Allocation and Employment Effect of the Paycheck Protection Program

Document type: PDF source document
Date: 2021-12-21

Source document: exhaustive list of papers that estimate the e ﬀect of PPP on employment, a brief description; document type: congressional-materials.

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Research Department
December 21, 2021
Current Policy Perspectives
Allocation and Employment Effect of
the Paycheck Protection Program
Gustavo Joaquim
The Paycheck Protection Program (PPP) was a large and unprecedented small-business support
program enacted as a response to the COVID-19 crisis in the United States. The PPP administered
almost $800 billion in loans and grants to small businesses through the banking system. However,
there is still limited consensus on its overall effect on employment. This paper explores why it is
challenging to estimate the effect of the PPP. To do so, we first focus on the timing of the allocation of
PPP funds across regions and firms. Counties less affected by COVID-19 and with a larger presence
of community banks, as well as larger firms, received loans earlier in the program. This differential
timing observed in the data suggests that the current estimates of the effect of the PPP are not
representative of the overall effect of the program. We qualitatively reconcile some of the conflicting
results in the empirical literature and point to key questions surrounding the program.

Gustavo Joaquim is an economist in the Research Department at the Federal Reserve Bank of Boston. His email address is
gustavo.joaquim@bos.frb.org.
The views expressed herein are those of the author and do not indicate concurrence by the Federal Reserve Bank of Boston, the
principals of the Board of Governors, or the Federal Reserve System.
The author thanks Falk Bräuning, Jose Fillat, Joe Peek, and Christina Wang for valuable comments and discussions. He also thanks
Morgan Klaeser for outstanding research assistance.

I.
Introduction
The COVID-19 pandemic led to an unprecedented decrease in economic activity aﬀecting
small businesses in particular. In April 2020, revenues of small businesses decreased more
than 40 percent compared with January of the same year and were still down 20 percent
in August 2020. As a response, Congress created the novel Paycheck Protection Program
(PPP) as part of the larger Coronavirus Aid, Relief, and Economic Security (CARES) Act. The
program provided loans, which could turn into grants, with the goal of preserving jobs of
small and medium-sized businesses that were substantially aﬀected by COVID-19. In 2020
and 2021, almost $800 billion in forgivable loans were made through the program. From a
policymaker’s perspective, it is paramount to understand how successful the program was in
preserving jobs at small businesses and how the program could have been more eﬀective.
However, despite the enormous size and importance of the program, there is still limited
consensus on its overall eﬀect on employment. We still can’t accurately pinpoint the extent
to which the program was simply a transfer from taxpayers to small-business owners and
the extent to which it did help to maintain jobs at small businesses. Table 1 displays a non-
exhaustive list of papers that estimate the eﬀect of PPP on employment, a brief description
of how these papers estimate that eﬀect, and the estimates themselves. The estimates range
from 1.5 million to 18.6 million jobs saved by the program (in a universe of 70 million jobs
at eligible ﬁrms according to Autor et al. (2020)).1
This note explores why it is challenging to estimate the eﬀect of the PPP. We do so by
ﬁrst discussing the allocation of PPP funds throughout the course of the program. We show
that PPP disbursement is very heterogeneous across banks, in particular in the ﬁrst phase
of the program. Moreover, we show that almost all changes in commercial and industrial
(C&I) lending in 2020 can be attributed to the PPP, with little evidence of crowding out. We
also ﬁnd that regions less aﬀected by COVID-19 (for instance, those that were not under a
government-mandated closure or that saw a smaller decline in spending) received loans ear-
lier in the program. Similarly, larger ﬁrms received loans earlier in the program. We develop
1It is worth noting that the 18.6 million estimate from Faulkender, Jackman and Miran (2021) is not directly
comparable with the estimates from the other papers in Table 1. However, even if we remove this particular es-
timate, the estimates range from 1.5 million to 13 million jobs saved by the program, which is still a substantial
discrepancy.
2

a stylized economic model to illustrate how this diﬀerential timing aﬀects the estimation of
the eﬀect on employment of the PPP. We show that it is possible to estimate the eﬀect of the
PPP for a very speciﬁc subset of ﬁrms by using exposure to some type of bank or regional
variation in PPP disbursement, as done by some of the papers in Table 1. This subset of
ﬁrms, however, is not representative of the overall set of ﬁrms that received PPP loans, and
it changed over time.
For concreteness, consider the papers by Granja et al. (2020) and Doniger and Kay (2020).
We observe in the data that the average size of a ﬁrm receiving PPP loans decreased over
time, such that larger ﬁrms received loans earlier. Moreover, let’s suppose that larger ﬁrms
were also those with the lowest treatment eﬀects.2 Granja et al. (2020) use bank variation in
PPP lending in the ﬁrst two weeks of the program: Some banks processed more than their
expected share of PPP loans, while others processed less. Thus, ﬁrms that were clients of
banks that processed more loans early were more likely to receive an early loan. Since larger
ﬁrms were more likely to receive an early loan and have lower treatment eﬀects, Granja et al.
(2020) are bound to ﬁnd a low treatment eﬀect of the program. The same rationale applies to
studies by Autor et al. (2020), Chetty et al. (2020b), and Bartik et al. (2020). Doniger and Kay
(2020), on the other hand, use regional variation in PPP disbursement in the middle of the
program, when smaller ﬁrms—and therefore those with higher treatment eﬀects—received
loans. Therefore, by comparing ﬁrms that received loans later in the program with those that
did not, Doniger and Kay (2020) ﬁnd much larger eﬀects of the PPP.
In our ﬁnal section, we discuss two natural questions that come from our analysis—which
we tackle in separate papers. First, if none of the earlier papers estimates the eﬀect of the PPP,
then what was the overall eﬀect of the PPP? We tackle this question in Joaquim and Netto
(2021b). Second, one can alternatively ask: given that we observe a diﬀerential timing of PPP
allocation based on ﬁrm characteristics (such as size), what should have been the allocation of
the PPP loan if the government wanted to minimize job losses at small businesses? We tackle
this question in Joaquim and Netto (2021a).
2In general, this assumption has support in other programs—see Zwick and Mahon (2017). Speciﬁcally for
the PPP, see the evidence of Bartlett and Morse (2020).
3

