Legacies of inequality: the case of Brazil

Abstract

This research examines the effects of inequality on long-run development within Brazil. I first exploit variation in temperature and precipitation to instrument for the local distribution of land in 1920 using a two stage least squares instrumental variables framework. My instrument is an index quantifying the suitability of local climatic conditions for plantation versus smallholder agriculture. I construct this index using information on the growing conditions of crops within certain plant taxonomies that are more biologically suited for smallholder or plantation production. I argue that this index more fully identifies the optimal environmental conditions for these two types of agricultural production, and I show that it serves as a robust predictor of local land inequality in the year 1920. IV estimates then reveal that greater inequality is associated with less local government spending on welfare and public goods over the 1995-2005 time period, as well as reductions in measures of local government quality and per-child education spending. It is also associated with lower levels of development, as measured by the local Human Development Index (HDI) for the year 2000. Inequality primarily affects the HDI through shorter life expectancies and lower incomes. I argue that the latter is consistent with the agrarian elite obstructing the transition of the local economy from agriculture to industry/services, as historically unequal municipalities contain a greater percentage of workers in the lower-wage agriculture sector, and this sector itself constitutes a larger share of local GDP.

9. Appendix

1.1 9.1. Prominent smallholder crops in Brazilian agricultural history

Manioc (cassava) has long been one of the most common smallholder crops in Brazil in terms of both quantity produced and area under cultivation. As a result of its nutritional value and ability to grow in a variety of soils and climates, it quickly became the primary food crop soon after Portuguese colonization. It was particularly widespread in settlements throughout the northeast, and was popular along the coast of the southeast, in states such as Espirito Santo, Rio de Janeiro, São Paulo and even Santa Catarina. Other crops, such as maize, were more widespread further inland: The “maize-manioc” dividing line seems to have been on the frontier between Bahia and Minas Gerais. But the importance of manioc should not be underestimated: Historically, it was the main foodstuff of plantations, where it was consumed by wealthy land-owners and slaves alike. Many plantations grew manioc in between rows of sugarcane, and slaves grew it on their own personal plots of land, which they would manage on their limited days off (Prado 1967).

Maize proved to be another critical food crop. Unlike manioc, it was historically much more popular in the south and in settlements further inland. It was especially widespread in Minas Gerais, but was grown widely throughout Rio Grande do Sul, Santa Catarina, Paraná, as well as inland São Paulo. The climatic conditions of the south are generally more favorable to maize production, which may explain its regional popularity. Interestingly, maize was also important as feed for mules and donkeys, which were the primary mode of transportation in the hilly southern interior. The popularity of the crop may have partly been due to its convenience for consumption by both people and pack animals (Prado 1967).

Rice, beans, and wheat constituted the next most important food crops. Beans were grown throughout Brazil since colonial times, and were prevalent in the diet of those in Minas Gerais, Rio de Janeiro, São Paulo and Espirito Santo. Rice was both an export and domestically consumed crop. It was grown for export in Maranhão, but also produced in Rio de Janeiro, Pará, and Northern São Paulo. Since rice favors a climate with a higher humidity, it was absent from southern states such as Santa Catarina and Rio Grande do Sul. In these states wheat was the staple crop, with some wheat production present in Minas Gerais and Bahia, where the latter province provided wheat flour to the capital (Prado 1967).

1.2 9.2. Prominent plantation crops in Brazilian history

Sugarcane was perhaps the most widely distributed plantation crop in colonial Brazil. It was grown along the coast from Pará to Santa Catarina. For nearly three hundred years, sugar proved to be the most valuable export crop, until it was surpassed by coffee in the 1830s. The organization of sugarcane production was remarkably similar throughout the country. It was centered on the Engenho, a term originally referring to the processing plant which turned the harvested cane into sugar, but later came to encompass the entire plantation. At the pinnacle of the organization was the owner. But the land was also cultivated by lavradores (sharecroppers), who rented land from the owner and were obliged to send their cane to the owner’s mill for processing. These lavradores typically paid the owner half of their cane crop for use of the mill; rent was further deducted from the lavradores’ remaining half. Nearly all day-to-day labor was provided by slaves, or sharecroppers after abolition in 1888 (Prado 1967).

