Bassam R Awad Florida State University Center for Economic Forecasting and Analysis 3200 Commonwealth Blvd. Tallahassee, FL 32304 Phone: (850) 567-2085 Fax: (850) 645-0191 Email: Homepage: Education Ph.D. Economics, Florida State University, Tallahassee - Florida, 2009. M.S. Economics, Florida State University, Tallahassee - Florida, 2007. MBA. Accounting, University of Jordan , Amman - Jordan, 1997. M.A. Economics, Yarmouk University, Irbid - Jordan, 1994. B.A. Economics, Yarmouk University, Irbid - Jordan, 1989. Research Interests Macroeconomics, Financial Economic and Econometrics. Experience Teaching Experience Mentor. Online course development for Cultural Economics. 2009. Mentor. Online course in Finance and Banking. 2008. Teaching assistant. Microeconomics. 2006. Instructor. Taught Economic Development at a community college in Jordan. 1993. Research and Teaching Assistant. Microeconomics and Macroeconomics at Yarmouk University. 1990- 1992. PIE Associate. Awarded the Program for Instruction Excellence (PIE) Certificate from Florida State University. 2008. Research Experience Research Associate: The FSU Center for Economic Forecasting and Analysis, 2006 –. Economist: Central Bank of Jordan, 1994 – 1996. Internal Auditor: Central Bank of Jordan, 1996 – 2003. Economist: Central Bank of Jordan, 2003 – 2005.
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Bassam R AwadFlorida State UniversityCenter for Economic Forecasting and Analysis3200 Commonwealth Blvd.Tallahassee, FL 32304
Long-Run Growth versus Welfare: the Importance of Transitional Dynamics When Assessing Alterna-tive Fiscal Policies. Submitted to the Journal of Macroeconomic Dynamics in 07/06/09.
Linearization and Higher-Order Approximations: How Good are They? Results from an EndogenousGrowth Model with Public Capital. Submitted to the Journal of Computational Economics in 09/30/09.
Research in Progress
Optimal Fiscal Policy with Time Invariant Tax Structure: The Importance of a Public Capital External-ity.
Technical Reports
Dollar and Sense: National High Magnetic Field Laboratory and Its Forecasted Impact on the FloridaEconomy. August 2009.
Goliath Grouper: A Survey Analysis of Dive Shop and Charter Boat Operators in Florida. June 2009.
The Tallahassee Economic, Quality of Life and Investment Climate. June 2008.
Business Listing In the Enterprize Zone of Tallahassee. June 2008.
Marketing and Economic Study of CNS Services in Cairo, Georgia. May 2008.
Model Predicts Florida Economy Will Gain By Property Tax Cut Without Changing Sales Tax. May2007.
Assessment of Student Learning in a Laboratory Setting. March 2007
Coastal Training Programs of Florida Needs Assessment: Report and Appendix. December 2006.
Grants
Awarded
August 2009. National High Magnetic Field Laboratory - Florida State University. 2008-2009 EconomicImpact Assessment (Dollar and Sense Report). $10,754
June 2009. Goliath Grouper Study A Survey Analysis of Dive Shop and Charter Boat Operators inFlorida. In partnership with Fish and Wildlife Conservation Commission. $10,000
June 2008. The Tallahassee Economic, Quality of Life and Investment Climate. The Tallahassee/ LeonCounty Economic Development Council. $5,000
March 2008. Database of International Economic Development Council’s of the sixteen county area ofFlorida’s Great Northwest (FGNW). $41,686 for first year, plus $16,379 for annual updates
October 2007. Marketing and Economic Study of CNS Services in Cairo, Georgia. Community NetworkServices, Cairo - GA. $4,795
December 2006. Coastal Training Programs of Florida Needs Assessment Report. (A Report funded inpart by the Florida Department of Environmental Protection, Florida Coastal Management Program,pursuant to National Oceanic and Atmospheric Administration Award Number NA05NOS4191074).$45,000
Grant Applications
October 2006. Analytical Services Relating to Property Taxation, Proposal to the Florida Legislature -Office of Demographic Research. $76,800
May 2009. Taxpayer Return on Investment in Florida Public Libraries. $149,800
July 2009. FGNW Targeted Industries Sub-Cluster Analysis. $78,800
Honors
Florida State University Golden Key International Honor Society.(2008-2009).
Yarmouk University Dean’s honor list for undergraduate students in Economics. (1986-1989).
Jordan Social Security Corporation grant for distinguished first-year economics major students. (1986-1989).
Training
Euro Mediterranean partnership, European Union, Brussels-Belgium, April 2005.
Managing Exchange Rate crisis, Arab Planning Institute, Kuwait, March 2005.
Economic Indicators, Arab Monetary Fund, United Arab Emirates, April 2004.
External Sector Policies, International Monetary Fund, Washington, DC, August-September 1997.
Memberships
Society for Computational Economics
American Economic Association.
Econometric Society
Computer Skills
SPSS, STATA, E-views and all Office applications, .
R, MATLAB and Mathematica
Text editing using Latex, WinEdt and Scientific Workplace.
Dr. Thomas W. Zuehlke, Associate Professor,Director of Graduate Studies,Department of Economics, Florida State University253A Bellamy Building, Florida State University, Tallahassee, FL 32306-2180
Dr. Carol Bullock, Graduate CoordinatorDepartment of Economics, Florida State University253 Bellamy Building, Florida State University, Tallahassee, FL 32306-2180
PHDWKSHP:EXPRMNTLECO ECO6938 S 0.00 0.00 0.00 0.00
PRELIM DOCTORAL EXAM ECO8969 P 0.00 0.00 0.00 0.00
Term Totals: 9.00 9.00 9.00 34.50
RECEIVED THE DEGREE
MASTER OF SCIENCE APRIL 28, 2007
3
Bassam R Awad 3/6
PGM : ECONOMICS MAJOR: EC NOMICS O
FLORIDA STATE UNIVERSITY
Term Class Division Major
Summer 2007 Graduate COLLEGE OF SOCIAL
SCIENCES ECONOMICS
Title Type Course Grade Hours
Attempted Hours Earned
GPA Hours
GPA Points
DIS:CMPTTLMETH/GENEQ ECO5907 A 3.00 3.00 3.00 12.00
Term Totals: 3.00 3.00 3.00 12.00
FLORIDA STATE UNIVERSITY
Term Class Division Major
Fall 2007 Graduate COLLEGE OF SOCIAL
SCIENCES ECONOMICS
Title Type Course Grade Hours
Attempted Hours Earned
GPA Hours
GPA Points
PUBLIC FINANCE ECO5505 B 3.00 3.00 3.00 9.00
PHDWKSHP:MACRO/MICRO ECO6938 S 0.00 0.00 0.00 0.00
DISSERTATION ECO6980 S 2.00 2.00 0.00 0.00
GIS LAB GEO5908 S 1.00 1.00 0.00 0.00
GEOG INFO SYS GIS5101 S 3.00 3.00 0.00 0.00
Term Totals: 9.00 9.00 3.00 9.00
FLORIDA STATE UNIVERSITY
Term Class Division Major
Spring 2008 Graduate COLLEGE OF SOCIAL
SCIENCES ECONOMICS
Title Type Course Grade Hours
Attempted Hours Earned
GPA Hours
GPA Points
DIS:COMPUTATNLMACRO ECO5907 A 2.00 2.00 2.00 8.00
WORKSHOP QUANT ECO6938 S 0.00 0.00 0.00 0.00
DISSERTATION ECO6980 S 7.00 7.00 0.00 0.00
4
Bassam R Awad 4/6
Term Totals: 9.00 9.00 2.00 8.00
FLORIDA STATE UNIVERSITY
Term Class Division Major
Summer 2008 Graduate COLLEGE OF
SOCIAL SCIENCES ECONOMICS
Title Type Course Grade Hours
Attempted Hours Earned
GPA Hours
GPA Points
DISSERTATION ECO6980 S 6.00 6.00 0.00 0.00
Term Totals: 6.00 6.00 0.00 0.00
FLORIDA STATE UNIVERSITY
Term Class Division Major
Fall 2008 Graduate COLLEGE OF
SOCIAL SCIENCES ECONOMICS
Title Type Course Grade Hours
Attempted Hours Earned
GPA Hours
GPA Points
DISSERTATION ECO6980 S 9.00 9.00 0.00 0.00
Term Totals: 9.00 9.00 0.00 0.00
FLORIDA STATE UNIVERSITY
Term Class Division Major
Spring 2009 Graduate COLLEGE OF
SOCIAL SCIENCES ECONOMICS
Title Type Course Grade Hours
Attempted Hours Earned
GPA Hours
GPA Points
DISSERTATION ECO6980 S 3.00 3.00 0.00 0.00
Term Totals: 3.00 3.00 0.00 0.00
TRANSFER INFORMATION
Hours Attempted: 0.00 Hours Earned: 0.00
5
Bassam R Awad 5/6
GRADING SYSTEM
USED TO COMPUTE GPA A Excellent
B Good
C Average
D Passing
F Failing
IE Incomplete Expired
GE No Grade Expired NOTE: A grade of "W" is used only to denote that a student was passing a course at the time of withdrawal from the University.
NOT USED TO COMPUTE GPA I Incomplete
S Satisfactory
U Unsatisfactory
EC CLEP Exam Credit/CEEB
P Passed (Graduate Tests)
ED Department Exam Credit
WD Withdrawn with permission of Dean
*W Withdrew
NG No Grade Reported
CR Credit Received
EVALUATION OF TRANSFER (see course type)
D Course duplicated by other work.
E Credit approved toward undergraduate degree.
G Grade below transferable level.
L Course below transferable level.
M Remedial coursework.
N Course not applicable towards degree.
P Credit approved toward graduate degree.
T Vocational or technical terminal course prior to Fall Semester, 1981.
V Vocational or technical terminal course beginning Fall Semester, 1981.
W Gordon Rule Writing Contest.
X Coursework taken while on dismissal.
Y Community college courses taken beyond AA degree.
FORGIVENESS POLICY INDICATORS (see course type)
T Repeated (initial attempt)
R Repeated (last attempted) The information provided is for student use only and can not be given out to a third party
without the student's permission.
