1 Introduction

The “The Curse of Cash” by Rogoff (2016) is anathema to the use of cash in modern economies, where the availability of new and differentiated means of payment is expected to marginalize the use of cash. The persistence of high demand for paper currency is mostly – according to Rogoff – due to the profitability of the use of cash for illegal activities such as tax evasion, criminal activity and terrorism. Krueger and Seitz (2018) reassume the debate on pros and cons in the use of cash.

Most analyses focus on the macro framework, suggesting the need for cash payment limitations imposed by governments whose efficacy against informal economy, tax evasion, criminal activities and terrorism is a matter of debate (Passas 2018).

An issue that is under-investigated in this field is the micro foundation of cash preference and its relevance to also determining high levels of cash usage in a totally legal framework. The policy evaluation of cash payment limitation should also address its implications for consumer behaviours, inequality issues and institutional design. Consequently, in this paper, we collect some insights from psychological and economic literature on the individual preferences for cash payments to investigate if a specific preference for cash usage can be a consumer’s trait, attitude or characteristic justifying a micro analysis of purchasing behaviour that could explain a relevant use of cash in a legal economy. On the bases of these insights from scientific literature, we propose an agent-based model describing an economy with individuals with heterogeneous preferences about the means of payment to analyse the aggregate results in different scenarios. The focus is on the shares of cash transactions in terms of number of transactions and transaction value, and how their divergent and different figures can be explained by different preferences and consumption structures. By assuming that the majority of consumers has preferences for means of payments differentiated according to the transaction value and that transactions are mainly concluded among individuals with similar preferences, simulations results show that the value and the number of cash transactions is determined both by the preference structure and the frequency of low-value transactions (consumption structure). Results are compared with main figures of cash usage in EU, where countries have strongly differentiated measures, both in their absolute value and in the distance between transaction numbers and their values. Simulations results are coherent with EU average data for the percentage value of cash transactions, but underestimate the share of cash transactions by number. Since the main objective of this study is to obtain simulations data that are comparable with countries’ data, according to different preferences distributions and legal rules on cash transactions, simulations results are compared with disaggregated data for 19 countries.

To the best of our knowledge, a similar attempt to model cash preferences was conducted by Arango-Arango and colleagues (2018), who compare simulation results with empirical data for 4 countries to test the validity of certain assumptions concerning cash payments and holdings. A major difference in our work is in assuming that individuals are heterogeneous in preferences for cash payments, and in testing whether these differences can explain the observed behaviour in terms of the share of cash transactions by number and value of transactions, considering a wider range of countries (19 countries). Furthermore, Arango-Arango and colleagues (2018) concentrate on the use of cash as a mean of payment and on cash management to test two optimal policies. Our work mainly concerns the use of cash as a mean of payment and how it is differentiated according to the transaction value. Results in the study by Arango-Arango and colleagues (2018) well explain cash payment shares by transaction value for Canada, France and Germany, but not for the Netherlands, whereas, our results sufficiently explain data for 14 of the 19 countries considered, including the Dutch and the German case. In details, countries’ validation confirms simulations results for almost all EU countries where no cash payment limitation is imposed by law. Where cash policies are adopted, results show a better fit for countries nudging consumers to adopt non-cash means of payments compared with countries forcing them not to use cash.

The paper is organized as follow. In the following sections, we review scientific literature and empirical evidence both from economics (Sect. 2) and psychology (Sect. 3) to develop basic hypotheses on consumer behaviour about the means of payments (Sect. 4). Section 5 describes the behavioural model and Sect. 6 presents the simulation results and their comparisons with country data. Concluding remarks are presented in Sect. 7.

