and the fact that each Markov state is equally likely we can use these equations to derive
■=2+-L- f Pi
μw N ι + Φl
Pl
г ιι
Pi + P2
Pi
where μx denotes the mean of x. The usual approach is to calibrate with actual data the terms
reflecting the slope of the yield curve ^2^/1 , ^2^twl and the terms μz and μp1 and then derive the
relative portfolio share φ. As noted by Buera and Nicolini (2004) and Faraglia, Marcet and Scott
(2007) the limited volatility in the slope of observed term structures requires the government to
set φ ≈ — 1 and N large and so the optimal portfolio is to issue a large amount of long term debt
and hold a large negative short position in order to magnify the limited shifts in the yield curve to
match , m'`-. The magnitude of these positions are large - frequently requiring very large multiples
MP1 m
of GDP to be held as assets or issued as debt. However, amongst our sample of OECD economies bɪ
and &2 are both positive (and on average φ ≈ 0.4). Issuing positive amounts of short and long term
debt can only be the optimal issuance policy if the term structure displays fluctuations an order
of magnitude greater than that observed. Given the limited volatility in observed term structures
even substantial differences in bɪ and b% around these positive values will make little contribution
towards achieving the complete market outcome of m'∙m . It is for this reason that despite the fact
lj,pγ m
countries differ in both their debt structure and the level of fiscal insurance achieved we are unable
to find a reliable relationship between the two. The flatness of the yield curve and its limited
volatility mean that the narrow range of different debt issuance that is witnessed across the OECD
countries is not sufficient to deliver substantial differences in fiscal insurance.
This in turn raises a further substantive research issue - why do governments tend to avoid the
“extreme” portfolios that a normative optimal taxation analysis proposes? Instead, as shown in
Missale (1999) and Faraglia, Marcet and Scott (2007) governments tend to issue positive amounts of
debt at most maturities and the maturity structure of debt changes smoothly as maturity changes.
This suggests once more either the presence of non-tax smoothing motives by governments or
the existence of numerous other constraints that affect the issuance of debt and that need to be
accounted for. A better understanding of these factors would help shed light on why governments
pursue other objectives than fiscal insurance. If small variations in debt structure affect fiscal
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