6
Bassam R Awad 6/6
Teaching PhilosophyBassam R. Awad
As a graduate student in Jordan, I had the opportunity to teach under-graduate courses in both micro- and macro- economics. For some, myclass was the first and only economics course they would ever take. Assuch, I understood that this was the only chance that I had to make alasting impression on them. For others, however, my class was the firstof many, and I understood that these students needed to be conditionedfor the more advanced economic courses. Regardless of their careerchoice, I taught my courses in such a way that those students pursuingbachelors or advanced degrees in economics would be prepared, andthose pursuing other degrees would be able to apply economic conceptsto the everyday decisions in their lives . My mission then, and still istoday, is to make sure that every student understands the basic eco-nomic concepts and their importance and usefulness in life.
When teaching, I make every effort to share my enthusiasm of the sub-ject matter with the students in the hopes that they too will becomeexcited about the material. I do this by incorporating examples frommy own research, and their interests into the lectures. One way I amable to gauge their interests is by having them email or bring in articlesthat they have questions about or would like to discuss in class. Whenappropriate, I will post these articles on the class website and orches-trate an interactive classroom discussion. I find that taking the timeto listen to my students and get them involved helps establish a line ofcommunication, wherein the students feel comfortable coming to me ifthey have questions about the material, need academic advisement, orhave general concerns that they would like to express.
Establishing individual relationships with my students is extremelyimportant to me, as I feel that a successful educator is not one whoflourishes solely in the classroom, does not flourish. Instead, I view asuccessful educator as someone who fully integrates themselves intothe community, institution, and classroom. Having been raised abroadI can relate to a diverse student body and try to immerse myself in asmany activities as possible.
While at Florida State University, I worked as a mentor for an online
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course in money and banking. As a mentor, I had no face-to-face contactwith the students I was working with. My teaching mission, however,remained the same. In order to accomplish this mission, I had to adaptmy teaching style to best serve the students of the online environment.This meant taking the time to ensure that my correspondence with thestudents was consistent, clear and concise, encouraging, and thorough.I accomplished this by promptly responding to emails, answering ques-tions on an anonymous message board, and by providing innovativeexamples and practice questions that supplemented the material. Ialso incorporated a wide variety of video clips into the lessons, whichhelp connect various topics to real world applications. Although I didnot develop the on-line course, I feel that my interactions with thiscourse provided me with the skill set necessary to create and maintainmy own distance learning courses.
18-11-2009
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Research StatementBassam R. Awad
I have worked at the Central Bank of Jordan for 12 years from 1994to 2005. My job duties were varied, but it included mostly the inter-national economic issues, papers and reports related to Jordan. I havebeen employed at the FSU Center for Economic Forecasting and Anal-ysis (CEFA) since August 2006. My primary area of expertise in CEFAis data collection and statistical, econometric analysis, writing reports,literature review and presentations. I have conducted beta testing andprovided feedback on a new software program WITS on economic work-force development in the Big Bend Region in Florida funded by FloridasGreat Northwest (an economic development group including 16 coun-ties in Florida). I have built a good experience in working with variouseconometric and statistical packages such as STATA, Latex, WinEdt,MATLAB, SPSS, Mathematica and Eviews. I have good skills in us-ing other software packages as well, including MS Office, ScientificWorkplace, Advanced SPSS, and REMI and IMPLAN (economic impactanalysis software). I am also the CEFA webpage webmaster. Parallelto that, I have worked as a teaching assistant at the FSU departmentof Economics in different semesters. During that work, I have beenawarded the Certificate of Instruction Excellence. My duties involveddeveloping an online course and mentorship using Blackboard.
My dissertation title is ”Essays in Fiscal Policy: Computational Accu-racy and Optimal Investments in Public, Private, and Human Capital.”focuses on the growth and welfare effects of alternative tax regimes ina setting where the growth process is driven by investment in humancapital and where public capital enhances the production process. Ihave demonstrated that (i) the policies that induce the highest ratesof economic growth do not always provide the highest welfare. (ii) Thetraditional methods of analyzing the economic: consequences of alter-native tax policy regime can be very large approximation errors, whichdo not occur in the method employed in my analysis. (iii) the short-runimplications of tax reforms can be very different from the longrun con-sequences, and it may take many years for the benefits of tax reform tooffset short-term losses.
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The second chapter of my dissertation is entitled ”Linearization andHigher-Order Approximations: How Good are They?: Results from anEndogenous Growth Model with Public Capital” I address the accuracyproblem linked to the approximation methods in analyzing the transi-tional dynamics. Where standard procedure for analyzing transitionaldynamics in non-linear macro models has been to employ linear ap-proximations. Recently quadratic approximations have been explored.This chapter examines the accuracy of these and higher-order approx-imations in an endogenous growth model with public capital, therebyextending the work done in the current literature on the neoclassicalgrowth model. We find that significant errors may persist in computedtransition paths and welfare even after resorting to approximations ashigh as fourth order. Moreover, the accuracy of approximations maynot increase monotonically with the increase in the order of approxi-mation. Also, as in the previous literature, we find that achieving ac-ceptable levels of accuracy when computing the welfare consequencesof a policy change typically requires a higher order approximation thanattaining similar levels of accuracy in the computation of the transi-tion path: typically an increase in order of approximation by one issufficient.
The third chapter, Long-Run Growth versus Welfare: The Importance ofTransitional Dynamics When Assessing Alternative Fiscal Policies, uti-lizes the evident superiority of nonlinear solution methods for optimaltransition path. analyzes the effects of distortionary taxes on growthand welfare in an endogenous growth model with a public capital ex-ternality. The model is calibrated to the U.S. economy, and experimentsare run under which the tax regime is shifted from the current mix ofcapital income, labor income, and consumption taxes to a fiscal policyregime with complete reliance on a single source of taxation, includ-ing lump-sum tax. We find that tax policy changes that induce highergrowth rate do not necessarily result in higher welfare due to differenttransitory effects. In fact, a shift to capital income tax while deliver-ing highest long-run growth results in lowest welfare. Furthermore,long-run gains take many years a generation to start getting realized.Among different sources of taxation, we find that, in the long run, com-plete reliance on a consumption tax dominates the current tax regime;however, the current tax regime dominates an exclusive labor income
2
tax, which in turn is less welfare-reducing than an exclusive capitalincome tax. These results are due to the fact that taxes on labor in-come and capital income distort investment decisions in reproduciblecapital, i.e., human capital and physical capital, and therefore have cu-mulative effects that do not result from a tax on consumption. Unlikeprevious studies, we account for the welfare effects of transition usingoptimal decision rules all along the transition path.
The title of the fourth chapter is ”Optimal Consumption Tax Rate in aDynamic Fiscal Policy with Time Invariant Tax Structure: the Impor-tance of Externality” There is a long-standing debate in the literatureon the choice between consumption or expenditure taxes versus capi-tal income taxes that goes back to Thomas Hobbes (1651), Mill (1871)and later Kaldor (1955) who advocated the consumption tax over theincome tax. The advocacy of consumption tax has its solid empiricalevidence as some studies indicated that the tax revenue collected inthe United States includes a relatively small contribution coming fromcapital tax (Roger Gordon, Laura Kalambokidis, Jeffrey Rohaly andJoel Slemrod (2004)). This chapter examines tax policy in an endoge-nous growth model with public capital externality, where human capi-tal serves as the engine of growth. In the previous chapter, this modelwas calibrated to the U.S. economy and experiments were run to cal-culate welfare gains from a shift in the fiscal regime from the currentmix of capital income, labor income, and consumption taxes to com-plete reliance on consumption tax. In those experiments, governmentexpenditures in public capital as a share of output was held fixed. Thechapter showed that the consumption-only tax regime was superior tothe current tax regime and to other tax regimes relying solely on a sin-gle source of taxation. In this chapter, the government tax revenuesas a portion of output are varied in order to find the optimal level ofinvestments in public capital under a consumption-only tax regime. Ifind that in the presence of a significant externality, a modest increasein the consumption tax with a greater investment in public capital canincrease welfare. I also show that a slight shift in taxes from consump-tion to capital income can be welfare improving if the externality ishigh enough.
During my work in the economic research at the Central Bank of Jor-
3
dan and CEFA, I have gained good research skills. These include lit-erature survey, data collection, extensive web-search, mastery of thesoftware requirements, working on different tasks at the same time,committing to deadlines, and continually following-up projects’ com-pletion requirement, and recently, I began applying for grants. Exam-ples of my work are the market survey research for the City of Cairoin Georgia, the preparation of the IEDC tables for the Florida GreatNorthwest, and the economic impact analysis reports. Links to theseare available on my web page under technical reports tab. More infor-mation are available at cefa.fsu.edu
16-11-2009
4
Electronic copy available at: http://ssrn.com/abstract=1336140Electronic copy available at: http://ssrn.com/abstract=1336140
Long-Run Growth versus Welfare: The Importance ofTransitional Dynamics When Assessing Alternative
Fiscal Policies∗
Manoj AtoliaFlorida State University †
Bassam AwadFlorida State University ‡
Milton MarquisFlorida State University §
First Draft: January 2009
∗We are very grateful to Paul Beaumont, Tor Einarsson, Bharat Trehan and other participants of theMacro summer workshop, 2008, at Department of Economics, Florida State University where an earlierversion of this paper was presented. All errors are ours.
†Department of Economics, Florida State University, Tallahassee, FL 32306, U.S.A. Telephone: 850-644-7088. Email: [email protected].
‡Department of Economics, Florida State University, Tallahassee, FL 32306, U.S.A. Telephone: 850-567-2085. Email: [email protected].
§Department of Economics, Florida State University, Tallahassee, FL 32306, U.S.A. Telephone: 850-645-1526. Email: [email protected].
1
Electronic copy available at: http://ssrn.com/abstract=1336140Electronic copy available at: http://ssrn.com/abstract=1336140
.
