Assessing the Payroll Protection Program: A Framework and Preliminary Results

Source document: Barrios Minnis Minnis Sijthoff Bfi Wp 2020 63 Assessing Payroll Protection Program; document type: congressional-materials.

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WORKING PAPER · NO. 2020-63
Assessing the Payroll Protection Program:
A Framework and Preliminary Results
John Barrios, Michael Minnis, William Minnis, Joost Sijthoff
MAY 2020

Assessing the Payroll Protection Program:
A Framework and Preliminary Results​*

John Barrios
University of Chicago Booth School of Business
Michael Minnis
University of Chicago Booth School of Business
William Minnis
Eastern Illinois University
Joost Sijthoff
University of Chicago Booth School of Business

May 13, 2020

ABSTRACT
We develop a simple model to predict requests for the Payroll Protection Program

(PPP) and compare these predictions to the actual allocations. The model suggests the

amount of requested funds could total $750 billion, though this is likely a high

watermark conditional on several assumptions. The model also generates expectations

by industry, state, and firm size, allowing us to assess model performance in the

cross-section. The model performs reasonably well. Through the May 1 funding, the

state-level cross-sectional model has an R​2 of 99.3% and the average absolute

prediction error across states is 6.4%. Interestingly, the prediction errors from the first

funding round are significantly negatively correlated to the errors in the second funding

round, revealing that the allocations were systematically different in the two rounds.

Ultimately, the results suggest that the payroll-based model predicts PPP allocations

well and that the funds were allocated as designed. One potential inference from these

results is that critique about PPP allocations should be focused on program design

rather than program execution. This analysis should be useful for subsequent studies

assessing the performance of the PPP.

*This is still a draft document and we welcome any comments (michael.minnis [at] chicagobooth.edu).
We initiated this project by developing a spreadsheet to provide a framework to estimate the magnitude
of the PPP, which we posted online on April 14 along with a discussion of factors which could affect the
magnitude. We continue to update that tool online as we learn more about the PPP and the actual
allocations. This document formalizes and discusses that work. The analysis in this version of the paper
uses actual disbursements data from the Small Business Administration as of May 1, 2020. The
spreadsheet tool is available online: ​https://sites.google.com/view/ppptool/home​. For disclosure, we also
provided commentary on the PPP in a Barron’s op-ed on April 8, which can be located here:
https://www.barrons.com/articles/small-businesses-without-prior-debt-are-at-risk-of-missing-the-rescu
e-51586369598​. We thank Pete Lisowsky for initial discussions on this topic.

1. INTRODUCTION
As a response to the COVID-19 pandemic, congress passed the Coronavirus

Aid, Relief, and Economic Security (CARES) Act on March 27, 2020. The Payroll

Protection Program (PPP) is one of the critical policy responses in the act. The PPP is

designed to provide funds to help small businesses cover payroll and other expenses

(such as rent and utilities) for eight weeks during the pandemic. As part of the first

phase of the CARES Act, the PPP received $349 billion of funding. The depletion of

these initial funds led to an additional infusion of $310 billion to the program on April

24. Despite being allocated approximately $660 billion in total, there have been two

substantive concerns: (1) whether the PPP is sufficiently funded to meet the demands

of small businesses and, if not, how much could potentially be requested; and, (2)

whether the funds are being allocated according to the design of the program.
To

1
provide insights into these two concerns, we use the program rules and publicly

available payroll data to develop a simple model to estimate the potential magnitude of

PPP requests in total and cross-sectionally by state, industry, and firm size. We then

compare our estimates with actual PPP allocation data to examine how funds have

been distributed. This exercise suggests that funds from the PPP have broadly been

allocated according to the distribution of eligible payroll, essentially as designed. We

also identify and examine interesting deviations from the model’s predictions.
The design and implementation rules for the PPP are set by the Treasury and

the Small Business Administration (SBA).
The primary directive of the PPP is to

2
allow any U.S.-based firm with either less than 500 employees or otherwise meeting

1 The range of publicly stated estimates is broad: from $626 billion
(https://www.sbalenders.com/conclusions- drawn-349-billion -sba-loan-program/) to over $1 trillion
(Consumer Bankers Association). See the discussion of the ranges in Newmyer, April 22, 2020, here:
https://www.washingtonpost.com/news/powerpost/paloma/the-finance-202/2020/04/22/the-finance-
202-economists-and-banking-analysts-debate-whether-new-small-business-money-will-be-enough/5e9f7
bcb602ff10d49aeae5a/?tid=ss_mail. For an initial assessment of how funds have been allocated across
banks, see Granja et al. (2020): https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3585258.
2 These rules have been regularly updated over time through the use of both “Interim Final Rules” and
“Frequently Asked Questions.” See
https://home.treasury.gov/policy-issues/cares/assistance-for-small-businesses for all Treasury
documentation about the program.