2 Economic literature review

According to historical research, the debate on the emergence of a cashless society originated in the 1950s, when a report by the Dynamic Analysis and Control Laboratory at MIT discussed possibilities and advantages of electronic exchange of money, to reduce costs involved in cash transactions (Bátiz-Lazo et al. 2014). Bankers were especially sensible to limit the costs associated with cash-based transactions, which were not resolved by other paper-based payments, such as checks or letters of credit. Today, the need for a cashless economy is mainly cited for reasons related to a better control of illegal activities such as tax evasion, criminality and terrorism. On the one hand, digital payments are seen as the best way to remove opportunity costs related to handling physical money and to promote ‘tomorrow’s global knowledge-intensive economy and electronic commerce’ (OECD 2002, p.7). Furthermore, the social institution of money co-evolves with technology (Peneder 2021). On the other hand, social costs of money digitalization may emerge for distributive effects associated with higher costs imposed on the poor and underbanked in the shift to a cashless economy (OECD 2002). Rösl and colleagues (2019) investigate the welfare costs of cash abolishment, finding large and enduring welfare losses. Focusing only on retailers, banks and infrastructures, an extensive analysis of both social and private costs of retail payment instruments concludes that – on average – cash has the lowest social cost per transaction in most countries, but social costs for household and consumers are not included (Schmiedel et al. 2012). Conversely, Alvarez et al. (2021) give an opposite result showing that the private costs of restricting the use of cash are at least twice as large as the social benefits. Garratt and Van Oordt (2021) investigate the use of cash for privacy reasons, by underlying the public good problem that occurs when firms use data collected through payments to discriminate among consumers. The authors underline the social cost of foregoing privacy in payments, whereas Kahn et al. (2005) study the private cost of information disclosure.

Some studies have dealt with the problem of cash management using the Baumol and Tobin inventory models, analysing the demand for cash holdings when withdrawal opportunities are available. Alvarez and Lippi (2009) find is that there is an ‘optimal minimum cash holding’ inducing individuals to withdraw cash even if they have some cash on hand, because of a precautionary motive. The cash management model is enriched with means-of-payment choices by Alvarez and Lippi (2017), who build their model on the hypothesis that the preferred mean of payment depends on the stock of cash holdings, so that agents use cash instead of cards whenever they have enough cash on hand (cash-first optimal choice). Starting from the hypotheses of the ‘optimal minimum cash holdings’ and ‘cash-first optimal choice’, Arango-Arango and colleagues (2018) extend the analysis to the share of cash and card payments by transaction values, comparing their theoretical results with empirical evidence from some countries. All these models assume that individuals have homogenous preferences about cash payments and behave rationally according to standard economic theory. It is worth to note that the actual cash behaviour of consumers can be strongly dependent on the cards acceptance by merchants, and vice versa (Bounie et al. 2017). Another explanatory factor, beyond preferences and card acceptance, is the cost of holding cash and the withdrawals costs (Rusu and Sticks, 2017).

2.1 Trust and the storage value

Economics traditionally indicates three basic function of money: account unit; mean of payments; and value storage. At the same time, however, ‘money is a form of credit, with state debt in the form of issued currency usually having the highest degree of credibility in terms of the expectation of future redeemability’ (OECD 2002 p.12). The precautionary reserve motivation has a dominant role in explaining the use of cash. Esselink and Hernández (2017), analysing consumers’ payment behaviours in the euro area, find that almost a quarter of consumers keep some cash at home as a precautionary reserve. This shows that cash has a storage function that is different from bank accounts. The recent financial crisis witnessed a slight increase in the use of cash, in the US and the UK, as trust in financial institutions decreased (Bátiz-Lazo et al. 2014). And traditionally, crises lead to the appearance of the bank run phenomenon. According to Stix (2013), cash preferences cannot be fully explained by whether people are banked or unbanked, because a lack of trust in banks, memories of past banking crises and weak tax enforcement are important factors. Often, a “safe” foreign currency serves as a store of value. Cash represents trust, because people know that others accept this piece of paper as a store of value, and this is particularly true when banks and financial institutions experience problems and people experience lower trust in other forms of money and financial institutions (Negueruela 2014).

Observations recorded during recent pandemic shock show that the fear of infection has led to a new implicit cost associated to each payment, shifting from cash to card-based transactions (Ardizzi et al. 2020; Coyle et al. 2021), affecting preferences from the demand-side. While the transactional use of cash has declined, the values of notes in circulation has sharply increased (Caswell et al. 2020).