Abstract
This paper analyzes the effects of distortionary taxes on growth and welfare in anendogenous growth model with a public capital externality. The model is calibratedto the U.S. economy, and experiments are run under which the tax regime is shiftedfrom the current mix of capital income, labor income, and consumption taxes to afiscal policy regime with complete reliance on a single source of taxation, includinglump-sum tax. We find that tax policy changes that induce higher growth rate do notnecessarily result in higher welfare due to different transitory effects. In fact, a shift tocapital income tax while delivering highest long-run growth results in lowest welfare.Furthermore, long-run gains take many years – a generation – to start getting realized.Among different sources of taxation, we find that, in the long run, complete reliance ona consumption tax dominates the current tax regime; however, the current tax regimedominates an exclusive labor income tax, which in turn is less welfare-reducing thanan exclusive capital income tax. These results are due to the fact that taxes on laborincome and capital income distort investment decisions in reproducible capital, i.e.,human capital and physical capital, and therefore have cumulative effects that do notresult from a tax on consumption. Unlike previous studies, we account for the welfareeffects of transition using optimal decision rules all along the transition path.
Keywords: Endogenous growth, tax policy analysis, welfare, public capital, humancapital
JEL Codes: O41, E62, H54
2
1 Introduction
This paper examines the consequences for economic growth and welfare of distortionary
taxes used to finance public capital in an endogenous growth model where public capital
creates a positive production externality as in Barro (1990). The model that we employ
differs from existing literature that either assumes exogenous growth, in which case there
are no long-run distortionary effects on growth, and/or there is no role for public capital in
the production process. We examine these issues from the perspective of shifting taxes from
the status quo, to which the model is calibrated, to alternative tax regimes, thus requiring
a period of transition as the economy adjusts to a new balanced growth path.
Previous analyses of tax distortions that compare alternative tax regimes either ignore the
transitional dynamics (as in King and Rebello, 1990) or use approximations to characterize
the transition paths (such as Mulligan and Sala-i-Martin, 1992).1 In this paper, we employ
a novel reverse-shooting algorithm introduced into economic modeling by Atolia and Buffie
(2009b), in which the decision rules coincide with exact solutions to the saddle-path equilibria
and thus avoid the approximation errors. We highlight the importance of accounting for the
transition when assessing the cumulative welfare consequences of a change in tax policy.2
The theoretical and empirical relevance of human capital in the process of economic
growth is discussed in the survey article by Temple (1999), wherein evidence indicates coun-
tries with high levels of human capital tend to have high levels of income. While investments
in human capital should bolster growth, the proposed mechanisms for increasing the rate of
accumulation of human capital are diverse. They include schooling, parental education, on-
the-job training, and learning-by-doing.3 Romer (1990)-style R&D-based endogenous growth
models also rely on human capital intensive processes to generate growth.4 In this paper, we
choose to use the Lucas (1988)-Uzawa (1965) model of investment in human capital through
the allocation of time that is taken away from either production or leisure. Human capital
is incorporated into the production function as labor-augmenting.
The class of models that treats public capital as generating a production externality relies
1 Also, see Futagmai, Morita and Shibata (1993), Mino (1990), Lee (1992), Einarsson and Marquis (2001),and Greiner (2005).
2 In a companion paper (Atolia, Awad, and Marquis, 2009), we demonstrate that the approximationerrors in a theoretical framework such as the one employed in this paper can be very large.
3Among the vast literature on the subject, see especially Stokey (1988, 1991a, 1991b); Lucas (1988,1993);Barro and Sala-i-Martin (1992); and Barro (1999).
4Other models in this literature include Aghion and Howitt (1992), Jones (1995), and Young (1998),among others.
3
on two empirical facts. First, expenditures on public capital represent a significant share
of GDP. (See Arrow and Kurz, 1969; Shah, 1992; Ratner, 1983; Tatom, 1991; Nadiri and
Mamuneas, 1994; Seitz, 1994; and Romp and de Haan, 2007.) Researchers such as Aschauer
(1989a,b) have offered persuasive arguments that public capital plays an important role in
economic development. Modeling public capital as a production externality, as we do in this
paper, is consistent with the practice of maintaining constant returns to factor inputs that
are endogenously chosen by firms that have no control over either the flow or stock decisions
of public capital.
The complexity of modern theoretical macroeconomic models used to analyze such issues
as distortionary taxes has led researchers to rely heavily on linear approximations of the
nonlinear dynamic system in order to compute approximate values for welfare gains and
losses across tax regimes inclusive of transitional periods. Noting that these errors can be
very large, Schmidt-Grohe and Uribe (2004) have examined the second-order approximations
using a perturbation method and found that significant reductions in approximation errors
are possible. However, the order of approximation required to reduce the errors to acceptable
levels is both model-specific and specific to the exercises that are being carried out for a given
model. We avoid these potential problems by employing the reverse-shooting algorithm of
Atolia and Buffie (2009b)5 which compute exact solutions.
The fiscal policy experiments in this paper begin with a model calibrated to the current
U.S. tax regime of the capital income, labor income, and consumption tax rates. For the
basis of comparison, we first compute the transitional dynamics and the cumulative welfare
gains (losses) associated with a shift to a nondistortionary lump-sum tax regime. We then
conduct similar experiments for shifts from the current status quo to exclusive reliance in
turn on a capital income tax, a labor income tax, and consumption tax, with the results for
each alternative tax regime compared to the shift to the nondistortionary regime.
In the long-run, we find that consumption taxes are preferable to the current tax regime,
which is preferred to an exclusive labor income tax regime, with capital income taxes the
most welfare-reducing. However, in the short-run, cumulative welfare gains and losses are
very different from the long-run consequences for welfare, and it may take many years for
the long-run gains or losses to be fully realized. For example, while a shift to consumption
tax raises overall welfare (and long-run growth), it takes almost a generation (36.7 years)
for the accumulated welfare gains to turn positive. More importantly, the tax regime that
5This algorithm is also used in a fiscal policy experiment by Atolia, Chatterjee, and Turnovsky (2008).
4
produces the highest growth rate is not necessarily the one that coincides with the highest
welfare. In fact, a shift to capital income tax while delivering highest long-run growth results
in lowest welfare. It is even dominated by a shift to labor income tax where the long-run
growth comes to an almost complete halt.
The remaining part of this paper is organized as follows. The model is described in
section 2 whereas details of solving the model are outlined in section 3. Section 4 calibrates
the model to U.S economy. The results for the alternative fiscal policy experiments are
contained in section 5. Section 6 concludes.
2 The Model
We work with continuous-time model with no uncertainty so that the decisions are made
with perfect foresight. The economy is closed and is populated by infinitely-lived homogenous
households.
The representative household derives utility from consumption, c, and leisure, l and is
endowed with one unit of time. It chooses the optimal time paths for consumption, leisure,
time devoted to production (or labor supply) and time devoted to the accumulation of human
capital in order to maximize its lifetime utility. It obtains income from renting his private
physical capital to the firm and receives a wage payment for the time devoted to production.
This income is allocated between consumption and private physical capital accumulation.
Therefore, the only direct form of saving for the household is in the form of private physical
capital accumulation. However, the household can also transfer resources to future indirectly
by accumulating human capital. In addition to the private physical capital and “effective”
units of labor, there is also public physical capital in the model that enters as an externality
in the production function.
The government collects revenue only through taxation; there are no other sources of
revenue. The government levies tax on the income from private physical capital. It also
levies a tax on the labor income of the household. The consumption expenditures are also
taxed. There is also a lump-sum tax available to the government. Tax revenue is used to
finance public capital accumulation and transfers.
5
2.1 Households
The representative household derives its utility from nonnegative streams of consumption,
c, and leisure, l, according to the following per-period utility function, which is logarithmic
in consumption and leisure
u(c, l) = log c + η log l, (1)
where u is defined on <++. It is continuous and strictly increasing in l and c, twice con-
tinuously differentiable and strictly concave. The log specification, which implies elasticity
of intertemporal substitution and coefficient of risk aversion of 1, is used following Marquis
and Einarsson (1999a, 1999b).
The household receives income, rk, from renting physical capital to the firm, where k is
the stock of private physical capital and r is real rental rate. It also receives labor income,
whn, for the time devoted to the production, n, which given the household’s stock of human
capital, h, corresponds to hn effective units of labor that are paid a wage rate of w. In
addition, it receives transfers, T , from the government and profits, π, from the firms in the
form of dividends. After the payment of taxes, net income in excess of consumption is used
to accumulate private physical capital. Accordingly, the household’s budget constraint is
where k is net investment in private physical capital, δk ∈ (0, 1) is the rate of depreciation
of private physical capital, τk, τn and τc are marginal tax rates on private physical capital,
labor and consumption, and X is the lump-sum tax.
In addition, the household is also constrained in the time it can allocate to leisure,
production, and accumulation of human capital, m, as
l + m + n = 1. (3)
The time devoted to human capital accumulation results in an increase in h according to the
following evolution process:
h = γmh− δhh, (4)
where γ > 0 is a productivity parameter and δh ∈ (0, 1) is rate of depreciation of human
capital. It may be noted that the evolution rule for the human capital is linear in the current
6
state of human capital which generates the endogenous growth in the model. The human
capital evolution equation above was used by Lucas (1988) without a depreciation of human
capital. Accounting for the depreciation of the private human capital is widely recognized
in the literature. See for example Marquis and Einarsson (1999a) and Heckman (1976).
The household maximizes its life time utility by choosing c, l,m, and n
max{c,l,m,n}
∞∫0
e−ρtu(c, l)dt, (5)
where ρ is rate of time preference and e−ρt is the corresponding discount factor. This maxi-
mization is subject to constraints in (2), (3) and (4) and the initial conditions k(0) = ko and
h(0) = ho, where ko and ho are the levels of private physical capital and human capital in
the economy at t = 0.
2.2 Firms
Output, y, is produced using the economy’s resources of public physical capital (kg), private
physical capital, private human capital and labor. The technology is Cobb-Douglas and is
given by
y = f(k, n; h, kg) = Akgα1kα2(hn)1−α2 , (6)
where A, α1, α2 are parameters, with α1, α2, (α1 + α2) ∈ (0, 1), A > 0. Thus, the technology
exhibits constant returns to scale in private capital, which includes the private physical
capital stock and the human capital stock. The parameter α2 is the private physical capital’s
share of output. The parameter A is a scaling parameter.
