the food basket. All foods provide calories; most foods provide proteins and several provide vitamins and minerals. Thus, should bread or legumes be included in the food basket? Should beef, mutton, codfish or other animal-derived foods be included as a source of vitamin B12?
Another important issue for the calculation of welfare ratios refers to the use of historical consumption habits. Allen (Reference Allen2001), Allen et al. (Reference Allen, Murphy and Schneider2012) and López and Piquero (Reference López and Piquero2021) used information about historical diets to make assumptions about the food basket. Historical diets contain valuable information for the study of nutrition. However, it is important to be aware of potential problems when estimating the food cost based on historical diets.
Consider, for example, the variety of diets across the population (even within groups with similar incomes) and, especially, across cities. Different cities had different diets due to climatic and cultural differences. Consequently, some studies have assumed different food baskets for different cities.Footnote 15 Although it is reasonable to consider different baskets for different cities, it is not clear whether those baskets should be used to compute comparable welfare ratios. Those baskets may provide similar calories, but do they provide similar quantities of other nutrients, such as vitamins and minerals? Should the researcher use those baskets to calculate welfare ratios if the quantities of vitamins and minerals are not the same?Footnote 16
On the other hand, it is important to be careful when using historical diets, if the differences in diets across countries respond to income, and not only to availability or relative prices. If the differences in food baskets across cities reflect differences in income (and not only differences in relative prices), it might be argued that the differences in welfare ratios do not really reflect differences in the capacity to cover basic needs. Meanwhile, if diets are different across cities because of relative prices, using the same basket for all cities may not be appropriate to compute comparable welfare ratios.
In general, the selection of the food basket should depend on what we intend to measure. If the intention is to measure the capacity of families to cover their actual diets, it is useful to reconstruct historical diets. However, if the intention is to measure the capacity of families to cover their nutritional needs (in addition to other basic needs), and to make cross-sectional and over-time comparisons of welfare ratios, the computation of welfare ratios should not rely on historical diets. It is preferable to find the basket that allowed people to cover their basic needs at the lowest possible cost. By doing so, it will be possible to determine whether low-income families earned enough to satisfy their basic needs.
3. Methodology
In this study, the welfare ratio measures the capacity of families to cover their basic needs, which are not necessarily the same as consumption habits. In order to obtain a reliable estimate of this capacity, it is necessary to pay attention to the alternative ways of satisfying those basic needs and choose the most efficient one. People require a variety of nutrients and there are different combinations of foods to obtain those nutrients.
I use linear programming to find the lowest-cost basket in Toledo and Barcelona. In order to find the optimal basket, it is important to determine the nutritional requirements. Calories and proteins are important for subsistence, but a healthy life requires much more than only calories and proteins; people also require fat, iron and vitamins. Nutritional requirements depend on age, height, weight and on the type of occupation. I relied on FAO (1985) to obtain the calorie requirements. I assumed adult men and women weighed 60 and 50 kg, respectively. In the basic model, I assumed a daily energy requirement of 2.2 BMR for men and 1.8 BMR for women, considering heavy work for men and moderate work for women. Following Allen (Reference Allen2017), I considered Indian dietary requirements of proteins, fat, iron and vitamins (Rao, Reference Rao2009). These requirements were calculated assuming a weight of 60 kg for men, so they may be very similar to the nutritional needs of people in modern Spain.Footnote 17
According to my calculations, an average adult man of 18-55 years old in modern Spain needed at least 3,428 kcal of calories and 60 g of proteins per day for subsistence.Footnote 18 In addition, for a balanced nutrition, an adult man also required at least 40 g of fat, 17 mg of iron, 1.7 mg of thiamine, 21 mg NE of niacin, 1.0 μg of vitamin B12, 200 μg of folate and 40 mg of vitamin C per day.
I assumed people could purchase the following foodstuffs: wheat bread, barley bread,Footnote 19 rice, dried beans, mutton, hens, dried codfish, eggs, sugar, honey, olive oil and wine. I considered these foodstuffs, because they are the only ones for which price information for both Toledo and Barcelona is available.
People obtained some foods from the market. Some foods could have been obtained through other means. The evidence suggests that some workers in modern Spain received an in-kind compensation besides their salaries (Drelichman and Gonzalez-Agudo, Reference Drelichman and Gonzalez-Agudo2020). Some families could also obtain foods, especially vegetables and fruits, from the garden.Footnote 20 It is possible to consider the in-kind compensation or garden provision of foods in the model, reducing the quantity of nutrients that a person would need to obtain from food markets.