2.2 Empirical evidence on the use of cash

Empirical evidence on the use of cash, often based on diary surveys, strongly differs among countries, but certain common features can be depicted. In Europe, cash is still the dominant mean of payment, with 79% of all transactions carried out in cash, resulting in 54% of the total value of all payments (Esselink & Hernández, 2017). The difference between incidence of cash payments on total number of transactions and incidence on total value is the first common feature of cash payments among different countries, and – with different values – is repeated inside those countries. People systematically prefer cash for low-value transactions and other kinds of payments for high-value transactions (Bagnall et al. 2014; Bennett et al., 2014).

Another common feature of cash payments concerns the influence of socio-economic characteristics on payment preferences. In the US, the lowest-income consumers used cash about twice as often as the highest-income consumers (Connolly and Stavins 2015). Cash use also decreases with income in Canada, Australia, Germany, Austria, the Netherlands and France (Bagnall et al. 2014). In the same countries and in the US, consumers with low levels of education use more cash (Connolly and Stavins 2015; Bagnall et al. 2014), but considering the whole euro area, Esselink and Hernández (2017) do not find systematic differences across level of education. As to age, in the EU, younger consumers use cash for only a limited amount of payments (Esselink & Hernández, 2017), and this result is confirmed by Bagnall and colleagues (2014); however, in the US, the opposite is true. Von Kalckreuth and colleagues (2014) highlight that the differences between older and younger consumers are linked to differences between characteristics of younger and older consumers and not to the slow adoption of technological devices by older people, nor to consolidated habits.

Preferences play a role in cash use. According to US data, those who declare to prefer credit card transactions usually carry out transactions with this mean, and the same occurs for people declaring a cash preference (Bennett et al., 2014). The preferences declared are also coherent with the income effect previously described: one-half of low-income consumers prefer cash, whereas this share declines sharply as income increases (Bennett et al., 2014). By contrast, in the euro area, contrasting results emerge: about 43% declare to prefer card payments, whereas only 32% rate cash first. This is puzzling when compared with the evidence of 79% of cash transactions and the high availability of choice between cash and non-cash payments (Esselink & Hernández, 2017). Investigating the payment patterns of Dutch consumers, van der Cruijsen and colleagues (2017) find a systematic difference between how consumers prefer to pay and how they actually pay, which the authors attribute to individual habits.

3 Insights and evidence from psychology and neurosciences

Psychology offers many insights into the role of physical money in individual personality, underlying that the idea of money is distinct from property or possessions. Consistent experimental effects show that the idea of money is particularly linked to its physical form, as individuals, after counting cash, feel less pain and less excluded than individuals who counted simple slips of paper (Vohs 2010; Vohs et al. 2006) conducted nine experiments whose results suggest that by activating the idea of money, people are enhanced to behave self-sufficiently. This is in line with Lea and Webley (2006), who characterize money as both a tool and a drug.

Neuroscience studies seem to confirm the relevance of money representation. Becchio and colleagues (2011) show that banknotes activate the same part of the brain that is associated with hammers and screwdrivers, confirming that money is a tool for representing the value of goods and services, especially in its physical representation. Furthermore, observing banknotes being ripped and torn induces a stronger reaction in the brain the higher the face value of the banknote.

According to Thaler (1999), ‘mental accounting matters’ in individual choices and people show different preferences for cash and electronic payments, because of their ‘decoupling’ features. Experimental results show that a payment made with non-cash instruments separates the payment from the purchases, making the expenses less vivid and salient (Soman 1998). Furthermore, people use separate expenses budgets to evaluate different allocations of fund use, with different rules concerning the temporal budget definition. For example, Gertner’s (1993) results show that a today’s winning has effect on a today bet, whereas prior won has no effect. In this mental organization of expenses, there is a ‘petty cash’ fund for small and routinized purchases that is not under rigorous scrutiny (Thaler 1999, p. 194). The basic idea is that money in one account is not perfectly fungible with money in another account, and each account has a specific mean of payment, implying the non-fungibility of means of payments. An experimental test of non-fungibility of means of payment is in the work of Solnick (2007), who tests the use of different means of exchange in a Trust Game. Her findings are that although the propensity to send the whole amount does not differ according to the mean of payment received, the returned amount does.