Furthermore, as seen in (6), output depends on the available stock of government-provided
public capital, which enters as an externality in the production technology and is taken as
given by the firm. The parameter α1 can be interpreted as the elasticity of output with
respect to public physical capital. A higher value of α1 implies a greater externality. The
inclusion of the government spending in the production process was pioneered by Barro
(1990). In his model, it is the flow of government spending that enters the production
function as an external productive input. However, it is more realistic to assume that it is
not the flow of government spending, but the stock of public capital such as infrastructure
which enters the production function as is done here. In this sense, our specification follows
Futagami, Morita and Shibata (1993). (See Atolia, Chatterjee and Turnovsky (2008) for a
7
detailed discussion of the two forms of government spending contribution to output.) It may
be noted again that the firm only chooses k and n and takes the stock of h and kg as given.
2.3 Government
The government levies four types of taxes: a tax τk on gross physical capital income, rk; a
tax τn on effective labor income, whn, where hn is quality-adjusted or effective units of labor,
each unit of which earns a real wage, w such that wh is the hourly wage rate; a tax τc on
consumption expenditures, c; and lump-sum tax, X. The first three taxes are distortionary,
whereas the last lump-sum tax is non-distortionary. The government tax revenue, R, is,
therefore, given by
R = τkrk + τnwhn + τcc + X, (7)
where τk, τn ∈ [0, 1) and τc > 0 .
The tax revenue is used to finance the expenditure on accumulation of public capital (G)
and to provide transfers to the households. Therefore, the government’s budget constraint
is
G = R − T. (8)
The public physical capital evolves according to the following rule:
kg = G− δgkg, (9)
where δg ∈ (0, 1) is the rate of depreciation of public capital.
3 Solving the Model
The household’s optimization problem can be solved using the standard optimal control
method. The current-period Hamiltonian for the problem is:
H = u(c, l)+λ1(π + ((1− τk)r − δk)k + (1− τn)whn− (1− τc)c−X + T )+λ2(γ(1−l−n)−δh)h,
and the first-order conditions for the household are:
c : uc(c, l) = (1 + τc)λ1 (10)
8
l : ul(c, l) = λ2γh (11)
n : λ1(1− τn)wh = λ2γh (12)
The left-hand side of (10), uc, is the marginal benefit of consumption and the right-hand
side, (1 + τc)λ1, is the marginal cost, where λ1 is the marginal utility of wealth, and one
unit of consumption costs (1+ τc) units of wealth because of the tax rate τc on consumption.
Equations (11) and (12) show that the optimal allocation equates the marginal benefit across
all uses of time.
The co-state equations for k and h are
λ1
λ1
= ρ + δk − r(1− τk). (13)
λ2
λ2
= ρ + δh − γ(1− l), (14)
The firm works in a perfectly competitive environment taking goods and factor prices
as given. Its maximization problem is essentially static. Every period it rents private phys-
ical capital from the household and uses the household’s labor to maximize profits. Its
optimization problem is therefore
max{k,n}
π = Af(k, n; h, kg)− rk − whn, (15)
where wh is payment per unit of labor time and r is the private physical capital rental. The
first-order conditions for the firm are:
fk = r (16)
fn = wh (17)
Having solved the household’s optimization problem, we now turn to solve for the overall
general equilibrium of the economy. In particular, we solve for the competitive equilibrium.
The variables in the core dynamic system of the economy are c, l, k, kg and h.
The evolution of kg is governed by (9). From (4), using (3), one obtains the differential
equation for h as
h = (γ(1− l − n)− δh)h. (18)
In the perfectly competitive environment, the firm’s maximized profits are zero. Using this
9
result and substituting (7), (8) and (9) in (2), we obtain the economy’s resource constraint
which gives the transition equation for k
k = f(k, n; h, kg)− c−G− δkk. (19)
Note that this shows that the output of the economy is allocated to consumption and gross
investment in private and public physical capital.
The equation for the dynamic path of consumption can be derived from the co-state
equation for the corresponding Lagrange multiplier λ1. In particular, using (10) and (13),
we get
c = ((1− τk)r − (ρ + δk))c. (20)
To derive the l equation, we begin by obtaining the optimality condition for the labor-leisure
choice of the household by eliminating λ1 from (10) using (11) and (12). This yields
uc
(1− τn
1 + τc
)wh = ul. (21)
This equation on log-differentiating gives
l = l
(c
c− h
h− w
w
). (22)
The details of deriving equation for w are standard, and hence, skipped.
The evolution of the core dynamic system is governed by (9), (18), (19), (20) and (22).
The dynamics of the economy is also subject to following transversality conditions:
limt→∞
λ1(t)k(t) = 0, (23)
limt→∞
λ2(t)h(t) = 0. (24)
Before solving the core-dynamic system for the transition dynamics of the model, we
need to solve for the balanced growth path of the economy to which we turn next.
10
3.1 Solving for the Balanced Growth Path
Along the balanced growth path (bgp), all variables of interest (c, h, k, kg, and y) grow at
constant rates (including, possibly some at the zero rate) which may differ across variables. It
is clear from the time allocation constraint in (3), the time allocated to leisure, accumulation
of human capital and labor remains constant along bgp. Further, using standard procedures,
it is possible to show that consumption, output, private physical capital, and public capital
grow at the same rate (denoted φ) along the bgp. On the other hand, human capital grows
at a slower rate ν. These growth rates are related as follows:
φ =1− α2
1− α1 − α2
ν (25)
Furthermore, along the bgp, r is constant and is given by:
r =ρ + δk + φ
(1− τk), (26)
The private capital to output ratio and consumption to output ratio are constant as all these
variables grow at the same ratek
y=
α2
r(27)
c
k=
rα2
(1− τn(1− α2))−Xy−T
yky
− (φ + δk + τkr)
(1 + τc)(28)
Given the tax policy {τk, τn, τc} and X/y and the expenditure policy G/R, the government’s
budget constraint yields
T
y=
(1− G
R
)(α2τk + (1− α2)τn + τc
c
k
k
y+
X
y
)(29)
Finally, other equilibrium conditions yield following relationship among variables that do
not grow along the bgp.
ν = γm− δh (30)
l + m + n = 1 (31)
η =r
α2
(1− τn)(1− α2)l
(1 + τc)ckn
(32)
11
φ = (1− τk)r − (ρ + δk) (33)
Equations (25-33) are nine equations which can be solved for m, l, n, r, c/k, k/y, T/y,
φ, and ν.
3.2 Solving for Transitional Dynamics
Recall that the core dynamics of the economy can be expressed in terms of c, l, k, kg, and h.
However, as the model has endogenous growth, except for l, all these variables experience
constant growth after transitory response to a shock dies out. In order to solve for the
dynamics of the system, therefore, it is necessary to first transform the variables in the
core-dynamic system to the ones that are stationary, i.e., those that ultimately reach a finite
non-zero value.
We perform this transformation by normalizing the variables by the private physical
capital stock. Accordingly, we define following new variables: c = c/k, kg = kg/k, and
h = hφ/ν/k. It is easy to see that c, kg and h are stationary variables. The equations
governing the evolution of stationary variables can be obtained from equations of the original
dynamic system as follows:
˙c =
(c
c− k
k
)c (34)
˙kg =
(kg
kg
− k
k
)kg (35)
˙h =
(φ
ν
h
h− k
k
)h (36)
wherein one can show that
k
k=
r
α2
(1 +
T
y− X
y
)− r
(α2τk + τn(1− α2)
α2
)− (1 + τc)c− δk, (37)
kg
kg
=1
kg
[r
(τkα2 + τn(1− α2)
α2
)− (1 + τc)c +
(X
y− T
y
)y
k− δgkg
]. (38)
The core-dynamic system in normalized variables, c, k, kg and l, consists of (34), (22),
(37) and (38). Having solved this system, we can use (37) to solve for the path of k. The
levels of other variables then follow immediately.
12
3.2.1 Numerical Solution of the Transition Dynamics
In the existing literature, transition dynamics is typically analyzed using linearization. Re-
cently, Schmidt-Grohe and Uribe (2004) have suggested second-order approximation method.
While a number of methods (e.g. projection methods and shooting methods) are now avail-
able to provide more accurate solutions, they are rarely being used.
Recently, in a series of papers Atolia and Buffie (2009a and 2009b) have developed reliable
and user-friendly program to accurately solve dynamic general equilibrium models such as one
of this paper. We use their reverse-shooting program ReverseShoot2D to solve for the global
nonlinear saddlepath of our model. It turns out (and as we show in a companion paper) that
linearization and lower-order Taylor series solutions fail to correctly assess the welfare effect
of the fiscal policy changes that are analyzed in the paper. The failure occurs due to errors in
the solution of the transitional dynamics. By solving for the global nonlinear saddlepath, this
paper avoids these problems and, to our knowledge, for the first time provides an accurate
assessment of the welfare effects of government policy changes in an endogenous growth
model. We present these results in section 5, however, before we can numerically solve the
model, it needs to be calibrated; a task that we undertake in the next section.
4 Calibrating the Model to the Benchmark
There are 22 unknowns in our model: nine endogenous variables (m, l, n, r, c/k, k/y, T/y,
φ, and ν), eight parameters (α1, α2, δk, δh, δg, ρ, η and γ), and five exogenous variables
(X/y and G/R, τk, τn and τc). We use the nine equations to solve for m, l, r, c/k, T/y, ν, ρ,
γ and η and use estimates from the previous literature and empirical data to get the values
φ, α1, α2, δk, δh, δg, τk, τn, τc, n, k/y and G/R. The ratio of lump-sum taxes to output,
X/y, is set to zero in the initial steady-state. Recall, we assume that the entire government
tax revenue in the initial steady-state is collected only from the proportional distortionary
taxes. The calibration results are summarized in Table 1.
Per capita output growth rate (φ). In the last 50 years, (1961-2005), the average long-
run growth rate of output per capita in the United States reached approximately 2.2% as
shown by the World Bank data in Figure 1, which plots of the U.S. growth rate during this
period. The dotted line represents the trend line for the same period. However, in our model
here we set φ to 1.8% based on evidence in Barro (1990). The logic behind our selection is
that Barro’s time series extends for a longer time span from 1870 to 2000.
