PS_1_Solutions - Problem 1: a) SW "Review the Concepts"...

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Problem 1: a) SW “Review the Concepts” 1.1, 1.3, 2.1, 2.4 Concept 1.1 We would have to select students who attend microeconomics classes into two groups (randomly) and have one group study more hours than the other group. It is difficult to implement this because we cannot make the assignment random unless we force the students to study more or less hours. Otherwise, students will self-select into the treatment or control group, and the so-called ‘selection bias’ will arise. Concept 1.3 a. We would randomly assign workers into two groups, the ‘treatment’ group and the ‘control’ group. The individuals in the treatment group will be given training while those in the ‘control’ group will not. We then measure the productivity of all workers and see whether there are systematic differences in productivity between the groups. b. We could study this effect in a cross section of workers if we have data on productivity, number of hours of training received, and other worker characteristics which would impact productivity. To identify the causal effect of hours of training on productivity, we would need to make sure that there are no omitted variables from the analysis. In other words, we should ensure that any other factors omitted from the analysis which impact productivity are not correlated with the number of hours of training. c. We could study this effect if we had data for the productivity (output per worker per hour) and the number of hours of training offered to workers for the observational unit (e.g. a country or industry) over many time periods. In the time series regression, we would need to make sure that the error term does not include ‘other factors’ that are correlated with number of hours of training given to workers and average productivity. d. Finally, we would like to use in this exercise a dataset with a panel structure, data for many workers/firms over multiple time periods. Concept 2.1 A random variable is a mapping (function) from the state space onto the real line. Thus, all the examples (a)-(e) can be thought of as random variables. Concept 2.4 The average weight of the students in the sample with n =4 will generally not equal 145 lbs. if it does, it can only be coincidentally so. The sample average, Y-bar, is a random variable because it is a linear combination of n random variables, where n denotes the size of the sample.
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b) Suggest a controlled randomized experiment to a causal question you are interested in. be specific about the causal effect, the right counterfactual, and what alternative to an experiment you see. The example below is drawn from “Women as policy makers: evidence from a randomized policy experiment in India” by R. Chattopadhyay and E. Duflo, Nov 2003 Economic question: Does the gender of a community council heads affect the types of public goods provided by the council? In other words, do council heads tend to invest in public goods more relevant to their gender? In effect, we are trying to identify the causal
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This note was uploaded on 04/15/2008 for the course ECON 3412 taught by Professor Vonwachter during the Spring '08 term at Columbia.

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PS_1_Solutions - Problem 1: a) SW "Review the Concepts"...

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