The imperfect fungibility of paper currency also occurs between coins and banknotes and among banknote denominations. Alter and Oppenheimer (2008) present three experiments where people attach a higher value to banknotes than coins of the same denomination, if they are more familiar with the banknote form. In five experiments, Tessari and colleagues (2011) show that people are willing to pay more when using coins than banknotes regardless of their familiarity. Among banknote denominations, the ‘bias for the whole’ (Mishra et al. 2006) induces consumers to have lower willingness to give up high denomination banknotes (Raghubir and Srivastava 2009). At the same time, when spending foreign currency, individuals systematically overspend or underspend according to the fractional or multiplicative ratio of the exchange rate (Raghubir and Srivastava 2002).

When talking of paper currency, many authors show that the descriptive invariance principle is systematically violated. Uhlmann and Zhu (2013) conducted experiments on the interchangeability of specific tokens of monetary currency, showing that when money lost its physical form, it is ‘not quite the same’ money. In the same way, the five experiments of Di Muro & Noseworthy (2013) show that the physical appearance of money has a strong influence on spending behaviour, overriding the influence of denomination, because people are proud to own and retain crisp currency. The relevance of the “face” of money is also recognized in anthropological studies, which go further in the interpretation of money’s denominational capacities, extending the tool function of money denominations to social and political struggles for dominance or hierarchy (Nelms and Maurer 2014).

Many authors investigated overspending behaviour (Schor 1999), showing that willingness to pay increases with credit cards rather than with cash (Prelec and Simester 2001) especially among children (Abramovitch et al. 1991), young adults and college students. Others suggest that credit card use is a moderating variable between money attitudes and compulsive buying (Roberts and Jones 2001). When considering pro-social behaviours, such as blood donations, Lacetera and Macis (2010) show that donors are not reluctant to receive compensation, but they would stop donating if compensated with cash.

In the food assistance field, by comparing cash transfer and voucher programmes, Aker (2013) shows that cash transfer programmes are more cost effective, whereas Hidrobo and colleagues (2014) find all modalities improving the quantity and quality of food consumed (for a review, see Gentilini 2016).

Cash incentives can also be used to discourage undesirable behaviours, such as drug abuse or gambling addiction. Festinger and colleagues (2014) find that cash-based reinforcement therapy is as effective as voucher-based reinforcement therapy for treating drug abuse. As to gambling addiction (see Parke et al. 2008, for a review), some studies show that one may lower gambling frequency by physically handling money (Weatherly et al. 2006). Finally, cash is also an instrument for payment inclusion for those with limited education and for refugees (Krueger and Seitz 2018). The report for the Council (2016) includes children, disabled, elderly and other socially vulnerable individuals among groups for which cash has a special role.

4 Research hypotheses

The above discussion shows that many mechanisms influence consumer behaviour in handling and using money. One can distinguish three fundamental choices concerning the three basic functions of money: (a) how much money an individual holds as a storage of value, and in which form; (b) how an individual counts different “faces” of money (currency, denominations, coins vs. banknotes, mental account, etc.); and (c) how an individual chooses the best mean of payment.

In this model we concentrate on the third point, adopting assumptions deduced by the previous literature review.

  1. 1)

    Preferences matter. Individuals have different preferences in the use of means of payment. They declare different preferences, and data show that socioeconomic characteristics (income, age, education) are associated with different payment behaviours.

  2. 2)

    Cash is for low payments. The imperfect fungibility of money justifies each mental account having its own mean of payment, so the account for high-value transactions may have a mean of payment that is different from the account for low expenditures. The “bias for the whole” can explain why for higher value transactions, people prefer non-cash instruments. Data confirm that the use of cash instead of other non-cash instruments depends on the transaction value.

  3. 3)

    Similarity: transactions mainly occur among agents with the same types of preferences. It is likely that transactions occur among agents with the same types of preferences. The relevance of familiarity with paper or coin money suggests that when moving money from hand to hand (physically or otherwise), people search for similar or familiar agents.