1

the usual definition of a small business as established by the SBA to qualify for payroll

relief. Specifically, qualified small businesses can request 2.5 times its average annual

3
payroll costs, which include employee benefits. A firm can request a maximum of $10

million with the constraint that the eligible annual wages for any single employee

considered in the payroll costs cannot exceed $100,000. In addition to payroll costs,

profits from both sole proprietors and farmers are eligible based on net income from

Schedules C and F, respectively.
We map this set of rules to publicly available payroll and tax data to derive an

upper bound PPP request estimate by industry, state, and firm size (which we detail in

Section 2). We estimate that total claims could reach $750 billion, but view this as a

likely high-water mark for several reasons.
First, we assume a 100% participation

4
rate across all potentially eligible firms. Noting that the Treasury recently emphasized

the “economic need” criterion, the participation rate is likely to be lower. Second, we

are unable to account for either the $100K per employee cap on wages or the $10

million per firm cap on total loan size. Third, the Census payroll data designates a

“firm” by aggregating establishments up to the level of each state only, not nationally.

Therefore, a firm that has fewer than 500 employees in more than one state will appear

to be more than one small business (and thus eligible) when, in fact, it is a larger

(ineligible) firm. It should also be noted that our estimate could be pushed higher if, for

5
3 There are notable exceptions to both the eligibility rules and application amounts which we discuss in
the next section. For example, affiliation rules require companies that are controlled by other companies
to aggregate all employees across affiliated companies. On the other hand, nonprofit organizations —
which are typically not allowed to participate in SBA programs — are eligible to participate in PPP. See
the SBA website for details about size standards:
https://www.sba.gov/document/support--table-size-standards.
4 Given the fact that the disbursement rate of round two funding has slowed considerably since May 1,
our view that our estimate is a high watermark seems justified ex-post. We also note that our estimate
has varied over time as we have learned about the program rules and refinements needed to the model —
e.g., as we have learned that finance companies and sole proprietorships are eligible. More recently, for
example, our predicted value was $730 billion but we refined the estimate by increasing the sole
proprietor estimate to consider only Schedule Cs with ​positive ​net income (which the IRS SOI separates),
not all aggregate Schedule C net income.

5 This distinction between firms, establishments, and payroll may be one reason why estimates and
analyses vary across research designs. For example, estimates of the PPP based on extrapolating the
number firms may overstate the value because the number of firms is actually smaller once multi-state
firms are aggregated. Moreover, examining dollars of allocations per establishment does not alleviate this

2

example, our adjustments to include benefits or inflation assumptions are too low, or

firms substantially game the system by appearing smaller than they are to gain

eligibility.
The payroll data allow us to make predictions not only in the aggregate, but also

by state, industry, and firm size. We use these cross-sectional predictions and the PPP

allocations to-date to test the joint hypothesis that our model correctly incorporates the

rules of the program and that the rules were followed in making allocations.
The

6
results suggest that based on the distributions reported by the SBA through May 1

(which includes the full $342bn of first-round allocations and $176bn of the second

round allocations) the PPP loans have been allocated similarly to the model’s

predictions.
For example, using the state-level allocations we find that the average

7
absolute deviation between actual and predicted allocations is only 6.4%. Moreover,

half of all states were within 5% of our predicted allocation and 82% of states were

within 10%. Nevada has the furthest deviation (24% below our expectation). This

8
deviation may be because the Treasury did not clarify until April 24 that legal gaming

operations (which are not typically eligible for SBA loans) would be eligible to

participate in the PPP, causing Nevada to have a severe under-allocation in the first

round relative to the model’s predictions.
Our analysis of cross-sectional deviations of actual allocations from predicted

suggests that PPP funds have been allocated in a manner consistent with the model’s

underlying assumptions based on the program’s rules. That is, the PPP funds have

concern because, once again, dollars are allocated based on payroll, not establishments, and payroll per
establishment varies across states and industries.
6 Note, at this point, we cannot verify the aggregate predicted level because the program has not been
completed.
7 The Treasury and SBA have now updated the data through May 10, which we have not yet
incorporated into this draft. We will do so in future iterations. Because the latest allocation figures have
only increased to $189 billion from the $176 billion we include in our current analyses, the results will
likely only change slightly.
8 The District of Columbia has strictly the largest prediction error (negative), but the allocations are
relatively small. We suspect, but do not test, that at least some of this prediction error is caused by
ineligible lobbying organizations that the model does not take into account. Future analyses can consider
this explanation.

