M. Bozinovich Column on Serbianna.com

One of the Albanian claims for independence of Kosovo is the ethnic makeup of the region. The argument points that, at least since 1948, Kosovo was majority Albanian populated hence it should be, at the most, given to Albania or at least granted international recognition as an independent state. The argument is supported by the statistical data which not only shows that since the end of WWII Albanians have been in the majority but that the majority has in fact increased from 68% of the total population in 1948 to 77% in 1981. Independence pundits cite that, in addition to the decades long absolute population majority, the apparent increasing homogenization of the Kosovo population is an additional reason for granting the sovereignty to that region.

Table 1: Kosovo Population
	Albanian	Serbian	Rest	Total
1948	498,242	199,961	29,617	727,820
	68.46%	27.47%	4.07%
1953	524,559	221,212	62,130	80,7901
	64.93%	27.38%	7.69%
1961	646,148	264,604	52,779	963,531
	67.06%	27.46%	5.48%
1971	916,168	259,819	67,706	1,243,693
	73.67%	20.89%	5.44%
1981	1,226,736	236,525	121,179	1,584,440
	77.42%	14.93%	7.65%

While not disputing Kosovo’s statistics, the population counter-argument claims that the initial 1948 Albanian majority was a result of the Yugoslav government’s prohibition on refugee returns, mostly Serbs that have been expelled by Albanian Nazis in WWII. Second, the increasing homogenization of Kosovo’s population in favor of Albanians has been achieved by means of political and economic repression of Kosovo Serbs. The repression was institutionalized with increased autonomy powers granted to Kosovo in the 1960s and especially in 1974. Instead of independence for Kosovo, a remedy should be found to the Serb plight, goes the argument.

In the extreme, the Western community seems to have endorsed the separatism argument while dismissing the institutionalized persecution of Kosovo Serbs as an inflated propaganda of the expansionist Serbian nationalist elements that led the country through much of the 1990s and took part in the broader Balkan wars. At the lesser extreme, on the other hand, the increased homogenization of Kosovo’s population in favor of Albanians has been explained away as a voluntary economic migration of Serbs that can be neatly correlated with the post-WWII economic stagnation of the region.

To the additional delight of the separatists, Western pundits cite that the increased homogenization of Kosovo in the Albanian favor is also a result of the birth rate: Albanians simply have more children then the Serbs.

While conclusions cited by all three sides rest on population statistics of Kosovo, all three sides, interestingly, use selective statistics that enhance the particular political persuasion at an expense of the dynamic analysis of Kosovo’s population trends.

For example, Kosovo’s Albanian homogenization is .47% per year - precisely the difference between Albanian growth rate and the growth rate of the total population. In other words, the total population is missing 0.47% annually, which is precisely the rate at which Albanian population share has been increasing. The implication is that the homogenization may not be due to disproportionally larger birth rate of the Albanians against others but rather due to a declining population of non-Albanians.

Further, economic incentives as sole reasons for migration of Kosovo Serbs strikes fundamentally unsound on two levels. First, while migratory economic incentives exert uniformly upon all populations, the Albanian majority, nevertheless, maintained its exponential growth rate while Serbs were forced into a parabolic decline. On the second level, there exists no population model where economic incentives are a sole cause for an overall population decline.

Additionally, argument that the repression caused the decline of the Serbian population also lacks a readily available population model against which data can be compared. Just because Serbian share of the total population went from 27% in 1948 to 15% in 1981 it does not necessarily follow that repression occurred.

Modern population theories suggest that populations behave rationally given incentives. Further, keeping all things equal with respect to given population’s religion, culture, mores, etc. populations grow at an exponential rate. Disruptions in exponential growth of the population tend to be typically episodic and extrinsic. For example, data shows that sudden epidemics and wars did indeed disrupt the exponential growth but as these adverse episodes dissipate exponential growth is, in the long run, re-established.

While the industrialization has reduced the rate of exponential growth of the Western countries, it has increased economic incentives for the less industrialized populations to migrate out of their environment. Comparative studies of Central American nations suggest, however, that such economic migration out these countries does not adversely impact the general exponential growth of these nations.

For example, Haiti has experienced a steady out migration during the 1982-96 period without any declining consequence on the overall population growth. Similar trends exist among other Latin American countries with high economic incentives to migrate out such as Panama, Guatemala, Dominican Republic, etc.

When appraised against the modern theoretical constructs of population trends, then, the peculiarity of Kosovo population statistics are rather apparent: How can a region, under rational population behavior axiom, experiencing absence of war but a uniform economic incentives to migrate out, exhibit an exponential growth for one ethnic group but a parabolic decline for another? Moreover, is there a comparative cross cultural population trend model, with known social circumstances, that resembles this peculiar circumstance? If it exists, are there means of measuring and testing such model against the one in Kosovo?

Various classes of algebraic functions exist that can numerically capture trends over a period of time. In addition, statistical methods exist that can enumerate and describe how well each developed mathematical equation fits the actual data. Such enumerated goodness of fit is referred to as a correlation coefficient.

In turn, a mathematical function with a good fit becomes a usefully predictor for the future expected population outcomes.

Thus, following the modern population theory suggesting that the algebraic population growth model is closely approximated with an exponential function, the data for each ethnic group in Table 1 is subjected to an exponential regression analysis. The exponential regression analysis, finally, produces an exponential function.