Aside from sugar, the most prominent cash crop in Brazilian agriculture was that of coffee. In 1830, coffee overtook sugar to become Brazil’s leading export commodity; by 1850, it accounted for half of all Brazil’s export earnings (Bethell 1989). Most coffee was produced according to a plantation system of production. The typical coffee fazenda included an owner’s mansion, slave (or worker) quarters, and processing sheds (Bethell 1989). The first coffee plantations began in the highlands above the Paraiba river, from Rio de Janeiro, through São Paulo and to Southeast Minas Gerais. Production later spread to other parts of these states, as well as to Espirito Santo. Occasionally, coffee was produced on a relatively smaller scale, espeically in the more mountainous reions of Minas Gerais. Here, the rugged topography likely reduced the returns to scale of coffee production.

Rubber proved to be another important, if relatively short-lived, cash crop that dominated the economy of Northern Brazil in the latter nineteenth and early twentieth centuries. After the discovery of the vulcanization process in 1839, world demand for rubber surged. As the natural habitat for the rubber tree Havea Brasiliensis is in the Amazon, Brazil was virtually the sole supplier of rubber until the 1880s (Weinstein 1983). In rubber growing regions, powerful landowners (patrões) would “lease” land to rubber-tappers (usually native Indians or caboclos, sometimes white Brazilians), who would collect latex from the trees. Unlike plantation production, rubber tappers lived in isolated settlements, and bought exorbitantly priced food, medicine, and equipment from the patrão. This often led to a quasi-feudal system of indebtedness and dependency, with abuse of rubber-tappers generally increasing in more isolated areas. Although demand for rubber slumped after WWI and the crop gradually decreased in its economic importance, it had a substantial impact on the economies of the remoter Brazilian states, such as Amazonas, Acre, Pará and northern Mato Grosso (Weinstein 1983).

Cotton and tobacco were other historically important cash crops. Cotton production was particularly common in Maranhão, but later spread to Pernambuco, Bahia, and Rio de Janeiro: Meanwhile, tobacco was produced more widely throughout the country (Prado 1967). Nevertheless, cotton only accounted for 2-3% of exports between 1900 and 1930, and tobacco accounted for even less (Instituto Brasileiro de Geografia e Estatistica (IBGE) 1960). The method of production for both crops was apparently quite varied. In some regions they were produced according to a plantation system similar to that of sugar (Prado 1967), while in others they were typically smallholder crops (Bethell 1989). In the case of cotton, different methods of production may have arisen since the crop requires less capital investment than sugar or coffee, and was also grown farther inland, away from the established plantations. Similarly, the tobacco plant is relatively delicate and must be shielded from excessive heat and a multitude of pests; therefore, the care required may have reduced the advantages of large-scale production (Bethell 1989).

1.3 9.3. Derivation of the optimal conditions for the synthetic crops

I begin by deriving optimal conditions for the synthetic smallholder (“SS”) crop. Note that this entails identifying $\text{T}^{\mathrm{ss}}_{\mathrm{opmin}}$, $\text{T}^{\mathrm{ss}}_{\mathrm{opmax}}$, $\text{R}^{\mathrm{ss}}_{\mathrm{opmin}}$, $\text{R}^{\mathrm{ss}}_{\mathrm{opmax}}$ since these parameters determine the range of optimal temperatures and precipitations. To do this, I choose the optimum range of temperatures and precipitations common to all crops within the Pooideae subfamily or Phaseolus genus as the optimum range for the SS crop. In other words, I first choose the maximum $\text{T}_{\mathrm{opmin}}$ (or $\text{R}_{\mathrm{opmin}}$) among all crops for each of the two taxonomies listed above; similarly, the minimum $\text{T}_{\mathrm{opmax}}$ (or $\text{R}_{\mathrm{opmax}}$) among crops in both the Pooideae family and Phaseolus genus is chosen. All temperatures and precipitations falling within these ranges are then taken to be optimum for the SS crop. For example, let superscripts “po” denote Pooideae and “ph” denote Phaseolus. Using the actual values for individual crops, $\text{T}^{\mathrm{po}}_{\mathrm{opmin}}$ and $\text{T}^{\mathrm{po}}_{\mathrm{opmax}}$ would take the following form:

