Final Phd Thesis Presentation

IntroductionAggl. and Growth with Endogenous Expenditure Shares

Regional Growth with Int. Knowledge Spillovers

Essays in New Economic Geography

Doctoral Thesis of Francesco Mureddu

March 26, 2009

Doctoral Thesis of Francesco Mureddu Essays in New Economic Geography



Contents of the Thesis: Literature Review

In chapter one we give an overview of the principal NewEconomic Geography (NEG) models:

The Core-Periphery (Krugman (1991))The Footloose capital (Martin and Rogers (1995))The Footloose entrepreneurs (Ottaviano (1996))

In chapter two we describe some of its further developments:The introduction of endogenous growth in a NEG framework(Baldwin and Martin (2004) and Baldwin et al. (2004))Possibility of a monotonic relation between agglomeration andintegration (Bellone and Maupertuis, 2003 and Andres, 2007)Introduction of firms heterogeneity (Melitz (2003), Baldwinand Okubo (2006) and Baldwin and Robert-Nicoud (2008))




Contents of the Thesis: Original Extensions to the Theory

In chapter three we elaborate the model "Agglomeration andGrowth with Endogenous Expenditure Shares" where we use aCES instead of a Cobb-Douglas utility function in thesecond-stage optimization problem

In particular we will focus on the study of stability analysis andgrowth rate. Our benchmark will be the model with globalspillovers presented in Baldwin and Martin (2004)

In chapter four we elaborate the model "Intersectoral Spilloversand Real Income Growth" where we introduce intersectoralknowledge spillovers from Innovation to a Non-tradable sector

In particular we will focus on the study of the real incomegrowth. Our benchmark will be the model with localizedspillovers presented in Baldwin, Martin and Ottaviano (2001)




Essays in New Economic GeographyIntroductionAgglomeration and Growth with Endogenous ExpenditureShares

BasicsStability AnalysisGrowth Rate

Agglomeration, Welfare and Regional Growth withIntersectoral Knowledge Spillovers

BasicsReal Growth RateRegional Welfare




Main Results in Baldwin and Martin (2004)

Using a CD utility function in the second-stage optimization theexpenditure shares for Manufacture is constant and the elasticity ofsubstitution between the Traditional and the Industrial goods is unitary

Implications on the stability analysis:

Catastrophic agglomeration takes place in case of capitalimmobility: in this case when trade costs fall beyond a certainthreshold agglomeration forces overcome the dispersion forces

Implications on the growth analysis:

The growth rate is not influenced by the allocation ofeconomic activities hence it is the same both in the coreperiphery and in the symmetric configurationMoreover the growth rate is in no way affected by the degreeof market integration (trade costs)




Extensions to BM (2004): Implications of Endogenous Expenditure Shares

Using a CES utility function in the second-stage optimization problem,allows for expenditure shares in Industrial goods to be endogenouslydetermined and opens the room to the following implications:

Catastrophic agglomeration may always take place, whatever thedegree of market integration, provided that the Traditional and theIndustrial goods are sufficiently good substitutes

The regional rate of growth is affected by the interregionalallocation of economic activities even in the absence of localizedspillovers, so that geography always matters for growth

The regional rate of growth is affected by the degree of marketopenness: in particular, depending on whether the Traditional andthe Industrial goods are good or poor substitutes, economicintegration may be respectively growth-enhancing orgrowth-detrimental




Main Results in Baldwin, Martin and Ottaviano (2001)

In standard NEGG models the growth rate is equal in bothregions both in cases of global and local spilloversIn case of agglomeration workers remaining in the region wherethere is no longer industry face two opposite welfare effects:

A static loss due to the increase in transport costs paid on theManufacture varieties that have to be importedA positive dynamic effect: if industry is concentrated in case oflocalized knowledge spillovers the growth rate will be higher

This is due to the introduction of endogenous growth andlocalized spillovers: growth is influenced by geographySo the increase in economic growth led by agglomeration canbe the welfare counterpart of the static loss, henceagglomeration is always welfare improving




Extensions to BMO (2001): Implications of Intersectoral Spillovers

By assuming intersectoral and localized knowledge spillovers fromthe Innovation sector to the Service sector, we show that firms’allocation affects regional real growth

