dataset_name: econometrics
description: "The following are multiple choice questions (with answers) about econometrics.\n\
  \nQ: 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?\n(A) 1\
  \ lag (B) 2 lags (C) 3 lags (D) 4 lags\nA: 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\u2019s 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\u2019s 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).\n\nQ: Consider the following\
  \ AR(1) model with the disturbances having zero mean and unit variance\nyt = 0.2\
  \ + 0.4 yt-1 + ut\nThe (unconditional) mean of y will be given by\n(A) 0.2 (B) 0.4\
  \ (C) 0.5 (D) 0.33\nA: 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:\n\
  unconditional 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).\n\nQ: What would be then consequences for the OLS estimator if heteroscedasticity\
  \ is present in a regression model but ignored?\n(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.\nA: 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).\n\nQ: Suppose\
  \ that a test statistic has associated with it a p-value of 0.08. Which one of the\
  \ following statements is true?\n(i) If the size of the test were exactly 8%, we\
  \ would be indifferent between rejecting and not rejecting the null hypothesis\n\
  (ii) The null would be rejected if a 10% size of test were used\n(iii) The null\
  \ would not be rejected if a 1% size of test were used\n(iv) The null would be rejected\
  \ if a 5% size of test were used.\n(A) (ii) and (iv) only (B) (i) and (iii) only\
  \ (C) (i), (ii), and (iii) only (D) (i), (ii), (iii), and (iv).\nA: Let's think\
  \ step by step. We refer to Wikipedia articles on econometrics for help. Let\u2019\
  s 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).\n\nQ: For a stationary autoregressive process, shocks\
  \ will\n(A) Eventually die away (B) Persist indefinitely (C) Grow exponentially\
  \ (D) Never occur\nA: 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)."
include: _mmlu_flan_cot_fewshot_template_yaml
task: mmlu_flan_cot_fewshot_econometrics
