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REVIEW
FEDERAL RESERVE BANK OF ST. LOUIS
SECOND QUARTER 2022
VOLUME 104 | NUMBER 2
Global Supply Chain Disruptions and Inflation
During the COVID-19 Pandemic
Ana Maria Santacreu and Jesse LaBelle
Who Should Work from Home During a Pandemic?
The Wage-Infection Trade-Off
Sangmin Aum, Sang Yoon (Tim) Lee, and Yongseok Shin
Failing to Provide Public Goods:
Why the Afghan Army Did Not Fight
Rohan Dutta, David K. Levine, and Salvatore Modica
Venture Capital: A Catalyst for Innovation and Growth
Jeremy Greenwood, Pengfei Han, and Juan M. Sánchez
On the Relative Performance of Inflation Forecasts
Julie K. Bennett and Michael T. Owyang
REVIEW
Volume 104 • Number 2
President and CEO
James Bullard
Director of Research
78
Carlos Garriga
Global Supply Chain Disruptions and Inflation
During the COVID-19 Pandemic
Deputy Director of Research
B. Ravikumar
Review Editors-in-Chief
Ana Maria Santacreu and Jesse LaBelle
Michael T. Owyang
Juan M. Sánchez
92
Special Policy Advisor
Who Should Work from Home During a Pandemic?
The Wage-Infection Trade-Off
David C. Wheelock
Sangmin Aum, Sang Yoon (Tim) Lee, and Yongseok Shin
Economists
David Andolfatto
Subhayu Bandyopadhyay
Serdar Birinci
Yu-Ting Chiang
YiLi Chien
Riccardo DiCecio
William Dupor
Maximiliano Dvorkin
Miguel Faria-e-Castro
Charles S. Gascon
Victoria Gregory
Nathan Jefferson
Kevin L. Kliesen
Julian Kozlowski
Fernando Leibovici
Oksana Leukhina
Fernando M. Martin
Michael W. McCracken
Amanda M. Michaud
Alexander Monge-Naranjo
Christopher J. Neely
Serdar Ozkan
Paulina Restrepo-Echavarría
Hannah Rubinton
Ana Maria Santacreu
Guillaume Vandenbroucke
Christian M. Zimmermann
110
Failing to Provide Public Goods:
Why the Afghan Army Did Not Fight
Rohan Dutta, David K. Levine, and Salvatore Modica
120
Venture Capital: A Catalyst for Innovation and Growth
Jeremy Greenwood, Pengfei Han, and Juan M. Sánchez
131
On the Relative Performance of Inflation Forecasts
Julie K. Bennett and Michael T. Owyang
Managing Editor
Lydia H. Johnson
Contributing Editors
George E. Fortier
Jennifer M. Ives
Designer | Production Coordinator
Donna M. Stiller
i
Federal Reserve Bank of St. Louis REVIEW . Second Quarter 2022
Review
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© 2022, Federal Reserve Bank of St. Louis.
ISSN 0014-9187
ii
Global Supply Chain Disruptions and
Inflation During the COVID-19 Pandemic
Ana Maria Santacreu and Jesse LaBelle
We investigate the role supply chain disruptions during the COVID-19 pandemic played in U.S. producer
price index (PPI) inflation. We exploit pre-pandemic cross-industry variation in sourcing patterns across
countries and interact it with measures of international supply chain bottlenecks during the pandemic. We
show that exposure to global supply chain disruptions played a significant role in U.S. cross-industry PPI
inflation between January and November 2021. If bottlenecks had followed the same path as in 2019, PPI
inflation in the manufacturing sector would have been 2 percentage points lower in January 2021 and 20
percentage points lower in November 2021. (JEL F13, F14, F44)
Federal Reserve Bank of St. Louis Review, Second Quarter 2022, 104(2), pp. 78-91.
https://doi.org/10.20955/r.104.78-91
1 INTRODUCTION
The COVID-19-pandemic recession and recovery have been unique compared with previous
recessions, largely due to policies that led to behavioral changes. Lockdowns meant people were
traveling less both for work and for leisure, eating out less, and going to fewer entertainment venues,
among other things. At the same time, work from home and fiscal stimulus packages increased the
demand for certain goods such as technological goods, cars, and furniture. These changes resulted
in an overall shift away from consumption of services and toward consumption of durable goods.
The rapid increase in the demand for durable goods, together with the global nature of the
pandemic, has exposed vulnerabilities in the current production structure of these goods. Over the
past several decades, production of durable goods has become more fragmented, relying heavily
on global value chain (GVCs).1 Instead of doing everything in-house, firms can outsource parts of
their production processes to other countries. Figure 1 shows that GVC participation has been rising
steadily over time, though it has plateaued in recent years (see Antrás, 2020).
While GVC participation has advantages, as firms can benefit from outsourcing production to
regions with a comparative advantage, it comes with risks (Santacreu and LaBelle, 2021a,b). Shocks
Ana Maria Santacreu is a senior economist and Jesse LaBelle is a research associate at the Federal Reserve Bank of St. Louis. We thank Julian
Kozlowski for very insightful comments and suggestions.
© 2022, Federal Reserve Bank of St. Louis. The views expressed in this article are those of the author(s) and do not necessarily reflect the views of
the Federal Reserve System, the Board of Governors, or the regional Federal Reserve Banks. Articles may be reprinted, reproduced, published,
distributed, displayed, and transmitted in their entirety if copyright notice, author name(s), and full citation are included. Abstracts, synopses, and
other derivative works may be made only with prior written permission of the Federal Reserve Bank of St. Louis.
78
Federal Reserve Bank of St. Louis REVIEW . Second Quarter 2022
Santacreu and LaBelle
Figure 1
GVC Participation Over Time, 1970-2015
GVC share of total trade (%)
55
50
45
40
35
30
1970
1975
1980
1985
1990
1995
2000
2005
2010
2015
NOTE: The figure represents the evolution in the share of total trade that requires inputs from at least two countries.
SOURCE: World Bank World Development Report 2020.
that hit a particular stage of the production process can propagate along the chain and expose firms
dependent on inputs from these regions. Some of these risks did materialize during the current
pandemic through global lockdowns (Leibovici, and Santacreu, and LaBelle, 2021), low vaccination
rates in emerging countries (Çakmaklı et al., 2021), and large shipping costs and disruptions in some
key ports, putting additional pressure on supply chains.2
These risks can be exacerbated when supply chains rely heavily on critical inputs from one or a
few regions. Take the example of semiconductors. The advancement of technology in nearly every
product has made semiconductors a vastly important input for the entire economy; however, their
production largely relies on a few countries, such as Taiwan and China. A sharp increase in the
demand for products that use this input may create large bottlenecks in semiconductor-dependent
industries. Therefore, due to the global nature of supply chains, even a relatively small demand shock
to a critical sector can propagate into a larger supply/demand disruption. This mismatch between
supply and demand puts upward pressure on prices. In this article, we address the following question: To what extent has the global nature of supply chain disruptions contributed to producer
price index (PPI) inflation across U.S. sectors?3
The main challenge to answer this question is the limited access to real-time data on supply
chain disruptions. We rely on the Purchasing Managers’ Index data from S&P Global. These data,
which are available with a subscription, comprise monthly surveys sent to senior executives at private
firms in 44 countries. We focus on two measures from this survey that capture supply chain disruptions: backlogs and supplier delivery times. Backlogs measure how much the number of unfulfilled
new orders has changed from the previous month; delivery times measure how much the average
time it takes for suppliers to deliver inputs has changed from the previous month. Each variable
represents a rate of change over the previous month, and both capture demand and supply effects.
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Federal Reserve Bank of St. Louis REVIEW . Second Quarter 2022
Higher backlogs typically indicate that demand is increasing at a rate producers cannot meet, while
the opposite indicates unused production capacity resulting from a lack of demand. Hence, backlogs measure how quickly suppliers can keep up with demand. The same logic applies to delivery
times. As such, these measures can be used to infer demand and supply mismatches that contribute
to price increases and inflation.
We begin by documenting three salient features of the data on supply chain disruptions. First,
bottlenecks have become worse since January 2021, as implied by an increasing number of unfulfilled orders and longer delivery times. Second, backlogs and delivery times track PPI inflation quite
well, with each having a correlation of about 90 percent for the period January 2020 to November
2021. Third, supply chain disruptions and their contribution to PPI inflation have been heterogeneous across industries. Backlogs increased sharply in the automobile and technology equipment
industries. These increases were followed by large increases in PPI inflation. In the pharmaceutical
industry, however, bottlenecks remained relatively steady, which were reflected in a steady increase
in PPI inflation over the same period. These results suggest that the supply and demand mismatch
was worse in the technology equipment sector and the automobile and auto parts sector than in
the pharmaceutical sector.
We then ask the following question: Did U.S. industries more exposed to global supply chain
disruptions experience higher PPI inflation over this time period? To answer this question formally,
we construct measures of industry exposure to supply chain disruptions, both domestic and foreign.4
In particular, we exploit heterogeneous variation in an industry’s sourcing patterns across countries
and interact it with our measures of supply chain disruption: changes in backlogs and in delivery
times, respectively. If an industry in the United States relies heavily on intermediate inputs from a
country where supply chain disruptions are severe, this industry will be more exposed. We consider
both the manufacturing and non-manufacturing sectors. To the extent that for each industry we
keep the value-added shares fixed at the levels in 2018, the interaction with the bottleneck variables
in our exposure measure captures the role of the supply shock in that particular industry.
Our empirical strategy consists of regressing industry PPI inflation on our measures of domestic
and foreign exposure, including industry fixed effects. We focus on the period January 2021 to
November 2021. We find that both domestic and foreign exposure have a positive effect on industry
PPI inflation. However, only foreign exposure is statistically significant. These results hold when
using either backlogs or supplier delivery times as the measure of disruption. Moreover, the effects
of global supply chain disruptions on PPI inflation are larger if the exposure variables are lagged
by one month, suggesting that supply chain disruptions have a delayed impact on inflation. We
then conduct the same regression analysis but separate the industries into manufacturing and non-
manufacturing sectors. In the non-manufacturing sector, both domestic and foreign exposure have a
positive and statistically significant effect on PPI inflation. In the manufacturing sector, however,
only foreign exposure is statistically significant.
Finally, we ask the following question: What would PPI inflation have been during 2021 if
backlogs in each country had followed their 2019 path? To answer this question, we do a back-ofthe-envelope calculation in which we take the results from our regression analysis and compute a
counterfactual PPI inflation rate using the data on bottlenecks from 2019. We find that PPI inflation
in the manufacturing sector during 2021 would have been 2 percentage points lower in January
and 20 percentage points lower in November 2021.
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Federal Reserve Bank of St. Louis REVIEW . Second Quarter 2022
Santacreu and LaBelle
Figure 2
Consumption Patterns During Recessions
B. Months following business cycle peaks: Durables
A. Months following business cycle peaks: Services
Percent change from peak month
Percent change from peak month
5
40
1990-91
2001
2007-09
0
2020-21
20
–5
2020-21
2001
–10
0
1990-91
–15
2007-09
–20
–20
0
5
10
15
20
0
Months since peak
5
10
15
20
Months since peak
NOTE: The figure shows the evolution of real consumption in services (Panel A) and nondurable goods (Panel B) 18 months after the business cycle
peaks of the 1990-91, 2001, 2007-09, and 2020-21 recessions.
SOURCE: FRED®, Federal Reserve Bank of St. Louis; National Bureau of Economic Research; and authors’ calculations.
Our results show that supply chain disruptions during the COVID-19 pandemic recession
and recovery have been unprecedented. The shift in demand toward durable goods consumption
and the heavy reliance on foreign suppliers to produce these goods has created a mismatch between
supply and demand resulting in price increases. Sectors that rely more heavily on foreign inputs
from countries that faced stronger disruptions experienced larger increases in PPI inflation.
This article complements a short but growing literature on inflation and supply chain disruptions. Ha, Kose, and Ohnsorge (2021) analyze the driving forces of global inflation, focusing on
the 2020 global recession. Comin and Johnson (2020) study the role of trade integration and offshoring on inflation. Leibovici and Dunn (2021) discuss the extent to which supply chain disruptions
account for the recent rise in inflation, focusing on the case of semiconductors. Finally, Amiti, Heise,
and Wang (2021) study the effects of rising import prices on U.S. producer prices.
2 SUPPLY CHAIN DISRUPTIONS DURING COVID-19
The COVID-19 recession and recovery have been different from previous recessions and
recoveries along several dimensions. One is related to consumption: There has been a shift in consumption away from services and toward durable goods. Figure 2 plots for the COVID-19 recession
and recovery and three earlier ones, the evolution of real consumption of services (Panel A) and
durable goods (Panel B) for 18 months after the business cycle peak (with consumption normalized
to 1 in each business cycle peak).5
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Federal Reserve Bank of St. Louis REVIEW . Second Quarter 2022
Figure 3
Delivery Times and Backlogs Over Time, May 2007-November 2021
A. Backlogs of work
B. Supplier delivery times
100
100
80
80
60
60
40
40
20
20
0
0
Nov-07 Nov-09 Nov-11 Nov-13 Nov-15 Nov-17 Nov-19 Nov-21
Nov-07 Nov-09 Nov-11 Nov-13 Nov-15 Nov-17 Nov-19 Nov-21
NOTE: The figure shows the monthly evolution of backlogs (Panel A) and supplier delivery times (Panel B) in the United States. Gray bars indicate
recessions as determined by the NBER.
SOURCE: S&P Global.
During a typical recession, services consumption tends to remain stable. In contrast, the
COVID-19 recession was characterized by a sharp decline in consumption of services during the
first months (over 20 percent in April 2020 from the peak in February 2020), which started recovering steadily after the initial shock. This recovery was helped when lockdowns were lifted and vaccines
became widely available. Durable goods consumption, on the other hand, tends to drop and stay low
for the duration of a recession and into the recovery, as consumers typically postpone consumption
of these types of goods. During the COVID-19 recession, however, there was an initial sharp drop
in durable goods consumption as expected; however, durables consumption recovered quickly and
remained 19 percent higher than the peak even 18 months later.
The shift of demand toward durables consumption, together with the fact that production of
these goods takes place along complex supply chains, has translated into large bottlenecks. We show
evidence of supply chain disruptions by plotting the evolution of backlogs (i.e., new orders that have
not been completed or started yet) and supplier delivery times (i.e., the time it takes for a manufacturer to receive inputs from suppliers) from May 2007 to November 2021 in Figure 3. Index
values greater than 50 represent increased backlogs (or lower delivery times) relative to those in
the previous month, with the reverse being true for index values less than 50.6
Backlogs of work (Panel A) and supplier delivery times (Panel B) during the COVID-19 recession and recovery have behaved differently than during the Great Recession. The previous recession
represents, in many ways, a typical demand shock: The rate of change of delivery times slightly
increased before quickly recovering (see Figure 3). By the end of the recession in June 2009, delivery
times had been actually getting shorter on a monthly basis for the previous six months. During this
time, backlogs were gradually disappearing as the recession deepened. In fact, there were no monthover-month backlog increases, denoted by index values greater than 50 from May 2008 to October
2009, four months after the recession officially ended. For the COVID-19 recession, delivery times
consistently worsened on a monthly basis but this rate flattened starting in June 2021. At the same
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Federal Reserve Bank of St. Louis REVIEW . Second Quarter 2022
Santacreu and LaBelle
Figure 4
Backlogs, Delivery Times, and PPI Inflation, January 2020-November 2021
B. Delivery times and PPI inflation
A. Backlogs and PPI inflation
0
100
100
100
80
80
80
20
60
60
60
40
40
40
0
Delivery times
80
-2
0
100
Fe
b
No
v21
0
No
v20
Fe
b21
M
ay
-2
1
Au
g21
No
v21
20
-2
0
Au
g
ay
-2
0
M
Fe
b
-2
0
0
20
20
No
v20
Fe
b21
M
ay
-2
1
Au
g21
Backlogs
Au
g-
20
60
Standardized PPI inflation
ay
-2
0
Standardized PPI inflation
M
40
NOTE: The figure shows the monthly evolution of backlogs and PPI inflation (Panel A) and suppliers’ delivery times and PPI inflation (Panel B) in the
United States. Delivery times are plotted on the right y-axis with an inverted scale so that higher values represent longer delivery times. Gray bars
indicate the COVID-19 recession as determined by the NBER.
SOURCE: S&P Global, BLS, and authors’ calculations.
Figure 5
Backlogs and PPI Inflation by Sector, January 2020-October 2021
A. World manufacturing backlogs
B. Monthly year-over-year PPI inflation
70
4
60
2
50
0
40
–2
–4
30
Feb-20
Jun-20
Oct-20
Feb-21
Jun-21
Oct-21
Feb-20
Pharmaceuticals
Automobiles & Parts
Jun-20
Oct-20
Feb-21
Jun-21
Oct-21
Technology equipment
Manufacturing
NOTE: The figure shows the monthly evolution of world backlogs (Panel A) and US PPI inflation (Panel B) for three sectors: automobiles and parts,
technology equipment, and pharmaceuticals.
SOURCE: S&P Global, BLS, and authors’ calculations.
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Federal Reserve Bank of St. Louis REVIEW . Second Quarter 2022
time, backlogs initially experienced the typical loosening associated with a drop in demand before
the supply chain shocks caused an even larger distortion and forced higher levels of backlogs.
Backlogs have consistently worsened on a monthly basis since August 2020.
These findings illustrate an unprecedented supply and demand mismatch, contributing to
price increases and, hence, inflation. Focusing on the period from January 2020 to November 2021,
Figure 4 shows that bottlenecks, measured either with backlogs (Panel A) or delivery times (Panel B;
the y-axis is inverted so that higher values represent longer delivery times) track current PPI inflation closely.7 Indeed, the correlation of PPI inflation with backlogs and with delivery times between
January 2020 and November 2021 are each about 90 percent.
The evidence reported in Figure 4 masks large cross-sector heterogeneity. Figure 5 plots backlogs (Panel A) for the world in three manufacturing sectors: automobiles and auto parts; technology
equipment; and pharmaceuticals.8 The world automobile and auto parts sector started experiencing
tightening of supply chains by July 2020, which manifested as consistent increases in the monthly
rate of change in backlogs. Strong demand for cars in the months following the start of the pandemic,
paired with disruptions in the supply of certain key inputs such as semiconductors, led to large
supply chain disruptions in this sector. In the case of the technology equipment sector, unused
capacity remained relatively stable for months after bottoming out before beginning to tighten at a
steep slope after the turn of the new year. The COVID-19 pandemic substantially increased demand
for computers and electronics, as people started working from home and fiscal stimulus increased
consumption of these goods. As a result, PPI inflation increased substantially in these sectors
(Panel B). The pharmaceutical sector behaved differently from the automobile and auto parts sector
and the technology equipment sector: Bottlenecks and PPI inflation remained relatively steady in
comparison. Hence, sectors that faced worse supply chain disruptions (i.e., automobile and auto
parts, and technology equipment) also experienced steeper price increases.9
3 GLOBAL SUPPLY CHAIN DISRUPTIONS AND PPI INFLATION
In this section, we investigate the channels through which an exposure to global supply chain
disruptions may have contributed to inflation during the COVID-19 pandemic. Bottlenecks in an
industry can be driven by domestic or foreign factors or both. For instance, if an industry relies
heavily on intermediate inputs from countries that experience more bottlenecks, that industry will
be more exposed to foreign supply chain disruptions. If demand for that industry’s products increases
quickly, then foreign exposure may lead to price increases. In this section, we ask the following
question: To what extent did exposure to domestic and foreign supply chain disruptions contribute
to U.S. PPI inflation between January and November 2021? To answer this question we construct,
for each industry of the United States, a domestic measure and a foreign measure of exposure to
supply chain disruptions. Our empirical strategy consists of regressing PPI inflation on the exposure measures.
We follow the same methodology employed in Leibovici, Santacreu, and LaBelle (2021) and
compute for each industry in the United States a measure of GVC participation—the share of gross
exports (GE) produced with foreign value added (FVA) in 2018—for 32 countries and 26 industries,
15 of which correspond to the manufacturing sector.10 This measure captures how much of the U.S.
GE in a particular industry rely on intermediate imports from other countries. We then interact
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Federal Reserve Bank of St. Louis REVIEW . Second Quarter 2022
Santacreu and LaBelle
Figure 6
Average Foreign Bottleneck Exposure and PPI Inflation, January-November 2021
A. Foreign bottleneck exposure
B. PPI inflation, percent
Motor vehicles
Coke and petroleum products
Basic metals
Machinery and equipment NEC
Other transport equipment
Electrical equipment
Fabricated metal products
Textiles
Rubber and plastics products
Wood products
Paper products
Food products
Manufacturing NEC
Other non-metallic mineral products
Computer equipment
Mining, non-energy products
Telecommunications
Mining, energy products
Mining support
Water transport
Warehousing and support acty
Accommodation
Postal and courier activities
Publishing and related activities
Wholesale and retail trade
Air transport
Coke and petroleum products
Basic metals
Wood products
Fabricated metal products
Rubber and plastics products
Textiles
Food products
Wholesale and retail trade
Motor vehicles
Paper products
Warehousing and support acty
Mining, non-energy products
Mining, energy products
Water transport
Accommodation
Electrical equipment
Other non-metallic mineral products
Machinery and equipment NEC
Postal and courier activities
Manufacturing NEC
Publishing and related activities
Mining support
Other transport equipment
Computer equipment
Telecommunications
Air transport
Non-Mfg
Mfg
0
5
10
15
0
20
40
60
80
NOTE: The figure shows for 26 U.S. industry averages for exposure to foreign backlogs (Panel A) and year-over-year PPI inflation (Panel B). Red bars
represent manufacturing industries; blue bars represent non-manufacturing services industries. NEC, not elsewhere classified; acty, activity.
