figures for Ukrainian famine mortality" and "[t]here is absolutely no basis for accepting a figure of 10 million Ukrainians dying as a result of the famine of 1932–1933." In 2001, Wheatcroft had calculated total population loss (including stillbirth) across the Union at 10 million and possibly up to 15 million between 1931 and 1934, including 2.8 million (and possibly up to 4.8 million excess deaths) and 3.7 million (up to 6.7 million) population losses including birth losses in Ukraine. In 2002, Ukrainian historian , using demographic data including those recently unclassified, narrowed the losses to about 3.2 million or, allowing for the lack of precise data, 3 million to 3.5 million. The number of recorded excess deaths extracted from the birth/death statistics from Soviet archives is contradictory. The data fail to add up to the differences between the results of the 1926 Census and the 1937 Census. Kulchytsky summarized the declassified Soviet statistics as showing a decrease of 538,000 people in the population of Soviet Ukraine between 1926 census (28,926,000) and 1937 census (28,388,000). Similarly, Wheatcroft's work from Soviet archives showed that excess deaths in Ukraine in 1932–1933 numbered a minimum of 1.8 million (2.7 including birth losses): "Depending upon the estimations made concerning unregistered mortality and natality, these figures could be increased to a level of 2.8 million to a maximum of 4.8 million excess deaths and to 3.7 million to a maximum of 6.7 million population losses (including birth losses)". A 2002 study by French demographer Jacques Vallin and colleagues utilising some similar primary sources to Kulchytsky, and performing an analysis with more sophisticated demographic tools with forward projection of expected growth from the 1926 census and backward projection from the 1939 census estimates the number of direct deaths for 1933 as 2.582 million. This number of deaths does not reflect the total demographic loss for Ukraine from these events as the fall of the birth rate during the crisis and the out-migration contribute to the latter as well. The total population shortfall from the expected value between 1926 and 1939 estimated by Vallin amounted to 4.566 million. Of this number, 1.057 million is attributed to the birth deficit, 930,000 to forced out-migration, and 2.582 million to the combination of excess mortality and voluntary out-migration. With the latter assumed to be negligible, this estimate gives the number of deaths as the result of the 1933 famine about 2.2