Kinship-based Resource Sharing in the Agrarian Economy of Frontier Slavonia, 1698:

Evidence from an Early Census

DRAFT 22 OCT 95

E. A. Hammel

H.-P. Kohler

Introduction This paper illuminates some features of social organization and productive activity of an eastern European population under the New Feudalism of the 17th century, using tools from historiography, historical ethnology, demography, and economics. We concentrate here on grain cultivation and the the marshalling of human and animal labor inputs to grain cultivation, reserving a more technical and broader analysis for another paper (Kohler and Hammel 1996). We examine particularly the possible role of kinship networks in exchange of human and animal labor. Historical Background Slavonia lies between the Sava, Drava, and Ilova rivers. thus between Zagreb and a line about 140 kms. west of Belgrade (the boundary of Srem), and within the borders of modern Croatia (Fig. 1).

Before the 17th century it included Moslavina, which lies west of the Ilova, and extended along the upper Sava as far as Zagreb. The region had been the western part of Roman Pannonia, with its capital at Siscia (modern Sisak). Overrun by Goths and others in the fifth century AD, it was settled by Slavs around the 6th and 7th centuries and controlled in various degrees by Croatian and Bosnian nobles until the 12th century. In 1122 AD the Croats came under the control of the Hungarian crown. In the late 13th century the Ottoman Turks began their drive into Europe, taking Belgrade in 1521 and annihilating the Hungarian forces at Mohacs on the Danube in 1526. At this point the Croats came under Habsburg control, and defensive zones were established along the Alpine and Dinaric foothills. Nevertheless by 1683 the Turks controlled Slavonia to the Ilova and were at the gates of Vienna. Routed there in that year, they were driven back to the Sava by 1691, and the prosperous population of about a quarter million persons in that region was reduced to about 80,000. Refugees from other Habsburg and Hungarian regions, and both Orthodox and Catholics from Bosnia and Serbia migrated in large numbers to Slavonia and other parts of Pannonia. In 1698 the Austrian Crown commissioned a census of Slavonia to establish the basis for taxation and conscription, in defense against the continuing Ottoman threat. Ultimately the population was divided into two parts, one of civil serfs in a resurrection of mediaeval serfdom, the other of military serfs free of the usual feudal dues but obliged to provide perpetual military service, in a resurrection of a system that had manned Roman forts as far back as the third century. These military serfs were settled in the Military Border, which before 1683 lay west of the Ilova and extended toward the Drava but which after 1683 was extended along the Sava to the Danube and ultimately into the Carpathians. In the late 17th century Slavonia was largely wilderness, its once settled portions devastated by war, with still enormous swamps, and stands of giant hardwoods like oak and beech surviving from the primeval European forest. The Data The census of 1698 provides most of the data for our analysis (Mazuran 1988). Written in the bureaucratic Latin of the time, it gives detailed information on about 4,500 households (and less detailed information on more). Where the information is detailed it gives the composition of the household by name of household head, kinship relationship to the head and a listing of the amount of land in various crops and the livestock owned, by kind of animal. (See Hammel and Wachter 1996a, Hammel and Wachter 1996b for analysis of the household structure and other population information in the census). After a village level summary, the census provides a prose account of current conditions and recent history, in a set of standardly numbered paragraphs. This prose summary provides important insights into the conditions faced by the inhabitants.

The census information is supplemented by data on the latitude, longitude, and altitude of the villages, most of these being identifiable on modern maps.[1] Because the religion of the inhabitants of the villages is often noted in the prose summary, it is also possible to assemble a list of first and last names that occur only in homogeneously Orthodox or homogeneously Catholic villages, in both of these kinds of villages, and in villages of mixed or unspecified religious composition.[2] From this evidence we are often able to impute religion at the household level, according to the name of the head. Similarly, the prose summary often gives an indication of whether the inhabitants of villages were military or civil serfs, or were inclined to accept one or the other status; we used this information as a village-level variable. Some villages, and some inhabitants within some villages, are identified as having come from Bosnia, but this information is not consistently provided, and we use it only tentatively.