SOURCE: TIVA, S&P Global, BLS, and authors’ calculations.
this variable with a measure of supply chain disruptions for each foreign supplier.11 Our conjecture
is that industries that are more exposed to global bottlenecks through GVCs experienced larger
increases in PPI inflation.12
Industry i’s exposure to foreign ( f ) bottlenecks at time t, E itf , is computed as
(1)
FVA ij j
Bt ,
j =1 GE i
N
Eitf =
FVA ij
is the share of GE from industry i that are composed of value added from country j
GE i
in that industry; Btj represents bottlenecks, either backlogs or delivery times, in country j at time t;
and N is the number of foreign suppliers. A period is a month. We restrict the analysis to the period
January 2021 to November 2021.
Similarly, we compute a measure of industry ’s exposure to domestic bottlenecks defined as
where
(2)
Eitd =
DVA iUS
Bt ,
GE i
DVA iUS
where
is the share of value added embedded in U.S. GE supplied by the United States itself.
GE i
Bt is the U.S. bottleneck variable, either backlogs or delivery times.
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Federal Reserve Bank of St. Louis REVIEW . Second Quarter 2022
Santacreu and LaBelle
Table 1
Exposure to Supply Chain Disruptions and PPI Inflation: Backlogs vs. Delivery Times,
January-November 2021
Backlogs
Delivery times (inverse)
Domestic exposure
0.00569
(0.004)
0.00314
(0.003)
Foreign exposure
0.239***
(0.071)
0.255***
(0.070)
Constant
–0.598***
(0.115)
2.272***
(0.565)
YES
YES
Industry FE
N
286
165
R2
0.752
0.756
NOTE: FE, fixed effects. Standard errors are in parentheses. *** p < 0.001.
SOURCE: Authors’ calculations.
Figure 6 plots our measure of foreign exposure computed in equation (1) (Panel A) and PPI
inflation (Panel B) for the 26 industries in the United States, averaged for January to November 2021.
Manufacturing industries are, on average, more exposed to foreign bottlenecks than services
industries. In the manufacturing sector, motor vehicles, coke and petroleum products, and basic
metals are the most exposed industries. The reason is twofold. On the one hand, these industries
rely heavily on foreign intermediate inputs. On the other hand, the main suppliers in these industries
have faced strong supply chain disruptions during the pandemic. Consistent with the measure of
foreign exposure, manufacturing industries experienced higher PPI inflation than services industries. In the manufacturing sector, the coke and petroleum products industry and the basic metals
industry are among the industries with the highest increases in prices. Therefore, there appears to
be a positive correlation between exposure to foreign supply chain disruptions and PPI inflation.
3.1 Empirical Strategy
Next, we study more formally the extent to which domestic and foreign exposure to supply
chain disruptions may have contributed to U.S. PPI inflation. In particular, we conduct the following
linear regression:
(3)
=
itPPI 0 1 Eitf 2 Eitd I i uit ,
where πitPPI represents the year-over-year PPI increase in industry i at time t; E itf is exposure to foreign
bottlenecks at time t; E itd is the exposure to domestic bottlenecks in industry i; Ii captures industry
fixed effects; and uit is the error term.
Table 1 reports the results. Foreign exposure, both in terms of supplier delivery times and
backlogs, has a statistically significant effect on PPI inflation. For backlogs, increasing the monthover-month backlogs by 1 percent increases the industry inflation rate by 0.24 percentage points,
while the same increase for delivery times causes an increase of about 0.26 percentage points. The
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Federal Reserve Bank of St. Louis REVIEW . Second Quarter 2022
Santacreu and LaBelle
Table 2
Exposure to Supply Chain Disruptions and PPI Inflation: Lags, January-November 2021
Backlogs
Delivery times
Domestic exposure
0.00755*
(0.004)
0.00029
(0.004)
Foreign exposure
–0.154
(0.094)
0.0630
(0.087)
Domestic exposure (t – 1)
0.00340
(0.003)
0.00069
(0.004)
Foreign exposure (t – 1)
0.260***
(0.078)
0.205*
(0.118)
Constant
–0.628***
(0.145)
2.356***
(0.664)
N
260
150
R2
0.824
0.819
NOTE: Standard errors are in parentheses. * p < 0.05, *** p < 0.001.
SOURCE: Authors’ calculations.
Table 3
Exposure to Supply Chain Disruptions and PPI Inflation: Manufacturing vs. Non-manufacturing,
January-November 2021
Manufacturing
Non-manufacturing
Domestic exposure
–0.00015
(0.005)
0.0161***
(0.003)
Foreign exposure
0.309**
(0.099)
0.397**
(0.122)
Constant
–3.549***
(0.978)
–1.355***
(0.172)
Industry FE
YES
YES
N
165
121
0.747
0.574
R
2
NOTE: FE, fixed effects. Standard errors are in parentheses. ** p < 0.01, *** p < 0.001.
R-squared is about 75 percent. Exposure to domestic bottlenecks, either measured as backlogs or
delivery times, has no statistically significant effect on an industry’s PPI inflation. This result may
be capturing the high costs of restructuring a global supply chain that relies heavily on foreign
suppliers. High fixed costs of setting up global supply chains could be resulting in stronger downstream production effects. For example, an industry heavily dependent on imported intermediates
may not be able to efficiently identify new sources for those inputs.
Since supply chain disruptions may have a delayed effect on PPI inflation, we conduct the
same regression in equation (3) but lag the domestic and foreign exposure measures. The results
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are reported in Table 2. Foreign supply chain disruptions get propagated to domestic PPI inflation
with a one-month lag. This result is robust to the use of both backlogs and delivery times as the
measure of supply chain disruptions.13 Hence, supply chain disruptions tend to have a delayed
impact on PPI inflation.
Table 3 reports the results with the industries separated into manufacturing and non-
manufacturing sectors. Data on delivery times are only available for manufacturing sectors. Hence,
we focus on backlogs as a measure of supply chain disruptions in Table 3. Notably, domestic exposure is only statistically significant when restricting the sample to the non-manufacturing sector.
This result may reflect the fact that non-manufacturing sectors typically rely far less on FVA than
manufacturing sectors do. Therefore, they are more susceptible to domestic fluctuations overall.
In the manufacturing sector, both domestic and foreign bottlenecks have a positive effect on PPI
inflation, but the effect is only significant for foreign bottlenecks. The R-squared is about 75 percent
in the manufacturing sector and 58 percent in the non-manufacturing sector.
Our results suggest that global supply chain disruptions, which reflect a mismatch between
demand and supply shocks, can propagate to domestic PPI inflation. The propagation is larger in
those sectors where GVCs are more important.
3.1.1 Back-of-the-Envelope Calculation. We now ask the following question: What would PPI
inflation have been during 2021 if bottlenecks in each country had followed their 2019 path? To
answer this question, we compute for each U.S. industry in the manufacturing sector a counterfactual PPI inflation rate that uses country-level data on supply chain disruptions from January to
November 2019. The focus is on the manufacturing sector, which has experienced worse supply
chain disruptions due to its higher dependence on GVCs.
We proceed in several steps. First, we recalculate our measures of domestic and foreign exposure
in equations (2) and (1), using country-level backlogs for each month of 2019. These counterfactual
measures capture the exposure of each U.S. manufacturing industry through GVC participation if
backlogs had followed the same paths of monthly changes as in 2019. Second, we substitute these
measures into equation (3), using the estimated coefficients and industry fixed effects from the first
column of Table 3. The result is a counterfactual measure of PPI inflation for each manufacturing
industry from January to November 2021. Third, we compute aggregate manufacturing PPI inflation, both in the data and in the counterfactual, as a weighted average across industries’ PPI inflation in each month of 2021. The weights are provided by the BLS for December 2020.14
Figure 7 plots the evolution of year-over-year monthly manufacturing PPI inflation from
January to November 2021, both in the data (solid line) and in the counterfactual (dashed line).
PPI inflation is always lower in the counterfactual than in the data, suggesting that bottlenecks
during 2021 significantly contributed to inflation. Differences between the data and the counterfactual were larger between June and September 2021 and then started narrowing in October 2021.
In particular, we find that manufacturing PPI inflation would have been 2 percentage points lower
in January 2021 and 20 percentage points lower in November 2021 if the monthly change in bottlenecks had followed the 2019 path.
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Santacreu and LaBelle
Figure 7
Manufacturing Year-Over-Year PPI Inflation in the Data and in the Counterfactual,
January-November 2021
Monthly year-over-year PPI inflation, percent
40
30
20
10
0
Data
Counterfactual
–10
1
2
3
4
5
6
7
Month (2021)
8
9
10
11
SOURCE: BLS and authors’ calculations.
4 CONCLUSIONS
In this article, we investigated the role of global supply chain disruptions in PPI inflation across
U.S. industries during the COVID-19 pandemic. We find that exposure to foreign bottlenecks
through GVCs played a significant role in transmitting the effects of supply chain disruptions to
U.S. prices. Our findings are driven by a combination of demand and supply shocks and the heterogeneous exposure to these shocks across industries. Industries that rely on inputs from countries
whose production has been most affected by disruptions also experienced large price increases due
to the inability to keep up with demand. Whether the inflation caused by supply chain disruptions
is temporary (i.e., a rise in the cost of living) or a more permanent phenomenon will depend—
absent any policy intervention—on the ability of supply chain disruptions to ease in order to meet
the higher demand. The unequal distribution of vaccines in emerging countries, the rise of new
variants, and disruptions in shipping could add some additional pressure on supply chains, creating
pessimism about inflation disappearing in the near future. n
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NOTES
1
See Santacreu and LaBelle (2021a,b) for a discussion on the rise of GVCs.
2
See Leibovici and Dunn (2021).
3
We focus on PPI inflation rather than consumer price index inflation, as the channels explored in the article (bottlenecks
and delivery times) are likely to have a more direct effect on producer prices. Increases in producer prices may then be
passed onto consumers with a lag. As such, the PPI serves as a leading indicator for the consumer price index.
4
We follow the methodology developed in LaBelle, Leibovici, and Santacreu (2021).
5
The plot shows monthly real consumption expenditures by major product type as reported on BEA release Table 2.8.3 of
durable goods, seasonally adjusted; the date of the business cycle peak for each of the four recessions is from the National
Bureau of Economic Research (NBER) Business Cycle Dating Committee (https://www.nber.org/research/business-cycle-dating). Plotting total consumption (i.e., including both durables and non-durables consumption) shows a similar
evolution as that of durables consumption, but the changes are less striking (see Barnes, Bauer, and Edelberg, 2021).
6
Data are from S&P Global, which surveys upper-level executives in different industries across the world. The questions
asked focus on the level of different aspects of production compared with one-month ago. The results are summarized
into a diffusion index: 50 indicates no change; values above (below) 50 signal an expansion (contraction).
7
We use the BLS PPI year-over-year change rate as our measure of PPI inflation. We then standardize it to bring the scale
in line with the S&P Global data. In particular, we first de-mean and divide by its sample standard deviation; second, we
multiply the resulting series by the standard deviation of the S&P Global backlogs measure and add the mean.
8
We do not have data on sectoral backlogs for the United States; instead we use S&P Global data that only report disaggregated data for a few countries. To the extent that these countries have a similar production structure as the United
States, we can assume that cross-sector bottlenecks in the United States follow the same pattern.
9
A value that goes from 42 to 47, for example, does not mean that bottlenecks are increasing but rather that the rate of
loosening of the supply chain is slowing down.
10 Data are from the OECD Trade in Value Added (TIVA) dataset, which reports the value-added content from each origin
country in the production of U.S. goods and services that are consumed worldwide.
11 Note that the backlog and delivery time measures are at the country-period level, whereas the FVA measure is at the
country-sector level.
12 The list of countries is Australia, Austria, Brazil, Canada, China, Colombia, the Czech Republic, France, Germany, Greece,
Indonesia, India, Ireland, Italy, Japan, Kazakhstan, Korea, Malaysia, Mexico, Myanmar, the Netherlands, the Philippines,
Poland, the Russian Federation, Spain, Switzerland, Taiwan, Thailand, Turkey, the United Kingdom, the United States,
and Vietnam.
13 The results (not included here) are robust to including two-month lags.
14 See https://www.bls.gov/ppi/#tables.
REFERENCES
Amiti, Mary; Heise, Sebastian and Wang, Aidan. “High Import Prices along the Global Supply Chain Feed Through to U.S.
Domestic Prices.” Federal Reserve Bank of New York Liberty Street Economics, November 8, 2021;
https://libertystreeteconomics.newyorkfed.org/2021/11/high-import-prices-along-the-global-supply-chain-feedthrough-to-u-s-domestic-prices/.
Antrás, Pol. “Conceptual Aspects of Global Value Chains.” World Bank Economic Review, 2020, 34(3), pp. 551-74;
https://doi.org/10.1093/wber/lhaa006.
Barnes, Mitchell; Bauer, Lauren, and Edelberg, Wendy. “11 Facts on the Economic Recovery from the COVID-19 Pandemic.”
Hamilton Project Economic Facts, September 2021; https://www.hamiltonproject.org/assets/files/COVID_Facts.pdf.
Çakmaklı, Cem; Demiralp, Selva; Kalemli-Özcan, S.ebnem; Yeşiltaş, Sevcan and Yıldırım, Muhammed A. “The Economic
Case for Global Vaccinations: An Epidemiological Model with International Production Networks.” NBER Working Paper
28395, National Bureau of Economic Research, 2021; https://doi.org/10.3386/w28395.
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Comin, Diego A. and Johnson, Robert C. “Offshoring and Inflation.” NBER Working Paper 27957, National Bureau of
Economic Research, October 2020; https://doi.org/10.3386/w27957.
Ha, Jongrim; Kose, M. Ayhan and Ohnsorge, Franziska. “Inflation During the Pandemic: What Happened? What Is Next?”
2021; https://doi.org/10.2139/ssrn.3881502.
Leibovici, Fernando and Dunn, Jason. “Supply Chain Bottlenecks and Inflation: The Role of Semiconductors.” Federal
Reserve Bank of St. Louis Economic Synopses, 2021, No. 28; https://doi.org/10.20955/es.2021.28.
Santacreu, Ana Maria; Leibovici, Fernando and Jesse, LaBelle. “Global Value Chains and U.S. Economic Activity During
COVID-19.” Federal Reserve Bank of St. Louis Review, Third Quarter 2021, 103(3), pp. 271-88;
https://doi.org/10.20955/r.103.271-88.
Santacreu, Ana Maria and LaBelle, Jesse. “Rethinking Global Value Chains During COVID-19: Part 1.” Federal Reserve Bank
of St. Louis Economic Synopses, 2021a, No. 16; https://research.stlouisfed.org/publications/economic-synopses/2021/07/01/rethinking-global-value-chains-during-covid-19-part-1.
Santacreu, Ana Maria and Jesse LaBelle. “Rethinking Global Value Chains During COVID-19: Part 2.” Federal Reserve Bank
of St. Louis Economic Synopses, 2021b, No. 17; https://doi.org/10.20955/es.2021.17.
91
Who Should Work from Home During a Pandemic?
The Wage-Infection Trade-off
Sangmin Aum, Sang Yoon (Tim) Lee, and Yongseok Shin
Shutting down the workplace is an effective means of reducing contagion but can induce large economic
losses. We harmonize the American Time Use Survey and O*NET data to construct a measure of infection
risk (exposure index) and a measure of the ease with which a job can be performed remotely (work-fromhome index) across both industries and occupations. The two indexes are negatively correlated but distinct,
so the economic costs of containing a pandemic can be minimized by sending home only those workers
that are highly exposed to infection risk but that can perform their jobs easily from home. Compared with
a lockdown of all non-essential jobs, which includes many jobs not easily performed from home, a more
selective policy can attain the same reduction in aggregate infection risk (32 percent) with one-third fewer
workers sent home to work (24 percent vs. 36 percent) and only half the aggregate wage loss (15 percent
vs. 30 percent). In addition, moving to such a policy reduces the infection risk of low-wage workers the
most and the wage losses of high-wage workers the most. Our crosswalk between the American Time Use
Survey and O*NET data can be applied to a broader set of topics. (JEL E24, I14, J21 )
Federal Reserve Bank of St. Louis Review, Second Quarter 2022, 104(2), pp. 92-109.
https://doi.org/10.20955/r.104.92-109
1 INTRODUCTION
Most countries have implemented lockdowns and social distancing to varying degrees to contain the COVID-19 pandemic. The obvious downside is the economic costs, since most economic
activities depend on in-person interaction. Thus, at least in the short run, policymakers face an
inherent trade-off between the risk of contagion and economic losses.
To analyze this trade-off, it is important to know, first, the exposure-to-infection risk from
performing a given job and, second, the ease with which the job can be performed remotely. The
actual trade-off will depend on how jobs are distributed along these two dimensions, which is the
focus of this article.
Sangmin Aum is an assistant professor of economics at Kyung Hee University. Sang Yoon (Tim) Lee is a reader at Queen Mary University of London
and an affiliate at the Center for Economic and Policy Research. Yongseok Shin is a professor of economics at Washington University in St. Louis, a
research fellow at the Federal Reserve Bank of St. Louis, and a faculty research fellow at the National Bureau of Economic Research. We are grateful
for many helpful suggestions from an anonymous referee. Sang Yoon (Tim) Lee gratefully acknowledges the financial support from the British
Academy (grant number COV19\201483).
© 2022, Federal Reserve Bank of St. Louis. The views expressed in this article are those of the author(s) and do not necessarily reflect the views of
the Federal Reserve System, the Board of Governors, or the regional Federal Reserve Banks. Articles may be reprinted, reproduced, published,
distributed, displayed, and transmitted in their entirety if copyright notice, author name(s), and full citation are included. Abstracts, synopses, and
other derivative works may be made only with prior written permission of the Federal Reserve Bank of St. Louis.
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We begin by constructing an index of exposure-to-infection risk across occupations by using
O*NET data and an index of how easily a job can be performed remotely (from home) across
industries and occupations by using the “time worked from home” variable in the American Time
Use Survey (ATUS). Such indexes are not new, but our approach is novel in that we harmonize the
two datasets through our own crosswalk to quantify the trade-off between infection risk and the
economic losses present in the economy, using the distribution of workers across jobs in the American
Community Survey (ACS).
We find that, although jobs not easily performed from home (low work-from-home [WFH]
ability) tend to be more exposed to infection risk on average, the negative correlation between the
two indexes across occupations and industries is far from tight. First, there are a number of jobs
with high exposure that can be easily performed from home (high WFH ability), such as IT sales
agent. Second, infection risk varies widely even among jobs with the same WFH ability: For example,
neither medical therapists nor experimental physicists can work from home, but the latter’s workplaces pose almost no risk of contagion. In addition, even the same occupation can have a very
different WFH ability depending on the industry: For example, a registered nurse employed by a
hospital has low WFH ability, but one in consulting services has high WFH ability.
In light of these findings, we consider an optimal policy that selectively sends home specific
occupations in specific industries to minimize the aggregate wage loss subject to a given reduction
in the aggregate exposure-to-infection risk. Intuitively, it is optimal to first send home workers with
jobs with high exposure at work and small productivity and wage losses when working from home,
the latter of which can be computed from a job’s wage and WFH ability. Mathematically, this translates into a linear threshold in the two-dimensional plane of exposure and wage loss.
The aggregate wage loss under the optimal policy is much smaller than under a lockdown of
all non-essential jobs as implemented in many U.S. states and European economies. Our version
of the real-world lockdown reduces aggregate exposure by 32 percent by sending home 36 percent
of all workers, costing 30 percent of aggregate wages. Our optimal policy attains the same reduction
in aggregate exposure by sending home only 24 percent of all workers, costing only 15 percent of
aggregate wages. That is, the optimal policy achieves the same reduction in aggregate infection risk
for half the economic cost. Under a constrained optimal policy in which healthcare-related workers
must continue to work normally, the aggregate wage loss is 20 percent, still a third smaller than
under a real-world lockdown. These gains are possible because the optimal policy exploits the large
variation in WFH ability across occupations and industries for any given level of exposure—the
novel fact we establish in this article.
It has become clear that low-wage workers are not only bearing the brunt of the pandemic
economically but are also bearing the brunt of the infection risk. Compared with a lockdown of all
non-essential jobs, the optimal policy reduces low-wage workers’ infection risk the most. On the
other hand, a move from such a lockdown to the optimal policy generates the largest wage gains
for high-wage workers, although more workers across the entire wage distribution are allowed to
work normally and thus earn more than when working from home. In fact, under all policy scenarios
we consider, high-wage workers are the least exposed to infection risk and also lose the least economically, pointing to the importance of redistributive policies during a pandemic.
A word of caution: By design, our optimal policy is simple and static, abstracting from the
essentiality of certain jobs (other than healthcare-related workers) that need to be performed even
in the midst of a pandemic; the complementarity among jobs that need to be performed in person;
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the economic propagation across jobs and sectors; and the possibility that people switch to jobs with
lower exposure or higher WFH ability (to help prevent wage loss). It also assumes that the indexes
we construct are constant, ignoring the potential change in exposure or WFH ability of specific
jobs due to more subtle non-pharmaceutical interventions such as wearing masks, reorganizing
the workplace, and changing individual behaviors as the population adjusts to the pandemic. How
ever, it does capture the direct trade-offs given the work patterns at the onset of the pandemic.
Furthermore, our analysis presents simple guidance for policymakers that is easy to implement in
practice, while also providing a benchmark for structural economic models that consider some of
the dimensions that we abstract from.1
It should also be noted that our industry-occupation crosswalk between ATUS and ACS/
O*NET is not specific to exposure and WFH ability and can be applied to a broader set of topics.
