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Spanish unemployment is characterized by three distinct regimes of low, medium, and high unemployment and by a fast transition between them. This paper presents a simple nonlinear dynamic model that is able to explain this behavior with multiple equilibria and jumps describing the transition between equilibria. The model has only a small number of parameters capturing the fundamentals of labor markets and macroeconomic and institutional factors. The model is capable of generating unemployment dynamics that encompass the “unique” natural rate hypothesis, the structuralist hypothesis, and the hysteresis hypothesis.

Spain's unemployment performance has been the focus of much theoretical and empirical literature. (On Spanish unemployment see, among others,
Bentolila and Blanchard [

This paper puts forward a simple nonlinear dynamic model that is able to generate these regime changes and their rapid transition with a small number of parameters capturing the main factors of Spanish unemployment, including labor market fundamentals and macroeconomic and institutional factors that may have acted upon it. In the model, changes in the institutional characteristics of the labor market or macroeconomic conditions can potentially lead to large unemployment equilibrium jumps. The model is also able to encompass the three main unemployment dynamics theories in the literature, namely, the natural rate hypothesis, the structuralist hypothesis, and unemployment hysteresis.

After briefly characterizing the Spanish unemployment in Section

As mentioned earlier, the evolution of
Spanish unemployment has been characterized by three main phases (see Figure

Spanish unemployment 1965:1-2007:2.

These rapid changes in unemployment
rates have coincided with important events and reforms taking place in the
Spanish economy in the last 30 years. (For an overview of labor market reforms in Spain
see Ferreiro and Serrano [

Against this background, the rapid and
significant unemployment changes can be characterized as a multiple equilibria
pattern. To illustrate this point, we can use a Markov switching in mean (MSM) model
as put forward by Hamilton [

This is a simple
representation of a multiple equilibria process for unemployment (see León-Ledesma and
McAdam [

Estimation of the model using the EM
algorithm yields three clear states of high, medium, and low unemployment. The
results in Table

Markov-switching model for Spain’s unemployment.

Regime means | |||
---|---|---|---|

Mean | St. error | ||

Regime 1 | 2.216 | 0.316 | |

Regime 2 | 10.77 | 0.407 | |

Regime 3 | 19.52 | 0.294 | |

Transition probabilities | |||

Regime 1 | Regime 2 | Regime 3 | |

Regime 1 | 0.9815 | 0.01853 | 1.27E-28 |

Regime 2 | 3.09E-12 | 0.978 | 0.022 |

Regime 3 | 2.61E-15 | 0.0142 | 0.9858 |

Regime duration | |||

% Observ. | Duration | ||

Regime 1 | 53 | 53.96 | |

Regime 2 | 46.5 | 45.45 | |

Regime 3 | 70.5 | 70.42 | |

Regime dating | |||

Regime 1 | 1965:1–1978:1 | ||

Regime 2 | 1978:2–1981:4 | ||

1999:4–2007:2 | |||

Regime 3 | 1982:1–1999:3 | ||

AIC | |||

6.92 | |||

5.57 | |||

4.65 |

Unemployment and regime probabilities for Spain.

The reported changes in equilibrium unemployment appear to coincide with some of the major labor market and tax reforms previously identified. They also coincide with major changes in economic performance, although these events may not be independent as some of the reforms took place after policy makers realized the need for reform and achieved sufficient political consensus. Hence, the Spanish unemployment can be characterized by multiple equilibria, where regime changes coincide with major economic and institutional changes in the Spanish economy. For this reason, a model of the Spanish unemployment dynamics has to be able to yield multiple equilibria as a consequence of internal and external changes in the labor market, and rapid transition between states.

The model describes the time evolution of Spanish unemployment,

The external forces are external interventions aimed at reducing
unemployment, affecting labor market equilibrium besides labor market
fundamentals. Among these external forces are macroeconomic policies and
institutional changes related to fiscal and monetary policies and goods markets.
These forces are represented by the function

Unemployment evolves according to

It is clear that in the steady state we have that

However, this standard model is not a priori equipped to deal with
multiple equilibria or to explain the transitions from one equilibrium
unemployment to another. If Spanish unemployment is characterized by several
distinct regimes, it has multiple equilibria. Moreover, the change from one
regime to another appears to have been very fast. As a consequence, a
reasonable model of Spanish unemployment has to generate at least two steady
state equilibria and be able to explain the factors that led to a fast
transition between them. The model in (

Starting with function

In the same vein, let us assume that function

Substituting

This model has multiple equilibria, the equilibrium values of
unemployment

In order to make the analysis of the model simpler, we scale the equation
by making

The points where the left and right-hand sides of (

From low to high unemployment equilibrium.

Figure

An example of the workings of the
model is the following. The economy is initially at point

The reverse is also
true, the model is able to generate a jump from high unemployment to low
unemployment, and this case is depicted in Figure

From high to low unemployment equilibrium.

The model can be
generalised to represent more complex internal forces, such as a logistic
growth (which implies multiplying the function

These simple nonlinear
dynamics can also encompass the case of three equilibria, one of them is an unstable
equilibrium. Figure

Unstable equilibrium.

The empirical literature
on unemployment dynamics has distinguished between three competing views,
namely, the “unique” natural rate Friedman-Phelps hypothesis, the structuralist
hypothesis represented by Phelps [

Our empirical results show that over the 1965–2007 time horizon,
the Spanish unemployment jumped from regime 1 to regime 2 to regime 3, and then
back to regime 2 (as in Figure

Evidence and theory appear to be at odds since the latter allows for either a single high stable equilibrium unemployment, or for a single low stable equilibrium unemployment, or for two stable (one high and one low) equilibria and one intermediate unstable equilibrium. In other words there are three regimens and at most two stable equilibria (we thank one of the referees and an associate editor for this observation). Here we try to reconcile the existence of three regimes for Spanish unemployment with our theoretical arguments.

In order to tackle this issue consider Figure

Three stable equilibria.

The reconciliation between our empirical results and the model runs along
the following lines. The economy is initially at low unemployment equilibrium,
L. There is an exogenous change in the parameter

The Spanish unemployment over the last 40 years is characterized by three regimes of low, medium, and high unemployment and by a fast transition between them. This paper puts forward a simple nonlinear dynamic model that is able to generate multiple unemployment equilibria and rapid transition from low to high unemployment. Additionally, the model is able to represent, with a small number of parameters, the main determinants of unemployment as represented by the fundamentals of labor market and macroeconomic and institutional factors. The model is capable of generating unemployment dynamics that encompass the “unique” natural rate hypothesis, the structuralist hypothesis, and the hysteresis hypothesis.

The authors would like to thank, without implicating, three anonymous referees and one associate editor for comments.