Organizational learning and optimal fiscal and monetary policy

Bidyut Talukdar

doi:10.1515/bejm-2012-0002

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Organizational learning and optimal fiscal and monetary policy

Bidyut Talukdar

Published/Copyright: May 21, 2014

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From the journal The B.E. Journal of Macroeconomics Volume 14 Issue 1

Abstract

We study optimal fiscal and monetary policy in a Ramsey economy where firms learn from their production experience and incur a real cost in changing their prices. Two central results emerge from our study. First, optimal tax policy is counter-cyclical – tax rates fall during recession and rise during boom. This finding contrasts with pro-cyclical tax results obtained in standard sticky price Ramsey models. In presence of learning-by-doing (LBD) mechanism, the Ramsey planner finds it relatively more costly to raise taxes in response to a negative technology shock. Higher taxes would reduce hours, output, and hence future level of organizational capital which will magnify the shock further by lowering future productivity. Hence, in response to a negative productivity shock, the planner finds it optimal to lower taxes in order to raise the after tax return to work and minimize the welfare-reducing effects of the shock. Second, optimal inflation is very stable and persistent over the business cycle. We show that while a dynamic link between current production and future productivity generates the inflation persistence, the real cost of price adjustment is the key factor behind the very low volatility in optimal inflation. Both of these mechanisms work through the monopolistic firms’ optimal pricing condition – namely the New Keynesian Philips Curve.

Keywords: learning-by-doing; optimal fiscal and monetary policy; Ramsey model; sticky prices

JEL Classification: E52; E61; E63

Corresponding author: Bidyut Talukdar, Department of Economics, Saint Mary’s University, 923 Robie Street, Halifax, NS, BCH 3C3 Canada, Tel.: +1 902 496 8164, Fax: +1 902 420 5129, e-mail: bidyut.talukdar@smu.ca

Acknowledgments

I am extremely grateful to Alok Johri for his advice, guidance and encouragement. I would like to thank the associate editor and two anonymous referees for constructive comments, Marc-André Letendre, and William Scarth for helpful discussions and advice, Katherine Cuff, Maxim Ivanov, Stephen Jones, Lonnie Magee, Mike Veall, and seminar participants at Midwest Macro Meetings, Canadian Economics Association Meetings, several universities including McMaster University, and Saint Mary’s University for insightful comments.

Appendix A: The New Keynesian Phillips Curve (NKPC)

We derive the New Keynesian Phillips Curve from intermediate goods producing firms’ profit maximization problem. The representative firm i chooses the plans for n_it, h_it+1, and P_it so as to maximize the present expected discounted value of life-time profits. That is the firms problem is to

(A.1)

maxnit,hit+1,PitE0∑t=0∞QtPt{PitPtyit−wtnit−φ2(PitPit−1−π)2} (A.1)

subject to technological constraint on output production

(A.2)

yit=ztnitαhitθ (A.2)

technological constraint on organizational capital accumulation

(A.3)

hi,t+1=(1−δh)hit+hitγyitε, (A.3)

and taking as given the demand function for variety i,

(A.4)

yit≥(PitPt)−ηyt. (A.4)

Letting Q_tP_tmc_it, and Q_tP_tΨ_it denote Lagrange multipliers associated with constraints (33) and (34) respectively, the Lagrangian associated with the firm’s optimization problem is

∑t=0∞QtPt{PitPt(PitPt)−ηyt−wtnit−φ2(PitPit−1−π)2+mcit[ztnitαhitθ−(PitPt)−ηyt]+Ψit[(1−δh)hit+hitγ((PitPt)−ηyt)ε−hit+1]}

The first order condition with respect to intermediate firm’s price, P_it, (i.e., the New Keynesian Phillips Curve) is,

(A.5)

(1−η)(PitPt)−ηyt+mcitη(PitPt)−ηyt(PtPit)=ηεΨithitγyitε(PtPit)+φ(PitPit−1−π)(PtPit−1)−Qt+1φ(PitPit−1−π)(Pit+1Pit)(Pt+1Pit). (A.5)