None of the foods included in the linear programming model provided vitamin C.Footnote 21 If it is assumed that people obtained foods only from the market, the model would have no solution. Recently, Allen (Reference Allen2020) assumed that people obtained vitamin C at no pecuniary cost. For the linear programming model, I assumed that families in Toledo and Barcelona obtained vegetables as an in-kind compensation (besides their pecuniary wages) or from the garden in sufficient quantities to cover their needs of vitamin C at no pecuniary cost.Footnote 22 In particular, I assumed that an average adult man obtained 271 g/day of fresh vegetables at no pecuniary cost, composed of 136 g/day of onions, 45 g/day of garlic, 45 g/day of lettuce and 45 g/day of cabbage.Footnote 23 These vegetables provided not only vitamin C, but also other nutrients (except vitamin B12). Their provision of calories, however, only represented 2 per cent of the minimum requirement for an adult man.Footnote 24
I relied on secondary sources to obtain the chemical composition of foodstuffs.Footnote 25 It is important to distinguish between the purchased quantity of an item and the consumed quantity. For instance, people purchased meat with bones, but discarded the bones. In the model, I included the price of a purchased kilogram and the intake of nutrients per purchased kilogram. If a portion of the food was not edible, the content of nutrients per purchased kilogram was lower than the content of nutrients per edible kilogram.
In this study, I estimated two types of food baskets: the calorie-protein basket (CP basket) and the balanced-nutrition basket (BN basket). For the CP basket, I only imposed restrictions on calories and proteins, not on other nutrients. If it is assumed that calories and proteins guarantee subsistence and that other nutrients are not necessary, the CP basket would be a subsistence basket. This basket, however, does not necessarily guarantee a balanced nutrition. Fat, minerals and vitamins are also important for a healthy life, so I estimated the BN basket including them.Footnote 26 For this basket, I imposed the same restrictions on calories and proteins as the CP basket, and added restrictions on fat, iron, thiamine, niacin, vitamin B12, folate and vitamin C.
Linear programming is useful to determine the quantities of foodstuffs that a person should purchase in order to satisfy their nutritional needs at the lowest possible cost. However, linear programming is not exempt from criticism. In particular, it is possible to argue that the lowest-cost basket does not necessarily reflect consumption habits. In addition, families did not have access to complete information about nutritional requirements and the chemical composition of foodstuffs. Furthermore, they did not use a mathematical tool to select their diets.Footnote 27
These criticisms do not invalidate linear programming as a methodology to estimate welfare ratios. I do not use linear programming to determine the actual consumption habits in the past. Rather I use the method to find the combination of foods people needed to consume to satisfy their needs at the minimum possible cost. As such, the corresponding welfare ratios do not measure whether people earned more than enough to pay for their consumption habits, but rather whether they earned enough to cover their basic needs.
4. Food baskets
I relied on a linear programming model to estimate the composition of the food basket in Toledo and Barcelona for the 1600-1800 period. Food baskets were allowed to vary over time. In particular, I estimated food baskets for each decade. I assumed p j was equal to the average prices for each decade.Footnote 28 I estimated two baskets for an adult man, the calorie-protein basket (CP basket) and the «balanced-nutrition basket» (BN basket).
4.1. Calorie-protein basket (CP basket)
The CP basket guarantees a minimum provision of calories and proteins. Table 2 shows the optimal CP baskets of an adult man. The basket in Toledo is only composed of cereals. The large participation of cereals, in particular wheat bread and barley bread, is consistent with the differences in the cost of calories and proteins. On average, in the 1600–1800 period, the two types of bread were relatively cheap sources of calories and proteins.Footnote 29 Beans provided proteins at a low cost, but also provided calories at a higher cost compared to wheat bread and barley bread. The composition of the food basket changed over time. For instance, barley bread increased in importance, due to the decline in its relative price with respect to wheat bread.
Table 2. Comparison between the CP and BN baskets and other studies’ baskets
Notes: The table reports the average composition of the CP and BN baskets and the baskets from Allen (Reference Allen2001, Reference Allen2009) and López and Piquero (Reference López and Piquero2021). The CP and BN baskets and those of Allen (Reference Allen2001) and Allen et al. (Reference Allen, Murphy and Schneider2012) refer to an adult man. López and Piquero's (Reference López and Piquero2021) baskets refer to an average person. For some foodstuffs, the original quantities in Allen (Reference Allen2001) are in litres or in units; I converted those figures to kilograms. The table also reports the quantity of nutrients as a percentage of their minimum requirements. For CP and BN baskets and those of Allen (Reference Allen2001) and Allen et al. (Reference Allen, Murphy and Schneider2012), the minimum requirements refer to an average man. For López and Piquero (Reference López and Piquero2021), to the average person. For Allen (Reference Allen2001, Reference Allen2009) and López and Piquero (Reference López and Piquero2021), I report two figures on the intake of nutrients as % of the minimum requirements. The first column assumes the person only consumed foodstuffs from the market; the second column assumes the person consumed foodstuffs from the market and from the garden (the same quantities as in the basic model in this study). a/ This item was not included in the linear programming model. b/ Allen et al. (Reference Allen, Murphy and Schneider2012) does not indicate the exact amount of cereals in the basket of Spain. They mention that the quantity of cereals was chosen to provide the same number of calories as 155 kg of oats. According to my estimates, the basket should then include 188 kg of wheat.
