Financial Risk Manager Part 1

Financial Risk Manager Part 1

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Suppose that the following regression is estimated using 25 quarterly observations:

yt=β1+β2x2t+β3x3t+uty_t = \beta_1 + \beta_2 x_{2t} + \beta_3 x_{3t} + u_t

What is the appropriate critical value for a 2-sided 5% size of test of H0:β2=1H_0 : \beta_2 = 1?_

TTanishq

Explanation:

Explanation

When we have a total of k "regressors" (including a constant) and n observations, the t-test statistic will follow a t-distribution with n - k degrees of freedom.

Given:

  • n = 25 observations
  • k = 3 regressors (β₁, β₂, β₃)
  • Degrees of freedom = n - k = 25 - 3 = 22

Test Details:

  • This is a two-tailed test
  • Significance level = 5%
  • Each tail has 2.5% of the distribution
  • We need the critical value for t_{0.025, 22}

Critical Value:

Looking up the t-distribution table with 22 degrees of freedom and 2.5% in each tail gives us a critical value of 2.07.

Key Points:

  • The fact that observations are quarterly is irrelevant for the calculation
  • When testing a hypothesis about a single coefficient in a model with multiple regressors, we use a t-test
  • The t-test is NOT suitable for testing hypotheses that involve more than one parameter (those require F-tests)
  • The correct critical value is 2.07, which corresponds to option C_
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