Descripción del software

The above calibration shows that our model with the cash-flow channel is able to capture the cash paradox with plausible quantitative results. To highlight the value-added of the cash-flow

22_{For the United States, the NCF model generates a lower NRMSE than the full model. We do another exercise} with the NCF model to check whether lowering its NRMSE to the level implied by the full model can help it to generate more reasonable predictions about the relative size of the cash-credit sector and the value of the cash share. The exercise suggests that for a comparable NRMSE, the NCF’s predictions about the relative size of the two sectors and the cash share are still unreasonable. The impliedq∗is 0.06, and the implied average cash share is 0.95 from 2005 to 2014.

channel, we discuss existing explanations about the cash paradox and carry out additional calibration exercises with a modified version of the NCF and full models described above.

Existing explanations about the cash paradox tend to be indicative and qualitative in nature (to the best of our knowledge, we are the first to quantitatively capture the cash paradox with a formal model). According to these qualitative arguments, the robust demand for cash is driven by the increasing demand in the underground economy or as a store of value by either domestic or foreign agents, which is less sensitive to competition from alternative means of payment. The main supporting evidence is the increasing fraction of large-denomination notes in CIC, with the logic that large-denomination notes are more likely to be used as a store of value or in underground economies.

We believe that this is an important first step to explain the cash paradox. The cash- only sector in our model captures these demand categories as economic activities where it is difficult for credit to replace cash (and our model predicts that cash is increasingly used for activities in that sector). The next and more challenging step is to identify the forces that can plausibly counteract the fall in cash demand driven by competition from other means of payment.

The increased demand in less credit-sensitive activities can result from (1) structural changes, which cause the money demand curve to shift, or (2) decreasing nominal interest rates, repre- sented by movement along the money demand curve.

We think it is unlikely that the structural changes could (fully) account for the cash para- dox. In general , there is no evidence that the underground economy has experienced sig- nificant growth. According to Schneider and Buehn (2012), from 1999 to 2010, the shadow economy as a percentage of GDP shrunk slightly in 39 OECD countries. Among the four countries for which we carry out the calibration exercise, the size decreased from 14.4% to 13.8% in Australia, from 16.3% to 15.4% in Canada, from 12.8% to 12.5% in the United

Another potential source of structural changes in the less credit-sensitive sector is in- creased perceived uncertainty and distrust in the financial system, which induces agents to hold cash for precautionary motives or as a store of value (see, for example, Williams, 2012; Berentsen and Schar, 2018). Note that in many countries the cash paradox phenomenon was observed long before the financial crisis, with the CIC/GDP starting to level off or increase since the 1980s or 1990s (see Figure 1 in Section 2). The financial crisis raised aggregate uncertainty and distrust in the financial system and spurred the particularly strong demand for cash afterward. Because of that, the cash-paradox phenomenon has drawn more attention after the crisis. However, we think that increased uncertainty and distrust in the financial system

are unlikely to be the main force behind the robust cash demand before the financial crisis.23

Foreign demand could be an important factor for major international reserve currencies, such as the US dollar or euro. It is, however, less applicable to other currencies. Given the ubiquity of the cash paradox, country-specific factors, such as a strong foreign demand, are

unlikely to fully account for the phenomenon.24

The critical question is then whether the fall in the interest rate can plausibly generate a robust demand for cash as a store of value or in the underground economy to sufficiently counteract the shrinking (transactional) demand for cash due to competition from credit usage. The answer to this question ultimately requires serious quantitative analysis, which is missing in existing papers on the cash paradox. In the following, we carry out such an analysis using a modified version of the NCF and full models outlined above. The demand for cash in the cash-only sector in these models can be interpreted as demand for a store of value or underground transactions, in the sense that these demand categories are much less sensitive

23_{A recent study by Bech et al. (2018) finds that the effect of aggregate uncertainty on cash demand is} statistically insignificant.

24_{Foreign demand is very unlikely to drive the robust demand for non-reserve currencies, such as the na-} tional currencies in Iceland, Denmark, New Zealand, and Finland, where the cash-paradox phenomenon is also observed.

to credit expansions than the demand for cash in the cash-credit sector.25 _{To account for the} possibility that the retail statistics, methods-of-payment surveys, and the official GDP figure may not capture cash usage as a store of wealth or in underground activities, we modify the

original NCF and full model by removing the cash-only transactions (y) in the expressions for

