Диссертация (1137741), страница 13

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This partially offsets the increase in output due to a downward shiftof the upward-sloping AD curve. As a result, a higher share of productive expenditure and itsproductivity decrease the magnitude of the multiplier. Roulleau-Pasdeloup (2013) has shownthat in the case of the ZLB the fiscal multiplier is lower than under a positive interest rate(0.55 and 0.57, respectively) and can become negative for a sufficiently high share ofproductive government expenditure. Although the negative effect of productive investmentremains in the framework considered here, the magnitude of the multiplier under the ZLB isstill higher than under a positive interest rate due to the introduction of liquidity-constrainedagents: 3.76 and 0.31, respectively. The results presented above correspond to the results ofEggertsson and Krugman (2012) and Christiano et al. (2011): the value of the fiscal multiplieris higher in the ZLB than in the normal case, despite the introduction of productivegovernment spending.

However, this result depends crucially on the calibration used and theassumption about the share of productive spending. The difference between the resultspresented in the work of Roulleau-Pasdeloup (2013), where a lower multiplier was foundunder ZLB than in "normal" times, can be explained by the introduction of an additionalchannel, by which fiscal policy proceeds through the presence of borrowers. This partiallyoffsets the negative impact of the productive expenditure and facilitates the higher impact ofpublic expenditure on the aggregate demand than on the aggregate supply.2.3.4. Comparison of the two cases: the role of zero lower boundThis subsection compares the effects of model parameters on the value of the multiplierunder ZLB and under a positive interest rate.

The results are summarized in Table 2.3 andTable 2.4.60Table 2.3. Impact of parameters' values on the multiplier under positive interest ratebDsign--/++-+-++b -+++-+++Higher price flexibility (steeper AS curve) assures a greater increase in output underZLB as it allows prices to change more in response to an increase in government expenditureleading to a greater increase in prices and to higher inflation, which is expansionary in thisframework. In the "normal" case with a downward-sloping AD curve, on the contrary, lessprice flexibility (lower  ) is better for the size of the fiscal multiplier as prices change less.Table 2.4. Impact of parameters' values on the multiplier under ZLB 49bDsign+-/+++----b ++++----b = 00000One of the crucial results concerns the share of borrowers  b .

It has a non-linear effecton the multiplier, negatively affecting it when this share is below the threshold level, andaffecting it positively when it is above this threshold. This threshold level strongly depends onthe values of parameters used in the calibration, and its relevance depends on whether thisthreshold level is in the interval provided by conditions on the  b (which ensures that   0 ).Nevertheless, this non-linearity is important to understand how the prerequisite about twotypes of agents and the introduction of productive government spending in the fiscal stimulusinteract with each other.The results concerning the effect of  , a coefficient in the AS equation in front of thegovernment expenditure and in front of the output, are the same in the case of ZLB and in thenormal case.

The Phillips curve has the following representation: t =  (1 +  )Yt −  gtP −  Gt + Et −1 t ,where  =49(2.37)1  −1(1 +  ) ,  =. 1− 1+ Although the case ofwhich ensures that b being equal to 0 does not satisfy the condition of the share of borrowers b  0.24 , in equation (2.19) is positive, it still shows the transmission channels of parameter effects.61It can be seen that the results concerning the sign cannot be compared with the baselinemodel of Eggertsson and Krugman (2012) without public investment due to the differenteffect on the prices. In their model  represents the sensitivity of the prices to the change ingovernment expenditure, and the higher  is, the lower prices are for a given level ofgovernment expenditure. Which in turn increases the real value of debt and has acontractionary impact on the economy due to the "paradox of toil". In the model withproductive expenditure it is also included in the coefficient in front of the output, changing theslope of the AS curve.