The CP basket for Barcelona is composed of cereals, beans and olive oil. It has some important differences compared to that of Toledo. In particular, the Barcelona basket includes beans and olive oil, unlike that of Toledo. These differences in the composition of the food basket can be explained by relative prices: beans and olive oil were relatively cheaper in Barcelona than in Toledo.
4.2. Balanced nutrition basket (BN basket)
Table 2 also shows the balanced-nutrition baskets of an average adult man in Toledo and Barcelona. The basket is largely composed of cereals, but also includes animal-derived foods and olive oil. Cereals are an important component of the food basket in Toledo and Barcelona. Animal-based foods are also included in the food basket, though in far smaller quantities than cereals. In Barcelona, beans are also part of the food basket. The basket satisfies all restrictions and the binding constraints are those for calories, vitamin B12 and vitamin C.
Wheat bread and barley bread have a large participation in the BN food basket in Toledo and Barcelona. This result is not surprising as these two items were relatively cheap sources of calories, proteins, fat, iron, thiamine, niacin and folate. Beans were also a relatively cheap source of nutrients in Barcelona. Not surprisingly, beans are included in the food basket of Barcelona. On the other hand, animal-derived foods (for instance, mutton) are included in the basket because they provided vitamin B12.
The composition of the food basket changed over time. Barley bread increased in importance, whereas wheat bread became less important. These changes in the food basket can be explained by the evolution of relative prices. Barley bread became relatively cheaper over time with respect to wheat bread. On the other hand, there were changes among animal-derived foods. In particular, in Barcelona mutton and codfish declined in importance compared to eggs.
4.3. Comparison with other food baskets
Allen (Reference Allen2001), Allen et al. (Reference Allen, Murphy and Schneider2012) and López and Piquero (Reference López and Piquero2021) made assumptions about the food baskets in order to estimate welfare ratios in Spain.Footnote 30 How do the CP and BN baskets in Toledo and Barcelona compare to the baskets of those studies?
Table 2 shows all food baskets.Footnote 31 There are some important similarities between the CP and BN baskets and the baskets of the three previous studies on Spain. One of the similarities is the inclusion of cereals. Cereals represented an important portion of all food baskets. There are also similarities in the exclusion of some items. As with the baskets of the three previous studies, the CP and BN baskets did not include hens, sugar and honey.
However, there are also important differences in the composition of the food basket. One difference refers to the inclusion of barley bread. This item had an important participation in the CP and BN baskets. In contrast, Allen (Reference Allen2001), Allen et al. (Reference Allen, Murphy and Schneider2012) and López and Piquero (Reference López and Piquero2021) did not include barley bread or barley. The second difference refers to animal-derived foods. In several decades, the BN basket included mutton; however, in some decades the BN basket in Barcelona also included codfish and eggs. In contrast, the three previous studies on Spain did not include fish or eggs. The third difference refers to the inclusion of legumes (beans or chickpeas). The BN basket in Toledo never included legumes. In contrast, the three previous studies included legumes in the food baskets of New Castile (Toledo or Madrid). The fourth difference refers to the evolution of the food basket. The CP and BN baskets were allowed to change over time. In contrast, the baskets in the three previous studies were assumed constant in spite of the changes in relative prices.
There are also differences in the provision of nutrients. By assumption, the BN basket provided more nutrients than the baskets of Allen (Reference Allen2001), Allen et al. (Reference Allen, Murphy and Schneider2012) and López and Piquero (Reference López and Piquero2021). The basket of Allen provided fewer calories than the BN basket. In addition, the basket of Allen et al. provided fewer calories, proteins, fat, iron, niacin and vitamin B12 than the BN basket,Footnote 32 whereas the basket of López and Piquero provided fewer calories, fat and vitamin B12 than the BN basket.Footnote 33 Thus, the baskets of these three studies did not provide enough calories to support the daily energy requirements of a labourer who did heavy work nor other nutrients important for a balanced nutrition.
5. Welfare ratios
In order to estimate welfare ratios, most studies assumed that the living cost of a family was a multiple of the cost for an adult man or of the cost for an average person. In the 2000s, most studies assumed a subsistence basket for an adult man and estimated the cost of subsistence of a family of four members (two adults and two children) as three times the cost for an adult man (Allen, Reference Allen2001, Reference Allen2009). Meanwhile, other studies assumed that the cost of subsistence of a family of four members was equal to four times the cost for an average person (Allen, Reference Allen2014, Reference Allen2020; López and Piquero, Reference López and Piquero2021; Zegarra, Reference Zegarra2022).