13
y = -0.0183x + 2.6181
-3
-2
-1
0
1
2
3
4
5
6
7
1961
1963
1965
1967
1969
1971
1973
1975
1977
1979
1981
1983
1985
1987
1989
1991
1993
1995
1997
1999
2001
2003
2005
Years
Gro
wth
Rat
e (%
)
Source: World Resources Institute, 2007.
Figure 1: Historical Per Capita Growth Rates in the US (1961-2005)
Elasticity of output with respect to public physical capital (α1). Based on the
evidence provided by Gramlich (1994), the elasticity of output with respect to public physical
capital, or, alternatively, the productivity elasticity of government spending, might range
from 0.1 to 0.2. We set α1 to 0.1 in our model, which is in the range of values used in the
literature. (See Atolia, Chatterjee and Turnovsky, 2008).
Private physical capital share of output (α2). The most frequently assigned value for
α2 in the literature is 0.36. (See for example Kydland and Prescott, 1982; Hansen, 1985; and
Prescott, 1986). A higher value of 0.4 was set by Cooley and Prescott (1995) to account for
the imputed income from public physical capital. However, since public capital is explicitly
considered in our model, a value of α2 between 0.30 and 0.36 may be more appropriate.
Accordingly, a value of 0.337 is assigned for α2 based on a more recent work by Einarsson
and Marquis (1996). They arrived at this value using long-term empirical U.S. data for the
period (1950-1994).
Depreciation rate of private physical capital (δk). Atolia, Chatterjee and Turnovsky
(2008) set this rate to 0.05, whereas Marquis and Einarsson (1999a) set it to 0.0512 in
their calibrated dynamic general equilibrium model of endogenous growth. These are typical
values used in the literature and, following them, we set δk = 0.05.
Depreciation rate of human capital (δh). There is a considerable variation in the choice
of δh in the literature. For example, Haley (1976) uses a value as low as 0.005, whereas
Heckman (1976) sets it to 0.047. In a more recent work, Einarsson and Marquis (2001)
choose a value of 0.05 which is obtained as a rough average of the estimated values from
14
the literature on the labor market. We choose δh = 0.015. A detailed discussion about the
estimation of this rate can be found in Mincer and Ofek (1982). 6
Depreciation rate of public capital (δg). We take the value of 0.035 used by Atolia,
Chatterjee and Turnovsky (2008). Note that the rate of depreciation of public physical
capital is lower than the private physical capital. This captures the fact that public physical
capital is mostly infrastructure which depreciates at a slower pace than plant and machinery.
Time allocated to production (n). Greenwood and Hercowitz (1991) calculated the
average ratio of total hours worked to total nonsleeping hours (16 hours per day) of the
working age population to be .24 while Einarsson and Marquis (2001) use .36. We go with
Einarsson and Marquis and set n = 0.36.
Private physical capital to output ratio (k/y). We set this ratio to 2.17. This value
is obtained from the data for the private physical capital and gross domestic product in
current dollar value in National Income and Product Accounts (NIPA) tables prepared by
the Bureau of Economic Analysis (BEA) at the US Department of Commerce. The data in
the tables covers the post WWII period (1946-2006). Figure 2 shows the time path of k/y
based on this data.
y = 0.0039x + 2.0487R2 = 0.2077
1.9
2.0
2.1
2.2
2.3
2.4
2.5
2.6
1946
1949
1952
1955
1958
1961
1964
1967
1970
1973
1976
1979
1982
1985
1988
1991
1994
1997
2000
2003
2006
Years
k/y
US Department of Commerce, 2008.
Figure 2: Private Physical Capital to Output Ratio in the United States (1929-2006)
Gross public investment to total tax receipts ratio (G/R). To estimate this ratio, we
again use the data for the post-WWII period (1946-2006) obtained from the BEA’s NIPA
tables. The average gross public investment to total tax receipts ratio for the period is 19.1%,
6The value of δh is controversial. However, a change in δh will only affect the allocation of non-work timebetween accumulating human capital and depreciation. For example, if δh = 1%, then the values that willchange in Table 1 are l, m, and η. They change as follows: lo = 0.452, mo = 0.188 and η = 0.74.
15
which is the number we use here. The time path of this ratio based on BEA’s data is shown
in Figure 3.
Table 1: Calibration to the Benchmark
Output Shares and Depreciation Rates α1 α2 δk δh δg
0.1 0.337 0.05 0.015 0.035
Data for Calibration k/y G/R n
2.17 0.191 0.36
Government Policy X τc τn τk
0 7% 25% 25%
Deep Parameters of the Model ρ γ η
.0485 .1347 0.67
Consumption and Time Allocations c l m
0.366 0.415 0.225
State Variables h kg y c/y
0.95 0.507 0.461 0.794
Human Capital & Output Growth ν φ
1.53% 1.80%
Tax rates (τk, τn, τc). For the capital income tax rate and labor income tax rate, Turnovsky
(2004) set these both rates to 28%. Here we set the benchmark values to 25%, following the
works of Greenwood and Hercowitz (1991) and Einarsson and Marquis (2001) who discuss
in greater detail the selection of their values. Regarding the consumption expenditure tax
rate, we set this rate as the pure U.S. sales tax rate which is currently 7%.
5 Results
Along the initial bgp, the only sources of government revenue are proportional distortionary
taxes. There is no lump-sum tax. The fiscal policy maintains a budget balance. We begin
by quantifying the distortion caused by the existing tax regime. For this, we consider an ex-
periment where the government replaces the distortionary tax regime with non-distortionary
16
y = -0.0013x + 0.2329
0
0.05
0.1
0.15
0.2
0.25
0.3
1946
1949
1952
1955
1958
1961
1964
1967
1970
1973
1976
1979
1982
1985
1988
1991
1994
1997
2000
2003
2006
Years
G/R
(%)
US Department of Commerce, 2008.
Figure 3: Gross Public Investment to Total Tax Receipts Ratio in the United States (1929-2006)
lump-sum taxes. The ratio of government revenue to GDP along the new bgp is the same as
for the initial bgp. Thus, the policy change is budget neutral. Furthermore, G/R, the ratio of
public physical capital to government revenue remains unchanged as well. In addition, with
the value of G/R determined exogenously and assumed constant, the government budget
constraint implies that the government can manipulate a maximum of three out of the four
policy tools, τc, τk, τn, X/y.
While the evaluation of the current tax regime by considering lump-sum taxation is
insightful, in practice governments do not have access to lump-sum taxes. We, therefore, next
turn attention to tax policies in which only distortionary taxes are available. In particular,
we assess the positive and normative implications of a movement to a tax regime that relies
only on one source of taxation. Comparing the outcome with the lump-sum taxation allows
us to evaluate the distortionary effect of each source of taxation.
Before we present the results, it is instructive to understand the nature of distortionary
effects of taxes on consumption expenditures, labor income, and private physical capital
income relative to financing of government revenue using lump-sum taxation.
The tax on capital is a source of intertemporal distortion which reduces saving. This
reduction in saving lowers the overall productive capacity of the economy as stocks of both
private and public physical capital decline. Consequently, consumption is reduced. Note
that the stock of public physical capital declines as the economy contracts thereby reducing
government revenues. As physical capital and human capital are gross complements in
17
production, a reduction in physical capital also reduces the marginal product of human
capital. The household responds by reducing the time devoted to the accumulation of human
capital and taking more leisure. Thus, the stock of human capital declines as well.
The labor income tax distorts decisions by reducing the return to human capital. The
household again respond by reducing time devoted to human capital accumulation and taking
more leisure. Thus, productive capacity of the economy falls thereby reducing consumption
as the stock of human capital falls. As stated previously, the gross complementarity of human
and physical capital then reduces return to private physical capital reducing incentive to save
and invest. The resulting decrease in physical capital stock further reduces the growth in
the economy.
The tax on consumption results in intra-temporal distortion raising the cost of consump-
tion. The household substitute away from consumption toward leisure. The extra leisure
time comes at the expense of time devoted to human capital accumulation. This reduces the
stock of human capital in the economy. While a consumption tax does not directly cause
intertemporal distortion reducing saving, the reduction in human capital does reduce the
productivity of private physical capital reducing the incentive to save. As a result, the stock
of private physical capital declines as well. The public capital stock falls as the economy as
a whole becomes smaller. Thus, in the end, the growth rate of the economy falls.
5.1 Experiment 1: Shift to Lump-Sum Taxation
In this section, we begin by assessing the extent of the tax distortion in the initial equilibrium.
For this purpose, we consider the experiment where all distortionary taxes are replaced by
non-distortionary lump-sum taxes. Note that the ratio of tax revenue to GDP remains
unchanged and so is the fraction of government revenue devoted to public investment. Figure
4 depicts the response of the main economic variables to this unanticipated change in the
governmental policy. The figures depict the ratios (normalized variables), logarithms, and
growth rates respectively. In each panel, the initial steady-state bgp that prevailed in the
economy before the new policy is shown as the solid line for t < 0. For t ≥ 0, the solid line
reveals the equilibrium path resulting from the new fiscal policy. The dotted line shows the
evolution of variables along the initial bgp in the absence of the change in the tax rates. The
response of various variables across the two balanced growth paths is summarized in Table
2.
As the taxes on physical capital income, labor income, and consumption are removed, the
18
accompanying distortions disappear which, as expected, improves welfare. We follow Atolia,
Chatterjee, and Turnovsky (2008) in using the Lucas’s method to assess the welfare gain in
terms of a proportional increase in consumption, ζ, along the initial bgp that delivers same
utility as the new tax policy. According to this measure, the shift to lump-sum taxation
confers a welfare benefit equivalent to 9.78 per cent increase in consumption.
In particular, the removal of the tax on private physical capital encourages the accu-
mulation of private physical capital, and the removal of tax on labor income motivates the
accumulation of human capital. As explained earlier, however, a reduction in all taxes ul-
timately gives impetus to the accumulation of both types of private capital either directly
or indirectly which raises the rate of growth of the economy. In fact, φ increases from 1.8%
along the initial bgp (benchmark) to 4.2% along the final bgp. Note that this growth rate is
fueled by the increase in the rate of growth of human capital. As Table 2 shows, ν increases
from 1.5% to 3.6%.
