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150 years ago, Stanley Jevons introduced the concept of energy rebound: that anticipated energy efficiency savings may be "taken back" by behavioural responses. This is an important issue today because, if energy rebound is significant, this would hamper the effectiveness of energy efficiency policies aimed at reducing energy use and associated carbon emissions. However, empirical studies which estimate national energy rebound are rare and, perhaps as a result, rebound is largely ignored in energy-economy models and associated policy. A significant difficulty lies in the components of energy rebound assessed in empirical studies: most examine direct and indirect rebound in the static economy, excluding potentially significant rebound of the longer term structural response of the national economy. In response, we develop a novel exergy-based approach to estimate national energy rebound for the UK and US and China (1981China ( -2010. Exergy-as "available energy"-allows a consistent, thermodynamic-based metric for national-level energy efficiency. We find large energy rebound in China, suggesting that improvements in China's energy efficiency may be associated with increased energy consumption ("backfire"). Conversely, we find much lower (partial) energy rebound for the case of the UK and US. These findings support the hypothesis that producer-sided economies (such as China) may exhibit large energy rebound, reducing the effectiveness of energy efficiency, unless other policy measures (e.g., carbon taxes) are implemented. It also raises the prospect we need to deploy renewable energy sources faster than currently planned, if (due to rebound) energy efficiency policies cannot deliver the scale of energy reduction envisaged to meet climate targets.

Capital-labour-energy Constant Elasticity of Substitution (CES) production functions and their estimated parameters now form a key part of energy-economy models which inform energy and emissions policy. However, the collation and guidance as to the specification and estimation choices involved with such energy-extended CES functions is disparate. This risks poorly specified and estimated CES functions, with knock-on implications for downstream energy-economic models and climate policy. In response, as a first step, this paper assembles in one place the major considerations involved in the empirical estimation of these CES functions. Discussions of the choices and their implications lead to recommendations for CES empiricists. The extensive bibliography allows those interested to dig deeper into any aspect of the CES parameter estimation process.

Development of energy policy is often informed by economic considerations via aggregate production functions (APFs). We identify a theory-to-policy process involving APFs comprised of six steps: (1) selecting a theoretical energy-economy framework; (2) formulating modeling approaches; (3) econometrically fitting an APF to historical economic and energy data; (4) comparing and evaluating modeling approaches; (5) interpreting the economy; and (6) formulating energy and economic policy. We find that choices made in Steps 1-4 can lead to very different interpretations of the economy (Step 5) and policies (Step 6). To investigate these effects, we use empirical data (Portugal and UK) and the Constant Elasticity of Substitution (CES) APF to evaluate four modeling choices: (a) rejecting (or not) the cost-share principle; (b) including (or not) energy; (c) quality-adjusting (or not) factors of production; and (d) CES nesting structure. Thereafter, we discuss two revealing examples for which different upstream modeling choices lead to very different policies. In the first example, the (kl)e nesting structure implies significant investment in energy, while other nesting structures suggest otherwise. In the second example, unadjusted factors of production suggest balanced investment in labor and energy, while quality-adjusting suggests significant investment in labor over energy. Divergent outcomes provide cautionary tales for policymakers: greater understanding of upstream modeling choices and their downstream implications is needed.

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