**The H-Curve**

by Guy Haselmann, Director, Capital Markets Strategy, Scotiabank GBM

• Let’s picture **a graph** where the *x* variable is a central bank’s official interest rate and the *y* variable is the resulting economic benefit.

• Economic benefits of central bank accommodation are non-linear. Non-linear functions have slopes that change. In fact, the ‘economic benefits’ **slope** will differ at every point along the curve. This is somewhat obvious as a slope measures the rate of change and central bankers admit that their effectiveness weakens over time and with each successive ease.

• This point is true, yet incomplete. It suggests that marginally declining utility will eventually cause the slope to drop zero; i.e., at some point further accommodation will simply provide no economic benefit. However, the truth is that central bank stimulus is **a parabolic function**, whereby the slope goes negative at a certain point. The peak point at which the slope begins to change direction is the parabola’s vertex, or the point at which the level of central bank accommodation is optimal.

• Central banks seem to be operating by a different function. Their rhetoric and ideology suggests belief in a perpetually positively sloped line, whose worst case slope is simply one that is less positive over time. In other words, the second derivative or rate of change in the slope is the only thing that falls; that is, until a **zero slope** is reached. In truth, too much accommodation can cause long-run damage and risks to financial stability.

• There are indeed many moving parts that impact and change the vertex level. Different paradigms result in different **optimal vertex levels**. However, the exercise is still worthwhile. After all, how many times in an economics class does a professor utter the words “all else being equal?” Certainly, a regime with tight regulatory and fiscal policies would move the vertex (the optimal level) to a more accommodative stance (lower official interest rates). The point is to find the true interest rate floor (a level that likely not 0%)

• A good analogy for the H-curve might be the **Laffer Curve**. This curve represents the relationship between rates of taxation and the resulting level of government revenue. The curve shows how taxable income changes in response to changes in the rate of taxation (i.e., income inelasticity). It theorizes that no income would be raised at the extreme rates of 0% and 100%.

• At the extremes, the y-axis of the Laffer Curve stops at zero (no revenue). However, on the H-curve, the y-axis outputs can fall well **below zero** (negative economic benefits) with the *wrong* amount of central bank stimulus.

• Moreover, the H-curve will be more time-varying and act different during policy reversals (exit strategies).

• I’ve argued for many years that central bank interest rates set below a certain level were **counter-productive**. Savers, pension funds, and insurance companies are certainly punished. It seems that zero and negative interest rates cause damage to consumer sentiment and elsewhere. (See March 4 note: “Toppling Scales of Balance”)

• Interest rates below a certain level hurt **lending**, because low margins disincentivize lenders who might feel margins do not adequately compensate them for the risks. In a fractional reserve banking system, bank lending is oil for the economic engine. Velocity of money has collapsed for a reason, probably other than regulation.