More precisely we assume that the unit labour requirements(and thereby the prices) in the Services production are anegative function of the output of Innovation, i.e. the stock ofknowledge capitalDue to this new specification, real growth rates in the tworegions always diverge when the firms allocation pattern differsfrom the symmetric oneThis result has strong policy implications because it suggeststhat concentrating industries in only one region may also bringa dynamic loss for the periphery




BasicsStability AnalysisGrowth Analysis



Agglomeration, Welfare and Regional Growth with IntersectoralKnowledge Spillovers






The Economy

We have two symmetric regions: North and South (labeled byan asterisk) and three sectors: Modern (Manufacture),Traditional (agriculture) and InnovationThere is only one type of workers interregionally immobile butintersectorally mobile (wages are equal among sectors)The Modern good is produced under Dixit-Stiglitz (1977)monopolistic competition with increasing returns to scale: thefixed cost is represented by a unit of capital while the variablecost is represented by aM units of LThe Traditional is homogeneously produced with constantreturns to scale in perfect competition and unit labor costThe Modern good is shipped with Iceberg Trade Costs whilethe Traditional one is freely shipped





The Innovation Sector

The Innovation sector works in perfect competition withendogenous growth à la Romer (1990)The cost of Innovation in the North is:

F = aIw =w

Kw

As we can see the cost of producing new knowledge decreaseswith the stock of knowledge already createdThe rate of growth of units of capital/varieties is:

g =KKw ; g∗ =

K ∗

Kw





Consumer’s Problem

We have an infinite lively consumer who maximizes thefollowing preferences:

U =

∫ ∞

t=0e−ρt ln Qt ; Qt =

[δ(nw

11−σ CM)α + (1− δ)Cα

T

] 1α

CM =

(∫ K+K∗

i=0c

1− 1σ

i

) 11− 1

σ

di ; |α| ≤ 1

It is arguable the intersectoral elasticity of substitution 11−α is

lower than the intrasectoral elasticity of substitution σ

The optimal consumption path is given by the Euler equation:

EE

= r − ρ





Analytical Deviations from the Benchmark Model

Following Cerina and Pigliaru (2007) we use a CES instead ofa Cobb-Douglas, thereby allowing the elasticity of substitution(1/(1− α)) between Manufacture and Traditional good todiverge from the unit value

Hence the share of expenditure on Manufacture is no longerconstant but it is affected by changes in the price index

Following Murata (2008) and Blanchard and Kiyotaki (1987)we abstract from the love for variety

There are several empirical analysis assessing a value for thelove of variety parameter lower than what assumed in standardNEGG models (see for instance Ardelean 2007)The introduction of the restriction according to which love forvariety is none is compensated by the introduction of theparameter α which, unlike the standard NEGG models, allowsthe elasticity of substitution to deviate from the unit value





Normalizations due to the No-specialization Condition

The Traditional good is shipped without incurring in trade costand is produced under perfect competition. It is thereforeconvenient to choose home labour as numeraire so that:

pT = p∗T = wT = w∗T = 1

By the No-specialization condition the Traditional sector ispresent in both regions. This together with labor intersectoralmobility let Manufacture wages to be tied to agricultural wageswhich, in turn, remain fixed at the level of the unit price:

wM = w∗M = wT = w∗T = w = 1





Modern Firm Optimization (1)

The optimal pricing rule is the following:

p = aM

(σ

σ − 1

)If we take the units of labor per unit of output in Manufactureas aM = (σ − 1)/σ even the varieties’ prices are normalizes to1, so p = w = 1 and p∗ = τp (τ represents the trade costs)

Setting pijM the price of a particular variety produced in region i

and sold in region j the Manufacture price index becomes:

PM =

(∫ n

0(pNN

M )1−σdi +

∫ n∗

0(pSN

M )1−σdi

) 11−σ

= (sn+(1−sn)φ)1

1−σ nw 11−σ

P∗M =

(∫ n

0(pNS

M )1−σdi +

∫ n∗

0(pSS

M )1−σdi

) 11−σ

= (φsn+1−sn)1

1−σ nw 11−σ





Modern Firm Optimization (2)

