The blue line at 4% is the upper limit of full employment, which is usually defined as less than 1% up to 4%. Rarely did unemployment fall below 4% in the late 19th century.
Of especial interest is the spike in unemployment from 1875–1878, for the real GNP estimates of Balke and Gordon show positive GNP growth rates in these years.
What went wrong with the US economy?
One possibility is that the real GNP estimates of Balke and Gordon are wrong.
Certainly, the relevant data from Davis’s US industrial output index show an industrial recession from 1873 to 1875:
US Industrial Index, 1870–1880This data is presented below in graph form. You can see the manufacturing recession and subsequent stagnation.
Index base is 1849–1850 = 100
Year | Index
1870 | 242.97
1871 | 255.29
1872 | 275.74
1873 | 302.17
1874 | 300.7
1875 | 284.2
1876 | 294.0
1877 | 297.8
1878 | 314.0
1879 | 356.4
1880 | 400.9
(Davis 2004: 1189).

From 1873, industrial output fell, mildly in 1874, but sharply in 1875. Davis (2004: 1203) finds that the cumulative industrial index loss (-10.83) was the second worst of the late 19th century, and only surpassed by the double dip recession of the 1890s.
By the 1870s the industrial sector of the US economy was large enough to be a good index of real GDP movements, and Davis finds that the US had a recession from 1873 to 1875 lasting less than 3 years.
A brief recovery in industrial output happened in 1876, but there was stagnation in 1877.
So, all in all, the rising unemployment until 1878 looks like the result of a severe recession from 1873 to 1875, poor recovery, and then stagnation in 1877 (perhaps a double dip recession in the mid to late 1870s is another possibility).
BIBLIOGRAPHY
Balke, N. S., and R. J. Gordon, 1989. “The Estimation of Prewar Gross National Product: Methodology and New Evidence,” Journal of Political Economy 97.1: 38–92.
Davis, Joseph H. 2004. “An Annual Index of U. S. Industrial Production, 1790-1915,” The Quarterly Journal of Economics 119.4: 1177–1215.
Davis, Joseph H. 2006. “An Improved Annual Chronology of U.S. Business Cycles since the 1790s,” Journal of Economic History 66.1: 103–121.
Vernon, J. R. 1994. “Unemployment Rates in Post-Bellum America: 1869–1899,” Journal of Macroeconomics 16: 701–714.
