General-equilibrium models for studying the zero lower bound on the nominal interest rate contain implicit theories of unemployment. In some cases, the theory is explicit. When the nominal rate is above the level that clears the current market for output, the excess supply shows up as diminished output, lower employment, and higher unemployment. Quite separately, the Diamond-Mortensen-Pissarides model is a widely accepted and well-developed account of turnover, wage determination, and unemployment. The standard DMP model is a clashing theory of unemployment, in the sense that its determinants of unemployment do not include any variables that signal an excess supply of current output. Altering the DMP model by allowing the rate of inflation to influence unemployment, as several authors have proposed, resolves the clash. I derive the condition needed to achieve the resolution when the zero lower bound is binding and thus to explain high unemployment in recent years. The condition implies that stale nominal values have a strong effect on the wages of new hires. It appears to be satisfied by existing models and is supported by the small decline in inflation that has occurred in the U.S. between 2007 and 2009.
With the short-term nominal interest rate near its minimum feasible value of zero in the U.S. and some other advanced economies for
the past few years, macroeconomics has renewed and advanced the study of the implications of the zero lower bound for economic activity in general and unemployment in particular. According to the
models, when the interest rate is held above its market-clearing level, the supply of current output exceeds demand. Actual current output falls short of its market-clearing level and
unemployment is above its normal level. The models provide a widely accepted account of the low levels of output and high levels of unemployment in recent years.
At the same time, the Diamond-Mortensen-Pissarides (DMP) model of unemployment is widely accepted as the most realistic account of unemployment based on a careful and full statement of the underlying economic principles governing labor turnover and wage determination. The DMP model prescribes the unemployment rate as a function of a limited set of variables. As originally developed, the DMP model does not connect excess supply in the product market with high unemployment.
The Basic Issue
In this section, I demonstrate the clash of unemployment theories using the simplest reduced forms. Technology is a proportional relation between output y and employment n:
y = An (1)
u = 1 - n/n = 1 - y/An (2)
The reduced form of the DMP model of unemployment maps productivity A into the unemployment rate u:
u = U(A) (3)
In principle, the interest rate also enters U, but nothing of importance is lost by neglecting that dependence.
Product demand is a strictly decreasing function of the real interest rate r:
y = D(r) (4)
u = 1 - D(r)/An (5)
The equilibrium real interest rate r satisfies
U(A) = 1 - D(r")/An (6)
At the zero lower bound, the real rate is minus the inflation rate: r = - i. If i > r", the zero lower bound binds - the real rate exceeds its equilibrium value. The lower is inflation, the more likely the bound is to bind. When the bound does bind, the unemployment rate on the left side of equation (6), derived from the DMP model, diers from the unemployment rate on the right side, derived from the product market. The clash arises.
Robert E. Hall
Hoover Institution and Department of Economics,
National Bureau of Economic Research
Diamond-Mortensen-Pissarides (Nobel prize 2010)