dataset_name: econometrics
description: The following are multiple choice questions (with answers) about econometrics.
fewshot_config:
  sampler: first_n
  samples:
  - question: 'Suppose now that a researcher wishes to use information criteria to determine
      the optimal lag length for a VAR. 500 observations are available for the bi-variate
      VAR, and the values of the determinant of the variance-covariance matrix of
      residuals are 0.0336, 0.0169, 0.0084, and 0.0062 for 1, 2, 3, and 4 lags respectively.
      What is the optimal model order according to Akaike''s information criterion?

      (A) 1 lag (B) 2 lags (C) 3 lags (D) 4 lags'
    target: "Let's think step by step. We refer to Wikipedia articles on econometrics\
      \ for help. Let\u2019s solve this problem step by step. First of all, let\u2019\
      s recall that for a given set of data, Akaike's information criterion (AIC)\
      \ allows us to measure how well a statistical model fits the data; it is an\
      \ estimator of prediction error. Here in this problem we will need to use the\
      \ formula ln(det(sigma_hat)) + (2 * k / T) to determine the values of Akaike\u2019\
      s criterion, where ln denotes the natural log function, det the determinant\
      \ function, k the total number of parameters in total (across both equations),\
      \ and T the number of observations (which, in this case, is equal to 500). For\
      \ 1 lag, the number of parameters in total is equal to 6; for 2 lags, it is\
      \ 10; for 3 lags, it is 14; and for 4 lags, it is 18. Now, let\u2019s calculate\
      \ the values of the criterion for each lag:\n(A) 1 lag: ln(0.0336) + (2 * 6\
      \ / 500) = ln(0.0336) + (12 / 500) = -3.369\n(B) 2 lags: ln(0.0169) + (2 * 10\
      \ / 500) = ln(0.0169) + (20 / 500) = -4.040\n(C) 3 lags: ln(0.0084) + (2 * 14\
      \ / 500) = ln(0.0084) + (28 / 500) =-4.724\n(D) 4 lags: ln(0.0062) + (2 * 18\
      \ / 500) = ln(0.0062) + (36 / 500) =-5.011\nBecause the optimal model order\
      \ according to AIC minimizes the information criterion, the answer should be\
      \ the one with the lowest value. In this case, (D) has the lowest value. The\
      \ answer is (C)."
  - question: 'Consider the following AR(1) model with the disturbances having zero mean
      and unit variance

      yt = 0.2 + 0.4 yt-1 + ut

      The (unconditional) mean of y will be given by

      (A) 0.2 (B) 0.4 (C) 0.5 (D) 0.33'
    target: "Let's think step by step. We refer to Wikipedia articles on econometrics\
      \ for help. Let\u2019s solve this problem step by step. If we have a an AR(1)\
      \ model with the disturbances having zero mean and unit variance, then the unconditional\
      \ mean of y is equal to the following:\nunconditional mean of y = (the intercept\
      \ term) / (1 - autoregressive coefficient)\nWe know that the intercept term\
      \ is 0.2 and the autoregressive coefficient is 0.4; thus, we have:\nunconditional\
      \ mean of y = (0.2) / (1 - 0.4) = (0.2) / (0.6) = 2 / 6 = 1 / 3, which is approximately\
      \ 0.33. That means that the answer should be (D) 0.33. The answer is (D)."
  - question: 'What would be then consequences for the OLS estimator if heteroscedasticity
      is present in a regression model but ignored?

      (A) It will be biased (B) It will be inconsistent (C) It will be inefficient
      (D) All of (a), (b) and (c) will be true.'
    target: Let's think step by step. We refer to Wikipedia articles on econometrics
      for help. Heteroscedasticity refers to the condition where the variance of the
      error terms is not constant across multiple observations. If heteroscedasticity
      is present in a regression model, then the coefficient estimates in the OLS
      estimator will be not only unbiased and consistent but also inefficient. Because
      (A) and (B) are incorrect choices and (C) is a correct choice, (D) cannot be
      the right answer. Ultimately, (C) is the only true choice. The answer is (C).
  - question: 'Suppose that a test statistic has associated with it a p-value of 0.08.
      Which one of the following statements is true?

      (i) If the size of the test were exactly 8%, we would be indifferent between
      rejecting and not rejecting the null hypothesis

      (ii) The null would be rejected if a 10% size of test were used

      (iii) The null would not be rejected if a 1% size of test were used

      (iv) The null would be rejected if a 5% size of test were used.

      (A) (ii) and (iv) only (B) (i) and (iii) only (C) (i), (ii), and (iii) only
      (D) (i), (ii), (iii), and (iv).'
    target: "Let's think step by step. We refer to Wikipedia articles on econometrics\
      \ for help. Let\u2019s reason about each of the options.\n(i) is a true statement.\n\
      (ii) is a true statement.\n(iii) is a true statement.\n(iv) is not a true statement.\
      \ Thus, (i), (ii), and (iii) are true. The answer is (C)."
  - question: 'For a stationary autoregressive process, shocks will

      (A) Eventually die away (B) Persist indefinitely (C) Grow exponentially (D)
      Never occur'
    target: 'Let''s think step by step. We refer to Wikipedia articles on econometrics
      for help. This is a formal logic problem about stationally process. For a stationary
      autoregressive process, shocks will eventually die away. The answer is (A).'
group: mmlu_flan_cot_fewshot_social_sciences
include: _mmlu_flan_cot_fewshot_template_yaml
task: mmlu_flan_cot_fewshot_econometrics