θand GDP (while the demand in the cash-only sector is still reflected in CIC). We label these

models NCF-UA and Full-UA, respectively, with “UA” standing for “unregistered activities.” Table 5 in Appendix F compares the results with and without the cash-flow channel based on this alternative interpretation of the cash-only sector. Both the NCF model and the full model capture the substantial fall in cash shares and the robust demand of cash. The (“offi- cial”) cash share number implied by the NCF-UA model improves a lot in comparison to the

original NCF model, where the cash-only transactions are also counted inθand GDP. Similar

to the original NCF model, the NCF-UA model also implies an extremely small cash-credit

sector (q∗ <10−4_{) for Australia and the United States.}

In other words, no matter whether the cash-only transactions are registered or not and irrespective of the interpretation of the cash-only sector, one must suppress the cash-credit sector to almost nil to boost the effect of the interest rate relative to credit expansions on cash demand. The extreme parameterization implied by the NCF model is very difficult to reconcile with data. For example, according to Schneider and Buehn (2012), from 1999 to 2010, the average size of the underground economy relative to GDP was 13.8% in Australia and 8.7% in the United States. In the same time period, the average size of the retail sector as a share of GDP was 4.15% in Australia, and 5.26% in the United States. The implied ratio of the size of the retail sector to the underground economy was therefore 30% in Australia and 60% in the United States. For foreign demand, Judson (2017) suggests that about 70% of US dollars are held abroad. A rough upper-bound estimate of the demand for cash as a store of

25_{In the current setup, the two sectors open simultaneously. It is straightforward to add a time dimension so} that the cash carried to the cash-only sector resembles more a store-of-value demand.

value is the share of large-denomination notes in CIC, which is 90% in Australia and 80-85%

in the United States.26 The bottom line is that, although the demand for cash as a store of

value and for the underground economy is significant, it is difficult to justify that cash used for these purposes is 10,000 times higher than cash used for day-to-day transactions. In a recent study, Wakefield and Finlay (2018) experiment with various methods to estimate different components of Australian cash demand, and conclude that 15–35% of circulating Australian banknotes are used to facilitate legitimate transactions (which correspond to the transactions in the cash-credit sector). According to the NCF model, the value of cash together with credit transactions in the cash-credit sector is almost zero relative to the value of cash transactions in the cash-only sector.

These calibration exercises help to formalize the existing indicative explanations about the cash paradox. The calibration results suggest that, in the absence of additional channels such as the cash-flow channel that we emphasize, existing explanations about the cash paradox are quantitatively implausible. Without the cash-flow channel, one can only account for the trend in cash demand under extreme assumptions about the relative size of the cash-credit sector. The existence of the cash-flow channel helps to explain the cash paradox with much more reasonable model parameterization. As shown in Tables 1 and 5, the model with the cash-flow channel does not rely on a large cash-only sector relative to the cash-credit sector to capture the cash paradox. In the next section, we also provide some empirical support for our model’s prediction on cash velocity.

Finally, before we move to the next Section, we would like to point out that the cash-flow channel is a natural feature of the real economy shared by all countries. The European Central Bank (2011) that analyzes the use of cash among small and medium enterprises in seven euro- area countries (Austria, Belgium, France, Germany, Italy, Netherlands, and Spain) based on

26_{In the United Kingdom, the share of large-denomination notes is 85%, if 20 British pounds are counted as} large-denomination notes (the share decreases to 20% if only 50 British pounds are counted as large denomina- tion). The combined $50 and $100 notes account for 69% of CIC in Canada.

a survey conducted in 2009. The results show that 57% of the companies surveyed use cash for their expenditure, and 11% pay more than 20% of their expenses with cash. For certain sectors, cash usage is heavy. For example, about 60% of hotels and restaurants (and about 40% retail and wholesale trade companies) pay more than 20% of their expenses in cash. Given the ubiquity of the cash paradox phenomenon, a ubiquitous channel such as the cash-flow channel is likely to be critical.

6

Empirical Support

One key, unique implication of our full model is that, in recent decades, the cash demand of type B agents, who receive cash from the cash-credit sector to spend in the cash-only sec- tor, has been increasing (type B agents are absent in models without the cash-flow channel). Ideally, we would categorize economic agents into different types based on their cash manage- ment practices (type A directly spend their cash while type B use cash receipts from customers to spend) and track their cash holdings over time. However, given that cash is difficult to track or locate, high-quality data on cash holdings are scarce. Micro-level data on the balance sheet of individual firms, for example, CompuStat, lump checkable deposits and currency together, so there is no separate information about cash (currency) holdings. Central banks have con- ducted methods-of-payment surveys among consumers every few years since the early 2000s, but the survey questions do not include information about occupations. Further, not enough

merchant surveys exist to infer the time trend of merchants’ cash holdings.27

To provide empirical support for the cash-flow channel, we examine another important, unique implication of the full model: cash velocity, defined as the total value of cash trans- actions in the retail sector over CIC, decreases over recent years (cash velocity is constant in