Building on these three points, we describe a model of market exchange where:

H1: Agents have heterogeneous preferences about the mean of payment.

H2: Preferences are differentiated according to transaction values.

H3: Agents follow routinized rules in purchasing behaviour.

H4: Buyers seek out sellers according to a similarity criterion, and transactions mainly occur among agents with the same type of preferences.

We assume that no legal restriction is imposed in the market as to payment means.

5 The behavioural model

We model an economy with 100 agents, who are both buyers and sellers. Each agent has a specific (x,y) position, displayed in a 10 × 10 box, and is endowed with a random value of saleable production V (0 < V ≤ 5). Saleable goods/services are of two types: low-price goods (L) sold at pL and high-price goods (H) sold at pH, with 1 > pH> pL>0. At the start of each simulation, each agent becomes a low- or high-price seller, and total production has a random share of low-price goods, so that each repetition has a different scenario of productive structure.

The agents have different preferences for the payment mean (H1). Cash lovers have a strong preference for cash payments, whereas cash haters prefer non-cash payments; cash mix individuals differentiate the payment mean according to the good/service price (H2): they prefer cash payments for low-price goods and non-cash payments for high-price goods. At the start of each simulation, a random percentage of the population is attributed to the cash mix category, and the residual to the other categories, so that each repetition has a different scenario of preference distribution, but on average, cash mix is the prevailing group.

The simulation starts with the casual selection of the first buyer who receives one unit of money. The first buyer chooses the good he wants to buy and the seller supplying that good according to the criteria described below. When the exchange takes place, the buyer receives the units of goods he can purchase according to the price (pH or pL), and the unit of money is transferred to the seller, who becomes the new buyer. Simulation stops when no more saleable commodities are available.

We define the routines for agent’s purchases (H3. H4), describing the rules they follow when searching (searching rules), and the way the exchange occurs (exchange rules).

5.1 Searching rules

We assume that buyers follow three criteria when searching for the seller with whom they make the exchange: proximity, cheapness and similarity.

  1. a)

    Proximity: buyers prefer the nearest sellers. A seller located near the buyer is preferred to a seller far from buyer’s location because of transportation costs, fast availability of purchase opportunity and, for cash exchanges, for the necessity of physical exchange of money. The proximity criterion implies that the buyer in position (x,y) checks the sellers in the square around him moving anticlockwise, starting from the seller in position (x-1, y-1). If he cannot find his preferred seller type and good type, he moves to the next square, starting from the seller with coordinates (x-2, y-2), and so on.

  2. b)

    Cheapness: buyers prefer low-price goods to high-price goods. The cheapness criterion implies that the buyer, moving according to the proximity criterion, searches for the sellers who have low-price goods. If the low-price goods are sold out, he again begins his search, checking the sellers of high-price goods.

  3. c)

    Similarity (H4): agents prefer to carry out the exchanges with their preferred mean of payment and therefore seek out a similar counterpart. Consequently:

    1. a.

      cash lover buyers prefer sellers who are cash lovers, as well as sellers who are cash mix if they are searching for low-price goods;

    2. b.

      cash hater buyers prefer sellers who are cash haters, as well as sellers who are cash mix if they are searching for high-price goods; and.

    3. c.

      cash mix buyers prefer sellers who are cash mix, as well as sellers who are cash lovers if they are searching for low-price goods, or sellers who are cash haters if they are searching for high-price goods.

Transactions mainly occur among buyers and sellers belonging to similar types, but as money circulation proceeds and goods are sold, agents may be rationed in their search. To make a purchase, agents should choose how to adapt their behaviour to available sellers’ types. Accordingly, the cheapness and the similarity criteria may have two different hierarchical orders.

If the similarity criterion prevails (similarity first), individual is willing to accept to pay higher prices just to continue to use his preferred mean of payment. When the similarity criterion prevails, the buyer, starting from his position, searches for low-price goods supplied by similar sellers. If he cannot find similar low price sellers in the economy, in the second step, starting again from his position, he will check for sellers who are similar to him, also if they sell at higher prices. He turns to dissimilar sellers only in the third step, checking first for low-price goods and then for high-price goods.