The higher rate of growth of human capital along the bgp implies that the time devoted
to human capital accumulation increases. This fact is evident in Table 2 which shows that m
jumps from 0.225 to 0.376. This increase comes at the expense of time devoted to leisure as
the time devoted to production does not change. Similarly, the higher rate of growth of the
private physical capital increases the investment as share of GDP. Accordingly, consumption
as share of GDP declines from 0.794 to 0.721.7
There are two determinants of return to capital that move in opposite direction as a
result of the change in the tax policy. The elimination of distorting capital tax reduces the
divergence between the private and the social marginal return to private physical capital
which reduces the required return on capital, r, as (26) shows. This boosts the private
physical capital accumulation as referred to earlier. However, as capital accumulation in
the economy (including that of private physical accumulation) rises, the growth rate, φ,
increases, and there is a second round effect that counteracts the fall in the required rate of
return on private physical capital (see (26)). The reason is that the increased growth in the
economy causes the marginal utility of wealth or consumption (λ1) to decline faster making
the household reluctant to save and therefore requiring higher compensation or return on
capital. As the initial effect dominates, r declines from 15.5 per cent to 14.0 per cent which
in turn implies an increase in private physical capital to output ratio (k/y) as Table 2 shows.
The impact effect of the tax policy change on macroeconomic behavior is very similar
to the long-run effect, but there are some differences. First the similarities. There is a
sharp increase in investment in private physical capital accumulation and the time devoted
to human capital accumulation whereas time devoted to leisure falls. However, note that
m increases by a smaller amount on impact than in the long run (Figure 4). On the other
hand, the investment in private capital accumulation overshoots it long-run rate (see path
7Note that the share of public investment to GDP is unchanged.
21
of φk in Figure 4).
The reason that m rises by less in the short run is that the reduction in tax on labor
raises the return on effective labor supply immediately. While investment in human capital
takes advantage of this in the long-run, it cannot do so in the short run as human capital
accumulation takes time. On the other hand, the household can take immediate advantage of
higher return on labor by increasing effective labor supply by increasing the time devoted to
production. Finally, when human capital accumulation has occurred, this labor supply can
be shifted back to accumulation of human capital. This short-run increase in labor supply
also raises the return to private physical capital in the short run, although it falls in the long
run (see Figure 4).
The other difference in the short run is in the response of consumption, which is related
to the incentive for private physical capital accumulation. Although, an increase in time
devoted to production increases economy’s output, it is not enough to meet the increased
demand for investment in private physical capital. The excess investment demand is met
by reduction in current consumption (see Figure 4). The household is willing to sacrifice
current consumption as the current return adequately compensates the household for the
postponement of consumption by providing a high return.
The return on investment is high in the short run and, in fact, overshoots its long-run
value, as private physical capital is relatively scarce initially. This overshooting implies that
not only does the economy’s capital stock grows at a higher rate in the long run but it also
reaches a higher level.
The fact that not only leisure but also consumption falls in short run implies that the
welfare gains are not realized immediately. Figure 5 shows the accumulated welfare gains
over different horizons. Accumulated welfare gain over a time horizon t is calculated as the
proportional increase in consumption (ζ) required over period 0 to t, along the initial bgp, to
deliver same utility over this period as the new policy (see Atolia, Chatterjee, and Turnovsky,
2008). As Figure 5 shows, welfare rises in the long run. However, note that this long-run
increase in welfare comes at a considerable sacrifice in the short run. The short-run welfare
cost amounts to as high as 30 per cent of consumption or more. It takes the economy more
than 50 years (56.1 years) to break even in the sense that it is only after 56.1 years that
utility level exceeds the utility that the household would enjoy along the initial bgp over the
same time horizon.
22
0 50 100 150Years
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2Ζ
Figure 5: Accumulated Welfare Gains From Permanent Shift to Lump-Sum Tax
5.2 Experiment 2: Capital Income Taxation
In this section, we evaluate the distortionary effect of a tax on private physical capital. For
this purpose, we consider a move from the existing tax regime to sole reliance on a capital
income tax. The resulting distortion is assessed by comparing the response of the economy
for a switch to capital income tax versus a switch to lump-sum tax.8 The shift to capital
income tax raises τk to 90.7 per cent. The resulting paths of variables of interest are collected
in Figure 6. The changes across the balanced growth paths are summarized in Table 3.
The removal of tax on labor income and consumption both provide impetus to build
human capital. Accordingly, m rises from 0.225 to 0.302 (see Table 3). On the other hand,
a large increase in taxation of capital substantially reduces the incentive to save and invest.
As a result, the economy’s stock of private capital falls significantly. As Table 3 shows, the
values of all variables in the core dynamic system such as c, h, and kg rises as these variables
are normalized by k. This outcome is exactly opposite of that for shift to lump-sum taxation
as seen from Table 2. As expected, a shift from capital income taxation to lump-sum taxation
would increase the relative availability of private physical capital.
8An alternative plausible experiment would be replace the initial capital income tax with lump-sumtaxation but such an experiment would confound the distortionary effect of capital income taxation with theinteraction effects between capital income tax and other taxes.
Temple, J. The new growth evidence. Journal of Economic Literature, 37(1):112-156, March
1999.
Turnovsky, S.J. The transitional dynamics of fiscal policy; long-run capital accumulation
and growth. Journal of Money, Credit, and Banking, 36(5):883–910, October 2004.
Young A. Growth without scale effects. Journal of Political Economy, 106(1):41, February
1998.
Uzawa, H. Optimum technical change in an aggregative model of economic growth. Inter-
national Economic Review, 6(1):18-31, 1965.
39
Linearization and Higher-Order Approximations:How Good are They?∗†
Results from an Endogenous Growth Model with Public Capital
Manoj AtoliaFlorida State University ‡
Bassam AwadFlorida State University §
Milton MarquisFlorida State University ¶
First Draft: October 2009
∗Based on the second chapter of PhD dissertation of Bassam Awad.†We are very grateful to Paul Beaumont, Tor Einarsson, Bharat Trehan and other participants of the
Macro summer workshop, 2008, at Department of Economics, Florida State University where an earlierversion of this paper was presented. All errors are ours.‡Department of Economics, Florida State University, Tallahassee, FL 32306, U.S.A. Telephone: 850-644-
7088. Email: [email protected].§Department of Economics, Florida State University, Tallahassee, FL 32306, U.S.A. Telephone: 850-567-
2085. Email: [email protected].¶Department of Economics, Florida State University, Tallahassee, FL 32306, U.S.A. Telephone: 850-645-
The standard procedure for analyzing transitional dynamics in non-linear macromodels has been to employ linear approximations. Recently quadratic approximationshave been explored. This paper examines the accuracy of these and higher-order ap-proximations in an endogenous growth model with public capital, thereby extendingthe work done in the current literature on the neoclassical growth model. We findthat significant errors may persist in computed transition paths and welfare even af-ter resorting to approximations as high as fourth order. Moreover, the accuracy ofapproximations may not increase monotonically with the increase in the order of ap-proximation. Also, as in the previous literature, we find that achieving acceptablelevels of accuracy when computing the welfare consequences of a policy change typi-cally requires a higher order approximation than attaining similar levels of accuracy inthe computation of the transition path: typically an increase in order of approximationby one is sufficient.
Keywords: Linearization, higher-order approximations, endogenous growth, welfare,public and human capital
JEL Codes: O41, C61, C63
2
1 Introduction
The importance of transitional dynamics for understanding the consequences of various
macroeconomic policies has received much attention in the literature. When the policy
changes are large, a welfare analysis based on comparisons across steady states or balanced
growth paths can be very misleading, often overstating the welfare effects. (See, for example,
Turnovsky (1992,1996) and Einarrson and Marquis (1999,2002).) Until recently, the analysis
of the transition paths and their consequences for the computation of welfare were conducted
using linear – or at best quadratic – approximations to decision rules that govern behavior
along the final (post-policy change) balanced growth path. The fact that optimal decision
rules are not stationary along the transition was ignored.1
The development of computational techniques that could be used to establish time-
varying optimal transition paths appropriate for the analysis of the time path of the econ-
omy and the attendant welfare consequences of once-and-for-all policy changes has been the
subject of work by Becker, Grune, and Semmler (2007), Turnovsky (2000), and Atolia, Chat-
terjee and Turnovsky (forthcoming) which apply the shooting algorithms of Judd (1998) and
Brunner and Strulik (2002), and Atolia and Buffie (2009).
The purpose of this paper is to extend the work of Atolia et al. (forthcoming) who ap-
plied the reverse-shooting algorithm to examine the accuracy of first-order approximation
(linearization) methods in describing the transition path and the welfare consequences of an
economy in which a significant fiscal policy reform is undertaken. In their model, public cap-
ital plays an important role in generating externalities that affect the economy’s transitional
dynamics. We consider two extensions. The public capital externality is examined in the
context of a growth model in which growth depends on the investment in human capital as
in Uzawa (1966) and Lucas (1988).2 This change introduces an important new dimension
to the optimal transition path. Second, we do not limit our comparisons of the accuracy of
approximate decision rules to first-order, but consider up to fourth-order approximations.
We obtain several results in this model that appear to be quite general, in that they are
likely to be present in other models where transitional dynamics play an important role in
1We use the term ‘optimal’ to mean welfare-maximizing decision rules in an economy with distortions,which of course is not Pareto optimal.
2We note that Turnovsky (1996) examined fiscal policy issues in an AK model, whose transitional dy-namics differs considerably from an Uzawa-Lucas type model. The work of Turnovsky has motivated sev-eral later works analyzing different aspects of alternative fiscal policies. See for example Petrucci (2009),Gokan(2008a,b), Baier (2001), Fung(2000), Turnovsky(1997), and Palivos (1995).
3
the analysis:
• The order of approximation required to obtain a tolerable level of accuracy in terms of
characterizing the transition path may not be the same as the order of approximation
required to obtain acceptable accuracy in the computation of welfare, which generally
requires a higher-order approximation.
