The instability of money demand

Transcription

1 Liverpool Economic Insights 2019/1 The instability of money demand Aleksander Berentsen, Samuel Huber and Alessandro Marchesiani University of Liverpool Management School Subject Group Economics

2 2 LEI 2019/01 The instability of money demand SUMMARY In their recent paper, entitled The Limited Commitment and The Demand for Money, Alessandro Marchesiani together with Aleksander Berentsen (University of Basel and Federal Reserve Bank of St. Louis) and Samuel Huber (University of Basel) investigated the link between limited commitment and money demand. The authors construct a micro-founded model and show that limited commitment can significantly improve the fit between the theoretical money demand function and data. They set up a limited commitment model where an agent s default on his debt is punished through permanent exclusion from the credit market. The authors show that limited commitment significantly improves the fit between the theoretical money demand function and the historical money demand data for the UK, Australia and Canada in the post-1985 period.

3 3 LEI 2019/01 The instability of money demand INTRODUCTION Understanding money demand is important for monetary policy. The instability of money demand has made this a challenge. A common explanation for this instability is that financial regulation and financial innovation have changed the money demand function over time. In the paper, we provide a complementary view showing that a model with limited commitment can significantly improve the fit between the theoretical money demand functions and data. Limited commitment also explains why the ratio of credit to M1 is soo low, even though nominal interest rates are at their lowest levels on record. however, this relationship is unstable and cannot be replicated by the standard model. For example, consider the empirical money demand curve for the UK shown in Figure 1. We used Lucas (2000) methodology to fit the curve and found that both specifications, loglog and semi-log specifications, failed to explain the flat part of the money demand curve at low interest rates (2%-4%) and high interest rates (6%-12%). It also ignores the sharp drop in money demand when the opportunity cost of holding money rises from 4% to 6%. 1 Figure 1: UK Money Demand We set up a limited commitment model under the assumptions that the punishment for agents who do not repay the loans is permanent exclusion from the credit market. In order to understand how limited commitment can affect the money demand in other countries except the UK, we also calibrate our model to Australia, Canada, and the United States. Australia and Canada support our claim that limited commitments can play an important role in explaining money demand behavior in the post-1980s period. For the United States, we have found that limited commitment does not improve the fit as opposed to full commitment. To better understand this difference, we presented an alternative punishment scheme, called Autarky. Numerically, we find that the model can produce the same distribution as that of an economy where agents can fully commit to repay their debts, under this alternative punishment scheme. We show that, compared with models of full commitment, limited commitment can significantly improve the fit between the theoretical money demand and the data for several developed economies. We derive the demand for money in a micro founded monetary model and calibrate it under two competing assumptions: Either agents can commit to repay their loans (full commitment) or they cannot (limited commitment). Limited commitment affects the shape of the money demand curve because it creates an endogenous borrowing constraint that depends on monetary policy in an interesting way. INSTABILITY MONEY DEMAND Monetary theory states that there is a stable negative relationship between money demand and nominal interest rate. For many countries, 1 We measure money demand as the ratio of M1 to the nominal gross domestic product. For the opportunity cost of holding money, we use the UK 10-year government bond rate. We use this rate in order to have a comparable data set for our cross-country analysis.

