We construct a growth model with intermediate and final goods and sector specific technology shocks. Theoretical restrictions from this model are used to compute time series for sector-specific productivity measures based solely on factor prices and the relative price of final to intermediate goods over the 1959-2000 period. The resulting measure of total factor productivity appears quite similar to the Bureau of Labor Statistics' measure. Our constructed measures exhibit evidence of two breaks. The first (in 1973) appears to reflect an economywide productivity slowdown, while the second (in 1995) represents a pickup in productivity in the intermediate goods sector. Using only these TFP measures, the model's predictions of output growth rates over intervals defined by the estimated break dates compare favorably with U.S. data.