If the cheapness criterion prevails (cheapness first), the search is characterised by individuals who give up to use preferred mean of payment to avoid higher prices purchases. Accordingly, the buyer first searches for the low-price sellers of the same type in the whole box, but – if he cannot find – as second step, he will check for low-price sellers of dissimilar type. If low-price goods are no longer available in the economy, in the third step he turns his attention to the high-price goods supplied by similar sellers, and then at the dissimilar sellers.

The matching rules are described in Fig. 1.

Fig. 1
figure 1

‘Cheapness first’ and ‘Similarity first’ criteria

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5.2 Exchange rules

Two exchange criteria are modelled. In the buyer preference criterion, exchange occurs according the buyer’s preference: when buyer is a cash lover, the exchange takes place in cash; when buyer is a cash hater, the exchange takes place with non-cash means of payment; when buyer is a cash mix, the exchange takes place in cash if the good is of the low-price type, or with non-cash payments if the good is of the high-price type. In the seller preference criterion, the same occurs according to the seller’s type.

To fully compare behavioural hypotheses in this model with existing literature, it is relevant to put in evidence how the ‘cash first policy’ hypothesis by Alvarez and Lippi (2017) is implicitly included in this model. According to the cash first policy agents use cash instead of cards whenever they have enough cash on hand, and this implies that the transactions always occur according to the buyer’s preferences. In this model, the corresponding exchange rule is the ‘buyer preference’ criterion, but also the ‘seller preference’ criterion is considered. In both criteria, transactions mainly occur among agents with the same type of preferences, so that cash lovers will always search for cash lover sellers. Consequently, the seller receiving cash, being the new buyer and a cash lover, will use cash in the following transaction, implicitly following the cash first policy. Exceptions may occur when: (i) the buyer loving cash, after receiving cash, is rationed in finding a similar seller; (ii) a cash hater seller is forced to receive cash that he will not use in the following purchase.

A possible result of the above modelFootnote 1 is shown in Fig. 2, where panel (a) depicts the initial state, with the endowment of saleable goods/services for each agent, according to the type of agent and good. Panels (b) and (c) respectively show the low-price and high price goods purchased with cash by agents’ type and quantities.

Fig. 2
figure 2

Initial and final states

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6 Metrics, results and validation

We ran the simulation for n = 600 repetitions for each exchange rule (total 1.200 repetitions), collecting in each one of them the statistics described in Table 1.

Table 1 Variables collected and descriptive statistics
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The percentage of cash transactions has an average value of 68%, whereas the value of transactions carried out with cash is, on average, 50% of the total transaction value. This result is coherent with data showing that the number of cash transactions is always higher than the correspondent value, because of the habit/preference of using cash for low-value transactions. To further validate our simulation results, we use data from Esselink and Hernández (2017) concerning 19 countries in the euro area in 2016. The authors report that in the euro area, the market share of cash payments at point of sale is, on average, equal to 78.8% for the number of transactions, and to 53.8% for their value, with strong differences among countries. Simulation values are coherent for the value percentage, but underestimate the share of cash transactions by number. To investigate the determinants of shares of transactions by number and value, we compare the results of our simulations with other countries’ data. Figure 3 shows that most countries are in the thicker portion of the graph, but there is a group of countries that behave differently.

Fig. 3
figure 3

– Share of cash payments (number and value) – simulations and countries’ data

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In the first group (G1Footnote 2), the share of cash transactions by value is in the range 0.49-0.75%, and the number of cash transactions varies from 0.63 to 0.92%. In the second groupFootnote 3 (G2), the percentages are 0.28-0.33% and 0.45-0.68%, respectively, with both ranges substantially lower. By extracting from the whole simulations set those with results included in the above ranges, we obtain two subsets (SG1 and SG2) of simulations with different descriptive statistics (Table 2). It is interesting to note that the subsets selected based on the shares of number and transaction values systematically differ from the whole set as to the mean value of two variables (#lover and #low), whereas the statistics for other variables are in line. Moreover, the subset SG1 has higher values for these two variables than the whole set, whereas the subset SG2 has lower values. This indicates that the differences among countries could be explained by different structures of preference distribution and consumption

Table 2 Descriptive statistics – simulations data
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To better investigate the influence of preference and productive structures on the market performances in terms of shares of cash value transactions and shares of number of cash transactions, we run ordinary least squares (OLS) estimations on the whole dataset of simulation standardized results, considering as dependent variables alternatively the total value of cash transactions and the number of cash transactions. The results are shown in Table 3.

