This is a (probably hopeless) attempt to clarify the debate between Brad DeLong and Eugene Fama over whether an increase in government spending, financed by borrowing, will increase aggregate demand. There's something important that's missing from the debate: the rate of interest; and money.
There is a supply of loans and a demand for loans. If government tries to borrow more to increase spending, that increases the demand for loans. That creates an excess demand for loans. The excess demand for loans increases the rate of interest on loans (if the central bank lets it increase). The increased rate of interest reduces the demand for money. The reduced demand for money creates an excess supply of money. People try to lend that excess supply of money. If they lend the excess supply of money, that creates the extra loans for the government to borrow. Or if the central bank does not want the interest rate to rise, it must print and lend extra money. That printing and lending of extra money creates the extra loans for the government to borrow.
Forget inventories; forget accounting identities; remember the rate of interest and money. Remember both the loanable funds and the liquidity preference theories of the rate of interest.
We live in an economy with monetary exchange (not barter). The very concept of "aggregate demand" only makes sense in a monetary economy, because it refers to the monetary demand for goods. To get an increased demand for goods, in terms of money, somewhere along the causal chain you need an excess supply of money. The initial excess demand for loans causes a rise in the rate of interest (loanable funds theory). The rise in the rate of interest causes an excess supply of money (liquidity preference theory). The excess supply of money is either spent, and so creates an increased demand for goods directly; or (more likely), is lent, and so creates an increased supply of loans and investment, and so creates an increased demand for goods indirectly.
Eventually, the increased income created by the increased demand for goods (assuming unemployed resources) will create the extra savings and supply of loanable funds, and the excess supply of money can disappear.
And if the demand (and supply) for money were (both) perfectly interest-inelastic, the increased rate of interest caused by the initial excess demand for loanable funds will not create an excess supply of money, so increased government borrowing would indeed crowd out private borrowing 100%. (I'm not saying it is perfectly interest-inelastic; I'm just using this example to demonstrate that you have to bring the rate of interest and the excess supply of money into the story.)
You need to think like a monetarist to properly understand how Keynesian policies can work.