3

been allocated based on firms’ payroll. In addition to our main finding, we note a few

nuances to the results. First, the prediction errors across states of the first round of

funding were generally offset by the prediction errors of the second round. For

example, New York and California received less than predicted in the first round, but

more than predicted in the second. Second, the first round of funding showed that the

Manufacturing and Construction industries received more than expected, while the

Professional Services and Health Care industries received less. The SBA has not

reported the second round allocation by industry; however, preliminary analyses

(exploiting
state-level
differences
in
industry
exposure)
suggest
that
this

across-industry disparity potentially reversed in a manner similar to the broad reversal

across states. Third, analyzing the actual allocations by firm size is difficult because the

SBA has only reported allocations by loan size and not firm size; however, our findings

reveal that both tails of the firm size distribution appear to have been under-allocated

relative to predictions. The deviation for the largest firms is particularly apparent in the

second round of funding which suggests that pressure on larger companies to return

funds or to not apply had an effect. Fourth, we find that remaining deviations from

9
modeled expectations are predictable based on the known flaws in the model. For

example, because Schedule F (farmer tax schedule) data is not available since 2005, we

do not include these amounts in the model. Consistent with this error, we find that

states with a higher proportion of GDP deriving from Agriculture receive more PPP

than the model predicts. We also find that states with higher average wages receive

slightly less than predicted, which we suspect corresponds to those states having a

higher proportion of employees who surpass the $100K wage cap, which, again, the

model does not incorporate.
9 The under-allocation for the smallest firms may be more an issue of our prediction amounts than true
underfunding. Specifically, sole proprietor income is difficult to predict and allocate by firm size. We
discuss this issue in more detail below.

4

In sum, our findings suggest that the PPP funds were primarily allocated based

on 2019’s estimated payroll, which was how the PPP was essentially designed.
As

10
such, the extent to which other possible objectives were not met (such as targeting

certain regions, specific firm sizes, or particular industries more intensively), the issue

is likely more the result of how the program was initially designed and less with how

the program was ultimately carried out. It is important to emphasize that this does not

mean that there was no fraud or that some firms which should not have received funds

received them anyway, but rather at a macro level, the data suggests that funds

broadly followed historical payroll. It is also the case that differences in disbursements

between the first and second funding rounds appear to address allocation concerns

relative to predictions. More conclusive inferences related to a specific allocation of

funds or, perhaps more importantly, the economic effect of the distributions, will need

to wait until the SBA reveals firm-level loan details and employment outcomes

manifest.

2. ESTIMATING THE POTENTIAL SIZE OF PPP REQUESTS
To estimate the potential size of the PPP we first identify eligible firms per the

SBA's rules and guidelines and then estimate the sum of the maximum loans for these

firms. Generally, eligible small businesses are those with less than 500 employees,

however, there are several exceptions to this threshold which we discuss below. The

maximum loan amount a firm is able to request is 2.5 times monthly payroll for the

previous year, using a $100,000 wage cap per employee, up to a maximum loan of $10

million per firm.
The U.S. Census Bureau provides payroll data by state, industry,

11
and employee number-based firm size in the Statistics of U.S. Businesses (SUSB)

tables.  The most recent tables are available for the year 2017.
12
10 Two factors may affect the ultimate distribution of funds — and, in particular, could affect the second
round of funds. First, the negative publicity surrounding larger firms, especially restaurants and hotels,
could cause firms to reconsider their requests. Second, the Treasury emphasized the “economic need”
certification criterion on April 30 in FAQ #31.
11 Seasonal businesses received an exception to using annual payroll figures.
12 See: ​https://www.census.gov/data/tables/2017/econ/susb/2017-susb-annual.html​.

5

Table 1 presents our estimated PPP calculations. We start with all payroll for

firms with less than 500 employees and then make adjustments for certain industries

that have higher limits for employee-based eligibility.
Importantly, we allow eligibility

13
for all firms in sector 72, which includes restaurants and hotels, because of an

exception granted by the Treasury specifically for this industry.
Second, the PPP

14
rules allow for the consideration of benefits in addition to wages in calculating the

eligible payroll costs, which the SUSB data does not include. We use the Internal

Revenue Service’s (IRS) Statistics of Income (SOI) data to estimate a gross-up for

eligible benefits.
Specifically, we use aggregate tax return data which reports the

