Econometrics homework

Econometrics I

Homework #1

Student ID number: ______________________________

Name: ________________________________________

The total is measured on 100

There are eight questions:

You need to answer only five questions of your choice.

There are partial points (as defined in each question)

I want the homework returned to me by midnight on the 21st of October (on that sad say known as election day).

Copies are either to be handed back to me in class or in the box on my office door (Office DL 305 in the Dante building)

I have attached two tables at the end of this homework. They are the Z-table and T-table. I do not tell you when to use them. You have to decide when it is appropriate to use them. However, you can use “approximate values” (if the value you get is between two values in the table)

Question 1:

Assume that a relationship is linear between two variables: gender inequality and economic freedom. Gender inequality is a continuous measure of differences in socioeconomic outcomes (e.g. wages, incomes, education, health) that is presented in an index form (between 0 and 1 where 0 is no inequality and 1 is high inequality). Economic freedom is a continuous measure of the liberties of individuals to engage in economic activity. It accounts for the size of government, the enforcement of property rights and the rule of law, business regulations and trade openness (i.e. barriers to international trade like tariffs and quotas). The economic freedom measure goes from 0 to 10 where higher values denote more freedom.

Imagine now that there is this economist who comes around and tells you that more economic freedom would increase equality of outcomes between men and women. He tells you that he predicts that each additional point of economic freedom would reduce the gender inequality by 0.15. He writes the following equation for predicting gender inequality:

Where EFW is the economic freedom of the world value for country i and EGI is the estimated gender inequality index value for country i. Given that he used the data in the table below, has he estimated the effect of EFW on EGI correctly? I want to see all the elements (not the calculations per se, just the different concepts that you needed) that you need to answer this so that I know you didn’t just go in excel or stata to do it (only half the points are given for the right answer).

	EFW	EGI
Albania	7.67	0.238
Argentina	5.67	0.358
Belgium	7.51	0.048
Bulgaria	7.54	0.217
Bahamas	7.25	0.34
Canada	8.08	0.092
Egypt	5.05	0.449
United Kingdom	8.09	0.116
Spain	7.55	0.08
Estonia	7.89	0.122
Kenya	7.05	0.549
Morocco	6.69	0.482
Singapore	8.71	0.067
Papua New Guinea	6.36	0.741
Serbia	6.89	0.181
Venezuela	2.58	0.454

Question 2:

Boston and Quebec City were two important colonial cities during the eighteenth century. One was the capital of the Massachusetts colony and the other was the administrative capital of the French empire in North America until 1759 (the city was conquered in 1759 and the colony formally capitulated to the British in 1760). However, economists and economic historians have pointed out that war-related shocks affected the Quebec economy more than the Boston economy. The reason they postulate for this is that the population of the rest of the colony was relatively small compared to that of Massachusetts. When wars occurred, warfare at sea meant that both cities would be isolated from the rest of the world because ships could not get to ports. However, Boston had a much larger internal market (because of Massachusetts’ relatively large population) than Quebec did. Because of that, prices were more volatile in Quebec than in Boston. If we wanted to know whether or not it is true that prices were more volatile in Quebec than in Boston, what measure would we use and why (half the points)? Calculate that measure given the price indexes reported below (half the points)

Table 2: Price Index for Quebec and Massachusetts, 1720-1735 (where base is 1840-1845 = 1)

	Massachusetts	Quebec
1720	0.787	0.929
1721	0.740	0.803
1722	0.779	0.784
1723	0.789	0.781
1724	0.832	0.787
1725	0.985	0.802
1726	0.953	0.736
1727	0.895	0.611
1728	0.838	0.584
1729	0.829	0.629
1730	0.832	0.739
1731	0.741	0.699
1732	0.694	0.773
1733	0.689	0.732
1734	0.694	0.748
1735	0.711	0.660

Question 3:

In the file “Prison 1820.xlsx” on OWL, you will find a population of non-Canadian adult prisoners accepted to the Quebec City prison and who were born in 1820 (but not necessarily admitted at the same time). The dataset provides information about their heights in inches. Take prisoner number 93 and tell me what you can from him relative to the population he is from. What is the best single measure that would inform us about how he differs from that population (half the points)? With that measure, can you tell me how he “stands” (pun intended) relative to the whole population (half the points)?