It is not appropriate to assume that the living cost of a family was three times the cost for an adult man. According to the calculations for Spain, the total requirement of calories for a family of two adults and two children was less than three times the requirement of an adult man who did hard work, whereas the requirements of iron and vitamin C were more than four times. On the other hand, assuming that the cost of living of a family was four times the cost for an average person is also questionable. Such a method would be valid for a family of four members as long as the average structure of the family reflected the distribution of the Spanish population.Footnote 34
In this study, I followed a different approach to estimate the cost of living of a family. I first computed the total nutritional requirements for a family based on its structure and then used linear programming to estimate the lowest-cost basket. There were different types of family structures. This section shows the welfare ratio for an average family of four members, two adults and two children. The next section shows the welfare ratio for alternative family structures.
In order to find the lowest-cost basket for the family of four members, I assumed that the two adults ranged between 18 and 55 years old and that the two children were up to 15 years old. I used the distribution of the population in Spain in the late 18th century to calculate the average nutritional requirements for each family member. To obtain the requirements of calories, I assumed that the husband did hard work and that the wife did moderate work, so the daily energy requirements were 2.2 BMR for the husband and 1.8 BMR for the wife. The total daily nutritional requirements for the entire family were 9,207 kcal of calories, 181 g of proteins, 130 g of fat, 74 mg of iron, 4.5 mg of thiamine, 59 mg NE of niacin, 2.5 μg of vitamin B12, 682 μg of folate and 163 mg of vitamin C. I also assumed that the family obtained vegetables at no pecuniary cost.Footnote 35
For the calculation of the total cost of living, I also considered fuel, linen, soap, candles, lamp oil and housing as basic needs. In particular, I assumed that on average a person required 2.0 M BTU of fuel, 3 m of cotton, 1.3 kg of candles, 1.3 kg of soap and 1.3 litres of lamp oil per year. In addition, following a standard assumption in the literature, I assumed that housing costs were equal to 5 per cent of the cost of other basic needs.
Figure 1 shows the daily living cost of a family in Toledo and Barcelona. The figure shows two series for each city. One series assumes that the cost of food was the cost of the CP basket. Another series assumes that the cost of food was the cost of the BN basket. The living costs in Toledo and Barcelona followed a similar pattern, although the growth rates were different.
Figure 1. Cost of living in Spain, 1600–1800 (grams of silver/day).
Notes: The figure depicts the evolution of the daily living cost of a family in Toledo and Barcelona in the period 1600-1800 in grams of silver, including food and non-food expenses. CP cost is the living cost if the food cost was equal to the cost of the CP basket. BN cost is the living cost if the food cost was equal to the cost of the BN basket.
The data on salaries of low-skilled workers were retrieved from secondary sources, especially from Hamilton (Reference Hamilton1934, Reference Hamilton1947) for Toledo and Feliu (Reference Feliu1991) for Barcelona.Footnote 36 The information refers to payments to male labourers for a day of work. Following most of the literature, I assumed that only one male adult worked per family and that he did so for 250 days per year.Footnote 37
Figure 2 shows the evolution of daily family income in grams of silver. I calculated the daily family income as the annual labour income divided by 365, assuming that labourers worked 250 days in a year. Family income in Toledo declined between 1600 and 1725 and remained relatively constant subsequently. In the case of Barcelona, family income increased in the mid-17th century, but then declined in the period 1676-1725. Income then increased in the second half of the 18th century.
Figure 2. Family income in Spain, 1600–1800 (grams of silver/day).
Notes: The figure depicts the evolution of family income in Toledo and Barcelona in the period 1600-1800 in grams of silver per day. I assume male labourers were the only source of family income and that they worked 250 days per year. The daily family income was calculated as the wage of a day of work multiplied by 250/365.
I calculated two types of welfare ratios using the two types of food baskets. The two types of welfare ratios are labelled as CP welfare ratios and BN welfare ratios.Footnote 38 The CP welfare ratio measures the capacity of families to cover their most basic needs, including calories and proteins, but not necessarily other nutrients. Meanwhile, the BN welfare ratio measures the capacity of families to cover their basic needs, including having a balanced nutrition. If the CP ratio is less than 1.0, the family could not even afford subsistence. If the BN is greater than 1.0, the family could cover their basic needs, including a balanced nutrition. If the CP ratio is greater than 1.0 and the BN ratio is less than 1.0, a family could cover their needs of calories and proteins, but not the needs of other nutrients.
