Testing Linear and Log-Linear Regressions for Functional Form
Testing Linear and Log-Linear Regressions for Functional Form
复制标题
DOI：
10.2307/2297160
复制
发表时间：
1981-07
期刊：
影响因子：
--
通讯作者：
L. Godfrey;M. Wickens
中科院分区：
文献类型：
--
作者：
L. Godfrey;M. Wickens
在指定计量经济模型时，知道选择什么函数形式通常是一个问题，因为经济理论通常不会提供非常精确的指导。然而，选择功能形式可能对随后的统计检验、预测和政策分析产生重要影响，例如见Hall（1978年）和Mizon（1977年）。由于其简单性，最常用的规范是线性和对数线性模型。有时对这两种变体的估计进行比较，以选择其中一种作为“正确”表示。虽然这种比较在某些情况下可能很有趣，但在其他情况下，根据更一般的函数形式测试线性或对数线性可能更合适，而不是相互比较。在本文中，我们讨论了两种方法来测试线性和对数线性规范的充分性，而不是Savin和White（1978）考虑的扩展Box-Cox（1964）回归模型的更一般选择。这些程序中的第一个是基于由Breusch和Pagan（1980）以及Godfrey和Wickens（1980）讨论的拉格朗日乘数方法，而第二个是由Andrews（1971）在选择数据转换方面的工作推导出来的这两种方法都会导致易于计算的测试，并且可以拒绝两种模型，并且能够选择一种形式而不是另一种形式。本文的内容如下。在第2节中，我们比较了一些现有的测试线性和对数线性模型的功能形式的程序。在第3节中，我们推导了基于拉格朗日乘数方法的新的大样本测试。第4节讨论了使用小样本测试的可能性，第5节给出了一个数值例子来说明我们的新测试的使用。
It is often a problem to know what functional form to choose when specifying an econometric model since economic theory does not usually provide a very precise guide. The choice of functional form may, however, have important implications for subsequent statistical tests, for forecasts and for policy analysis, e.g. see Hall (1978)and Mizon (1977). Due to their simplicity, the specifications most commonly used are the linear and log-linear models. Sometimes the estimates of these two variants are compared with a view to choosing one of them as the "correct" representation. Although this comparison may be of interest in certain cases, in others it may be more appropriate to test linearity or log-linearity against a more general functional form rather than against each other. In this paper, we discuss two approaches to testing the adequacy of the linear and log-linear specifications against the more general alternative of the extended Box-Cox (1964) regression model considered by Savin and White (1978). The first of these procedures is based on the Lagrange multiplier approach discussed by Breusch and Pagan (1980) and by Godfrey and Wickens (1980), while the second is derived from work by Andrews (1971) on the selection of data transformations.1 Both approaches lead to tests which are easy to compute and which can reject both models as well as being capable of selecting one form rather than the other. The paper is set out as follows. In Section 2 we compare some existing procedures for testing the functional form of linear and log-linear models. In Section 3 we derive new large sample tests which are based on the Lagrange multiplier approach. The possibility of using small sample tests is discussed in Section 4 and a numerical example to illustrate the use of our new tests is given in Section 5.