Диссертация (1137741), страница 12
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Thus (1 − b ) / ( b D ) or b 1/ ( D + ) .454654is steeper than in Eggertsson and Krugman (2012) due to the higher sensitivity of Y b to theoutput ( 1 , as opposed to the case with a one input production function).The equation (2.31) for the equilibrium output gap is obtained from the combination ofthe equation (2.28) for the AD and the equation for the Phillips curve from Table 2.1: ( + −1 ) + b D b Dˆ + b TSbYˆS = − s(is − r ) −+1 − b ( + D (1 + ))1 − b ( + D (1 + ))1 + −1 −1 s − b ( −1 + D ) −b ( D (1 + ) + (1 + ) −1 )+GS .1 − b ( + D (1 + ))(2.31)The negative impact of productive government expenditure on demand is supplementedby an additional negative impact of productive expenditure on prices.
Both these effectsdisappear when there are no borrowers in the economy. Productive expenditure affects theoutput gap, because the current consumption of borrowers depends positively on the currentlevel of inflation, which decreases the real value of debt. Thus, this additional impact on theoutput disappears when there are only savers in the economy.Depending on the size of the deleveraging shock two cases are considered: when thenominal interest rate remains positive, and when the ZLB becomes binding and the AD curveis upward-sloping. The parameter values used for calibration are presented in Table 2.2.Table 2.2. Parameter valuesVariableSymbolValueSourceDiscount factorResponse to inflationElasticity of intertemporal substitutionInverse of Frisch labor supply elasticityShare of productive public spendingProduction function elasticityDebt shareShare of firms with flexible prices0.991.5110.50.080.50.5StandardStandard47Eggertsson, Krugman (2012)Eggertsson, Krugman (2012)Roulleau-Pasdeloup (2013)Roulleau-Pasdeloup (2013)Eggertsson, Krugman (2012)Eggertsson, Krugman (2012)DNote: Calibration is based on the assumption of the constant return to scale, + = 1 .These values define = 1.1739 and = 0.4792 .47It was used in Christiano et al.
(2011).552.3.2. Fiscal multiplier under a positive nominal interest rateIf the ZLB is not binding, the central bank follows the Taylor rule for the nominalinterest rate:it = rt n + t , with 1 .(2.32)Under a positive interest rate, the government expenditure multiplier is obtained bysubstituting an equation (2.32) for a positive nominal interest rate and the Phillips curve in theIS curve, equation (2.29):mult GPR = ( + −1 ) + b D YˆS = − s(iS − rSn ),1 − b(2.33) ( (1 + ) + )( s ( + −1 ) + b D ).1 − b + (1 + )( s ( + −1 ) + b D )(2.34)In Roulleau-Pasdeloup (2013), where the economy consists only of Ricardian agents,the fiscal multiplier equals 0.57 when the ZLB is not binding.
In the case of heterogeneousagents the multiplier equals 0.3148 for b = 0.33 . Although the government multiplierincreases with the share of constrained agents, this estimate is lower than in the paper byRoulleau-Pasdeloup (2013). The divergence of the current estimates and the results presentedin Roulleau-Pasdeloup (2013) can be explained by the non-linear relationship of the multiplierand the share of borrowers.
The value of the multiplier as a function of the share of borrowersunder a positive interest rate is presented in Figure 2.1. The government expendituremultiplier is a hyperbolic function of b with an asymptote at b = 0.89 (point of singularity).The multiplier is monotonically increasing with the share of borrowers for b ( 0;0.89) . Theshare of borrowers which exceeds 0.89 leads to the negative value of the fiscal multiplier.However, these values of b are significantly higher than empirical estimates of the share ofnon-Ricardian agents and do not satisfy the condition of b 0.48 which ensures that theoutput decreases with the higher interest rate (equation (2.29)).562,5multPR21,510,50-0,500,51-0,51,5χb-1-1,5Figure 2.1.
Fiscal multiplier as a function of the share of borrowers, it 0Source: estimates based on the model.Under a positive interest rate and, thus, a standard downward-sloping AD curve, thefiscal multiplier increases with price rigidity. An increase in the aggregate demand underhigher price rigidity would lead to lower inflation, which is contractionary under a positiveinterest rate. Moreover, higher share of productive expenditure and its higher productivityincrease the multiplier: higher productive expenditure shifts the AS curve down, and this shiftis expansionary in the case of a downward-sloping AD curve. Both these positive effectsbecome stronger with an increase in the share of borrowers.
