. MIGRATION AND BUSINESS CYCLES
the solid b'ack dots are used. For each intercensal period any discrepancy
 which appears between the index and the Census is
prorated over the intervening months so that the final curve shows
no sudden changes at the junctures with the Census years.
After 1907, as previously noted, the annual censuses do not
overlap, and it becomes necessary to estimate the December-to-January
 change.
December-to-January Interpolations.
Beginning in 1907, as we have noted, the Massachusetts
Census of Industries was designed to be virtually a complete census.
However, on plotting the data, it became apparent that in some
years, particularly in those immediately after the abandonment of
the former method of making each census cover twenty-four
months, in order to make the series reasonably continuous, it would
be necessary to substitute for the December-to-January change
which is indicated by the raw data, an estimated percentage change.
This was done for the December-to-January change of 1906-07,
1907-08, 1908-09, 1909-10, 1913-14, 1914-15, and 1918-19. For
the other years since 1907, it was judged, upon the basis of a comparison
 of the raw data, that no adjustments were necessary.
The principle upon which these interpolations were made is that
the best clew to the joint effect of the seasonal and cyclical influences
 is found in the typical relation in the past of the Decemberto-January
 change to the changes in contiguous months. Two
estimates were made for each year in question. For one, the
median ratio in the years 1889-1906 between the November-to-December
 and the December-to-January movements was found
and this ratio assumed to hold in the years for which the actual December-to-January
 movement was not known. A similar estimate
was made for the relation of the December-to-January changejto the
January-to-February change. The two estimates were then averaged
 for the final estimate.
For 1923 the estimate is based upon the index of employment in
Massachusetts, recently inaugurated by the Massachusetts Bureau
of Statistics. The final result of the Massachusetts computation is
an estimate of the average number of wage earners employed in
factories with a product of $500 or more, from 1889 to 1923 by
months.

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