The profits are respectively for northern and southern varieties:

π =Ew

σKw

[sE

(sn + (1− sn)φ)µ(sn, φ) +

φ(1− sE )

(φsn + 1− sn)µ∗(sn, φ)

]

π∗ =Ew

σKw

[φsE

(sn + (1− sn)φ)µ(sn, φ) +

(1− sE )

(φsn + 1− sn)µ∗(sn, φ)

]Where φ = τ1−σ is the so called "phi-ness of trade" whichranges from 0 (prohibitive trade) to 1 (costless trade)As we can see profits change with the expenditure shares





Expenditure Shares

The expenditure shares, which are constant in steady state are:

µ(sn, φ) =

(1

1 + (1−δδ )

α1−α (sn + (1− sn)φ)

− σ(1−α)(1−σ)

)

µ∗(sn, φ) =

(1

1 + (1−δδ )

α1−α (φsn + 1− sn)

− σ(1−α)(1−σ)

)A crucial feature for our analysis is that the expenditure sharesdepend on Manufacture location and trade costs





Stability of the Symmetric Equilibrium

The ratio of northern and southern Tobin’s q is:

qq∗

=

[sE

(sn+(1−sn)φ)µ(sn, φ) + φ(1−sE )

(φsn+1−sn)µ∗(sn, φ)

][

φsE(sn+(1−sn)φ)

µ(sn, φ) + (1−sE )(φsn+1−sn)

µ∗(sn, φ)] = γ(sE , sn, φ)

Starting from γ(sE , sn, φ) = 1, an increase (decrease) inγ(sE , sn, φ) will make investments in the North (South) moreprofitable and thus will lead to a production shiftingHence, the symmetric equilibrium will be stable (instable) if:∣∣∣∣∂γ(sE , sn, φ)

∂sn

∣∣∣∣sn=sE=1/2

< (>)0





Endogenous Expenditure Shares: the Capital Imm. Case

In case of capital immobility we have:

∂γ (sE , sK , φ)

∂sK

∣∣∣∣sK=sE=1/2

= 4(

1− φ

1 + φ

)2 α (1− µ (1/2, φ))

(σ − 1) (1− α)︷︸︸︷Substitution

−4(

1− φ

1 + φ

)2

︷︸︸︷Market-crowding

+4(1− φ)

(1 + φ)

∂sE∂sK︷︸︸︷

Demand-linked

If α > (<)0 the substitution effect acts as a newagglomeration (dispersion) force thereby agglomeration isreached for lower (higher) values of freeness of tradeMoreover if α > 0 there are values of the parameter for thesymmetric equilibrium to be unstable for every level of tradecost





Mechanism of the Substitution Effect

The variability of the expenditure shares gives birth to a new forcecalled substitution effect. Let’s see how it works:

If Manufacture and the Traditional commodities are goodsubstitutes (α > 0) an increase in the share of firm present ina region (say North) determines a decrease in the price indexfor ManufactureHence the share of expenditure in Manufacture (and also theprofits) will rise determining an increase in the incentive toinvestThis rise in the incentive to invest will augment the share offirms owned a region, thereby feedbacking the mechanismIf Manufacture and the Traditional commodities are poorsubstitutes (α < 0) the mechanism is reversed





Growth Always Depends on Geography

In the benchmark model growth does not depend on geographyand is the same both in Core-Periphery and symmetry:

g =2µL− (σ − µ)ρ

σ

Instead in our analysis the growth rate depends on geographyboth in symmetry and in Core-Periphery:

gS =2L(σ − µ(1/2, φ))− ρ(σ − µ(1/2, φ))

σ

gC =L(µ(1, φ) + µ∗(1, φ))− ρ(σ − µ(1, φ))

σ

Clearly the Core-Periphery growth rate can be higher (lower)than the symmetric one according to parameters value:

µ(1, φ) + µ∗(1, φ) > (<)2µ(1/2, φ)⇒ gC > (<)gS





Integration Always Affects Growth Rate

The growth rate in our analysis depends on trade costs inCore-Periphery and in the symmetric equilibriumIn particular if Manufacture and Agriculture are good/poorsubstitutes the impact of integration (lowering trade costs) canbe positive/negative:

