Tests for specification error are applied to a number of alternative production function models using aggregate U. S. manufacturing data by states for the year 1957. On the basis of the test results, the CES production function is tentatively chosen in preference to the Cobb-Douglas, variable elasticity, one form of the generalized production function, and a simple quadratic in capital and labor. The CES function estimated in this case gives indications of increasing returns to scale and of having an elasticity of substitution parameter greater than one.