Exponential functions have a form of y = ab^x where x is located in the exponent and represents any given census year, while y variable measures the population level for that given year. Letters a and b are coefficients where a represents an adjusted number of the base year population in order to fit the equation, while b depicts the compound rate of growth of the population.

While Table 2 encapsulates the regression results, it also suggests that the Albanian ethnic group enjoys a 99.35% exponential data fit of goodness while the Serbian exponential model only 59.67%. The data suggests that the Albanian ethnic group has grown according to the standard population model without adverse growth effects while Serbian ethnic population has not.

Table 2: Kosovo Exponential Growth Regression
	Albanian	Serbian	Rest
a	470484.7	217828.8	36641.4
b	1.028899	1.005189	1.034225
r	99.35%	59.67%	89.01%

Instead of a standard exponential growth, Kosovo Serb population trend resembles a downward opening parabola. Parabolas have a following form: y = aX2 + bX + c , where a, b, and c are coefficients and X is the time variable of the census.

With the correlation coefficient of 0.98, Table 3 presents a function that dramatically fits the actual census data for the Kosovo Serbs.

To find the date of maximum population, find the vertex of the original equation. To find when will Kosovo Serbs be extinct, set equation dy = 0 and solve for X.

The high correlation coefficient in Table 3 implies that an equation that explains the Kosovo Serb population trend is a downward opening parabola. The derivative function, dy, represents the rate of change Serbs have experienced over the period of time. For example, the rate of change function tells that, on average over the years, Kosovo Serbs experienced a depopulation pressure multiple of 346.6. Further, the equation suggests that the Kosovo Serb population maximum occurred 19.81 years from 1948 or more precisely on September 22, 1967.

Table 3: Kosovo Serb Parabolic Growth
a	-173.3
b	6869.25
c	1975.764
r	0.98031
dy = -346.6X + 6869.25

By inference then, this date also marks the beginning of Kosovo Serb exodus out of Kosovo - nearly a year after the end of the communist brutal suppression of Albanian separatism. Moreover, the equation suggests that Kosovo Serb population should reach zero 58.96 years from 1948 or more precisely, Serbs will be exterminated from Kosovo on November 16, 2006.

IV. Parabolic Population Trend: Jewish Experience 1900-1941

A similar, but not so peculiar population trend is the Jewish experience under Nazi Germany. While the pre-Hitlerian cultural anti-Semitism in Germany was institutionalized, by 1941 hate of Jews was turned into an exterminatory policy. Out of 615,000 Jews in Germany in 1910, virtually none were left by 1945.

Table 4: Jewish Parabolic Growth in Nazi Germany

a -609.36

b 15,890.12

c 562,004.04

r 0.9724

dy = -1218.72X + 15890.12

When modeled with an exponential function, the Jewish population data during the Nazi period has a correlation coefficient of 0.774, which is below the 90%, thus a bad goodness of fit. Given that a parabolic model shown in Table 4 carries a correlation coefficient of 0.9724, it implies that under circumstances of ethnic animosity and/or genocidal policies a parabolic function is a more appropriate mathematical model for the population trends.

The implications of mathematical analysis of the Jewish population in preWWII Germany are multifold. First, under circumstances of ethnic animosity and/or genocidal policies a parabolic function is a more appropriate mathematical model for the population trends. Given that a parabola appropriately models Kosovo Serb population trend, the analysis strongly suggests that Kosovo Serbs have also been exposed to ethnic animosity and/or genocidal policies.

In addition, under parabolic analysis, it is possible to enumerate the depopulation pressure multiple. Such possibility allows for a cross-cultural numerical comparison of depopulation multiples wherever a parabolic model fits the population trend.

Both Jews under NAZIs and Serbs under Albanian-dominated Kosovo exhibit the same downward parabolic depopulation trend. The apparent steepness of the Jewish trend line illustrates the drastic exterminatory severity Jews under NAZIs have been exposed.

For example, the Jewish population in preWWII Germany registers a depopulation pressure multiple of 1218.72 while Kosovo Serbs exhibit a multiple of 346.6. Comparison of the multiples indicates that animosity exposure/genocidal infliction upon Kosovo Serbs is 28.44% that of the Jewish exposure in preWWII Germany. Conversely, the comparison also demonstrates a severity of the Jewish experience: their extermination in Germany occurs 13 years before the extermination of Kosovo Serbs even though the Jewish absolute population is 64.84% larger then the Kosovo Serb one.

V. Conclusion

While Jewish population analysis during preWWII Germany establishes that a more appropriate mathematical model of ethnic populations under duress is a parabola, an argument can be raised whether the converse is true: Just because population’s trend line can be modeled by a parabola it does not necessarily follow that the population is under duress. Significantly, however, demonstrating that the converse is also true may lend us into a new and bold blanket statement: wherever population exhibits a parabolic decline such population has been under ethnic duress.

While the truth of the converse may be beyond the discussion here, the suspicion that a parabolic population decline immediately means ethnicity under siege may indeed be true.

The suspicion is fueled by peculiarity of Kosovo Serb case and its similarity with Jewish experience in Nazi Germany. Presuming rational behavior of nations, uniform impact of migratory economic incentives, absence of war… such textbook population growth assumptions have impacted Kosovo Albanians to increase their population while Kosovo Serbs to decline in a mathematically similar way the Jews of Nazi Germany.

To the extent that Kosovo Serb population trend line is a parabola, there is a strong evidence to suggest then that Kosovo Serbs have been exposed to a level of ethnic duress sufficient enough to induce them to migrate out of Kosovo.