II.
The Paycheck Protection Program
Created on March 27, 2020, as part of the CARES Act, the PPP was designed to address
liquidity shortages that could lead to employment losses from small businesses. The Small
Business Administration (SBA) oversaw the program. To guarantee a timely disbursement of
funds, ﬁrms applied for a loan through qualiﬁed ﬁnancial intermediaries.
In this paper, we consider only the ﬁrst draw of the PPP program, which ran from April 3
through August 8, 2020.3 Given the PPP’s small-business focus, only ﬁrms with fewer than
500 employees were eligible to apply,4 and each ﬁrm could apply for only one loan in the
ﬁrst draw of the PPP. The maximum loan amount was 2.5 times the ﬁrm’s average monthly
payroll costs in the preceding year up to $10 million. PPP loans have an interest rate of 1
percent, deferred payments for six months, and maturity of two years for loans issued in the
ﬁrst phase of the program and ﬁve years for loans issued after June 5, 2020. Moreover, PPP
loans did not require collateral or personal guarantees.
A PPP loan is fully forgiven if funds are used for the speciﬁc purpose of payroll mainte-
nance. Originally, to obtain full loan forgiveness, businesses were required to use at least 75
percent of the amount on payroll expenses and to maintain pre-crisis employment headcount
and wage levels. This percentage was retroactively reduced to 60 percent after the Flexibil-
ity Act was passed in June 2020. The amount forgiven is reduced if a business’s wages or
full-time headcount decreases. Initially, funds had to be used to pay for these costs over the
eight-week period following the disbursement of the loan. This period was extended to 24
weeks in June 2020.
Each loan application was processed by an eligible ﬁnancial intermediary (referred to
as banks for simplicity), for example, a federally insured depository institution or a credit
union, which were responsible for checking documentation submitted by an applicant. Banks
were paid a fee by the federal government to cover these processing costs. Importantly, loans
from the PPP are fully guaranteed by the government and carry a zero-risk weight for the
calculation of risk-weighted assets, with the purpose of minimizing the impact on banks’
3In December 2020, Congress authorized an additional $284 billion in funding for the program as part of
the $900 billion Coronavirus stimulus package. The PPP started making loans again in 2021, including second-
draw loans for some of the ﬁrms that had received a PPP loan in the ﬁrst draw.
4The exceptions were ﬁrms in the restaurant and hospitality sectors (NAICS code 72), which were allowed
to apply as long as they had no more than 500 employees in each location.
4

capital requirements. Additionally, Federal Reserve Banks were authorized to provide liq-
uidity to banks through the Paycheck Protection Program Lending Facility (PPPLF Facility).
This allowed Federal Reserve Banks to extend loans to institutions that were eligible to make
PPP loans using such loans as collateral. Overall, the program was designed to allow a large
number of institutions to process loan requests while minimizing the impact on their balance
sheet structure.
Table 2 shows aggregate statistics of the program on key dates, and Figure 1 shows the
cumulative volume of loans made through the ﬁrst draw of the program. We provide a
description of the data used in Appendix A. Through a combination of the disbursement and
application data, we deﬁne four distinct phases in the evolution of the ﬁrst draw of the PPP:
1. Phase 1: April 3 to April 16, 2020. The ﬁrst PPP loan was approved on April 3, 2020.
During the ﬁrst days of the program, PPP loans were being made at a fast pace, but PPP
loan demand vastly exceeded supply. For instance, we see in Figure 2 that 72 percent
of ﬁrms reported applying for the program, but only 36 percent reported receiving a
PPP loan at the end of phase 1. This excess loan demand gave banks a signiﬁcant role
in the allocation of PPP funds. As we can see in Table 2, more than 1.6 million loans
were made in this phase, with an average loan size of approximately $198,000.
2. Phase 2: April 17 to April 26, 2020. As a consequence of the enormous demand for PPP
loans, the program ran out of funding on April 16, and there was a 10-day hiatus when
no PPP loans were made. On April 24, in response to the enormous demand for PPP
loans, Congress enacted the PPP Act, which appropriated an additional $321 billion
(for a total of $670 billion) for PPP loans. Banks resumed approving PPP applications
on April 27.
3. Phase 3: April 27 to May 1, 2020. There was still a backlog of applications, and loans
were being made at a fast pace. At this stage, demand for PPP loans still outpaced
supply, and banks continued to play some role in the overall allocation of PPP funds.
As we can see in Table 2, more than 3.7 million loans had been made up to May 1 (70
percent of all loans made in the program). The cumulative average loan size decreased
from $198,000 to $129,000, indicating that loans made from April 27 to May 1 were
signiﬁcantly smaller than those made in the ﬁrst phase of the program.
5