$$\begin{aligned} \text{T}^{\mathrm{po}}_{\mathrm{opmin}}&= \text{Max }{[}15, 15, 15, 16{]} = 16 \\ \text{T}^{\mathrm{po}}_{\mathrm{opmax}}&= \text{Min }{[}23, 20, 20, 20{]} = 20 \end{aligned}$$

Where the numbers in brackets refer to the $\text{T}_{\mathrm{opmin}}$ values for individual Pooideae crops in the first line and individual $\text{T}_{\mathrm{opmax}}$ values for such crops in the second. Thus, the optimal range of temperatures for the Pooideae subfamily is 16-20C, since this temperature range is optimal for all crops in the subfamily.

This same procedure would apply for deriving the optimum values for rainfall as well, which yields:

$$\begin{aligned} \text{R}^{\mathrm{po}}_{\mathrm{opmin}}=247\text{mm}\, \text{R}^{\mathrm{po}}_{\mathrm{opmax}}= 296\text{mm} \end{aligned}$$

And these values are obtained for the Phaseolus genus:

$$\begin{aligned} \text{T}^{\mathrm{ph}}_{\mathrm{opmin}} = 20\text{C}\, \text{T}^{\mathrm{ph}}_{\mathrm{opmax}} = 25\text{C}\, \text{R}^{\mathrm{ph}}_{\mathrm{opmin}} = 263\text{mm}\, \text{R}^{\mathrm{ph}}_{\mathrm{opmax}} = 329\text{mm} \end{aligned}$$

All temperatures and precipitations falling in the ranges above are considered optimal for the SS crop. That is: $\text{T}^{\mathrm{SS}}_{\mathrm{opmin}}= 16 \,\text{T}^{\mathrm{SS}}_{\mathrm{opmax}}= 25 \text{R}^{\mathrm{SS}}_{\mathrm{opmin}} = 247\text{mm }\text{R}^{\mathrm{SS}}_{\mathrm{opmax}} = 329\text{mm}$

The same procedure is then used to calculate the optimum conditions for the synthetic plantation (“SP”) crop. Using the methodology above yields the following: $\text{T}^{\mathrm{SP}}_{\mathrm{opmin}} = 24\text{C }\text{T}^{\mathrm{SP}}_{\mathrm{opmax}} = 32\text{C }\text{R}^{\mathrm{SP}}_{\mathrm{opmin}} = 1233\text{mm }\text{R}^{\mathrm{SP}}_{\mathrm{opmax}} = 1890\text{mm}$

The graphs below offer a visualization that helps put these values in context:

Fig. 5

Optimal conditions for plantation and smallholder agriculture

Much in the same way that optimal temperatures and precipitation were calculated for the synthetic plantation and smallholder crops, an optimal growing season can be derived as well. The FAO lists the minimum and maximum growing seasons needed for each crop. A similar procedure to the one described above can be used to assign a growing season to the SS and SP crops. That is, the maximum of the minimum growing seasons for all crops constitutes $\text{G}^{\mathrm{SS}}_{\mathrm{min}}$ /$\text{G}^{\mathrm{SP}}_{\mathrm{min}}$; the minimum of all maximum growing seasons will constitute $\text{G}^{\mathrm{SS}}_{\mathrm{max}}$/ $\text{G}^{\mathrm{SP}}_{\mathrm{max}}$. I then average the minimum and maximum growing seasons for the synthetic crops to obtain a SS growing season of 120 days (4 months) and a SP growing season of 300 days (10 months).

