Диссертация (1137741), страница 10

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3635This Chapter is an extended version of Mamedli, M. O. (2016). Analysis of Government ExpenditureMultiplier Under Zero Lower Bound: The Role of Public Investment. The Journal of Economic Asymmetries,Volume 14, Nov. 2016, pp. 103–111.36Bilbiie et al. (2012) extend further the borrower-saver framework by incorporating financial imperfections inorder to examine the distributional consequences of stimulus programs (revenue-neutral tax cuts to borrowersfinanced by higher taxes on savers and debt financed uniform tax cuts to compare the basis of the present valueof fiscal multipliers under flexible and sticky prices).44Meanwhile, Roulleau-Pasdeloup (2013) analyzes the government expenditure multipliertaking into account the structure of public spending: namely, productive and utility-enhancingtypes of government expenditure. As opposed to the results of Eggertsson and Krugman(2012), Roulleau-Pasdeloup (2013) has found the fiscal multiplier to be lower in the case ofan excess-savings liquidity trap than under a positive interest rate.

He shows that for a highshare of productive spending in total expenditures private consumption is crowded out byproductive government spending, and the multiplier can even become negative.This chapter presents an analysis of the short-run government spending multiplier, inthe extended borrower-saver model of Eggertsson and Krugman (2012). The modelincorporates public investment, which was shown to gain a higher share in the totalgovernment expenditures during the recessions (Bachmann and Sims, 2012). The developedframework, therefore, combines the introduction of debt-constrained consumers, which isknown to increase the multiplier (Galí et al., 2007; Eggertsson and Krugman, 2012), with anassumption about productive government expenditure, which lowers the multiplier under theZLB (Roulleau-Pasdeloup, 2013).

The heterogeneity of the population in the model withpublic investment intensifies the non-linear impact of the borrowers' share on the multiplier.The share of borrowers increases the multiplier when there is no productive expenditure.However, the negative effect of productive spending under the ZLB is proportional to theborrowers' share, implying the ambiguity of its impact on the multiplier. As opposed to theresults of Roulleau-Pasdeloup (2013), the multiplier under the ZLB remains higher than undera positive interest rate (3.76 and 0.31, respectively) due to the introduction of constrainedagents, as they provide an additional transmission channel to the fiscal policy. The multipliercan still become negative under the ZLB with a sufficiently high share of productive spendingand with a high share of borrowers in the economy.

However, this threshold level ofproductive spending is higher than the one found by Roulleau-Pasdeloup (2013) anddecreases with the share of borrowers.There is no consensus in the empirical research about the value of the fiscal multipliereither. Empirical evidence suggests that private consumption tends to rise with governmentexpenditure. Blanchard and Perotti (2002) show on the basis of structural VAR model thatgovernment spending increases private consumption. Moreover, the estimated governmentexpenditure multiplier is always positive in the short-term and lower than 1.

Ramey (2011)extends Blanchard and Perotti (2002) by comparing the VAR and the narrative approach ofRamey and Shapiro (1998), which incorporates the impact of the anticipation of the fiscal45policy. Ramey (2011) obtains government expenditure multipliers between 0.6 and 1.2.However, Ramey (2011) finds no evidence of the multiplier being higher under low interestrates.

Another study extends Blanchard and Perotti (2002) by estimating the fiscal multiplierseparately for the periods of expansions and recessions. As low interest rates are theconsequence of recessions (Woodford, 2011), the results of this research are usuallyconsidered to be empirical evidence for the higher multiplier under the ZLB. Almunia et al.(2009) obtained fiscal multipliers higher than those found during recessions on the basis ofpanel data from 27 countries. Auerbach and Gorodnichenko (2012) on the basis of a regimeswitching SVAR model obtained a positive multiplier that exceeds 1 in recessions, and asmaller multiplier in expansions.

While Owyang et al. (2013), applying the approach ofRamey (2011) to the sample of two countries, the US and Canada, obtained for Canada asmaller multiplier under positive interest rates and long-run multipliers greater than 1 for theperiods of recessions.The results presented in this chapter can provide an explanation of the diverse empiricalestimates of the government expenditure multiplier as both the structure of the governmentexpenditure and the heterogeneity of the population affect the value of the multiplier.

Theresults suggest that the government expenditure multiplier can still be higher in the ZLB thanunder a positive interest rate, even when the fiscal stimulus consists partly of the productiveexpenditure, if some consumers in the economy are liquidity-constrained.This chapter is organized as follows.

