ECON4060H Assignment 1, input-output analysis
ECON4060H Assignment 1, input‑output analysis 27 January 2022
20 points in total. Due: Fe
uary 10, 2021.
1. Download the symmetric input‑output table (summary level) at Statistics Canada website,
www.statcan.gc.ca. The table id number is Table: 36‑10‑0084‑01 (formerly CANSIM 381‑0038).
In downloading the data, choose the following:9
• Valuation: basic price.
• Reference period: from 2017 to 2017.
2. From the input‑output table, calculate the GDP at basic price for each sector, which is the sum
of the following items under “Supply”.
• Subsidies on production.
• Taxes on production.
• Wages and salaries.
• Employers’ social contributions.
• Gross mixed income.
• Gross operating surplus.
GDP for each sector can also be calculated by summing final demand items under “Use”, these in‑
clude Household final consumption expenditure, Government final consumption expenditure, Inter‑
national exports, etc.
3. (4 points) Follow the equations on lecture slides and construct the input‑output matrix A. The
example on lecture slides has two sectors, in the Statistics Canada data, there are about 30
sectors. You can and probably should aggregate sectors, for example, adding the values fo
government sectors to form one sector Government. Some of the services sectors can also be
aggregated, e.g., finance and real estate. Please do not reduce the number of sectors to below
5.
4. (4 points) Calculate the eigenvector centrality for all sectors in the input‑output matrix A. This
matrix is directed, two sectors ? and ? are not just connected, the connection is directedbecause
? supplies products ? and/or vice versa. Youonly need to calculate the centrality in onedirection.
Thismeans that youmay set some elements of? to zero to shut down one direction (ingoing o
outgoing), only for calculating centrality.
5. (4 points) Obtain the Leontief inverse matrix L = (I − A)−1.
6. (4 points) Calculate the share of GDP of sector ? in aggregate GDP, ?? =
GDP?
aggregate GDP .
7. (4 points) Obtain theDomarweight for each sector. Domarweight of sector ? is the ratio of out‑
put of sector ? over the aggregate GDP. Domar weights are important in quantifying the impact
of shocks to a particular sector on the aggregate GDP. Let ?? be the Domar weight of sector ?,
then ?? = ∑
?
?=1 ????? where ??? is the entry (?, ?) of the Leontief inverse matrix L.
Shutao Cao 1
www.statcan.gc.ca