2 DATA
2.1 Employment and Wages by Occupation and Industry
We compute employment weights and mean hourly wages by occupation and industry from
the ACS. We include only civilian prime-age workers (between 16 and 65 years old). An individual’s
employment weight is their sampling weight multiplied by their usual annual hours worked (usual
hours worked in a week times usual weeks worked in a year). For each year, we multiply top-coded
wages by 1.5 and bottom-code the lowest hourly wage percentiles. Then, the hours-adjusted employment weight and mean hourly wage of each occupation-industry combination are computed using
consistent industry and occupation codes following Autor and Dorn (2013), modified to incorporate
changes in the Census industry and occupation codes from 2014 to 2018 as in Lee and Shin (2017).
Finally, we take a simple average of the employment weights and hourly wages over the five years.
2.2 Constructing the Exposure and WFH Indexes
Exposure Index. The O*NET asks experts and workers to give numerical answers to questions
that capture detailed characteristics of an occupation, where an occupation is defined by its Standard
Occupation Classification (SOC) code. To construct our exposure index, we take the weighted
average of the answers to two questions: one about physical proximity (PP) to other people in the
workplace and the other about potential exposure to disease or infection (EDI) in the workplace.2
We first convert O*NET titles to SOC codes using the accompanying crosswalk.3 The SOC codes
are then mapped to ACS OCC (occupation) codes using a crosswalk from IPUMS USA, which is
heavily modified so that each ACS OCC code has a unique value for both descriptors.4 Finally, we
normalize PP and EDI to have a mean of zero and standard deviation of 1, and take the average of
the two as our exposure index value.5
WFH Index. Some earlier studies on COVID-19 used O*NET descriptors to construct a WFH
index (e.g., Dingel and Neiman, 2020, and Mongey, Pilossoph, and Weinberg, 2020). However, a
more accurate measure of the ease with which a job can be performed from home may be whether
people actually do the job from home, such as reported in the ATUS. While Mongey, Pilossoph,
and Weinberg (2020) do show that the former is positively correlated with the latter, there are both
qualitative and quantitative reasons to favor the latter. Qualitatively, some descriptors included in
O*NET-based WFH indexes are misleading: For example, O*NET’s “outdoor” categories (implying
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Aum, Lee, Shin
Figure 1
Relationship Between Exposure and WFH Ability
Exposure index
3
Hospitals
Dentists
Management, scientific and technical consulting services
Registered nurses
Hospitals
Registered nurses
2
1
Elementary and secondary schools
Elementary and middle school teachers
Construction
Construction laborers
Truck transportation
Driver/sales workers and truck drivers
0
National security and international affairs
First−line supervisors of office and administrative support workers
Warehousing and storage
Shipping, receiving, and traffic clerks
−1
Logging
Logging workers
−2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
WFH index
NOTE: Each circle represents a specific occupation within a specific industry (458 occupations × 254 industries). The size of
the circle denotes the hours-adjusted employment share, averaged from 2014 to 2018. Black circles indicate examples of
occupations either with very large employment shares or with extreme values of exposure and/or WFH ability. The first description for these examples is the industry, and the second is the occupation.
low WFH ability) include farmers who in fact have a high incidence of actually working from home,
since they work in self-owned plots and land.6 Quantitatively, the ATUS allows WFH ability to vary
across industries, as well as across occupations, and indeed even the same occupation has very different WFH ability across industries in the data.7
For each industry-occupation combination in the ATUS, we compute the total time spent
working and total time spent working from home across all individuals in the corresponding cell
for each year from 2014 to 2018, using each year’s sampling weight. We then take a simple average
over all five years, and the ratio of the average time worked from home to the average time spent
working is our WFH index value. Each cell is then matched to the ACS; in the process, we merge
and impute missing cells using ACS employment weights and also ensure that each OCC code has
at least one O*NET descriptor.
All in all, we end up with 458 occupations across 254 industries (458 × 254), each with an
exposure index value, a WFH index value, hours worked, and hourly wages.
2.3 The Relationship Between Exposure and WFH Ability
Are jobs with higher infection risk harder to perform from home? In Figure 1, each circle represents a job, defined as a specific occupation in a specific industry, and its location on the WFH
index (horizontal axis) and exposure index (vertical axis). The size of the circle denotes the (hoursweighted) employment share of that job, averaged from 2014 to 2018.
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Table 1
WFH Index
Industry-occupation pairs
By occupation
By industry
Exposure
–0.033
(0.004)
–0.033
(0.005)
–0.045
(0.010)
Observations
54,108
458
254
0.034
0.109
0.126
R
2
NOTE: The table shows the result of regressing WFH ability on exposure, with observations weighted by their hours-adjusted
employment shares. Robust standard errors are in parentheses. The units of observation are an industry-occupation pair (first
column), occupation (second column), and industry (last column).
Three patterns emerge. First, consistent with conventional wisdom, jobs with higher infection
risk tend not to be performed from home. For example, hospital nurses have high infection risk
and rarely work from home. Second, the negative correlation is not very tight. In Figure 1, there
are many industry-occupation pairs that do not work from home, regardless of their exposure-to-
infection risk. Most notably, loggers have one of the least exposed occupations, but for obvious
reasons they do not work from home. Third, even the same occupation shows substantial variations
in WFH ability across industries. For example, while hospital nurses do not work from home, a
small number of registered nurses in the consulting services industry exclusively work from home.
Table 1 shows the coefficients from regressing the WFH index on the exposure index for our
whole industry-occupation sample (first column), only by occupation (second column), and only
by industry (third column). For the latter cases, the exposure and WFH indexes are computed by
averaging across each occupation’s exposure and WFH ability within an industry, respectively,
weighted by each occupation’s within-industry employment share. In all three cases, the negative
correlation between the exposure index and the WFH index is statistically significant. However, a
large fraction of the dispersion in one index still remains unexplained by the other, as represented
by the low R2’s in all regressions. In particular, the R2 is as low as 0.034 for the full sample of industry-
occupation pairs. Since the exposure index varies only across occupations and not industries, by
construction, the large increase in R2 from the first to the second column mirrors the wide variation
in WFH ability across industries—even for the same occupation.8
3 OPTIMAL POLICY
We interpret the fact that a job is more likely to be worked from home (high WFH ability) to
mean that it will have little productivity loss when worked from home. Thus, the large dispersion in
WFH ability among jobs with similar levels of exposure implies that the economic cost of sending
home workers to reduce infection risk depends on whether their jobs have high or low WFH ability.
Let (si ,wi ,ei ,hi ) denote the employment share, average wage, exposure index, and WFH index
for each industry-occupation pair i. The optimal policy minimizes the economic cost from sending
home a fraction 0 ≤ xi ≤ 1 of each industry-occupation pair, subject to reducing aggregate exposure
by at least a given fraction 0 ≤ y ≤ ψ:
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(1)
I
I
min si (1 hi ) wi xi
I
xi [0,1]i =1
I
s.t. si ei xi y si ei ,
i=
1
i=
1
i=
1
where ψ is a “compliance” constant that measures how many workers in the jobs sent home comply
with the policy—that is, they work from home—and I is the total number of occupation-industry
pairs.9
Designing the optimal policy is merely a high-dimensional linear programming problem.10
The hi in the objective function is our WFH index value that lies between 0 and 1. For the problem
to be well defined, all ei ’s need to be nonnegative, so we simply shift our exposure index by subtracting off its minimum value. Since the problem is linear, the solution xi* will be either 0 or 1 for all i,
unless the job happens to fall exactly on the threshold.
The objective function is meant to capture the aggregate economic loss from sending home
workers. As a result, the economic loss is larger not only when workers low on the WFH index are
sent home, but also when industry-occupation pairs with a high wage and a large number of workers
are sent home.11 This finding does not necessarily mean that we are not interested in the distributive
consequences of such policies. In fact, we discuss the unequal impact across workers in Section 4.
We are merely separating the question of efficiency (i.e., minimizing the aggregate economic loss)
from the question of redistribution, although we do not consider any redistributive policies in this
article.
Figure 2 shows the optimal policy when ψ = 0.473.12 In Panels A and B, each industry-
occupation pair is plotted as a circle along the exposure (ei , vertical axis) and the wage losses from
sending home workers (wi (1 – hi ), horizontal axis) dimensions. The size of a circle represents job
i’s employment share. The optimal policy is a linear threshold in this two-dimensional space, where
only workers in jobs that are above the threshold are sent home (black circles). The slope of the
threshold is positive since the optimal policy takes into account both exposure and wage losses
from sending home workers. That is, even if a job has high infection risk, it is not sent home if it
cannot be done remotely (low WFH ability) and has a high average wage, implying large wage losses
from working remotely. Panel A is the solution when aggregate exposure is reduced by 10 percent
and Panel B by 40 percent.
Panel C plots the fraction of workers sent home under the optimal policy (black lines with
triangles) for each level of reduction in aggregate exposure (y) on the horizontal axis. Panel D shows
the aggregate wage loss from the optimal policy (black lines with triangles against the same horizontal axis). Both black lines with triangles are upward sloping, since reducing exposure requires
sending more workers home, which also leads to larger wage losses. More important, the lines are
convex, because the optimal policy sends home the jobs with highest exposure and lowest wage
losses first.
One unpleasant feature of the optimal policy we solve above is that many healthcare-related
workers are sent home because they tend to have very high exposure, even though most of them
cannot work from home and thus incur large wage losses. For a more realistic problem during a
pandemic, we also solve a constrained optimal policy in which healthcare-related workers must
work normally. These are workers in the healthcare and social assistance sectors (industry codes
7970-8390) and healthcare practitioners, technical, and support occupations (OCC codes 30003655), who together comprise about 11 percent of (hours-adjusted) aggregate employment. Com
bined, these jobs account for about 20 percent of aggregate exposure.
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Figure 2
Optimal Policy
A. Jobs working from home with y = 0.1
B. Jobs working from home with y = 0.4
Exposure index
Exposure index
3
3
2
2
1
1
0
0
−1
−1
−2
−2
0
50
100
150
50
0
200
100
150
200
Wage loss
Wage loss
C. Fraction working from home
D. Aggregate wage loss
Aggregate wage loss
Fraction working from home
0.5
Unconstrained
Constrained
0.4
0.5
Unconstrained
Constrained
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
0
0
0.1
0.2
0.3
0.4
0
0.5
0.1
0.2
0.3
0.4
0.5
Fraction of exposure reduced
Fraction of exposure reduced
NOTE: In Panels A and B, each circle represents a specific occupation within a specific industry (458 occupations × 254 industries). The size of the
circle denotes the hours-adjusted employment share, averaged from 2014 to 2018. The black circles represent jobs sent home by the optimal policy
(group i such that xi* = 1), and the gray circles indicate jobs performed normally. Panel A is when the aggregate exposure is reduced by 10 percent
and Panel B by 40 percent. In Panels C and D, for a fraction y of aggregate exposure reduction on the horizontal axis, the fraction of workers sent
home and the aggregate wage loss (with the scaling constant ψ = 0.473 under the optimal policy) are shown as black lines with triangles in Panels
C and D, respectively. The constrained optimal policy solves the same problem (1), but with the added constraint that all healthcare-related workers must work normally, as shown by the gray lines with circles.
In Panels C and D of Figure 2, the gray lines with circles plot the fractions of workers sent home
under the constrained optimal policy in Panel C and the aggregate wage loss in Panel D, both against
the reduction in aggregate exposure y on the horizontal axis. Compared with the unconstrained
optimal policy, the constrained policy sends more workers home and causes higher wage losses for
any given reduction in aggregate exposure, but it is still visibly convex.
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The analysis is based on the pre-pandemic employment structure and wages of the United States
as well as our exposure and WFH indexes for the United States. To the extent that the employment
and wage distributions across occupations and industries differ across countries, the trade-off
between infection and economic losses will differ across countries, even if countries share the same
exposure and WFH indexes. In fact, trade-off patterns will also vary across regions or states within
the United States.
4 OPTIMAL POLICY VS. REAL-WORLD LOCKDOWNS
We now compare our optimal policy with a lockdown that mimics those implemented in many
U.S. states and most European countries. Although lockdowns were implemented with varying
degrees of severity across countries and U.S. states, they did share common features. Most often,
governments classified industries as essential or non-essential and tried to keep essential workers
working as normally as possible while also forbidding non-essential workers from commuting to
work. For example, the Cybersecurity and Infrastructure Security Agency of the U.S. Department
of Homeland Security provides guidelines on which jobs are essential for critical infrastructure.
Our version of the real-world lockdown follows Palomino, Rodríguez, and Sebastian (2020), who
show which occupations and industries were effectively locked down in Europe.13 In the context
of our problem (1), jobs sent home in a real-world lockdown are a set {i ∈ {1,2,…,I}|xi = 1}, which
in general will differ from the optimal solution. We set ψ = 0.473, as we did in the previous section,
which generates a 30 percent drop in aggregate wages under the actual lockdown.14 Given ψ, we
find that a real-world lockdown reduces aggregate exposure by 32 percent.
Panel A of Figure 3 shows the non-essential jobs that sent workers home under the actual
lockdown (dark-gray circles) and the jobs that sent workers home under the optimal policy (black
circles). Both policies achieve the same reduction in aggregate exposure, but there is not much overlap between the two policies in terms of which jobs send workers home. In particular, the actual
lockdown sent home many workers in jobs that have relatively low exposure. Panel B shows the
jobs that sent workers home under the constrained optimal policy (black circles) (i.e., all healthcare-related workers working normally) still reduce aggregate exposure by 32 percent.
Table 2 shows exactly how this difference manifests in terms of the fractions of workers sent
home and the aggregate wage loss. The gains from implementing the optimal policy are substantial: The same reduction in exposure can be attained by sending home one-third fewer workers
(36 percent under the lockdown vs. 24 percent under the optimal policy) at half the economic cost
(aggregate wage loss of 30 percent under the lockdown vs. 15 percent under the optimal policy).
Even with the constraint that all healthcare-related workers continue to work normally, the
constrained optimal policy does substantially better than the actual lockdown. It delivers the same
reduction in aggregate exposure, with a one-third smaller loss in aggregate wages.15
Distribution of Exposure Reduction and Wage Loss. Because jobs are different in terms of exposure and WFH ability across occupations and industries, the reductions in exposure and in wage
losses from the policies are distributed unequally across workers. In fact, low-wage jobs tend to
have high exposure and low WFH ability, while high-wage jobs tend to have low exposure and
high WFH ability. As a result, on average, low-wage workers see a large reduction in exposure and
higher wage losses under a real-world lockdown, while high-wage workers see only a small reduction
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Figure 3
Optimal Policy vs. Lockdown
A. Optimal
B. Constrained
Exposure index
Exposure index
3
3
2
2
1
1
0
0
−1
−1
−2
−2
0
50
100
Wage loss
150
0
200
Lockdown
Unconstrained
50
100
150
200
Wage loss
NOTE: Each circle is a specific occupation within a specific industry (458 occupations × 254 industries). The size of a circle represents its employment
share. Dark-gray circles indicate jobs sent home during the actual lockdown. Black circles are the jobs sent home under the unconstrained optimal
policy in Panel A and under the constrained optimal policy in the Panel B.
Table 2
Policy Outcomes
Fraction sent home
Wage loss
A. Lockdown
0.359
0.300
B. Optimal
0.244
0.146
C. Constrained optimal
0.308
0.196
NOTE: The first column is the (hours-adjusted) fraction of workers sent home, and the second is the aggregate wage loss. In all
three cases, aggregate exposure is reduced by 32 percent.
in exposure and lower wage losses.16 Furthermore, since the real-world lockdown and the optimal
policy target different jobs, the two policies have different distributional, as well as aggregate,
consequences.
Figure 4 shows the distributional impacts of the actual lockdown and the optimal policy, across
wage quartiles constructed from the average wage across the occupation-industry pairs.17 In Panel A,
the black bars are the shares of workers in each quartile, each 25 percent by definition. The other
two bars within each quartile show the fractions of workers sent home under the actual lockdown
(light-gray bars, right scale) and the optimal policy (dark-gray bars, right scale). The actual lockdown, which follows the essential/non-essential distinction, sends more low-wage workers home
than high-wage workers (40 percent of the lowest wage quartile vs. 34 percent of the highest wage
quartile). The difference is magnified under the optimal policy (37 percent of the lowest quartile vs.
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Figure 4
Policy Impact Across Wage Quintiles
B. Reduction in exposure
A. Fraction working from home
Fraction working from home
Employment share
0.25
0.5
0.20
0.4
0.15
0.3
0.10
0.2
0.05
0.1
Exposure share
Reduction in exposure
0.4
0.3
0.3
0.2
0.2
0
0.1
0.1
0
Q1
Q2
Q3
0
0
Q1
Q4
Q2
Q3
Q4
C. Wage loss
Wage share
Employment share (left axis)
Wage loss
0.6
Lockdown (right axis)
0.4
Optimal (right axis)
0.3
0.4
0.2
0.2
0.1
0
0
Q1
Q2
Q3
Q4
NOTE: Each industry-occupation pair is ordered by its average wage and assigned to a quartile. In Panel A, the black bars are each wage quartile’s
employment share, which is 0.25 by definition. The light-gray and the dark-gray bars depict the fraction of each quartile sent home due to the actual
lockdown and the optimal policy, respectively, on the right scale. In Panel B, the black bars are each wage quartile’s share of aggregate exposure,
and the light-gray and the dark-gray bars depict the within-quartile reduction in exposure under the actual lockdown and the optimal policy,
respectively. In Panel C, the black bars are each wage quartile’s share of the aggregate wage, and the light-gray and the dark-gray bars depict
within-quartile wage losses under each policy.
13 percent of the highest quartile). There are two reasons for this difference. First, high-wage workers
tend to have low exposure and are hence less likely to be sent home. Second, because of their high
wages, holding other things equal, it is more costly to send home high-wage workers. Nevertheless,
the optimal policy sends fewer workers home in all quartiles than the actual lockdown does.
In Panel B, the black bars are each wage quartile’s share of aggregate exposure, confirming
that low-wage workers have higher exposure on average. The other two bars show the reduction in
exposure due to the actual lockdown (light-gray bars, right scale) and the optimal policy (dark-gray
bars, right scale). Note that both policies reduce exposure more for low-wage workers than high-wage
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workers. The optimal policy strengthens this pattern, reducing exposure more for low-wage than
high-wage workers than the actual lockdown does.18 More significant, for the lower wage quartiles,
the optimal policy achieves a larger reduction in exposure while sending fewer workers home than
the actual lockdown does.
In Panel C, the black bars are each wage quartile’s share of aggregate labor income, which is
higher for higher quartiles, by construction. The other two bars are the wage losses due to the actual
lockdown (light-gray bars, right scale) and the optimal policy (dark-gray bars, right scale). Both
policies incur larger wage losses for the lower wage quartiles. This is because low-wage jobs are more
likely to send workers home under both policies but tend to be harder to perform from home (low
WFH ability). The optimal policy leads to especially small wage losses for the top quartile, although it
generates smaller wage losses than the actual lockdown does across all wage quartiles, as it sends
home fewer workers across the board and also takes into account wage losses.
In summary, low-wage workers are more affected than high-wage workers by both policies:
They are more likely to be sent home. As a result, they experience a larger reduction in exposure
but also larger wage losses. Comparing the two policies, holding the reduction in aggregate exposure constant, low-wage workers see a larger reduction in exposure under the optimal policy, while
high-wage workers see a smaller reduction. However, although the optimal policy results in smaller
wage losses for all wage quartiles, high-wage workers lose the least relative to the actual lockdown.
5 CONCLUSION
We construct exposure and WFH indexes that vary by both occupation and industry and
study their relationship across jobs. WFH ability varies widely even among jobs with similar levels
of exposure, indicating that a planner could reduce the economic cost of a workplace lockdown by
selectively sending home groups of workers based on the two indexes, rather than using broad
essential/non-essential categories. Compared with the actual lockdown, the optimal policy sends
home one-third fewer workers and causes only half the losses in aggregate wages while also reducing aggregate exposure by the same magnitude. In addition, under the optimal policy, high-wage
workers have the smallest wage losses but low-wage workers have the largest reduction in exposure.
While we abstract from some key dimensions, our work is a blueprint for an easily implement
able smarter lockdown of the workplace during a pandemic. In addition, our crosswalk and merging
of the ACS/O*NET and the ATUS can be applied to a wider range of research—beyond the exposure and WFH indexes used in this article. n
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APPENDIX A: RELATED LITERATURE
A new strand of literature measures the degree to which jobs can be performed from home or
are contact intensive. One of the earlier articles is by Dingel and Neiman (2020), who use job characteristics in the O*NET data to determine which occupations can work from home. Koren and
Pető (2020), Hicks, Faulk, and Devaraj (2020), and Leibovici, Santacreau, and Familglietti (2020)
use O*NET data to compute contact intensity. Only a few studies consider differences in such job
characteristics across both industries and occupations. Adams-Prassl et al. (2020) collect information on WFH ability from geographically representative U.S. and British surveys and demonstrate
large variation in WFH ability across industries even for the same occupation.
Most articles consider only either exposure or WFH ability. One exception is by Mongey,
Pilossoph, and Weinberg (2020), who measure both PP (one component of our exposure index)
and WFH ability and show that there is a negative correlation between the two. Their WFH index
is based on occupational characteristics from O*NET alone and does not vary by industry, and
they find a tighter correlation between PP and WFH ability than what we find using WFH ability
based on the ATUS, even when we ignore the industry dimension. Adams-Prassl et al. (2020) also
document a negative relationship between their WFH index and the O*NET PP data.