1.4 9.4. Derivation of the non-optimal conditions for the synthetic crops

It is also necessary to identify the non-optimal conditions for these synthetic crops in order to determine the complete range of conditions under which they might grow. Again, using the terminology of the FAO and the example of the synthetic smallholder crop, this entails determining $\text{T}^{\mathrm{ss}}_{\mathrm{min}}$ and $\text{T}^{\mathrm{ss}}_{\mathrm{max}}$ as well as $\text{R}^{\mathrm{ss}}_{\mathrm{min}}$ and $\text{R}^{\mathrm{ss}}_{\mathrm{max}}$ (the minimum and maximum temperatures/precipitations beyond which the SS crop would not grow). The same parameters need to be identified for the SP crop.

Recall the underlying rationale for constructing this suitability index is that climatic conditions in part determine whether efficiency in agriculture lies in smallholder or plantation production. The “ideal” smallholder crops presented above all thrive with lower rainfall and generally lower temperatures. Thus, at very cold temperatures and/or low levels of precipitation, it is likely that the only agricultural activity that can take place, if any can take place at all, will be smallholder. A similar story applies to those regions with high rainfall and high temperatures; here large-scale agriculture may be unambiguously more efficient.

Identifying a lower bound on the temperature and precipitation requirements for the synthetic smallholder crop, and an upper bound for the synthetic plantation crop, can be done in a straightforward manner. In particular, the minimum temperature and precipitation for the SS crop can be calculated as the minimum $\text{T}_{\mathrm{min}}$ / $\text{R}_{\mathrm{min}}$ for all crops in the Phaseolus and Pooideae groups. Using this methodology, the minimum rainfall requirement for the SS crop, $\text{R}^{\mathrm{SS}}_{\mathrm{min}}$, would be 66mm and the minimum temperature requirement, $\text{T}^{\mathrm{SS}}_{\mathrm{min}}$, would be 2C. More generally, for individual smallholder crops a through z, $\text{R}^{\mathrm{SS}}_{\mathrm{min}}$ and $\text{T}^{\mathrm{SS}}_{\mathrm{min}}$ can be calculated as:

$$\begin{aligned} \text{R}^{\mathrm{SS}}_{\mathrm{min}}&= \text{Min } {[}\text{R}^{\mathrm{a}}_{\mathrm{min}},\dots , \text{R}^{\mathrm{z}}_{\mathrm{min}}{]} \\ \text{T}^{\mathrm{SS}}_{\mathrm{min}}&= \text{Min } {[}\text{T}^{\mathrm{a}}_{\mathrm{min}},\dots ,\text{T}^{\mathrm{z}}_{\mathrm{min}}{]} \end{aligned}$$

Identifying the upper bound on temperature and rainfall for the synthetic plantation crop can be done in an analogous manner. The maximum temperature for the SP crop $\text{T}^{\mathrm{SP}}_{\mathrm{max}}$, and the maximum rainfall for the plantation crop $\text{R}^{\mathrm{SP}}_{\mathrm{max}}$, can be calculated as the maximum $\text{T}_{\mathrm{max}}$ / $\text{R}_{\mathrm{max}}$ of all individual crops in the Coffea and Saccharum genera. This would yield $\text{T}^{\mathrm{SP}}_{\mathrm{max}} = 41\text{C}$, and $\text{R}^{\mathrm{SP}}_{\mathrm{max}}= 4110\text{mm}$. The general method for calculating these two parameters would be similar to the above; that is, for plantation crops a through z:

$$\begin{aligned} \text{R}^{\mathrm{SP}}_{\mathrm{max}}&= \text{Max } {[}\text{R}^{\mathrm{a}}_{\mathrm{max}},\dots , \text{R}^{\mathrm{z}}_{\mathrm{max}}{]} \\ \text{T}^{\mathrm{SP}}_{\mathrm{max}}&= \text{Min } {[}\text{T}^{\mathrm{a}}_{\mathrm{max}},\dots ,\text{T}^{\mathrm{z}}_{\mathrm{max}}{]} \end{aligned}$$

