Amartya Sen revisited: population, grain production and income inequality in 18th century Guadalajara (Spain)
Carlos Santiago Caballero, LSE
c.santiagocaballero@lse.ac.uk

Introduction:
This paper presents original series from the historical diocesan archives of Sigüenza and Getafe, and includes baptismal records and cereal production for the province of Guadalajara and grain prices for the province of Madrid for the eighteenth century. The main purpose of the paper consists in giving an answer to the demographic paradox that took place in Guadalajara during the second half of the eighteenth century when fertility maintained a sustained and intense growth while the total production of cereals in the same province was constant and even declined in per capita terms.
The first section will present the baptismal record and cereal production series to show the existence of a demographic paradox. After describing the dataset, the paper will introduce a possible solution to this puzzle based on Amartya Sen’s entitlement theory and present the Gini coefficient of the cereal production series, and its relationship with the demographic and productive trends. Finally the last section will look at the reasons behind the changes in inequality, concluding that the improvements made by small producers were the driving force of the process.

The Data. The dataset includes estimations from primary sources of grain production, fertility rates and grain prices for eighteenth century Guadalajara and Madrid. To proxy grain production we have used tithe records kept by the local priest in 25 towns and villages of Guadalajara.^{1} For the period under analysis the use of tithes offers a good estimation of real production, as the level of taxation remained constant at 10% and cheating was not significant until the end of the Napoleonic wars in the early nineteenth century. Fertility has been estimated by using baptismal records, also kept by the local parishes and widely used in the demographic literature including 25 locations in the province of Guadalajara.^{2} Finally new series of wheat and barley prices were produced for Madrid from accounting books of the parish of Santa Maria Magdalena in Getafe. The final dataset includes more than 200,000 observations from individual producers, households and ecclesiastical authorities directly extracted from the manuscripts kept in the Historical Diocesan Archive of SigüenzaGuadalajara and in the Historical Diocesan Archive of Getafe.

Population and production in eighteenth century Guadalajara
In agrarian terms, the eighteenth century is a period of very modest growth. The crisis of the late seventeenth century extended its effects until the first year of the eighteenth century. After the economic slump, a quick and consistent recovery started in 1710 and until 1720 the positions that had been lost during the crisis were clearly recovered and even surpassed with an increase in grain production of nearly 50% in only ten years. The following forty years were a period of stagnation with brief crises and recoveries that finished with the crisis of the late eighteenth century, that started in the second half of the century and that was marked by an early decline of grain production during the 1750s and a later stagnation in the production of grain that would last until the end of the century.
Figure 1: Grain Production in 18^{th} century Guadalajara
Source: same as footnote 1.
In demographic terms, baptismal series show that the eighteenth century was a period of intense fertility growth, a fact supported by a growth of 40% in the number of baptisms. There were three very clear trends. The first one and after the last effects of the crisis of the late seventeenth century was a period of growth that started in 1710 and that was sustained until the mid 1720s when it reached its peak to be followed by a crisis until the late 1740s with a decrease of almost 20% in the number of baptisms. The last period was a constant and long process of demographic growth that started in the 1740s and continued during the rest of the century with an increase in the number of baptisms of nearly 40%.
Figure 2: Baptisms in 18^{th} century Guadalajara
Source: same as footnote 2.
Combining the information from both graphs the most striking feature is how the demographic growth continued in Guadalajara during the second half of the century when the production remained stagnant or even declined. We have seen that during the second half of the eighteenth century grain production was constant while after the analysis of baptismal series it is quite probable that total population grew in Guadalajara. Therefore in per capita terms the availability of grain diminished. So the question is how can population grow when the supply of food is constant or in per capita terms even declines? A possible explanation is that the distribution of that production became more equal, and therefore that distribution is as important as production levels.

The entitlements approach:
According to Amartya Sen in his studies of demographic shocks, the distribution of food is as important as the level of food production itself. In his entitlements theory Sen states that ‘The entitlement approach to starvation and famines concentrates on the ability of people to command food through the legal means available in the society, including the use of production possibilities, trade opportunities, entitlements visàvis the state, and other methods of acquiring food’^{3}. For Sen there are four ways of commanding food, through trade, own production, own labour and inheritance. To study the relationship between food production and demographic movements, we should therefore look not just at the total levels of food production, but also at the ability of every individual to command his own supply
Sen’s theories appeared to explain the emergence of famines in cases where the production of food did not suffer a reduction. In this paper we will use the same theory not to explain a famine, but to explicate the opposite, how the demographic growth of the late eighteenth century Guadalajara took place when total production of food remained constant and per capita levels probably diminished.
The Gini Coefficient measures the dispersion of the observations in a sample, and has been widely used to measure inequality. The coefficient takes values between 0 and 1 being 0 perfect equality and 1 perfect inequality, or in other words and in the case that we are studying the Gini Coefficient would be 0 if all the producers produce exactly the same amount of grain and 1 if one single peasant owns all the production. In mathematical terms the Gini Coefficient can be defined as:

(1)