Few studies explicitly consider the costs of real-world lockdowns. Adams-Prassl et al. (2020)
construct an occupation-level remote labor index using O*NET data and combine it with industry-
wide lockdown measures to assess the heterogeneous effect of industry-level supply shocks across
occupations. Palomino, Rodríguez, and Sebastian (2020) construct a lockdown working ability
(LWA) index by combining a telework index from O*NET and lockdown measures based on government policies in Italy and Spain. They then simulate the impact of social distancing policies on
inequality across European countries. Gottlieb et al. (2020) simulate the economic costs of various
lockdown policies in developing countries, exploiting detailed data on each country’s demographic
and labor market composition. Aum, Lee, and Shin (2021a) do the same for Korea and the United
Kingdom but also model the individual choice of voluntarily working from home out of fear of
infection.
To the best of our knowledge, we are the first to analyze both WFH ability and exposure by
industry and occupation and to go beyond merely documenting their correlation, by using indexes
to determine which jobs to send home to minimize the aggregate wage loss for a given reduction
in exposure.19
APPENDIX B: ALTERNATIVE POLICIES
B1 Exposure Reduction or Wage Loss
The optimal policy minimizes the aggregate wage loss subject to a given reduction in exposure.
We consider alternative programs that minimize exposure or wage losses subject to a given fraction
of workers sent home.
The program that minimizes the aggregate exposure is
(B1)
I
max si ei xi
{ xi [0,1]}iI=1
I
s.t. si xi z,
i=
1
i=
1
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Figure B1
Optimal Policy vs. Alternatives
A. Exposure reduction
B. Wage loss
Fraction of exposure reduced
0.5
Aggregate wage loss
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
0
0
0.1
0.2
0.3
0.4
0
0.5
0.1
0.2
0.3
0.4
0.5
Fraction working from home
Fraction working from home
Unconstrained
Exposure minimized
Constrained
Wage-loss minimized
NOTE: In Panel A, for a given fraction of workers sent home on the horizontal axis, the reduction in aggregate exposure is plotted for the optimal
policy (dashed line), the constrained optimal policy (solid line), the policy that minimizes aggregate exposure (line with diamonds), and the policy
that minimizes the aggregate wage loss (line with circles). Panel B plots the corresponding aggregate wage loss.
which is in fact a maximization of the reduction in exposure subject to a given fraction of workers
sent home. Clearly, the solution is to first send home workers in jobs with the highest exposure,
regardless of wage losses. The other program that minimizes the aggregate wage loss subject to a
given fraction of workers sent home is
(B2)
I
min si wi (1 hi ) xi
{ xi [0,1]}iI=1
I
s.t. si xi z ,
i=
1
i=
1
with the result that only workers with jobs that pay a low wage and/or are easy to perform from
home are sent home.
Figure B1 plots the reduction in exposure and the aggregate wage loss from these two alternative
policies for all levels of z (the fraction of workers sent home) with ψ = 0.473. The outcomes of the
optimal policy and the constrained optimal policy are also plotted for comparison. As shown in
Panel A, unsurprisingly, the exposure minimization policy (line with diamonds) reduces aggregate
exposure by more than any other policy, but at the cost of higher aggregate wage loss, as shown in
Panel B. Conversely, the wage-loss minimization policy (line with circles) has the smallest aggregate
wage loss of all policies, but at the cost of a smaller reduction in exposure than the other policies.
The outcomes of the optimal policy lie between those of the two alternative policies.
B2 Impact of Constrained Optimal Policy Across Wage Quartiles
Finally, in Figure B2 we show the counterpart of Figure 4 for the constrained optimal policy
that keeps all healthcare-related workers working normally.
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Figure B2
Policy Impact Across Wage Quartiles
B. Reduction in exposure
A. Fraction working from home
Fraction working from home
Employment share
0.25
0.5
0.20
0.4
0.15
0.3
0.10
0.2
0.05
0.1
Exposure share
Reduction in exposure
0.4
0.3
0.3
0.2
0.2
0
0.1
0.1
0
Q1
Q2
Q3
0
0
Q1
Q4
Q2
Q3
Q4
C. Wage loss
Wage share
Employment share (left axis)
Wage loss
0.6
Lockdown (right axis)
0.4
Optimal (right axis)
0.3
0.4
0.2
0.2
0.1
0
0
Q1
Q2
Q3
Q4
NOTE: Each industry-occupation pair is ordered by its average wage and assigned to a quartile. In Panel A, the black bars are each wage quartile’s
employment share, which is 0.25 by definition. The light-gray and the dark-gray bars depict the fraction of each quartile sent home due to the
actual lockdown and the constrained optimal policy, respectively, on the right scale. In Panel B, the black bars are each wage quartile’s share of the
aggregate exposure, and the light-gray and the dark-gray bars are the within-quartile reduction in exposure under the actual lockdown and the
constrained optimal policy, respectively. In Panel C, the black bars are each wage quartile’s share of the aggregate wage, and the light-gray and
the dark-gray bars depict within-quartile wage losses by each policy.
The patterns across wage quartiles are similar to those in Figure 4, but there is one important
difference. Relative to the actual lockdown, the constrained optimal policy sends home more workers
in the bottom-wage quartile, resulting in larger wage losses for this group.
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Table C1
Regression Results
Occupation
Industry
Occupation-industry pair
Exposure
WFH ability
Exposure
WFH ability
Exposure
WFH ability
Females
1.24***
(0.43)
–0.02
(0.02)
2.08***
(0.45)
–0.07*
(0.04)
1.11***
(0.22)
–0.00
(0.02)
≥ Bachelor’s degree or
more education
–0.88*
(0.51)
0.12***
(0.04)
–1.45***
(0.51)
0.23***
(0.06)
–0.61*
(0.33)
0.13***
(0.03)
Blacks
4.32***
(1.12)
–0.03
(0.08)
0.68
(0.76)
0.11
(0.11)
1.85***
(0.37)
–0.01
(0.04)
Hispanics
–1.48*
(0.81)
–0.23***
(0.08)
–1.50**
(0.74)
–0.19*
(0.11)
–0.67**
(0.28)
–0.14***
(0.04)
Young (under 30 years
of age)
–2.71***
(0.99)
0.13
(0.08)
–4.71***
(1.08)
0.22
(0.15)
–0.64
(0.41)
0.05
(0.04)
Old (over 50 years of age)
–5.37***
(1.14)
0.15*
(0.09)
–5.15***
(1.29)
0.13
(0.17)
–1.74***
(0.36)
0.03
(0.03)
Self-employed
0.81
(0.49)
0.29***
(0.07)
–0.64*
(0.39)
0.40***
(0.07)
0.26
(0.24)
0.26***
(0.05)
Average hourly wage (in
logs)
0.05
(0.57)
–0.00
(0.04)
–0.45
(0.42)
0.02
(0.06)
0.03
(0.29)
0.01
(0.03)
Constant
1.54
(2.12)
0.01
(0.15)
3.82**
(1.63)
–0.12
(0.23)
0.17
(0.99)
0.02
(0.09)
R2
0.320
0.448
0.606
0.510
0.222
0.159
Observations
458
254
53,694
NOTE: Robust standard errors are in parentheses. *, **, and *** indicate significance at the 90 percent, 95 percent, 99 percent
levels, respectively.
APPENDIX C: EXPOSURE AND WFH ABILITY BY DEMOGRAPHIC
GROUP
How different demographic groups are affected by our index-based optimal policy depends on
whether the variations in the indexes are captured by demographics. Thus, we regress the exposure
index and the WFH index on demographic variables constructed for each occupation, industry,
or industry-occupation pair: the female share, college share, Black and Hispanic shares, young
(under 30 years of age) and old (over 50 years of age) shares, and the self-employment share. The
excluded groups in the regression are males, those without a four-year college degree, Whites, the
middle aged (between 30 and 50 years of age), and employees.
The results are shown in Table C1. Some groups of workers, in particular college graduates,
are both less exposed to infection risk and less likely to be sent home. But as expected from Figure 1,
low exposure does not necessarily mean high WFH ability. Female, Black, and middle-aged workers tend to be more exposed to infection risk, but it is not related to how easily they can work from
home. Hispanics are less likely to work from home but also face relatively lower infection risk. In
contrast, the self-employed are more likely to work from home but do not necessarily face lower
infection risk.
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Demographics are correlated with both the exposure index and the WFH index more by industry
and less by occupation. And when the industry-occupation pairs are used, demographics barely
predict either index. This finding implies that industry-based lockdowns are at risk of disadvantaging vulnerable demographic groups, while more sophisticated policies that take into consideration
both industry and occupation could reduce the likelihood of disproportionately affecting those
groups.
NOTES
1
A review of the relevant literature is in the appendix.
2
These are questions 4.C.2.a.3 and 4.C.2.c.1.b, respectively. These two descriptors were analyzed in detail by the New York
Times (Gamio, 2020) for the United States and reproduced for the United Kingdom by the U.K. Office for National Statistics.
The New York Times and U.K. Office for National Statistics focused on each measure separately and showed that the two
are strongly positively correlated. The economics literature has only used physical proximity as a measure of exposure
(Leibovici, Santacreau, and Famiglietti, 2020, and Mongey, Pilossoph, and Weinberg, 2020).
3
Available at https://www.onetcenter.org/crosswalks.html.
4
In general, the O*NET SOC codes are finer than the ACS OCC codes, so each descriptor for a lower-level SOC occupation
is averaged and subsumed into a higher-level SOC occupation using the SOC-OCC crosswalk. However, O*NET does not
list descriptors for any lower level of some of the three-digit OCC codes, and OCC codes changed in 2018, necessitating
additional manipulation by us.
5
PP and EDI are positively correlated. In particular, the highest EDI occupations (mostly healthcare-related occupations)
also have high PP. At the same time, there are occupations that have high EDI but low PP (e.g., couriers, refuse collectors,
and janitors and building cleaners) and those that have high PP but low EDI (e.g., meeting and event planners, engine
and other machine assemblers, and parts salespersons).
6
Bick, Blandin, and Mertens (2020) also emphasize the difference between index-based potential home-based work and
actual home-based work.
7
Adams-Prassl et al. (2020) show that this is also true in their own surveys in the United States and the United Kingdom.
8
Appendix C shows that the correlation between our indexes and demographics are also weak.
9
Thus, the maximal possible reduction in aggregate exposure is ψ, which may be due to non-compliance, selective furloughs, or a reduction in working hours (such as a curfew on pubs and restaurants) as opposed to a shutdown order, and
so on. Note that the value of ψ does not affect the optimal solution {x*i } but only the magnitudes of the reductions in
wage loss and exposure.
10 Problem (1) is the dual problem of minimizing exposure subject to a given level of the aggregate wage loss.
11 We are not considering job losses at the extensive margin. One could assume that a WFH index h
i below a certain
–
threshold h implies workers sent home are too unproductive to be employed and hence lose their jobs. With this
assumption, one could work out an alternative problem that minimizes job losses rather than the aggregate wage loss.
12 ψ = 0.473 corresponds to a 30 percent drop in aggregate wages under the real-world lockdown, to be shown in Section 4.
13 Palomino , Rodríguez, and Sebastian (2020) identify essential jobs by ISCO (two digit) and NACE (one digit) from the
lockdowns implemented in Italy and Spain. We match these jobs to the OCC and IND codes in the Census. Their list of
essential jobs are broadly consistent with the CISA (Cybersecurity and Infrastructure Security Agency) guidelines.
14 A labor income share of 60 percent implies an 18 percent drop in gross domestic product (GDP) due to the lockdown,
which is between the GDP loss in the United States (10 percent) and the GDP loss in the United Kingdom (20 percent)
from the first to the second quarter of 2020.
15 Of course, there are other jobs that are truly essential. Those jobs can be incorporated as additional constraints to the
minimization problem in (1). While the exemption of a larger set of truly essential jobs will bring our constrained policy
closer to real-world lockdowns, one important distinction is that our constrained policy is at the level of industry-occupation pairs, while the real-world policies were industry based and hence more blunt.
16 Aum, Lee, and Shin (2021b) document a similar unequal impact of the pandemic—even without a lockdown.
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17 The distributional impact of the constrained optimal policy is in the appendix.
18 This is by design, since we solved the optimal policy subject to the same reduction in aggregate exposure as for the
lockdown. The total reduction across all groups must be the same for the lockdown (light-gray bars) and the optimal
policy (dark-gray bars).
19 While most theoretical and structural articles that analyze the effect of the pandemic and lockdowns incorporate a
trade-off between exposure and WFH ability (e.g., Krueger, Uhlig, and Xie, 2020, and Assenza et al., 2020), few consider
the heterogeneity of the trade-off at the micro level. Some exceptions are Alon et al. (2020) and Brotherhood et al. (2020),
who consider differences by age, and Aum, Lee, and Shin (2021a), who consider differences by worker occupation and
skill level.
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Alon, T.; Kim, M.; Lagakos, D. and VanVuren, M. “How Should Policy Responses to the COVID-19 Pandemic Differ in the
Developing World?” NBER Working Paper 27273, National Bureau of Economic Research, May 2020;
https://doi.org/10.3386/w27273.
Assenza, T.; Collard, F.; Dupaigne, M.; P. Féve; Hellwig, C.; Kankanamge, S. and Werquin, N. “The Hammer and the Dance:
Equilibrium and Optimal Policy during a Pandemic Crisis.” CEPR Discussion Paper 14731, Centre for Economic Policy
Research, May 2020; https://cepr.org/active/publications/discussion_papers/dp.php?dpno=14731.
Aum, Sangmin; Lee, Sang Yoon (Tim) and Shin, Yongseok. “Inequality of Fear and Self-Quarantine: Is There a Trade-Off
Between GDP and Public Health?” Journal of Public Economics, February 2021a, Volume 194;
https://doi.org/10.1016/j.jpubeco.2020.104354.
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Effect of Local Outbreaks in Korea.” Labour Economics, June 2021b, Volume 70;
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Economic Review, August 2020, 103(5), 2013, pp. 1553-97; https://doi.org/10.1257/aer.103.5.1553.
Bick, A.; Blandin, A. and Mertens, K. “Work from Home after the COVID-19 Outbreak.” Unpublished manuscript, 2020.
Brotherhood, Luiz; Kircher, Philipp; Santos, Cezar and Tertilt, Michèle. “An Economic Model of the Covid-19 Epidemic: The
Importance of Testing and Age-Specific Policies.” CESifo Working Paper Series 8316, 2020;
http://dx.doi.org/10.2139/ssrn.3618840.
del Rio-Chanona, R.M.; Mealy, P.; Pichler, A.; Lafond, F. and Farmer, J.D. “Supply and Demand Shocks in the COVID-19
Pandemic: An Industry and Occupation Perspective.” Oxford Review of Economic Policy, August 2020, 36(Supplement 1),
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Dingel, J.I. and Neiman, B. “How Many Jobs Can Be Done at Home?” Journal of Public Economics, September 2020, 189,
104235; https://doi.org/10.1016/j.jpubeco.2020.104235.
Gamio, L. “The Workers Who Face the Greatest Coronavirus Risk.” New York Times, March 15, 2020.
Gottlieb, C.; Grobovšek, J; Poschke, M. and Saltiel, F. “Lockdown Accounting.” Centre for Economic Policy Research Covid
Economics: Vetted and Real-Time Papers, June 2020.
Hicks, M.J.; Faulk, D. and Devaraj, S. “Occupational Exposure to Social Distancing: A Preliminary Analysis Using O*NET
Data.” Technical report, Center for Business and Economic Research, Ball State University, March 2020.
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https://doi.org/10.1371/journal.pone.0239113.
Krueger, D.; Uhlig, H. and Xie, T. “Macroeconomic Dynamics and Reallocation in an Epidemic.” Centre for Economic Policy
Research Covid Economics: Vetted and Real-Time Papers, April 2020;
https://cepr.org/sites/default/files/CovidEconomics5.pdf.
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Lee, S.Y. and Shin, Y. “Horizontal and Vertical Polarization: Task-Specific Technological Change in a Multi-Sector
Economy.” NBER Working Paper 23283, National Bureau of Economic Research, March 2017;
https://doi.org/10.3386/w23283.
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Mongey, S.; Pilossoph, L. and Weinberg, A. “Which Workers Bear the Burden of Social Distancing Policies?” Centre for
Economic Policy Research Covid Economics: Vetted and Real-Time Papers, May 2020;
https://cepr.org/sites/default/files/CovidEconomics12.pdf.
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in Europe.” European Economic Review, 2020, 129, 103564; https://doi.org/10.1016/j.euroecorev.2020.103564.
109
Failing to Provide Public Goods:
Why the Afghan Army Did Not Fight
Rohan Dutta, David K. Levine, and Salvatore Modica
The theory of public goods is mainly about the difficulty in paying for them. Our question here is this:
Why might public goods not be provided, even if funding is available? We use the Afghan Army as our case
study. We explore this issue using a simple model of a public good that can be provided through collective
action and peer pressure, by modeling the self-organization of a group (the Afghan Army) as a mechanism
design problem. We consider two kinds of transfer subsidies from an external entity such as the U.S. government. One is a Pigouvian subsidy that simply pays the salaries, rewarding individuals who provide effort.
The second is an output/resource multiplier (the provision of military equipment, tactical skill training, and
so forth) that amplifies the effort provided through collective action. We show that the introduction of a
Pigouvian subsidy can result in less effort being provided than in the absence of a subsidy. By contrast, an
output/resource multiplier subsidy, which is useful only if collective action is taken, necessarily increases
output via an increase in effort. Our conclusion is that the United States provided the wrong kind of subsidy,
which may have been among the reasons why the Afghan Army did not fight. (JEL A1, D7, D9)
Federal Reserve Bank of St. Louis Review, Second Quarter 2022, 104(2), pp. 110-19.
https://doi.org/10.20955/r.104.110-19
“We paid their salaries...What we could not provide was the will to fight.” President Joe Biden1
1 INTRODUCTION
The speed with which the Afghan Army collapsed and the Taliban took over Afghanistan came
as a surprise to many, but not to economists or individuals versed in game theory. By backward
induction, if you plan to surrender anyway, then sooner is generally better than later (unless you
are indifferent between present versus future payoffs). This article, however, explores a deeper
question: Why would a well-equipped army that outnumbered their opponents by three or four to
one in manpower and with decades of training plan to surrender to an apparently much inferior
opponent?
Rohan Dutta is an associate professor of economics at McGill University. David K. Levine is a professor of economics at the European University
Institute, a professor of economics emeritus at Washington University in St. Louis, and a research fellow at the Federal Reserve Bank of St. Louis.
Salvatore Modica is a professor of economics at Università di Palermo, Dipartimento SEAS. We thank Andrea Mattozzi. We gratefully acknowledge
support from the MIUR PRIN 2017 n. 2017H5KPLL_01.
© 2022, Federal Reserve Bank of St. Louis. The views expressed in this article are those of the author(s) and do not necessarily reflect the views of
the Federal Reserve System, the Board of Governors, or the regional Federal Reserve Banks. Articles may be reprinted, reproduced, published,
distributed, displayed, and transmitted in their entirety if copyright notice, author name(s), and full citation are included. Abstracts, synopses, and
other derivative works may be made only with prior written permission of the Federal Reserve Bank of St. Louis.
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The quote from President Joe Biden’s speech following the fall of Kabul is revealing: What
Biden and many others fail to understand is that there is a causal connection between paying the
salaries of the Afghan Army and the fact that they lacked the will to fight. Our goal in this article is
to explain why that is so and why it need not have been so.
Insofar as nation building is measured by the national defense, the place to start is to understand
that national defense is a public good. Many Afghans would prefer not to be ruled by the Taliban,
but most would prefer that someone else do the fighting. This problem of free riding is endemic to
public goods problems, and economists and other social scientists have analyzed these problems for
over a century. We recognize three ways of overcoming the free-rider problem. The most familiar
one involves collective action through formal systems, usually Pigouvian taxes or subsidies, which
are widely recommended by economists to achieve, for example, reductions in carbon emissions
to combat global warming. A second, less formal means of providing public goods is through voluntary provision: People contribute to a public good either because the personal benefit of the public
good is sufficiently great to outweigh the cost of contributing or because they are altruistic and
desirous of helping society (e.g., by funding public radio and television in the United States [NPR
and PBS]). There is little evidence, however, that voluntary public goods provision can provide
public goods on a large scale—for an entire country, for example, as in the case of an army.
We wish to focus on a third means of public good provision: providing incentives informally
or “socially” through means such as peer pressure, resulting in various forms of ostracism of those
who fail to contribute. Although economists have not studied this to the extent that they have
studied taxes and subsidies, we know, particularly from the work of Coase (1960), Ostrom (1990),
and Townsend (1994), that these methods work in practice. Indeed, the effectiveness of large-scale
lobbying organizations such as farmers show that peer pressure can be effective even on a very large
scale. After all, all farmers want the benefits of farm subsidies but prefer that other farmers bear
the cost of lobbying.
Of course, while groups and societies can collectively self-organize social norms that induce
provision of public goods, they may also choose simply to follow the “law of the jungle” and allow
members to go their own way and free ride as they wish. The right choice depends on how valuable
the public good is and how costly it is to organize and enforce collective decisions. Our starting
observation is that the intervention of outside agencies—be they non-governmental organizations
(NGOs) or the United States—changes the trade-offs for collective decisionmaking. Simply put, if
the United States pays the salaries of the Afghan Army, then there is little benefit from the Afghans
collectively organizing to encourage people to join the army and fight for their country. In practice,
if the salary is sufficiently high relative to the outside option, people might join but will not fight
when it is time to deliver. Indeed, General Wesley Clark, former NATO supreme allied commander,
gives the following description of the motivation of Afghan soldiers: “People signed up with the
Afghan military to make money...but they did not sign up to fight to the death, for the most part.”2
Contrast this with J.R.R. Tolkien’s description of Britain at the start of World War I: “In those days
chaps joined up, or were scorned publicly.”3 We think it is reasonable to assume that such peer
pressure to defend the country did not exist in Afghanistan.
