GEOGRAPHICAL ECONOMICS

GEOGRAPHICAL ECONOMICS

Sponsored by a Grant TÁMOP-4.1.2-08/2/A/KMR-2009-0041 Course Material Developed by Department of Economics, Faculty of Social Sciences, Eötvös Loránd University Budapest (ELTE)

Department of Economics, Eötvös Loránd University Budapest Institute of Economics, Hungarian Academy of Sciences

Balassi Kiadó, Budapest

Authors: Gábor Békés, Sarolta Rózsás Supervised by Gábor Békés

June 2011

ELTE Faculty of Social Sciences, Department of Economics

GEOGRAPHICAL ECONOMICS

week 12

Agglomeration and productivity

Gábor Békés, Sarolta Rózsás

1 Agglomeration and the productivity of firms

Agglomeration and the productivity of firms

• Ciccone, A., and R. E. Hall (1996), Productivity and the density of economic activity, American Economic Review, 86: 54–70.

• Start-up - differences in average labor productivity across US states are large

– Output per worker in the most productive state was two thirds larger than in the least pro- ductive state.

– Output per worker in the top ten productive states was one third larger than in the ten states ranked at the bottom

• The spatial density of economic activity is the source of aggregate increasing returns.

– Spatial density = intensity of labor or capital /km²

– Transport costs depend on distance (technology for the production have increasing returns – the ratio of output to input will rise with density: FC production, MC transportation)

• Two explanations – Spatial externalities

– Diversity of business services

1.1 Ciccone-Hall (1996): US

Ciccone-Hall (1996)

• At which level?

• output, input: state level, density: county level

• Results: capital accounts for some of the differences in productivity but leaves most of the varia- tion unexplained

• The density of economic activity is crucial for explaining the variation of productivity

• There is no first geography, evenly distributed space

• Simple production function (labor and land, but no capital) f(n,q,a) =n^αq

a

(λ−1)/λ

(1)

• quantity of goods produced on an area of 1km²space in a given county;ndenotes labor,qrepre- sents total output of the county andais the size of the county

Theoretical model

• The labor employed in a countyc,nc, is distributed equally among all thekm²in the county. Total output in the county:

qc=_ac nc

ac

αqc

ac

(λ−1)/λ

(1a)

• Technology in the county:

qc

ac

= nc

ac

γ

(2)

• whereγ = αλis the product of the production elasticity (α), and the elasticity of the externality (λ);

– α– the effect of congestion – λ– the effect of agglomeration

– γ– the common effect of two opposite forces - this can be identified in the data Theoretical model

• Aggregating to the state level, Cs denotes those counties that cover state s. Total output in the state:

•

Qs =

∑

c∈C_s

n^γca^−(γ−1)c (3)

• Let Ns be the number of workers in the particular state (=∑c∈C_snc), then the average labor pro- ductivity in the state:

• Productivity is a function of density:

Qs

Ns

=

∑

c∈C_s

nc

ac

γ ac

Ns

=

∑

c∈C_s

n^γ_ca^−(γ_c ⁻¹⁾/Ns =Ds(γ) ₍₄₎

Theoretical model

• Ds(γ)– factor density index

• Ds– the average number of workers perkm²in a particular state

• D– the average number of workers perkm²in the US

• dc– the average number of workers perkm²in a particular county

Ds(γ) =D^γ−1 Ds

D γ−1

c∈C

∑

nc

dc

Ds

γ−1

/Ns (5)

In a given state the effect of density is the product of three factors

• national effect

• state effect (state vs US)

• inequality of density across counties within the state

If the density in a given state equals the density of the US, productivity hings on the distribution of employment within the state only.

• γ<1 – congestion effects

• Externality is positive, if the agglomeration effect outweigh congestion

• The paper contains another model, where IRS arises from the greater variety of intermediate prod- ucts

• In terms of testing we get the same results, the technology of production at the county level re- mains ^q_a^c_c =^q_a^c

c

γ

Estimation Estimation

• A simple equation to estimate

logQs/Ns =logφ+logDs+us (6)

• logφderiving from the production function, a constant

• Data: US states and counties

• Result: 5.2%

1.2 Ciccone (2002): EU

Agglomeration and the productivity of firms 2

Ciccone, A. (2002), Agglomeration effects in Europe, European Economic Review, 46: 213–37.

