stock has its own energy efficiency, which is a function of input prices at the time of investment, and exogenous technological change. As with most new model developments, introducing capital vintages is costly; to make the model estimable we have to assume that the services of assets of different vintages are perfect substitutes, and these assets depreciate geometrically at a constant rate. Under those assumptions we can represent the efficiency of the capital stock with a single index, weighted by the relative efficiencies of the past vintages of capital.<sup>2</sup> Adding vintage structure captures the adaptation of capital stock to energy prices, while preserving the flexibility of substitution between input factors to production (labour, energy and materials).

Our paper is relevant to several recent studies aimed at understanding determinants of energy efficiency improvements. Perhaps the most closely related paper is Koopmans and te Velde (2001), who also develop a vintage capital model of energy demand, in which the efficiency of energy-using capital stocks responds endogenously to energy prices. Unlike our paper, Koopmans and te Velde (2001) do not structurally estimate the parameters of their model. Instead they calibrate their model based on a large bottom-up database for the economy of the Netherlands, and then solve it numerically. They find that the average pace at which new, energy-efficient technologies become available varies across time, thus elucidating the key weakness of the bottom-up modeling approach, which relies on extrapolation of historical trends of energy efficiency improvements. Metcalf (2008) adapts an index number based theoretical approach, and finds that roughly three-quarters of the improvements in the U.S. energy intensity since 1970 results from efficiency improvements due to rising energy prices and per-capita income. Sue Wing (2008) estimates a structural model, which attributes most of the changes in the U.S. energy intensity to adjustments of quasi-fixed inputs and disembodied autonomous technological progress. The study concludes that “price-induced substitution of variable inputs generated who introduced this concept in the context of deterministic growth model. Other notable contributions investigating different properties of vintage capital include Solow et al. (1966), Sheshinski (1967), Malcomson (1975), Fuss (1977), and, more recently, Chari and Hopenhayn (1991), Benhabib and Rusticini (1991), and Boucekkine et al. (1997). In the energy and environmental economics literature, vintage capital models have been intensively used mainly in the context of understanding the properties of embodied energy-saving technological progress. Recent contributions include Meijers (1994), Mulder et al. (2003), Hart (2004), P ́erez-Barahona and Zou (2006), and Azomahou et al. (2012).

2In this regard our econometric approach is similar to Haas and Schipper (1998) and Koopmans and te Velde (2001), who advocate calculating an index of energy efficiency, and using it directly in econometric specification for energy demand. The index of Haas and Schipper (1998) though is obtained through factor decomposition, and is thus purely exogenous.

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