IMMIGRATION PRIOR TO 1890 
the probable maximum and minimum limits of the typical lag. An 
examination of the curve of imports from 1820 to date (on both the 
calendar year and fiscal year basis after 1870) and a comparison 
with the curve for total immigration, indicates that Immigration 
probably lags behind imports a few months, the period evidently 
being nearer six months than a full year and possibly less than six 
months. 
A similiar serutiny of the pig iron and immigration curves from 
1854 to date reveals a similiar tendency for some laginimmigration 
of an apparent length of less than one year, as evidenced by the 
fact that, in about half of the instances, the troughs and peaks are 
reached in the same year by the immigration and pig iron curves, 
and, in the other half, the annual immigration movement reaches 
the corresponding maximum or minimum a year later than pig iron. 
It remains to examine the question of lag more closely with the 
aid of quarterly and monthly data and by numerical computation 
of the allowance for lag which gives the highest degree of correlation 
between immigration and industrial activity. 
Numerical Computation of the Typical Lag. 
In the usual statistical terminology, the arithmetic evidence of 
the lag giving the closest correspondence between the curves may 
be expressed by the following summary: 
Correlation coeffcient when the gwen number of years 
Period compared lag is imputed to immigration as compared with pig iron. 
No lag One year Two years 
1857-1914 +.64 +.35 —_ 3 
1857-1919 +.51 +.27 — 
1872-1914 +.78 +.48 J 
This numerical interpretation of the statistical evidence, in terms 
of the coefficient of correlation, indicates that the closest relation- 
ship is found between pig iron and immigration when the years 
between the Civil War and the Great War are selected for study and 
it is assumed that such lag as may exist is less than one year. 
COMPARISONS BASED UPON QUARTERLY DATA: 
1868-1889 
Male Immigration. 
Quarterly immigration data are available by sex beginning with 
the quarter ending September 30, 1856. For reasons previously 
5