We also use last names in another way, to impute kinship relatedness. This leap of faith is justified by family reconstitution records from c. 1720-1900, in which last names are fairly regularly inherited in the paternal line.[3] Our assumptions could be upset if the ancestral Slavic system of assigning patronymics as last names, based on the baptismal name of the father, were in full force, but it appears not to have been.[4]

Initial statistical examination of the census data showed that households held on average about 3 yokes of grainland[5], variously distributed across different kinds of grain, a row and a half of grape vines, about 2 yokes in hayfield, around 1 ox, 1 cow, 1 calf, 3 sheep and goats, 2 pigs, and a beehive, plus 1 horse for every two households (Table 1).[6] The distributions are all sharply skewed; most medians are zero. There is little or no evidence for specialization or substitution. For example, the correlation coefficients between all forms of livestock are positive (Table 2). This circumstance argues for a general differentiation of the population by wealth, with the richer having more of all kinds of stock, and the poorer less. Similarly, there is no strong evidence of substitution in crops (Table 3).[7] A more technical analysis (Kohler and Hammel 1996) also shows no evidence of specialization or the possibility of interhousehold trade. The only apparently strong exception is the negative correlation between frumentum on the one hand and milli and tritici on the other. Milli and tritici are millet and wheat, while frumentum means grain in general (like the German Korn); it may have been a synonym for either millet or wheat, although it appears not to have been for oats (avenae) or barley (hordei). Thus, this substitution appears to have been performed verbally by the census takers, not actually by the peasants.

There is some weak support for the idea that maize (kukuruz) was a substitute for other kinds of grain, from statements in the prose descriptions (see below). Maize was introduced to the Balkans by the Ottomans probably in the 16th or 17th C. The Slavic term, kukuruz, is derived from Turkish kokoroz, possibly from -oroz (rice) and koko- (stench), thus the "rice of the lower classes." Note the alternative Serbian term, mumuruz, possibly from -oroz and mumu- (with meaning parallel to koko- ); see also the alternative term from Rumanian, mamaliga (Skok 1972: 228-229). The census gives no evidence of the cultivation of the potato, but it is likely it had recently been introduced. The Slavic term, krumpir, is from German Gruntbir , Grundbirne (ground pear, cf. pomme de terre Skok 1972: 215). The potato was cultivated in Spain by the third quarter of the 16th C (Salaman 1949: 143) and possibly introduced to Austria by the Habsburgs. Most of the scanty evidence suggests it reached the Balkans after maize (J. Capo, personal communication 1995). Even the Austrian censuses of 1830-47 do not mention the potato, but neither do they mention any other tubers or vegetables such as turnips, cabbage, etc., which were surely being grown. There is thus every reason to believe that some households were growing potatoes and other garden crops in addition to grain, and to conjecture that some may have been engaged in essentially swidden horticulture without growing grain at all. Thus it appears that the census concentrated on economic assets that were felt taxable or capable of commercial exploitation; this area did engage later in extensive commercial grain production on the large estates. It is also of interest to note a weak but significant negative correlation (r2 = .10, p < .0001) between the percentile rank of households in a village list and the total amount of land devoted to grain cultivation; that is, there is some weak ordering of households by wealth, the poorer being listed last.

Travellers through the region in the 19th century generally deplored the state of agricultural practice, especially in the Military Border where there was no commercial development but only subsistence agriculture. The accounts suggest that agriculture was extensive rather than intensive. Certainly in 1698 there appear to have been too few farm animals to provide enough manure for regular fertilization. Fragmentary evidence from the chronicle of the monastery of Cernik from an even later date (Jancula 1980) suggests that cattle were usually pastured in the commons or waste; without stall-feeding it is difficult to recover enough manure for fertilization. Similarly, sheep must be carefully penned on the grainfields to utilize their manure; there is no evidence of this practice in Slavonia at all at any time. The large swine herds later characteristic of the region seem not have appeared by 1698, and even in the 19th century swine were pastured mostly in forest, not on stubble. To be sure, the relationships that emerge from our analysis cannot take into account that realm of economic activity unrelated to major field crops, but we believe that they provide a reasonable description of grain agriculture.