Figure 3 shows the evolution of the welfare ratios. As expected, the BN ratios were lower than the CP ratios. For each city, both welfare ratios followed a similar trend. In the case of Toledo, the CP welfare ratio declined from 1.4 between 1600 and 1625 to 1.2 in the period 1626-50, but then increased above 1.6 between 1701 and 1725. In the following decades, the ratio followed a downward trend. In the late 18th century, the ratio was 0.8. The BN ratio followed a similar trend, falling from almost 1.3 in the early 17th century to 1.1 between 1626 and 1650, increasing to 1.4 in the period 1701–25, and declining to 0.7 in the late 18th century. In the case of Barcelona, the two welfare ratios increased from 0.75–1.0 in the early 17th century to 1.0-1.2 in the period 1651–75, declined to 0.75–0.9 between 1751 and 1775, and increased to 0.9-1.1 in the late 18th century.
Figure 3. Welfare ratios in Spain, 1600–1800.
Notes: The figure depicts the evolution of welfare ratios in Toledo and Barcelona in the period 1600-1800. CP ratios are the welfare ratios under the assumption that the cost of food was equal to the cost of the CP basket. BN ratios are the welfare ratios under the assumption that the cost of food was equal to the cost of the BN basket.
The CP and BN welfare ratios in Toledo were above 1.0 until the mid-18th century. Four-member families in the city were able to cover their basic needs, including a balanced nutrition. In the second half of the 18th century, however, both ratios were below 1.0. By then, four-member families were not able to satisfy their most basic needs. Meanwhile, the two ratios in Barcelona were below those of Toledo during most of the period. Compared to families in Toledo, families in Barcelona faced more difficulties to cover their basic needs.
How do my results compare with those from Allen (Reference Allen2001), Allen et al. (Reference Allen, Murphy and Schneider2012) and López and Piquero (Reference López and Piquero2021)? Table 3 compares the CP and BN welfare ratios in Spain with those from the three previous studies. The CP and BN ratios in Spain are higher than the estimates of Allen (Reference Allen2001). For instance, the welfare ratio of Allen for Toledo was always below 1.0 for the period 1600–1800. In contrast, the CP and BN ratios in Toledo were above 1.0 between 1600 and 1750. The ratio of Allen for Valencia was around the same level as Toledo. In comparison, the CP and BN ratios in Barcelona were below those in Toledo. On the other hand, for New Castile and Barcelona/Valencia, the BN welfare ratios are far lower than the ratios of Allen et al. (Reference Allen, Murphy and Schneider2012) and slightly lower than those of López and Piquero (Reference López and Piquero2021).
Table 3. Welfare ratios: a comparison
Notes: The table reports my estimates of welfare ratios in Spain, as well as the welfare ratios of Allen (Reference Allen2001), Allen et al. (Reference Allen, Murphy and Schneider2012) and López and Piquero (Reference López and Piquero2021). My estimates refer to Toledo and Barcelona. Allen (Reference Allen2001) and Allen et al. (Reference Allen, Murphy and Schneider2012) report ratios in Toledo and Valencia, whereas López and Piquero report ratios in Madrid and Valencia. I also recalculated the welfare ratios from Allen (Reference Allen2001), Allen et al. (Reference Allen, Murphy and Schneider2012) and López and Piquero (Reference López and Piquero2021) to make them comparable with my estimates. I adjusted the cost of food of those studies by multiplying the original cost of food by a factor K, where K is the ratio of the calories in the present study divided by the calories in the previous studies. I calculated the cost of food of the previous studies using their original prices. For Allen et al. (Reference Allen, Murphy and Schneider2012), I assumed that the basket was composed of 188 kg/year of wheat, instead of 155 kg/year of oats. I also assumed that the cost of fuel, lamp oil, linen, soap and candles for a family was four times the cost for an average person. The ratios, prices and wages of Allen (Reference Allen2001) were obtained from https://gpih.ucdavis.edu/Datafilelist.htm. The ratios of Allen et al. (Reference Allen, Murphy and Schneider2012) come from the appendix of the same study. The welfare ratios, prices and wages of López and Piquero (Reference López and Piquero2021) were obtained from https://addi.ehu.es/handle/10810/40426?show=full. Wages and prices in Madrid come from López and Piquero. 1/ Allen (Reference Allen2001) did not report welfare ratios for this period. 2/ I estimated the CP ratios in Madrid using linear programming.
Compared with the three previous studies on Spain, I estimated the welfare ratios using a different methodology (linear programming vs. historical diets) and assuming different nutritional requirements. The use of linear programming would produce a lower cost of subsistence than historical diets and so a higher welfare ratio. However, this study assumes a higher requirement of calories than the three previous studies on Spain. A higher calorie intake would produce a higher cost of subsistence and then a lower welfare ratio.