Here is the key point: The displacement of self-organization by subsidy can result in less
provision of the public good than in the absence of the subsidy. In other words, subsidizing a
public good—the Pigouvian approach—can reduce the provision of that good if it displaces
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self-organization. The reason is that self-organization is costly, and so the benefit of not organizing
can exceed the cost of having less of the public good.
In this article, we examine a simple model of a public good that can be provided through collective action and peer pressure and examine the effect of subsidies. Our model follows Townsend
(1994), Levine and Modica (2016), and Dutta, Levine, and Modica (2022) by modeling the self-
organization of a group as a mechanism design problem. The group establishes an output quota, it
has a noisy monitoring technology for observing whether the quota is followed, and it can punish
group members based on these signals. A key feature of the model is that if monitoring and punishment is to be used, it has an associated fixed cost that includes both the physical cost of monitoring
and the costs of negotiating and finding an agreement as to what the mechanism will be.
In this setting, we consider two kinds of subsidies. One is a Pigouvian subsidy that simply “pays
the salaries,” rewarding individuals who provide effort. We show that this can result in less effort
being provided than in the absence of a subsidy. The other is an output multiplier: the provision
of training, equipment, and so forth, that amplifies the effort provided through collective action.
Because such provision is useful only if collective action is taken, unlike with a Pigouvian subsidy,
it necessarily increases output.
In Dutta, Levine, and Modica (2022), we showed more broadly how Pigouvian subsidies can
have the perverse effect of undermining existing collective action. We pointed there to the case of
NGOs. Bano (2012) did extensive field research in Pakistan. She documented how public goods,
particularly welfare, were provided through voluntary efforts with socially provided incentives for
contribution. Donor organizations—mostly NGOs—subsequently attempted to increase public
good provision through subsidies in the form of salaries to those contributing to the public good.
In a series of case studies, she showed how such subsidies led to the unraveling of the provision of
social incentives and ultimately to decreased provision of the public good. In one of several cases,
she indicates that “the Maternity and Child Welfare Association...almost collapsed with the influx
of such aid.”4
The evidence now shows that similar considerations can be applied to the Afghan Army. We
cannot know how strong the social pressure to self-organize resistance to the Taliban would have
been without subsidies; but the fact is that by paying the salaries of soldiers, the incentive for collective action to encourage volunteers to join the army for the common good was reduced so much
that provision of the public good—measured not by the number of soldiers, but by the number of
soldiers willing to fight—was minimal. Hence, the Taliban, an army recruited through social incentives, predominates and once again rules Afghanistan.
The collapse of Afghanistan is often compared to the collapse of South Vietnam. In this context
it is worth pointing out that the United States did not pay soldiers’ salaries in South Vietnam but
only provided subsidies in the form of training and equipment. What is less well know is that, as a
result, the South Vietnamese Army (ARVN) did fight.5 The United States withdrew from Vietnam
in 1973. In the next year the ARVN largely drove the Vietcong, the North Vietnam irregular army
somewhat akin to the Taliban, out of South Vietnam. In 1975 the North invaded with a large regular
army of similar strength to the ARVN, including a great many artillery pieces. The fighting lasted
about four months, and the casualties on both sides combined were about 45,000 killed and 80,000
wounded. This is greatly different from Afghanistan, where a large superior well-equipped military
refused to fight and was defeated in weeks by a small, lightly armed group of irregular fighters.
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The bottom line is not entirely negative—either for nation building or for NGOs. It is not that
help cannot be provided, but care must be taken that the help provided does not undermine the
provision of effort through collective action and social norms. Hence, providing military training
and equipment will generally result in greater defense, just as providing computers and training to
charitable organizations can do the same.
2 THE MODEL
Identical group members i ∈ [0,1] engage in production, choosing a real valued level of output
X ≥ x i ≥ 0 such as fighting effort in the case of Afghanistan. The utility of a member i depends on
a vector-valued state of the world ω ≥ 0, their own output, and the average output of the group
x = xi di according to u(ω,x,x i ), where u(ω,x,x i ) is specified below.
The output of the group x is a public good—in our case national defense. Because all members
benefit from the public good, the group collectively faces a mechanism design problem, and we
assume that incentives can be given to group members in the form of individual punishments based
on monitoring: The group can set a production quota y and receives signals of whether or not individual output adheres to the quota. Based on these signals it can impose punishments. Specifically,
monitoring generates a noisy signal zi ∈ {0,1}, where zero means “good, likely respected the quota”
and 1 means “bad, likely produced less than the quota.” The probability of the bad signal is π > 0 if
x i ≥ y and πB > π if x i < y. When the signal is bad, the group imposes an endogenous utility penalty
of P. This may be in the form of social disapproval or even in the form of monetary penalties.
The social cost of the punishment P is ψP, where ψ > 0 could be greater or less than 1. For example, if the punishment is that group members are prohibited from drinking beer with the culprit,
that might be costly to the culprit’s friends as well as the culprit. In this case, ψ > 1. Or it might be
that the punishment is a monetary fine, most of which is shared among the group members. In that
case, there would be very little social loss, so we would expect ψ < 1.
In addition to the social cost of punishment, there is a fixed cost F ≥ 0 of choosing P > 0. There
are two reasons we expect F to be positive. First, there will generally be costs of operating the monitoring system—for example, sending spies to observe output. Second, it is costly to gather group
members to negotiate an agreement and form a consensus on what the mechanism will be.
The tools available for mechanism design consist of a quota y and a punishment level for a bad
signal P. The overall utility of a member i is u(ω,x,x i ) – πP if x i ≥ y and u(ω,x,x i ) – πBP if x i < y. These
utilities define a game for the group members. If the mechanism designer chooses (y,P), we denote
by X(y,P) the set of x such that x i = x is a symmetric pure strategy Nash equilibrium of this game.
We refer to a triple (x,y,P) with x ∈ X(y,P) as an incentive compatible social norm.6 If an incentive
compatible social norm issues no punishments (P = 0), we call it noncooperative. The mechanism
designer is benevolent, and welfare from an incentive compatible social norm (x,y,P) is given by
W(x,y,P) ≡ u(ω,x,x) – πψP – F . 1{P > 0}.
We now specify the utility function and interventions. Each individual has a private cost of
output (c/2)(x i )2, and the benefit of the public good is x – (1 – c)(1/2)x2. These units are chosen so
that the first-best x f maximizing –(c/2)x2 + x – (1 – c)(1/2)x2 is normalized so that x f = 1. We take
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the effort limit X to coincide with the satiation level for the public good gross benefit x – (1 – c)(1/2)x2;
so X = 1/(1 – c), and we assume that 0 < c < 1.
A novel aspect of the present article—which is what drives its main result—is the exact specification of the state variable. The state ω has two components: a Pigouvian subsidy ωs , which may be
thought of as contributing to the salary of group members who provide effort, and an output multiplier ωm, which may be thought of as equipment and training that increases the effectiveness of effort
provided by group members. Overall individual utility is then given by u(ω,x,x i ) = –(c/2)(x i )2 +
ωs x i + (1 + ωm)x – (1 – c)(1/2)((1 + ωm)x)2. We are going to show that the two types of subsidies—
in our case provided mainly by the United States—have quite different consequences in terms of
effort provision in the organization.
We define the monitoring difficulty as θ = ψπ/(πB – π).
3 SUBSIDIES ARE BAD, TRAINING IS GOOD
We are interested in reversals, that is, conditions under which introducing a subsidy reduces
the effort level x̂(ω) that solves the mechanism design problem. Recalling that the group solves a
mechanism design problem, we denote the optimal choice of x conditional on P > 0 by xM(ω) and
the output of the noncooperative social norm (the Nash equilibrium) by xN(ω). The solution to the
design problem x̂ may be either xM or xN. Formally, there is a reversal if (1 + ωm)x̂(ω) < x̂(0). By no
reversal we mean the opposite inequality holds (strictly). We show in the appendix that xN(ω) and
xM(ω) are strictly increasing and that for the relevant range of ω it is xM(0) > (1 + ωm)xN(ω). It follows that the only way in which a reversal can occur is if the group prefers to use the mechanism M
with punishment at ω = 0 but reverts to noncooperation at ω > 0. That is, the subsidy, salaries paid
by the United States for example, substitutes for the costly use of peer pressure. Our main result
states the conditions under which this may or may not occur:
– and for all sufficiently small F > 0 and ω ≥ 0, there is
Theorum 1. For each ωs in a range 0 < ωs < ω
s
m
– and for all F ≥ 0 and sufficiently small
a reversal. On the contrary, for each ωm in a range 0 < ωm < ω
m
ωs ≥ 0, there is no reversal.
Subsidies, in other words, are bad in the sense that they can reduce output, while training can
only increase output. The result is proved in the appendix.
4 DISCUSSION
How does the model explain the collapse of the Afghan Army? According to our theory, the
payment of salaries by the United States substituted for a peer enforcement system: When the salary
payments were withdrawn, we might expect that it would have been replaced by a peer enforcement
system—but there was no time for this. Hence, it was best to surrender right away and not, for example, allow the relatively small number of commandos who were ready to fight to do so. We can of
course point to other elements: the corruption of the Afghan government, the removal of air support
when the United States withdrew, and the fact that those who were called upon to fight—mostly
young men—were different from those who benefited significantly from the fighting—mostly women
and older men.7 The point to emphasize is that none of these things are peculiar to Afghanistan. In
the case of Vietnam, where the ARVN did fight, it is equally true that the government was corrupt
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and that the United States stopped providing air support. Moreover, it is hard to think of any war in
which those who fought were not young men—a group that typically has the lowest relative benefit
from victory. The stay-at-homes, be they women or older men, tend to benefit the most. More broadly,
while support for the Taliban was strong in opium-producing areas, they were opposed in most
other areas, and self-organization in the absence of salary subsidies is not implausible.8
We conclude by pointing out that the theory that the collapse of social norms can produce the
“perverse” effect of reducing public good output has support in other realms. In the introduction,
we pointed to the work of Bano (2012) on NGOs in Pakistan. In a field experiment, Gneezy and
Rustichini (2000) examined the effect of a fine on the provision of a public bad—picking children
up late from a day-care center. They found that the fine resulted in more parents picking up their
children late—an increase of the public bad and the opposite of the expected and intended effect.
In a quite different context, Dutta, Levine, and Modica (2022) showed that similar considerations
explain why in the face of an enormous drop in demand for oil due to COVID-19 the OPEC+ cartel
increased their output. Here also, increased output is a public bad and the exogenous state is not a
Pigouvian fine but a reduction in demand. Ordinarily we would expect lower demand to reduce
output, but in fact it resulted instead in the inability to reach an agreement over quotas and in a
noncooperative social norm in which output—the public bad—went up. n
APPENDIX
Here we prove Theorem 1. The proof follows from a few lemmas proven below.
Recalling that the group solves a mechanism design problem, we denote the optimal choice of
x conditional on P > 0 by xM(ω) and the output of the noncooperative social norm by xN(ω). The
solution to the design problem x̂ may be either xM or xN. The corresponding optimal values exclusive of fixed cost are uM(ω) and uN(ω). We say that ω is of moderate size if (1 + ωm)ωs ≤ c/(1 + θc).
Lemma 3 shows that xN(ω) and xM(ω) have strictly positive partial derivatives so are strictly
increasing. We also show for moderate ω that xM(0) > (1 + ωm)xN(ω). It follows that the only way in
which a reversal can occur—(1 + ωm)x̂(ω) < x̂(0)—is if the group prefers to use the mechanism M
with punishment at ω = 0 but reverts to noncooperation at ω > 0.
The group will only use M at ω = 0 if F ≤ uM(0) – uN(0) and will only use N at ω if F ≥ uM(ω) –
N
u (ω) and has strict preferences when the inequalities are strict. If uM(ω) – uN(ω) > uM(0) – uN(0),
then there can be no such F. Conversely, if uM(ω) – uN(ω) < uM(0) – uN(0), then there will be a reversal for any uM(ω) – uN(ω) < F < uM(0) – uN(0). Hence, we must know if uM(ω) – uN(ω) increases or
decreases with ω.
In Lemma 3 we show that at ω = 0 the partial derivative of uM(ω) – uN(ω) is negative with
respect to ωs and positive with respect to ωm.
Take ωs first. Since the partial derivative of uM(ω) – uN(ω) is negative at zero, there is a range of
ωs for which uM(ω) – uN(ω) is strictly decreasing; hence, for any ωs in that range and ωm = 0, we have
uM(ω) – uN(ω) < uM(0) – uN(0). Since uM(ω) and uN(ω) are continuous by Lemmas 1 and 2, it follows
that this remains true for ωm sufficiently small. Hence, we obtain the first result, that there is a range
of F’s for which there is a reversal.
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Similar reasoning with respect to ωm shows that there is a range of ωm with ωs = 0 for which
u (ω) – uN(ω) > uM(0) – uN(0), and again by continuity this continues to hold for sufficiently small
ωs , giving the result about no reversal.
The cited lemmas follow.
M
Lemma 1. The individual optimum is xB(ω) = ωs/c with utility u(ω,x,xB) = ωs2/(2c) + (1 + ωm)x –
(1 – c)(1/2)((1 + ωm)x)2. As the optimum is independent of x, this is also the noncooperative (Nash)
social norm: xN(ω) = ωs /c, with corresponding welfare
u N ( ) = u ( , x N , x N )= s2 / (2c ) (1 m )s / c (1 c)(1 / 2)((1 m )s / c) 2 .
Proof. The first sentence follows from maximizing the objective, u(ω,x,x i ) = –(c/2)(x i )2 + ωs x i +
(1 + ωm)x – (1 – c)(1/2)((1 + ωm)x)2 with respect to xi.
Lemma 2. The optimal incentive compatible quota x M(ω) and the corresponding utility uM(ω) are
given by
x M ( ) =
(1 )s 1 m
(1 )c (1 c)(1 m ) 2
and
2
1 (1 )s 1 m
=
s2 / (2c ).
u ( )
2 (1 )c (1 c)(1 m )2
M
Proof. Given ω and a quota y = x, the incentive constraint is u(ω,x,x) – πP ≥ u(ω,x,x B) – πBP, so the
quota is made incentive compatible by punishment
P = u ( , x, x B ) u ( , x, x ) / ( B ).
Then monitoring cost is πP, yielding a social utility exclusive of fixed costs of
u ( , x, x ) u ( , x, x B ) u ( , x, x)
=
=
=
s 1 m x (1 c)(1 m )2 c x 2 / 2 s2 / (2c) s x cx 2 / 2
s 1 m s x (1 c)(1 m )2 c x 2 / 2 s2 / (2c) cx 2 / 2
s 1 m s x (1 c)(1 m )2 c c x 2 / 2 s2 / (2c)
= (1 / 2) (1 c)(1 m )2 (1 )c x 2 (1 )s 1 m x s2 / (2c).
Using the fact that maximizing Ax – (B/2)(x)2 has solution x = A/B and optimum value, A2/(2B)
yields the values of xM,uM given in the result.
We say that ω is of moderate size if (1 + ωm)ωs ≤ c/(1 + θc).
Lemma 3. If ω is of moderate size, then xM(0) > (1 + ωm)xN(ω),
(1 m ) x M
,
s
(1 m ) x M
>0
m
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and
[u M u N ]
[u M u N ]
< 0,
> 0.
s
m
=
0
=
0
Proof. From Lemma 2,
M
x=
(0)
1
1
=
,
(1 )c (1 c) 1 c
while from Lemma 1, (1 + ωm)xN(ω) = (1 + ωm)ωs /c. Hence, xM(0) > (1 + ωm)xN(ω) exactly when
(1 m )s <
c
,
1c
which says that ω is of moderate size.
Next we assess the partial derivatives of (1 + ωm)xM(ω), where x M(ω) is given in Lemma 2.
We have
(1 m ) x M
(1 m )(1 )
=
> 0.
s
(1 )c (1 c)(1 m ) 2
A little algebra shows that
(1 m ) x M
(1 )cs 2c(1 m ) (1 c)s (1 m ) 2
= (1 )
.
2
m
(1 )c (1 c )(1 ) 2
m
Divide the numerator by 1 – c and observe that
c
c
(1 )s 2(1 m ) s (1 m ) 2
2(1 m ) s (1 m ) 2 ,
1 c
1 c
where the right-hand side has the same sign as
2c
s (1 m ).
1 c
So the derivative is positive if ωs(1 + ωm) < 2c/(1 – c); and this holds by moderation: ωs(1 + ωm) <
c/(1 + θc) < 2c/(1 – c).
Finally, we assess the partial derivatives of uM(ω) – uN(ω) at ω = 0. From Lemmas 1 and 2, the
difference uM(ω) – uN(ω) is given by
s2 s2 (1 m )s 1
1 (1 )s 1 m
(1 m )s
(1 c)
2
2 (1 )c (1 c)(1 m )
2c
2c
c
2
c
2
2
(1 )s2 (1 m )s 1
(1 m )2 s2
1 (1 )s 1 m
(1
)
.
c
2 (1 )c (1 c)(1 m ) 2
2c
2
c
c2
2
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Dutta, Levine, Modica
From this,
[u M u N ]
(1 )
c (1 ) (1 )c (1 c )
=
=
1 / c
s
(1 )c (1 c )
c (1 )c (1 c)
=0
=
(1 c)
<0
c (1 )c (1 c)
and
2
2
[u M u N ]
1 2 1 m (1 )c (1 c)(1 m ) 2 1 m (1 c )(1 m )
=
2
m
2
(1 )c (1 c)(1 ) 2
= 0
=
(1 )c (1 c) (1 c)
=
(1 )c (1 c) 2
m
(1 )c
(1 )c (1 c) 2
> 0.
This concludes the proof.
NOTES
1
Biden (2021).
2
Clark (2021).
3
Tolkien (1981).
4
Bano (2012, p. 126).
5
The historical facts are not controversial and are discussed in many histories; see, for example, Willbanks (2004).
6
In the language of contract theory, it is an enforcement contract with costly state verification.
7
Winning a war would require a great benefit to provide a net benefit to those who fight it. Indeed, fighters are generally
those from relatively modest backgrounds for whom the type of government is not of crucial importance. In the case of
Afghanistan, men are actually likely to do relatively well under Taliban rule.
8
See Mery-Khosrowshahi (2021).
REFERENCES
Bano, M. Breakdown in Pakistan: How Aid Is Eroding Institutions for Collective Action. Stanford University Press, 2012.
Biden, Joe. “Remarks by President Biden on the Economy.” White House, September 16, 2021; https://www.whitehouse.
gov/briefing-room/speeches-remarks/2021/09/16/remarks-by-president-biden-on-the-economy-4/.
Clark, Wesley. Interview with CNN. “Former NATO Commander Speaks to CNN About the Taliban’s Takeover.” August 18,
2021; https://www.cnn.com/world/live-news/
afghanistan-taliban-us-news-08-18-21/h_10d2c797318aff2a0d10497b762164d5.
Coase, R.H. “The Problem of Social Cost.” Journal of Law and Economics, 1960, 3, pp. 1-44; https://doi.org/10.1086/466560.
Dutta, R.; Levine, D.K. and Modica, S. “Interventions with Sticky Social Norms: A Critique.” Journal of the European Economic
Association, February 2022, 20(1), pp. 39-76; https://doi.org/10.1093/jeea/jvab015.
Gneezy, U. and Rustichini, A. “A Fine Is a Price.” Journal of Legal Studies, 2000, 29(1), pp. 1-17;
https://doi.org/10.1086/468061.
Levine, David and Modica, Salvatore. “Peer Discipline and Incentives Within Groups.” Journal of Economic Behavior and
Organization, 2016, 123, pp. 19-30; https://doi.org/10.1016/j.jebo.2015.12.006.
118
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Federal Reserve Bank of St. Louis REVIEW . Second Quarter 2022
Mery-Khosrowshahi, Aschkan. “The Opium of the People: Essays on Counter-Narcotics Efforts in Afghanistan.” PhD Thesis,
European University Institute, 2021.
Ostrom, Elinor. Governing the Commons: The Evolution of Institutions for Collective Action. Cambridge University Press, 1990.
Tolkien, J.R.R. “Letter 43,” in H. Carpenter and C. Tolkien, eds., The Letters of JRR Tolkien. Houghton Mifflin, 1981.
Townsend, Robert M. “Risk and Insurance in Village India.” Econometrica, 1994, 62, pp. 539-39;
https://doi.org/10.2307/2951659.
Willibanks, James H. Abandoning Vietnam: How America Left and South Vietnam Lost Its War. University Press of Kansas, 2004.
119
Venture Capital:
A Catalyst for Innovation and Growth
Jeremy Greenwood, Pengfei Han, and Juan M. Sánchez
This article studies the development of the venture capital (VC) industry in the United States and assesses
how VC financing affects firm innovation and growth. The results highlight the essential role of VC financing for U.S. innovation and growth and suggest that VC development in other countries could promote
their economic growth. (JEL E13, E22, G24, L26, O16, O31, O40)
Federal Reserve Bank of St. Louis Review, Second Quarter 2022, 104(2), pp. 120-30.
https://doi.org/10.20955/r.104.120-30
1 INTRODUCTION
Venture capital (VC) is a particular type of private equity that focuses on investing in young
companies with high-growth potential. The companies and products and services VC helped
develop are ubiquitous in our daily lives: the Apple iPhone, Google Search, Amazon, Facebook and
Twitter, Starbucks, Uber, Tesla electric vehicles, Airbnb, Instacart, and the Moderna COVID-19
vaccine. Although these companies operate in drastically different industries and with dramatically
different business models, they share one common and crucial footprint in their corporate histories:
All of them received major financing and mentorship support from VC investors in the early stages
of their development.
This article outlines the history of VC and characterizes some stylized facts about VC’s impact
on innovation and growth. In particular, this article empirically evaluates the relationship between
VC, firm growth, and innovation.