15
deductions for total employee costs, Figurewhich include salaries, wages, retirement,

benefits, and costs of labor. To derive the gross-up factor, we divide the total costs by

the costs of wages only. Our estimated factor is 110% of the costs of wages. Third, sole

proprietor net income is also eligible for PPP, so we add total net income from Schedule

C provided by the IRS SOI. Because only individuals with positive Schedule C net

income will apply, we use total aggregate net income conditional on those Schedule Cs

with positive net income.
The first three steps provide a total annual eligible payroll amount for the year

2017. We then need to adjust this figure to derive our estimate of total potential PPP

requests. First, not all firms in an industry are eligible, so we assume an industry

participation factor. Specifically, in our default specification we assume 100%

participation across all industries except NAICS codes 52 (Finance and Insurance) and

13 The regulations state that all firms with less than 500 employees are eligible or those which are
classified as small businesses according to the SBA’s size standards. The size standards for
approximately 300 six-digit NAICS codes surpass 500 employees. Size standards are also based on
revenues and net income, but SUSB data limitations restrict our ability to account for these size
standards.
14 Essentially, the Treasury removed the employee size cap and made an exception to the affiliation rules
for firms in industry 72 ostensibly because hotels and restaurants were badly affected by COVID-19 but
are often “chains” which have less than 500 employees at any individual location, but collectively more
than 500.
15 See: ​https://www.irs.gov/statistics/soi-tax-stats-business-tax-statistics​.

6

53 (Real Estate) as some of these entities have been deemed ineligible.
Next, because

16
the most recent data is from 2017, but our eligible payroll for the PPP calculations is

based on 2019 data, we include an inflation factor of 5%.
Finally, PPP requests can

17
not exceed 2.5 months of payroll costs, so we divide our total by 12 and multiply by 2.5

to derive our upper bound on the total expected PPP requests. As Table 1 reveals,

estimated PPP requests according to the model could total $750 billion.
It is important to understand the sensitivity around the estimated total. Most

issues and assumptions with the model make the estimated value too high, but others

could suggest that the value is too low. Factors that suggest that our estimates are too

high include: (i) our approach assumes that all firms apply and are eligible based solely

on employee size. This does not consider various factors that could drive participation

rates lower. For example, the Treasury has emphasized that firms must certify an

economic need and that if they are able to get liquidity from other sources, then they

are not eligible. Additionally, there are likely many firms that no longer demand funds

because they no longer have employees or have otherwise decided not to apply. (ii) The

SUSB data aggregates firms to the state level only. This means that some firms which

appear to be small businesses (because they employ fewer than 500 employees in the

data) are actually too large to participate when considering all establishments across

states. (iii) We are also unable to account for affiliation rules. For example, if one

person owns several different companies (e.g., a restaurant business and car wash

business), these separate firms must be considered collectively for the purposes of

16 To put it bluntly, 50% is a very rough estimate for industries 52 and 53. In our initial model
specification we had 0% because typically firms in industries 52 and 53 are completely ineligible to
participate in the SBA’s 7(a) program. After the first round of PPP, we noted that firms in these
industries were getting allocations, but at a lower rate than other industries. The participation factor is
also intended to be used to adjust for other program rules, like the $100,000 per employee and $10
million in total cap. However, our default model does not make these adjustments because we do not have
a good way to estimate them. Therefore, we view these estimates as likely upper bounds. Undoubtedly,
one way in which our model is misspecified in the industry participation factor.
17 The inflationary factor is intended to account for payroll growth from both an increase in wages and
an increase in employment. One potential issue is that we assume this factor to be homogenous across
states, industries, and firm sizes, which is likely not correct. Also note that the Treasury allows seasonal
businesses to use a timeframe other than the full year 2019. Our estimates do not account for this
seasonality.

7

eligibility, but it is likely that these are considered separate entities in the SUSB data.

Relatedly, some firms are controlled by venture capital and private equity firms and are

not eligible to participate. (iv) The PPP places a cap on the eligible wages per employee

($100K) and the total requested amount per firm ($10 million). Because the SUSB

data is aggregated, we are unable to account for these caps which inflates our

estimates. (v) We include all Schedule C sole proprietor net income, but some portion of

this is “side income” incidental to the individual’s main occupation. A big uncertainty is

how many Schedule C filers will request funds.
Factors that could push our estimated figure higher include: (i) Our assumption

of payroll growth between 2017 and 2019 (which captures both employment and wage

growth) could have been higher than our assumed 5%. (ii) Firms may find ways to

“game the system” by either making their companies appear smaller and therefore

eligible or commit outright fraud and make claims for nonexistent employees. Our

estimates attempt to model legitimate claims. (iii) Firms in the finance, insurance, and

real estate industries could participate at more than our assumed 50% participation

rates. (iv) As noted above, we do not include Schedule F net income in our estimates.