To determine the effect of linear programming on the results, I recalculated the welfare ratios of Allen (Reference Allen2001), Allen et al. (Reference Allen, Murphy and Schneider2012) and López and Piquero (Reference López and Piquero2021) for Toledo and Madrid, maintaining the same proportions of foodstuffs as those studies, but using the same intake of calories as in this study. I also assumed that the cost of fuel, lamp oil, linen, soap and candles for a family was four times the cost for an average person.
The bottom section of Table 3 shows the results. Since the baskets of Allen (Reference Allen2001), Allen et al. (Reference Allen, Murphy and Schneider2012) and López and Piquero (Reference López and Piquero2021) provided fewer calories than the minimum requirements, the cost of food of those studies increased after the adjustment.Footnote 39 The adjusted ratios are now lower than the CP ratios in all cases and all periods. The original welfare ratio of Allen (Reference Allen2001) was already lower than the CP ratio. After the adjustment, the ratio of Allen represented 60 per cent of the CP ratio.Footnote 40 The original ratio of Allen et al. (Reference Allen, Murphy and Schneider2012) was higher than the CP ratio in the 17th century and in the late 18th century. After the adjustment, however, the ratio of Allen et al. became 70-80 per cent of the CP ratio. Meanwhile, the original ratio of López and Piquero (Reference López and Piquero2021) was slightly higher than the CP ratio. After the adjustment, however, the ratio became 80-90 per cent of the CP ratio. Therefore, linear programming yielded important changes in the cost of food and so in the welfare ratio. Had poor families opted for consuming the lowest-cost basket instead of the typical diet, they would have had a better chance of covering their basic nutritional needs.
6. Family structures and life cycle
In the basic model, I calculated the cost of living for a family of four members (two adults and two children) and assumed that only a man worked in the family and that he did so for 250 days per year. These assumptions may have reflected the reality of some families, but not all. Women and even children could also have worked for a salary. In addition, the workload and the structure of the family may have changed over time.Footnote 41 At an early stage, before having children, both adult men and women could work. As people got married and started having children, one of the parents probably had to stay at home to raise the children. Eventually, however, children left the house. Families had different welfare ratios through life. How did welfare ratios vary depending on family size, the length of workdays and the number of people who worked?
Horrell et al. (Reference Horrell, Humphries and Weisdorf2022) estimated welfare ratios in England and Wales for six life stages after young people left the home of their parents at the age of 15.Footnote 42 These stages are youth, young-family, peak-family, old-family, post-family and old-age. I follow Horrell et al. and make assumptions for each stage, regarding the ages in these stages, the number of people who worked, the time worked and the number of children. The first stage, called youth, began at the age of 15 and ended at 24. During this stage, men and women were independent and had no children. I assumed they worked full time during this stage, that is, 250 days per year. I assumed men and women got married and started a family at the age of 25. During the young-family stage (25-34 years), the family had two young children. I assumed the husband continued working 250 days/year and the wife reduced her workload to 50 days/year to raise children. During the peak-family stage (35-44 years), the family grew. I assumed the family now had three children (two adolescents and one young child), and that the couple maintained their workload. During the fourth stage, the old-family stage, the parents were between 46 and 55 years old. I assumed that two of the children had now left home, the husband worked 250 days/year and the wife worked 100 days/year. In the fifth stage, the post-family stage (55-64 years), the third child had also left home and both parents worked 250 days/year. In the sixth stage, the old age (65-75 years), the couple reduced their workload due to their advanced age. In particular, I assumed that the husband worked 125 days/year and the wife did so for 50 days/year.
I estimated welfare ratios for the six life stages. I assumed that people did not save or borrow. I calculated the nutritional requirements of the family for each stage. The requirements depended on gender, age and type of work. I assumed energy requirements of 2.2, 2.0 and 1.8 BMR when working 250 days/year, 100-125 days/year and 50 days/year, respectively. I then estimated the linear programming model and found the BN food basket for each life stage. The cost of other goods and services (fuel, linen, etc.) was calculated as the number of people in the family times the cost per person. I assumed the same quantities of fuel, linen, lamp oil, candles and soap per person as in the basic model. I assumed salaries of women were equal to 40 per cent of those of men.Footnote 43
Table 4 shows the evolution of welfare ratios for alternative life stages. In Toledo and Barcelona, the welfare ratios reached their highest levels in the first stage, when men and women did not have children. As they formed families and started having children, the welfare ratios declined. The welfare ratios reached their lowest levels in the third stage, when the family had five members (two adults and three children). As children left home, the welfare ratios increased. The ratios reached a relatively high level in the fifth stage, when the two parents lived alone and did not have to support their children. In the sixth stage, however, as the two parents, now older, could not work as much as before, the welfare ratios were lower.
