,, correct answers only
The following questions relate to the Bayesian extensive forth game given on tule a bolow. 9 ) convert this game into Bayesian nominal form. by Find a pure strategy Bayesian Hash equilibrium of this game . A X 3, 1 1/ 2 1 5 Nature 513 1 Game Thee for the problem aboveConsider an economy that produces two goods F and M with a single factor of production, labor, denoted by L. The total labor force of the economy is given by L. While good F exhibits constant returns to scale, production of good M exhibits increasing returns to scale. The production functions are: F = 6L ;5>0 M : a(L)L ;a'>0 Show that the PPF for this economy is " bowed in" towards the origin. Consider a game of n players in which each player chooses an effort level 8, 20,i=1, ...,n. The marginal benefit of effort for player i depends on the effort exerted by the other players. In particular, the payoff of player i is: u , ( 8 , , 8 , ) = de, WEE, 2 j=1,j#1 where parameters a, > 0, w, 2 0 are commonly known for all i and j. The players choose their effort levels simultaneously and independently. (a) Solve for the FOC that maximises the effort of player i. [16] (b) Solve for a best reply of player i. [17]+ 75% High-school dropout rates and performance at graduation by score at entrance exam Grade at entrance exam Percent that dropped out from Score on the final exam at - cutoff score for admission high school end of high school 50 0 0 62 elite schools Admitted in 0.53 0.45 51.0 0.50 4810 0 30 0.20 Not admitted in elite schools 42 5 0.25 0.17 45.0 011 Source: Adapted from the analysis of de lanwry, Dustan, Sadoulet (b) Draw two regression lines (Excel commands: Chart, Add linear trend line in Excel, Display equation on graph) separately for the points above the cutoff score (i.e., for those admitted to the elite schools) and for those below the cutoff score (i.e., not admitted to elite schools). Measure the "discontinuity" that you observe at the limit at the point where students were just admitted, i.e., the vertical difference in the two trend lines evaluated at the cutoff. (c) Explain why this may be a credible measure of the causal impact of attending an elite school on the risk of not graduating from high school. In what sense is it a "local" treatment effect? What are some of the factors that might lead to a different impact for students with entrance exam scores far above the cutoff? (d) Repeat the analysis as in question (1b) using the score on the final exam at the end of high school as the dependent variable. Report the impact of attending an elite school on final exam scores at the end of high school. (e) Discuss the trade-off faced by students upon deciding whether to attend an elite school. (f) What is the condition for the validity of this method, and what does this imply about the characteristics of individuals around the cutoff? Discuss what data would you need to have to test that this condition applies and what analysis would you do to support it. Report your results using two graphs: one for the graduation rate and the other for the score on the final exam at the end of high school.1, Impact Evaluation using Regression Discontinuity Mexico City has a very large public school system, which accepts about 300, 000 stu- dents each year. Within that system 16 high schools affiliated with the Instituto Polite- nico Nacional (IPN) are considered to be elite schools, Many parents and students will probably consider that admission to an elite school promises a more successful ex- perience and higher rewards. This may be true, but there is also a substantial risk, especially for the weaker students, that they may fail in that school. And failing to complete high school - even from an elite school - is likely to be a worse outcome than completing a lower level high school. The purpose of the paper "Flourish or Fail? The Risky Reward of Elite High School Admission in Mexico City" (by Alain de Janvry, Andrew Dustan, and Elisabeth Sadoulet) is to evaluate the rewards and risks of being admitted to one of Mexico City's elite schools. The identification strategy to enable the estimation of a causal effect is based on the admissions system. This is a system whereby . students express their choice (through a selection and ranking of 20 schools they would like to attend). . take an exam at the end of junior high school, and . are admitted in decreasing order from the student with the highest score to the one with the lowest score. Each student is assigned to the most preferred school that has seats available. Consider now the IPN elite schools and all the stufents that requested admission to these schools. The schools admitted the best students first and then students with descending scores until they filled up all the slots in the schools, Let "cutof" be the lowest score that they could admit. Students with scores at this level or just above were "barely admitted" while students below this level were "barely rejected" and had to go to a non-elite school. The following table records their dropout rates from high school and for those that did not drop out, their score on the final exam at the end of high school, three years later. (a) Make a graph with the grade at entrance exam and cutoff score for elite school admission on the horizontal axis and dropout rate on the vertical axis. What is the overall relationship between grade at entrance exam and dropout rate? Does it make sense
