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# ps2 2007 answer - EEP 118 Assignment 2 Answer Key Clair...

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Unformatted text preview: EEP 118 Assignment 2 - Answer Key Clair Null Exercise 1. Is poverty associated with the size of a city? 1. [7 points - 1 each for parts a-d, 1 for the two graphs, and 2 for comments on the graphs; 2 points are deducted for answers not written in paragraph form] In this analysis, we use data on a sample of 905 municipalities with more than 10,000 urban inhabitants from the Brazilian Census of 2000 (data available from the IBGE website www.ibge.com.br ). The majority of the municipalities (75%) have fewer than 50,000 residents, while 12% of our sample are municipalities between 50-100 thou- sand residents. Municipalities of 100-500 thousand residents constitute another 11% of the sample. There are 6 municipalities with between 1 2 and 1 million residents (0.66% of the sample) and 7 mu- nicipalities with more than 1 million residents (0.77% of the sample). Using the municipality as the level of analysis, poverty rates range from 0.01 to 0.71 (measured as the proportion of people under the poverty line), with an average of 0.27. If we consider each population category of municipalities, we nd that the largest municipalities are less poor (with average poverty rates of 0.10 and 0.14 in municipalities of more than 1 million residents and those with 1 2- 1 million residents, respectively), compared to municipalities with fewer than 50,000 residents, whose average poverty rate is 0.29. The two middle categories of city size fall in between, with an average poverty rate of 0.20 in municipalities of 50-100 thousand residents and a rate of 0.18 in municipalities with 100-500 thousand residents. We show the relationship between city size and poverty rate in the two following scatter diagrams. .2 .4 .6 .8 Poverty Rate (Headcount Ratio) Proportion Below Poverty Line 2000000 4000000 6000000 Population Poverty Rate vs. Population .2 .4 .6 .8 Poverty Rate (Headcount Ratio) Proportion Below Poverty Line 8 10 12 14 16 Log(Population) Poverty Rate vs. Log(Population) Because our sample has only a few large municipalities but so many smaller municipalities, and these municipalities have such a wide range of poverty rates, the graph in terms of level of population is di cult to read. Using log of population helps to spread out the distribution of municipalities on the x axis, but it is still di cult to say what sort of relationship there is between population and poverty rates. We should use the graph in terms of level of population if we think that an increase of 1000 residents has the same e ect on a municipality which originally had 10,000 residents as on a munici- pality that originally has 1 million residents. If instead we think that small changes in population in smaller cities are as relevant as the same proportional change in the population of a larger city (which would mean a bigger increase in population in level terms in the larger city), then we should use the graph in terms of log of population. For example, if we thought that an increase of 1000 residents ingraph in terms of log of population....
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