Simple OLS regressions of the various kinds of grain or of all grain in general on potential factors of production, show that plausible independent variables have a positive effect. Households with abundant male labor tend to be those with more animals and more land under cultivation. This result, of course, could be no more than the general wealth effect already noted (Table 4). But there are intriguing clues in the prose summaries that led us to look further. Here are some examples:

Incolae hi haidonicales pro exercenda sua rurali oeconomia et terreno incolendo per defectum pecorum insufficentes sunt, ex eo vicinos fundos non usuant. (These military serf inhabitants have insufficient cattle for the exercise of their rural economy and inhabited terrain and on account of that do not use neighboring lands.) Sentences of this meaning, with numerous variations, are extremely common and almost universally found in some districts. Sometimes the statement only says that the inhabitants are incapable of cultivating their land, without mentioning the lack of cattle, but such statements are much rarer. It is extremely rare to find the statement that the inhabitants of a village have sufficient capacity to use the land of a neighboring village. The collective noun pecus (gen. pl. pecorum) means "stock" and could refer to any of the animals listed in the census. However, sheep, goats, pigs, and bees are not employed in working the land. Similarly, although horses and cows can be used to pull a plow, their use is rare except on light soils (or where plow horses like Belgians have been bred for the purpose). The best horses in Pannonia in historical times have usually been Hungarian, and they are riding horses, not plow horses.[8] Thus, it seems most likely that the lack of cattle refers particularly to oxen, who were the main source of power for plowing in mediaeval Europe and in 19th century Croatia. Oxen would have been important in Slavonia also for pulling stumps in the extensive forest clearing that was necessary prior to cultivation of field crops (but not garden crops). We concentrate on the oxen as a limiting factor of production.

A second clue is an occasional sentence that refers to annual floods of the Sava, e.g. Locus hic inter palludes et sylvas alninas collocatus.... (This place is located between swamps and alder forests). (Note that alders prefer damp, even swampy ground.) ...Quamvis fundus hic tam palludinosus sit per inundationes Savi....(This land is very swampy because of the floods of the Sava...). In the chronicle of the monastery of Cernik in the 18th century there is evidence that these swamps were malarial (Jancula 1980), and later travellers in the region also noted such conditions in Pannonia (e.g. "Banat fever" after the neighboring region of Banat in Pannonia). We use information on the altitude of villages to approximate these circumstances, which would have made tillage more difficult, not only because of disease but because of drainage and other soil problems.

A third clue is the rare sentence that suggests that inhabitants in forested regions and lacking oxen might plant maize in the clearings as a substitute for other grains; e.g.... ob defectum iumentorum sunt incapaces, suntque meri fossores kukurczarii...(...because of a lack of plow oxen they are incapable [of field agriculture] and only [plant] maize in clearings...). This suggests the modest substitution noted in the correlations earlier. Some General Points of Economic Analysis We have already suggested the general absence of specialization and substitution between kinds of crops or kinds of animals listed in the census. This is an interesting finding, since the inhabitants of the area came from diverse ecological and cultural backgrounds. For example, about 33 percent of the households have names that are found only in homogeneously Orthodox villages. The Orthodox population of the region is generally thought to have been more inclined to pastoralism and are usually referred to as Vlachs in the general historical literature on the region. There were also Catholic Vlachs, known as Bunjevci, but they are indistinguishable in these data from other Catholics. While a complete analysis of the economics of households is beyond the scope of this paper, we can briefly observe that there appear to be no substantial differences between Orthodox and Catholics other than that the Orthodox seem to be slightly richer. Thus, the Orthodox have more animals per household than do the Catholics, but they also have more grain land. The ratio of grainland to livestock and of oxen to male labor is also higher for the Orthodox, suggesting a more settled and secure existence rather than the poverty of upland pastoralism with which they are associated in the mountains of Bosnia, Serbia, and the Dalmatian hinterland. It is of course possible that most of the Catholics were Bunjevci, but that seems unlikely in regions so close to the Danube, since some Catholics had been resident under the Ottomans and others had migrated in from more northerly regions of Croatia or from Hungary. Most Croatian historians assume that the remnant population of Slavonia in 1691-1698 was Catholic. We might imagine that the remnant population might have more assets than any immigrants, yet the data fro 1698 suggest that the Orthodox had more assets than the Catholics. The census does show that individuals labelled as immigrants from Bosnia had less than average assets. Were such immigrants more often Catholic than Orthodox? Were Catholics the core of the remnant population, or did Orthodox form a large part? These are important historical puzzles (fraught with current political implication), and we do not attempt to treat them herein more than a cursory way.