4. Phase 4: May 2 to August 8, 2020. Demand for PPP loans was more subdued, and there
was an excess supply of PPP loans, which reduced the role of banks in the allocation
of PPP funds. This change in the role of banks from the ﬁrst to the last phase is key
to our empirical and theoretical analyses. The program stopped accepting applications
on August 8 with $144 billion remaining from the PPP Act appropriation. More than
5 million loans were granted for a total amount of approximately $526 billion. More
than 61.1 million workers were employed by ﬁrms that received a PPP loan.
III.
PPP Disbursement and Bank Heterogeneity
This section explores the disbursement of PPP loans from the perspective of banks. We have
three main results. First, disbursement of PPP loans was very heterogeneous across banks, in
particular in the ﬁrst phase of the program. Second, almost all of the change in C&I loans in
2020 was due to the PPP, and there is little evidence of crowding out of private loans.
Following the events of March 2020, banks saw a large increase in their amount of C&I
loans as corporations dashed for cash. Li, Strahan and Zhang (2020) show that ﬁrms drew
funds from preexisting credit lines at the fastest rate ever. This channel was ﬁrst highlighted
by Li and Strahan (2020) and can be seen in the increase in outstanding C&I loans in Fig-
ure 3. This eﬀect was more pronounced for larger banks, given their higher share of unused
C&I loan commitments (Table 3).5 Banks were able to satisfy this demand for liquidity by
the corporate sector due to a combination of deposit inﬂows and the Federal Reserve’s in-
terventions. As a result, this drawdown eﬀect was short-lived. On the other hand, we see a
signiﬁcant increase in the volume of outstanding C&I loans after the beginning of the PPP
on April 3, 2020, in particular for the smaller banks.
One potential explanation for the results in Figure 3 is that the largest banks were not the
main providers of loans to small businesses before the pandemic—and thus didn’t expand
their C&I loan portfolios following the introduction of the program. To test this hypothesis,
we follow Granja et al. (2020) and measure the gap between the market share of a bank in
PPP lending in the ﬁrst phase and its pre-pandemic small-business lending as a measure of
5Larger banks generally serve the largest ﬁrms, which are exactly those with a higher share of unused credit
lines—see, for instance, the evidence in Chodorow-Reich et al. (2021).
6

a bank-level PPP shock, as in Eq.(1)
P P P Eb = Share PPPb −Share SBLb
Share PPPb + Share SBLb
× 0.5,
(1)
where Share PPPb is the share of PPP lending from bank b at the end of the ﬁrst phase of the
program, and Share SBLb is the share of bank b lending in small-business loans in 2019Q4
(in terms of dollar volume). We plot community bank status and bank P P P Eb as a function
of assets in Figure 4. 6 We ﬁnd that P P P Eb is increasing in bank size for small and mid-sized
banks and decreasing for the largest banks. With the exclusion of the largest banks, we do
not see a signiﬁcant diﬀerence among banks in terms of community bank status.
Finally, we show in Table 3 that the majority of the change in C&I credit (loans and unused
commitments) in 2020 came through the PPP. For instance, from a total increase of 5.78
percentage points of C&I credit relative to assets (compared with 2019Q4), 5.49 percentage
points came from the program in Q2. Table 3 suggests that there was no crowding out of
private lending. After the introduction of the program, the relative change of non-PPP C&I
lending to PPP was small in 2020Q2 and negligible in 2020Q4. Although we can’t interpret
this as causal evidence of no crowding out, we can conclude that conditional on the economic
conditions and all other government interventions, the outstanding amount of non-PPP C&I
loans did not decrease in the presence of the PPP.
IV.
Allocation of the PPP
In this section, we discuss the allocation of the PPP loans across counties and ﬁrms. First, we
present visual evidence that counties receiving PPP loans early in the program had charac-
teristics that were diﬀerent from those of ﬁrms receiving PPP loans later in the program. We
do so by following Doniger and Kay (2020) and take a set of county r characteristics in the
baseline (before the PPP was introduced), X0,r, and take the daily weighted average of those
characteristics using PPP disbursement by counties as weights. Mathematically, if county r
6We use the FDIC’s database of community banks to establish which ﬁnancial institutions are com-
munity banks.
An institution is a community bank if it satisﬁes various criteria (see, for instance,
https://www.fdic.gov/resources/community-banking/report/2020/2020-cbi-study-app-a.pdf). Overall, com-
munity banks are those that provide loans and deposits and have assets below a certain threshold ($ 1.65 billion
in 2019).
7

had P P Pr,t volume of loans allocated to that county in day t, we compute
¯Xt =
P
r X0,rP P Pr,t
P
r P P Pr,t
.
(2)
To facilitate the interpretation of the output, we normalize ¯Xt by its mean over time and plot
the percentage deviations from this mean; that is
˜Xt = 100 ·
"
¯Xt
T −1 PT
t=1 ¯Xt
−1
#
.
(3)
The idea behind the index in Eq.(3) is to measure the average characteristic across coun-
ties relative to their PPP allocation. Therefore, if we ﬁnd that ˜XApr−−3 is small relative to
˜XMay−−15, we can conclude that counties with a low X0,r received PPP loans earlier in the
program.
The results are in Figure 5. Counties that received PPP loans earlier had a larger share of
deposits and branches of community banks (Panel A), had a larger share of ﬁrms with more
than 20 employees (Panel B), were less likely to be under government-mandated closures
(Panel C), had fewer COVID-19 deaths/cases (Panel D), saw a smaller decrease in spending
and revenues (Panel E), and overall had more branches per capita (Panel F). Overall, the
results in Figure 5 indicate that counties less aﬀected by COVID-19, that have larger ﬁrms,
and that had a higher share of community banks were the ones that received loans earlier in
the program.
We show in Figure 6 the heterogeneous allocation across ﬁrms. The average loan size and
number of employees of PPP recipients were decreasing over the course of the program. For
instance, the average loan size dropped from $300,000 on the ﬁrst day of the program, April
3, 2020, to approximately $25,000 by May 15, 2020. Importantly, note that the changes in
county (Figure 5) and ﬁrm (Figure 6) characteristics receiving PPP loans were concentrated
in Phases 1 through 3 of the program (from April 3 to May 1), exactly when demand for PPP
funds outpaced supply and banks played a major role in the allocation of PPP funds.
The results in this section are not necessarily causal. That is, the ﬁgures do not imply
that more PPP funds went earlier to counties because they were less aﬀected by COVID-19.
What we show is that there was signiﬁcant heterogeneity in the allocation of PPP loans across
8

