Measuring Output
Sujan Bandyopadhyay
ECN 313
Summer 2023
Outline
1. Introduction
2. Measuring output
1. Expenditure approach
2. Income approach
3. Production/value added approach
3. Measuring inflation
1. Nominal and real GDP
2. GDP deflator
3. Consumer Price Index
Introduction
What are some of the top statistical indicators
of the economy?
Some examples
1.
2.
3.
4.
5.
6.
7.
GDP
Unemployment
Labor force participation
Inflation
Consumer spending
Construction
Industrial production
Measuring output
GDP: gross domestic product
• Definition:
The market value of all final goods and services produced within a country
during a given period
• Published by Bureau of Economic Analysis (BEA)
• Since it is a challenge to measure GDP in practice, the BEA compares the
results from three different approaches:
• Expenditure approach
• Income approach
• Production/value added approach
• Stock or flow?
• Flow
Three Ways to Measure GDP
• Production= Expenditure =
Income
• Example
• Farmer produces apples using
intermediate goods: $1,000 –
Production (value added)
• Household buys apples from a
farmer: $1,000 – Expenditure
• Farmer pays wages of $600 and
makes profits of $400 – Income
• GDP is $1,000 in all cases
Expenditure Approach
𝑌 = 𝐶 + 𝐼 + 𝐺 + 𝑁𝑋
• 𝑌 = GDP (in dollars)
• 𝐶 = consumption
• 𝐼 = investment
• 𝐺 = government purchases
• 𝑁𝑋= net exports
• 𝑁𝑋 = 𝐸𝑋 − 𝐼𝑀 = exports – imports
• Why are imports subtracted?
Double counting
Consumption
• Household spending on
• nondurable goods
• durable goods
• services
• “Personal consumption expenditures”
Investment
• Three components:
1. Business fixed investment: spending by firms on plants,
equipment, R&D spending, etc.
2. Residential investment: construction of new residential buildings
3. Inventory investment: changes in inventories
• “Gross private domestic investment”
Question
This year, a real estate agent helped you buy a house for $200,000. The
house was originally built in 1985. The agent’s commission was
$12,000. How will this commission on affect this year’s GDP?
a.
b.
c.
d.
Consumption expenditures will increase by $212,000.
Consumption expenditures will increase by $12,000.
Investment expenditures will increase by $212,000.
Investment expenditures will increase by $12,000.
Government purchase
1. Nondefense
• New highways, research funding, etc
2. National Defense
Are government transfers considered as government purchase?
e.g. stimulus paycheck
Variables
Gross Domestic Product
Personal Consumption Expenditures
Goods
Durable Goods
Nondurable goods
Services
Gross Private Domestic Investment
Fixed Investment
Nonresidential
Structures
Equipment
Intellectual Property Products
Residential
Change in private inventories
Net Exports of Goods and Services
Exports
Goods
Services
Imports
Goods
Services
Government Consumption Expenditures and Gross
Investment
Federal
National Defense
Nondefense
State and Local
2018
20,580.20
13,998.70
4,364.80
1,475.60
2,889.20
9,633.90
3,628.30
3,573.60
2,786.90
633.2
1,222.60
931.1
786.7
54.7
-638.2
2,510.30
1,661.30
848.9
3,148.50
