Aggregate productivity and aggregate technology are meaningful but distinct concepts. We show that a slightly-modified Solow productivity residual measures changes in economic welfare, even when productivity and technology differ because of distortions such as imperfect competition. We then present a general accounting framework that identifies several new non-technological gaps between productivity and technology, gaps reflecting imperfections and frictions in output and factor markets. Empirically, we find that these gaps are important, even though we abstract from variations in factor utilization and estimate only small average sectoral markups. Compared with productivity growth, our measured technology shocks are significantly less correlated with output, and are essentially uncorrelated with inputs. Our results imply that calibrating dynamic general equilibrium models as if Solow residuals were technology shocks confuses impulses and propagation mechanisms.