Calculating the maximum temperature and rainfall values for the SS crop, and minimum values for the SP crop is more difficult. In essence, this involves a determination as to when the climate shifts from offering efficiency in smallholder agriculture to efficiency in plantation agriculture. That is, as one moves away from the “smallholder” end of the spectrum, conditions become more and more suitable for plantation agriculture. When some maximum values for temperature and precipitation for the SS crop are surpassed, then plantation production will be the most suitable form of agricultural activity. An analogous argument can be made when one moves away from the plantation end of the spectrum.

I therefore calculate $\text{R}^{\mathrm{SS}}_{\mathrm{max}}$, $\text{T}^{\mathrm{SS}}_{\mathrm{max}}$, $\text{R}^{\mathrm{SP}}_{\mathrm{min}}$, and $\text{T}^{\mathrm{SP}}_{\mathrm{min}}$ in the following manner. To obtain values for $\text{R}^{\mathrm{SS}}_{\mathrm{max}}$ and $\text{T}^{\mathrm{SS}}_{\mathrm{max}}$, I define the maximum temperature for the Pooideae group ($\text{T}^{\mathrm{po}}_{\mathrm{max}}$) as the minimum $\text{T}_{\mathrm{max}}$ for all crops within this subfamily; the same methodology would apply for the Phaseolus group ($\text{T}^{\mathrm{ph}}_{\mathrm{max}}$). $\text{T}^{\mathrm{SS}}_{\mathrm{max}}$ is then set equal to the minimum of ${[}\text{T}^{\mathrm{po}}_{\mathrm{max}}$, $\text{T}^{\mathrm{ph}}_{\mathrm{max}}{]}$. Similarly, I obtain an $\text{R}^{\mathrm{po}}_{\mathrm{max}}$ and an $\text{R}^{\mathrm{ph}}_{\mathrm{max}}$ by choosing the minimum $\text{R}_{\mathrm{max}}$ in each group. I then take $\text{R}^{\mathrm{SS}}_{\mathrm{max}}$ to be the minimum of ${[}\text{R}^{\mathrm{ph}}_{\mathrm{max}}$, $\text{R}^{\mathrm{po}}_{\mathrm{max}}{]}$. This yields $\text{R}^{\mathrm{SS}}_{\mathrm{max}} = 493\text{mm}$, and $\text{T}^{\mathrm{SS}}_{\mathrm{max}} = 27\text{C}$.

A similar method can be used to calculate $\text{R}^{\mathrm{SP}}_{\mathrm{min}}$ and $\text{T}^{\mathrm{SP}}_{\mathrm{min}}$. I first define a minimum temperature for both the Coffea and Saccharum genera ($\text{T}^{\mathrm{c}}_{\mathrm{min}}$ and $\text{T}^{\mathrm{s}}_{\mathrm{min}}$, respectively), by choosing the maximum $\text{T}_{\mathrm{min}}$ within each genus. I then set $\text{T}^{\mathrm{SP}}_{\mathrm{min}}$ equal to the maximum of ${[}\text{T}^{\mathrm{c}}_{\mathrm{min}}$, $\text{T}^{\mathrm{s}}_{\mathrm{min}}{]}$. I identify an $\text{R}^{\mathrm{c}}_{\mathrm{min}}$ and $\text{R}^{\mathrm{s}}_{\mathrm{min}}$ by choosing the maximum $\text{R}_{\mathrm{min}}$ within each genus of crops; I then set $\text{R}^{\mathrm{SP}}_{\mathrm{min}}$ equal to the maximum of ${[}\text{R}^{\mathrm{c}}_{\mathrm{min }}$and $\text{R}^{\mathrm{s}}_{\mathrm{min}}{]}$. This yields $\text{R}^{\mathrm{SP}}_{\mathrm{min}}= 616\text{mm}$ and $\text{T}^{\mathrm{SP}}_{\mathrm{min}} = 12\text{C}$.

