Three analysts at the Federal Reserve Bank of Cleveland asked why reduction in unemployment since 2009 from 9.1 per cent to 8.2 per cent in 2012 is not behaving according to past trends in relation to average growth in the national output since 1985. They analyzed the data econometrically using Okun’s law and data over various time periods.
Their analysis is predicated upon the wrong question. They should instead have examined the relationship between average quarterly unemployment change and average quarterly change in gross domestic product (GDP) over the data time periods they were looking at. There is no puzzle to be pondered over. The solution to the unemployment predicament is in the monetary policy bias of the central bank.
At a Washington, D.C event of the National Economists Club (NEC) which I attended on Thursday, April 12, 2012, the President and Chief Executive Officer (CEO) of of the Federal Reserve Bank of Philadelphia, Charles Plosser, expressed the difficulties the Federal Reserve’s 19-person Federal Open Market Committee (FOMC) was experiencing in communicating monetary policy to the public in light of the Fed’s efforts to become more transparent.
Monetary policy making by the world’s central banks is a technical exercise. It principally relies on five economic theories: (a) Quantity Theory of Money (QTM) since Hobbes (b) Phillips Curve trade-off in the short run (since Friedman and Phelps) between inflation and unemployment (c) Fisher Equation and Fisher Principle (d) Okun’s law relationship between GDP and Unemployment and (e) Taylor Rule relationship between a central bank’s nominal interest rate, inflation and GDP.
The Federal Reserve is no exception. At issue is the application of these theories to economic circumstances for which the relationship between the variables upon which the theories are constructed, with some of the same variables recurring in all four.
A new theory of monetary policy must first be constructed standing on the shoulders of these giants.
In principle, in the long run, typically a period beyond the 5 year horizon from the present, the classical QTM model always holds, invalidating the short-run Phillips Curve trade-off according to Friedman and Phelps, but per my analysis inflation still being always a function of the exogenous, Schumpetarian, economic structure under the presumption that economic theory as it exists has no control over structural change or its rate for the purposes of this analysis.
Despite the constraint of the Fisher Principle that at least a 1 per cent rise in the nominal interest rate for every 1 per cent rise in inflation is to be expected, the optimal nominal interest rate, always in the short run, to balance between unemployment, inflation and GDP is still dependent on the choice of inflation by the central bank for expectations of the real interest rate faced by investors and for the timing of interest rate changes.
“Okun’s law (named after Arthur Melvin Okun) is an empirically observed relationship relating unemployment to losses in a country’s production. The “gap version” states that for every 1% increase in the unemployment rate, a country’s GDP will be at an additional roughly 2% lower than its potential GDP” (Wikipedia).
US unemployment has increased by 4.2 per cent since 2007 and in the same period US GDP has increased by zero per cent. The economy has been stagnant, on net, in the period 2007 to 2012, the medium term.
(1) 1 -Y/Yp = C1(U – Un), C1 being some constant to fit the data that is expected to encapsulate the
exogenous determinants of unemployment U and its natural rate Un (Abel and Bernanke).
(2) At any given time t Abel and Bernanke can be rewritten as follows:
(3) 1 – Y(t)/Yp = C1(Ut – Un)
(4) From (3) above, Y(p) = [1 – Y(t)]/C1(Ut – Un)
Restating the Taylor Rule, assuming, according to the Fischer Equation, that the real equilibrium interest rate is always equal to the difference of i(t) and pi(t), nominal interest rate and inflation at any point in time t, picking C2 and C3 arbitrarily from past empirical data, as John Taylor and the rest of copious literature has done to trace Fed policy over time,
(5) C2[pi(t) – pi*] = C3[LogY(t) – LogYp], these are logarithms to base 10, unstated by convention.
Substituting for Yp written in terms of Y(t) in (2) to arrive at the relationship between inflation, central banks inflation target pi*, and output in terms of measured and known variables only at any time t, assuming the natural rate of unemployment, Un, to be the average very long run unemployment (for example, for the United States it is around 5.5 per cent in the 20th century).
(6) C2[pi(t) – pi*] = C3[LogY(t) – Log[1 – Y(t)/C1(Ut – Un)]] = C3[LogY(t) – Log[1 – Y(t)] – logC1 – log (Ut – Un)]
Rewriting (6) above to make unemployment a function of output and inflation,
(7) C3log (Ut – Un) = C3[LogY(t) – Log[1 – Y(t)] – logC1] – C2[pi(t) – pi*]
Let us assume that the new natural rate of US unemployment since the 1990s, Un, is 4 per cent, a preferred target lower than the very long run average of 5.5.
From (7) we arrive at the linear regression model:
(8) log (Ut – Un) + logC1 = LogY(t) – C2/C3[pi(t) – pi*] – Log[1 – Y(t)]
In theory, to note:
(A) – logC1 must be netted out with the regression intercept for the model LogY(t) – C2/C3[pi(t) – pi*] – Log[1 – Y(t)] to arrive at the model intercept.
(B) When Ut = Un, log (Ut – Un) = negative infinity, communicating the uncertainty of Un because of (C) below.
(C) Log[1 – Y(t)] – because Y(t) is always >= 0 – is white noise epsilon, when [1 – Y(t)] <= 0 given the exogeneity of technical/structural change, again for the purposes of this analysis, which is a determinant of Yp, the potential growth rate.
(D) Endogenization of technical/structural change always carries with it white noise, however, minuscule, to imply that technical/structural change cannot be perfectly timed.
(E) Nominal interest rate does not matter. What matters is modulating money supply to achieve and remain at Un and pi*.
(F) (E) implies that both Un and pi* must be ex ante specified.
The above theoretical result of mine, the archetype for any central bank’s reaction function, is amenable to empirics and fully satisfies precedence (a) through (e) in the literature of monetary theory above and bolsters, depending on economic conditions, the necessity to be sufficiently intrusive in monetary policy to ensure healthy monetary transmission as the current law already permits the Federal Reserve to do. No central bank, including the Fed, is currently engaging in such a practice which explains the current economic conditions.
Central banks must ex ante communicate both their inflation and unemployment targets. Deviation in observed data for Ut and pi(t) from targets must be explain the rationale for policy decisions.