The general wealth effect can be seen in OLS regressions of household grain land on the major factors of household production, animal power and manpower, for which we take the number of oxen and the number of adult males as indicators, as noted in Table 4. To avoid the effect that mere household size would have on these relationships we also regress per capita grainland on the number of oxen and males in Table 5 (per capita here meaning male household members listed). In Table 5 we see that additional oxen are a positive factor, while additional males are a negative factor. The marginal productivity of oxen appears to increase with additional oxen, but but the marginal productivity of human labor appears to decrease with additional labor. The "ethnic" variables are of interest. The omitted category is the small number of households living in mixed Orthodox-Protestant villages. Families with homogeneously Orthodox names have about the same per capita level of grainland as those living in mixed Orthodox-Protestant villages (where they dominate). Those families with names occurring in mixed Orthodox-Catholic villages have somewhat less, and families with names that occur in homogeneously Catholic villages have the least. This result confirms that the Catholics were on the whole poorer than the Orthodox.

These simple initial results also lead us to the indication that there was some optimal ratio of men to oxen for plow teams, such that adding additional males to some fixed number of oxen diminished per capita productivity. We might imagine that this effect was simply an artifact of having more males in the denominator of the per capita grain measure. However, if an additional male had marginal productivity equal to the previous average, the effect of adding another male would be zero. If an additional male had marginal productivity above the pre-existing average, the effect of adding another male would be positive. This might happen if there were returns to scale in important tasks. However, the result of adding an additional male is negative, as shown; additional males depress per capita productivity, given some number of oxen. Unless an additional man brings additional ox power with him, he lowers the per capita productivity of the enterprise. The optimal ratio of men to oxen appears to be quite low, around 1:3 (see below). Closer Economic Analysis These OLS results are hard to interpret and we seek to illuminate the marginal productivity both of men and of oxen for per capita production. We use a modified Cobb-Douglas production function estimated by maximum likelihood methods, in which the logarithm of grain under cultivation in each household (Y) was held to be a function of altitude and other "environmental" characteristics such as ethnicity (A) and two main factors of production, oxen (O) and the male labor force (M). As noted earlier, we do not much elaborate the technical details of the analysis here but concentrate on the results. The general form of the function is

Y = A * Ob0 * Mc0

However, patterns of interhousehold cooperation are common in agrarian societies. Such cooperation is often based on kinship. While in most rural societies there is virtually no rental market in livestock because of the potential for abuse of animals rented out, trust and mutual obligations between kin may overcome this barrier. This led us to speculate that the oft-mentioned insufficiency of oxen (defectum pecorum) might have been ameliorated by the lending of oxen between kin-related households. Thus we might imagine that a brother would lend an ox to a brother who had none, or to a brother who had some, in supplementation. Brothers who had some oxen but not enough might help eachother seriatim. We might imagine that human labor might reciprocate loans of ox power, either if the recipient had no oxen at all, or in supplementation if he did. We might imagine that human labor would be also reciprocally exchanged.

Oxen are useful in plowing, harrowing, stump pulling and other intense and relatively short-term activities in preparation of the land for sowing. Apart from providing traction power for haulage, they are not important in harvesting. Their use is thus episodic, but they must be maintained year-round. Oxen cannot plow alone, of course, and at least one man is necessary to guide the plow. The constraint on plowing is the weight and maneuverability of the plow, which must be handled by the man or men. Plows useful for heavy soils can be quite cumbersome. Plow teams of 2, 4, 8, and perhaps more oxen can be managed by one or two men. In 19th century Slavonia, at which time some detailed ethnographic information is available, but by which time grain agriculture was much more developed, plow teams consisted of from 2 to 8 oxen (J. Capo, personal communication 1995). An additional man, or more commonly a boy, can lead the oxen. There is a potential reciprocal relationship with grain land, because oxen are sometimes pastured on fallow land and stubble in addition to grazing on pasture and waste land. Thus there may be some problems of reciprocal causation in analysis, but we do not attempt to explore them here.

Male labor power is used not only for plowing grainland but also sowing grain, scything grain, transporting the harvested stalks, and threshing and storing grain. Weeding, raking, bundling, and sometimes sowing are usually done by women and children, but we did not try to take account of female labor, since it would be closely correlated with male labor in a household economy in which virtually all adults were married. Imputing Kinship There were 1679 Catholic households with 1064 unique names, and 1467 Orthodox households with 836 unique names, thus 0.63 names per household among Catholics and .57 names per household among Orthodox. By "unique name" we mean a unique tokenized name that ignores minor spelling differences. In imputing kinship we eliminated all names that were indicative simply of Bosnian origin, e.g. tokenized as Bosnjak, since sharing such a name would be no grounds for assuming kinship relation. This removes one token from the Catholic and Orthodox namelists, 26 households from the Catholic and 126 households from the Orthodox household lists. The ratios of households to names are then 1063:1657 and 835:1341, thus .64 and .62 for Catholic and Orthodox, respectively. These ratios are virtually identical, but simulation experiments show that the distribution of names is such that a randomly drawn Orthodox household is more likely to find another household with a matching name than is a Catholic household.

