Murphy provides a simple model to illustrate how any model that predicts a stimulus to have a multiplier effect depends on certain parameters, and how differing estimates of those parameters drastically change the outcome of whether one is for or against a stimulus. This can be shown as follows:
The parameters are alpha- which measures inefficiency of government (if –ve it implies government is more efficient relative to private sector). Chicago economists typically see alpha as positive, which means that it reduces the nominal measure of government spending. This alpha is effectively a measure of how useful the government purchases and tax cuts are in terms of causing second round and multiple effects of increasing income, and whether a ‘bridge to nowhere’ will actually lead to improved outcomes for society- by raising welfare, rather than just providing an increased measure of GDP. Krugman for example believes the social marginal benefit of increased government purchases exceeds the marginal cost when the economy is below full employment (with the additional constraint of the 0 lower bound preventing a monetary equilibrium from achieving full employment). However conservatives argue that the social benefit is at times unjustified in light of the fact that
i) There are a limited number of ‘shovel ready’ infrastructure projects
ii) There are time lags involved with bidding and organising projects
iii) Some re-allocation of resources is involved in terms of absorbing resources from the private sector.
iv) There is an implicit trade-off between the notion of stimulating the weak parts of the economy- such as Detroit, and the fact that money would be better spent in booming parts of the economy- in which there is inherently higher demand for infrastructure projects.
v) Suppose the projects are aimed at revitalising defunct sectors, such as construction (due to the stock overhang and the severe reduction in demand for housing). It is debateable whether trying to improve the construction industry will pay off in terms of adding to a current excess stock. Re-allocation of workers should occur in a way in which it can be productive for the economy.
vi) In trying to solve v), we could try to re-train construction workers to commit themselves to different activities, for example. Whether this is practical is debateable as trying to reallocate labour is hard to coerce.
These, and many other reasons from the conservative to argue for alpha being positive, and certainly this must be taken into account in terms of assessing the efficacy of the stimulus package.
D is deadweight loss- that is incurred due to the distortions that arise with debt-financed taxes that will be dealt with in the long-term. This goes under the assumption that net present value of taxes are tied to government purchases, implying that taxes need to be raised at some point. Furthermore, Murphy makes the point that the Obama stimulus package seems to consist of tax rebates and transfers in the short-run followed by increases in the marginal rates in the long run. The distortionary effects of taxes, such as the substitution effect, measured by the difference in work effort from a reduction in the marginal income tax rate compared to a tax rebate, show clearly that there are distortions/ deadweight losses incurred from raising marginal tax rates.
F is the fraction of ‘idle resources’ in the economy. Typically, when at full employment, F is 0. However, in these circumstances, with investment below par due to the credit crunch, severely affecting both private sector consumption and investment, with GDP below trend by about 4% and projected at 8% for the end of 2009, F is most likely in close correlation with the business cycle. As mentioned by Murphy, F is also an indicator of the multiplier. If F>1, then the government spending not only uses idle resources, but the rise in income enables the use of more idle resources than intended in the direct effect of increased G. Note that, with accommodative monetary policy (as noted by the fact that any increases in Government financing typically uses the excess loanable funds created by excess supply of money at the above equilibrium interest rate), this means that the crowding out effect is minimal and the level of savings allocated to private sector will change only slightly, if any.
Lamda is the value of idle resources. This is an interesting parameter, as typically one would think that lamda is 0, that any idle resources are of no value. But we know that unwanted inventory accumulation will be written down in value- but it still has value. People not working still value time and are intrinsically worth something…so perhaps there is reason to believe lamda can be positive. Suppose the value of lamda is too high. Would it be more or less encouraging to pro-fiscal stimulus? Interestingly it would mean that the cost of using idle resources increase, and what lamda does is accept the fact that the use of resources, whether private or idle- does incur a cost which must be dealt with in the cost-benefit analysis. And so here it is:
Notice that the first term is the benefit, which is weighed against the 3 costs, the cost of using private resources, the cost of using idle resources, and the deadweight cost. Notice that to put numerical estimates we make G=1, as that way f can be an estimate of the multiplier. Notice that G=1 is required as suppose c is value of private sector resources, then technically the above equation should have (1-f)*c. However, given that we assume the value of private sector resources is equal to value of government spending (with alpha=0), the c is implicitly 1. Thus, we can simplify the inequality to
Now for the fiscal stimulus to have net benefits then it would have to satisfy the above inequality. Now Murphy gives 3 estimates. Let us take team Obama.
Team obama believe that f=1.5, that lamda is 0, alpha is 0 or possibly negative, and d at a conservative estimate of 0.8 (Using Murphy’s neutral estimate from Feldstein’s analysis). The inequality naturally holds as 1.5>0.8. Take Fama’s case. He believes in a complete crowding out effect, and so holds that f=0, and that government spending can only occur in as far as any deadweight loss of future taxes is offset by a relative efficiency of government spending over private sector spending- compensating for future taxes. This may well be the analysis behind government spending during an economic boom. A middle-ground analysis, with conservative estimates of f=0.5, lamda=0.5, means that with d=0.8, government spending needs to be atleast 55% more efficient than private sector spending (ie alpha needs to be less or equal to –0.55). Thus one can see why so many Chicago economists scoff at this Keynesian stimulus package!
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