Considering all sensitivity factors, we suspect that the $750 billion represents an upper

bound, but there is a wide confidence interval around this figure. We now turn to

examine the cross-sectional variation in predictions to assess how the model performs.

3. ASSESSING THE MODEL AND ACTUAL PPP ALLOCATIONS
The SBA provides the actual PPP allocations to-date allowing us to compare the

model predictions to actual results. Given the program is not yet complete, we cannot at

this point examine total allocations or participation rates, but we can examine

cross-sectional predictions. We also note that any test of the allocations is a joint test

that the model incorporates the rules of the PPP and that the allocations were made

according to the rules. We further note that because the SBA has provided more

complete allocation data by state, our cross-sectional analyses focus on the state-level

8

allocations. However, we do some preliminary analysis of the allocations by industry

and firm size.

3.1 State-Level Analysis
The SUSB provides payroll data by state allowing us to disaggregate the totals

from Table 1 on a state-by-state basis. However, two data limitations prevent us from

having the total by state equal the national total in Table 1. First, we cannot adjust for

firm sizes which are eligible above 500 employees because employment-based size

details are missing in the SUSB files at the state, 6-digit NAICS level.
Second, sole

18
proprietor net income data is not available at the state level from the IRS SOI and thus

the across state comparisons rely on SUSB payroll data for firms with less than 500

employees. Given that this portion of the sample represents more than 85% of the

estimated PPP eligibility (and that the remaining portion is likely highly correlated

with the distribution of SUSB payroll figures) and that we are only examining across

state variation and not total figures, the across state share approximations should be

very close to what they would be if we could use the full data.
Table 2 tabulates the predicted allocation shares for each state. We also provide

the actual allocation shares per the SBA for both rounds and the cumulative through

May 1. The last column displays the prediction error of our estimate, relative to actual

allocations to date, where the prediction error is calculated as ($ Actual Allocation - $

Predicted Allocation)/$ Predicted Allocation.
The first observation to note in Table 2

19
is that the ​cumulative ​prediction errors are relatively small for most states, with a few

outliers. Nevada has the largest negative deviation in actual allocation versus our

prediction — with a substantial negative deviation in the first round and a slightly

positive deviation in the second. This is potentially explained by the Treasury not

18 We are in contact with the Census Bureau and we may be able to include this adjustment in future
iterations.
19 The predicted value for each state is a total, so we scale this total by the total amount allocated. For
the first round, the scaling factor for each state is $342 billion/ $748 billion = 45.7%. For the second
round, the scaling factor for each state is $176 billion/ $748 billion = 23.5%.

9

clarifying until April 24th that legal gaming operations, which are not typically eligible

for SBA loans, would be eligible in the PPP. The cumulative absolute average

prediction error is 6.4%, and excluding Nevada and the District of Columbia, it is

5.5%. The second observation from Table 2 is that the prediction errors are much

larger in each of the individual rounds, compared to the cumulative prediction error.

The average absolute prediction errors of rounds 1 and 2 are 20% and 28%,

respectively. Moreover — and quite importantly — the prediction errors between

rounds are highly negatively correlated, and only eight states have errors with the

same signs in both rounds. For example, both California and New York — about which

there was much discussion of being under-allocated in the first round — received much

more than predicted in the second round. Figure 1 illustrates the prediction errors for

both rounds. Note that for most states, the errors from the first round go in the

opposite direction from the second.
We more formally analyze the fit of our model in Table 3. We regress the

natural log of the actual PPP allocations on the natural log of our model's predicted

PPP allocation by state. In Panels A and B, we examine rounds 1 and 2, respectively,

and in Panel C we examine the cumulative distribution. First note that the fit of the

model is quite high in all panels, but particularly high (R​2 = 99.3%) when examining

the cumulative distribution to date. We further illustrate the fit across states in Figures

2 (A, B, and C), noting that most states fall very close to the prediction, particularly in

Figure 2C, which is the cumulative amount.
20
In each of the panels in Table 3, we also explore why states deviate from

expectations. These variables are included to examine potential shortcomings of our

model and how allocations changed across rounds. First, our model is unable to account

for farmers who file Schedule F to claim PPP funds. Note in Table 2 that states

typically associated with farming (e.g., Indiana, Iowa, Kansas, Minnesota, Nebraska,

20 We also note that the Pearson correlation of the residuals between Rounds 1 and 2 is -90%, reflecting
the reversal of the allocation disparity across rounds.