482.3.3. Fiscal multiplier under zero lower boundIf the deleveraging shock is sufficiently high, the ZLB becomes binding due to thedeflation effect. The output gap in this case is:YˆS = −bbDˆ −TSb +1 − b ( + D (1 + ))1 − b ( + D (1 + ))1 + −1 −1 s − b ( −1 + D )b ( D (1 + ) + (1 + ) −1 ) p+GS −gS ,1 − b ( + D (1 + ))1 − b ( + D (1 + ))48The effect of all other parameters was analyzed and the summary is presented in subsection 2.3.4.57(2.35)= s ( + −1 ) + b D r.1 − b ( + D (1 + ))There are two effects of productive spending on the output: through total governmentexpenditure and through a productive government expenditure which has a separate negativeeffect. If an increase in government expenditure is financed by taxes on savers or debt andgtP = Gt , the government spending multiplier is:mult GZLB =1 + −1 −1 s − b ( −1 + D ) −b ( D (1 + ) + (1 + ) −1 ).1 − b ( + D (1 + ))(2.36)Let us compare the multiplier obtained in equation (2.36) with the multiplier obtainedby Eggertsson and Krugman (2012).
The numerator of (2.36) now consists of two items: thefirst is the same as in Eggertsson and Krugman (2012), while the second item represents anadditional negative effect that comes from productive government spending. This effect is acombination of the negative impact of productive expenditure on the AD and the AS. Boththese effects decrease with a lower share of borrowers, and disappear when there are noborrowers in the economy. The negative effect on the price level comes from the negativeeffect of productive expenditure on the marginal cost.
It affects the output gap throughborrowers, as their current consumption depends positively on the current level of inflation.Inflation is negatively affected by the production part of expenditure. The second negativecomponent, (1 + ) −1 , comes from the effect of productive expenditure on the wage andhours worked through the increased marginal product of labor, making workers moreproductive.When the share of borrowers equals 0.33, the multiplier equals 3.76.
Despite theintroduction of productive government expenditure, the value of the fiscal multiplier is higherunder ZLB than under a positive interest rate. This result is in line with the results ofEggertsson and Krugman (2012) and Christiano et al. (2011). However, the higher value ofthe multiplier under ZLB contradicts the results of Roulleau-Pasdeloup (2013).
This can beexplained by the introduction of an additional channel, by which fiscal policy affects theoutput, through the presence of borrowers. It partially offsets the negative impact of theproductive expenditure and ensures the higher impact of public expenditure on the AD thanon the AS.58However, this additional increase in the output through the channel of borrowers islimited: under ZLB the multiplier is also a non-linear function of the share of borrowers(Figure 2.2).4multZLB3210-0,500,5-111,5χb-2-3-4Figure 2.2. Fiscal multiplier as a function of the share of borrowers, it = 0Source: estimates based on the model.The fiscal multiplier is positive if the share of borrowers is below the threshold level.The multiplier becomes negative if the share of borrowers exceeds 0.396 (for b 0.396when = 0.5 ).
However, for a share of borrowers equaling 0.33, the multiplier remainspositive even for the highest share of productive spending, = 1 . On the one hand, themultiplier increases with respect to the share of borrowers, when there is no productivespending. On the other hand, in the model with productive expenditure, its negative effect isproportional to b , and disappears when there are no borrowers in the economy.The government multiplier would be positive if 1 + −1 −1 s − b ( −1 + D ) b ( D (1 + ) + (1 + ) −1 ) , as the denominator of the multiplier is positive.
Thiscondition corresponds to the case when the positive effect of productive spending on theoutput through demand is higher than its effect on supply.In Roulleau-Pasdeloup (2013), consumption is crowded out by public spending if theproductive part of government expenditure is higher than 0.64. This share of productiveexpenditure in the model with the liquidity-constrained agents would be sufficient to bring the59multiplier below zero, if the share of borrowers is higher than 0.82.
This does not satisfyseveral restricting conditions on b , introduced earlier. Therefore, if an assumption about twotypes of consumers is taken into account, the government expenditure multiplier remainspositive for any values of , if the share of borrowers is low enough.Under the ZLB both the share and the productivity of public investment have a negativeimpact on the value of the multiplier. A higher share of productive expenditure and itsproductivity lead to a bigger increase in AS (compared to the model without productivegovernment expenditure).
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