counties and ﬁrms, and that this heterogeneity was related to deep economic factors. These
factors were very likely linked to both (1) employment in the absence of PPP and (2) the eﬀect
of the PPP on employment. As we show in the next section, these correlations are important
for understanding the challenges with estimating the eﬀect of PPP on employment.
Although we focus here on the visual evidence of Figures 5 and 6, we provide in Joaquim
and Netto (2021b) a more complete statistical analysis of these eﬀects. For instance, we show
that the county heterogeneous allocation eﬀects existed—and were statistically signiﬁcant—
even in the comparison of counties within a given state and relative to the number of eligible
ﬁrms in a given county. Similarly, we show that even in a within-bank comparison, the size
of the average ﬁrm receiving a PPP loan was decreasing over the course of the program.
V.
Estimating the Effects of the PPP
This section explores the implications of the results of Section IV for the estimation of the
overall eﬀect of the PPP on employment. We conduct this exploration using a stylized eco-
nomic model. In our model, there are two regions, A and B. Both regions have a continuum
of ﬁrms. For simplicity, we assume that for each ﬁrm in region A, there is an identical ﬁrm
in region B—with the only diﬀerence between them being a potential PPP loan. We index
diﬀerent ﬁrms by j in each region r = A,B. Each region has a unique bank disbursing PPP
loans, which we denote by the same name as the region. Firms can borrow only from the
bank in their region. Bank A disburses more PPP loans than bank B at any moment in time
(for instance, bank A is a community bank). We deﬁne two key characteristics of ﬁrm j in
region r:
• θj,r: represents the probability of ﬁrm closure without a PPP loan.
• Tj,r: represents the change in the probability of ﬁrm closure upon receipt of a PPP loan.
From our previous deﬁnitions, the probability that a ﬁrm survives is given by
P(j, in region r, survives at time t) = θt
j,r + P P P t
j,rT t
j,r,
where P P P t
j,r = 1 for ﬁrms that receive PPP loans up to time t, and P P P t
j,r = 0 otherwise.
9

Our model has four periods, each corresponding to a phase of the program we described in
Section II:
• Period t = 1: Banks play a key role in the allocation of PPP loans.
• Period t = 2: No PPP loans are made.
• Period t = 3: Banks still have a role in the allocation of PPP loans.
• Period t = 4: The supply of PPP loans exceeds demand, and banks play no role in the
allocation of PPP loans.
The setting described above is very stylized, but it captures the key economic channels we
want to highlight. A few comments are in order. First, we implicitly assume that ﬁrms in the
model either survive or don’t, but in reality, they could downsize after the COVID-19 shock.
To take downsizing into account, we could simply rewrite our model at the job level (rather
than at the ﬁrm level). Second, we could extend our model to feature banks that make loans
in multiple regions or ﬁrms that borrow from banks in regions other than the one where
they are located. Third, we also could extend our model to feature regions of diﬀerent sizes,
diﬀerent distributions of ﬁrms, or other dimensions of heterogeneity. We develop a model
with these extensions in Joaquim and Netto (2021b).
The ﬁrst result we can show in our setting is that we can’t simply compare ﬁrms that re-
ceived PPP loans with those that didn’t receive PPP loans (even conditional on application)
at any given moment in time to estimate the eﬀect of the program. We show this mathemat-
ically in Example 1. Intuitively, if ﬁrms that received PPP loans early (for instance, because
they are larger) had a diﬀerent θt
j,r compared with ﬁrms that didn’t receive PPP loans early,
the ﬁrms that didn’t receive PPP loans are not a good control group.
Example 1: Why can’t we just compare ﬁrms that received PPP loans with those that
didn’t?
Consider only region A in our setting, and assume for this example that region A has
two types of ﬁrms: H and L. We assume that all ﬁrms have the same eﬀect of receiving PPP
loans on employment; that is, TH = TL = T ∈(0,1). Firms of type H survive with probability
θH = 1−T > 0 without PPP funds, while of ﬁrms of type L survive with θL = 0 without PPP funds.
In this setting, the eﬀect of the PPP is T . Moreover, suppose that bank A has enough funds to
10

allocate to half of the ﬁrms and chooses to allocate those funds to ﬁrms of type H, that is, those with
a higher probability of survival without PPP funds (for instance, the larger ﬁrms). In this case, all
ﬁrms that receive PPP loans will survive. All ﬁrms that don’t receive PPP are of type L and won’t
survive. The comparison between ﬁrms that received PPP loans and those that didn’t would lead
to the conclusion that the eﬀect of the PPP is 1, even though the true eﬀect of the PPP is given by
T < 1.
■
Given that we can’t simply compare ﬁrms that received PPP loans with those than didn’t,
we can use the fact that ﬁrms in region A have a bank that was better at disbursing PPP loans
in every period and thus are more likely to have received PPP funds—not because they are
of a diﬀerent type (as in Example 1), but simply because they are clients of a diﬀerent bank,
which is exogenous in our stylized setting. To be able to discuss the implications of banks
choosing which ﬁrms to lend to at each moment in time, we need to introduce the concept of
compliers:
Deﬁnition. Complier: A complier at time t is a ﬁrm that did receive a loan from bank A but
wouldn’t have received a loan from bank B by time t.
The second result in our setting is that we can, at any moment in time, estimate only the
eﬀect of the PPP on compliers. Consider ﬁrm j in region A and its identical counterpart in
region B (except potentially for PPP receipt). Let their diﬀerence in probability of survival at
a moment t be given by ∆j,t. We have that
∆j,t = θt
j,A + P P P t
j,AT t
j,A −
h
θt
j,B + P P P t
j,BTj,B
i
.
Since these are identical ﬁrms, T t
j ≡T t
j,A = T t
j,B (and analogously for θt
j). Let Ct be the set of
ﬁrms that are compliers; that is, a ﬁrm j is in Ct if P P P t
j,A = 1 and P P P t
j,B = 0.7 We can rewrite
7We assume here that since bank A is better at disbursing PPP loans, there is no ﬁrm j such that P P P t
j,A = 0
and P P P t
j,B = 1; that is, there is no ﬁrm that did not receive a PPP loan in region A that would have received one
in region B.
11