α > (<)0 ⇒ ∂gS

∂φ,∂gC

∂φ> (<)0





Economic Intuitions and Policy Implications

If the freeness of trade or the share of firms in a regionincrease, the price index decreases. Then if α > (<)0 theshare of expenditure in Manufacture augments/diminishes.Hence firms gain more/less profits and the incentive to investis enhanced/decreased, thus boosting/slowing down growthGrowth Rate Depends on Geography: if the growth rate ishigher/lower in Core-Periphery hence the conclusion of thebenchmark model stating that agglomeration is welfareenhancing is reinforced/rejectedGrowth Rate Depends on Trade Costs: if α > (<)0 anincrease in trade costs is growth enhancing/harming hence theconclusion of the benchmark model stating that integration iswelfare improving is reinforced/rejected





Introducing Intersectoral Spillovers: the Picture Changes

The result displayed in Baldwin, Martin and Ottaviano (2001)saying that agglomeration of industry benefits both regions isquestionableIntroducing the possibility of intersectoral spillovers betweenknowledge production and Services it is arguable thatclustering Innovation and the Modern sector in a unique regionwould influence also the productivity of the Non-tradable sectorThereby agglomeration would bring to two losses for South:

A static loss due to the increase in trade costs paidA dynamic loss (lower real growth rate) in the region whereremain only the Traditional and the Non-tradable sectors

Hence in case of agglomeration we have ever increasing welfareinequality between regions





Deviations from the Canonical Case

In our work we focus on the analysis of the real growth rateThe mechanisms of agglomeration and the growth rateanalysis are equal to the benchmark caseWe introduce a further sector that is not traded: the ServicesThe productivity of the Services depends positively on thequantity of knowledge capital already present in the sameregionThis dependence is due to the introduction of localizedintersectoral spilloversIn case of agglomeration this modification let the negative rateof growth of the price index to be different between the tworegions





The Economy

The analytical framework is very similar to the one presented in thefirst session for the Endogenous Expenditure Shares case. Thedifferences are the following:

We reintroduce the Cobb-Douglas in the second step of utilitymaximization, like in the benchmark modelWe consider the case of localized spillovers between theInnovation sectors in the two regions so that the innovationcost is aI = 1/AKw where A = (sK + λ(1− sK ))

We introduce the Non-tradable sector: Services are producedunder perfect competition and constant returns to scale, andare not interregionally traded





The Non-tradable Sector

The Services production function, where aS(·) represents theunits of labor necessary to produce a unit of output is:

S =LS

aS(·)

The profit function is:

πS = pSS − wLS

Optimization implies (int. labor mobility drives wages to 1):

pS = aS(·)

We assume knowledge intersectoral spillovers from Innovationto Services: the productivity parameter is a negative functionof K , i.e. we have aS(K ) < 0





Consumer’s Problem (1)

We have an infinite lively consumer that maximizes:

U =

∫ ∞

t=0e−ρt ln Qdt;Q = ln

[Cα

MCβTCγ

S

];CM =

(∫ K+K∗

i=0c

1− 1σ

i di

) 11− 1

σ

Where CM and CT are respectively the demand of the Modern(CES) and Traditional good and CS is the demand for ServicesThe optimal consumption path is given by the Euler equation:

EE

= r − ρ





Consumer’s Problem (2)

The maximization of the Cobb-Douglas gives the followingrelations1:

PMCM = αE ; pTCT = βE ; pSCS = γE

Where pS is the price of the Non-tradable goodAs we can see consumers devote a fixed share of expenditureto the three commoditiesFinally the optimizations of the composite index gives the CESdemand function for the typical variety:

cj =p−σj

P1−σM

αE

1We assume α + β + γ = 1Doctoral Thesis of Francesco Mureddu Essays in New Economic Geography




Income Growth Rate

Real growth merely stems from the constant fall in the price indexthat is driven by a continuously widening range of varieties

Steady state income in the two regions is the sum of labourincome plus profit income and can be written as:

