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Economists seem to have found it difficult to measure the economic performance of a planned socialist economy like the USSR's using indicators created for market economies. Many economic principles taken for granted in capitalist economies just didn't exist in the USSR, and this applies to everything from pricing to motivation, mobilization of labor, debt & credit, ideas of economic solvency and efficiency, etc. In effect, apart from direct comparisons on things like industrial and agricultural output, resource extraction, construction of infrastructure, etc. it's very hard to compare the economies of the two very different systems using one overall indicator. This Wikipedia article explains part of the problem:
https://en.wikipedia.org/wiki/Net_material_productAccording to the State Statistics Committee of the USSR's 1990 Yearbook, based on figures from 1988 and 1989, the country had a 'net material product' of one trillion rubles, and a 'net social product' (accounting for non-material production) of 1,631,600,000,000 rubles. Converting that to dollars at a rate of 0.6 dollars per ruble, you get $2.7 trillion. Based on that, Japan's GDP of $3.14 trillion in 1990 according to the World Bank does make the latter's economy bigger.
http://istmat.info/node/435https://data.worldbank.org/country/JapanOne problem worth noting with this estimate was the lack of a single exchange rate, since the Soviet system used both convertible and non-convertible rubles.
By PPP calculations (again a market-oriented measurement tool) observers still tend to rank the USSR second. According to a 2003 study by researchers from the Moscow-based Institute of World Economy and International Relations, Soviet PPP GDP in 1990 in 2000 dollars was 3.325 trillion, compared with 7.475 trillion for the US and 3.115 trillion for Japan.
In his book "The USSR and the Countries of the World in Figures", statistician I.G. Kalabekov discusses a few of the mechanisms of the Soviet economic system which resulted in its undervaluation in GDP terms. He notes for example that market prices existed only for a small segment of goods sold at the consumer level, with most goods sold for just above production cost (which eventually became one of the reasons for shortages for some goods in stores). The state also set prices for most services, including things like legal fees. The USSR also essentially had no housing market, with the vast majority of apartments provided free and not allowed to be resold. The same is true for the commercial real estate market. Furthermore, things like energy prices were heavily subsidized, and often sold for below production cost. Finally, things like health and education were completely free, or more accurately, their price was absorbed by the state through what in market terms may be seen as an invisible tax.
http://su90.ru/su465.pdf (page 60)
P.S. Even Grigory Khanin, the statistician who famously condemned official Soviet statistics in a 1987 article as being "false" and gained widespread recognition and praise among Perestroika's supporters and Western economists, has estimated in his 2010 magnum opus The Economic History of Russia in Modern Times Vol 2 that by PPP, the Soviet economy remained second in the world in the mid-late 80s.