It seems that Mitt Romney and his team are revving up for another big battle over the stimulus. They want to tell the story that the economy would be off to the races if only President Obama had not tried to boost growth with his stimulus package of spending increases and tax cuts. In their story all we have to do is cut wasteful government spending.

At this point, we might think the game was over. There has been extensive research on the impact of the stimulus on the economy by independent analysts.  The vast majority of it is consistent with the Obama administration's predictions that the stimulus created between 2-3 million jobs. (Of course we needed 12-13 million, but that is another story.)

For example, the Congressional Budget Office came up with an estimate along these lines in 2010. Using an entirely different methodology, last year two Dartmouth professors found job estimates that were consistent with the 2-3 million jobs number.

But Mitt Romney and his crew apparently want us to believe that we would be better off if the government had just stood back and let the economy continue to sink. Its main support for this claim is a series of studies by Harvard professor Alberto Alesina. These papers purport to show that governments that reduced their budget deficits had more rapid growth. Alesina found that the boost to growth from deficit reduction was strongest when the deficit reduction was accomplished by reducing spending rather than raising taxes. Alesina’s takeaway is that cutting government spending is the quickest route to recovery.

There are two important problems with Alesina’s work. First, he did not distinguish clearly between deficit reduction that was the result of economic growth and deficit reduction that was the result of deliberate policy. Second, he did not distinguish between deficit reduction that was carried through when an economy was operating near its potential and deficit reduction that took place when an economy was badly depressed, as is the case with the U.S. economy at present.

The problem raised with the first issue is that deficits tend to get smaller when an economy is growing rapidly. The reason the U.S. economy had a large surplus in 2000 was that the economy, and especially the stock market, grew much faster than had been expected. In 1996, the Congressional Budget Office had projected a deficit of 2.5 percent of GDP for the 2000 fiscal year (roughly $380 billion in today’s economy), instead we had a surplus of 2.5 percent of GDP.

Alesina’s measure would show this as a case of deficit reduction being associated with rapid growth, but the causation ran entirely in the opposite direction. The legislated changes to the budget over this four-year period actually would have increased the deficit slightly.   

To get around this problem, the IMF constructed a series of 173 instances of legislated budget changes over the period 1978 to 2009 in 17 OECD countries. They then examined whether these legislated deficit reductions were expansionary or contractionary. They distinguished between deficit reduction in recessions and during expansions. They also compared the relative effectiveness of deficit reductions accomplished through spending cuts and tax increases.

The IMF found what many of us expected. Deficit reductions that were done in the middle of downturns were in fact contractionary. Deficit reductions that were done near the peak of the business cycle did lead to stronger growth. They did find that spending cuts were more effective in boosting growth than tax increases, but this was entirely the result of central bank policy. The implication of this finding is that if central banks responded the same way to tax increases and spending cuts, then both would be equally effective in boosting growth.

To better understand the logic behind this story, we visit our old friend Mr. Arithmetic. This is a case where simple arithmetic is very helpful.

Demand in the economy is driven by its four components, consumption, investment, government expenditures, and net exports. If we don’t get an increase in one or more of these components, then we cannot have growth. To show the simple equation that everyone remembers from their intro to economics:

Y = C+I+G+(X-M)

Where Y is national income and the other letters correspond to the components of demand.

Now suppose that we have deficit reduction. If we raise taxes then the immediate effect is on consumption. Higher taxes mean people have less money in their pockets, which means that they will consume less. Higher taxes can also have a negative effect on investment, but most research finds this effect to be small (for example, see this paper by Glenn Hubbard, the second President Bush’s chief economist).

Cutting government spending will also lower demand. This will occur through two channels. First the government directly spends money on items like roads and schools. If it cuts back this spending it will mean less output and fewer jobs. However it also provides people with income through transfers like Social Security benefits. If it cuts back these payments, then families will have less money, and therefore will cut back their consumption.

So there are several clear channels through which a reduction in the deficit will mean a reduction in demand. This means that at the most immediate level, deficit reduction will be contractionary. The question is whether there can be offsetting effects that cause deficit reduction to actually boost the economy.

There is a story that can be told. It goes that when the government reduces the deficit, it allows the central bank to have more expansionary monetary policy without fears of inflation. This means that the central bank lowers interest rates.