10

North Dakota, and South Dakota) have positive cumulative prediction errors.
In

21
Table 3, we include a cross-sectional variable which is the Log(Gross Farm Income).

22
For Round 1 (Panel A) and cumulatively (Panel C), the coefficient on this variable is

significantly positive, supporting the idea that at least some of the “abnormal” PPP

allocated to these states is the result of farm income allocations. Another known

problem with the prediction model is that we cannot account for the $100K per

employee wage cap. We predict that states with higher wages will appear to be

under-allocated as a result of these caps. We include Log(Average Pay per Employee)

to proxy for wage levels across states. Table 3, Panel C shows that the coefficient on

this variable is significantly negative consistent with the higher wages creating a

binding constraint in some states. Our model is also not able to account for the $10

million cap in funds allocated per firm. States with a relatively higher proportion of

large firms will, therefore, appear to be under-allocated. However, there is also an

alternative hypothesis for this firm size explanation. It could also be that if large firms

were able to more easily gain access to funds, it could be that states with relatively

more large companies would appear to be overallocated. To examine this, we include a

variable which is the percentage of total state payrolls which are in firms of 400 to 500

employees. Consistent with the assertions that larger companies were more successful

in the first round but that the second round went predominantly to small companies, we

see that the coefficient on the firm size variable is significantly positive (negative) in

Panel A (B), but insignificant in Panel C, suggesting that the early advantage for

larger firms was at least partially offset in the second round.
We conduct one more state-level cross-sectional test in Table 3. States differ in

the relative industry concentration; moreover, we noted in the first round that certain

industries appeared to be overallocated relative to our expectations. Therefore, some of

21 The allocation based on farming is also likely one reason for initial reports of overallocation per
establishment to states such as Nebraska and North Dakota versus New York and California in the first
round of funding. As long as Schedule F farmers are not included in the number of establishments (e.g.,
they are not included in SUSB data), then allocations per establishment will appear high in states
overrepresented with agriculture.
22 See: https://www.ers.usda.gov/data-products/farm-income-and-wealth-statistics/

11

the across-state differences in PPP allocations could be driven by heterogeneity in

industry shares. To test this, we include the ratio of the payroll of NAICS sectors 23

(Construction) plus 31-33 (Manufacturing) divided by 54 (Professional Services) and

62 (Health Care) to capture the relative dominance of these industries across states. In

Table 3, Panel C we see that this variable is significantly negative suggesting that

some of the across state variation is related to industry heterogeneity. However, we

also note that this appears to be reversing in Round 2 allocations.
Overall, we find that actual allocations to date correspond well to payroll-based

predictions while we observe variation in the prediction errors in rounds one and two

separately. We further note that the reversal between rounds could be the result of

several factors. One possible explanation is simply that this is a natural mean reversion.

Some states had more firms that were “ready to go” in the first round and in the second

round those states just did not have as many firms needing to apply. Another

possibility is that the changes the Treasury and SBA made between rounds could have

affected the distribution. Yet another possibility is that larger banks, which were shown

to have made an under allocation of funds in the first round (Granja et al. 2020), were

better prepared in the second round. This, in turn, affected the allocations. Regardless

of the explanation, the cumulative distribution to-date tracks very closely to our

expectations because of reversals in the second round compared to the first.

Collectively, our state-level analysis suggests that the cumulative actual allocations

closely correspond to payroll-based predicted allocations, suggesting that PPP funds

have been allocated following to the design of the program (i.e., according to the

distribution of payroll records).

3.2 Industry-Level Analysis
We next briefly examine the predicted and actual allocations across industries.

Unfortunately, the SBA has only provided the actual industry-level allocations for the

first round, thus limiting our analysis. Table 4 shows the amounts and shares of

predicted and actual PPP allocations by industry. Excluding sectors 11 and 99, the

12

average absolute prediction error is 25%, which is similar to the errors we observed at

the state level in the first round. A few sectors have substantial deviations. As

mentioned previously, our model lacks data for farmers with Schedule F and indeed the

Agricultural sector reports a large positive prediction error. In addition, the real estate

sector has a large positive prediction error, which is likely because we made a

particularly conjectural assumption on the participation rate of this sector. Finally, the

model performs poorly in Sector 99, but this is a particularly small sector. Figure 3

graphically illustrates the PPP allocations and predictions by industry.

3.3 Loan-Size Analysis
We
conclude
our
analysis
by
examining
the
allocations
by
firm
size.

Unfortunately, the SBA only provides data by loan size and not by company size.

