You have the right idea, but the wrong direction. In theory, interest rate on government debt should be slightly below dividend payments of equity (stocks of p

You have the right idea, but the wrong direction. In theory, interest rate on government debt should be slightly below dividend payments of equity (stocks of private companies). That's because the dividends are more risky, so investors demand a higher yield. If interest rates on government debt go up, then people should, in theory, sell some of their stocks and buy government bonds. Think of it this way, if there is (in your words) "a clear choice between equities [and] bonds", then people will sell whichever one is less desirable and buy whichever one is more desirable. This will make the less desirable asset cheaper and the more desirable asset more expensive, and this process will continue until you reach a market equilibrium where investors as a whole are indifferent between stocks and bonds.