Since all intermediate firms face the same wage rate, face the same downward sloping demand curves, and have access to the same production technology, marginal costs, mc_it, are identical across all firms. Consequently, they hire the same amount of labor and produce the same amount of output. Therefore, we can restrict our attention to a symmetric equilibrium in which all firms make the same decisions. We thus drop all the subscripts i. That is, in equilibrium y_it=y_t, p_it=p_t, mc_it=mc_t, Ψ_it=Ψ_t, n_it=n_t, h_it=h_t. Therefore, equations (36), can be simplified as:

(A.6)

[1−η+ηmct]yt=Ψtηεhtγytε+φ(πt−π)πt−φEt[qt+1(πt+1−π)πt+1], (A.6)

where, πt=PtPt−1, and q_t (=Q_t+1π_t+1) is the real discount factor. After some algebraic manipulations and the substitution of Ψ_t (using equation (21) we have the final form of NKPC as

(A.7)

[η−1η−mct]ηyt=−φ(πt−π)πt+φEt[Qt+1(πt+1−π)πt+1]−Qt+1πt+1[mct+1θyt+1ht+1+Ψt+1{(1−δh)+γht+1γ−1yt+1ε}]ηεhtγytε. (A.7)

Steady state NKPC

Note that all the (π_t/t₊₁–π) terms become zero in the steady state. Now, imposing steady sate in equation (A.6), and after some algebraic manipulations, we can express the steady-state NKPC as

(A.8)

mc=η−1η+Ψεhγyε−1. (A.8)

Appendix B: Sensitivity analysis

Table B.5

Sensitivity of dynamic results with respect to the intertemporal elasticity of substitution (CRRA).

Variable	Mean	Std. Dev.	Auto. corr.	Corr(x,y)	Corr(x,g)	Corr(x,z)
φ=1.15
τⁿ	0.2374	0.3856	0.9577	0.7121	0.6118	0.4642
π–1	–2.3978	0.0093	0.9599	–0.1381	0.7042	–0.3437
R–1	1.5040	0.3158	0.8515	–0.2497	–0.6693	0.1562
y	0.7529	0.0054	0.9144	1.0000	0.5308	0.8928
n	0.3310	0.0026	0.9033	–0.2264	0.7508	–0.5688
c	0.6970	0.0052	0.9250	0.8102	–0.2221	0.9603
m/g	0.4335	0.0174	0.9095	–0.3585	0.2708	–0.7820
φ=1.25
τⁿ	0.2375	0.4274	0.9652	0.7404	0.4541	0.4947
π–1	–2.3165	0.0106	0.9600	–0.1785	0.6727	–0.4010
R–1	1.5191	0.3406	0.8097	–0.2602	–0.5986	0.1764
y	0.7139	0.0052	0.9140	1.0000	0.5660	0.9136
n	0.3330	0.0029	0.8816	–0.2365	0.7155	–0.6123
c	0.6760	0.0049	0.9270	0.7926	–0.2124	0.9597
m/g	0.4337	0.0170	0.8831	–0.4572	0.2302	–0.7948

Table B.6

Sensitivity of dynamic results with respect the elasticity of substitution between monopolistically competitive goods.

