Econometrics Models Case Study

ECONOMETRICS (ECON 441) Semester 2, 2020-2021 CASE STUDY Problem I: An economist has collected the data on output and inputs from 30 farmers involved in the production of tomato to estimate the Cobb-Douglas Production Function as: Y = AX 11 X 2 2 X 3 3 , where Y = Output (quintals of tomato), and X1, X2 and X3 are the inputs which respectively measure Land (hectors of land ), Labor (total labor hours), and Capital (total machine hours). 1. Convert Cobb-Douglas production function stated above into econometric model for the purpose of estimation 2. Write down the formula for the output elasticity with respect to the input land. What do you mean by it? 3. Estimate the regression model using EXCEL solver and write down the estimated equation. 4. Write down the Estimated Equation in Multiplication form. 5. A farmer has a land area of 0.8 hector and he plans to devote 1600 labor hours and 130 machine hours. What is the expected production of potato by the farmer? 6. Interpret the coefficients of all inputs (Download Data I.xls) Problem II- A researcher has collected the data on crime rate from 50 cities/villages around the globe.

He wants to show the impact of two quantitative variables –such as POV (% of population in country living below the poverty level) and POPDENS (population per square mile) along with two qualitative variables – Area (defined as Rural/Urban) and Region (defined as Asian/Non-Asian). 1. Write down the econometric model which defines the problem above. 2. Use the EXCEL solver to estimate the linear regression model and write down the estimated equation. 3. Write down the estimated equation for each group separately. 4. Is the overall model significant? Test the relevant hypothesis. 5. Does the area have any significant impact on crime rate? Test the relevant hypothesis? 6. Interpret the coefficient of the variable “Region”. 7. Does the poverty have any significant impact on crime rate? Test the relevant hypothesis and interpret the value of its coefficient. 8. What is the expected rate of crime of a city which is categorized as urban area of country X?

Population density of the country X is 140 and the % of population below the poverty line is 11.5. Country X is in Asian region. (Download Data II.xls) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Potato Production Land 11165,2 8960 10046,6 11354,8 12800 10739,8 12373,4 10880 11077 11636,4 12116,6 11789,4 12990,2 10779 10105,2 12849,4 11000 11265,4 12753,6 11520 10322,6 10666,6 11924 11377,8 10427 8000 12108,2 10526,4 9600 11402,4 6,4 0,5 3,1 1,2 2,1 1,5 3,4 0,4 1,1 3,6 2,1 3,1 2 2,9 0,6 2,6 0,6 3,9 3,6 1,5 0,3 0,3 2,6 4,5 1,8 0,3 0,7 1,5 0,4 0,3 Labor Capital 1401,9 436,1 1360 260 910,9 314 2500 399,2 1428,6 504,8 2191,8 328,8 1866,7 623,3 1350 467,5 1346,2 423,1 1376,3 444,4 1504,9 427,2 1611,8 434,2 1608,9 490,1 1210,5 270,2 1579 289,5 1776,1 382,2 2343,8 343,8 1466,8 392,9 1811,6 493,8 1600 440 2258,1 354,8 2333,3 366,7 2053,2 460,8 966,7 355,6 2247,2 405,1 2187,5 343,8 1959,5 446 2368,4 361,8 1650 305 1149,4 270,1 Y = Output (quintals of tomato) X1=Land (hectors of land ) X2=Labor (total labor hours) X3=Capital (total machine hours) (quintals of tomato) ectors of land ) total labor hours) (total machine hours) Crime 2533 2820 2905 2958 3154 3260 3271 3845 3846 3972 4054 4116 4117 4163 4386 4418 4465 4485 4499 4560 4790 4801 4811 4872 4879 4894 4975 5095 5237 5240 5294 5453 5527 5551 5568 5618 5652 5766 5903 5952 6107 6180 6193 6266 6277 pov 22.2 11.2 9.9 14.2 15.4 20.4 13.2 13.1 10.3 10.0 12.6 9.7 10.3 13.3 11.6 24.7 12.2 13.0 11.2 8.5 14.9 10.9 20.0 10.2 17.4 10.7 13.1 16.1 10.7 19.6 19.9 15.4 9.9 16.4 9.1 13.6 14.4 11.8 18.7 12.1 9.7 9.8 13.5 17.4 8.0 popdens 75.6 9.2 125.5 9.4 40.2 95.4 268.8 13.3 50.4 62.2 92.8 163.9 20.9 4.8 56.7 56.3 159.3 270.8 956.9 676.4 5.8 1062.0 46.6 358.2 82.5 767.1 30.9 76.0 22.6 123.7 47.1 166.8 34.4 385.3 1.1 210.4 142.6 31.6 121.0 78.9 507.9 12.6 119.4 13.3 182.4 AREA Rural Rural Rural Rural Rural Rural Rural Rural Rural Rural Rural Rural Urban Urban Urban Urban Urban Urban Urban Urban Urban Urban Urban Urban Urban Rural Rural Rural Rural Rural Rural Rural Rural Rural Rural Rural Rural Urban Urban Urban Urban Urban Urban Urban Urban Region Asian Asian Asian Asian Asian Asian Asian Asian Asian Asian Asian Asian Asian Asian Asian Asian Asian Asian Asian Asian Asian Asian Asian Asian Asian Non-Asian Non-Asian Non-Asian Non-Asian Non-Asian Non-Asian Non-Asian Non-Asian Non-Asian Non-Asian Non-Asian Non-Asian Non-Asian Non-Asian Non-Asian Non-Asian Non-Asian Non-Asian Non-Asian Non-Asian ASSIGNMENT 3 crime = total crimes in 1993 / 1 pov = % of population in count popdens = population per squa Area= Region= 6439 6457 6847 7432 8351 11761 17.4 18.2 26.4 15.4 17.8 26.4 68.8 200.1 98.6 34.6 253.3 9482.8 Urban Urban Urban Urban Urban Urban Non-Asian Non-Asian Non-Asian Non-Asian Non-Asian Non-Asian ASSIGNMENT 3 PROBLEM 3 crime = total crimes in 1993 / 100,000 population by country pov = % of population in country living below the poverty level in 1993 popdens = population per square mile Rural/Urban Asian/Non-Asian.

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