Section 2 presents the extended Eggertsson andKrugman model (2012), with the focus on two types of government expenditures. In Section 3the expenditure multiplier is derived under a positive interest rate and in the case of the zerolower bound. The effects of productive expenditure on the multiplier are compared in the twocases, specifying how these effects changes with the share of borrowers. Section 4summarizes the results of the chapter.2.2.The modelThe model of Eggertsson and Krugman (2012) with heterogeneous agents and standardutility-enhancing government expenditure was extended by incorporating productivegovernment expenditure.462.2.1. HouseholdsUnit mass continuum of households consists of savers,  s , and borrowers, 1 −  s .Agents differ in their time preferences,  (s) =    (b) , where  (i)  (0,1) and i s, b .Savers, who are standard Ricardian agents, smooth their consumption over time.

Borrowersare liquidity-constrained and consume all their disposable income in each period and can beconsidered standard Keynesian type agents.Both types of consumers maximize an expected present value of instantaneous utility,which is additively separable between consumption Ct (i) , hours worked ht (i ) and utilityenhancing government expenditures GtU .E0   t (i ) U i ((Ct (i)) − ti (ht (i)) + ti (GtU )  , i = s, b.(2.1)t =0Equations (2.2)-(2.3) specify the consumption of a differentiated good, Ct (i) ,represented by the Dixit-Stiglitz aggregator, and the corresponding price index, where p jt isprice of a particular good j and i is a type of the agent (saver or borrower). / −11Ct (i ) =   ct (i, j )( −1)/ dj 0,(2.2)1/ −11Pt =   pt ( j )1− dj 0.(2.3)The demand function of good j , ct ( j ) , aggregated by two types of consumers, obtainedfrom the household maximization problem, is:37− p jt ct ( j ) = Ct  . Pt (2.4)The aggregate per capita consumption in the economy is a weighted sum of per capitaconsumption of two types of agents:Ct =  s Cts + (1 −  s )Ctb ,(2.5)where Cts is the consumption of savers and Ctb is the consumption of borrowers at the time t .They are defined below.The intertemporal choice of the consumption and labor supply are defined by solvingthe utility maximization problem subject to the budget constraint and debt limit constraint:383738For more details see Appendix 1 (Section A1.1.1).For more details see Appendix 1.471Bt (i) + Wt Pht t (i ) +  Пt (i ) = (1 + it −1 ) Bt −1 (i ) + PCt t (i ) + PTt t (i ),(2.6)0(1 + rt )Bt (i ) D, i = s, b.Pt(2.7)Borrowing is realized by the selling and purchasing of one period riskless nominalbonds, Bt (i ) , with a nominal rate of return, it .

Each agent also receives an hourly real wageWt paid for hours worked ht (i ) . Total income consists of labor income and profit from firmownership П t (i ) , distributed equally among agents. The income is spent on consumption, onrepayment of debt with interest (in the case of a borrower) and on the payment of lump-sumtaxes. They can differ for each type of consumer.Inequality (2.7) is the debt limit constraint.

It postulates that the real value of debtincluding the real interest rt cannot exceed an exogenous real debt limit D .For the savers the debt limit constraint is not binding, so they maximize their objectivefunction subject to the equations (2.6)-(2.7) with respect to consumption, hours worked andthe amount lent. After solving this problem, the following optimality conditions can beobtained:( )(U cs Cts =  (1 + it ) Et [U cs Cts+1Wt =hi (hti )U ci (Cti )) PPt],(2.8)t +1, i = s, b.(2.9)Equation (2.8) sets the savers' optimal consumption path, while equation (2.9) specifieslabor supply for both types of consumers.For the borrowers, the debt limit constraint is binding.

Their consumption is defined bythe budget constraint in real terms, taking into account that debtors borrow up to the debtlimit:391D1C = − Dt −1 + t + Wt b htb +  Пtb − Tt b .1 + rtPt0bt(2.10)Consumers of this type spend all their disposable income and the borrowed amount afterrepaying the debt of the previous period with interest.39For more details see Appendix 1.482.2.2. FirmsThere is a unit mass of firms, with a fraction  setting prices each period, and 1 − setting prices one period in advance.

Firms choose their optimal price by maximizing thepresent value of profits subject to the demand function and the production function:40Et   t  pt ( j ) yt ( j ) − Wt Pht t ( j ) ,(2.11)t =0− p jt s.t. yt ( j ) = Yt  , Pt yt ( j ) = (GtP ) ( ht ( j )) ,where Wt = W ( s )t W (b)t ,  t =  s 1st − (1 −  s ) 2bt is a discount factor and  1st ,  2bt aresbLagrangian multipliers from the utility maximization problem.Inputs for the production of each type of good j are labor, ht ( j ) , and productivegovernment spending, GtP . Productive spending, which is included directly into theproduction function, can be interpreted as the infrastructure (see e.g.

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