Consumer studies can estimate missing cash

Consumer cash-use studies like the U.S. Federal Reserve’s Consumer Payment Choice study can be an effective means of estimating missing funds in cash skimming cases. The authors explain how they’ve used these studies in fraud cases and how fraud examiners may deploy these studies.

Despite the growing use of digital payment methods, peer-to-peer payment apps and mobile wallets, cash remains a primary payment method for many. This is especially true for certain populations, like the unbanked and older adults. And for many small businesses, such as food trucks, restaurants and convenience stores, cash is the primary way to pay.

Small businesses often rely on cash to avoid credit card processing fees and maintain a simpler accounting system, but cash-based businesses do have their drawbacks. Many businesses don’t have the same sort of detailed paper trail that accompanies digital payments, making them especially susceptible to skimming schemes. In cash skimming cases, an employee (or owner) will take the customer’s payment and pocket the money before it can be recorded in the accounting system. Cash-based business owners often perpetrate this scheme to reduce their tax liability or avoid paying taxes all together.

When investigating cases of cash skimming, fraud examiners rely on register totals, sales information and estimates of projected goods sold to determine unaccounted for or underreported revenues. In cases where documents aren’t available for review, they might estimate total sales from goods sold or used adjusted for gross profit margins to determine missing cash. However, we’ve developed another method of determining missing or underreported cash using the U.S. Federal Reserve’s (the Fed) Diary of Consumer Payment Choice studies.

The Fed conducts these studies every year to better understand consumer payment habits. We’ve found them to be useful in estimating the proportion of cash deposits in cases involving suspected cash skimming. Here, we’ll describe how we’ve applied these studies to our own cases and how fraud examiners can use them too.

Federal Reserve studies

Since 2016, the Fed, the central bank of the U.S., has conducted an annual study surveying how U.S. consumers make purchases. These studies show that more and more people are opting to use digital payments; however, as the 2025 Fed study reports, cash is the third most-used payment method behind card and debit cards.

Participants in the Fed studies answer questions about the types of payments they’ve made over a brief period, like three consecutive days, and whether they’ve used paper, card or electronic payments from a bank account. They record what they spent on groceries, online purchases, restaurants and bars, gas, insurance, financial services and payments to friends, family and co-workers, among other expenditures. Respondents also report how much cash they have on hand.

This short-term reporting produces an accurate snapshot of participants' spending as they’re recording their transactions in real time instead of relying on memory and estimating what they’ve purchased over a longer period of time.

With this information, researchers better understand the spending habits of various demographic groups. We’ve found this information especially helpful in legal cases where cash sales have been underreported. Because the studies include information about industries, purchases and the demographics of consumers who frequent different types of businesses, we can make reliable estimates regarding cash receipts in similar businesses. 

In the following section, we’ll describe how we’ve used these studies in two legal cases to estimate missing cash.

The seafood truck

In the first case, a seafood sales truck operator underreported cash receipts from his sales, claiming that cash sales were about 2.8% of his total sales over four years. Unreported cash income reduces reported profits and the present value of future cash flows, which resulted in a lower valuation of his business for asset allocation during his divorce settlement. Because the owner didn’t have data on the average cost of sales transactions and underreported cash sales, it was difficult to determine actual sales and profits without the Fed’s study. In Figure 1, we report percentages of cash sales by transaction amount from the Fed’s 2018 study, which covered the time period at question in this case.

Figure 1

Based on the 2018 study, we expected that most purchases would cost more than $10, but less than $100 as seafood is expensive and most customers reported carrying less than $100 in cash. According to the 2018 study, consumers between the ages of 25 and 55 reported carrying $37 to $68 in cash, on average. A $100 purchase in cash would be high for a casual or unplanned food purchase.

Cash sales ranging between 16% and 33% of total sales (corresponding to sales between $10 and $50) are more reasonable to expect than the 2.8% reported by the owner. Luckily, the owner’s spouse was able to obtain her husband’s handwritten diary of sales transactions shortly after the case was initially filed. She photographed 15 days of the truck’s operations, which showed that during those days, cash receipts were 27% of total sales. Using the 27% rate of cash receipts in calculations increased the valuation of the business by more than $200,000.

Since the percentage determined from the diary so closely aligned with our expectations from the Fed study, we were able to provide a compelling reason for the court to accept the seafood truck’s increased valuation.

Missing gate receipts

The Fed studies were also useful for a case involving cash skimming of gate receipts from ticket sales for an annual artistic event between 2006 and 2018.

A former member of the venue’s board saved gate counts for those years and passed the information to investigators. The former member’s information showed that gate counts during those years didn’t match up with gate sales from earlier years. Average receipts per attendee were as low as $1.43 for an event with significantly higher ticket prices. For such a low average, the venue would’ve needed to admit thousands of people for free. This raised suspicions of fraud.