Question 4:

In the file “GDP CO2 France.xlsx”, you will observe that there are three series. The first is the year between 1870 and 2010. The second is the GDP per capita of France for each of those years (adjusted for inflation). The third is the amount of CO2 emitted per person in France in each of those years. Using the dataset (you are free to use excel or Stata), how does GDP per capita predict CO2 emissions per capita in each year? Fill in the equation below (half the points).

If you explore the dataset, do you think this equation is an appropriate way to predict CO2? Provide an explanation for your answer (half the points).

Question 5:

Say that there is a herd of cows at a stampede (probably the one in Calgary). People must guess the exact number of cows and the mean weight of the herd. There is a challenge whereby you can win 1,000$ if you guess the number of cows and the weight right. If more than one person gets it right, the prize is shared equally. A large number of people participate in the challenge. If I share with you the idiom that there is a certain “wisdom of crowds”, how would that idiom speak to guessing the true size and mean weight of the herd? Please provide an explanation in less than 100 words.

Question 6:

Lower Canada (as Quebec was known) in 1831 was a largely agricultural society. Most individuals lived in the countryside (more than 80%). Only a small share of the population lived in cities or small towns. While it was gradually urbanizing, people tended to be reluctant to move the cities. A part of this reluctance stemmed from the fact that cities were known to be problematic in terms of health. Foreign ships would often carry diseases from abroad such as smallpox. Deficient water infrastructures made yellow fever more likely. Both diseases being contagious, the high density of population in the cities meant that they could spread faster. True, wages were higher in the cities, but this health risk was an important deterrent to moving to the cities.

In that year, the colonial government made a census that collected information about wages across the colony. Not all districts returned their schedules, but a large enough number of them did. The census can be combined with parish registers that compile the number of burials in the same year. It can also be combined with geographic information such as distance of each parish from the closest large cities and the quality of land in the area.

In the file titled “Death Rates 1831.xlsx” in OWL, you will find this information compiled as follows: death rates (per 1,000), wage rates (expressed in terms of how many bushel of wheat you could buy with one day’s wage), distance from the closest urban center (in KM) and the length of the growing season (in days).

You can use excel or Stata for this exercise. Please report how well each variable explains death rates (half the points). If you had to pick only one variable to predict death rates, which one would it be (explain why given the information given in the first paragraph) (half the points)?

Question 7:

In 1831, Lower Canada (modern day Quebec) was a largely French-speaking Catholic colony. The Catholic church is known to be a very well-run organization with a centralized structure. This stands in contrast with protestant churches that are more decentralized. This governance structure is of relevance because the virtual totality burials and births were conducted by religious organizations. However, the Catholic parishes would keep well-detailed registered that compiled burials and deaths and sent back reports to their archbishop. The archbishop would, in turn, share this information with the colonial legislature which would report the number of deaths and births per parish on a roughly annual basis in a publication called the Appendix to the Journals of the House of Assembly of Lower Canada. However, the Protestant churches (which represented roughly 20% of the colony’s population) rarely provided this information to the legislature and when they did, it was incomplete and cannot be compared with the Catholic districts. Thus, we have a large sample of parishes in the colony but it is still a sample.

In the file titled “Death Rates 1831.xlsx” in OWL, you will find this information compiled as follows: death rates (per 1,000), wage rates (expressed in terms of how many bushel of wheat you could buy with one day’s wage), distance from the closest urban center (in KM) and the length of the growing season (in days). Consider only the “Death Rates” variable (the others are related to question 6) in order to answer the following questions:

How would you go about measuring how well the mean death rate of the sample of Catholic parishes speaks to the mean of death rates for the whole colony? (Half the points, you must provide numbers, not just a verbal explanation)

What could make you doubt this answer? Provide an explanation (in less than 150 words) of what could make reluctant to say something about the colony using only the Catholic parishes (there are several possible answers that I can accept?). (Half the points).

Question 8:

We are interested in the idea of whether or not there are gains to productivity from larger farms. In the table below, you will see that we provide output per acre on the different farms of Quebec in 1861 and the average size of farms in that same year.

Given that information, can you find out how the average size of a farm best predicts output per acre (half the points)? How would you interpret that answer in light of economic theory claiming that there is a link between scale (i.e. average farm size) and productivity (output per acre) (half the points)?

Statistic	Average Size of Farm (in Acres)	Output Per Acre ($)
Mean	40.96795	9.714949
Variance	1288.224
Standard Deviation		8.290091
Min	.8	0
Max	627.8142	110.6153
Median	35.56877	7.919821
Covariance between variables	-57.6544945

Z-TABLE

T-TABLE