the pair-wise diﬀerence as
∆j,t =

P P P t
j,A −P P P t
j,A

Tj =

0, if ﬁrmj in Ct
Tj, 0, if ﬁrmj not in Ct
.
And let T t
C be the average eﬀect of the PPP on the ﬁrms that are compliers. Aggregating
across all pairs of ﬁrms, we ﬁnd that the diﬀerence ∆in the share of ﬁrms that survive in A
versus B is given by
∆t ≡
Z
j
∆j,tdj =
h
P P P t
A −P P P t
B
i
·
Z
j in Ct T t
j dj =
h
P P P t
A −P P P t
B
i
· T t
C.
Therefore, the diﬀerence in survival relative to the diﬀerence in PPP allocation is given by
T t
C, that is, the eﬀect of the PPP on compliers. We provide in Example 2 a version of this result
with only two types of ﬁrms. Intuitively, ﬁrms that are not compliers either receive or don’t
receive PPP loans regardless of their region, and thus when we compare across regions (or
across banks), their eﬀects cancel out. The crux of the argument of this paper involves which
ﬁrms are in the set of compliers at each moment in time.
Example 2: Why can we estimate the employment eﬀect only on compliers? Suppose that
there are only two types of ﬁrms, H and L, and each consists of half of the population of ﬁrms in
each region. Firms of type H have a treatment eﬀect of TH, larger than the treatment eﬀect of ﬁrms
of type L, TL; that is, TH > TL. The bank in region A can provide PPP funds for 100 percent of the
ﬁrms, while the bank in region B can provide funds to 50 percent of the ﬁrms. Suppose that banks
choose to allocate funds ﬁrst to the ﬁrms with the lowest treatment eﬀects (for instance, the largest
ﬁrms). In region B, where 50 percent of the ﬁrms receive PPP funds, all of the type L ﬁrms and
none of the type H will receive PPP funds. The type H ﬁrms in region B are the compliers in this
setting. The overall eﬀect of the PPP (adjusted by the share of ﬁrms that receive PPP loans, which
in this case is three-quarters) is given by:
PPP Eﬀect = 4
3
1
2
1
2TH + 1
2TL

+ 1
4TL

= 2
3TL + 1
3TH.
12

Comparing survival in region A with survival in region B (adjusted by the diﬀerences in PPP
disbursement, which in this case is one-half) delivers
∆= 2
1
2TL + 1
2TH −1
2TL

= TH,
that is, the eﬀect of the PPP on compliers.
■
Which ﬁrms are compliers at each moment in time? To characterize who the set of com-
pliers are at each phase of the program, we need to introduce some additional assumptions
and notations. We assume that there is some ﬁrm characteristic η (such as size, the degree to
which this ﬁrm was aﬀected by COVID-19, or another characteristic) and that banks choose
which ﬁrms to lend to based on this characteristic. Banks have a decreasing proﬁt in η, such
that they prefer to allocate funds to low-η ﬁrms. We assume that η is also related to the
treatment eﬀect of ﬁrms. In particular, we assume for exposition purposes that Tj is hump
shaped in η, as depicted in Figure 7. This shape for the Tj curve is based on the idea that
ﬁrms less aﬀected by COVID-19 (low-η) and ﬁrms too aﬀected by COVID-19 (high-η) have
similar treatment eﬀects but for diﬀerent reasons: Low-η ﬁrms are likely to survive regard-
less of their PPP allocation, while high-η ﬁrms are unlikely to survive regardless of their PPP
allocation. At each moment in time, we deﬁne the set of ﬁrms that receive loans in regions A
and B by, respectively, At and Bt.
We show in Figure 7 which ﬁrms are compliers at each phase of the program. At t = 1,
where banks play a key role in the allocation of PPP funds, the set of compliers is given by
the ﬁrms in At and not in Bt. Note that at this stage the overall eﬀect of the program (T 1
All) is
low and diﬀerent from the eﬀect of the program on the compliers (T 1
C). A similar situation is
present at t = 3. However, note how the set of compliers shifts, and thus the set of ﬁrms for
which the PPP eﬀect is being estimated shifts as well. More speciﬁcally, we ﬁnd that the eﬀect
of the PPP on t = 3 compliers is larger than the eﬀect on t = 1 compliers; that is, T 3
C > T 1
C. In
t = 4, we suppose that A4 = B4; that is, banks A and B serve the same set of ﬁrms in terms of
their type (even though bank A still serves a higher number of ﬁrms). At this stage, banks
don’t play a role in the allocation of PPP funds, and the set of compliers is simply a random
set of the ﬁrms that receive PPP loans at this stage. In summary, Figure 7 shows that in the
13