2,570.60
577.9
% of GDP
100.00
68.02
21.21
7.17
14.04
46.81
17.63
17.36
13.54
3.08
5.94
4.52
3.82
0.27
-3.10
12.20
8.07
4.12
15.30
12.49
2.81
Per Capita
62,794.60
42,713.03
13,317.94
4,502.37
8,815.57
29,395.09
11,070.72
10,903.82
8,503.43
1,932.03
3,730.41
2,840.99
2,400.39
166.90
-1,947.28
7,659.46
5,068.98
2,590.18
9,606.75
7,843.45
1,763.30
3,591.50
1,347.30
793.6
553.7
2,244.20
17.45
6.55
3.86
2.69
10.90
10,958.44
4,110.90
2,421.44
1,689.46
6,847.54
Source: Bureau of Economic Analysis
Notes: Billions of Dollars (per capita in dollars): Last Revised on: September 30, 2019
Income Approach
• GDI: Measures sum of all income earned in the economy adjusting for
taxes, subsidies, and depreciation
• 𝐺𝐷𝐼 = 𝑐𝑜𝑚𝑝𝑒𝑛𝑠𝑡𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑒𝑚𝑝𝑙𝑜𝑦𝑒𝑒𝑠 +
𝑛𝑒𝑡 𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝑠𝑢𝑟𝑝𝑙𝑢𝑠 𝑜𝑓 𝑏𝑢𝑠𝑖𝑛𝑒𝑠𝑠𝑒𝑠 + 𝑡𝑎𝑥𝑒𝑠 𝑜𝑛 𝑏𝑢𝑠𝑖𝑛𝑒𝑠𝑠 −
𝑠𝑢𝑏𝑠𝑖𝑑𝑖𝑒𝑠 𝑜𝑛 𝑏𝑢𝑠𝑖𝑛𝑒𝑠𝑠 + 𝑑𝑒𝑝𝑟𝑒𝑐𝑖𝑎𝑡𝑖𝑜𝑛
• Depreciation: “consumption of fixed capital”
• In theory, 𝐺𝐷𝐼 = 𝐺𝐷𝑃
• Data source: tax returns
The Income Approach to U.S. GDP in 2018
Total Share of GDP to Inputs
• Can calculate “labor income” and “capital income”
• Share of GDP to labor
• Two-thirds (approx.)
• Labor’s share of GDP has remained approximately constant over
time.
• Share of GDP to capital
• One-third (approx.)
Labor’s Share of GDP
Production/Value Added Approach
• Value added = Revenue - costs of intermediate inputs
• GDP – sum of all value added
• Logic:
• Final expenditure can be decomposed into value added
components
• Intermediate inputs are counted as another firm’s value added
Production Approach Example
• Farm produces apples worth $1,000 as before. But now it pays $300
for fertilizer (an intermediate input)
• A chemical company produces fertilizer worth $300. It does not use
intermediate inputs.
• The final product is still $1,000. It equals the sum of all value added:
$1,000 = $1,000 − $300 +
$300
Farm value added Chemical company value added
• Intermediate goods are another firm’s value added
• Production method counts value added once to avoid double
counting
2018 data. Source: https://apps.bea.gov/iTable/iTable.cfm?reqid=150&step=3&isuri=1&table_list=1&categories=gdpxind
Question
• A construction company produces a $200,000 house using $50,000
worth of wood and steel, in addition to $50,000 of labor hours. The
value added by the construction company is ___
• Note: Labor does not count as intermediate good
Things not included in GDP
• Does not include non-transacted goods and services
• Does not take into account life-expectancy and other measures of
health and welfare
• Does not include changes in environmental resources
Measuring Changes over Time
Nominal and Real GDP
• Nominal GDP: total value of final quantities in current year prices
• In a world with 𝐼 goods in year 𝑡, this is
𝐼
𝑌𝑡 = ෍ 𝑃𝑖,𝑡 𝑄𝑖,𝑡
𝑖=1
• Growth of nominal GDP represents growth in prices and quantity
• Real GDP: use base year (𝑏) prices
𝐼
𝑌𝑡 𝑏 = ෍ 𝑃𝑖,𝑏 𝑄𝑖,𝑡
𝑖=1
• Growth of real GDP represents only quantity growth
• In base year, these are equal
