Despite the fact that interest rates determine all asset valuations, there is nothing close to a general theory of interest rate determination. The rule of thumb when I started working in financial markets was that real interest rates should equal real GDP growth rates, and people mumbled about Solow models. Fed Governors opined in public that the equilibrium real fed funds rate was 2%. If you queried them in private they looked puzzled, as if everyone just knew this was the case. Later, time-varying empirical models became the vogue – but what determines the mean around which they vary cyclically?

So much of this was nonsense. A cursory glance at the cross-sectional distribution of global real rates revealed that there was no simple link between growth and real policy rates. Some of the economies with low real growth rates had high real interest rates, like South Africa. Economies with high real growth rates had very low real interest rates, like Taiwan. Christopher Bliss in a superb summary of the literature, written in 1999, confirmed my prejudices. He concludes that none of the long run models have practical relevance!

Most of the empirical work on r* – the equilibium real interest rate – seemed to be based on national (usually US) time series. The conclusions were completely undermined by cross-sectional global data, which most economists writing on the subject simply ignored. As a practitioner, and a global investor, I gradually came to the conclusion that demographic factors (notably youth dependency), GDP per capita, and changing risk properties were the most important variables in determining the centre of gravity for policy rates and government bond yields. An aside in Krugman’s classic paper on Japan, a relatively obscure paragraph in Keynes’s General Theory (more below), and a very old paper by Paul Samuelson linking interest rates to birth rates sent me down this path. My own thinking on asset pricing led me to the conclusion that viewed through the lens of risk properties, a developed government bond in the 1970s was a different asset to a government bond in the 2000s, so most of the conventional thinking on the subject was wide of the mark, and remains so. These factors explained the distribution of real interest rate structures across countries far better than anything else, and much of the developments within countries over the last twenty to thirty years.

This all makes intuitive sense. The basic theory, putting the financial system to one side, is that interest rates are compensation for deferring consumption (the early formalisations off this can be found in Bohm-Bawerk, and Fisher). In very poor countries with high birth rates, saving is an unaffordable luxury – real interest rates have to be high to induce savings. In high GDP per capita countries with low birth rates (and increasing longevity and healthcare costs) desired savings preferences will be strong.

I started with these semi-intuitions and then went in search of unifying theories. The first problem, which is a recurring one in economics, was identifying the real-world counterpart to the ‘r’ in the models. Economists, often effortlessly, assume r is the policy rate, or the 10-year government bond yield, or the return on capital – but the theories don’t. The Solow model, which I had studied, assumes the return on capital is the ‘interest rate’. It is a great model for thinking about the effects of changes in population growth and savings propensities to the determination of r. But it says nothing really about levels. It also raises a far bigger problem than it solves. What is r in the Solow model? Or more importantly, what is r more generally? Is it the cost of equity, a proxy for which is the earnings yield, or is it the policy rate set by central banks, or the cost of debt to the private sector? Or is it some weighted average of all of these?

I had also studied Keynes. Ironically, Keynes was the most perceptive on demographics. In *The General Theory* he talks about demographic change lengthening the cycle. His *Notes on the Trade Cycle* taught me more about Japan then anything else I’d read (and this remains the case). A high capital labour ratio and a falling birth rate is disastrous after a decade or more of over-investment in the physical capital stock. Depreciation rates are critical to understanding the consequences of investment booms. But most of Keynes’s discussion of interest rates in *The General Theory* is not about the fundamental structural determinants, but about how interest rates, specifically money market rates and bond yields, are actually set in markets. This separation of a fundamental interest rate set by structural features of an economy, and the interest rates we observe in financial markets, set by central banks and market participants, lies at the heart of most economic thinking about interest rates. It can be mapped on to Wicksell’s theory, which is so popular today. Wicksell’s classic, literally translated as “Money interest and commodity prices”, is the first work to map out the argument that if the money of interest (that set by the central bank in the money markets) is above or below the ‘natural rate of interest’ (the fundamental, ‘equilibrium’, interest rate) inflation will either fall or rise. This provides the basis for most contemporary monetary policy-making, exhaustively outlined in Michael Woodford’s turgid ‘classic’, “Interest and Prices”. But sleight of hand disguises a key problem. As typically practised, r* is almost defined by tautology: it is the level of r consistent with inflation stability, or the level or r that brings the policy rate in line with the natural rate. We know what the immediate policy rate is, it is easily identifiable, but what is Wicksell’s natural rate, independently defined? Is it the return on capital? Is it Solow’s r? Is it a weighted average of all parts of the cost of capital, across all maturities? Does it change with the policy rate? Is there one policy rate with which it is consistent, or a range? Why is the policy rate restricted to the money market rate? Can the yield curve be the target of policy, can credit spreads, can the cost of equity? What about non-price based forms of monetary policy? Woodford wants to believe everything is about overnight interest rates and ‘expectations’ of policy rates. Of course he does – if they are less relevant, so is his entire framework. (See Stan Fisher’s excellent summary of Woodford’s influence, the historical context of his work, and its limitations.)

I have since spent many hours pursuing theories of interest rate determination, and all of them can, I think, be placed within this framework (as this fantastic twitter review of interest rate theories by Jo Michel reveals). There are theories related to the structure of the economy which set some centre of gravity for r* – whatever that is – and there are theories about how money market rates rates are in fact set. It remains striking how much focus is placed on thinking about the ‘equilibrium’ policy rate, and how little thinking is done on the ‘equilibrium’ cost of capital to the private sector, including the cost of equity (Krugman (1998) is an important exception – he draws attention to Japan’s widening equity risk premium negating the effects of policy rates). Also, there must be a relationship between the two.