Therefore, we have to estimate a mapping from the firm size categories in the SUSB

(which is based on the number of employees) to the SBA’s actual PPP data (based on

loan amounts). To create this mapping, we estimate the likely loan size category by

using the average payroll per employee and the range of the number of employees in

each industry by state by firm size category in the SUSB data set.
In addition to the

23
SUSB payroll figures, we must allocate sole proprietor net income data across loan

sizes. Unfortunately, the IRS SOI does not provide this data by employee size, so we

simply assign half of the sole proprietor PPP eligible amount to the two smallest loan

size categories.
23 An example of our estimation procedure is as follows: for the size category 30-34 employees with an
average annual payroll of $50k, annual eligible payroll is between $1,5m and $1,7m, and maximum loan
size between $312,500 and $354,167. In the current case, 90% of observation’s payroll is attributed to
$150k - $350k, and 10% to $350k - $1m. In addition to the allocation of payroll to the loan size
categories, we are required to make several other assumptions in our estimation procedure. Specifically,
we attribute the full amount of PPP eligible payroll of small business firms with more than 500
employees to loans in the larger than $5m category. Moreover, depending on a company's salaries and
wages, it is possible for such a firm to have a maximum loan amount lower than $5m. At exactly 500
employees with no employees making over $100k, the maximum loan amount is under $5m if the
average payroll is less than $48k. In the SUSB data, the average payroll of firms with more than 500
employees is under $48k for only 3 out of 358 state x 2-digit NAICS observations which make it
unlikely this possibility substantially affects our estimates. Additional details of this distribution are
available upon request.

13

Table 5 reports the allocations by loan size for both rounds and the model’s

predictions based on the estimated mapping (Figure 4 also illustrates the distribution).

Consistent with widespread reporting, the actual allocation across firm sizes changed

substantially from the first round to the second. For example, while smaller companies

(i.e., the first two loan size categories) received approximately 32% of the funds in the

first round, they received 54% in the second. Comparing the allocation relative to

expectations, it appears that both tails of the firm size distribution are under-allocated

— i.e., both the largest and smallest firms appear to be getting less than expected. For

larger firms, this may be the result of pressure to return funds or not participate;

whereas smaller firms may have had more difficulty participating initially. Moreover,

some may be reluctant to participate if they no longer have their employees. It is

important to note regarding the small companies, though, that sole proprietor

participation may also be responsible for some of this apparent under-allocation. For

example, we assume 100% participation of sole proprietors and then evenly distribute

these amounts to the smallest two buckets. If we remove sole proprietors, then the

allocations to the small firms are consistent with expectations.

4. CONCLUSION AND DISCUSSION
The Payroll Protection Program is a massive governmental response to the

COVID-19 epidemic. Two initial key questions are how big could the requests for funds

be and how will those funds be allocated based on the way the program has been

designed? We develop a simple model using publicly available payroll and tax data to

establish a framework to answer these questions. Our preliminary findings lead to three

points for future analysis of the PPP to consider. First, total requests could reach $750

billion, surpassing the currently allocated $660 billion, though our estimate has a high

degree of uncertainty because of several assumptions we have to make. Our current

view is that this figure is a high water market given that several assumptions bias this

figure upward, but it could also be that some features — such as growth, benefit

expenses, gaming the system by firms, etc. — could push the figure higher.

14

Unfortunately, testing the model’s predictions on the total allotment will be difficult if

the $660 billion is fully allocated and the program is not replenished. Moreover, we

emphasize that the model’s $750 billion estimate is not intended to be an expectation,

but rather a framework for considering the amounts that get ultimately distributed.
Second, based on the publicly available data to date (for activity through May

1), the model works well in predicting the cross-sectional variation in PPP approvals.

In short, the first order finding is that the program’s allocations — across states,

industries, and firm sizes —
generally follows the program’s design. The PPP has

generally been allocated to firms based on payroll. From a broad perspective, this

appears to be how the program was designed. We think, therefore, that such a model

should serve as a reasonable launching point for future evaluation of the PPP. One

potential inference from the preliminary results is that to the extent that policymakers

are dissatisfied with how the funds were allocated, the initial place to look will be in the

original program design and to a lesser extent in the program’s execution.
24
Third, our analysis has very little to say at this point about aspects such as

fraud or even normative questions such as “how should the funds be allocated?” or

“were they allocated to the right places?” Nor does this analysis answer very likely the

more important questions such as “was the program effective?” or “did it prevent job

losses?” Our objective to this point has been much more modest in trying to assess

what the size of the program could be and the extent to which the funds were allocated

given the set of rules that the Treasury and SBA provided. This should serve as a

starting point to begin answering the other questions as data becomes available.

