The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Hypothesis Testing

  • Gregory C. Chow
Reference work entry


For those who believe that economic hypotheses have to be confirmed by empirical observations, hypothesis testing is an important subject in economics. As a classical example, when an economic relation is represented by a linear regression model:
$$ Y= X\beta +\upvarepsilon $$
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:
$$ R\beta =r $$
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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© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Gregory C. Chow
    • 1
  1. 1.