ETC2410 Prac Exam 2019 PDF

A screenshot of a document Description automatically generated - Dataset A is panel data since it tracks the same individuals over multiple years. - Dataset B is also panel data because it tracks multiple entities (different countries) over multiple years, not just one. ![A white back...

A screenshot of a document Description automatically generated - Dataset A is panel data since it tracks the same individuals over multiple years. - Dataset B is also panel data because it tracks multiple entities (different countries) over multiple years, not just one.  - Independent and Identically Distributed (i.i.d.) means that each observation is independent of the others and drawn from the same probability distribution. - Time series data are generally not i.i.d. since observations are often correlated with one another across time. A math equations on a white background Description automatically generated  A screenshot of a math problem Description automatically generated  A math equations on a white background Description automatically generated  A white paper with black text Description automatically generated  A white sheet with black text and numbers Description automatically generated  A white background with black text Description automatically generated  A white text with black text Description automatically generated  a.  A white and black text on a white sheet Description automatically generated i. - 2.837: the intercept -- this is the expected value of log(*WAGE*) for a person with 12 years of education and no experience (EDUC -- 12 and EXPER are zero). The actual value is e\^2.837 = \$17.064. - 0.095: for each additional year of education, the predicted wage increases by 100 \* 0.095 = 9.5%. - 0.055 and -0.001: these values are not interpretable by themselves since they work together to determine the overall impact of experience on wage. - For any given level of experience, keeping education constant, the total impact of experience on wage is found by combining both terms: Effect of EXPER on log(*WAGE*) = 0.055 -- 2 \* 0.001 \* EXPER Due to the diminishing returns, there's a point where the positive impact of experience on wage stops growing and starts to decline. We can find this point by setting the combined effect equal to zero (when additional experience no longer increases wage). Hence, log (*WAGE*) reaches a maximum when: 0.055 -- 2 \* 0.001 \* EXPER = 0 EXPER = 0.055 / 2 \* 0.001 = 27.5 years (The 0.055 means that experience initially has a positive impact on wage and -0.001 pulls this effect back down as experience increases, reducing the impact of each additional year). ii. No. In order to do so, we need to be confident that all factors that can affect both education and wage are controlled for. The interpretation of the coefficient (EDUC -- 12) assumes that education alone is causing the increase in wages. However, in reality, other factors also come into play. For instance, intellectual ability affects both wages and education, and experience cannot control for intellectual ability. If such factors are omitted from the model, the results may be biased. iii. \*An auxiliary model is a secondary regression model that helps us test for specific properties of the main model's residuals (errors), like heteroskedasticity (when the variance of errors isn't constant across observations).  a. i. A time series (Y~t~) is covariance stationary if its mean and variance are finite and time invariant -- do not depend on *t.* Additionally, the covariance between y~t~ and any of its lags only depend on the lag, and not *t.* ii. As evident from the graph, the S&P500 index is not covariance stationary as there is a clear upward trend over time, indicating that its mean is not constant and depends on *t.* A stationary time series should however, fluctuate around a constant mean. b. i. The negative coefficients for Q~1t,~ Q~2t~ and Q~3t~ indicate that the intercepts in the first, second, and third quarters are smaller than the intercept in the fourth quarter. Therefore, all else being equal, tourist arrivals are predicted to be lower in these three quarters compared to the fourth quarter. Furthermore, the negative sign of coefficient of AUD suggests that after accounting for the trend (*t*) and seasonal variations (the dummy variables), tourist arrivals are predicted to decrease as the value of the Australian dollar in the previous quarter increases. ii. Null hypothesis: H~0~: B~2~ = 0 and B~3~ = B~4~ Alternative hypothesis: H~1~: B~2~ ≠ 0 or B~3~ ≠ B~4~ (at least one of these restrictions is false) To test these hypotheses, we will use an F-test for multiple linear restrictions:  - Where, - SSR (restricted) = n/a - SSR (unrestricted) = n/a - q = number of restrictions = 2 - n = number of observations - k = number of coefficients in the unrestricted model = 5 - Degrees of freedom (df) = n -- k -- 1 = 109 -- 5 -- 1 = 103