The law of the tendential fall in the rate of profit has been at the center of theoretical and empirical debates within Marxian political economy ever since the publication of Volume III of Capital. An important limitation of this literature is the absence of a comprehensive econometric analysis of the behaviour of the rate of profit. In this paper, we attempt to fill this lacuna in two ways. First, we investigate the time series properties of the profit rate series. The evidence suggests that the rate of profit behaves like a random walk and exhibits "long waves" interestingly correlated with major epochs of U.S. economic history. In the second part, we test Marx's law of the tendential fall in the rate of profit with a novel econometric model that explicitly accounts for the counter-tendencies. We find evidence of a long-run downward trend in the general profit rate for the US economy for the period 1948-2007.