4 4 LEI 2019/01 The instability of money demand Our limited commitment model assumes that the punishment is permanent exclusion from borrowing and saving again for an agent who does not repay his loan. Thus, a borrower faces a classic trade-off: the short-term utility gain from not repaying his debt versus the discounted sum of utility losses from not being able to access financial markets in the future. Financial intermediaries understand this trade-off and are only willing to extend credit to an endogenous upper-bound. This bound is the maximum amount of loan that a borrower can voluntarily pay back. Our model shows a positive correlation between nominal interest rates and credit activity. At first glance, this positive relationship is counterintuitive, as one might think that people are willing to borrow more when interest rates are lower, and vice versa. However, this intuition ignores the fact that credit constraints are more binding when interest rates are low, so agent receive less credit than they wish to obtain. For the UK, we observed a positive correlation between the credit-to-m1 ratio and the nominal interest rate of 0.93 for the private non-financial sector, compared with our model estimates of The positive correlation suggests that limited commitment matters for the UK. Models with full commitment have a hard time to replicate such a strong positive holding a debt which yields so low a rate of interest. Keynes (1936, p. 187). Our theory is consistent with Keynes's (1936) quote that agents do not want to hold debt in a low interest rate environment. Limited commitment provides the rationale: in a low interest rate environment, savers do not want to lend money because borrowers have a high incentive to default. It is also consistent with the fact that while currently nominal interest rates are at their lowest levels on record, credit activity is very low too. RESULTS The calibration and simulation results of our model with full commitment and limited commitment are shown in table 1. The results show that the sum of squared difference between the theoretical money demand curve and the data is the smallest under the condition of limited commitment. For the limited commitment case, the resulting welfare cost of inflation is around 12%, which is of similar magnitude to the values obtained under the other specifications. 2 For example, the welfare costs of inflation is much higher in the UK than in the US. The reason is that money demand in UK is about 10 times higher than in the US. correlation between nominal interest rates and credit activity. Thus, limited commitments can explain the "liquidity trap", as defined by Keynes: There is a possibility that after the rate of interest has fallen to a certain level, liquiditypreference may become virtually absolute in the sense that almost everyone prefers cash to 2 For both the full commitment and limited commitment models, we calculate the welfare cost of inflation as the percentage of total consumption that agents would be willing to give up in order to be in a steady state with a nominal interest rate of 3% instead of 13%. For the log-log and the semi-log specification, we follow Lucas (2000) and calculate the welfare cost of inflation as the area underneath the money demand function for interest rates between 3% and 13%.

5 5 LEI 2019/01 The instability of money demand Under limited commitment, the calibrated probability of money market access is ρ=0.625, and ρ=0 (no financial intermediation) is obtained under the full commitment. This is clearly in contrast to the facts that the UK s financial sector is highly developed, so we have neglected the full commitment model for UK. A further observation that supports our finding that limited commitment is important in the UK is that the correlation between the credit to M1 ratio and the nominal interest rates is 0.93 in the private non-financial sector. Our commitment model is very close to this estimate, producing a value of 0.89, and we get a value of 0 with full commitment since ρ =0. Australia As for the UK, limited commitment is best suitable for Australia. The welfare cost of inflation under limited commitment is lower, 1.9%, than the other two methods which lead to estimates between 2.6% and 3.7%. As for the UK, the calibration under full commitment yields ρ=0.27, which clearly indicates that the full commitment model does not fit the data well, since Australia s financial system is developed well. Canada For Canada, limited commitment improves the fit as well, and we find that our limited commitment model replicates the Canadian money demand data well, if we assume a real interest rate of r < This "negative" result does not indicate that limited commitments are unimportant to the United States. It only means our model cannot identify it properly. One reason could be that, for the United States, we don't have a good capture of the legal system in term of punishment scheme. Another reason is that financial regulation and financial innovation also affect the money demand function, which are probably more important than the limited commitment friction to explain the US money demand. CONCLUSION Using the "New Monetarist" approach, we built a model with a money market where agents can borrow and deposit money. First, we show how limited commitments affect the link between money demand and nominal interest rates. Then we calibrate the model and show that limited commitment significantly improves the fit between the theoretical money demand function and historical money demand data for the UK, Australia, and Canada, in the post-1985 period. Our model also shows a positive correlation between nominal interest rate and credit activity, a finding that is consistent with the data for the three countries mentioned above. Standard models of full commitment have a difficult time to replicate this fact. United States For the United States, limited commitment does not improve the fit between the theoretical money demand curve and its empirical counterpart. In addition, we get a positive probability of money market access under full commitment which is ρ=0.375, and the result of limited commitment is ρ=0.

6 6 LEI 2019/01 The instability of money demand UNIVERSITY OF LIVERPOOL MANAGEMENT SCHOOL ECONOMICS CHATHAM STREET LIVERPOOL, UK ALEKSANDER BERENTSEN UNIVERSITY OF BASEL AND FEDERAL RESERVE BANK OF ST. LOUIS SAMUEL HUBER UNIVERSITY OF BASEL ALESSANDRO MARCHESIANI UNIVERSITY OF LIVERPOOL MANAGEMENT SCHOOL; The Liverpool Economic Insights (LEI) aim to support the debate on economic challenges and development of regions by short and accessible non-technical contributions covering the latest research from the Economics subject group at the University of Liverpool Management School. An electronic version of the briefings is available on the LMS Econ-website: