SEQUENTIALLY ESTIMATING THE STRUCTURAL EQUATION BY POWER TRANSFORMATION
提出距离差检验来检测经济变量间的非线性结构关系，若线性模型被拒绝，则用顺序检验程序估计多项式函数逼近非线性方程，并用美国企业数据验证生产函数存在要素偏向型技术进步。
This study provides an econometric methodology to test a linear structural relationship among economic variables. We propose the so-called distance-difference (DD) test and show that it has omnibus power against arbitrary nonlinear structural relationships. If the DD-test rejects the linear model hypothesis, a sequential testing procedure assisted by the DD-test can consistently estimate the degree of a polynomial function that arbitrarily approximates the nonlinear structural equation. Using extensive Monte Carlo simulations, we confirm the DD-test’s finite sample properties and compare its performance with the sequential testing procedure assisted by the J-test and moment selection criteria. Finally, through investigation, we empirically illustrate the relationship between the value-added and its production factors using firm-level data from the United States. We demonstrate that the production function has exhibited a factor-biased technological change instead of Hicks-neutral technology presumed by the Cobb–Douglas production function.