Total Factor Productivity

Labour productivity is a partial measure — output per unit of labour (per worker or per hour) — and it can rise simply because each worker has more capital to work with (capital deepening), even if joint efficiency is unchanged. TFP is a total measure: output relative to a composite of all inputs (capital, labour, and often materials) taken together. TFP isolates the efficiency gain that remains after accounting for the contribution of every input, so it is the cleaner indicator of genuine technological and organizational improvement, whereas labour productivity mixes efficiency with the amount of capital per worker.

Firms observe their own productivity before choosing inputs, so a highly productive firm tends to use more inputs. This creates a correlation between the regressors (inputs) and the unobserved productivity term, biasing ordinary least squares — the so-called transmission or simultaneity bias. Control-function estimators such as Olley-Pakes (using investment) and Levinsohn-Petrin (using intermediate inputs) proxy for unobserved productivity using a monotone input demand, breaking the correlation and delivering consistent coefficient estimates. The Ackerberg-Caves-Frazer refinement corrects a collinearity problem in the first stage of these procedures.

Use the index-number (superlative) approach when you have good price and quantity or value-and-share data and want a transparent, theory-consistent measure that requires no model estimation — this is ideal for national and industry accounts where competitive-market assumptions are reasonable. Use the production-function approach when you have firm-level micro-data, are interested in productivity heterogeneity across producers, or cannot assume that observed shares equal output elasticities (for example, under imperfect competition). The two approaches are complementary: index numbers excel at aggregate accounting, econometrics at micro-level heterogeneity and causal analysis.