My synthesis of most interest rate theories has continued. I think the fundamental factors listed above do explain most of the global cross sectional data in money market rates. But I think there is also path dependence associated with leverage and changing risk properties: if interest rates fall, and leverage rises – perhaps overreacts for cyclical reasons – the centre of gravity may fall. And I think other ‘interest rates’ – the cost of equity, credit spreads, and term premia, often matter more than policy rates. The Eurocrisis did not propagated via policy rates, nor did the consequences of Bernanke’s ‘taper tantrum’. Relative to these phenomena, changes in policy rates since 2009 have been trivial. I also argue that in the current developed world non-policy rate based monetary policy has far more power than money market rates and their expectations.

So far, so conventional. There are still two major gaps in most thinking on this subject. The first – finally – brings me to the title of this blog: the range of irrelevance. I can see fundamental reasons why Brazilian real policy rates have spent most of the past twenty years around 2 or 3 times higher than US real policy rates – this ‘proves’ that central banks cannot simply set rates wherever they want. But I also believe that there may well be a range of as much as 2-3% where it does not really matter where US (and perhaps Brazilian) interest rates sit. That is a big range, and renders most of the Fed’s policy changes irrelevant. Hence the range of irrelevance. I also believe that when real rates get extremely low, further changes may become irrelevant to the real economy, but important to the financial economy. If correct, both of these views provide strong macro-prudential reasons for official policy rates sitting substantially higher than where they are today.

It is important to be clear about this point. I am not saying that the ‘natural’ rate may lie somewhere between say a fed funds rate of 2% and 4%, I am saying what the Fed does between 1% and 4% is likely irrelevant, and reductions below 1% are likely ineffective – at close to zero, helicopter drops dominate. This fundamentally changes how one thinks about policy. For reasons of financial stability, the Fed should sit with rates between 3% and 4%, most of time. If there is a genuine inflation problem, it raises rates significantly. But perhaps most importantly, if there is a recession, it needs a bazooka, and in a world of effective price stability, money market rates and expectations of future money market rates, will not always be enough. The Fed, more than any other major central bank, should be thinking about this.

Finally, there should be far more focus on r beyond policy rates. What determines the cost of equity? The finance literature says it is cyclical, the naive theory says it should be implausibly low. But this has been given insufficient thought, and relegated to an obscure debate in finance theory. Roger Farmer has, perhaps uniquely, put equity prices centre-stage in his thinking – and to this extent I am in full agreement with him. But many questions are unanswered: the global earnings yield is not low in the context of history (in other words, the equity risk premium is very high) – does this imply that Solow’s r is high? Does a high ERP negate the effect of a low policy rate? If the ERP falls, does the ‘equilibrium’ policy rate rise? Is the earnings yield determined by volatility, by recession probabilities, by memories of the last trauma, by behavioural forces? Is investment being constrained by the high cost of equity or encouraged by sectoral euphoria?

And what about bond prices and the yield curve? Does QE matter more to the term premium than the covariance with risk assets?

I conclude where I started. The concept of r is poorly understood, and its determination is strikingly vague. Within the range of irrelevance, which is wide, policy makers matter little. And there are states of the world where official interest rates are irrelevant. As for r more broadly – the yield curve, the cost of equity, the term premium and credit spreads – that is where the real firepower may lie, and the factors which determine it are very broad indeed, and rarely articulated.

How about this for a “general theory of interest rate determination”: r* or the “equilibrium rate of interest” is simple the rate that prevails when there is no artificial interference with interest rates by the state (i.e. government or central banks).

Unfortunately government borrowing has a big influence on interest rates, which begs the question as to what constitutes “zero government interference with interest rates”. One possibility (advocated by Milton Friedman and Warren Mosler) is that governments should borrow nothing. Another is the popular idea that governments should borrow enough to fund infrastructure. Unfortunately for the latter argument, education is one huge investment, thus if the latter infrastructure argument is valid, then the entire education budget should be funded via borrowing: an obvious nonsense. For that and other reasons I therefor go along with the Friedman/Mosler zero borrowing idea.

I wish total demand for long bonds could be determined in the new normal. How many trillions of dollars of bionds are in demand for collateral? Trump tax plan is passed and yields of long bonds decline! Bonds ard being gobbled up and the bond market ignores growth policies and demand for low yielding long bonds go up. Without the new normal as an explanation, it makes no sense. We know the big banks have bet on low interest rates. And low rates rule.

Most convincing treatment of interest rates remains Hugh Townshend, Economic Journal 1937,

“Liquidity Premium and the Theory of Value”

If real rates are only partially related to risk, how do you explain the relatively modest returns (and potentially zero returns of late) of the FX carry trade?

I suspect the answer is moves in FX. But then it would seem somewhat pointless to study rates in isolation as all assets are denominated in a currency. If you can’t capture the gains from a higher rate, does that rate actually exist? The true impact of rates may lie elsewhere.

I think the returns to carry strategies are relatively well established, but I am not sure of the relevance. I don’t think we really know *why* FX carry strategies work, albeit with very bumpy return profiles. The standard view is that it is compensation for *risk*. But this view is not the well defined. The existence of carry may itself determine some of the volatility and correlation properties of currencies – so the causality actually works in the other direction – i.e. carry creates *risk*. Not sure …