Total Factor Productivity and Final-to-Useful Exergy Efficiency in Austria, 1960–2019: A Cointegration Analysis

The sources of total factor productivity (TFP) remain a central puzzle in growth theory. This paper examines the long-run statistical relationship between TFP growth and aggregate final-to-useful exergy efficiency—a physical measure of machine performance. Using Austria (1960–2019), we test for cointegration within a vector error correction framework. To address specification uncertainty, we systematically evaluate 100 model permutations using an ultra-conservative Bonferroni correction. The surviving models converge on a no-trend specification: no additional deterministic trend term is required to fit the long-run evolution of TFP once exergy efficiency is included, within the specifications tested. Extending earlier evidence for Portugal to a mature frontier economy, we find lower estimated elasticities than previously reported for Portugal, a pattern consistent with, though not formally established as, a decline in this relationship’s strength with economic maturity. A formal test for structural breaks further reveals that this relationship is not stable across the full sample: the estimated elasticity is significantly higher before the mid–1970s oil crisis than after, though cointegration itself is not undermined by allowing for this break. Formal tests of weak exogeneity and Granger causality indicate that TFP and exergy efficiency share a long-run co-movement, with TFP performing proportionally more of the equilibrium adjustment, but without clean evidence of unidirectional causality. This pattern is consistent with TFP reflecting physically constrained, embodied innovation rather than disembodied change, raising questions about the unconstrained exogenous trends used in long-run growth and climate economy models.