Variable	Mean	Std. Dev.	Auto. corr.	Corr(x,y)	Corr(x,g)	Corr(x,z)
η=5
τⁿ	0.2416	0.3387	0.9470	0.7275	0.8058	0.4730
π–1	–2.5895	0.0408	0.9146	–0.0029	0.7551	–0.4524
R–1	1.3442	0.2117	0.9179	–0.1979	–0.8212	0.2389
y	0.8305	0.0122	0.9005	1.0000	0.4865	0.8358
n	0.3138	0.0033	0.9106	–0.0437	0.8068	–0.5373
c	0.6887	0.0106	0.8977	0.7578	–0.1364	0.9873
m/g	0.4476	0.0085	0.9270	–0.4650	0.3555	–0.7883
η=7
τⁿ	0.2254	0.3187	0.9577	0.6335	0.8359	0.3687
π–1	–2.4102	0.0412	0.9324	–0.0008	0.7638	–0.4277
R–1	1.5397	0.1725	0.9409	–0.2544	–0.6542	0.0593
y	0.8826	0.0133	0.9009	1.0000	0.4646	0.8504
n	0.3335	0.0033	0.9136	–0.0250	0.8352	–0.4982
c	0.7319	0.0118	0.8975	0.7729	–0.1387	0.9876
m/g	0.4461	0.0080	0.9500	–0.4394	0.3496	–0.7282

Table B.7

Sensitivity of dynamic results with respect to the the degree of substitution between cash and credit goods.

Variable	Mean	Std. Dev.	Auto. corr.	Corr(x,y)	Corr(x,g)	Corr(x,z)
σ=0.60
τⁿ	0.2325	0.3191	0.9519	0.7229	0.6116	0.5293
π–1	–2.3627	0.0481	0.9562	0.1087	0.7360	–0.3930
R–1	1.6502	0.2830	0.9201	–0.2125	–0.1388	0.1298
y	0.8609	0.0131	0.9030	1.0000	0.5487	0.7909
n	0.3252	0.0038	0.9197	0.0722	0.8347	–0.4968
c	0.7138	0.0108	0.8939	0.7714	–0.0470	0.9930
m/g	0.4494	0.0142	0.9706	–0.1359	0.4625	–0.6360
σ=0.64
τⁿ	0.2337	0.3479	0.9256	0.5942	0.8677	0.3477
π–1	–2.5320	0.0354	0.8809	–0.0813	0.7389	–0.4619
R–1	1.4461	0.2824	0.8902	–0.0734	–0.8322	0.3265
y	0.8614	0.0128	0.8999	1.0000	0.4181	0.8765
n	0.3254	0.0030	0.9087	–0.1064	0.8102	–0.5283
c	0.7143	0.0118	0.8999	0.7699	–0.1927	0.9757
m/g	0.4251	0.0066	0.9004	–0.6092	0.2125	–0.7553

Table B.8

Sensitivity of dynamic results with respect the the price stickiness parameter.

Variable	Mean	Std. Dev.	Auto. corr.	Corr(x,y)	Corr(x,g)	Corr(x,z)
ϕ=4
τⁿ	0.2337	0.3262	0.9531	0.6747	0.8279	0.4119
π–1	–2.4865	0.0596	0.9250	–0.0034	0.7608	–0.4392
R–1	1.4563	0.1685	0.9297	–0.2529	–0.7249	0.1037
y	0.8613	0.0128	0.9007	1.0000	0.4732	0.8448
n	0.3254	0.0033	0.9123	–0.0339	0.8235	–0.5149
c	0.7142	0.0113	0.8976	0.7668	–0.1381	0.9875
m/g	0.2468	0.0080	0.9405	–0.4682	0.3404	–0.7663
ϕ=7
τⁿ	0.2319	0.3267	0.9529	0.6726	0.8283	0.4109
π–1	–2.4858	0.0345	0.9248	–0.0052	0.7607	–0.4398
R–1	1.4569	0.1884	0.9342	–0.2243	–0.7658	0.1598
y	0.8613	0.0128	0.9007	1.0000	0.4718	0.8456
n	0.3254	0.0033	0.9122	–0.0354	0.8233	–0.5150
c	0.7142	0.0113	0.8976	0.7669	–0.1394	0.9872
m/g	0.4468	0.0081	0.9404	–0.4614	0.3528	–0.7647

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Published Online: 2014-5-21

Published in Print: 2014-1-1

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https://doi.org/10.1515/bejm-2012-0002

Keywords for this article

learning-by-doing; optimal fiscal and monetary policy; Ramsey model; sticky prices