Example: GDP in 2x2 Economy
Real GDP with Base Year 2000
Real GDP with Base Year 2001
Real GDP Growth
• Summary of real GDP from above:
• Laspeyres Index of GDP growth (base year 2000, yesterday’s prices)
62 − 46
𝐿
𝑔𝑌,2000 =
= 34.8%
46
• Paasche index of GDP growth (base year 2001, today’s prices)
66 − 51
𝑃
𝑔𝑌,2000 =
= 29.4%
51
Fisher Index
• Laspeyres and Paasche Index differ considerably
• Fisher Index: geometric average of the Laspeyres and Paashe Index
𝐹
𝑔𝑌,2000
=
𝐿
𝑔𝑌,2000
1ൗ
2
𝑃
𝑔𝑌,2000
1ൗ
2
= 32.0%
• Accumulated Fisher Index/Fisher index on year by year basis is “Chain Index” of real GDP
• EX: chaining forward from 2000 to 2003:
𝐹
𝑌2001 2000 = 𝑌2000 2000 ⋅ (1 + 𝑔𝑌,2000
) and
𝐹
𝑌2002 2000 = 𝑌2001 2000 ⋅ (1 + 𝑔𝑌,2001
)⇒
𝐹
𝐹
𝑌2002 2000 = 𝑌2000 (2000) ⋅ (1 + 𝑔𝑌,2000
) ⋅ (1 + 𝑔𝑌,2001
)
Why Fisher Index?
• A more accurate view of how standards of living changes over time
• Suppose compare real GDP in 1960 with real GDP in 2022
• Laspeyres index: using 1960 prices -> computers were relatively very
expensive compared to other goods -> rapid computer output growth
-> overstate growth rate
• Paasche index: using 2022 prices -> computers are relatively much
cheaper -> underestimate growth rate
1st generation iMac
price in 1998: $1,299
Comparing GDP over Time
• Need to account for two things:
1. Take into account changes in prices
• Use GDP in constant prices
2. Take into account changes in population
• Divide GDP by population → GDP per capita
• GDP per capita = total GDP / total population
GDP Deflator
• Generally,
𝑉𝑎𝑙𝑢𝑒
𝑃𝑟𝑖𝑐𝑒 =
𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦
• With respect to GDP,
𝑁𝑜𝑚𝑖𝑛𝑎𝑙 𝐺𝐷𝑃
𝐺𝐷𝑃 𝑑𝑒𝑓𝑙𝑎𝑡𝑜𝑟 =
𝑅𝑒𝑎𝑙 𝐺𝐷𝑃
• We may think of the GDP deflator as a measure of average prices
• So, 𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 = % Δ 𝑛𝐺𝐷𝑃 − % Δ 𝑟𝐺𝐷𝑃
• The GDP deflator in year 𝑡 with base year 𝑏 is
𝑌𝑡
𝑃𝑡 𝑏 =
𝑌𝑡 𝑏
GDP Deflator and Inflation
• Inflation rate (𝜋) is %Δ in GDP deflator
• Using previous results,
•
•
1.06−1
Laspeyres Index of inflation =
= 6%
1
1−0.9
Paashe Index of inflation =
= 11%
0.9
1
2
• Fisher Index of inflation = .06 .11
• Try solving for these – work is at end
1
2
= 8%
Consumer Price Index (CPI)
• Another measure of average prices
• “Cost-of-living index”
• Uses a basket of goods and services that includes only items
households buy
• Uses changes in cost of basket to measure cost-of-living changes
Composition of CPI Basket in 2018
Source: BLS
CPI vs GDP Deflator
Substitution Bias
• Why does CPI outgrow the GDP Deflator? One reason is that the CPI
suffers from “substitution bias”
• GDP deflator uses changing basket, CPI uses fixed basket
• Households substitute towards goods with decreasing relative prices
• Decrease quantities of goods with increasing relative prices
• Increase quantities of goods with decreasing relative prices
• Since fixed CPI basket ignores substitution and keeps quantities fixed,
CPI overestimates inflation
Inflation Answers
2x2 Economy: GDP Deflator and Inflation
2x2 Economy: GDP Deflator and Inflation