We allowed putative kinship to decay exponentially with distance, so that for some household with last name X, another household with name X in the same village was assumed to be in the same kinship network, but inclusion in the network fell off rapidly as households with the same name were found further and further away. Experiments showed that the rate of exponential decay made little difference to the outcome; it is the shape of the function that is important. Results Analysis using a production function was restricted in two steps: first to the 4114 of 4453 households on which we were able to obtain adequate information, especially on location and thus on altitude. OLS regressions using just these 4114 households gave results essentially the same as for the 4453 households. In the second step, analysis was restricted to households. Further analysis using the production function was restricted to those households that had at least one ox and that were not named simply "Bosnian."[9] These numbered 2427.

Table 6 gives the results from the Cobb-Douglas production function, in which Y is per capita grainland[10], A includes a constant ([[alpha]]0), coefficients for altitude ([[alpha]]1), altitude squared ([[alpha]]2), and a dummy for Orthodox ([[alpha]]3), (with all non-Orthodox and those of unknown religion grouped together). d0 and d1 are the coefficients for having more or less oxen than the optimal ratio to human labor. [[theta]]0, [[theta]]1 and [[theta]]2 are the coefficients for the effects of having oxen in the household, in the network and outside the network, respectively. [[phi]]0, [[phi]]1, and [[phi]]2 are the analogous coefficients for male labor.

The principal results are as follows:

* The amount of grainland increases with altitude but decreases with altitude squared, showing that more extensive cultivation and productivity were possible above the swampy bottomlands but below the higher, mountainous regions.

* The Orthodox households are have more grainland than other groups; this advantage amounts to about 7 percent, all else equal.

* The mean optimal ratio of labor to oxen is 1.18 men per ox or conversely 0.85 oxen per man. If the average household could optimize its possession of oxen it would have oxen where Li is the number of males. This implies that 1626 of the 2427 households (about two thirds) have a deficit of oxen with respect to their male labor force, while only one third have the optimal ratio or more. It can be shown that the optimal ratio of oxen to males increases with altitude, meaning that households with the best soil for grain farming have relatively more oxen per male worker. They benefit twice; they have better soil to cultivate, and they have more oxen to do it with.

* The coefficients [[theta]]0 and [[phi]]0 add to one. This means that the optimal demand for oxen and the amount of cultivated land T* vary proportionally with the number of males in the household. Thus, there are constant returns to scale, as we would expect under conditions of extensive, undeveloped agriculture in which the technical means of intensification (other than increases in the labor supply) were unattainable or in which the additional land coming under cultivation was as yet of no poorer quality than the core holding.

* Households with a relative excess of oxen (more than the optimum) seem to engage in an exchange of male labor, but having males in the network seems to confer no particular advantage. Thus it seems that the traditional patterns of cooperative labor exchange (Croatian sprega) crossed kinship lines. The average household with an excess of oxen gains about 1.49 workers in help from other households.

* On the other hand, households with a deficit of oxen compared to their labor force seem to benefit from having oxen in their kinship network but get little or no benefit from having oxen just in their neighborhood. These results for the exchange of labor and of oxen confirm the expectations grounded in the idea of trust prevailing between kin more than between neighbors.

* Oxen are much more important determinants of the extent of cultivated land than are human workers; based on the coefficients [[theta]]0 and [[phi]]0, oxen are about three times as important.

* Similarly it can be estimated that the relative prices of oxen to labor are in excess of 2.5:1

Some of these results can be shown graphically. Fig. 2 shows the output and marginal productivity of oxen, against the ratio of oxen to workers. As the number of oxen per worker increases, output (per capita grainland) increases almost linearly. The marginal productivity of oxen, per one worker, declines, but only modestly.