Table 3 Estimates of the effects on the value and the number of cash transactions – simulation data
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With respect to the total number of cash transactions and the transactions value, the coefficients have the expected signs. The number of agents who are cash lover or cash mix, and the number of sellers of low-price goods, increase the number of cash transactions and the value of cash transactions. Variables capturing how the search is conducted and how the exchange is carried out are not significant, signalling that only the preference structure and the productive structure are relevant in determining the total number of transactions.

The effects of preference structure are stronger on the number of cash transactions than on their value, especially when considering mix-agents. One more agent of the mix type increases the number of cash transaction of about 1% point, and the value of cash transaction of about 0,6 points. The effect of one more cash lover is about the same on the two variables. As to the consumption structure, one more seller of low-price goods increases the number of transactions of 0,3% points, and their value of about 0,6 points, showing that consumption structure is more relevant for the value of cash transactions than for its number.

As a whole, the number of cash transactions and their value are represented by the consumption structure (#low) and by the preference structure (#lover and #mix), with a stronger effect of the consumption structure on the value of cash transactions compared to their number.

Finally, we also compute the average number of transactions violating the ‘cash first policy’ described by Alvarez and Lippi (2017), who assume that people having enough cash in hand always prefer to use cash. Violations occur because rationed agents fail in finding sellers with similar preferences and an agent receiving cash can be forced to do not use cash in the following purchase. Transactions where violations of the ‘cash first policy’ occur account for about 0,05% points of total cash transactions value and 0,1% points for the number of transactions. This confirms that the model substantially respects the ‘cash first policy.

To validate these results, we use additional information from the work of Esselink and Hernández (2017), which contains a survey question concerning the cash preferences that we use as a proxy of the preference structure (lover). Another question concerns motives for payment by cash or non-cash means. We use the answer that rates the transacted value as the main element to choose the best mean of payments as a proxy of the percentage of cash mix in the economy (mix). The average value of a transaction at the point of sale is the proxy for the consumption structure (low estim), but with the opposite sign, because a higher value for the average transaction signals a lower availability of low-price goods. Furthermore, we include a dummy to distinguish countries belonging to the two groups described above (G1 and G2). Descriptive statistics for these data are shown in Table 4.

Table 4 Descriptive statistics – Countries data*
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We run OLS estimations considering as dependent variables alternatively the total value of cash transactions and the number of cash transactions. The results presented in Table 5 show two different specifications, with and without the dummy variable.

Table 5 Estimates of the effects on the value and the number of cash transactions – countries’ data
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The results are in line with the simulations. The number of cash transactions only depends on the preference structure, represented by the variables lover and mix, whereas the correspondent value depends both on the preference structure and the consumption structure (represented by the variable low estim). When the dummy variable is included (model II), its significance confirms that the two groups of countries exhibit strong differences.

6.1 Countries’ validation

The various countries strongly differ in the figures concerning the value and the number of cash transactions, and in the distance between the two variables values. It is therefore useful to verify if the model assumptions fit well with each country’s behaviour. Accordingly, we compare results from simulations with data for each country.