• The order of approximation required to obtain acceptable accuracy varies with the
manner in which the tax distortions in the economy are varied under a fiscal policy
reform.
• While higher-order approximations tend to improve the accuracy of the welfare cal-
culations, these improvements are not universally monotonic with increasing order.
For some parameterizations of the model, second-order approximations do not yield
transitional patterns or welfare calculations that are superior to first-order.
• Finally, even fourth-order approximations can be insufficient to obtain acceptable levels
of accuracy.
The paper proceeds with a description of the model in Section 2, the solution of the
economy’s balanced growth path and the calibration exercise in Sections 3, the solution of
the transitional dynamics in Section 4, the fiscal policy exercises in Section 5, and sensitivity
analysis in Section 6. Section 7 concludes.
2 The Model
In this perfect foresight representative agent economy, households choose time allocations
between labor, leisure, and human capital accumulation. The last of these ultimately de-
termines the rate of growth of the econmoy. Public capital introduces a positive externality
in production and is funded by a combination of consumption, labor income, and capital
income taxes, while the government runs a balanced budget.
2.1 Household’s Optimization
The household maximizes lifetime utility by choosing time paths for consumption, c, and its
allocation of time between leisure, l, labor, n, and human capital accumulation, m.
4
max{c,l,m,n}
∞∫0
e−ρtu(c, l)dt, (1)
where ρ is rate of time preference and e−ρt is the corresponding discount factor, and the CES
felicity function is given by:
u(c, l) =
11−µ
[(clη)1−µ − 1
]if µ > 1,
log c+ η log l if µ = 1.(2)
where µ−1 is the intertemporal elasticity of substitution.
The household faces a budget constraint that determines its gross investment in private
physical capital, k, as its income less its consumption, its taxes, and the depreciation loss in
capital, δkk, where δk ∈ (0, 1) is the depreciation rate. It receives income from labor, whn,
where w is the wage rate paid on effective units of labor, hn, with h equal to the household’s
stock of human capital, its rental income from capital, rk, where r is the real rental rate,
dividends from the (aggregate) firm, π, which are a per capita share of the firm’s profits, and
a lump-sum transfer from the government, T . In addition to a lump-sum tax, X, (which
may be zero), the household faces tax rates of τc on consumption, τn on labor income, and
τk on capital income.
k = π + rk + whn+ T − c− δkk − (τkrk + τnwhn+ τcc+X), (3)
The technology available to the household to build human capital is given by:
h = γmh− δhh, (4)
where γ > 0 is a productivity parameter and δh ∈ (0, 1) is rate of depreciation of human
capital.3
The time resource constraint is:
l +m+ n = 1 (5)
3It may be noted that the evolution rule for the human capital is linear in the current state of humancapital which generates the endogenous growth in the model. The human capital evolution equation abovewas used by Lucas (1988) without a depreciation of human capital. Accounting for the depreciation of theprivate human capital is widely recognized in the literature. See, for example, Heckman (1976) and Marquisand Einarsson (1990).
5
This maximization of (1) is then subject to constraints (3), (4) and (5), the initial con-
ditions k(0) = ko, h(0) = ho, kg(0) = kgo, and the transversality conditions:
limt→∞
λ1(t)k(t) = 0 (6)
limt→∞
λ2(t)h(t) = 0 (7)
where ko, ho, kgo are the levels of private physical capital stock, human capital stock, and
public physical capital stock in the initial state of the economy and λ1 and λ2 are the
Lagrange multipliers on (3) and (4).
The maximization yields the following Euler equation for the labor-leisure decision and
co-state equations for investments in private physical capital and human capital:
uc(1− τn)wh = ul(1 + τc) (8)
λ1
λ1
= ρ− r(1− τk) + δk (9)
λ2
λ2
= ρ− γ(m+ n) + δh (10)
where
λ1 = uc/(1 + τc) (11)
and
λ2 = ul/γh (12)
with uc and ul being the marginal utilities of consumption and leisure.
2.2 Firm’s Optimization
Output per capita, y, is determined by a technology that transforms the economy’s resources
of public and private physical capital, private human capital and labor into desired output
goods. The technology assumes the following constant elasticity of substitution (CES) form:
6
y = f(k, n;h, kg) =
A[(1− α2)(kg
θhn)(1− 1σ
) + α2k(1− 1
σ)]( 1
1− 1σ
)if σ 6= 1;
Akgα1kα2(hn)1−α2 if σ = 1
(13)
where A,α1, α2 are parameters, with α2 ∈ (0, 1), A > 0, and θ = α1
1−α2.
As seen in (13), output depends on the available stock of government-provided public
capital, kg, which enters as an externality in the production technology and is taken by the
firm as given. The parameter α1 can be interpreted as the elasticity of output with respect
to public physical capital. A higher value of α1 implies a greater externality.4
The firm operates in a perfectly competitive environment taking goods and factor prices
as given. Its profit-maximization problem is essentially static, choosing the quantity of
private physical capital to rent from the household and the amount of labor to employ.
max{k,n}
π = Af(k, n;h, kg)− rk − whn, (14)
where whn is the firm’s wage bill with wh the unit labor cost, and rk is the rental
payment on private physical capital. The first-order conditions for the firm are:
fn = wh (15)
fk = r (16)
where fn and fk are the marginal products of labor and capital.
2.3 Government
The government levies four types of taxes: a tax τk on gross physical capital income, rk; a tax
τn on effective labor income, whn; a tax τc on consumption expenditures, c; and lump-sum,
non-distortionary tax, X. Total tax revenue for the government tax can be written as:
R +X = τkrk + τnwhn+ τcc+X, (17)
4The inclusion of the government spending in the production process was pioneered by Barro (1990). Inthis model, we assume that it is not the flow of government spending, but the stock of public capital, such asinfrastructure, that enters the production function. In this regard, we follow Futagami, Morita and Shibata(1993). See Atolia, Chatterjee and Turnovsky (2008) for a detailed discussion of the two forms of governmentspending contribution to output.
7
where τk, τn ∈ [0, 1), τc > 0. R represents the total tax revenue raised from distortionary
taxes.
This revenue is used to finance government spending on public capital (G) and to provide
transfers to the households. The government observes policy rules governing gross investment
as a share of output and lump-sum taxes as a share of output, which we write as:
G = G(y) (18)
and
X = X(y). (19)
Subject to these policy rules, the government runs a balanced-budget:
G = R +X − T (20)
Net investment in public physical capital is given by the government’s gross investment
less capital depreciation, or
kg = G− δgkg, (21)
where δg ∈ (0, 1) is the rate of depreciation of public capital.
2.4 Competitive Equilibrium
Equilibrium in the goods market is given by:
f(k, n;h, kg) = c+ k + δkk + kg + δgkg (22)
where output is allocated between consumption, gross investment in private capital, and
gross investment in public physical capital.
The dynamic path for the economy is found as the solution to the set of equations: (4),
(5), (8) – (22), given the economy’s initial state, k(0) = ko, h(0) = ho, kg(0) = kgo, which
satisfy the transversality conditions (6) and (7).
The model can reduced to a core dynamic system consisting of h, λ1, λ2, kg, and k that
are represented in the five differential equations (3), (4), (9), (10) and (21). It includes the
8
following endogenous variables r, w, y, π, G, X, T , R, c, l, m, and n which can be eliminated
from the system by using (5), (8), and (11) – (20). We then choose to replace the dynamic
shadow prices λ1 and λ2 in the core dynamic system by the control variables c and l using
(11) and (12), allowing us to solve the core system for the dynamic paths of c, l, k, kg, and
h.
3 Calibrating the Model for the Benchmark Balanced
Growth Path
Along the balanced growth path (bgp), the set of variables (c, k, kg, h) in the core system
are growing at constant, but not necessarily identical rates, while l is a constant. Of the
remaining variables, (G,X, T,R, π, w, y) are also growing at constant rates,5 while (r,m, n, l)
are constant.
As shown in the Appendix:
c
c=kgkg
=k
k=y
y=G
G=X
X=T
T= φ (23)
h
h= ν = (1− θ)φ (24)
w
w= φ− ν (25)
Note that equation (4) makes clear that the engine of growth is human capital; it drives
output growth. A lesser investment of time, m, in human capital will retard the economy’s
growth rate. However, the presence of public capital amplifies the effect of human capital on
output. That is, φ > ν when α1 > 0, or the higher the share of public capital in production,
α1, the wider is the gap between the growth rate of private physical capital and human
capital.6
5We note again that lump-sum taxes, X, may be zero.6We note that φ does not have an analytical solution in this model, but can be approximated arbitrarily
close with numerical methods.
9
3.1 Normalization
To calibrate the model, a normalization must be chosen that renders the model stationary.
We choose to normalize by the private physical capital stock, k. Given the different growth
rates for the system’s core variables, the normalization may also differ for the variables in the
model. Begin with c, kg, y, G, X, and T , which grow by the same rate, φ, as the normalizing
variable k, and define the normalized variables to be:
c =c
k, kg =
kgk, y =
y
k, G =
G
k, X =
X
k, R =
R
k, and T =
T
k. (26)
Human capital, h, grows at a rate ν. Therefore, a stationary normalization can be chosen
as:
h =h
1(1−θ)
k, (27)
The wage rate, w, grows at a rate (φ − ν), which suggests a stationary normalization
given by:
w =w
1θ
k(28)
We can now proceed with the calibration.
3.2 Calibration
The normalized model consists of fifteen equations: five from the household’s problem, con-
straints (4), the static Euler equation (5), and the co-state equations (8) – (10) (with the
multipliers eliminated); the output and profit functions (13) and (14) and two first-order
conditions from the firm’s problem, (15) and (16); four equations from the government sec-
tor, the accounting identity (17), two policy rules (18) and (19), and the balanced budget
(20); and goods market equilibrium (22). The fifteen endogenous variables are: m, l, n, r,
w, c, y, kg, h, T , X, G, R, φ, and ν. The model contains fourteen parameters: θ, µ, σ, α2,
δk, δh, δg, ρ, η, A, γ, and the tax rates τk, τn, and τc.