Fig. 3 shows similar data for the output and marginal productivity of labor, per ox. Output per laborer increases more slowly and with more obvious flattening than output per ox (cf. Fig. 2). The marginal productivity of labor declines much more rapidly than that of oxen (cf. Fig. 2).

All of these results confirm the textual evidence of the census but provide an analytic view that is not apparent merely in statements about "a lack of oxen." Conclusions In this paper we have tried to interpret the economically relevant portions of an early census in a frontier area of the Habsburg Empire, with particular attention to inputs from oxen and male labor, and to the utility of kinship connections between households. The text contains important general clues about economic conditions. Simple OLS analysis reveals interesting features, especially an advantage to living at altitudes above swamps but below high elevations, a modest wealth advantage for those of Orthodox religion, clear positive returns to the ownership of oxen, and much lower returns to human labor. More sensitive analysis using a production function confirms these results. The marginal productivity of oxen per worker declines quite slowly, while productivity increases quite rapidly and with little flattening as the number of oxen increases. Conversely, the marginal productivity of labor (per ox) declines very rapidly, and productivity achieved by adding more workers increases only modestly. The quantitative evidence in the census supports the idea that grain agriculture was not highly developed technically but lacked intensification (e.g., through manuring) and that marginal land seems to have been of about the same quality as core holdings. Land, then, was not in short supply as it came to be within a few generations. The population probably also engaged in garden horticulture, perhaps cultivating potatoes and other root crops as well as vegetables, so that grain production was not the sole source of subsistence. Nevertheless, if peasants optimized their resources, allocating them in some Chayanovian pattern, the picture of their grain agriculture is a reasonable one, even though their horticulture remains unknown to us.

Table 1

Descriptive Statistics

N= 4453

                  Mean      Std.      Std.       Count    Minimum    Maximum     
                            Dev.      Error                                      
Rr                .383      .486      .007       4453     0.000      1.000       
Ro                .329      .470      .007       4453     0.000      1.000       
Rpo               .009      .097      .001       4453     0.000      1.000       
Rro               .124      .329      .005       4453     0.000      1.000       
Cm                .454      .498      .007       4453     0.000      1.000       
Ob                .026      .159      .002       4453     0.000      1.000       
Equi              .425      .702      .011       4453     0.000      6.000       
Boves             .936      1.076     .016       4453     0.000      10.000      
Vaccae            1.012     .895      .013       4453     0.000      8.000       
Vituli            1.258     1.304     .020       4453     0.000      16.000      
Ov&Cap            2.662     6.313     .095       4453     0.000      80.000      
Porci             1.829     3.329     .050       4453     0.000      52.000      
Alvearia          .786      1.749     .026       4453     0.000      30.000      
Vin.Foss.         .689      1.271     .019       4453     0.000      12.000      
Frum.             1.396     1.878     .028       4453     0.000      15.000      
Hordei            .210      .504      .008       4453     0.000      12.000      
Avenae            .293      .605      .009       4453     0.000      12.000      
Currus            1.830     2.018     .030       4453     0.000      20.000      
Kukuruz           .187      .433      .006       4453     0.000      6.000       
Falcator          .051      .441      .007       4453     0.000      6.000       
Milli             .391      .943      .014       4453     0.000      20.000      
Tritici           .669      1.505     .023       4453     0.000      20.000      
Terr. in.         1.031     2.636     .039       4453     0.000      28.000      
Grain             3.146     2.950     .044       4453     0.000      33.000      
Males             2.291     1.105     .017       4453     1.000      14.000      
Big Stock         2.373     2.219     .033       4453     0.000      22.000      
p/cGrain          1.523     1.563     .023       4453     0.000      23.000      
Smallstock        4.490     8.133     .122       4453     0.000      95.000      
AllAnimals        8.907     10.736    .161       4453     0.000      118.000     
p/cSmallstock     2.075     3.903     .058       4453     0.000      72.000      
p/c Bigstock      1.157     1.246     .019       4453     0.000      22.000      
p/c Animals       4.218     5.347     .080       4453     0.000      118.000     

Table 2

Correlation Matrix for Animals

N = 4453

           Equi   Boves   Vaccae   Vituli   Ov&Cap    Porci    Alvearia    
Equi       1.000  .493    .416     .396     .323      .388     .210        
Boves      .493   1.000   .626     .573     .434      .468     .212        
Vaccae     .416   .626    1.000    .763     .237      .421     .227        
Vituli     .396   .573    .763     1.000    .180      .408     .205        
Ov&Cap     .323   .434    .237     .180     1.000     .362     .144        
Porci      .388   .468    .421     .408     .362      1.000    .307        
Alvearia   .210   .212    .227     .205     .144      .307     1.000       

