Abstract
1. Testing Restrictions on Parameters. For those who believe that economic hypotheses have to be confirmed by empirical observations, hypotheses testing is an important subject in economics. As a classical example, when an economic relation is represented by a linear regression model:
where Y is a column vector of n observations on the dependent variable y, X is an n × k matrix with each column giving the corresponding n observations on each of k explanatory variables (which typically include a column of ones), β is a column of k regression coefficients and ε is a vector of n independent and identically distributed residuals with mean zero and variance σ2, it is of interest to test a hypothesis consisting of m linear restrictions on β:
where R is m × k and r is m × 1. A most common case occurs when there is only one restriction (m = 1) and (2) is reduced to βi = 0, the hypothesis being that the ith explanatory variable has no effect on y.
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© 1990 Palgrave Macmillan, a division of Macmillan Publishers Limited
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Chow, G.C. (1990). Hypothesis Testing. In: Eatwell, J., Milgate, M., Newman, P. (eds) Time Series and Statistics. The New Palgrave. Palgrave Macmillan, London. https://doi.org/10.1007/978-1-349-20865-4_14
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