To solve the normalized model in steady state, we need fourteen constraints. We use
estimates from the previous literature and empirical data to get the values φ, α1, α2, δk, δh,
δg, τk, τn, τc, n, y and GR
. The normalized lump-sum tax, X, is set to zero and the scale
variable A is normalized to one. The solution determines the three deep parameters ρ, γ
10
and η that are consistent with the benchmark bgp. The discussion of the choice of unknown
parameters and key ratios follows.
Per capita output growth rate (φ). Over the 54-year sample period 1961-2005, the
average long-run growth rate of output per capita in the United States was approximately
2.2 percent. Over a longer time period from 1870 to 2000, Barro (2003) estimates a slightly
lower figure of 1.8 percent. We chose to use the Barro figure for our calibration.
Private physical capital share of output (α2). The most frequently assigned value for
α2 in the literature is 0.36. (See for example Kydland and Prescott (1982), Hansen (1985),
Cooley and Prescott (1995). A higher value of 0.4 was set by Cooley (1995) to account for
the imputed income from public physical capital. However, since the government is explicitly
set in our model, a value of α2 between 0.30 and 0.36 may be more appropriate. Accordingly,
a value of 0.337 is assigned for α2 based on a more recent work by Einarsson and Marquis
(1996). They arrived at this value using long-term empirical U.S. data for the period (1950-
1994) treating proprietor’s income as having the same share of labor income as the public
corporations.
Elasticity of output with respect to public physical capital [θ(1 − α2)]. Based on
the evidence provided by Gramlich, the elasticity of output with respect to public physical
capital, or, alternatively, the productivity elasticity of government spending, might range
from 0.1 to 0.2. We set θ(1 − α2) to 0.1 in our model. Which is essentially in the range
obtained in the empirical investigation. See Atolia, Chatterjee and Turnovsky (forthcoming).
And since α2 = 0.337, then the value of θ = 0.151.
Depreciation rate of private physical capital (δk). Atolia, Chatterjee and Turnovsky
(forthcoming) set this rate to 0.05, whereas Marquis and Einarsson (1996) set it to 0.0512 in
their calibrated dynamic general equilibrium model of endogenous growth. These are typical
values used in the literature and, following them, we set δk = 0.05.
Depreciation rate of human capital (δh). There is a considerable variation in the choice
of δh in the literature. For example, Haley (1976) uses a value as low as 0.005, whereas
Heckman (1976) sets it to 0.047. In a more recent work, Einarsson and Marquis (1996)
choose a value of 0.05 which is obtained as a rough average of the estimated values from
the literature on the labor market. We choose δh = 0.015. A detailed discussion about the
11
estimation of this rate can be found in Mincer and Ofek(1982). 7
Depreciation rate of public capital (δg). We take the value of 0.035 used by Atolia,
Chatterjee and Turnovsky (forthcoming). Note that the rate of depreciation of public phys-
ical capital is lower than the private physical capital. This captures the fact that public
physical capital is mostly infrastructure which depreciates at a slower pace than plant and
machinery.
Time allocated to production (n). The proportion of time allocated to work is often
computed in the literature to be the ratio of hours worked to total non-sleep time, which
is 0.357 for a 40-hour workweek, assuming total non-sleep time per day is 16 hours. See
Greenwood and Hercowitz (1991) and Einarsson and Marquis (2001). We set the steady-
state fraction of time allocated to work at n = 0.36.
y = 0.0039x + 2.0487R2 = 0.2077
1.9
2.0
2.1
2.2
2.3
2.4
2.5
2.6
1946
1949
1952
1955
1958
1961
1964
1967
1970
1973
1976
1979
1982
1985
1988
1991
1994
1997
2000
2003
2006
Years
k/y
US Department of Commerce, 2008.
Figure 1: Private Physical Capital to Output Ratio in the United States (1929-2006)
Private physical capital to output ratio (y). We set the steady-state value of y equal
to the inverse of the capital-labor ratio of 2.17 (or y = 0.461) This value is obtained from the
data for the private physical capital and gross domestic product in current dollar value in
National Income and Product Accounts (NIPA) tables prepared by the Bureau of Economic
Analysis (BEA) at the US Department of Commerce. The data in the tables covers the post
7We note that a change in δh will only affect the allocation of non-work time between accumulatinghuman capital and leisure. For example, if δh = 1%, then the values that will change in Table 1 are l, m,and η. They change as follows: lo = 0.452, mo = 0.188 and η = 0.74.
12
y = -0.0013x + 0.2329
0
0.05
0.1
0.15
0.2
0.25
0.3
1946
1949
1952
1955
1958
1961
1964
1967
1970
1973
1976
1979
1982
1985
1988
1991
1994
1997
2000
2003
2006
Years
G/R
(%)
US Department of Commerce, 2008.
Figure 2: Gross Public Investment to Total Tax Receipts Ratio in the United States (1929-2006)
WWII period (1946-2006). The actual data for private physical capital and GDP is shown
in Figure 1, and is seen to have experienced a modest upward trend.
Gross public investment to total tax receipts ratio (G/R). To estimate this ratio, we
again use the data for the post-WWII period (1946-2006) obtained from the BEA’s NIPA.
The average gross public investment to total tax receipts ratio for the period is 19.1%,
which is the number we use here. The actual data for the government’s current receipts and
expenditures is shown in Figure 2, where it is seen to be relatively absent of a trend in recent
years.
Tax rates (τk, τn, τc). For the gross tax rate on capital rental income and labor income,
Turnovsky (2000) set both rates to 28%. Here we set the benchmark values to 25%, following
the works of Greenwood and Hercowitz (1991) and Einarsson and Marquis (2001) who discuss
in greater detail the selection of their values. Regarding the consumption expenditure tax
rate, we set this rate as the pure U.S. sales tax rate currently, which is 7%.8
The calibration results are summarized in Table 1.
8Note that the τk is the tax rate on gross capital income. The tax rate on net capital income τk′ ismathematically given by (rk− δkk)τk′ = τkrk. Hence, τk′ = r
r−δkτk. Substituting for the steady-state value
of r in the above equation, we get τk′ = ρ+δk+µφρ+δk+µφ−δk(1−τk)τk. In our model, τk′ ranged from 34.5%-42.9%
depending on the value of σ, with an average of 38.1%. This number is close to empirical literature. Forexample, Mendoza et al. (1994) estimated it to be 41.5%. Since then, the tax rates on capital in the U.S.has fallen.
Average 5.43 2.58 1.01 0.42(7.53) (7.01) (4.30) (2.41)
6.2 Fiscal Policy Instruments
Due to the large number of cases examined (68) in this sensitivity analysis, we report the
results in the form of summary statistics.11 We begin by computing the average of the
absolute values of the errors in the calculation of welfare gains (losses) across all cases for each
order of the approximation using the same metric as in Section 5.2. The results at various
time horizons during the transitions to the new balanced growth paths are reported in Table
5. The number in parenthesis is the standard deviation of the mean errors. We note two
broad patterns that emerge in these statistics. First, the higher is the order of approximation,
the lower tends to be the errors, with fourth-order approximations producing error estimates
whose average is roughly one-half of one percent or less at all time horizons. As we know
from the previous Section 5, these results are not uniform across all tax regime changes,
with the capital-income-tax-only cases contributing disproportionately to these estimates.
Second, we find that the average error estimates tend to accumulate over time, with rough
convergence for each order of approximation achieved after about 100 periods. These results
11We note that four of the labor-income-tax-only regime cases reported in Table 4 are extreme, withnear zero or negative growth rates. These cases are deleted from the subsequent sensitivity analysis. Morecomplete results are available from the authors on request.
28
are also consistent with the lengthy transition periods required to absorb the dramatic fiscal
policy changes examined in this model.
To examine how these results likely vary across the alternative fiscal policy regimes, we
compute for each of the alternative tax regimes, the average approximation errors across all
cases after convergence to the new long-run balanced growth path is achieved. The results
(with standard deviations in parentheses) are reported in Table 6. Two broad patterns
emerge. The first is the general tendency of the errors to fall as the order of the approximation
increases. However, a monotonic decline in the long-run approximation errors with the order
of approximation does not always occur. For the capital-income-tax-only case, we find that
the second-order approximation results in larger long-run errors in estimating the welfare
gains (or losses) than the first-order approximation. This pattern had previously revealed
itself in the standard case, as reported in Table 3.
The other two core system equations is straightforward. For the public capital, kg, it is simply
the government investment equation normalized the private physical capital. Whereas the
human capital transitional dynamics was in our model setup.
˙kg =
[1
kg(τkr + τnw
θh1−θn+ τcc+ X + T − δgkg)−k
k
]kg (B.12)
˙h =
[γ(1− l − n)− δh −
k
k
]h (B.13)
39
.
Abstract
There is a long-standing debate in the literature on the choice between consumptionor expenditure taxes versus capital income taxes that goes back to Thomas Hobbes(1651), Mill (1871) and later Kaldor (1955) who advocated the consumption tax overthe income tax. The advocacy of consumption tax has its solid empirical evidence assome studies indicated that the tax revenue collected in the United States includes arelatively small contribution coming from capital tax (Roger Gordon, Laura Kalam-bokidis, Jeffrey Rohaly and Joel Slemrod (2004)). This paper examines tax policyin an endogenous growth model with public capital externality, where human capitalserves as the engine of growth. In a companion paper, this model was calibrated tothe U.S. economy and experiments were run to calculate welfare gains from a shift inthe fiscal regime from the current mix of capital income, labor income, and consump-tion taxes to complete reliance on consumption tax. In those experiments, governmentexpenditures in public capital as a share of output was held fixed. The paper showedthat the consumption-only tax regime was superior to the current tax regime and toother tax regimes relying solely on a single source of taxation. In this paper, the gov-ernment tax revenues as a portion of output are varied in order to find the optimallevel of investments in public capital under a consumption-only tax regime. I find thatin the presence of a significant externality, a modest increase in the consumption taxwith a greater investment in public capital can increase welfare. I also show that aslight shift in taxes from consumption to capital income can be welfare improving ifthe externality is high enough.
Keywords: Consumption tax, public capital externality, endogenous growth, welfare,public and human capital