Numerous studies assume that the price elasticity of electricity demand remains constant through the years. This, in turn, means that these studies assume that industrial consumers react in the same way to price fluctuations regardless of the actual price level. This paper proposes that the price elasticity of industrial electricity demand varies over time. The Kalman filter methodology is employed in an effort to provide policy-makers with more information on the behaviour of the industrial sector with regards to electricity price changes, focusing on the period 1970 to 2007. Other factors affecting electricity consumption, such as real output and employment, are also captured. The findings of this paper show that price sensitivity has changed since the 1970s. It has decreased in absolute values from -1 in 1980 to -0.953 in 1990 and then stabilised at approximately -0.95 which indicates that the industrial sector has experienced an inelastic demand. In other words, the behaviour of industrial consumers did not vary significantly during the 2000s. In the long run and as the prices increase, probably reaching the levels of the 1970s or even before, the industrial sector’s behaviour might change and the elasticity might end up at levels higher than one (elastic).