27_{For example, the Bank of Canada has conducted two merchant surveys: one in 2006 and one in 2015. The} 2006 survey did not ask about cash holdings. The 2015 survey started to collect the information, but we cannot

models without the cash-flow channel). We proxy the value of cash transactions with ATM withdrawals: higher ATM withdrawals imply more intensive cash activities. For Australia, the data are acquired from the website of the Reserve Bank of Australia. For the other three coun- tries, Canada, the United Kingdom and the United States, the data are acquired from “The Red Book: Statistics on Payment, Clearing and Settlement Systems in the CPMI countries,” pub- lished by the Committee on Payments and Market Infrastructures at the Bank of International Settlements. Figure 11 plots the ratio of the value of ATM withdrawals over CIC. Consistent with our model prediction, the ATM withdrawals/CIC have been declining since the late 1990s or early 2000s (the increase in ATM withdrawals in the 1990s was mainly driven by the adop- tion/diffusion of ATMs). The Federal Reserve Board publishes the receipts of currency from circulation, which is also a measure of cash activity and can be used a proxy for the value of cash transactions. Figure 12 plots the time series of receipts of currency from circulation/CIC,

which exhibits a clear downward trend starting from 2000.28

7

Conclusion

We build a parsimonious model of two competing means of payment, cash and credit, to capture the long-term time trend in cash usage and demand. In many countries, cash usage has been falling owing to intense competition from other means of payment such as credit cards; at the same time, although the total demand for cash , measured by CIC over GDP, had been decreasing until the 1980s or 1990s, it has remained robust afterward. This phenomenon of simultaneously declining cash usage and flat or rising cash demand is difficult to reconcile

28_{Another prediction of the full model (which is shared by the NCF model) is that increasingly cash is held} to support transactions in the cash-only sector, or for activities where cash is less substitutable by credit. It is reasonable to think that the transactions in the cash-credit sector are more likely to involve small denominations (for example, the purchase of lunches and drinks) as shown in various consumer payment surveys (see Bagnall et al., 2016), while the transactions in the cash-only sector are more likely to involve large denominations (as a store of value, or to pay suppliers). The increase in large-denomination notes in circulation in many countries (see Davies et al., 2016, Judson, 2017, and Fujiki, 2018) is consistent with our model, too.

year 1990 1995 2000 2005 2010 2015 ATM Withdrawal/CIC 2 2.5 3 3.5 4 Australia year 1985 1990 1995 2000 2005 2010 ATM Withdrawal/CIC 1 1.5 2 2.5 3 Canada year 1990 1995 2000 2005 2010 2015 ATM Withdrawal/CIC 2.5 3 3.5 4 UK year 1990 1995 2000 2005 2010 2015 ATM Withdrawal/CIC 0.6 0.8 1 1.2 1.4 1.6 1.8 US

Figure 11: The Value of ATM withdrawals over CIC

year 1995 2000 2005 2010 2015 2020 Cash Receipts/CIC 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

with standard monetary models, and is therefore termed the “cash paradox.”

To explain the cash paradox, we introduce two new features to standard monetary models: the first is different substitutability between cash and credit for different economic activities, and the second is the cash flow across the different activities (as some agents use cash receipts in less-cash-intensive sectors to finance spending in more-cash-intensive sectors). The model implies that once the expansion of credit usage exceeds a certain level, these agents prepare more cash in advance to offset falling cash receipts from their customers who use credit more. The increase in cash demand by these agents counteracts the reduction in cash demand by their customers, so that the total demand for cash remains flat despite diminishing cash transactions. At the same time, the redistribution of cash demand induces the velocity of cash to fall because cash acquired by these agents has a lower velocity than cash acquired by their customers.

This decoupling between cash usage and cash demand in response to credit expansions allows our model to effectively capture the cash paradox. In particular, expanding credit and the decreasing nominal interest rate can generate decreasing cash usage and increasing cash demand. We calibrate our model to the case of four countries: Australia, Canada, the United Kingdom, and the United States. The calibration exercise suggests that the cash-flow channel is critical in capturing the cash paradox. In the absence of it, one must resort to extreme assumptions about the size of the cash-credit sector relative to the cash-only sector (the latter is more than 10,000 larger than the former) to account for the robust demand for cash in response to competition from alternative means of payment. In contrast, the model with the cash-flow channel can capture the cash paradox with much more reasonable model parameterization. We also find empirical support for our model’s prediction on cash velocity in the retail sector.