2 THE VC INDUSTRY IN THE UNITED STATES
This section outlines the historical background on the rise of VC firms as limited partnerships
and characterizes some stylized facts about the VC industry in the United States.
Jeremy Greenwood is a professor of economics at the University of Pennsylvania. Pengfei Han is an assistant professor of finance at Guanghua
School of Management at Peking University. Juan M. Sánchez is a vice president and economist at the Federal Reserve Bank St. Louis. We thank
Ana Maria Santacreu for helpful comments.
© 2022, Federal Reserve Bank of St. Louis. The views expressed in this article are those of the author(s) and do not necessarily reflect the views of
the Federal Reserve System, the Board of Governors, or the regional Federal Reserve Banks. Articles may be reprinted, reproduced, published,
distributed, displayed, and transmitted in their entirety if copyright notice, author name(s), and full citation are included. Abstracts, synopses, and
other derivative works may be made only with prior written permission of the Federal Reserve Bank of St. Louis.
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2.1 Historical Background: VC Firms as Limited Partnerships
Financing cutting-edge technologies has always been challenging.1 It is difficult to know
whether new ideas are viable, if they will be salable, and how best to bring them to market. Also, it
is important to ensure that entrepreneurs’ and investors’ incentives are aligned. Traditional financial institutions, such as banks and equity/securities markets, are not well suited to engage in this
sort of underwriting. Historically, the introduction of new technologies was privately financed by
wealthy individuals. Investors were plugged into networks of inventive activity in which they learned
about new ideas, vetted them, and drew on the expertise needed to operationalize them. These financiers are similar to today’s “angel investors.”
The Brush Electric Company provided such a network for inventors and investors in Cleveland
around the turn of the twentieth century. The use of electricity rapidly expanded during the Second
Industrial Revolution. Individuals linked with the Brush Electric Company network spawned ideas
for arc lighting, liquefying air, smelting ores electrically, and electric cars and trolleys, among other
things. The shops at Brush were a meeting place for inventors; they could develop and debug new
ideas with help from others. Investors connected with the Brush network learned about promising
new ideas from the scuttlebutt at the shops. They became partners/owners in the firms that they
financed. Interestingly, in the Midwest at the time, prolific inventors (those with more than 15
patents) who were principals in companies were much more likely than other investors to keep
their patents or assign them to the companies where they were principals; other investors typically
sold their patents to businesses where they had no concern. These practices aligned the incentives
of innovators and investors.
World War II and the start of the Cold War ushered in new technologies, such as jets, nuclear
weapons, radars, and rockets, along with a splurge of spending by the U.S. Department of Defense.
A handful of VC firms were formed to leverage the commercialization of scientific advances.
American Research and Development (ARD), founded by General Georges Doriot and others,
was one of these. ARD pulled in money from mutual funds, insurance companies, and an initial
public stock offering. The founders knew that it was important for venture capitalists to provide
advice to the fledging enterprises in which they were investing. In 1956, ARD invested $70,000 in
Digital Equipment Corporation (DEC) in exchange for a 70 percent equity stake. ARD’s share was
worth $38.5 million when DEC went public in 1966, which represented an annual return of 100
percent. While this investment was incredibly successful, the organizational form of ARD did not
come to dominate the industry. The compensation structure of ARD made it difficult for the company to retain the VC professionals needed to evaluate startups and provide the guidance necessary
for success.
An alternative organizational form came to emblematize the industry: the limited partnership.
This form is exemplified by the formation of Davis and Rock in 1961. These partnerships allowed
VC professionals to share in the gains from startups along with the entrepreneurs and investors.
Limited partnerships served to align venture capitalists’ interests with those of entrepreneurs,
investors, and key employees. Money was put in only at the beginning of the partnership. The general partners received management fees as a salary plus a share of the capital gains from the investments, say 40 percent, with the limited partners earning 60 percent. The limited partners had no
say in the decisions of the general partners. The partnerships were structured for a limited length
of time, say seven to ten years. The returns from the partnership were paid out to the investors only
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when the partnership was dissolved—there were no dividends, interest payments, etc. Therefore,
the returns upon dissolution were subject only to capital gains taxation at the investor level. The
VC industry also used stock options to reward founders, CEOs, and key employees. Thus, these
recipients too were subject to capital gains taxation rather than taxation on labor income. The short
time horizon created pressure to ensure a venture’s rapid success.
Banks and other financial institutions are not well suited to invest in cutting-edge new ventures.
While banks are good at evaluating systematic lending risk, they have limited ability to judge the
skill of entrepreneurs or the worth of new technologies and limited expertise to help commercialize
them. Additionally, financial institutions have faced roadblocks to investing in ventures. The GlassSteagall Banking Act of 1993, which was later repealed in 1999, prohibited banks from taking equity
positions in industrial firms. The Allstate Insurance Company created a private placements program
in the 1960s to undertake VC-type investments; however, it abandoned the program because it
could not compensate the VC professionals enough to retain them. The Employee Retirement
Income Security Act of 1974 prevented pension funds (and dissuaded other traditional fiduciaries)
from investing in high-risk ventures. The act has been reinterpreted since 1979 to allow pension
funds to invest in VC-operating companies, which provided a fillip for the VC industry.
2.2 Stylized Facts About the VC Industry
Venture capitalists provide funding to startup companies in exchange for a share of company
equity. Apart from money, venture capitalists also provide mentorship services to foster the growth
of startups. Since the life span of a VC fund is typically 10 years, venture capitalists are incentivized
to target deals where a small amount of investment can generate a large financial return within a
short period. Hence, VC investment tends to focus on high-growth companies in the high-tech
sector. To illustrate, Figure 1 shows the share of VC investment received by each industry in 2016.2
Attracting almost one-half of total VC investment, software companies are the top choice of VC
investors. Pharmaceutical and biotech companies rank second, accounting for about one-eighth
of total VC investment. Together, these two top industries comprise 60 percent of total VC investment. Other major industries receiving VC investment include healthcare devices and supplies (6
percent), healthcare services and systems (5 percent), commercial services (5 percent), IT hardware
(4 percent), consumer goods and recreation (3 percent), energy (2 percent), and media (2 percent).3
As the figure shows, venture capitalists are active investors in virtually all cutting-edge technologies.
There are 898 VC firms in existence in the United States as of 2016.4 These VC firms are managing 1,562 venture funds with a total amount of assets under management (AUM) of $333 billion.
The distribution of VC firms by AUM is shown in Figure 2. Many VC firms are rather small in
terms of AUM. One-sixth of VC firms have an AUM of less than $10 million, and the majority of
them (92 percent) have an AUM below $1 billion. In fact, only 68 VC firms (8 percent) have an
AUM above $1 billion. As revealed by Figure 2, VC is a fairly competitive industry populated with
many small players and only a few large ones.
To track the evolution of the VC industry in the United States, Figure 3 plots the time series of
VC investment. Numerous prominent VC firms were created in the 1970s, including the renowned
industry leader Sequoia Capital, and Kleiner Perkins Caufield & Byers. In the 1980s, VC firms
financed a series of successful companies, including Apple, Microsoft, and Cisco in the IT industry;
Genentech in the biotech industry; and FedEx in the courier industry. Thanks to the “gold rush” in
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Figure 1
Share of VC Investment Received By Each Industry
Media
2.1%
Energy
2%
Other industries
14.9%
Consumer goods & recreation
3.1%
IT hardware
3.6%
Software
47.7%
Commercial services
5%
Healthcare services & systems
4.8%
Healthcare devices & supplies
5.6%
Pharmaceutical & biotech
11.3%
SOURCE: NVCA (2016).
Figure 2
Distribution of VC Firms by Assets Under Management
$250M-$500M
8.8%
$500M-$1B
5.8%
$100M-$250M
16.7%
$1B+
7.6%
$50M-$100M
14.5%
Unknown
9.5%
$25M-$50M
10.4%
$10M-$25M
10%
NOTE: M, million; B, billion.
SOURCE: NVCA (2016).
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Figure 3
Investment by VC
VC investment,
billions of 2009 dollars
VC-to-total-investment ratio,
percent
6
140
Dotcom
bubble
120
5
4
100
80
3
60
2
40
1
20
0
0
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015
NOTE: The gray shaded area indicates recession as determined by the National Bureau of Economic Research.
SOURCE: Greenwood, Han, and Sánchez (forthcoming).
the internet sector during the dot.com bubble, the amount of VC investment soared during the
1990s. Many internet-related companies received VC financing during this era, including Amazon,
eBay, Netscape, Sun Microsystems, and Yahoo!. The bursting of the dot.com bubble in 2000, however, triggered an unprecedented collapse of VC investment in the early 2000s. Nevertheless, the
amount of VC investment in the post-bubble era was still well above its pre-bubble level and has
returned to its long-run trend. Despite suffering from a decline during the Great Recession, the
VC industry quickly recovered and continued to grow over time.
Though the amount of VC investment only accounts for a small share of aggregate U.S. investment, VC-backed companies (i.e., the ones financed by VC before going public) are playing an
increasingly critical role in the aggregate economy, as demonstrated in Figures 4, 5, and 6. The
fraction of VC-backed companies in all publicly traded firms is shown in Figure 4. The fraction of
VC-backed companies in terms of market capitalization surged from 4 percent in 1970 to 20 percent
by 2015.
Figure 5 reports the employment and R&D shares of VC-backed companies in all publicly
traded firms. As indicated by the booming share of VC-backed companies, such companies are
increasingly important for job creation and technological innovation. Analogously, Figure 6 displays
the shares of patents and patents adjusted by the quality (proxied by citations) of VC-backed companies. It confirms the increasing importance of VC-backed companies for innovation.
The VC industry has exhibited remarkable resiliency despite the COVID-19 pandemic. The
race for a COVID-19 vaccine has been a boon for startups in the pharmaceutical and biotech sector.
Social distancing requirements have spurred VC investment in e-commerce, delivery, and work124
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Greenwood, Han, Sánchez
Figure 4
Share of VC-Backed Companies Among Publicly Traded Firms
Fraction
0.25
0.20
Fraction of firms
0.15
0.10
Capitalization
0.05
0
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015
SOURCE: Greenwood, Han, and Sánchez (forthcoming).
Figure 5
Shares of VC-Backed Public Companies in Employment and R&D Spending Among All Publicly
Traded Firms
Fraction
0.40
0.35
0.30
R&D
0.25
0.20
0.15
0.10
Employment
0.05
0
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015
SOURCE: Greenwood, Han, and Sánchez (forthcoming).
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Figure 6
Shares of VC-Backed Public Companies in Innovation Among All Publicly Traded Firms
Patents, fraction
0.40
0.35
0.30
Quality adjusted
0.25
0.20
0.15
0.10
Unadjusted
0.05
0
1970
1975
1980
1985
1990
1995
2000
2005
2010
SOURCE: Greenwood, Han, and Sánchez (forthcoming).
from-home technologies. For instance, DoorDash (a VC-backed online food ordering and delivery
company) succeeded in going public in December 2020, raising $3.37 billion from the capital market.
3 THE IMPACT OF VC ON FIRM INNOVATION AND FIRM GROWTH
Building on the descriptive statistics in the last section, some regression evidence is presented
in this section to disentangle the relationship between VC, firm growth, and innovation.
3.1 VC and Firm Growth
Regression analysis is now conducted to evaluate the performance of VC-backed and non-VCbacked firms along four dimensions for the years following an initial public offering (IPO) of stock:
the R&D-to-sales ratio, growth rate of employment, growth rate of sales, and firm market value (in
natural logarithm). The results are presented in Table 1. The regressions are based on U.S. public
companies between 1970 and 2014. To compare VC-backed companies with their non-VC-backed
counterparts, a VC dummy is entered as an independent variable that takes the value of 1 if the
company is funded by VC before its IPO. In all regressions, industry dummies, year dummies, and
a year dummy for the IPO are included. In addition, a cross term is added between the VC dummy
and the number of years since the firm’s IPO.
As shown in the first row of Table 1, VC-backed companies are more R&D intensive and grow
faster than their non-VC-backed counterparts. On average the R&D-to-sales ratio of a public VC-
backed company is higher than its non-VC-backed counterpart by 5.2 percentage points, and it
grows faster—by 4.9 percentage points in terms of employment and 7.0 percentage points in terms
of sales. These superior performances translate into higher market values: VC-backed companies
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Table 1
VC-Backed vs. Non-VC-Backed Public Companies
R&D/Sales
VC-backed
VC-backed × years since IPO
ln(employment)
0.0521***
(0.0017)
–0.000780***
(0.0001)
–0.0133***
(0.0002)
Employment
growth
0.0490***
(0.0021)
–0.00304***
(0.0002)
–0.00567***
(0.0002)
Sales
growth
0.0696***
(0.0027)
–0.00406***
(0.0002)
–0.00641***
(0.0003)
ln(firm value)
0.373***
(0.0141)
–0.0110***
(0.0011)
0.851***
(0.0017)
Observations
84,116
148,834
149,672
168,549
R2
0.383
0.084
0.108
0.737
NOTE: All specifications include year dummies, industry dummies (4-digit SIC codes), and a year dummy for the IPO. Standard
errors are in parentheses. *** denotes significance at the 1 percent level.
are valued 37.3 percent higher than their non-VC-backed counterparts. The difference in performance, however, gradually dwindles over time, as shown by the negative estimates of the regression
coefficients in the second row. As a consequence, the performances of VC- and non-VC-backed
public companies tend to converge in the long run, though the speed of convergence is fairly low,
as revealed by the magnitudes of the estimates in the second row.
3.2 VC and Innovation
The role of VC in encouraging technological innovation is now gauged at an annual periodicity;
specifically, the impact of VC funding on patenting performance is evaluated at the firm level, and
the impact of VC on employment and sales growth is assessed at the industry level. The data contains all companies funded by venture capitalists between 1970 and 2015. These VC-funded patentees
are identified by matching firm names in VentureXpert and PatentsView.
3.2.1 Firm-Level Regressions. In the firm-level regressions, the primary independent variable is
(the natural logarithm of) annual VC funding, while the dependent variable is a measure of patenting performance three years after the firm receives the funding. The primary independent variable
may suffer from both measurement error and selection issues.5 So, an instrumental variable (IV) is
used in some of the regressions. The IV is based on the deregulation of pension funds since 1979, as
highlighted in Section 2.1. The deregulation of pension funds reduced the fundraising costs of VC
and led to increasing VC investment in all industries. In addition, industries that relied more on
external finance enjoyed a stronger boost of VC funding.6 Hence, a cross term between a “deregulation dummy” and a variable reflecting the industry’s (i.e., the industry in which the firm operates)
dependence on external finance is introduced as an IV. The deregulation dummy takes the value
of 1 after 1979. The dependence on external finance is a Rajan-Zingales-type measure (Rajan and
Zingales, 1998) that reflects the extent to which outside funds are used in the industry for expendi-
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Table 2
VC Funding and Patenting
Panel A: Firm-level regressions, extensive margin analysis
1{Patent > 0}
ln(firm VC funding)
Observations
1{“Breakthrough patent” > 0}
Probit
(1)
IV
(2)
Probit
(3)
IV
(4)
0.126***
(0.0123)
0.610***
(0.0932)
0.125***
(0.0118)
0.525***
(0.123)
7,589
7,589
7,589
7,589
Panel B: Firm-level regressions, intensive margin analysis
ln(patent)
OLS
(5)
ln(firm VC funding)
Observations
R
2
ln(patent, quality adjusted)
IV
(6)
0.137***
(0.0107)
0.792***
(0.233)
5,538
5,538
0.244
OLS
(7)
0.182***
(0.0173)
4,958
IV
(8)
0.748**
(0.369)
4,958
0.135
NOTE: See the main text for a description of the dependent and independent variables. The control variables are the number
of patents held by the firm at the beginning of the year, the age of the firm, the total amount of privately and federally funded
R&D of the industry in which the firm operates, and a cluster dummy for a firm headquartered in California or Massachusetts.
All regressions include year fixed effects and industry fixed effects. Standard errors are in parentheses. *** denotes significance
at the 1 percent level, ** at the 5 percent level.
tures on property, plant and equipment, R&D, advertising, and employee training. In all of the
regressions, controls are added for the number of patents held by the firm at the beginning of the
year, the age of the firm, and the total amount of privately and federally funded R&D of the industry
in which the firm operates. Additionally, both a year dummy and an industry dummy (a 2-digit
Standard Industrial Classification [SIC] code) are entered. Last, since both innovation and VC
activities are remarkably clustered in California and Massachusetts, a “cluster dummy” for a firm
headquartered in California or Massachusetts is included.
The results of the regression analysis are reported in Table 2. Panel A of Table 2 conducts the
analysis along the extensive margin, that is, based on whether the firm obtains any patents three
years after receiving VC funding. In regressions (1) and (2), the dependent variable is a dummy
that takes the value of 1 if the firm files any successful patent applications at the U.S. Patents and
Trademark Office within three years following funding. Regressions (3) and (4) focus on “breakthrough” patents, a measure pioneered by Kerr (2010). Breakthrough patents refer to those in the
right tail of the citation distribution. Here the dependent variable in regressions (3) and (4) is a
dummy variable that takes the value of 1 if the firm files any patents in the top 10 percent of the
citation distribution in its cohort (i.e., patents with the same technological class and same application year) within three years following funding. Panel B of Table 2 turns to the intensive margin. In
regressions (5) and (6), the dependent variable is (the natural logarithm of) the number of patents
filed within three years following funding. The (natural logarithm of the) number of patents is
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Table 3
VC Funding and Industry Growth
Employment growth
OLS
(1)
IV
(2)
Sales growth
OLS
(3)
IV
(4)
ln(industry VC funding)
0.00338***
(0.000748)
0.00608***
(0.00178)
0.00495***
(0.000958)
0.00898***
(0.00228)
ln(employment)
–0.00646***
(0.00161)
–0.00817***
(0.00189)
–0.00476**
(0.00207)
–0.00730***
(0.00243)
Observations
1,909
R2
0.285
1,909
1,909
1,909
0.334
NOTE: See the main text for a description of the dependent and independent variables. The control variable is logged employment in each industry, and all regressions include year fixed effects and industry fixed effects. Standard errors are in parentheses.
*** denotes significance at the 1 percent level, ** at the 5 percent level.
weighted by citations in regressions (7) and (8).
As shown by the positive estimates for VC funding in Panel A, larger VC funding increases the
likelihood of a firm filing a patent. Larger funding also increases the likelihood of a firm coming up
with a breakthrough patent, although the impact of VC funding is somewhat smaller in spurring
breakthrough patents than ordinary patents. According to the IV estimates in regressions (6) and
(8), a 10 percent increase in VC funding will induce in the three years subsequent to that funding a
7.9 percent boost in patenting and 7.5 percent boost in quality-adjusted patenting.
3.2.2 Impact of VC on Industry Growth. Attention is now turned to evaluating the impact of VC
funding on growth at the industry level between 1970 and 2011. The main explanatory variable is
the (natural logarithm of the) amount of VC funding each industry receives in each year. The
dependent variables are the average annual growth rates of employment and sales for the three-year
period after an industry receives VC funding.7 In all the regressions, controls are added for logged
employment in each industry, year dummies, and industry dummies (2-digit SIC codes). An IV is
applied to address the issues of measurement errors and selection bias in the ordinary-least squares
regressions. As detailed earlier, the IV is a cross term between the deregulation dummy and a variable reflecting the industry’s dependence on external finance.
As demonstrated in Table 3, increasing VC funding in an industry in a given year is associated
with a higher growth rate of employment and sales in the subsequent three years. According to IV
regressions (2) and (4), a one-standard-deviation increase in logged industry-level VC funding is
associated with increases of 1.3 percentage points and 1.9 percentage points in annual employment
and sales growth, respectively, following funding.
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4 CONCLUSION
The empirical evidence presented in this article suggests that VC financing is positively associated
with firm innovation and growth in the United States. A structural model of VC is developed in
Greenwood, Han, and Sánchez (forthcoming). The model is calibrated to fit stylized facts about VC
in the United States. Through the lens of this model, the effects of VC and its taxation are examined.
One of the crucial questions left unanswered is the role of VC financing in accounting for differences
in development across countries. Although more research is needed in this area, the findings in Cole,
Greenwood, and Sánchez (2016) and Greenwood, Han, and Sánchez (forthcoming) suggest that
differences in the cost of enforcing contracts, the efficiency of financial intermediation in which VC
plays a role, and the taxation of successful startups may be behind such cross-country differences. n
NOTES
1
This section draws heavily on Lamoreaux, Levenstein, and Sokoloff (2007) for the period prior to World War II and on
Kenney (2011) for the period after.
2
The data source is the 2016 National Venture Capital Association Yearbook (NVCA, 2016).
3
The category of “other industries” in this figure comprises the following industries: commercial products, commercial
transportation, other business products and services, consumer durables, consumer non-durables services (non-financial),
transportation, other consumer products and services, utilities, other energy, capital markets/institutions, commercial
banks, insurance, other financial services, other healthcare, IT services, other information technology, agriculture, chemicals and gases, construction (non-wood), containers and packaging, forestry, metals, minerals and mining, textiles, and
other materials. The data source is NVCA (2016).
4
The number of VC firms in existence is defined as a rolling count of firms that have raised a fund in the last eight years.
The data source for all statistics in this paragraph is NVCA (2016).
5
The selection issue refers to the possibility that the positive relationship between VC investment and firm performance
may be attributed to the ability of VCs to select promising companies to invest in.
6
This is revealed by the first-stage results of the IV regressions. The first-stage results are not presented due to space
limitations.
7
The employment and sales information is based on the NBER-CES Manufacturing Industry Database available at
https://www.nber.org/nberces/.
REFERENCES
Cole, Harold L. and Greenwood, Jeremy and Sánchez, Juan M. “Why Doesn’t Technology Flow from Rich to Poor Countries?
Econometrica, July 2016, 84(4), pp. 1477-521; https://doi.org/10.3982/ECTA11150.
Greenwood, Jeremy; Han, Pengfei and Sánchez, Juan M. “Financing Ventures.” International Economic Review, forthcoming 2022.
Kenney, Martin. “How Venture Capital Became a Component of the U.S. National System of Innovation.” Industrial and
Corporate Change, 2011, 20(6), pp. 1677-723; https://doi.org/10.1093/icc/dtr061.
Kerr, William R. “Breakthrough Inventions and Migrating Clusters of Innovation.” Journal of Urban Economics, January 2010,
67(1), pp. 46-60; https://doi.org/10.1016/j.jue.2009.09.006.
Lamoreaux, Naomi; Levenstein, Margaret and Sokoloff, Kenneth L. “Financing Invention During the Second Industrial
Revolution: Cleveland, Ohio, 1870-1920,” in Naomi Lamoreaux and Kenneth L. Sokoloff, eds., Financing Innovation in
the United States: 1870 to the Present. MIT Press, 2007; https://doi.org/10.7551/mitpress/9780262122894.003.0002.
National Venture Capital Association. 2016 National Venture Capital Association Yearbook. Thomas Reuters, 2016.
Rajan, Raghuram G. and Zingales, Luigi. “Financial Dependence and Growth.” American Economic Review, 1998, 88(3),
pp. 559-86.
130
On the Relative Performance of
Inflation Forecasts
Julie K. Bennett and Michael T. Owyang
Inflation expectations constitute important components of macroeconomic models and monetary policy
rules. We investigate the relative performance of consumer, professional, market-based, and model-based
inflation forecasts. Consistent with the previous literature, professional forecasts most accurately predict
one-year-ahead year-over-year inflation. Both consumers and professionals overestimate inflation over their
respective sample periods. Market-based forecasts as measured by the swap market breakeven inflation
rates significantly overestimate actual inflation; Treasury Inflation-Protected Securities market breakeven
inflation rates exhibit no significant bias. We find that none of the forecasts can be considered rationalizable
under symmetric loss. We also find that each forecast has predictive information that is not encompassed
within that of another. (JEL E31, E37)
Federal Reserve Bank of St. Louis Review, Second Quarter 2022, 104(2), pp. 131-48.
https://doi.org/10.20955/r.104.131-48
1 INTRODUCTION
Pandemic-related product and labor supply shortages have led to an uptick in inflation that
represents some of the fastest price growth since the beginning of the Great Recession. This uptick
has renewed interest in forecasts of future inflation. Moreover, in some macroeconomic models,
expectations of inflation (or, alternatively, forecasts of inflation) can be nearly as important as
realizations of inflation. For example, in models with a short-run Phillips curve, unemployment
and expectations of inflation are assumed to have a negative relationship. In some monetary policy
rules, the policymaker sets the interest rate, in part, as a function of the deviation between inflation
expectations and the inflation target.
Long periods of relatively low and steady price growth had apparently made inflation forecasting
easier, where simple random walk models’ performance belied their computational ease (Atkeson
and Ohanian, 2001, and Stock and Watson, 2007). Still, during that low-inflation period, professional
forecasters seemingly still held an advantage over pure model-based forecasts (Faust and Wright,
2013). Here, we investigate the relative performance of consumer, professional, market-based, and
model-based forecasts of inflation over a few different forecasting horizons.
Julie K. Bennett is a research associate and Michael T. Owyang is an assistant vice president and economist at the Federal Reserve Bank of St. Louis.
© 2022, Federal Reserve Bank of St. Louis. The views expressed in this article are those of the author(s) and do not necessarily reflect the views of
the Federal Reserve System, the Board of Governors, or the regional Federal Reserve Banks. Articles may be reprinted, reproduced, published,
distributed, displayed, and transmitted in their entirety if copyright notice, author name(s), and full citation are included. Abstracts, synopses, and
other derivative works may be made only with prior written permission of the Federal Reserve Bank of St. Louis.
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Macroeconomists use various measures of inflation expectations. In the absence of a sophisticated econometric model, consumers could construct forecasts based on information from outside
sources with simple models, heuristics, personal experience, or some combination of these. Profes
sional survey consensus forecasts such as the Blue Chip Economic Indicators (hereafter Blue Chip)
are an amalgam of individual forecasts. Market-based forecasts are breakeven inflation rates (BEIs)
derived from the Treasury Inflation-Protected Securities (TIPS) and inflation swap markets. We
include a few simple model-based forecasts as a baseline for comparison.
How well do agents forecast inflation? That question lies at the root of a vast literature comparing consumer, professional, financial market, and model-based forecasts (Gramlich, 1983; Thomas,
1999; Mehra, 2002; Ang, Bekaert, and Wei, 2007; Gil-Alana, Moreno, and Pérez de Gracia, 2012;
Wright, 2009; Faust and Wright, 2013; and Trehan, 2015, among others). Inflation forecasts are
often evaluated for (i) accuracy, (ii) bias (whether the forecaster exhibits a tendency to overestimate
or underestimate actual inflation), (iii) rationality (whether forecasts were made using relevant
information known to the forecaster), and (iv) encompassing (whether one forecast has additional
predictive information relative to another).
We evaluate forecasts for one-year-ahead year-over-year inflation (consumer, professional,
and model-based) and five-year average inflation (market-based and model-based) with regard to
these four metrics. We define five-year average inflation as the average year-over-year inflation rate
over a five-year span, consistent with the inflation rate that five-year TIPS and swaps BEIs are interpreted to forecast. In terms of accuracy, professional forecasts most accurately predict actual oneyear-ahead year-over-year inflation, while market-based forecasts and simple model-based forecasts
perform similarly well in forecasting actual five-year average inflation. In terms of bias, both professional and consumer forecasts significantly overestimate one-year-ahead year-over-year inflation,
while model-based forecasts do not exhibit any significant bias. Market-based forecasts of five-year
average inflation as measured by the swaps BEI significantly overestimate inflation, while those
measured by the TIPS BEI do not exhibit significant bias. This difference likely arises because of
inflation and risk premia embedded in the rates. For rationality, none of the forecasts evaluated
can be considered rational under the assumption of a symmetric loss function and an information
set consisting of the unemployment rate (UR), federal funds rate (FFR), and lagged inflation rate
available at the forecasting origin. Last, for encompassing, all forecasts have predictive information
that is not fully contained within that of another forecast.
2 INFLATION FORECASTS
We consider a few examples of four types of forecasts: (i) consumer forecasts; (ii) professional
forecasts; (iii) financial market implied forecasts; and (iv) econometric model-based forecasts, each
described in more detail below. Consumer forecasts are taken from the University of Michigan
Surveys of Consumers (Michigan Surveys). Professional forecasts are from the Blue Chip consensus
forecasts. While forecasts from individual firms are available, these forecasts vary in their samples,
have missing observations, and may not always be trying to minimize the squared forecast error.
Thus, we consider only consensus-level forecasts. Survey of Professional Forecasters (SPF) forecasts
are also commonly cited professional forecasts of inflation; however, we do not use these in our
analysis, as SPF forecasts are published on a quarterly basis and thus more difficult to compare with
monthly forecasts. Financial market implied forecasts are breakeven inflation rates computed from
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Federal Reserve Bank of St. Louis REVIEW . Second Quarter 2022
the TIPS and inflation swap markets. We employ two simple types of model-based forecasts: (i) the
Atkeson-Ohanian-type (hereafter AO) random walk forecast (Atkeson and Ohanion, 2001) and
(ii) a simple vector autoregression- (VAR-) based forecast. We evaluate these forecasts in reference
to inflation rates calculated using the seasonally adjusted consumer price index (CPI) from the
Bureau of Labor Statistics (BLS).
2.1 Consumer Expectations
To examine the performance and formation of consumer inflation forecasts, researchers often
employ the consumer inflation expectations data series from the Michigan Surveys. These monthly
surveys ask regular people about their outlook on current and future economic conditions. The
results of the surveys help assess how the average consumer processes economic data in forming
expectations of future outcomes. Questions in the surveys include the following:
• During the next 12 months, do you think that prices in general will go up, or go down, or
stay where they are now?
• By about what percent do you expect prices to go (up/down) on the average, during the
next 12 months?
Using responses to these questions, the Michigan Surveys constructs a data series of consumers’
median expectations of year-over-year inflation.1 This data series is available going back to January
1978 and is available in the Federal Reserve Bank of St. Louis FRED® database.2
When taken on their own, consumer inflation forecasts are often evaluated in the context of
determining what factors influence the formation of inflation expectations. Ehrmann, Pfajar, and
Santoro (2015) use the Michigan Surveys microdata from 1980 to 2011 and find that consumers
with current or expected financial difficulties, pessimistic attitudes about major purchases, or
expectations that income will go down tend to have a stronger upward bias compared with other
households. Consumer inflation expectations have also been found to be responsive to media
reporting (Carroll, 2003) and influenced by price changes in frequently purchased items such as
gasoline (Coibion and Gorodnichenko, 2015).
2.2 Professional Forecasts
When assessing professional inflation forecasts, researchers have used a variety of metrics,
including forecasts from the SPF, Livingston Survey, and Blue Chip. The Blue Chip, for example,
surveys some of America’s top business economists each month and collects their forecasts of various macroeconomic indicators, including inflation. The Blue Chip publishes forecasts from each
surveyed economist as well as an average—or consensus—of their forecasts for each variable. These
forecasts are often cited by media outlets and used by corporate and government decisionmakers.
We use the Blue Chip consensus forecast for one-year-ahead inflation, constructed by Haver Analytics,
which is available going back to January 1986.3
Numerous earlier studies have evaluated the bias and rationality of professional inflation forecasts. Brown and Maital (1981) find that the average Livingston Survey forecasts of inflation from
1961 to 1977 were not biased, but that information on monetary growth was often underutilized
in the forecasts. Figlewski and Watchel (1981) use individual Livingston Survey inflation forecasts
from 1947 to 1975 and find that they exhibit a significant downward bias and that forecast errors
are positively serially correlated. Keane and Runkle (1989, 1990) use individual price forecasts
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Federal Reserve Bank of St. Louis REVIEW . Second Quarter 2022
from the SPF (at the time conducted jointly by the American Statistical Association and National
Bureau of Economic Research) and conclude that the forecasts are rational, a contrast to most other
studies evaluating professional inflation forecast rationality. Croushore (2010) evaluates the performance of the Livingston Survey and SPF forecasts from 1971 to 2006 in comparison to inflation
as measured by the gross domestic product deflator (as opposed to CPI or personal consumption
expenditure inflation used in other studies) and finds that there are only short periods where professional forecasters showed persistent and significant bias. Using individual forecasts from the
Blue Chip from 1976 to 1986, Batchelor and Dua (1991) find that inflation and unemployment
forecasts show the most cases of deviation from rationality, and real gross national product and
interest rate forecasts the least; the authors posit, however, that it may not be optimal for individual
commercial forecasters to change their forecasts to be rational, as they are attempting to differentiate
their products from consensus forecasts.
2.3 Financial Market Forecasts
We use two measures of financial market inflation forecasts: BEIs as measured by the TIPS
market and those as measured by the inflation swaps market.
Traders in the TIPS market make implicit forecasts of inflation rates based on the difference
between the yield of a nominal bond and the yield of an inflation-linked bond of the same maturity.
These forecasts are called breakeven inflation rates (BEIs), as an investor would receive the same
yield on an inflation or non-inflation-indexed security if inflation averages that level over the course
of the maturity. We focus on the five-year TIPS BEI, which is (i) calculated by subtracting the fiveyear Treasury Inflation-Indexed Constant Maturity Securities yield from the five-year Treasury
Constant Maturity Securities yield and (ii) is often interpreted as what market participants expect
the year-over-year inflation to be over the next five years, on average. We use monthly averages of
daily observations for the five-year TIPS BEI; these data are available going back to January 2003
and are obtained from the Board of Governors of the Federal Reserve System and Haver Analytics.
In the inflation swaps market, two parties negotiate a contract under which inflation risk is
transferred through an exchange of fixed cash flows. As both parties are trying to negotiate a fair
price under the contract, the inflation swap rate can be seen as the expected BEI over the length of
the contract. We focus on the five-year swaps BEI, which is often interpreted as what market participants expect the year-over-year inflation rate to be over the next five years, on average. We use
monthly averages of daily observations for the five-year swaps BEI; these data are available going
back to August 2004 and are obtained from Bloomberg.
Bauer (2014) finds that both TIPS and swaps BEIs are closely related to movements in the
nominal interest rates and are sensitive to macroeconomic data surprises. The TIPS and swaps BEIs
are not necessarily straightforward forecasts of inflation, though, as they reflect market participants’
inflation expectations as well as inflation and liquidity risk premia. A number of articles decompose
the TIPS and swaps BEIs into these components using different methods and find that both the
TIPS and swaps BEIs embed nontrivial inflation and liquidity risk premia (Gurkaynak, Sack, and
Wright, 2010; Zeng, 2013; Abrahams et al., 2016; D’Amico, Kim, and Wei, 2018; Haubrich, Pennacchi,
and Ritchken, 2012; and Casiraghi and Miccoli, 2019; for a full review, see Kupfer, 2018).
Zeng (2013) finds that TIPS BEIs tend to underestimate inflation due to the liquidity risk and
that model-implied inflation expectations at various horizons outperform the SPF and Michigan
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Surveys forecasts. For TIPS BEIs, Abrahams et al. (2016) find that the estimated inflation risk premium is highly correlated with observable macroeconomic and financial variables, such as disagreement about future inflation among professional forecasters. They also find that the BEIs adjusted
for risk and liquidity premia outperform unadjusted BEIs and a random walk in predicting realized
inflation in sample and out of sample. Casiraghi and Miccoli (2019) find that swaps BEIs incorporate sizable inflation risk premia and that these premia increase with maturity. They also find that
the inflation risk premium was positive before the financial crisis, became negative at the end of
2008 after the bankruptcy of Lehman Brothers, and recovered shortly afterward.
For simplicity, we use BEIs unadjusted for liquidity and inflation risk premia as the financial
market forecasts in our analysis.
2.4 Model-Based Forecasts
As a baseline for comparison, we use two model-based forecasts: (i) the AO random walk forecast (Atkeson and Ohanion, 2001) and (ii) a VAR-based forecast.
The AO forecast uses the inflation rate over the previous four quarters as the forecast for what
inflation will be over the next four quarters. To fit with our other monthly forecast series, we adapt
the AO forecast using the inflation rate over the previous 12 months as the forecast for inflation over
the next 12 months.4 We use a similar model to forecast the five-year average inflation rate to compare with the five-year BEI. In this case, the average year-over-year inflation rate over the previous
five years is used to forecast the average year-over-year inflation rate over the next five years.
We also produce simple VAR-based forecasts for both one-year-ahead inflation and five-year
average inflation. We estimate three different VAR forecasts for one-year-ahead CPI inflation: (i)
a VAR including lags of year-over-year CPI inflation and lags of year-over-year industrial production (IP) growth; (ii) a VAR including lags of year-over-year inflation and lags of the UR; and (iii)
a VAR including lags of year-over-year inflation, lags of IP growth, and lags of the UR.5 We use the
same three VARs to forecast five-year average inflation using lags of five-year average inflation
rather than lags of year-over-year inflation.
For the one-year-ahead inflation model-based forecasts, the first forecast origin is March 1960,
corresponding to the first available vintage of UR data that can be used to estimate the VAR. For
the five-year average inflation model-based forecasts, the first forecast origin is June 1966, corresponding to the first forecast origin whose VAR model can be estimated with at least 100 observations given the available data.
3 FORECAST EVALUATION
Figure 1 shows forecast errors corresponding to a few of the forecasts we discuss.6 Panel A
shows forecast errors for one-year-ahead year-over-year inflation forecasts. Panel B shows forecast
errors for five-year average inflation forecasts. For each panel, the date on the x-axis corresponds
to the date the forecast was made. The forecast errors (and, thus, the forecasts themselves) generally move together, with the one-year-ahead year-over-year inflation forecasts tracking each other
more closely than the five-year average inflation forecasts.
Some notation will facilitate discussion of the properties of the forecasts. At a forecast origin t,
suppose the forecaster has information Xt to construct the h-period-ahead forecast, denoted Yt + h|t .
Each forecast produces an error relative to the realization, Yt+ h , defined as
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Figure 1
Inflation Forecast Errors
A. One-year-ahead year-over-year inflation forecast errors
Forecast errors (percentage points)
8
Michigan Surveys forecast errors
VAR (IP covariate) forecast errors
6
4
2
0
–2
–4
–6
–8
1980
1985
1990
1995
2000
2005
2010
2015
2020
B. Five-year average inflation forecast errors
Forecast errors (percentage points)
4
3
2
1
0
–1
–2
Five-year TIPS BEI forecast error
Five-year swap BEI forecast errors
VAR (IP covariate) forecast errors
–3
–4
2004
2006
2008
2010
2012
2014
2016
NOTE: This figure shows the forecast errors for both one-year-ahead year-over-year inflation forecast metrics (Panel A) and
five-year average inflation forecast metrics (Panel B). The date on the x-axis corresponds to the forecast origin. Gray shaded
regions indicate NBER recessions.
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Bennett and Owyang
=
t h Yt h Yt h|t .
(1)
We can evaluate these forecasts using a number of measures described in detail below.
3.1 Accuracy
One way to evaluate forecasts is to examine their relative accuracy. We first compute the root
mean squared error (RMSE) as
(2)
RMSE
=
1 P 2
t h ,
P t =1
where P is the number of forecasts being evaluated. Squaring the error focuses on the magnitude
of the forecast’s deviation from the realized value rather than on whether the forecast is underestimated or overestimated. We compare the relative accuracy of two forecasts by computing the ratio
of one forecast’s RMSE to another’s. A relative RMSE less (greater) than 1 indicates that the forecast
represented in the numerator (denominator) is relatively more accurate over the sample period.
While the relative RMSEs provide some suggestion of which of the two forecasts is more accurate, statistical tests are required to determine whether we can assert that one forecast is significantly
“better” than another. These tests (e.g., Diebold and Mariano, 1995) are typically formulated with
the null of equal predictive ability and require assumptions about the data generating process and
how the forecasts were constructed. We forgo formal statistical testing of equal predictive ability
here and refer the reader to the literature.
3.2 Bias
A forecast is considered biased if the average forecast error over the sample period is statistically
different from zero. Thus, we compute the average forecast error over all available forecast origins
for each inflation forecast metric and test whether this average is statistically different from zero
using a standard z-statistic.
Forecasts might be biased for a number of reasons. A forecaster may prefer to underestimate
the variable they are forecasting (rather than overestimate it). For example, say a firm is forecasting
demand for its product and there is a high carrying cost for extra inventory. In this case, the forecaster might prefer to underestimate demand, leading to underproduction so that no goods need
to be stored in inventory.
3.3 Rationality
Keane and Runkle (1989) define rational (or rationalizable) forecasts as those whose forecast
errors are unpredictable given what the forecaster knew at the time they made the forecast. Ration
ality is evaluated conditional on both a loss function and a fixed information set. The loss function
implicit in Keane and Runkle (1989) is quadratic loss, where the loss is an increasing function of
the forecast error, regardless of the direction of the error. The information set consists of potentially
relevant variables known to the forecaster at the forecast origin. If not taken into account (i.e.,
incorporated into the forecast), a variable could explain the realization but not the forecast, making
the forecast error a function of the variable.
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Bennett and Owyang
We can test the rationalizability of inflation forecasts by determining whether the forecast
errors can be predicted by factors known to the forecaster at the forecast origin, t. To do this, we
regress the forecast error on a constant, the forecaster’s prediction (Yt + h|t ), and a set of variable(s),
Xt , in the forecaster’s information set:
(3)
=
Yt h Yt h|t 0 1Yt h|t 2 X t ut h .
For the forecasts to be rationalizable given information Xt , the values of α1 and α2 should not be
significantly different from zero; otherwise, the forecast error could be predicted by Xt . Thus, we
consider a forecast rationalizable if we cannot reject the null hypothesis that α1 and α2 are jointly
zero using an F-test.7
We test rationality in this way for each inflation forecast series, using all available forecasting
origins for each series. The information set, Xt , for each rationality test consists of past data that are
common in macroeconomic models of the inflation rate: the UR, effective FFR, and most recent
value of inflation (either year-over-year or five-year average inflation).8 The composition of Xt varies
slightly across rationality tests for different forecasts. The tests for the VAR forecasts and the AO
forecasts do not include the most recent value of inflation in Xt , as that lagged inflation value is
inherently part of the forecast for both of those models. The VAR forecasts that include the UR as
a covariate also do not include the UR in Xt , as that value is incorporated into the forecast for those
models.
3.4 Encompassing
Comparing the relative RMSEs of two forecasts may determine which is more accurate on its
own. However, a substantial literature has shown that combining forecasts can lead to improved
accuracy. Tests for forecast encompassing determine whether one forecast has additional predictive
information relative to another. Another way of interpreting this statement asks whether one forecast would have any weight in a forecast combination with the other. For example, previous studies
have examined the hypothesis that the Fed’s forecasts encompass those made by the private sector.
To conduct an encompassing test, we follow similar methodology to that used by Fair and
Shiller (1989) and Romer and Romer (2000). We regress the realized values, Yt + h , on a constant
and the two forecasts, Y1,t + h|t (Forecast 1) and Y2,t + h|t (Forecast 2):
Yt h 1Y1,t h|t 2Y2,t h|t t h ,
(4) =
and we test the null hypothesis that (α, β1, β2)´ = (0,1,0)´. The null assumes that Forecast 2 has no
significant predictive information not already contained in Forecast 1. Previous studies have found
that forecasts of the inflation rate and output growth rates are biased (see Caunedo et al., 2020);
thus, a test could reject this joint null hypothesis because α ≠ 0. Therefore, we also conduct the
encompassing test, omitting the unbiasedness condition, and test only the null (β1, β2)´ = (1,0)´.
We conduct encompassing tests for all pairs of inflation forecast metrics that are forecasting the
same inflation metric (i.e., one-year-ahead year-over-year inflation or five-year average inflation),
using a Wald test to test the null hypotheses posited in the preceding paragraph. The encompassing
tests use data from the forecasting origins that are available for both Forecasts 1 and 2.
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Table 1
Relative RMSEs
A. One-year-ahead inflation
Michigan Surveys
Michigan
Surveys
Blue Chip
AO
VAR
(IP covariate)
VAR
(UR covariate)
VAR (IP and
UR covariates)
1.000
1.342
0.869
0.824
0.771
0.780
1.000
0.697
0.634
0.590
0.606
1.000
0.908
0.859
0.847
1.000
0.946
0.933
1.000
0.986
Blue Chip
AO
VAR (IP covariate)
VAR (UR covariate)
1.000
VAR (IP and UR covariates)
B. Five-year average inflation
Five-year TIPS BEI
Five-year swaps BEI
Five-year
TIPS BEI
Five-year
swaps BEI
AO
VAR
(IP covariate)
VAR
(UR covariate)
VAR (IP and
UR covariates)
1.000
0.908
1.027
0.577
0.608
0.662
1.000
0.980
0.533
0.563
0.619
1.000
0.630
0.597
0.610
1.000
0.948
0.969
1.000
1.022
AO
VAR (IP covariate)
VAR (UR covariate)
1.000
VAR (IP and UR covariates)
NOTE: This table displays the RMSEs for each combination of relevant forecasts. Each relative RMSE is the RMSE of the forecast indicated in the row
divided by the RMSE of the forecast indicated in the column. For each entry, the two RMSEs are calculated using the date range of whichever forecast
of the two has the smallest available date range. A relative RMSE < 1 indicates that the row forecast is more accurate than the column forecast over the
evaluated date range. A relative RMSE > 1 indicates that the column forecast is more accurate than the row forecast over the evaluated date range.
4 RESULTS
4.1 Accuracy
Table 1 compares the forecasts’ accuracy, reporting the RMSE of the forecast indicated in the
row relative to the RMSE of the forecast indicated in the column. For each entry, the two RMSEs
are calculated using the common date range of the two forecasts. A relative RMSE < 1 (> 1) indicates
that the row forecast is more (less) accurate than the column forecast over the evaluated date range.
Panel A of Table 1 presents results for one-year-ahead inflation forecasts. In terms of accuracy,
the Blue Chip outperforms all other evaluated metrics. The Michigan Surveys forecasts outperform
all metrics except those for the Blue Chip. The AO model does better than any of the VARs, and
the VARs all perform similarly well. The result that survey-based forecasts outperform simple time-
series models is consistent with previous findings (Thomas, 1999; Ang, Bekaert, and Wei, 2007;
and Gil-Alana, Moreno, and Pérez de Gracia, 2012).
Panel B of Table 1 presents results for five-year average inflation forecasts. The five-year TIPS
BEI outperforms the five-year swaps BEI and the VARs, but the AO model narrowly outperforms
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Table 2
Forecast Bias and Rationality Results
Rationality
Restrict α = 0
Bias
Mean error
Allow α ≠ 0
p-Value
F-statistic
p-Value
F-statistic
p-Value
A. One-year-ahead inflation
Michigan Surveys
–0.187
0.013
15.993
0.000
18.239
0.000
Blue Chip
–0.130
0.016
7.754
0.000
8.140
0.000
0.005
0.950
29.717
0.000
39.621
0.000
VAR (IP covariate)
0.247
0.003
25.848
0.000
31.043
0.000
VAR (UR covariate)
–0.038
0.660
49.379
0.000
73.952
0.000
0.098
0.268
55.444
0.000
82.414
0.000
AO
VAR (IP and UR covariates)
B. Five-year average inflation
Five-year TIPS BEI
0.056
0.352
53.860
0.000
66.752
0.000
Five-year swaps BEI
–0.424
0.000
157.654
0.000
121.366
0.000
AO
–0.147
0.100
102.665
0.000
135.380
0.000
VAR (IP covariate)
–0.490
0.000
247.684
0.000
319.729
0.000
VAR (UR covariate)
–0.351
0.018
362.431
0.000
535.812
0.000
VAR (IP and UR covariates)
–0.179
0.221
351.027
0.000
524.483
0.000
NOTE: This table presents results for tests of bias and rationality for each of the forecast metrics, separated by whether the metric is forecasting oneyear-ahead inflation or five-year average inflation. The two leftmost columns for the rationality results report the F-statistics and associated p-values
corresponding to testing the joint null hypothesis that (α0, α1, α2) = (0, 0, 0). The two rightmost columns for the rationality results report the F-statistics
and associated p-values corresponding to testing the joint null hypothesis that (α1, α2) = (0, 0).
the TIPS BEI. The five-year swaps BEI outperforms all metrics except for the five-year TIPS BEI.
The TIPS BEI outperforming the swaps BEI, the swaps BEI outperforming the AO model, and the
AO model outperforming the TIPS BEI each arise because of the differences in the timespans of
data available for the TIPS BEI and the swaps BEI. The AO model does better than any of the VARs,
and the VARs all perform similarly well.
4.2 Bias
The first two columns of Table 2 present the results of evaluating forecast bias over the entirety
of each forecast’s sample period. A positive (negative) bias value indicates that the forecast systematically underpredicts (overpredicts) actual inflation. For one-year-ahead inflation metrics, both
the Michigan Surveys forecasts and the Blue Chip forecasts significantly overestimate actual inflation. Meanwhile, the AO model is not significantly biased. Results for the VARs vary, though they
typically do not show significant bias.
The five-year TIPS BEI does not exhibit any significant bias in forecasting actual inflation,
while the five-year swaps BEI significantly overestimates it. While they are both financial market
forecasts, the distinction may arise from the differences in liquidity and inflation risk premia in
the two markets.
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Figure 2
Ten-Year Rolling Bias for One-Year-Ahead Inflation Forecasts
A. Michigan Surveys
B. Blue Chip
Bias
Bias
2
2
1
1
0
0
–1
–1
1980
2000
2020
1980
2000
C. AO
D. VAR (UR covariate)
Bias
Bias
2
2
1
1
0
0
–1
–1
1980
2000
2020
1980
2000
2020
2020
NOTE: The figure shows the average bias of a given one-year-ahead inflation forecast for the 10-year period that ends on the
date indicated by the x-axis. Orange shaded regions indicate subsamples in which the forecast bias is negative (overestimate)
and statistically significant at the 10 percent level. Blue shaded regions indicate subsamples in which the forecast bias is positive (underestimate) and statistically significant at the 10 percent level. Gray shaded regions indicate NBER recessions.
The five-year swaps BEI incorporates an inflation risk premium that is, on average, positive,
resulting in overestimation of actual inflation (Casiraghi and Miccoli, 2019). On the other hand,
previous research has argued that the TIPS BEI is subject to countercyclical risk premia (Abrahams
et al., 2016, and Andreasen, Christensen, and Riddell, 2020). Because these premia are time varying,
this variance leads to the overestimation of actual inflation at some points and underestimation at
others. Results for the VARs vary.
Previous work suggests that forecast bias results may be sensitive to the time period chosen for
evaluation (Croushore, 2010). Therefore, we also look at each forecast’s bias over a 10-year rolling
window. Figures 2 and 3 display these results for one-year-ahead year-over-year inflation forecasts
and five-year average inflation forecasts, respectively. Each line in Figures 2 and 3 shows the average
bias of a given forecast for the 10-year period that ends on the date indicated by the x-axis. Orange
shaded regions indicate subsamples in which the forecast bias is an overestimate and statistically
significant at the 10 percent level. Blue shaded regions indicate subsamples in which the forecast
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Bennett and Owyang
Figure 3
Ten-Year Rolling Bias for Five-Year Average Inflation Forecasts
A. Five-year TIPS BEI
B. Five-year swap BEI
Bias
Bias
0
0
–0.5
–0.5
–1.0
–1.0
2013
2014
2015
2016
2013
2014
C. AO
D. VAR (UR covariate)
Bias
Bias
0
0
–0.5
–0.5
–1.0
–1.0
2013
2014
2015
2016
2013
2014
2015
2016
2015
2016
NOTE: This figure shows the average bias of a given five-year average inflation forecast for the 10-year period that ends on
the date indicated by the x-axis. Orange shaded regions indicate subsamples in which the forecast bias is negative (overestimate) and statistically significant at the 10 percent level.
bias is an underestimate and statistically significant at the 10 percent level. Gray shaded regions
indicate National Bureau of Economic Research (NBER) recessions.
For one-year-ahead inflation forecasts, the sign and significance of the forecast bias varies
across the sample periods. For example, at the beginning of the Michigan Surveys forecast sample
period, consumers tended to underestimate inflation; however, beginning in the mid-1990s, they
tend to overestimate it. Consumers’ forecast bias is significant across a majority of the 10-year
rolling windows, though there are two short periods in which it is not. On the other hand, Blue
Chip forecasters overestimated inflation in the beginning of their sample, underestimated it during
the mid-2000s to mid-2010s, and more recently have overestimated it. Similar to that of consumers,
professionals’ forecast bias is significant across a majority of the 10-year rolling windows, though
there are three short periods in which it is not.
For five-year average inflation forecasts, the 10-year rolling-window forecasts overestimate
actual inflation, save for a short window at the beginning of the TIPS BEI sample period that is
insignificant. Looking at the time period comparable to the BEI forecasts (which is displayed in
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Figure 3), the swaps BEI, AO model, and VAR significantly overestimate actual inflation over all
10-year windows, while the TIPS BEI significantly overestimates inflation only for a specific period
of windows (window with end date November 2013 to window with end date November 2015).
The AO model and VAR model, however, do have periods preceding 2013 in which they do not
exhibit significant bias.
4.3 Rationality
The four rightmost columns in Table 2 presents the results of the forecast rationality tests
described in Section 3.3. Columns 3 and 4 report the F-statistics and associated p-values corresponding to testing the joint null hypothesis that (α0, α1, α2) = (0,0,0) (i.e., restricting the forecast to be
unbiased); Columns 5 and 6 report the F-statistics and associated p-values corresponding to testing
the joint null hypothesis that (α1, α2) = (0,0) (i.e., allowing the forecast to be biased). In either case,
failure to reject the null indicates that the forecast is rationalizable. Rejection of the null indicates
that the forecast error can be predicted by relevant macroeconomic variables known to the forecaster at the forecast origin; thus, the forecaster did not incorporate all relevant, known information
into their forecast.
Based on our results, we reject rationality for all forecasts, regardless of whether the forecast is
allowed to be biased. These results fall in line with previous work that rejects rationalizability for
consumer, professional, financial market, and model-based forecasts (Brown and Maital, 1981;
Batchelor and Dua, 1991; and Thomas 1999, among others).
No particular economic indicator appears unaccounted for across forecasts. Instead, the rejection of the null hypothesis appears to be driven by different factors across types of forecasts. For
example, consumers appear to appropriately incorporate the most recent value of inflation into
their forecasts, but leave information from the UR and FFR on the table. Meanwhile, five-year TIPS
BEIs appropriately incorporate information from the FFR into their forecasts but leave information
from the UR and most recent value of inflation underutilized. Professional forecasters underutilize
information from all considered regressors. These results suggest that agents make inflation forecasts based on different information sets.
These results on rationalizability are predicated on the selected information set and assumed
loss function (quadratic). Previous work finds that forecasts, particularly professional forecasts,
are often rationalizable under the assumption of an asymmetric loss function (Elliot, Komunjer,
and Timmerman, 2008; and Capistran and Timmerman, 2009; among others).
4.4 Encompassing
Table 3 presents the results of the encompassing tests for one-year-ahead inflation forecast
metrics. Panel A displays the p-values associated with testing the joint null hypothesis (α, β1, β2) =
(0,1,0) based on the regression described in Section 3.4, and Panel B displays the p-values associated with testing the joint null hypothesis (β1, β2) = (1,0). In either case, a failure to reject the null
indicates that the predictive information contained in Forecast 1 encompasses that which is contained in Forecast 2; a rejection of the null indicates that Forecast 2 contains predictive information
that is not contained in Forecast 1.
In each of the pairwise combinations evaluated in Table 3—regardless of whether or not the
forecasts are allowed to be biased—the null hypothesis is rejected at the 10 percent significance level.
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Bennett and Owyang
Table 3
One-Year Ahead Inflation Encompassing Results
Forecast 2
Michigan
Surveys
Blue Chip
AO
VAR
(IP covariate)
VAR
(UR covariate)
VAR (IP and
UR covariates)
0.000
0.000
0.000
0.000
0.000
0.002
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
A. Restrict α = 0
Forecast 1
Michigan Surveys
Blue Chip
0.000
AO
0.000
0.000
VAR (IP covariate)
0.000
0.000
0.000
VAR (UR covariate)
0.000
0.000
0.000
0.000
VAR (IP and UR covariates)
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.013
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
B. Allow α ≠ 0
Forecast 1
Michigan Surveys
Blue Chip
0.000
AO
0.000
0.000
VAR (IP covariate)
0.000
0.000
0.000
VAR (UR covariate)
0.000
0.000
0.000
0.000
VAR (IP and UR covariates)
0.000
0.000
0.000
0.000
0.000
0.000
NOTE: This table presents results of encompassing tests that test whether Forecast 1 encompasses Forecast 2 for a given row/column pair. Panel A
presents results for encompassing tests where the regression constant is tested to be zero in the joint null hypothesis (α, β1, β2)‘ = ( 0,1,0)‘. Panel B
presents results for encompassing tests where the regression constant is not tested under the joint null hypothesis, (β1, β2)‘ = (1,0)‘ The values reported
in both panels are the p-values associated with the F-statistic testing the relevant joint null hypothesis.
Thus, each of the forecasts has predictive content that is not fully contained within that of another.
When the forecast is allowed to be biased (Panel B), we could conclude that Blue Chip forecasts
encompass the AO model forecasts if evaluating the results using a 1 percent significance level.
Because professional forecasters likely take the most recent value of inflation into consideration,
Blue Chip forecasts nearly encompass the AO model forecasts. One might expect Blue Chip forecasts to nearly encompass the Michigan Surveys forecasts, assuming that professional forecasters
have more and better information than the average consumer. That consumer forecasts have predictive information not contained in professional forecasts, however, is consistent with previous
findings that households and professionals focus on different factors when making inflation forecasts (Berge, 2018, and Palardy and Ovaska, 2015). Moreover, consumer forecasts have outperformed professional forecasts over some sample periods (Gramlich, 1983, and Mehra, 2002).
Table 4 presents the results of the encompassing tests for five-year average inflation metrics.
Analogous to Table 3, Panel A displays the p-values associated with restricting Forecast 1 to be
unbiased, and Panel B displays the p-values associated with allowing Forecast 1 to be biased. As
before, the results in Table 4 indicate that, regardless of whether Forecast 1 is allowed to be biased,
the null hypothesis is rejected at the 10 percent significance level; thus, each of the forecasts has a
distinct information set that is not fully contained within that of another.
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Table 4
Five-Year Average Inflation Encompassing Results
Forecast 2
Five-year
TIPS BEI
Five-year
swaps BEI
AO
VAR
(IP covariate)
VAR
(UR covariate)
VAR (IP and
UR covariates)
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
A. Restrict α = 0
Forecast 1
Five-year TIPS BEI
Five-year swaps BEI
0.000
AO
0.000
0.000
VAR (IP covariate)
0.000
0.000
0.000
VAR (UR covariate)
0.000
0.000
0.000
0.000
VAR (IP and UR covariates)
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
B. Allow α ≠ 0
Forecast 1
Five-year TIPS BEI
Five-year swaps BEI
0.000
AO
0.000
0.000
VAR (IP covariate)
0.000
0.000
0.000
VAR (UR covariate)
0.000
0.000
0.000
0.000
VAR (IP and UR covariates)
0.000
0.000
0.000
0.000
0.000
0.000
NOTE: This table presents results of encompassing tests that test whether Forecast 1 encompasses Forecast 2 for a given row/column pair. Panel A
presents results for encompassing tests where the regression constant is tested to be zero in the joint null hypothesis (α, β1, β2)‘ = ( 0,1,0)‘. Panel B
presents results for encompassing tests where the regression constant is not tested under the joint null hypothesis, (β1, β2)‘ = (1,0)‘ The values reported
in both panels are the p-values associated with the F-statistic testing the relevant joint null hypothesis.
4.5 Interpretation
Based on these results and the results in previous studies, no single forecast (or forecaster)
appears to dominate any other. What does this imply for the comparison of the consumer and
professional survey forecasts, both relative to each other and relative to the model-based forecasts?
First, professional forecasters are generally better than consumers and simple models at predicting inflation. This finding aligns with what one might expect, as professionals may have information
and resources to make more informed forecasts than the average consumer.
Second, consumers are not bad at predicting inflation. Although they are not generally as
accurate as professional forecasters, they outperform simple econometric models. This finding
suggests that the average consumer understands inflation trends. Energy prices and food prices
are often correlated with headline inflation (energy and headline correlation: 0.68; food and headline
correlation: 0.71).9 Even if consumers rely on heuristics that overemphasize energy and food prices,
they may predict the direction of price growth through casual observation of prices in their everyday experiences.
Third, the BEIs cannot be interpreted as straightforward forecasts of inflation. These rates are
extracted from financial market instruments, and they embed time-varying liquidity and inflation
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risk premia that mask market participants’ actual inflation expectations. Taken at face value as
inflation forecasts, they may be misleading.
Fourth, there appears to be exploitable predictive information in all forecasts. Moreover, it
appears that consumers, forecasting professionals, and financial market analysts consider different
information sets when constructing forecasts. As none of the forecasts evaluated here are rationalizable under the assumption of a symmetric loss function, it may be relevant to consider whether
agents form inflation forecasts based on asymmetric preferences.
5 CONCLUSION
We evaluate the performance of consumer, professional, market-based, and model-based
inflation forecasts with regard to accuracy, bias, rationality, and encompassing. Consistent with
previous studies, survey-based forecasts are more accurate than model-based forecasts. Consumer,
professional, and swap market forecasts all tend to overestimate inflation on average, but the sign
of the bias varies across the sample period for consumer, professional, and TIPS market forecasts.
Results of rationality tests indicate that none of the forecasts can be considered rationalizable under
the assumption of symmetric loss, and economic agents use different information sets when forming
their inflation forecasts. Encompassing tests indicate that each forecast contains predictive information that is not encompassed by another forecast. Future work could consider additional survey-
based inflation forecast metrics, such as the consumer inflation expectations series from the Federal
Reserve Bank of New York, as well as market-based forecasts adjusted for inflation and risk premia.
Further tests of equal predictive ability or rationality under asymmetric loss could also provide
additional information on the relative performance of various inflation forecasts. n
NOTES
1
More information regarding the survey questionnaire and the construction of the consumers’ median inflation expectation series can be found at https://data.sca.isr.umich.edu/.
2
The Federal Reserve Bank of New York also produces consumer inflation expectations series at one-year and three-year
horizons. These data are only available for a relatively short sample (from 2012 to the present); thus, we omit them from
our analysis. These series could be used in future work.
3
This series is constructed using the Blue Chip one-year-ahead consumer price index (CPI) consensus forecast four quarters
ahead as the monthly value. The quarterly series are aggregated from the monthly series. For example, the one-yearahead inflation forecast value made in January 2020 is constructed using the CPI forecast for 2021:Q1 in the January 2020
survey. The one-year-ahead inflation forecast value made in February 2020 is constructed using the CPI forecast for
2021:Q1 in the February 2020 survey.
4
For example, at the forecasting origin January 2000, one would use the year-over-year value of inflation measured in
December 1999 as the forecast for year-over-year inflation measured in January 2001, as the December 1999 value would
be the most recent year-over-year inflation value available to the forecaster in January 2000.
5
The seasonally adjusted CPI from the Bureau of Labor Statistics (BLS) is used to calculate inflation rates; the UR data are
produced by the BLS; and the IP data are produced by the Board of Governors of the Federal Reserve System. We use
vintages of both IP and UR data obtained from the Federal Reserve Bank of St. Louis ALFRED® database:
https://alfred.stlouisfed.org/. These series are subject to frequent and substantial revisions. We do not use CPI vintages
to calculate year-over-year inflation rates, as CPI revisions are typically insubstantial.
6
Blue Chip forecasts are proprietary and cannot be depicted here.
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7
Rationality tests often include α0 ≠ 0 in the null. In this case, if the forecasts are biased, rationality is rejected. We include
results for tests that include or exclude α0 ≠ 0 in the null.
8
The information at month t depends on when the forecast is made within a given month. The University of Michigan
typically conducts the Surveys of Consumers in the last week of t–1 through approximately the third week of month t.
We assume the most recent value of the UR, the FFR, and inflation available to consumers is t–2. Blue Chip surveys are
conducted in the first week of t. We assume the most recent value of the UR and inflation available to professionals is t–2
and the most recent value of the FFR is t–1. Both the TIPS and swap market BEIs are monthly averages of daily rates. The
information set available to a market forecaster on the first day of the month consists of UR and inflation values from t–2
and the FFR from t–1. The model-based forecasts all use t–1 lagged inflation in their forecast calculation. Those forecasts
are made on the CPI release date of t; thus, all regressors are from t–1.
9
These correlations are calculated using CPI inflation data from January 1978 to May 2021, the dates corresponding with
the Michigan Surveys inflation forecasts.
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