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- 10.14 Total economic output in three years. The n - vector xt denotes the economic output of a country in n different sectors, in yeart. An economist models the economic output using a linear dynamical system model xt+1 = Axt, where A is an n \times n matrix. Assuming her model is correct, find an expression for the total economic output in yeart + 3, in terms of xt and A. (The total economic output is the sum of the economic output in the n sectors.)Assume that the average or mean monthly household consumption expenditure for Malaysia rose from RM3,578 in 2018 to RM4,033 in 2020, growing 6% per annum at nominal value, according to the statistics department. However, in terms of real value — which refers to the constant price using the Consumer Price Index with the base year 2014 as the deflator — annual growth rate is 3.9% for the same period, mentioned on its Household Expenditure Survey Report 2020. b) i. Use the aggregate expenditures model to show how government fiscal policy could eliminate either a recessionary expenditure gap or an inflationary expenditure gap. ii. Explain how equal-size increases in G and T could eliminate a recessionary gap and how equal-size decreases in G and T could eliminate an inflationary gap.3) true or false and give a brief explanation on why its correct or wrong. a) To correct for seasonality in daily data, we add seven dummy variables for eachday of the week to the model. b) In time series models, OLS estimators are consistent under thecontemporaneous exogeneity assumption. c)Suppose yt is an I(1) process. Does This means that yt is a stationary process.
- Q2B. Which of the following are limitations of using Impulse Response Functions(IRFs) in time series analysis?i. IRFs are only valid for linear time series models.ii. IRFs assume that the underlying time series is stationary.iii. IRFs can provide information about the short-term dynamics of the relationshipbetween variables, but they do not capture longer-term effects or otherimportant aspects of the relationship.iv. IRFs depend on the specification of the model used to estimate the relationshipbetween variables.4- The manager of Collins Import Autos believes the number of cars sold in a day(Q) depends on two factors: (1) the number of hours the dealership is open (H) and (2) the number of salespersons working that day (S ). After collecting data for two months (53 days), the manager estimates the following log-linear model: Q = aHbSc ----- a. Explain how to transform this log-linear model into a linear form that can be estimated using multiple regression analysis. b. How do you interpret coefficients b and c? If the dealership increases the number of salespersons by 20 percent, what will be the percentage increase in daily sales? c. Test the overall model for statistical significance at the 5 percent significance level.We have estimated the impact of gross domestic product (GDP), energy consumption (ENERGY) and population (POP) on CO2 emiisions (CO2) in Cyprus. The results are as follows;Dependent Variable: CO2Method: Least SquaresDate: 04/20/17 Time: 09:46Sample: 1990 2013Included observations: 24 Write down the economic function for the above estimation by using the information obtained from above table b- Write down the economic model for the above estimation by using the information obtained from above table . c- Write down the econometric model for the above estimation by using the information obtained from above table d- Write down the least squares line by using the information obtained from above tablee- Explain what each coefficient of the least squares line indicates
- The number of pending corporate fraud cases in federal court stood at 545 at the beginning of 2008 (t = 0). The number of cases had grown to 726 at the beginning of 2012. Assume the growth has been approximately linear. Develop the equation of the line that describes this linear growth. Then use that linear equation to estimate the number of cases pending at the beginning of 2014, assuming that the linear growth continues at the same rate.A researcher has a sample of 6 annual observations {94, 104, 102, 99, 111 and 107} for the CPI in country Z for the period 2015 to 2020, and wants to forecast CPI for the years 2021, 2022 and 2023. The researcher uses 3 different forecasting models: A, B and C. Model A is an AR(1) model with no drift and with an estimated autoregressive coefficient = 0.7. Model B is a MA(1) model with no constant and with an estimated MA coefficient = -0.4 (note the minus !). Model C is a random walk model with no drift. The error terms over the 2015-2020 period were estimated to have the values: {3, -1, 2, 4, -3, 1}. a. Compute the 2021, 2022 and 2023 forecasted values for the consumer price index based on the three models. Show the formulas and the details of your calculations, and explain all the related symbols. b. Suppose that the actual values of the CPI over the 2021, 2022 and 2023 were {108, 114, 105}. Calculate the Root mean square error of the three model forecasts over the 2021-2023…If the annual rate of world oil consumption t years after 1970 is modeledby the equation R(t) = 16.1e^.07t (billions of barrels per year), how much total oil (net change) was used between 1976 and 1980?
- Assume a model economy with the following parameters: C= 100+0.25Yd I=100+0.5Y-3000i G=125 T=100 (M/P)d= 6Y-24000i (M/P)s=4500 Derive the IS and LM relationThe Questor Corporation has experienced the following sales pattern over a 10-year period: Compute the equation of a trend line (similar to Equation 5.4) for these sales data to forecast sales for the next year. (Let 2004=0,2005=1, etc., for the time variable.) What does this equation forecast for sales in the year 2014? Use a first-order exponential smoothing model with a w of 0.9 to forecast sales for the year 2014.Estimate the double-log (log linear) time trend model for log cruise ship arrivals against log time. Estimate a linear time trend model of cruise ship arrivals against time. Calculate the root mean square error between the predicted and actual value of cruise ship arrivals. Is the root mean square error greater for the double log non-linear time trend model or for the linear time trend model?