Accounting is not the same as Economics

This is probably self-evident, but violations of this seem to be sprouting up all over the place, often from respectable sources.  Brad DeLong does a much better job on savaging these people that I could do, so if you want red meat, head there. 

But here is the issue. Several economists have been arguing against the stimulus bill.  Now, there are valid reasons to be skeptical about government stimulus (as I pointed out a couple of days ago, the timing of the stimulus matters as much as the size).  But some people are proposing that stimulus will have zero effect on the economy because it will "crowd out" private investment and consumption.  This is a dumb reason to be skeptical about the stimulus plan.

What I just recently got through teaching my intermediate students was the national income accounting identity:
Y = C + I + G + NX
This is an accounting identity.  It says that GDP (Y) can be subdivided into four different buckets.  Consumption (C), Investment (I), Government Spending (G), and Net Exports (NX).   GDP is the value of all the transactions that take place in the economy.  Each of those transactions can be classified as either consumption (like buying a new jacket), investment (like buying a house), government spending (like buying a M1126 Stryker personnel carrier), or net exports (which can be negative, and would be if you bought a Sony 37" 1080p HD television but didn't sell anything to Japan in return).

There is nothing about the above identity that says GDP (Y) is fixed, constant, or unchanging. If there are more transactions in the economy, the GDP goes up, and by definition the sum total of C, G, I, and NX must go up as well. 

The government stimulus bill involves the government spending a lot money.  That is, it will buy more M1126 Stryker personnel carriers.  Thus there are more transactions in the economy, and - by itself - GDP will go up and so will G.  The identity will hold. 

Now, in addition to this initial increase in GDP from the new transactions, we can think of two follow up effects:
a) the increased spending on M1126 Stryker personnel carriers means that the manufacturer hires more workers and buys more machine tools.  These are new transactions in the economy, and GDP will go up even more.  The new workers will buy jackets and houses and Sony 1080p HD TV's.  The machine tool manufacturer will hire more workers and buy more paper clips.  More transactions, higher GDP.  And so on and so forth. 
b) the increased spending on M1126 Stryker personnel carriers is made possible by the government borrowing money.  This increased demand for funds from the financial sector drives up the interest rate (remember that interest rates are the price of borrowing).  The increase in interest rates means that fewer people like you or businesses like your employer will be willing to take out loans to buy things like cars, houses, and machine tools.  So we lose some transactions, and GDP would go down.

If a) dominates, then on net the government stimulus spending will raise GDP.
If b) dominates, then on net the government stimulus spending will lower GDP.
If a) and b) roughly offest, then GDP will be about the same.

The question of whether a) or b) dominates is open. One can have a legitimate argument about how businesses and people will respond to the stimulus, and whether the effect on interest rates will be big or small.

What you cannot do is say this:  "If G goes up, I has to go down by an equal amount to satisfy the accounting identity, and there is no change in GDP (Y)."  Why are you not allowed to say this?  Because the identity has nothing to do with how many transactions there are in the economy.  It is an ACCOUNTING identity.  If you buy an extra $5.12 soy mocha double-shot chai venti latte tomorrow, then tomorrow both sides of that identity get updated.  GDP goes up by $5.12, and consumption (C) goes up by $5.12.  Why? Because it is an ACCOUNTING identity.  Double entry, baby.  Debits must equal credits, so to speak. 

Making the above statement is the same thing as saying: "I conclude that the stimulus package will not raise GDP because I have assumed GDP will not change."  That is dumb.