Yet, the UK, which in many ways has a similar size budget deficit and net public sector debt has seen bond yields falling.

David Cameron claims that the fall in bond yields is vindication of the governments resolve in pushing through spending cuts to bring down the deficit.
This is not entirely without merit. By comparison to European competitors, the UK looks very unlikely to default. (though this is not so much due to austerity as the fact the UK has the flexibility of having a Central Bank willing and able to buy bonds in liquidity shortage. See: why UK bonds have not risen).
However, there is another stronger reason why bond yields have fallen in UK (and also US) and remain very low in Japan despite massive public sector borrowing.
Prospects for Low Growth / Low inflation
- When markets expect low growth and low inflation, they tend to move out of stocks and into bonds.
- In a period of deflation, bond yields of even 1% can offer a better return than cash under the bed.
- In a period of sluggish growth and low consumer spending, we see a rise in private sector saving. These higher savings often are used to buy government bonds. This is why in a liquidity trap, in a recession, governments can usually borrow more without causing higher interest rates.
RelatedGovernment Deficit

Highest budget deficits - Ireland, Japan, UK and US
10 Year Bond Yields

The link between size of budget deficit and bond yields is very weak.
Portugal and Spain have very high bond yields despite low borrowing.
US, Japan and UK have very low bond yields - despite highest levels of government borrowing
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