Cost overruns in transport infrastructure projects are prevalent and have been well documented in the literature; see, for instance, Flyvbjerg et al. (2003), Odeck (2004 and 2014) and Cantarelli et al. (2010). Governments may therefore exert efforts to reduce overruns by implementing strategies such as quality assurance of cost estimates, whereby external consultants are engaged to assure the accuracy of estimates. However, the literature has to a lesser extent provided evidence on what governments do to combat overruns and whether those efforts work in practice. This paper provides such evidence for the case of Norway, where the government implemented a quality assurance regime for cost estimates above 500 million NOK in the early 2000. Apart from explaining the Norwegian quality assurance regime, the paper uses statistical inferences to compare the magnitudes of cost overruns in the pre-and post- quality assurance periods. The statistically significant derived results are as follows: (i) quality assurance has led to a reduction in cost overruns; (ii) quality assurance has not, however, led to improved accuracy of the estimates provided by the authorities – rather, it has led to systematic overestimation by the authorities; and (iii) external consultants are more accurate than the authorities. We conclude that the quality assurance regime is achieving the objectives of reducing cost overruns and that similar regimes should be considered for smaller projects where overruns have been shown to be very large.