Y = L+πsKKw = L+αEw

σ

[sE

(sK + (1− sK )φ)+

φ(1− sE )

(φsK + 1− sK )

]

Y ∗ = L+π∗(1−sK )Kw = L+αEw

σ

[φsE

(sK + (1− sK )φ)+

1− sE(φsK + 1− sK )

]Being sK , sE and Ew constant in steady state, Y and Y ∗ areconstant as well:

YY

=Y ∗

Y ∗ = 0

The income growth is zero unregarding the location of industry





Price Index

The Cobb-Douglas price index for the consumer is:

P = PαMpβ

TpγS ;P∗ = P∗α

M p∗βT p∗γ

S

The growth rate of prices in the two regions becomes:

PP

= αPM

PM+ β

pT

pT+ γ

pS

pS

P∗

P∗ = αP∗

MP∗

M+ β

p∗Tp∗T

+ γp∗Sp∗S

Hence the real income growth rate is:

YY− P

P= −α

PM

PM− β

pT

pT− γ

pS

pS

Y ∗

Y ∗ −P∗

P∗ = −αP∗

MP∗

M− β

p∗Tp∗T

− γp∗Sp∗S





Price Index Manufacture

The price index for the Manufacture good is:

PM = (sn + (1− sn)φ)1

1−σ Kw 11−σ

P∗M = (φsn + (1− sn))1

1−σ Kw 11−σ

The growth rate of prices for the Manufacture good is:

PM

PM=

P∗MP∗M

=1

1− σ

Kw

Kw = − gσ − 1





Traditional Good Price Index

The normalized price for the Traditional good:

pT = p∗T = 1

The growth rate of prices for the Traditional good is:

pT

pT=

p∗Tp∗T

= 0





Non-tradable Good Price Index

Instead the optimizing price for Services in North and South is:

pS = aS(K ); p∗S = a∗S(K ∗)

The growth rate of prices for the Non-tradable good is:

pS

pS=

aS(K )

aS(K )=

∂aS(K )/∂KaS(K )

KKK

= θ(K )KK

p∗Sp∗S

=a∗S(K ∗)a∗S(K ∗)

=∂a∗S(K ∗)/∂K ∗

a∗S(K ∗)K ∗

K ∗

K ∗= θ∗(K ∗)

K ∗

K ∗

Where θ(K ) and θ∗(K ∗) are the (negative) elasticities ofServices production cost with respect to capital in the tworegions





Real Growth Rate

The difference in the real growth rate between the two regionsis given by:

θ∗(K ∗)K ∗

K ∗− θ(K )

KK⇒

(YY− P

P

)−

(Y ∗

Y ∗ −P∗

P∗

)

Thus we have a positive steady state real growth differential if:

θ∗(K ∗)K ∗

K ∗> θ(K )

KK⇒

(YY− P

P

)>

(Y ∗

Y ∗ −P∗

P∗

)





Geography Affects Growth

In the symmetric equilibrium K∗K∗ = K

K = g hence the realincome growth is the same:

θ∗(K ∗)g = θ(K )g ⇒

(YY− P

P

)=

(Y ∗

Y ∗ −P∗

P∗

)

In each asymmetric equilibrium K∗K∗ = g∗ = 0 6= K

K = g thusthe real income growth diverges:

θ∗(K ∗)g∗ = 0 > θ(K )g ⇒

(YY− P

P

)>

(Y ∗

Y ∗ −P∗

P∗

)





Real Growth Rate in the North

The North enjoys two dynamical gains from agglomerationIndeed the northern real growth rate in symmetry is:

ϕsym =(αL (1 + λ)− ρ (σ − α)) (α− γθ(K ) (σ − 1))

σ (σ − 1)

Instead in core-periphery the northern real growth rate is:

ϕcp =(2αL− ρ (σ − α)) (α− γθ(K ) (σ − 1))

σ (σ − 1)

Clearly the real growth rate of the North is higher incore-periphery:

ϕcp > ϕsym





Real Growth Rate in the South

On the contrary the South may loose from agglomerationThe southern real growth rate in symmetry is:

ϕ∗sym =(αL (1 + λ)− ρ (σ − α)) (α− (σ − 1) γθ∗(K∗))

