Econ questions

Econometrics I

Homework #1

Student ID number: ______________________________

Name: ________________________________________

The total is measured on 50

There are eight questions:

You need to answer only seven questions of your choice.

There are partial points (as defined in each question)

Two of the seven questions you answer are considered “bonus” questions.

I want the homework returned to me by beginning of class on the 2nd of December

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 (10 points): Here is a sample of fictitious countries in a fictitious year. Economists have long argued that reductions in the share of the total labor force employed in agriculture are associated with increases in per capita incomes. Simultaneously, more educated workforces (measured in years of schooling) lead to higher incomes. However, more educated workforces are less likely to be involved in agriculture.

How would you write the regression prediction (i.e. how would you predict the values of real per capita given the variations in employment share in agriculture and average years of schooling?) (5 points)? Are the two independent variables statistically significant from zero at the 5% level (half the points if you show me why by setting up and performing the hypothesis test that their effects on real per capita income are different from zero).

Real Per Capita Income	Employment Share in Agriculture	Average Years of Schooling
6	9	8
8	10	13
8	8	11
7	7	10
7	10	12
12	4	16
9	5	10
8	5	10
9	6	12
10	8	14
10	7	12
11	4	16
9	9	14
10	5	10
11	8	12

Question 2 (10 points): The table below provides you with a sample of variables. There is an independent variable (X), a dependent variable (Y) and the predicted value of that dependent variable (. From this table, with the exception of the estimators themselves, extract two valuable pieces of information that relate to hypothesis testing and three that relates to the goodness of fit, provide them (2 points each)

	X	Y
	1.00	1.00	1.16
	2.00	2.00	1.635
	3.00	1.30	2.11
	4.00	3.75	2.585
	5.00	2.25	3.06

Question 3 (10 points): The table below presents the value of aggregate consumption and disposable income in a fictitious country between 2008 and 2019. Disposable income is defined as the earned income of an individual (i.e. wages, salaries, profits, rents paid, inheritance sums, interest earned, dividends received) after taxes (i.e. including income taxes, consumption taxes etc.) net of transfers (i.e. subsidies to households, in-kind help by governments etc.). If workers become more productive, their disposable incomes go up. If workers enjoy a reduction in their tax rates, their disposable incomes go up. In both cases, they can consume more goods and services. On the aggregate, an increase in disposable income increases consumption in the aggregate. Given the information in table below, if a tax cut of 1M$ was to implemented, what would be the effect on aggregate consumption (half the points)? Is that effect significant (half the points)?

Year	Aggregate Consumption (M$)	Aggregate Disposable Income (M$)
2008	102	114
2009	106	118
2010	108	126
2011	110	130
2012	122	136
2013	124	140
2014	128	148
2015	130	156
2016	142	160
2017	148	164
2018	150	170
2019	154	178

Question 4 (10 points): A military official at the department of national defence in Ottawa (Canada’s worst city) attempts to grade the performance of cadets at the Royal Military College in Kingston (Canada’s second worst city). He picks their grades on final exams and gives them a rank of their intelligence quotient (IQ). In the process, he generates this table of value and claims that there is a strong negative correlation between IQ and grades obtained on the final exam. He claims that the correlation coefficient is -0.6031. Is he correct? (2.5 points) Prove your answer! (7.5 points depending on how complete the explanation is).

Grade in points	77	78	65	84	85	88	67	92	68	96
IQ Rank (in ascending order)	10	3	8	5	7	6	9	2	4	1

Question 5 (10 points): You are informed that there were two institutional regimes governing land tenure in Quebec in 1831. One applies to the areas settled before 1791. In those areas, French land tenure laws are being applied. These laws differed from those that were applied in areas settled after 1791. In this second category of areas, British land tenure laws were applied. Using the census of 1831, researchers have extracted a sample of subdistricts across the colony that provided wage rates for daily workers in farming. These are reported in the table below. As can be seen, there is a difference between the mean of the two legal systems that is exceeds half a shilling per day (assuming a 250 days work-year, this is equivalent to the income needed to consume half of what can be deemed the “poverty basket” – i.e. the resources you need to not fall be in a situation of absolute poverty marked by privation and extreme malnutrition). However, is that difference statistically meaningful at the 95% level? Partial points will be allocated for the different steps.

Year	French Law Areas	English Law Areas
Number of districts	170	49
Mean Wage Rage	1.76824432 shillings per day	2.3322789 shillings per day
Standard Deviation	0.4248624 shillings	0.4359043 shillings

Question 6 (10 points): A researcher believes that wages in Lower Canada (modern day Quebec) in 1842 were significantly different than wages in Upper Canada (modern day Ontario) at the same point in time. All he knows is the average wage rate in Upper Canada (2.7 shillings) and he has a sample of wages for 42 districts in Lower Canada in 1842. For the Lower Canada sample, he finds a mean of 2.2 shillings per day of work and a standard deviation of 0.6 shillings. Is there a significant difference between Lower and Upper Canada (partial points allocated for the different steps)?

Question 7 (10 points): For this question, you will have to use excel (I have no doubt). In the table below, monthly wages in farming in different areas of Lower Canada in 1831 are taken to be a function of the share of the conceded land that has been improved (cleared land) for farming and the recency of settlement (how many years have elapsed since the year of the first settlement). What is the effect of cleared land on monthly wages (5 points)? Is the effect statistically significant at the 95% level, provide the t-value for the estimator of cleared land (5 points)?

District	Sub-District	Monthly Wages (Shilling)	Cleared land (Share of conceded estate)	Years since 1st settlement
PORTNEUF	Deschambaults	35.5	0.37	118
PORTNEUF	Cap Santé	23.75	0.33	152
QUEBEC	Rivière St-Charles	25	0.61	156
QUEBEC	St-Ambroise	50	0.37	155
RICHELIEU	St-Ours	15	0.46	159
RICHELIEU	St-Denis	15	0.53	137
ROUVILLE	Foucault	20	0.46	98
ROUVILLE	Sabrevois	45	0.15	14
SHERBROOKE	Compton	45	0.33	29
SHERBROOKE	Dudswell	60	0.21	26
SHERBROOKE	Shipton	50	0.29	30
SHERBROOKE	Windsor	50	0.26	29
STANSTEAD	Barnston	50	0.28	30
STANSTEAD	Barford	45	0.05	29
TERREBONNE	St-Martin	20	0.61	57
TERREBONNE	Ste-Rose	20	0.67	86
VAUDREUIL	Rigaud	37.5	0.62	29
YAMASKA	Baie St-Antoine	22.5	0.46	109

Question 8: A dataset contains data on birth to women in Canada. A researcher is concerned with the possibility that the behavior of mothers during pregnancy significantly affect the health of infants. The researcher is particularly concerned with the birthweight of infants (in grams) (bwght) and the effect of the number of cigarettes smoked per day (cigs). He estimates the following regression using a sample of 1,388 births:

What is the effect of smoking zero cigarettes (2 point)? What is the effect of smoking 20 cigarettes per day (3 points)? If you are told that cigarette consumption is strongly correlated with alcohol consumption (the two being substitutes) and that the adverse health effects on infants from alcohol consumption are more worrisome, how do you expect the coefficient for cigs to be altered (5 points)?

Z-TABLE

T-TABLE