24 Of course, the execution of the program is still open to critique and analysis, for example, with respect
to how quickly the funds were disbursed, among other issues. Our point is simply that the ultimate
allocations appear to be broadly in line with how the program was designed based on high-level
estimates.

15

Figure 1: Prediction errors by state and funding round
This figure shows the prediction errors (calculated as ($ Actual - $ Predicted)/$
Predicted) for the first round (dark) and second-round (light). Bars to the right indicate
states which appear to be “overfunded” relative to expectations, while bars the left
indicate states which appear to be “underfunded.”

16

Figure 2A: Predicted vs. actual by state in round 1
This figure is a scatterplot of Log($ Allocated) on the y-axis and Log($ Predicted) on
the x-axis by state through the first round of funding. States above (below) the linear
fit received relatively more (less) funding than expected in the first round.

17

Figure 2B: Predicted vs. actual by state in round 2
This figure is a scatterplot of Log($ Allocated) on the y-axis and Log($ Predicted) on
the x-axis by state in the second round of funding. States above (below) the linear fit
received relatively more (less) funding than expected in the second round.

18

Figure 2C: Predicted vs. actual by state in both rounds
This figure is a scatterplot of Log($ Allocated) on the y-axis and Log($ Predicted) on
the x-axis by the state for both cumulative rounds of funding. States above (below) the
linear fit received relatively more (less) funding than expected in total.

19

Figure 3: Predicted vs. actual by industry in round 1
This figure is a scatterplot of Log($ Allocated) on the y-axis and Log($ Predicted) on
the x-axis by the industry for the first round of funding. Industries above (below) the
linear fit received relatively more (less) funding than expected in the first round.

20

Figure 4: PPP allocation by loan and firm size
This figure presents the share of PPP funds allocated by loan size. The actual data for
rounds 1 and 2 are provided by the SBA. The predictions are derived from our model.
Because the model predicts amounts by firm size and not by loan size, we have to map
firm sizes into loan sizes based on data about employee sizes and average wages per
employee by industry and state. See the text for details.

21

Table 1: PPP Prediction Model Summary
This table presents the estimated calculations of the potential total PPP eligibility
requests. We begin with payroll data from the SUSB for firms with less than 500
employees and add to this payroll for firms in certain industries with an exception for
greater than 500 employees. We then assume a gross up factor of 10% of payroll for
benefits (e.g., healthcare and retirement) which we estimate using IRS SOI data. We
then add sole proprietor net income per the IRS SOI data for Schedule Cs with positive
net income. We further assume an eligible participation rate of 100% for all industries
except finance, insurance, and real estate, for which we assume 50% eligibility.
Because all figures are based on 2017 data, we assume 5% inflation for higher wages
and employment in 2019. Finally, we divide by 12 and multiply by 2.5 to calculate the
estimated PPP eligibility total.

22

23

Table 2: Predicted and allocated PPP shares by state
This table presents the predicted share of PPP eligibility by state and the actual
allocations for both round 1 and round 2 through May 1. The prediction errors have
been calculated as ($ actual - $ predicted)/$ predicted, where $ predicted has been
scaled by a factor to account for the fact that only $342 billion was allocated in the first
round and $176 billion in the second thus far.

24

25

Table 3: State level regressions examining the actual distribution of PPP
This table shows regressions of the Log($ Actual) on Log($ Predicted) and other
covariates by state. The additional covariates are Log(Gross farm income) per the
USDA, Log(Average wages) per SUSB, percentage of total state payrolls which are in
firms of 400 to 500 employees, and ratio of the payroll of NAICS sectors 23
(Construction) plus 31-33 (Manufacturing) divided by 54 (Professional Services) and
62 (Health Care). Panel A (B) includes data for the first (second) round, while Panel C
includes data for the cumulative funding through May 1.

26

27

Table 4: Predicted and allocated PPP shares by industry
This table presents the predicted share of PPP eligibility by industry and the actual
allocations for round 1. The prediction errors have been calculated as ($ actual - $
predicted)/$ predicted, where $ predicted has been scaled by a factor to account for the
fact that only $342 billion was allocated in the first round.

28

Table 5: Predicted and allocated PPP shares by loan and firm size
This table presents the share of PPP funds allocated by loan size. The actual data for
rounds 1 and 2 are provided by the SBA. The predictions are derived from our model.
Because the model predicts amounts by firm size and not by loan size, we have to map
firm sizes into loan sizes based on data about employee sizes and average wages per
employee by industry and state. See the text for details.

29

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