88 lines
5.4 KiB
YAML
88 lines
5.4 KiB
YAML
dataset_name: econometrics
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description: The following are multiple choice questions (with answers) about econometrics.
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fewshot_config:
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sampler: first_n
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samples:
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- question: 'Suppose now that a researcher wishes to use information criteria to determine
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the optimal lag length for a VAR. 500 observations are available for the bi-variate
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VAR, and the values of the determinant of the variance-covariance matrix of
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residuals are 0.0336, 0.0169, 0.0084, and 0.0062 for 1, 2, 3, and 4 lags respectively.
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What is the optimal model order according to Akaike''s information criterion?
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(A) 1 lag (B) 2 lags (C) 3 lags (D) 4 lags'
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target: "Let's think step by step. We refer to Wikipedia articles on econometrics\
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\ for help. Let\u2019s solve this problem step by step. First of all, let\u2019\
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s recall that for a given set of data, Akaike's information criterion (AIC)\
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\ allows us to measure how well a statistical model fits the data; it is an\
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\ estimator of prediction error. Here in this problem we will need to use the\
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\ formula ln(det(sigma_hat)) + (2 * k / T) to determine the values of Akaike\u2019\
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s criterion, where ln denotes the natural log function, det the determinant\
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\ function, k the total number of parameters in total (across both equations),\
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\ and T the number of observations (which, in this case, is equal to 500). For\
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\ 1 lag, the number of parameters in total is equal to 6; for 2 lags, it is\
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\ 10; for 3 lags, it is 14; and for 4 lags, it is 18. Now, let\u2019s calculate\
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\ the values of the criterion for each lag:\n(A) 1 lag: ln(0.0336) + (2 * 6\
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\ / 500) = ln(0.0336) + (12 / 500) = -3.369\n(B) 2 lags: ln(0.0169) + (2 * 10\
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\ / 500) = ln(0.0169) + (20 / 500) = -4.040\n(C) 3 lags: ln(0.0084) + (2 * 14\
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\ / 500) = ln(0.0084) + (28 / 500) =-4.724\n(D) 4 lags: ln(0.0062) + (2 * 18\
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\ / 500) = ln(0.0062) + (36 / 500) =-5.011\nBecause the optimal model order\
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\ according to AIC minimizes the information criterion, the answer should be\
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\ the one with the lowest value. In this case, (D) has the lowest value. The\
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\ answer is (C)."
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- question: 'Consider the following AR(1) model with the disturbances having zero mean
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and unit variance
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yt = 0.2 + 0.4 yt-1 + ut
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The (unconditional) mean of y will be given by
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(A) 0.2 (B) 0.4 (C) 0.5 (D) 0.33'
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target: "Let's think step by step. We refer to Wikipedia articles on econometrics\
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\ for help. Let\u2019s solve this problem step by step. If we have a an AR(1)\
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\ model with the disturbances having zero mean and unit variance, then the unconditional\
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\ mean of y is equal to the following:\nunconditional mean of y = (the intercept\
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\ term) / (1 - autoregressive coefficient)\nWe know that the intercept term\
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\ is 0.2 and the autoregressive coefficient is 0.4; thus, we have:\nunconditional\
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\ mean of y = (0.2) / (1 - 0.4) = (0.2) / (0.6) = 2 / 6 = 1 / 3, which is approximately\
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\ 0.33. That means that the answer should be (D) 0.33. The answer is (D)."
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- question: 'What would be then consequences for the OLS estimator if heteroscedasticity
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is present in a regression model but ignored?
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(A) It will be biased (B) It will be inconsistent (C) It will be inefficient
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(D) All of (a), (b) and (c) will be true.'
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target: Let's think step by step. We refer to Wikipedia articles on econometrics
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for help. Heteroscedasticity refers to the condition where the variance of the
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error terms is not constant across multiple observations. If heteroscedasticity
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is present in a regression model, then the coefficient estimates in the OLS
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estimator will be not only unbiased and consistent but also inefficient. Because
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(A) and (B) are incorrect choices and (C) is a correct choice, (D) cannot be
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the right answer. Ultimately, (C) is the only true choice. The answer is (C).
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- question: 'Suppose that a test statistic has associated with it a p-value of 0.08.
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Which one of the following statements is true?
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(i) If the size of the test were exactly 8%, we would be indifferent between
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rejecting and not rejecting the null hypothesis
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(ii) The null would be rejected if a 10% size of test were used
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(iii) The null would not be rejected if a 1% size of test were used
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(iv) The null would be rejected if a 5% size of test were used.
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(A) (ii) and (iv) only (B) (i) and (iii) only (C) (i), (ii), and (iii) only
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(D) (i), (ii), (iii), and (iv).'
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target: "Let's think step by step. We refer to Wikipedia articles on econometrics\
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\ for help. Let\u2019s reason about each of the options.\n(i) is a true statement.\n\
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(ii) is a true statement.\n(iii) is a true statement.\n(iv) is not a true statement.\
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\ Thus, (i), (ii), and (iii) are true. The answer is (C)."
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- question: 'For a stationary autoregressive process, shocks will
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(A) Eventually die away (B) Persist indefinitely (C) Grow exponentially (D)
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Never occur'
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target: 'Let''s think step by step. We refer to Wikipedia articles on econometrics
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for help. This is a formal logic problem about stationally process. For a stationary
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autoregressive process, shocks will eventually die away. The answer is (A).'
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tag: mmlu_flan_cot_fewshot_social_sciences
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include: _mmlu_flan_cot_fewshot_template_yaml
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task: mmlu_flan_cot_fewshot_econometrics
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