case of the PPP, the set of compliers (1) was changing over time and is (2) not representative
of the overall set of ﬁrms that received PPP loans.
Reconciling the evidence from the papers in Table 1. We focus here on the diﬀerence be-
tween the ﬁndings of Granja et al. (2020) and Doniger and Kay (2020). The reason for this
is that the other papers either do not have a precise estimate of PPP on employment (Bartik
et al. (2020)), do not allow for a direct comparison with other estimates (Faulkender, Jackman
and Miran (2021)), or use the 500-employee eligibility cutoﬀto estimate the eﬀect of the PPP
(Autor et al. (2020), Chetty et al. (2020b)) and thus can credibly estimate only the eﬀect on
the largest ﬁrms eligible for the program. Granja et al. (2020) use variation in PPP allocation
in the ﬁrst phase (t = 1) in our model. At this phase, the set of compliers, that is, ﬁrms in
B1 and not in A1, is composed of the smaller ﬁrms among the largest ﬁrms. That is, the true
eﬀect of the program at this stage is small, and the estimated eﬀect of the PPP is higher than
the true eﬀect of the PPP at t = 1.
Doniger and Kay (2020) leverage the fact that the PPP program did not approve any loans
from April 16 through 26, 2020, to identify the eﬀects of the PPP. The idea is that around
this 10-day window the timing variation in PPP disbursement was as good as random. As
our analysis shows, ﬁrms that received funds around the 10-day window were not similar to
those that did not. At this phase (t = 3), the true eﬀect of the program is higher than t = 1,
but the set of compliers is still diﬀerent from the set of overall ﬁrms that received PPP loans,
and the estimated eﬀect of the PPP is higher than the true eﬀect of the PPP at t = 3.
Our stylized model can thus provide a unifying explanation for the results found in the
literature: Firms of diﬀerent sizes that were aﬀected diﬀerently by COVID-19 received PPP
loans at diﬀerent moments in time. Thus, depending on when the variation in PPP occurs in
an empirical strategy will also determine the set of compliers, which will be diﬀerent from
the overall set of ﬁrms. Studies that leverage early variation in PPP allocation will tend to
ﬁnd lower treatment eﬀects, while studies that leverage variation later will likely ﬁnd higher
treatment eﬀects. Neither of the estimated eﬀects, however, corresponds to the overall eﬀect
of the program at any moment in time.
14

VI.
The $800 Billion Questions
The PPP was a key part of the policy response of the U.S. government to the COVID-19 crisis.
Throughout 2020 and 2021 the program ultimately disbursed almost $800 billion dollars
in forgivable loans to small businesses in order to reduce job losses during the COVID-19
pandemic. Given the size of the program, extensive research has tried to estimate its eﬀect on
employment, but no consensus has emerged from the empirical literature. We have shown
in this paper that the allocation of these loans across regions and ﬁrms was not random.
Regions less aﬀected by the pandemic, as well as larger ﬁrms, received PPP loans earlier.
We have illustrated that this diﬀerent timing in allocation can aﬀect our interpretation of
the empirical evidence and that apparently conﬂicting empirical results can be reconciled—
although none captures the overall eﬀect of the program.
Two natural questions emerge from this note, which we tackle in two separate papers.
First, what is the overall eﬀect of the PPP on employment? In Joaquim and Netto (2021b), we
provide comprehensive evidence of heterogeneous allocations of PPP funds. How the target-
ing of PPP funds aﬀects our interpretation of the estimated eﬀect of PPP on employment is
formalized in a model that features rich bank and regional heterogeneity. We estimate the
eﬀect of the program to be a reduction in nonemployment at eligible ﬁrms of 12.9 percentage
points, which corresponds to roughly 7.5 million jobs at a cost of $70,000 per job. Second,
if this eﬀect of PPP on employment depends on the allocation of funds across ﬁrms, how
should the government want these funds to be allocated? Alternatively, what could the ef-
fect of the PPP have been if funds were optimally allocated across ﬁrms and over time? We
tackle this question in Joaquim and Netto (2021a). We develop an economic model in which
the government must choose which ﬁrms to allocate PPP loans to in order to maximize em-
ployment at those ﬁrms. We show that funds were misallocated mostly in the ﬁrst phase of
the PPP, and that a policy targeting the smallest ﬁrms could have increased the program’s
eﬀectiveness signiﬁcantly.
15

References
Autor, David, David Cho, Leland D Crane, Byron Lutz, Joshua Montes, William B Pe-
terman, David Ratner, Daniel Villar, and Ahu Yildirmaz. 2020. “An Evaluation of the
Paycheck Protection Program Using Administrative Payroll Microdata.” 2, 3, 14, 18
Bartik, Alexander W., Zoe E. Cullen, Edward L. Glaeser, Michael Luca, Christopher T.
Stanton, and Adi Sunderam. 2020. “The Targeting And Impact of Paycheck Protection
Program Loans to Small Businesses.” NBER Working Paper No. 27623. 3, 14, 18
Bartlett, Robert P, and Adair Morse. 2020. “Small Business Survival Capabilities and Policy
Eﬀectiveness: Evidence from Oakland.” 3
Chetty, Raj, John N Friedman, Nathaniel Hendren, and Michael Stepner. 2020a. “How Did
COVID-19 and Stabilization Policies Aﬀect Spending and Employment? A New Real-Time
Economic Tracker Based on Private Sector Data.” NBER Working Paper. 18, 23, 26
Chetty, Raj, John N Friedman, Nathaniel Hendren, Michael Stepner, and Opportunity In-
sights Team. 2020b. “The Economic Impacts of COVID-19: Evidence from a New Public
Database Built from Private Sector Data.” 3, 14
Chodorow-Reich, Gabriel, Olivier Darmouni, Stephan Luck, and Matthew Plosser. 2021.
“Bank Liquidity Provision across the Firm Size Distribution.” Journal of Financial Eco-
nomics. 6
Doniger, Cynthia, and Benjamin Kay. 2020. “Ten Days Late and Billions of Dollars Short:
The Employment Eﬀects of Delays in Paycheck Protection Program Financing.” Available
at SSRN. 3, 7, 14, 18
Faulkender, Michael W., Robert Jackman, and Stephen Miran. 2021. “The Job Preservation
Eﬀects of Paycheck Protection Program Loans.” SSRN Electronic Journal. 2, 14, 18
Granja, João, Christos Makridis, Constantine Yannelis, and Eric Zwick. 2020. “Did the
Paycheck Protection Program Hit the Target?” 3, 6, 14, 18, 21
16