Data on cash, Automated Clearing House (ACH) transfers and checks deposited into the event organizer’s bank account during the month of the event showed cash deposits averaging more than 50% in 2006 and 2007. By 2011, cash deposits had fallen to about 29% of total bank deposits. In 2012, the key period in the case, cash deposits fell to 10.8%.

Based on the 2012 Fed study, we’d expect cash receipts to exceed 40% of total deposits, as reported in Figure 2 below. Investigators learned that the event lacked controls such as turnstiles, register totals and summaries. In 2019, new management took over the event and cash deposits soared to 40% of total deposits. These numbers were in line with the results from the Fed’s 2012 study. 

Figure 2

The Fed studies show that consumers’ use of cash declined from 31% of transactions to 31% to 20% between 2016 and 2021. For in-person transactions, cash use declined from 40% to 29%, as reported in the table below from the 2021 study. Despite the decline, cash use is still the most common payment method for small transaction amounts. 

Change in proportion of cash payments between 2016 and 2021

Our model

Here we’ll show how we developed our model and provide a tabular presentation and algebraic model illustrating how changes in variables can cause differences in an entity’s percentage of cash collections. This model supports traditional methods of estimating sales and cash receipts, such as cost of goods sold or purchases grossed up for profit margins.

This is an algebraic model for the amount of cash estimated to be missing from an entity’s books: ((CD+X))/((TD+X) )=FRC%. Where CD represents cash deposits reported by the entity, TD represents total deposits reported by the entity, FRC% is the cash percentage estimate from Federal Reserve studies and X is the estimated amount of missing cash.

Here’s a simplified basic equation: 

CD+X=FRC% (TD+X)
CD+X=CFR% (TD)+FRC% (X)
X-FRC% (X)=FRC% (TD)-CD
X (1-FRC%)=FRC% (TD)-CD
X=((FRC% (TD)-CD))/((1-FRC%))

If there are factors causing the percentage of cash collections for an entity to differ from that reported by the Fed, this equation can be used to estimate the amount of cash missing from the books. For example, if a business reports $345,750 total deposits and $83,583 cash deposits, and the Fed study shows that 41% of total deposits were normally from cash sales for this type of entity, missing cash is estimated to be $98,601 (i.e., [(41% Federal Reserve Studies cash percentage x $345,750 total reported sales) + $83,583 reported cash sales) / (1 - 41% Federal Reserve Study estimate of cash percentage)]).

A tabular presentation shows how the amount of missing cash would change if the cash sale percentage for the entity varied from the Fed study data. For example, a lawyer for the entity may argue that demographic variables (e.g., age of typical customer) or geographic variables (e.g., weather) caused the cash sale percentage to be lower than what the Fed study suggests. In this case, tabular presentation, in conjunction with the algebraic model, is better to help a judge in court proceedings understand how the amount of missing cash changes with the percentage. Using the same data from the previous example, the following table is a tabular presentation of how missing cash changes as the cash percentage of total sales is reduced.

Sensitivity analysis for estimated missing cash to changes in Federal Reserve study cash percentage

The following tabular presentation shows how the amount of missing cash would change if mitigating factors caused the actual cash collection percentage to vary from the percentage reported by the Fed.

Cash-study considerations

Despite the growing use of digital payment methods, cash is a mainstay for making small purchases. But when source data for sales volumes and amounts are missing or manipulated, fraud examiners have a significant challenge ahead of them in determining how much cash was skimmed or how many sales were underreported. Our proposed model can help estimate the amount of skimmed cash sales when receipts and other records aren’t available for analysis.

The Fed cash studies can be modified for local or regional factors, using same-store proportions of cash deposits to demonstrate higher or lower cash payments versus other payment options. In short, fraud examiners may use the Fed studies as benchmarks for expected proportions of cash receipts or to create benchmarks using other available data paralleling cash payments.

Regional factors may affect the proportion of cash payments. People living in rural areas often lack access to banks and may use cash more than people living in urban and suburban areas. Moreover, many small businesses don’t have the infrastructure to process digital payments or use digital payment platforms. This will increase the expected proportion of cash payments relative to the Fed’s studies. If you choose to implement this model, it’s essential to consider local conditions and other available information to determine the most reliable data for a business.

Amy Cooper, Ph.D., CFE, CPA, is an assistant professor of accounting at University of Alaska, Fairbanks. Contact her at akcooper@alaska.edu.

Ken Abramowicz, Ph.D., is an associate professor of accounting at University of Alaska, Fairbanks. Contact him at kfabramowicz@alaska.edu.

Robert Logan, Ph.D., is the owner of Northern Economic Research.

H. Charles Sparks, Ph.D., CPA, is a professor of accounting, emeritus, at the University of Alaska, Fairbanks. Contact him at hcsparks@alaska.edu.