The positive effect of  can be explained by the fact that in the case ofthe zero lower bound this effect works to increase flexibility of prices, compensating thenegative effect of  through the change in prices, due to the change in total governmentexpenditures. In the case of the positive interest rate, with a standard downward sloping ADcurve, the decrease in prices due to increased AS in response to fiscal stimulus is greater thanthe jump in prices due to the increase in AD. As this result is very sensitive to the calibration,further investigation is needed to specify the precise the role of this parameter in theframework.The effect of the debt to GDP ratio  D is different under ZLB and in the "normal" case.This parameter appears in the expression of borrowers’ consumption, specifying howconsumption changes in response to the real interest rate.

Under ZLB its effect is positive, asthe increase in prices, which follows an expansionary fiscal policy, would result in a higherconsumption by borrowers due to the lower level of real debt while the nominal interest rate iszero. This effect is the same as in the case of the ZLB without public investment. In the caseof a positive nominal interest rate this parameter is part of the coefficient in front of theinterest rate in the IS curve, which specifies the negative relationship between the output gapand the deviation of the nominal interest rate from its steady state value. Thus, in this case thenegative impact of  D comes from the fact that the higher value is the interest rate on the debtof borrowers and the lower is their consumption.An impact of  , an elasticity of intertemporal substitution, has a different sign underthe two cases considered.

It has a negative impact under ZLB. With a higher  labor supplyis less responsive to consumption, or to put it in another way, with an increase in wage underhigher  workers tend to work more and increase their consumption less. In the case of thepositive interest rate there is an effect coming from the behavior of the savers and the effect ofpublic spending on prices: higher government expenditure increase aggregate supply,62decreasing price and lowering the nominal interest rate.

With higher  this will lead to abigger increase in the current consumption of the savers. This is only an impact from theaggregate supply side. The other effects of increased government expenditure are captured bythe other parameters in the multiplier.In the positive interest rate case the impact of the elasticity of intertemporal substitutiondecreases with respect to the share of borrowers because the positive effect of  comesthrough the savers' channel. In the case of ZLB this impact comes through borrowers andbecomes more negative as their share in the economy increases.The effect of  (measures the curvature of the disutility of labor), can be seen from anexpression of the labor income of borrowers, equation (2.19). It is negative in both cases,increasing in absolute value with the higher share of borrowers.

The higher  (the lowerlabor supply elasticity) leads to a smaller increase in labor supply in response to an increase inthe wage, which decreases the labor income of borrowers taking wage as given.2.4. ConclusionThis chapter incorporates productive government expenditure in a borrower-savermodel in order to analyze how the presence of debt-constrained agents affects the value of themultiplier when two types of government expenditure are considered: utility-enhancing andproductive expenditure. Productive expenditure provides an additional increase in the AS(contractionary in the framework of zero lower bound). The introduction of borrowers, whoseconsumption depends on their current income, results in a higher value of the multiplier underZLB, compared to the case when only Ricardian agents are considered.

A non-linear impactof the borrowers' share on the fiscal multiplier was revealed under a positive interest rate andunder the ZLB. The non-linear relationship leads to the fact that the multiplier can becomenegative for a sufficiently high share of productive investment in total governmentexpenditure and for a sufficiently high share of borrowers.

This condition for the share ofproductive expenditure postulates that the positive effect of productive spending on the outputthrough the demand is lower than its effect on the aggregate supply. The negative short-termeffect of productive spending comes from the negative impact that productive expenditure hason the aggregate demand and on prices. Both these effects decrease with the share ofborrowers, and disappear when there are no borrowers in the economy.In the case of a positive nominal interest rate, both the productivity of public investmentand its share in total expenditure positively affect the fiscal multiplier.

An increase in the63share of borrowers strengthens the effect of production expenditure on the value of themultiplier. In the case of the ZLB, the impact is reversed: the share of productive expenditureand its productivity lower the fiscal multiplier in the short-run. This result is in favour of oldKeynesian wasteful government expenditure. The negative effect of productive expenditurecan be partly compensated by the higher number of borrowers in the economy.

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