Again, a graph offers a visualization that may help illuminate the conditions derived above (Figs. 5, 6).

Fig. 6

Optimal and non-optimal conditions for plantation and smallholder agriculture

1.5 9.5. Mapping environmental conditions into a spectrum

Recall that for each AMC, twelve temperature suitability indices are calculated, one for each month i. For each month i of AMC p, the temperature suitability index for the synthetic smallholder crop is zero if average temperature is below (above) $\text{T}_{\mathrm{min}}$ ($\text{T}_{\mathrm{max}}$); 100 if average temperature is within the range $\text{T}^{\mathrm{SS}}_{\mathrm{opmin}}$ - $\text{T}^{\mathrm{SS}}_{\mathrm{opmax}}$; and determined by a linear interpolation if an observed temperature falls between ($\text{T}^{\mathrm{SS}}_{\mathrm{min}}$ - $\text{T}^{\mathrm{SS}}_{\mathrm{opmin}}$) or ($\text{T}^{\mathrm{SS}}_{\mathrm{opmax}}$ - $\text{T}^{\mathrm{SS}}_{\mathrm{max}}$). That is:

$\text{T}^{\mathrm{SS}}_{\mathrm{suit}},_{\mathrm{i}}$ =	0	$\text{T}_{\mathrm{average p,i}} < \text{T}^{\mathrm{SS}}_{\mathrm{min}}$
	$\text{a}_{\mathrm{T1}} + \text{m}_{\mathrm{T1}}$*$\text{T}_{\mathrm{average\, p,i}}$	$\text{T}^{\mathrm{SS}}_{\mathrm{min}} \le \text{T}_{\mathrm{average \,p,i}} < \text{T}^{\mathrm{SS}}_{\mathrm{opmin}}$
	100	$\text{T}^{\mathrm{SS}}_{\mathrm{opmin}} \le \text{T}_{\mathrm{average \,p,i}} < \text{T}^{\mathrm{SS}}_{\mathrm{opmax}}$
	$\text{a}_{\mathrm{T2}}$ + $\text{m}_{\mathrm{T2}}$*$\text{T}_{\mathrm{average \,p,i}}$	$\text{T}^{\mathrm{SS}}_{\mathrm{opmax}} \le \text{T}_{\mathrm{average \,p,i}}< \text{T}^{\mathrm{SS}}_{\mathrm{max}}$
	0	$\text{T}^{\mathrm{SS}}_{\mathrm{max}} \le \text{T}_{\mathrm{average\, p,i}}$

Where $\text{T}_{\mathrm{average\, p}}$, is the average temperature in in municipality p during month i. $\text{a}_{\mathrm{T1}}$ and $\text{m}_{\mathrm{T1}}$ are the intercept and slope of the regression line between ${[}\text{T}^{\mathrm{SS}}_{\mathrm{min}}$, 0] and ${[}\text{T}^{\mathrm{SS}}_{\mathrm{opmin}}$, 100]. Similarly, $\text{a}_{\mathrm{T2}}$ and $\text{m}_{\mathrm{T2}}$ are the intercept and slope of the regression line between ${[}\text{T}^{\mathrm{SS}}_{\mathrm{opmax}}$, 100] and ${[}\text{T}^{\mathrm{SS}}_{\mathrm{max}}$, 0]. These piecewise linear portions are used to interpolate the suitability of observed temperatures that fall between $\text{T}^{\mathrm{SS}}_{\mathrm{min }}$and $\text{T}^{\mathrm{SS}}_{\mathrm{opmin}}$, or between $\text{T}^{\mathrm{SS}}_{\mathrm{opmax}}$ and $\text{T}^{\mathrm{SS}}_{\mathrm{max}}$ (a visualization of this is shown in Fig. 1, in the text).

