Suchergebnisse

This post was motivated by a conversation with Eric Lonergan. It began with a simple question: what should be the interest rate paid on reserves? I answered that according to theories I'm familiar with, reserves should earn the "natural" rate of interest, which I defined as the sum of population and productivity growth. So, assuming 2% "real" growth and 2% inflation, reserves (and government debt more generally) should be yielding around 4%. I think it's fair to say most people did not find my answer very satisfying. So I thought I'd take a moment to explain how I arrived at it. I want to do so in the context of a model economy. Let me describe the model first. We can discuss its limitations and possible extensions later on. Consider an economy where people live for two periods; they are "young" and then become "old." Let N(t) denote the population of young at date t. Assume that the population grows at (gross) rate n; that is, N(t) = nN(t-1). In this "overlapping generations" model, the population at date t is given by N(t)+N(t-1). Individuals in this economy generate y units of perishable output (goods and services) when they are young. I'm going to treat y as fixed over time. This implies that the RGDP at date t is given by N(t)y and that the RGDP grows at rate n over time (there is no productivity growth). In what follows, I label n the "natural" rate of interest. Suppose that people only value consumption when they are old. This poses an interesting economic problem. The young can produce goods that the old value, but the old have no way of paying for these goods. Private credit markets don't work here. The cooperative solution is very simple: the young should "gift" their goods y to the old. If everyone followed this cooperative protocol, then the young of generation t would consume (in their old age) c(t+1) = N(t+1)y/N(t) = ny. That is, by following this protocol, it's as if the young "deposit" their income y in a savings account that generates a (gross) real yield equal to n, the "natural" rate of interest. Since private competitive markets cannot be expected to implement this socially-desirable outcome, what other mechanisms might be employed? In small communities, reciprocal gift exchange seems to work quite well. In the present context, the young look after their parents, expecting their children to return the favor, and so on. Larger communities need to rely on other mechanisms. In the present context, a PAYGO social security system that taxes the young y and pays the old ny would do the trick. The same outcome could be achieved through monetary exchange. Suppose the government lets all individuals open a central bank money account. The government creates (out of thin air) M dollars and credit the accounts of the "initial old" with M/N(0) dollars. Assume that M is kept constant over time. The old are expected to spend these dollars on a competitive spot market, where goods exchange for dollars at price p(t). The equilibrium price-level is easy to derive in this example. At any date t, we have N(t-1) old people collectively holding M dollars. These M dollars will be spent (the old have no reason not to) on the goods available for sale, N(t)y. The market-clearing condition here is M = p(t)N(t)y at every date t. Because both M and y are constant, and because population N(t) is growing at rate n, it follows that the equilibrium price-level p(t) must be falling at rate n. So, if we interpret M as "reserves" in this model economy, then reserves yielding the natural rate of interest would be consistent with economic efficiency. If reserves yield zero nominal interest rate, then efficiency requires some deflation. But the same outcome is possible if reserves were to yield a nominal interest rate n in a zero-inflation rate regime. This result continues to hold for more general preferences. Suppose that people care about consumption when young and old. Then the young will only want to consume a fraction of their income. That fraction will depend on (among other things) the real rate of return they expect on their retirement savings. As it turns out, the so-called "Golden Rule" allocation requires that money/bonds yield the natural rate of interest. Is this a good place to start thinking about Eric's question? It may be a good place to start, but we don't want to stop here. The analytical framework above is "bare bones." Among other things, my analysis implicitly assumes that there is no difference between reserves and government treasury securities. Does this matter? If it does, the reasons need to be spelled out. What modifications to the simple model above would imply that to meet a given social objective, it is desirable to have reserves yield less than treasury securities? In reality there is duration risk. But why does the Treasury issue bonds with different maturities in the first place? Moreover, why are these bonds purposefully rendered illiquid (for example, by discouraging the Fed from monetizing the entire bond issue or, at least, from setting up standing purchase facilities?). The answers to these questions are not immediately obvious to me. But they may be to you! 

We analyze the properties of the natural rate of interest in an economy where nominal debt contracts generate a spread between loan rates and the policy interest rate. In our model, monetary policy has real effects in the flexible-price equilibrium, because it affects the credit spread. Relying on a definition suitable for this environment, we demonstrate that: (i) the natural rate is independent of monetary policy and (ii) it delivers price stability, if used as the intercept of a monetary policy rule. The second result holds exactly if real balances are remunerated at a constant spread below policy interest rates, approximately otherwise. We also highlight, however, that the natural rate is not robust to model un-certainty. The natural rate reacts differently to aggregate shocks - not only quantitatively but also qualitatively - depending on the underlying model assumptions (e.g. whether or not financial markets are frictionless).

The Taylor rule suggests that the federal funds rate should be adjusted when inflation deviates from the Fed's inflation target or when output deviates from the Fed's estimate of potential output. Typical formulations of the rule assume that the level of the inflation-adjusted federal funds rate that is expected to prevail in the long run, sometimes thought of as the "natural" rate of interest, is constant over time. Since this assumption is likely incorrect, we show how the Taylor rule can account for a variable natural rate by incorporating long-term productivity growth. We also show that better monetary policy outcomes may be achieved if the Fed regularly adjusts the funds rate in response to perceived changes in productivity growth, even if these changes are often measured with error.

AbstractWe measure the natural rate of interest of Hong Kong in a flexible VAR model. We find that the natural rate of interest of Hong Kong fell below zero after the SARS shock in 2003 and reached the lowest after the great recession in 2007–2009. Variance decomposition shows that mainland China, instead of the USA, has a larger impact on the natural rate of interest of Hong Kong.