log θt = pθ log θt-ι + εf
for εf, εt i∙i∙d., mean zero and mutually independent. We assume ε^ ^ N(0, 0.0072), εf ^ N(0,1.442),
g* = 25, with an upper bound g equal to 35% and a lower bound g = 15% of average GDP. We
consider two sets of cases. In our first model both shocks are i.i.d e.g. p9 = p = 0 but we also
consider the case of highly persistent shocks when p5 = p0 = 0.95. We solve the models using
the Parameterized Expectations Algorithm described in den Haan and Marcet (1990). We solve
each model 1000 times and simulate for 200 observations but discard the first 150 observations and
compute our statistics on the remaining data.
One possible and simple way of testing for debt stability is to estimate an AR(1) process for
debt of the form :
.Ui) = a + bMEt*.1 + εt.
This autoregressive representation for debt can be thought of as consistent with a fiscal rule
with a target level a/(1 — b). If b ≥ 1 then debt is unstable and has no well defined average and will
show explosive dynamics (if b>1). In the case of b = 0 then debt shows no autoregressive behaviour
and aside from temporary shocks εt is stable with a value a.
Figures 1a-c shows the Monte Carlo distribution of estimates of b obtained by OLS regression
on simulated data of 40 periods (similar to the length of sample with our OECD data). For all three
models (without capital and i.i.d shocks, no capital and persistent shocks, capital and persistent
shocks) we find that incomplete markets leads to substantially higher estimates of persistence in
debt e.g higher b. For instance, in the case of no capital and persistent shocks we have for complete
markets E(bOLS) = 0.814 whereas under incomplete markets E(bOLS) = 0.988. For i.i.d shocks the
difference is even more stark - -0.008 for complete markets and 0.826 for incomplete markets. These
results clearly illustrate that under incomplete markets, regardless of the persistence of shocks, it is
optimal for debt to show large and substantial persistent fluctuations. When shocks are persistent
then even under complete markets it is optimal for debt to show persistent fluctuations - maintaining
a constant value of debt is not a feature of optimal policy under complete markets. However,
while debt fluctuations are part of optimal policy it is also clear that under complete markets these
fluctuations tend to be stable whereas under incomplete markets there is often evidence of apparent
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