We construct a 2 sector growth model with sector specific technology shocks where one sector produces intermediate goods while the other produces final goods. Theoretical restrictions from this model are used to compute the time series for sector-specific TFPs based solely on factor prices and the relative price of intermediate goods to final goods over the 1959-2000 period. An aggregate TFP measure based on these series appears quite similar to the multifactor productivity measure constructed by the BLS. We find statistical evidence of structural breaks in the growth rate of our productivity measures in 1973 and 1995. The first of these breaks appears to be due to an economy-wide productivity slowdown, while the second is attributed to a sharp pickup in the growth rate of productivity in the intermediate goods sector. Using only these TFP measures, the model's predictions of output growth rates in the two sectors over the intervals defined by the estimated break dates compare favorably with the actual data on consumer nondurables and services (final goods) and consumer and producer durables (intermediate goods).