Table 3

Correlation Matrix

Crops

         Vin.Fos  Frum.  Hordei  Avenae   Currus   Kukuruz  Falcato  Milli    Tritici  Terr.    
         s.                                                 r                          in.      
Vin.Fos  1.000    .291   .106    .215     .237     .017     -.042    .081     .067     .086     
s.                                                                                              
Frum.    .291     1.000  .116    .214     .246     .221     .136     -.261    -.330    -.267    
Hordei   .106     .116   1.000   .201     .250     .005     .056     .159     .248     .220     
Avenae   .215     .214   .201    1.000    .294     .005     .027     .267     .358     .266     
Currus   .237     .246   .250    .294     1.000    -.037    -.105    .201     .313     .299     
Kukuruz  .017     .221   .005    .005     -.037    1.000    .219     -.162    -.192    -.169    
Falcato  -.042    .136   .056    .027     -.105    .219     1.000    -.048    -.052    -.046    
r                                                                                               
Milli    .081     -.261  .159    .267     .201     -.162    -.048    1.000    .603     .492     
Tritici  .067     -.330  .248    .358     .313     -.192    -.052    .603     1.000    .642     
Terr.    .086     -.267  .220    .266     .299     -.169    -.046    .492     .642     1.000    
in.                                                                                             

Table 4

Regression Summary

Grain vs. 6 Independents

Count 4453

Num. Missing 0

R .730

R Squared .533

Adjusted R Squared .532

RMS Residual 2.018

                Coefficient     Std. Error      Std. Coeff.     t-Value         P-Value         
Intercept       .801            .095            .801            8.402           <.0001          
Rr              -.534           .091            -.088           -5.859          <.0001          
Ro              .064            .096            .010            .672            .5019           
Rro             -.435           .116            -.049           -3.755          .0002           
Cm              .147            .063            .025            2.317           .0205           
Boves           1.842           .029            .672            62.844          <.0001          
Males           .345            .029            .129            12.090          <.0001          

Table 5

Regression Summary

p/cGrain vs. 6 Independents

Count 4453

Num. Missing 0

R .626

R Squared .391

Adjusted R Squared .391

RMS Residual 1.220

                Coefficient     Std. Error      Std. Coeff.     t-Value         P-Value         
Intercept       1.974           .058            1.974           34.260          <.0001          
Rr              -.284           .055            -.088           -5.152          <.0001          
Ro              -.011           .058            -.003           -.194           .8462           
Rro             -.174           .070            -.037           -2.479          .0132           
Cm              .018            .038            .006            .465            .6421           
Boves           .874            .018            .602            49.307          <.0001          
Males           -.499           .017            -.353           -28.910         <.0001          

Table 6

Production Function

Log likelihood = 391.7

N Observations = 2427

        Parameter           Estimate                Std.Err.                t                       
Constant [[alpha]]0         .2101                   .0563                   3.73                    
Altitude [[alpha]]1         .00313                  .000048                 6.49                    
Altitude2 [[alpha]]2        -.443E-5                .816E-6                 -5.43                   
Orthodox [[alpha]]3         .1008                   .0346                   2.91                    
d0  see footnote 1          2.2512                  N/A                     N/A                     
d1  see footnote 1          -1.0262                 N/A                     N/A                     
[[phi]]0  HHoxen            .7632                   .0330                   23.09                   
[[phi]]1  NWoxen            .0499                   .0200                   3.45                    
[[phi]]2 NNWoxen            .0083                   .0002                   2.9                     
[[theta]]0 HHmales          .2736                   .0398                   6.88                    
[[theta]]1 NWmales          .0187                   .0762                   .24                     
[[theta]]2 NNWmales         .0028                   .0008                   3.72                    
[[sigma]]2 (error)          .2664                   .0069                   38.85                   

Note 1: the coefficients d0 and d1 are used to estimate the optimal ratio of oxen to labor.

Note 2: the coefficients [[phi]]0 and [[theta]]0 can be taken as the coefficients for HHoxen and HHmales, respectively, if the values of NWoxen and NWmales, and of NNWoxen and NNWmales, respectively, are held constant.

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