As described above, the precipitation suitability index is calculated using the total rainfall during a crop’s growing season. There are twelve candidate growing seasons, since each month is treated as if it could be the start of the season. Similar to the temperature suitability indices, the precipitation suitability indices are calculated according to the table shown below.

$\text{R}^{\mathrm{SS}}_{\mathrm{suit}} =$	0	$\text{R}_{\mathrm{total, p}} < \text{R}^{\mathrm{SS}}_{\mathrm{min}}$
	$\text{a}_{\mathrm{r1}} + \text{m}_{\mathrm{r1}}$*$\text{R}_{\mathrm{total, p}}$	$\text{R}^{\mathrm{SS}}_{\mathrm{min}} \le \text{R}_{\mathrm{total, p}} < \text{R}_{{{\mathrm{SS}}}_{\mathrm{opmin}}}$
	100	$\text{R}_{{{\mathrm{SS}}}_{\mathrm{opmin}}} \le \text{R}_{\mathrm{total, p}} < \text{R}^{\mathrm{SS}}_{\mathrm{opmax}}$
	$\text{a}_{\mathrm{r2}} + \text{m}_{\mathrm{r2}}$*$\text{R}_{\mathrm{total, p}}$	$\text{R}^{\mathrm{SS}}_{\mathrm{opmax}} \le \text{R}_{\mathrm{total, p}} \le \text{R}^{\mathrm{SS}}_{\mathrm{max}}$
	0	$\text{R}^{\mathrm{SS}}_{\mathrm{max}} {\le }\text{R}_{\mathrm{total,p}}$

Where $\text{R}_{\mathrm{total, p}}$ is the total amount of observed precipitation in a growing season. $\text{a}_{\mathrm{r1}}$ and $\text{m}_{\mathrm{r1}}$ are the intercept and slope of the regression line between ${[}\text{R}^{\mathrm{SS}}_{\mathrm{min}}$, 0] and ${[}\text{R}^{\mathrm{SS}}_{\mathrm{opmin}}$, 100] and $\text{a}_{\mathrm{r2}}$ and $\text{m}_{\mathrm{r2}}$ are the intercept and slope of a regression curve between ${[}\text{R}^{\mathrm{SS}}_{\mathrm{opmax}}$, 100] and ${[}\text{R}^{\mathrm{SS}}_{\mathrm{max}}$, 0].

As stated previously, there are twelve temperature suitability indices (one for each month) and twelve precipitation suitability indices (one for each potential growing season). To obtain temperature indices on the basis of a growing season, I take each month of the year as the potential start of the season, and choose the lowest monthly suitability index within that season as the season’s temperature suitability index. For each potential growing season g, a suitability index for the synthetic smallholder crop is calculated as $\text{Suit}_{\mathrm{g}}^{\mathrm{SS}} = \text{T}_{\mathrm{g}}^{\mathrm{SS}}\text{suit}^{*}\text{R}_{\mathrm{g}}^{\mathrm{SS}}\text{suit}$. The final suitability index for the SS crop is taken to be the maximum of these twelve suitability indices. The suitability index for the SP crop would be calculated in the same manner, using the parameters for the SP crop.

Finally, note that the calculations above all utilize data on average monthly temperatures and precipitations. Unfortunately, such data omits useful information regarding climatic variation. This is a particularly important point in regard to temperature, since regions with temperatures that regularly exceed (or fall below) a crop’s $\text{T}_{\mathrm{max}}$ (or $\text{T}_{\mathrm{min}}$) are unlikely to be amenable for growing that plant (even if, on average, temperatures are close to the optimum). Such fluctuations will cause the plant to experience a heat or cold shock, in which growth stops and yields are considerably diminished. If these extremes are reached frequently enough, it would likely alter the relative suitability between plantation or smallholder agriculture.

