I read a paper this week on the economic performance of the Soviet Union during its history, entitled "Soviet Economic Decline: Historical and Republican data". It's available through Google Scholar, if you are interested. Some of my students from transition countries ask me about the USSR's performance relative to capitalism, so hopefully this will bolster my knowledge - I was a little ignorant as the USSR dissolved twenty years ago and many economists had dismissed communist economics long before and looked for more current challenges. Examining the USSR's performance also helps to answer questions about the origins of economic growth, and how much can be attributed to the different productive factors.
The authors use Western and Soviet data to find that Soviet growth declined from extremely high rates in the 1950s to low rates in the 1980s, despite high investment rates and education. The authors find that the physical capital stock grew steadily, but its return declined sharply, so that the Soviet physical capital to output ratio was very high by world standards in the 1980s. The estimates of productivity growth depends on the source of data, although it is at best low after the 1950s assuming a Cobb-Douglas production function. Industrial productivity growth remained positive until the 1980s, and non-industrial productivity growth was negative, most of all in agriculture.
The authors perform non-linear least squares estimations to get the parameters of a CES production function, replacing the Cobb-Douglas function to see if they get other explanations than declining productivity growth. They find, with three of the four datasets, that the CES parameter is low, meaning that labour and capital do not substitute easily for each other if their marginal returns change. The authors give a possible interpretation where capital accumulation would normally be replacing labour and so increasing its own return, but this was not happening in the USSR, perhaps because the type of capital was not labour-replacing. Other explanations are possible; for example, if capital was so unproductive in a market economy, more labour would be hired in its place, but Soviet labour markets were not flexible.
The authors emphasise the explanations of the CES production function estimations in preference to the competing explanation of the Cobb-Douglas function, and are probably right to do so given that Cobb-Douglas is a limiting case of the CES function. More generally in growth theory, the Cobb-Douglas function is widely used, but its implication that capital and labour freely substitute for each other is a major one given the significance of market rigidities in constraining growth, and the CES function may lead to different interpretations of growth performance. The authors themselves point out the relevance of their observations for Asian countries with rapid growth through capital accumulation (although the causes of their growth are debated).