σ (σ − 1)

Whilst in core periphery the real growth rate becomes:

ϕ∗cp =(2αL− ρ (σ − α)) α

σ (σ − 1)

Hence agglomeration is welfare harming for the South if:

λ >α2L + (αL− ρ (σ − α)) (σ − 1) γθ∗(K∗)

αL (α− (σ − 1) γθ∗(K∗))

If spillovers are less localized (λ higher) the firms’ location is lessimportant therefore the dynamic gain from agglomeration is lower





Conclusions and Policy Implications

In agglomeration we have different effects for the two regionsThe core would be better off enjoying two dynamic gains:

The first one is an increase in the growth rate of Manufacturedue to the localized knowledge spilloversThe second one is a decrease in the decrease in the Servicesprice index growth due to the intersectoral knowledge spillovers

Instead the periphery would experience two opposite effects:A dynamic gain given by the increase in the growth rate ofManufacture (that is imported from the core) due to thelocalized knowledge spilloversA dynamic loss due to the fact that southern capital does nolonger grow hence the Services price is fixed

This conclusion clashes with BMO (2001) who state thatagglomeration is welfare improving for both regions





References (1)

Andres F., (2007), "Divergence, Wage-Gap and Geography", EconomieInternationale, 4Q, pages 83-112.

Ardelean A. (2007), "How Strong is Love for Variety?", Working Paper,Leavey School of Business, University of Santa Clara, California.

Baldwin R., R. Forslid, P. Martin, G. Ottaviano and F. Robert-Nicoud(2004), "Economic Geography and Public Policy", Princeton UniversityPress.

Baldwin R., Martin P., (2004), “Agglomeration and Regional Growth”,Handbook of Regional and Urban Economics, in: J. V. Henderson and J.F. Thisse (ed.), Handbook of Regional and Urban Economics, edition 1,volume 4, chapter 60, pages 2671-2711 Elsevier.





References (2)

Baldwin R., Martin P., Ottaviano G., (2001), “Global Income Divergence,Trade, and Industrialization: The Geography of Growt Take-Offs”,Journal of Economic Growth, Springer, vol. 6(1), pages 5-37, March.

Baldwin R., Okubo T., (2006), "Heterogeneous firms, agglomeration andeconomic geography: spatial selection and sorting," Journal of EconomicGeography, Oxford University Press, vol. 6(3), pages 323-346, June.

Baldwin R., Robert-Nicoud F., (2008), "Trade and growth withheterogeneous firms", Journal of International Economics, Elsevier, vol.74(1), pages 21-34, January.

Bellone F., Maupertuis M., (2003), "Economic Integration and RegionalIncome Inequalities: Competing Dynamics of Regional Wages andInnovative Capabilities", Review of International Economics, 11, 512-526.





References (3)

Blanchard O., Kiyotaky N., (1987), "Monopolistic Competition andAggregate Demand", American Economic Review, 77, 647-666.

Fabio Cerina F., Pigliaru F., 2007, "Agglomeration and Growth: acritical assessment", in Bernard Fingleton (ed.), 2007, NewDirections in Economic Geography, Edward Elgar Publishing,Cheltenham.

Dixit A.K., Stiglitz J.E., (1977), "Monopolistic Competition andoptimum product diversity", American Economic Review 67,297-308.

Krugman P., (1991), “Increasing Return and Economic Geography”,Journal of Political Economy 99, 483-99.





References (4)

Martin P., Rogers C., (1995), "Industrial location and publicinfrastructure", Journal of International Economics, Elsevier, vol.39(3-4), pages 335-351, November.

Melitz M., (2003), "The Impact of Trade on Intra-Industry Reallocationsand Aggregate Industry Productivity", Econometrica, EconometricSociety, vol. 71(6), pages 1695-1725, November.

Ottaviano G., (1996), "Monopolistic competition, trade, and endogenousspatial fluctuations", CEPR Discussion Paper, No. 1327.

Romer P., (1990), "Endogenous Technological Change", Journal ofPolitical Economy 98.5, S71-S102.


Final Phd Thesis Presentation

Economy & Finance

Transcript of Final Phd Thesis Presentation