Lower interest rates have several effects. They lead to some boost to consumption as more people will buy items like cars and washing machines if they can borrow at lower interest rates. People will also buy more homes if mortgage interest rates drop. Lower interest rates will also provide a boost to investment, although this effect is likely to be small, as Hubbard’s work showed.

Finally, lower interest rates can lead to a lower value for a country’s currency. If the interest rate on Danish or Swiss bonds fell, then investors will be less interested in holding them. This means that they will sell Danish and Swiss currency, driving down the value of these currencies relative to other currencies.

This is very important in the expansionary story because a lower valued currency means that exports are cheaper to people living in other countries and imports are more expensive to people living in Denmark and Switzerland. That means that Denmark and Switzerland will export more goods and import fewer goods, substituting domestically produced goods in their place. In the case of small countries that are heavily dependent on trade, this means a big boost to net exports (X-M), which can be an important factor in boosting growth.

So that’s the story of how deficit reduction can lead to more rapid growth. The central bank responds to the deficit reduction by lowering interest rates, which in turns leads to more consumption and housing purchases, some boost to investment and a jump in net exports following a drop in the value of the currency.

Now let’s see how the story fits the United States economy at present. Suppose the Mitt Romney gang sweeps into office in 2013 and starts off by slashing spending on education, research and development, highway construction and everything else by 50 percent. This directly lowers demand in the economy by cutting G.

How would we expect to offset this reduction in demand? The classic story would be that the Federal Reserve Board would see this big cut in the deficit and respond by having a more expansionary monetary policy. However that would not be very easy right now. The short-term federal funds rate is already at zero. It can’t go any lower. Perhaps the Fed could do another bigger round of quantitative easing, but with long-term interest rates near 2.0 percent, it is hard to see them going much lower.

Furthermore, it is not clear that even if we did have a modest decline in interest rates that the other components of demand would be very responsive. Consumers have cut back their spending in response to the loss of $8 trillion in housing wealth. It is difficult to see them rushing out and going on a spending spree if the interest rate on car loans or credit cards falls by a half percentage point.

It’s also hard to imagine much impact on the housing market. Mortgage interest rates have hovered near 60 year lows for the last three years. It is difficult to imagine that a further drop will provide much boost to the market. And, given the enormous excess supply of housing, no one is going to rush out and build more homes.

Businesses are at least as likely to respond by cutting investment as increasing it. As Hubbard’s research showed, the negative effect on investment from a loss in demand is likely to be much larger than any positive impact from a reduction in interest rates. Furthermore, if the reduction in demand is associated with lower expectations of inflation, then it could mean a rise in the real interest rate (the nominal interest rate minus the expected inflation rate), which would actually reduce investment.

Finally we get to the impact of the decline in interest rates on the value of the dollar. At the moment, many governments are pegging the value of their currency against the dollar. (China is the most important one, but other countries are pursuing the same policy.) They are not buying dollars because of the interest yield; they are buying dollars to preserve their export markets in the United States.

It is very difficult to imagine that they would change this policy because interest rates in the United States fell slightly. The United States will have to negotiate a decline in the value of the dollar with these countries.  This can be done without deficit reduction.

Furthermore, it is worth noting that even with a decline in the dollar the boost to net exports in the United States would not have the same impact as in many of the countries that Alesina examined. His sample included countries like Ireland, where exports and imports are both more than 50 percent of GDP. By contrast, imports are roughly 15 percent of U.S. GDP and exports are close to 11 percent. This makes it much more difficult for trade to provide the same sort of boost to the U.S. economy as it does to the economies of smaller countries.

In short, it is very hard to see the story whereby a cut in spending and/or an increase in taxes is supposed to boost growth in the United States at the moment. It’s great to talk about “job creators” or consumers knowing better how to use their money than the government, but once you get beyond campaign clichés, there is not a coherent story for how deficit reduction will lead to more rapid growth in the middle of a downturn like the one we are currently seeing.

There is an argument that we can sometimes boost growth by cutting government spending through the channels described above. But that is a story that only makes sense when the economy is near full employment and government spending can actually be seen as pulling resources away from the private sector.

That is clearly not the world we are in now. There are huge numbers of unemployed workers and huge amounts of excess capacity in most sectors of the economy. The economy is not supply constrained at the moment; it is constrained by a lack of demand.

Cutting demand further by cutting government spending would only make things worse. At least that is what Mr. Arithmetic says.