Table 4. Welfare ratios in different life stages
Notes: The table reports BN welfare ratios for six life stages in Toledo and Barcelona. In stage 1, men and women were between 15 and 24 years of age and had no children. In stage 2, men and women were between 25 and 34 years old. The two adults had two children. In stage 3, the two parents were between 35 and 44 years old. The family was composed of the father, the mother and three children. In stage 4, the two parents were between 45 and 54 years of age. In addition, two children had moved out. In stage 5, the two parents were between 55 and 64 years and the family was only composed of the two parents. In stage 6, the two parents were between 65 and 75 years of age. The adult man worked 250 days/year in stages 1-5 and 125 days/year in stage 6, whereas the adult woman worked 250 days/year in stages 1 and 5, 50 days/year in stages 2, 3 and 6 and 100 days/year in stage 4. For the first stage, I determined the food baskets for men and women of 15–24 years of age, using the average nutritional requirements for each of them. The welfare ratio in this stage is the average of the man's welfare ratio and the woman's welfare ratio. For the other stages, the total nutritional requirements of the family were calculated as the sum of the average requirements of each member of the family.
In the first stage, young adults from Toledo did not face difficulties to cover their basic needs, even in the late 18th century, when welfare ratios were lower. As families had children, the welfare ratio declined. In the second stage, the welfare ratio was between 1.2 and 1.5 between 1600 and 1750. In the period 1750-1800, however, the ratio was less than 1.0. In the third stage, the ratio was below 1.2 in the entire period, and it was below 1.0 in the 1750-1800 period. In the fourth stage, the welfare ratio in Toledo was usually above 1.0. In the fifth stage, the welfare ratio was always above 1.0, even in the late 18th century. In the sixth stage, families faced more difficulties to afford their living expenses, especially in the second half of the 18th century.Footnote 44
Families in Barcelona usually faced more difficulties than those in Toledo, especially until the mid-18th century. In the first stage, at the time of independence and with no children, the welfare ratio was above 1.0. In the second stage, the welfare ratio was below 1.0 in 1600–50, 1701–25 and 1751–75. In the third stage, the welfare ratio was always below 1.0. As families had to support children and the wife could not work as before, families could not cover their basic needs during most of the period. In the fourth stage, the welfare ratio was above 1.0 and was higher than in the previous two stages. In the fifth stage, as all children had already left home, the welfare ratio was higher than 1.7. In the sixth stage, the two parents did not have to support their children. However, the welfare ratio was usually less than 1.0 or barely above 1.0. Since the parents could not work full time, their income was not high enough to cover their basic needs.
Therefore, in general, families in Toledo and Barcelona faced larger difficulties to cover their basic needs in the periods 1600-1650 and 17501800. However, the welfare ratio depended on the life stage. Families faced more difficulties in the second, third and sixth stages, when families had to raise children or when the parents could not work full time.
7. International comparison
Some studies have compared the welfare ratios of Spain and other countries. According to Allen (Reference Allen2001) and Allen et al. (Reference Allen, Murphy and Schneider2012), the welfare ratios in Northern Europe in the period 1600-1800 were above those in Toledo, Valencia and other European cities, so the divergence between Northern Europe and the rest of Europe started long before the Industrial Revolution. In contrast, López and Piquero (Reference López and Piquero2021) found that the divergence in welfare ratios between Northern Europe and Spain only started in the 18th century.
To determine the differences in welfare ratios between Spain and other countries, it is necessary to compare welfare ratios obtained using similar methodologies. However, most estimations of welfare ratios for other European cities have been obtained using historical diets, not linear programming. Only recently, I used linear programming to estimate BN welfare ratios in London, Amsterdam, Paris, Strasbourg, Munich and Leipzig (Zegarra, Reference Zegarra2022). In the following paragraphs, I compare the BN ratios in Spain with the BN estimates for those six cities (Figure 4).Footnote 45
Figure 4. BN welfare ratios.
Notes: The figure depicts the evolution of BN welfare ratios in Europe. For Toledo and Barcelona, the figure depicts my estimates of the BN welfare ratios. For London, Amsterdam, Paris, Strasbourg, Munich and Leipzig, I adjusted the BN welfare ratios from Zegarra (Reference Zegarra2022) to make them comparable with my estimates. I multiplied the cost of food in those cities by a factor of 0.942, equal to the ratio between the calories of a family in my study and the calories of a family in Zegarra (Reference Zegarra2022). For all studies, it is assumed that only one male adult of the family worked, and he did so for 250 days/year. For all countries, the BN food basket was obtained using linear programming.
In the early 17th century, the BN ratios in Spain were below the ratios in London and Amsterdam: in the period 1600-25, the welfare ratio was around 1.3 in Toledo, 0.8 in Barcelona, 1.4 in London and 1.5 in Amsterdam. From then and until the mid-18th century, the BN ratios in London and Amsterdam followed an upward trend, whereas the ratios in Toledo and Barcelona remained below 1.4. The BN ratios in Toledo and Barcelona were usually similar to those in Paris, Strasbourg, Munich and Leipzig.
