All Bitcoin transactions are anonymous and can't be traced, Unless you decide to reveal your identity. But i'm not so sure what your Government capable of maybe they can't if you're not careful enough.
I believe bitcoin transactions remained to be anonymous up to the present but with the appearance of some exchangers today who already require KYC,then the government might have high chances today of tracing those people who owned btc.You just need to be very careful in choosing of your exchanger so you won't be identify.