Resultados del entrenamiento

”The parameters are grouped into two sets: the first set includes parameters that can be calibrated using steady state targets, some of which are common in the real business cycle literature; and the second one includes parameters that cannot be calibrated using steady state targets. Time periods are measured in quarters.”

1.5.1.1 Parameters set with Steady State targets

”In the case of the parameters set with steady state target, I set β = 0.9825, implying that the annual steady state return from holding shares is 7.32 percent, according toJermann and Quadrini(2012) estimations. The utility function has the functional form U(c, n) = ln(c) +α.ln(1−n), where α = 1.8834 is chosen to have steady state hours equal to 0.3. The Cobb-Douglas parameter in the production function is set to θ = 0.36 and the depreciation to δ = 0.025. The mean value of z is normalized to 1. These values are standard and the quantitative properties of the model are not very sensitive to this first group of parameters.

The tax wedge is set to τ = 0.35, which corresponds to the benefit of debt over equity if the marginal tax rate is 35 percent. This parameter is very important for the model because it determines whether the enforcement constraint is binding

or not. In fact, this value of τ and the all the remaining parameterizations of the model are set in order to make the enforcement constraint always binding in the simulations (except when we set τ = 0 in order to simulate the model without the interest rate benefit).

The mean value of the financial variable, ¯ξ, is chosen to have a steady state ratio of debt over quarterly GDP equal to 3.36. this is the average ratio over the first quarter of 1984 until the second quarter of 2010 for the nonfinancial business sector based on data from the Flow of Funds (for debt) and National Income and Product Accounts (for business GDP). The required value is ¯ξ= 0.1634.”

1.5.1.2 Parameters that cannot be set with Steady State targets

”The parameters that cannot be set with steady state targets are those deter- mining the stochastic properties of the shocks and the cost of equity payout - the parameterκ. In a steady state the stochastic properties of the shocks do not matter and the equity payout is always equal to the long-term target, therefore an alter- native procedure was followed to construct the series of productivity and financial shocks.

For the productivity variable zt it was used the standard Solow residuals ap-

proach. Using the production function we get

ˆ

zt = ˆyt−θkˆt−(1−θ)ˆnt (1.54)

where ˆzt, ˆyt, ˆktand ˆntare the percentage or log-deviations from the deterministic

trend. Using the calibration for θ and the empirical series for ˆyt, ˆkt and ˆnt, we

construct the ˆzt series.

To construct the series for the financial variable ξt, we follow a similar approach

but using the enforcement constraint under the assumption that it is always binding, that is:

ξt kt+1−

bt+1

1 +rt !

=yt (1.55)

The variableξt is determined residually using empirical series forkt+1,bt+1/(1 +

rt) andyt. However, the validity of this procedures depends crucially on the validity

of the assumption that the enforcement constraint is always binding.”

Jermann and Quadrini(2012) have verified ex-post, after constructing the series for the shocks and feed them into the model, whether the enforcement constraint in always binding, but without forcing any of the endogenous variables to perfectly match an individual empirical series.

”The data series of capital kt+1 and debt

bt+1

1 +rt

are end-of period balance sheet data from the Flow of funds Accounts, and the empirical series for the product yt

is taken from the national Income and Product Accounts (NIPA). All series are in real terms and the log value is linearly detrended.”

In order to compute the processes for the two shocks, Jermann and Quadrini (2012) have estimated a vector autoregressive system of order one (VAR(1)), after constructing the series for the productivity and financial variables over the first quarter of 1984 until the second quarter of 2010:

ˆ zt+1 ˆ ξt+1 ! =A zˆt ˆ ξt ! + z,t+1 ξ,t+1 ! (1.56)

where z,t+1 and ξ,t+1 are iid with standard deviations σz and σξ, respectively.

From this description of the procedure used to construct the series for the pro- ductivity and the financial shocks, the fact that ”these series do not depend on the number of shocks included in the model becomes more clear. Since no matter how many shocks we include in the model, equations (1.54) and (1.55) will not be af- fected”. Jermann and Quadrini (2012) state that ”the only way an additional shock could affect the ξt series is in the eventuality that it could change the tightness of

the enforcement constraint. With additional shocks, one cannot guarantee that the enforcement constraint will be always binding in the simulated period”. Jermann

and Quadrini (2012) consider it unlikely with the typical shocks considered in the literature. However, they extend the model following theSmets and Wouters(2007) approach, and use a structural estimation with eight shocks (besides the productiv- ity and the financial shocks) to simulate the model and check whether the inclusion of more shocks affects substantially the main results of the model.

The only remaining parameter is the equity cost parameter κ. This is chosen to have a standard deviation of equity payout (normalized by output) generated by the model over the same period of time 1984.I-2010.II equal to the empirical standard deviation.

The full set of parameters are reported in Table 1.2. Table 1.2: Parameterization Description Parameters Discount factor β= 0.9825 Tax advantage τ = 0.3500 Utility parameter α = 1.8834 Production technology θ= 0.3600 Depreciation rate δ= 0.0250 Enforcement parameter ξ¯= 0.1634

Payout cost parameter κ= 0.1460

Standard deviation productivity shock σz = 0.0045

Standard deviation financial shock σξ= 0.0098

Matrix for the shocks process A=

"

0.9457 −0.0091 0.0321 0.9703

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Source: Jermann and Quadrini(2012)