Let us define Vi and Ni as the share of value of cash transaction and the share of number of cash transactions, respectively, for country i. We extract from the whole set of simulation results those with a share of value of cash transactions Vie = Vi+0.005. On these subsets of simulations, we compute the average number of cash transaction (Nie) and the distance of simulation results from the data (di = Nie- Ni). From Table 6, we can observe that the simulations sufficiently fit the countries’ data with an average error of di = 2.5% points. Almost all countries exhibit a difference between the share of the number of cash transactions estimated from simulations and actual data in the range 0-4% (column E in Table 6). In five countries, figures estimated by simulations did not perform as well. For ES, FR, IE, IT and MT, simulations underestimate the country data with higher errors than other countries, in the error range of 7.5–12.5% points. For IE and MT, the underestimation can be explained by the peculiarity of these two economies, characterized by a significant number of foreign-owned multinational enterprises and a large size of cross-border capital flows relative to the size of their economies (Claeys et al. 2018). For IT, FR and ES, a common feature is the cash payment limitations imposed by law. We refer to cash payment limitations imposed between 2015 and 2016, because data from Esselink and Hernández (2017) are referred to payment diaries collected between the end of 2015 and the first few months of 2016.

In France and Italy,Footnote 4 the limit has been 1,000 euro for fiscal residents since 2015, whereas in Spain, the limit is 2,500 euro (Gikas et al. 2018). In these countries, experiencing cash payment limitations, it is possible that purchases of higher value were fragmented into multiple transactions, resulting in a higher number of transactions than expected, given the consumer preferences and the value of cash transactions. It is worth noting that Greece and Portugal also have cash payment limitations of 500 and 1,000 euro, respectively, but in June 2015 in Greece, severe controls to avoid bank run were introduced, and a cash deficiency occurred. Other countries had higher cash payment limitationsFootnote 5 or no limitations.

Table 6 Comparison between simulation results and countries’ data
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As a whole, we can conclude that the countries’ figures are coherent with the model’s assumptions, except for those countries where consumer preferences are constrained by cash payment limitations, where the model results underestimate the share of the number of cash transactions.

7 Discussion and concluding remarks

Building on insights from economic and psychological literature, we present a model of market exchange where agents have heterogeneous preferences about means of payment and, following routinized rules in their purchasing behaviour, they conclude transactions mainly with agents with the same payment preferences. By assuming that consumers who have preferences for means of payment differentiated on the basis of the transaction value are the majority, simulations results show that the share of cash transactions (in value) and the total number of transactions carried out with cash strongly depends both on the consumption structure and preferences.

Results are compared with data for the euro area by Esselink and Hernández (2017). Regressions performed on countries’ data confirm the main relationships highlighted in the simulation results. Furthermore, when looking at each country’s figures, the simulation results sufficiently estimate the number of cash transactions, given their value. This occurs for almost all EU countries where no cash payment limitation is imposed by law. Where consumers’ behaviour is constrained by imposed limitations, the model underestimates the share of the number of cash transactions. This implies that, given consumption and preferences structures, legal restrictions on the use of cash increase the number of cash transaction.

The comparison with results by Arango-Arango and colleagues (2018) further confirms this implication. Their results well explain cash payment shares by transaction value for Canada, France and Germany, but not for the Netherlands, and their argument for the irrelevance of the “Cash First” policy in this latter case is based on policies to promote card usage that were introduced in the Netherland in the 2000s. By contrast, our results sufficiently explain the Dutch and the German cases, but our results fail in estimating the cash transaction number in France. It is worth to note that the main difference between the two studies is in assuming the homogeneity/heterogeneity of preferences. Consequently, by assuming that consumers have different preferences, we can explain the Dutch case by showing that Dutch people do have different preferences, as the data demonstrate. It can be argued that marketing policies implemented in the Netherlands have been effective in changing Dutch preferences. On the opposite, simulations data cannot well fit the case of France, because of cash payment limitations imposed by law. Without cash limitations, it is likely that consumption and preference structures would result in a lower share of cash transaction number. Comparing the Dutch and the French cases, one can conclude that a better policy in modifying payment behaviours should be to convince consumers to adopt non-cash means of payments instead of to force them not to use cash.

In light of the longstanding debate on the use of cash, these results show that if preferences matter in the choice of means of payment, any policy programme concerning the use of cash should be carefully evaluated. Further research is needed to disentangle how preferences and the consumption structure influence not only the transactional use of cash but also its precautionary use, since while the transactional use of cash declined, the value of notes in circulation steadily increased (Caswell et al. 2020). Furthermore, different socio-economic characteristics have been shown as relevant for cash usage and a better understanding on this topic is needed.