HUD.
2020.
“HUD
USPS
ZIP
Code
Crosswalk
Files.”
https://www.
huduser.gov/portal/datasets/usps_crosswalk.html. 26
Joaquim, Gustavo, and Felipe Netto. 2021a. “Bank Incentives and the Eﬀect of the Paycheck
Protection Program.” Federal Reserve Bank of Boston Research Department Working Paper. 3,
15
Joaquim, Gustavo, and Felipe Netto. 2021b. “The Optimal Allocation of Relief Funds: The
Case of the Paycheck Protection Program.” Federal Reserve Bank of Boston Research Depart-
ment Working Paper. 3, 9, 10, 15
Li, Lei, and Philip Strahan. 2020. “Who Supplies PPP Loans (And Does It Matter)? Banks,
Relationships and the Covid Crisis.” NBER Working Paper 28286. 6
Li, Lei, Philip E Strahan, and Song Zhang. 2020. “Banks as Lenders of First Resort: Evidence
from the COVID-19 Crisis.” The Review of Corporate Finance Studies, 9(3): 472–500. 6
Zwick, Eric, and James Mahon. 2017. “Tax Policy and Heterogeneous Investment Behavior.”
American Economic Review, 107(1): 217–48. 3
17

Figures and Tables
Table 1: Non-exhaustive List of Papers and Estimates of the Eﬀect of PPP on Employment
Paper
Identiﬁcation
Jobs Saved (Million)
Chetty et al. (2020a)
500 Eligibility Cutoﬀ
1.51
Autor et al. (2020)
500 Eligibility Cutoﬀ
2.31
Granja et al. (2020)
Bank Heterogeneity in PPP Disbursement
in the 1st Phase
3.2-4.8
Doniger
and
Kay
(2020)
Share of Loans Delayed between 1st
and 3rd Phases
13
Faulkender,
Jackman
and Miran (2021)
Community Bank Heterogeneity in PPP
Disbursement
18.6
Bartik et al. (2020)
Bank Heterogeneity in PPP Disbursement
in the 1st Phase
Wide CIs
Note: Compiled by the author. Whenever the cost per job estimate is available, we use those provided in the
papers. Faulkender, Jackman and Miran (2021) estimate a dynamic eﬀect of the PPP and interpret their results
as an interquartile change, so the numbers are not directly comparable with those from other studies.
18

Figure 1: Cumulative PPP Disbursement over Time ($Billions)
Note: Aggregation of loan-level data from SBA/Treasury February 2021 PPP release. Billions of dollars of
PPP loans approved by day, from April 3, 2020 (CARES Act) through Aug. 8, 2020 (Modiﬁed deadline for
applications). Dashed horizontal lines represent the cumulative capacity of the program.
Table 2: Summary Statistics of the Paycheck Protection Program
Apr-16
May-1
Jun-30
Aug-08
Loan Amount ($Billions)
322.28
480.0
517.8
526.6
# Loans (,000)
1619.7
3700.02
4820.45
5,147.6
Jobs Reported (Millions)
33.2
54.62
59.96
61.1
Average Loan Size ($Thousands)
198.96
129.74
107.42
102.30
Average Jobs Supported
20.5
14.76
12.44
11.8
Note: Aggregation of loan-level data from the SBA/Treasury February 2021 release. Loan amount (in billions of
dollars) and number of loans (in thousands) cumulated from the start of the program (April 3, 2020). Average
loan size is the ratio of the cumulative loan amount over the number of loans. Jobs supported are reported by
the ﬁrms during the PPP application. The top 4 banks (by assets in 2019Q4) are (1) JP Morgan Chase, (2) Bank
of America, (3) Wells Fargo, and (4) Citibank, N.A.
19

Figure 2: Small Business Pulse Survey: PPP Application vs. PPP Receipt (% of Firms)
Note: U.S.-level data from the Small Business Pulse Survey (SBPS) collected weekly from April 26, 2020 through
Aug. 9, 2020). Blue line denotes the percentage of ﬁrms that report applying for a PPP loan. Yellow line denotes
the ﬁrms that report receiving a PPP loan. For details on data collection, see Appendix A.
Figure 3: Small vs. Large Banks C&I Lending During PPP Program
Note: Data from the H.8 Schedule:
Assets and Liabilities of Commercial Banks in the United States. We plot
the cumulative change in C&I lending from March 6, 2020 (normalized to zero). Large domestically chartered
commercial banks are deﬁned as the top 25 domestically chartered commercial banks, ranked by domestic
assets as of the previous commercial bank Call Report to which the H.8 release data were benchmarked.
20

Figure 4: PPPE and Bank Size: Volume and Number of Loans
Note: Data from the SBA/Treasury February 2021 Release and Call Reports. P P P E is computed as in Granja
et al. (2020). It is the symmetric diﬀerence of PPP loans and small-business lending (SBL) from schedule RC-C,
Part II of the Call Reports. Mathematically, P P P Eb = 0.5× Share PPP−Share SBL
Share PPP+Share SBL for the volume of loans. The share of
PPP is computed from PPP loans made in the ﬁrst phase (until April 16, 2020). Log(Assets) is the natural loga-
rithm of assets in 2019Q4 from the Call Reports. Each dot represents an individual bank, and the dark blue dots
are the conditional averages of PPPE by Log(Assets). We use the FDIC’s database of community banks to estab-
lish which ﬁnancial institutions are community banks. An institution is a community bank if it satisﬁes various
criteria (see, for instance, https://www.fdic.gov/resources/community-banking/report/2020/2020-cbi-study-
app-a.pdf). Overall, community banks are those that provide loans and deposits and have assets below a certain
a threshold ($ 1.65 billion in 2019), although there are exceptions to this rule.
21