The evidence suggests that in the 17th century the welfare ratios in Spain were already lower than those in Northern Europe. Over time, the welfare ratios differed even more. According to my estimates, the BN welfare ratio of Toledo represented around 88 per cent of the ratio in London in the period 1600-25. This percentage declined over time, reaching 33 per cent between 1776 and 1800. As a percentage of the welfare ratio in London, the ratio in Barcelona also declined over time from more than 50 per cent in the early 17th century to 46 per cent in the late 18th century.
My estimates support some of the findings in Allen (Reference Allen2001) and Allen et al. (Reference Allen, Murphy and Schneider2012), in particular that Spain had lower welfare ratios than Northern Europe long before the Industrial Revolution. However, my estimations also show that in the early 17th century the differences between Northern Europe and Spain were lower than those found by Allen and Allen et al. On the other hand, my estimates contradict the argument of López and Piquero that the divergence in welfare ratios started in the 18th century. An important similarity between my estimates and those from previous studies is that the differences in welfare ratios between Northern Europe and Spain increased over time.
8. Conclusions
Welfare ratios constitute a useful indicator for the study of living standards. Two methodologies can be used to estimate welfare ratios. It is possible to use historical diets to calculate the food cost at subsistence levels. In addition, it is possible to use linear programming to find the lowest-cost food basket. When using historical diets, welfare ratios measure the capacity of families to cover their consumption habits. When using linear programming, welfare ratios measure the capacity of families to cover their basic needs.
In their studies, Allen (Reference Allen2001), Allen et al. (Reference Allen, Murphy and Schneider2012) and López and Piquero (Reference López and Piquero2021) estimated welfare ratios for pre-1800 Spain using historical diets. Allen (Reference Allen2001) and Allen et al. (Reference Allen, Murphy and Schneider2012) found that between 1600 and 1800 the welfare ratio in Spain was always below that of Northern Europe. In contrast, López and Piquero found that the divergence in welfare ratios between Northern Europe and Spain only started in the 18th century.
In this study, I estimated welfare ratios in Spain using a linear programming model. By doing so, I obtained the optimal food basket that allowed people to cover the requirements of several nutrients. The BN baskets include a large quantity of cereals, in particular wheat bread and barley bread. The basket of Barcelona also includes beans. In several decades, the baskets of Toledo and Barcelona include mutton; at times, the basket of Barcelona includes codfish and eggs. One similarity between this study and previous studies refers to the inclusion of large quantities of cereals, although the quantities vary. In addition, unlike previous studies, the food baskets are not assumed constant over time (in fact, they change over time). There are also differences in the inclusion of legumes, codfish and eggs, among other items.
The results of this study show that the welfare ratio of a family of four members in Toledo was above 1.0 in the period from 1600 to 1750 and below 1.0 between 1751 and 1800, whereas the welfare ratio in Barcelona was usually below the ratio in Toledo. My estimates differ from previous studies. The welfare ratios of this study are higher than those of Allen (Reference Allen2001), far lower than those of Allen et al. (Reference Allen, Murphy and Schneider2012) and slightly lower than those of López and Piquero (Reference López and Piquero2021). On the other hand, my estimates show that welfare ratios depended on the life stage. Welfare ratios were lower when families had to raise children and when the parents could not work full time.
According to my calculations, Spain did not compare favourably with Northern Europe. In most of the period 1600-1800, the BN welfare ratios in Toledo and Barcelona were below those in London and Amsterdam. However, the ratios in Spain were similar to those in France and Germany. My results show that Spain had lower welfare ratios than Northern Europe before the Industrial Revolution.
Supplementary material
The supplementary material for this article can be found at https://doi.org/10.1017/S0212610924000107.
Acknowledgements
I am very grateful to the Editors of Revista de Historia Económica/Journal of Iberian and Latin American Economic History and the three anonymous referees for their comments and suggestions. Those comments were very helpful for improving the article. I am also grateful to the personal of the National Library of Spain at Madrid and the Library of the University of Barcelona in the process of data collection. In 2022, I presented the methodology used in this article (linear programming) in VII CLADHE and seminars organised by the University of Barcelona, University of Valencia and the University of Sevilla. The comments of the participants in those seminars were very helpful for improving the methodology used in this article. In 2022, I spent time as Visiting Professor in the University of Barcelona. I worked on this article during my stay in Spain. Funding for this travel was provided by the Pontificia Universidad Católica del Perú (PUCP) and the Research Group of Economic History (Grupo de Investigación de Historia Económica) of PUCP.
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