Modeling a Free Banking economy and NGDP: a Wicksellian portfolio approach (guest post by Justin Merrill)

My friend Alex Salter and his coauthor, Andrew Young, have an interesting new paper called “Would a Free Banking System Target NGDP Growth?” that I believe was presented at a symposium on monetary policy and NGDP targeting.

I too have wondered the same question. I believe there are real reasons why a dynamic economy might not have stable NGDP. One reason is demographic changes (maybe target NGDP per capita?). Another reason is problems with GDP accounting in general such as the underground economy, changes in workforce participation of women and the vertical integration of firms. Another micro-founded effect might be the income elasticity of demand and substitution effects. But even abstracting from these problems, it is still a worthy question to ask if monetary equilibrium is synonymous with stable NGDP and its relationship to free banking. If they are synonymous, we might expect stable NGDP from free banking. In my paper on a theoretical digital currency called “Wixle” I outline a currency that automatically adjusts its supply to respond to demand by arbitraging away the liquidity premium over a specified set of securities. This is a way to ensure monetary equilibrium without regard for aggregate spending, which is particularly useful if the currency is internationally used.

A small criticism I have of my free banking and Market Monetarist friends is that they often assert that monetary equilibrium and stable NGDP are the same thing, usually by applying the equation of exchange. As useful as the equation of exchange is, it is tautologically true as an accounting identity. But just as we know from C+I+G=Y, accounting identities’ predictive powers are limited when thinking about component variables. I have argued for the conceptual disaggregation of the money supply and money demand, because the motives for holding currency and deposits are different and the classification of money is more of a spectrum. So I was pleased to see that Salter and Young did this in their paper and added the transaction demand for money into their model. This leads them to conclude that a free banking system will respond to a positive supply shock, which results in an increased transaction demand for money, by stabilizing the price level rather than NGDP. This might be true, and whether this is good or bad is another question. Would this increase in currency lead to a credit fueled boom, or is this a feature and not a bug?

I have long been upset with the way that economists overly focus on reserve ratios and net clearings from a quantity perspective. This abstracts away from the micro-foundations of the banking system and ignores the mechanics of banking. This is the point I made at the Mises Institute when I rebutted Bagus and Howden. My moment of clarity for the theory of free banking actually came from reading the works of James Tobin and Gurley & Shaw, as well as Knut Wicksell. The determination of the money supply is the public’s willingness to hold inside money, and this willingness creates the profit opportunity for the financial sector to intermediate by borrowing short and lending long. I believe the case for free banking can be made more robust by adding the portfolio approach, as well as the transactions approach. I will outline here what that would look like without sketching a formal model.

The Model is a three sector economy: households, corporations and banks. Households hold savings in the form of corporate and bank liabilities and have bank loans as liabilities. Corporations hold real capital, bank notes and deposits as assets and bank loans, stocks and bonds as liabilities. Banks hold reserves, securities and loans as assets and net borrowed reserves, notes, deposits and equity as liabilities.

JM 1

Households can hold their wealth in risky securities or safe, but lower yielding interest paying deposits that pay the risk-free rate in the economy or non-interest paying notes used for transactions. The model could include interest-free checking accounts, but these are economically the same as notes in my model.

Banks can then choose to invest in loans, securities or lending reserves. They fund investments largely by borrowing at the risk-free rate and borrowing reserves at the margin. Logically then, the cost of borrowed reserves will be higher than deposits but lower than that of loans and securities and arbitraging ensures this. If the cost of reserves goes above the return on securities, banks will sell bonds to households and lend reserves to each other. If the cost of reserves goes below the rate on deposits, banks will borrow reserves and deposit with each other. The return on loans and securities (adjusted for risk) will tend towards uniformity because they are close substitutes. Also, as Wicksell pointed out, if loan rates are below the return on securities or the return on real capital, households and firms would borrow from banks and invest.

Empirical evidence for the interest rate channels is provided here. Interestingly, the rules set out above were only violated in times of monetary disequilibrium, such as the Volcker contraction:

JM 2

The natural rate of interest is equal to the return on assets for corporations. Most economists that try to model the natural rate mistakenly do it as the risk free rate or the policy rate. This is a misreading of Wicksell since he identified the “market rate” as the rate which banks charge for loans, and the important thing was the difference between the market rate and the natural rate. If the market rate is too low, people will borrow from banks and invest, increasing the money supply.

We can now apply the framework to the CAPM model and conceptualize the returns on various assets:

JM 3

The slope of the securities market line (SML) is determined by the risk aversion/liquidity preference of the public. Should the public become more risk averse and demand a larger share of their wealth be in the form of money, they will sell securities in favor of deposits. If in aggregate, the household sector is a net seller, the only buyers are banks (ignoring corporate buybacks since this doesn’t change the results since corporations would end up needing to finance the repurchases with bank loans). So the banking sector would purchase the securities (at a bargain price) from households, crediting their accounts and simultaneously increasing the inside money supply. This becomes more lucrative as the yield curve steepens or other kinds of risk premia widen, increasing the net interest margins (NIMs). As the banking sector responds to changes in demand it equilibrates asset prices.

JM 4

This is another way of coming to the same conclusion: that a free banking system would tend to stabilize NGDP in response to endogenous demand shocks. But how about supply shocks? We know that when the spread between the banks’ return on assets and costs of funding widens, the balance sheet will increase. An increase in productivity will raise both the return on new investments and the rate the banks have pay on deposits. We can assume for now these cancel out. But the public will have a higher demand for notes, and since notes pay no interest, they are a very cheap source of funding. This lowers the average cost of funding overall. However, more gross clearings will increase the demand for reserves and their cost of borrowing relative to the yield on other assets. This would put a check on overexpansion and excess maturity transformation. The net effect on the total inside money supply is uncertain, but probably positive assuming the amount of currency held by the public is larger than borrowed reserves by banks.

Another thing to consider about supply shocks: despite the lower funding costs of increased note issuance, an increase in the natural rate of interest will decrease banks’ net interest margins because their loan book will be locked in at the old, lower rate, but the rate on deposits will have to go up. This is a counter-cyclical effect (in both directions) that may outweigh the transaction demand effect. Another possible counter-cyclical effect is the psychological liquidity preference effect that accompanies optimism associated with supply shocks. So in a strong economy individuals will be more willing to hold the market portfolio directly, which flattens the SML. Depending on the strength of these effects, it may lead to different results than Salter and Young.


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