Table 3: Bank C&I and PPP Lending from Call Reports in 2020, Quarterly
Change from 2019Q4
Relative to Assets (p.p.)
Baseline
Q1
Q2
Q3
Q4
Panel A. Unweighted
C&I Credit
11.36
0.20
6.54
6.87
5.30
C&I Loans
8.16
0.20
6.14
6.33
4.65
C&I Unused
3.20
0.00
0.40
0.54
0.65
PPP
0.00
0.00
6.34
6.48
4.56
C&I Loans - PPP
8.16
0.20
-0.20
-0.15
0.09
Panel B. Weighted by Assets
C&I Credit
16.07
0.10
5.78
6.18
5.28
C&I Loans
10.35
0.57
5.49
5.60
4.55
C&I Unused
5.72
-0.46
0.29
0.57
0.72
PPP
0.00
0.03
5.71
5.83
4.58
C&I Loans - PPP
10.35
0.57
-0.22
-0.23
-0.02
Observations
4,970
4,970
4,970
4,970
4,970
Note: Data from merger-adjusted Call Reports, from 2019Q4 through 2020Q4. For each variable in rows X, we
show the average, across banks, of 100 × X−X2019−Q4
Assets2019−Q4 , that is, the average change in percentage points relative
to assets in 2019Q4. C&I Credit refers to the extended loans and unused part of credit lines. Panel A shows a
simple average across banks. Panel B shows the data averaged using assets in 2019Q4 as weights.
22

Figure 5: Average County Characteristics of PPP Recipients by Day
(a) Community Banks
(b) Firm Size
(c) Government-Mandated Closures
(d) COVID-19 Exposure
(e) Revenue and Spending
(f) Branches per Capita
Note: PPP data come from the SBA/Treasury February 2021 PPP release. County-level data come from the
Summary of Deposits (Panel A and F ), County Business Patterns (Panel B), and Chetty et al. (2020a) (Panels C–
E). For a baseline county characteristic X0 (e.g., cumulative revenue shortfall from January to April 2), at county
c, we plot percentage deviations from the mean (over time) of the weighted average of a county characteristics
using PPP fund allocations as weights. The variables X0 we use are the share of branches and deposits held in
community banks (Panel A, see deﬁnition in Figure 4); the share of ﬁrms with 0 to 20, 20 to 100, and 100 to 500
employees (Panel B); a dummy that is 1 for counties in states with government-mandated closures (Panel C);
COVID-19 cases and deaths per capita (Panel D); cumulative changes in revenue, spending, and employment
(Panel E); and bank branches per capita (Panel F).
23

Figure 6: PPP Loans by Day: Average Loan Size and Jobs Reported
(a) Loan Size ($1,000)
(b) Jobs Reported (Average)
Note: SBA/Treasury February 2021 PPP release. Average size (in thousands of dollars) and reported number
of jobs saved of PPP loans approved by day, from April 3,2020 (CARES Act) through May 15, 2020 (non-
cumulative).
24

Figure 7: PPP Program Evolution and Identiﬁcation of Treatment Eﬀects
(a) First Phase (t = 1)
TAll
TC
B1
A1
η
T ,Ω
Tj
Ωj
(b) Third Phase (t = 3)
TAll
TC
B3
A3
η
T ,Ω
Tj
Ωj
(c) Remainder of the Program (t = 4)
TAll
TC
B4
A4
η
T ,Ω
Tj
Ωj
Note: This ﬁgure illustrates the diﬀerence between the overall eﬀect of the PPP (TAll) and the eﬀect on compliers
(TC at diﬀerent stages of the program based on stylized curves of treatment eﬀects (Tj) and bank proﬁts (Ωj) as
a function of ﬁrm characteristics η.
25

Appendix
A.
Data
In this section, we brieﬂy describe our main data sources.
Our main data source is the
SBA/Treasury data on PPP loans (February 2021 version), which includes all loans made
in the program. The data set includes information self-reported by the borrower (name, ad-
dress, Zip code, NAICS code, and jobs supported) as well as the loan amount, approval date,
and lender name. Throughout the paper, we use the PPP data at the loan level or aggregated
at the bank-, county- or county-bank level. To aggregate the data to the county level, we use
the HUD Zip crosswalk to match each loan to a county (HUD (2020)). Our sample includes
all loans made in the program in 2020.
For our analysis at the bank- and county-bank levels, we merge the lenders in the PPP re-
lease by name with those institutions that were active in 2020 and registered in the National
Information Center database (which includes, among others, commercial banks and credit
unions). We are able to match 94 percent of the number and 95 percent of the volume of PPP
loans. From the Call Reports, we obtain ﬁnancial characteristics of all banks, the outstand-
ing volume of small business loans (overall) and the outstanding volume in the PPP program.
Within the set of banks that ﬁle Call Reports, 846 out of 4,970 had no outstanding PPP loans
in 2020Q2. To check the quality of our merge procedure, we compare the PPP volume from
the SBA/Treasury release on June 30, 2020, with that from the Call Report in 2020Q2. We
ﬁnd that the two alternative measures of PPP disbursement by bank are very close to each
other. The correlation between them is 0.99. Additionally, for banks that have a zero amount
of PPP loans outstanding in the Call Reports, our procedure does not match any loans from
the PPP loan-level data.
We use the high-frequency (daily) data from Chetty et al. (2020a) to obtain county-level
measures of employment, revenue, spending, COVID-19 cases and deaths, mobility and un-
employment insurance claims. For details on the data collection, see Chetty et al. (2020a).
From the Small Business Pulse Survey (SBPS), we obtain ﬁrms’ application and approval sta-
tus in the program (for a small subset of ﬁrms). From the Federal Reserve’s H8 Schedule, we
obtain C&I lending at a weekly frequency, broken down by large (top 25) and small banks.
26

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