To account for this, I utilize data on average monthly minimum and maximum temperatures; that is, the mean daily high (or low) temperature for a given month. I integrate this information into the index in the following manner. Recall that $\text{T}_{\mathrm{max}}$ is defined as the minimum of ${[}\text{T}^{\mathrm{po}}$ $_{\mathrm{max}}$, $\text{T}^{\mathrm{ph}}$ $_{\mathrm{max}}{]}$. In this case, I set a given month’s temperature suitability index for the SS crop equal to zero if the mean daily maximum temperature exceeds the maximum of ${[}\text{T}^{\mathrm{po}}$ $_{\mathrm{max}}$, $\text{T}^{\mathrm{ph}}_{\mathrm{max}}{]}$, which is 30C. Similarly, $\text{T}^{\mathrm{SP}}_{\mathrm{min}}$ is defined as the minimum of ${[}\text{T}^{\mathrm{c}}_{\mathrm{min}}$, $\text{T}^{\mathrm{s}}$ $_{\mathrm{min}}{]}$, so I set a month’s temperature suitability index for the SP crop equal to zero if the mean daily minimum temperature is below the minimum of ${[}\text{T}^{\mathrm{c}}_{\mathrm{min}}$, $\text{T}^{\mathrm{s}}_{\mathrm{min}}{]}$, which would be 9C. In essence, I assume that these temperatures are thresholds which, if exceeded often enough, will cause the SS or SP crops to become unviable. To obtain the PSI I take the ratio of the indices calculated above, as given in equation (1) in the text.

Finally, note that the methodology used to calculate this index generally makes it stable to the exclusion of one particular crop. This is because crops within each of the above taxonomic groups are very similar in their temperature and precipitation requirements. As noted in the text, barley (which of all of the above crops is probably the least common to Brazil), can be excluded from the index and the quantitative impact of the PSI is unchanged. That is, excluding this crop only changes $\text{T}^{\mathrm{ss}}_{\mathrm{min}}$ from 2C to 3C, and $\text{R}^{\mathrm{ss}}_{\mathrm{min}}$ from 66mm to 82mm; such changes are too minor to have an effect on the predicative power of the PSI. The general stability of the index with respect to the omission of a single crop therefore constitutes an advantage of this methodology.

1.6 9.6. Comparison of suit^SS and suit^SP to FAO crop suitability indices

To help verify that the methodology used above yields a $\text{Suit}^{\mathrm{SS}}$ and a $\text{Suit}^{\mathrm{SP}}$that accurately reflect the suitability for smallholder and plantation crops, I correlate them with the FAOs indices for sugar, coffee, wheat and beans (I also correlate each of these FAOs indices with each other). Unfortunately, the FAO’s suitability indices for coffee and beans are not available at a fine geographic resolution as the wheat and sugar indices are: The FAO only provides averages of the former indices at a state level for Brazil. Table 16 below therefore displays the correlations between average state-level suitability for the four crops above, as well as for $\text{Suit}^{\mathrm{SS}}$ and $\text{Suit}^{\mathrm{SP}}$(which are also averaged by state). As one might expect, both $\text{Suit}^{\mathrm{SS}}$ and $\text{Suit}^{\mathrm{SP}}$ are strongly correlated with the crops of which they are comprised, and negatively correlated with each other. Note there is actually a positive correlation between $\text{Suit}^{\mathrm{SS}}$ and sugar, as well as between wheat and sugar. This is probably due to the short growing season for Pooideae crops, which enables them to be sucessfully grown in the few dry months of an otherwise tropical climate.

Table 16 Correlations between FAO indices and $\text{Suit}^\mathrm{{SS}}$ and $\text{Suit}^{{\mathrm{SP}}}$