Whatever estimates you use, it is clear that the US economy had serious problems in the 1890s (from 1893 onwards) and rising and then high unemployment until 1898.
The actual estimates of unemployment come from
(1) Lebergott (1964);We can see the height of unemployment estimates range from 8% (in Vernon) to 18% (in Lebergott).
(2) Romer (1986);
(3) Vernon (1994), and
(4) Weir (1992), with two unemployment measures:(1) a standard civilian unemployment rate (deducting employment in the armed forces), and
(2) a “private nonfarm unemployment” rate that deducts agricultural and government employment.
The question of who is right hinges on whether (1) labour force participation rates were countercyclical (in the sense of rising during recessions) before 1914 and (2) whether Okun’s law actually applies to the 19th century.
Lebergott, S. 1964. Manpower in Economic Growth: The American Record since 1800. McGraw-Hill, New York.
Romer, C. D. 1986. “Spurious Volatility in Historical Unemployment Data,” Journal of Political Economy 94: 1–37.
Weir, D. R. 1992. “A Century of U.S. Unemployment, 1890–1990: Revised Estimates and Evidence for Stabilization,” Research in Economic History 14: 301–346.
Vernon, J. R. 1994. “Unemployment Rates in Post-Bellum America: 1869–1899,” Journal of Macroeconomics 16: 701–714.