"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’s solve this problem step by\
  \ step. First of all, let’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’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’s 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\n\
  The (unconditional) mean of y will be given by\n(A) 0.2 (B) 0.4 (C) 0.5 (D) 0.33\n\
  A: Let's think step by step. We refer to Wikipedia articles on econometrics for\
  \ help. Let’s 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).\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’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).\n\n"
"group": "mmlu_flan_cot_fewshot_social_sciences"
"include": "_mmlu_flan_cot_fewshot_template_yaml"
"task": "mmlu_flan_cot_fewshot_econometrics"
