Microeconomic models usually have negative feedback. Take a simple demand and supply model. Suppose there is a shock that causes the demand for apples to increase by 100 apples. That creates an excess demand for apples that causes the price to rise, that causes the quantity demanded to fall. If the supply and demand curves have the same elasticity, the equilibrium quantity of apples demanded will rise by only 50. That model has a multiplier of 0.5.
Now take a very simple macroeconomic model. The simple Keynesian Cross model with unemployed resources. That model has positive feedback. Suppose there is a shock that causes the demand for goods to increase by 100. That causes an increase in income and a further increase in the demand for goods. If the marginal propensity to consume is 0.5, the equilibrium quantity of goods demanded will rise by 200. The multiplier in that model is 2.
Negative feedback creates a multiplier of less than one, and positive feedback creates a multiplier of greater than one.
The Old Keynesian ISLM model has both positive and negative feedback processes at work. Inside the IS curve, there's a positive feedback process exactly the same as in the Keynesian Cross model. With mpc=0.5, a shock which increases the demand for goods by 100 shifts the IS curve right by 200. But that's maybe not the end of the story. If the LM curve is horizontal (perhaps because the central bank makes it horizontal by targeting an interest rate) it is the end of the story. We get a multiplier of 2, just like in the Keynesian Cross model. If the LM curve is vertical (perhaps because the central bank makes it vertical by targeting aggregate demand) the rate of interest rises and reduces the demand for goods and the multiplier is 0. Or somewhere in between, if the LM and IS curves are neither horizontal nor vertical.
One result from the ISLM model, that will be useful for later, is that the slope of the IS curve is given by (1-mpc)/i where i is the interest elasticity of demand. If a 1% cut in the interest rate directly increases demand by 2%, which is multiplied by 2 to get a 4% increase in equilibrium demand, the slope of the IS will be -1/4. (Yes, I'm muddling slopes, elasticities, and semi-elasticities here, but it doesn't matter.)
What about the New Keynesian model?
We need to make things as simple as possible so I can explain things clearly. Ignore investment, government spending and taxes, and net exports. Consumption is the only demand for goods.
Old Keynesian models assume that consumption is a function of current income and the real rate of interest. New Keynesian models assume that consumption is a function of permanent income and the real rate of interest. The Euler equation tells us that the planned growth rate of consumption will be a positive function of the difference between the real rate of interest and the rate of time preference. If the real rate of interest is above the rate of time preference, people will want to consume less than their permanent income now, and more than their permanent income in the future, which means that they plan to have consumption growing over time.
Start in equilibrium where the real rate of interest is equal to the rate of time preference, and the representative agent expects his income to stay the same in future, and is planning to consume all his income in all periods.
The marginal propensity to consume out of permanent income is one. If the representative agent expects his income to increase by 100 permanently, with the real rate of interest staying constant, he will increase his planned consumption by 100 permanently.
Does this mpc=1 mean that any permanent positive shock to demand will shift the IS curve an infinite amount to the right? Well, yes and no. Because with mpc=1, the IS curve is horizontal. In other words, if we put permanent income on the horizontal axis of the IS curve, there is only one real interest rate (strictly, only one time-path for the real interest rate) that is compatible with planned demand for goods equalling expected income from the sale of goods. But that one real interest rate is compatible with any level of permanent income. Permanent income is indeterminate in the New Keynesian model, even if the central bank sets the right interest rate.
If you shift a horizontal IS curve right by an infinite amount, it doesn't shift at all. We are not in Kansas any more.
All shocks to expected income can be decomposed into shocks to permanent income and shocks to transitory income. We have considered shocks to permanent income. Now lets consider shocks to transitory income (which means, by definition, shocks to the time-path of income that leave permanent income unchanged).
The representative agent in a New Keynesian model will have an mpc=0 in response to changes in transitory income. If we put transitory income on the horizontal axis, and hold permanent income constant, what will the IS curve look like?
The short answer is that it won't look like anything at all. Because the Euler equation tells us that the rate of change of consumption, not the level of consumption, is a positive function of the real rate of interest.
Holding permanent income constant, we should put the growth rate of transitory income on the horizontal axis of the New Keynesian IS curve, and draw an upward-sloping IS curve. A higher growth rate of income requires a higher real rate of interest for the growth rate of demand to equal the growth rate of income. We very definitely are not in Kansas any more.
Now let's introduce government demand for goods into the model. To keep it simple, assume that the representative agent's utility function is separable in consumption and government spending. This means that, holding private consumption constant, an increase in government spending may (or may not) increase utility, but it won't affect the marginal utility of consumption, and so won't affect the consumption-Euler equation.
We can decompose all changes in government spending into permanent and transitory changes.
A permanent increase in government spending shifts the permanent IS curve an infinite amount to the right. But that doesn't matter, since it's horizontal. So let's hold permanent government spending constant.
The growth rate of transitory income equals the growth rate of transitory consumption plus the growth rate of transitory government spending. So if we put the growth rate of transitory income on the horizontal axis, an increase in the growth rate of transitory government spending will shift that IS curve to the right, with a multiplier of one.
But remember, that IS curve slopes up, not down. This means an increase in the growth rate of government spending will reduce the real rate of interest compatible with keeping the economy growing at potential. Because with output growing at potential, faster growth of government spending means slower growth of consumption, which will only be an equilibrium if the real rate of interest is lower.
Now let's introduce some shocks to the model. For simplicity, let there be shocks to the rate of time preference. Sometimes the rate of time preference is low, so people want to save; and other times the rate of time preference is high, so people want to dissave. A positive shock to the rate of time preference (a decreased preference for saving) would shift the IS curve up, vertically, by the amount of the shock. A negative shock to the rate of time preference (an increased preference for saving) would shift the IS curve down, vertically, by the amount of the shock.
Normally the New Keynesian model says that monetary policy should handle those shocks, by raising or lowering the real interest rate in response to upward and downward shifts in the IS curve, to keep output growing at potential. But suppose we want fiscal policy to handle those shocks (maybe because the central bank is unwilling or unable to change the real interest rate in response to those shocks). How should fiscal policy respond, to keep output growing at potential?
What should the government do, if there is an increased desire to save, and the central bank is unable or unwilling to cut real interest rates enough to offset it? The answer is that the government should cut the growth rate of government spending, to shift the IS curve left, which raises the natural rate of interest (i.e. prevents it falling), because the IS curve slopes up when we have the growth rate of transitory income on the axis.
I'm going to end with a quote from John Cochrane, from his post on a related topic:
"You may disagree with all of this, but that reinforces another important lesson. In macroeconomics, the step of crafting a story from the equations, figuring out what our little quantitative parables mean for policy, and understanding and explaining the mechanisms, is really hard, even when the equations are very simple. And it's important. Nobody trusts black boxes. The Chicago-Minnesota equilibrium school never really got people to understand what was in the black box and trust the answers. The DSGE new Keynesian black box has some very unexpected stories in it, and is very very far from providing justification for old-Keynesian intuition."
I especially like the bits I've bolded. Fiscal policy in Old and New Keynesian models is even more different than John Cochrane thinks it is. And understanding why is hard.