Housing fever is a popular term to describe an overheated housing market or housing price bubble. Like other financial asset bubbles, housing fever can inflict harm on the real economy, as indeed the US housing bubble did in the period following 2006 leading up to the general financial crisis and great recession. One contribution that econometricians can make to minimize the harm created by a housing bubble is to provide a quantitative ‘thermometer’ for diagnosing ongoing housing fever. Early diagnosis can enable prompt and effective policy action that reduces long term damage to the real economy. This paper provides a selective review of the relevant literature on econometric methods for identifying housing bubbles together with some new methods of research and an empirical application. We first present a technical definition of a housing bubble that facilitates empirical work and discuss significant difficulties encountered in practical work and the solutions that have been proposed in the past literature. A major challenge in all econometric identification procedures is to assess prices in relation to fundamentals, which requires measurement of fundamentals. One solution to address this challenge is to estimate the fundamental component from an underlying structural relationship involving measurable variables. A second aim of the paper is to improve the estimation accuracy of fundamentals by means of an easy-to-implement reduced-form approach. Since many of the relevant variables that determine fundamentals are nonstationary and interdependent we use the IVX (Phillips et al. (2009); Kostakis et al. (2015)) method to estimate the reduced-form model to reduce the finite sample bias which arises from highly persistent regressors and endogeneity. The recursive evolving test of Phillips, Shi, and Yu (2015a, PSY) is applied to the estimated non-fundamental component for the identification of speculative bubbles. The new bubble test developed here is referred to as PSY-IVX. An empirical application to the eight Australian capital city housing markets over the period 1999 to 2017 shows that bubble testing results are sensitive to different ways of controlling for fundamentals and highlights the importance of accurate estimation of these housing market fundamentals.