Using the dataset extracted from the tazmias books we created decadal calculations of the Gini coefficient for cereal production in Guadalajara. In order to get a better approximation to real incomes, the production of different grains was transformed from capacity measurements to a monetary one, using the series of prices created for Madrid, the closest available one and the market for the grain from Guadalajara. The new series were therefore not in volume of different grains but in grams of silver. Around 85% of the inhabitants in the villages included in this work were peasants that cultivated their own land and that obtained the bulk of their income from the cultivation of grain (Figure 1). Therefore the study of inequality in the production of grains is a raw although good proxy on income inequality. The results of the Gini Coeffients of the transformed series for every decade of the eighteenth century are presented in the following figure:
Figure 3: Gini Coeffcient in Guadalajara 17001800
Source: same as figure 1
The results show three clear trends during the eighteenth century. The first one is a period of convergence and inequality reduction from 1710 until 1740. The second one shows an increase of the inequality starting around 1750 and ending around 1770. The last period is again a convergence one that took place from 1770 until the end of the century. In general terms we can confirm that the trend during the eighteenth century is a period of falling inequality.
But what is the significance of these numbers? What was the effect of the reduction in the Gini coefficient from 0.51 to 0.47 that took place during the last third of the century? Is it consequence of small producers catching up? We can provide some answer to these questions. In our sample, doubling the production of the bottom 12% would reduce the Gini coefficient in 0.1 points. In the same way in order to achieve the reduction of 0.4 points we would have to double the production of the bottom 33%. Therefore if the changes are based on improvements of the smaller producers then the effects of the change in inequality would be considerable.
To check if that was the case, all the producers were divided into ten groups depending on their production levels. Taking index numbers and 100 as the output of the maximum producer, the observations were divided depending on their percentile in relation to this maximum. Therefore the first group includes the number of peasants whose production levels are between 12% of the output of the biggest producer, etc. Three graphs will be showed for each period, the first one with the distribution of the producers in each inflexion point, the second one with the variations in percentage in the number of individuals in each group and a third one with a summary of the second graph containing not 10 groups but three, small, medium and big producers.
The results show that the period 17701800 shows a very clear convergence, the number of small producers was reduced by more than 10% while the number of medium producers grew by 7% (Figures 46). The fall in inequality was mainly consequence of very small producers improving their positions and many of them probably joining the group of medium producers. The biggest fall was in the 2/5 and 0/1 percentiles while the biggest rise took place in the 5/20 and 20/30 percentiles. Therefore the reduction of inequality during the eighteenth century in Guadalajara was mainly conditioned by a catching up of small producers that improved their situation in relationship to the biggest ones.
Figure 4: Distribution of producers 1770 and 1800
Source: same as figure 1
Figure 5: Changes in the number of producers by group 17701800 (I)
Source: same as figure 1
Figure 6: Changes in the number of producers by group 17701800 (II)
Source: same as figure 1
Although the Gini coefficient is a good way of measuring the changes in total inequality, it also presents some limitations. The Theil Index is an alternative to the Gini Coefficien that also measures the distribution of a sample and that has been widely used in the literature of income inequality. ^{4} However the Theil index offers some interesting properties, for example it can be easily decomposed. Its calculation is defined by the formula:

(2)

Where in our case n would be the number of producers, wi the production of the individual i and µ the arithmetical average of the sample. As it was explained before, the Theil index can be decomposed. If we divide the observations of a sample in different groups, the Theil index can tell us what are the changes in inequality within each group and between them. In our case we decided to divide the producers in the sample by villages grouping them by size. Therefore three groups were created with small, medium and big villages. There are good reasons to support this division, the size of the village also defined its economic and social structure. Small villages were mainly occupied by a homogenous group of small peasants that were owners, while big villages included also manufactures producers and workers that did not own land. We can therefore expect differences between in inequality between the three groups that can be explored by the Theil index. Following the methodology presented above, for every group g, µg is the average production, ng the number of producers and Tg is the Theil index for that specific group. Then the new formula for the Theil index would be:

(3)

Being

(4)

The first term in (3) corresponds to the weighted addition of the Theil indexes of every group and therefore presents the inequality within each group, in other words it measures the inequality within small, medium and big villages. The second term shows the inequality between the three groups. Therefore for the period 17701800 we can measure if the reduction of inequality was consequence of reduction of inequality within or between groups. The results are presented in the following table.
Table 1: Inequality changes decomposed by size of village 17701800
Inequality within groups


107,19%


Small villages


5,48%


Medium villages


74,26%


Big villages


38,41%






Inequality between groups


7,19%






Total change in inequality


100,00%

Source: same as figure 1
The results show that during the period 17701800, the reduction of inequality was mainly driven by within groups convergence, and very especially in medium and big villages. On the other hand there was a small increase in the inequality within small villages. The reason is that in small villages inequality levels were already low in 1770, and that the following three decades would experience a catch up from high inequality levels by medium and big villages (Table 2).
Table 2: Theil index by size of village 1770 and 1800

Theil 1770

Theil 1800

Big Villages

0,43

0,33

Medium Villages

0,42

0,18

Small Villages

0,34

0,36

Source: same as figure 1
Conclusion:
We can therefore conclude that the eighteenth century is a period of strong demographic growth in the Spanish province of Guadalajara This growth was possible even during the last third of the century when the production per capita of cereals decreased under the effects of one of the last production crises in modern Spain. One of the possible explanations of this demographic paradox relies on a reduction of income inequality, based on an increase in the production of grain by small producers that generated an increase of their food entitlements and therefore the possibility of increasing fertility rates.
Bibliography:
Sen, A Poverty and famines: An essay on entitlement and deprivation (Clarendon Press, Oxford, 1981)
Steckel, R.H. and Moehling, C.M., “Rising Inequality: Trends in the Distribution of Wealth in Industrializing New England”, Journal of Economic History, (2001)
Mora Sitja, N., “Exploring Changes in Earnings Inequality During Industrialization: Barcelona, 18561905”, Discussion Papers in Economic and Social History N. 61. April 2006
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