• France, Germany, Italy, Spain and the UK

• Germany counties (Kreise): top 5/bottom 5 = 240%

• 628 Nuts3 region

• More and better data

• Estimating an extended model Theoretical model

• The model – extension

• The firm is replaced by space. It can be said that eachkm²equals one firm.

• Production function of a givenkm²: in regionsand statec

q=_Ωscf(nH,k;Qsc,Asc) =_Ωsc(nH)^βk^1−βα Qsc

Asc

(λ−1)/λ

(7)

• qdenotes output produced on 1km²of land

• n- the number of workers employed on thekm²

• H- human capital,k- physical capital,

• Ω- index of total factor productivity (TFP) in the region

• Qsc- total output of the region,Asc- the size of the region

• Qsc/Asc→spatial externality - IFλ>1

• and 0<α<1 - marginal product of capital and labor (DRS=congestion)

Theoretical model

• Labor and capital are distributed equallywithinthe region

• Nsc - totalemployment in the region, Hsc - the average level of human capital of workers in the region,Ksc- the total amount of physical capital used in the region,

• Production function in the region:

Qsc= Ascq=

=AscΩsc

(NscHsc/Asc)^β(Ksc/Asc)^1−βα Qsc

Asc

(λ−1)/λ (8)

• Labor productivity:

Qsc

Nsc

=_Ωsc

(Hsc^β(^Ksc Nsc

)^1−β

αλ

Nsc

Asc

αλ−1

(9)

Theoretical model

• there is no data on the quantity of physical capital

• Assume that the rental price of capital is the same everywhere within a country

• Capital-demand function:Ksc = ^α(1−_r ^β)

c Qsc

• Labor productivity:

Qsc

Nsc

=_ΛcΩscHsc

NscHsc

Asc

θ

(10)

• θmeasures the effect of the regional density of employment and human capital on regional pro- ductivity.

θ= ^αλ−1

1−αλ(1−β) ⁽¹¹⁾

• Λccountry FE - estimated Agglomeration effect

• θ= the effect of the regional density of employment and human capital on regional productivity, θ= _{1−αλ(1−β)}^αλ−1

• =Agglomeration effect

• Recall:α- marginal products of labor and capital,λ- spatial (positive) externalities in the region – If the two effects are equal:α=1/λ, nor role for density

• Ifαλ>1, then the greater(1−β)the greaterθ. ((1−β)is the exponent of capital)

– The effect of an increase in total factor productivity - driven by an increase in the density of employment - on regional average labor productivity will therefore be reinforced by an inflow of physical capital (assuming free flow of capital)

– This effect will become stronger as the role of capital (1−β) becomes greater.

• Estimation

logQsc−logNsc=

=logΛc+θ(logNsc−logAsc) + (θ+1)Hsc+vlogΩsc

(12)

logQsc−logNsc=DU Mc+θ(logNsc−logAsc) +δFsc+usc (13)

• DU Mcountry and NUTS2 dummy, F - the fraction of workers with tertiary education

• usc - differences between total factor productivity in region and the country that contains those region;

• + the effect of neighboring regions+φ(logNscn−logAscn) Empirical model

• Difficulty:θis the common agglomeration effect

• in order to be an externality (^λ−1_λ ) it needs to be assumed, that

• 1−αis the income share of land and

• α(1−β)is the income share of physical capital

•

λ−1

λ =1−^α+α(1−β)θ

1+θ (14)

Estimation

• Estimation

• 1. OLS

• If regional/country fixed effects do not capture exogenous differences in total factor productivity and if regions with higher exogenous total factor productivity attract more workers, the OLS yields inconsistent estimates

• 2. IV/2SLS

• IV = total land area of regions. Historically predetermined variable (in the 19. century), negatively correlated with modern differences in employment density (administrative shocks), not affected by modern differences in exogenous total factor productivity

• US (Ciccone-Hall) - IV

– 1850 population of the state

– railroad dummy, distance from the eastern seaboard of the US

Results

Results

• Effect: OLS - 5.1% , 2SLS - 4.5%

• NUTS1,2 dummies do not modify

• (compare US above - 5.2%)

• Differences in agglomeration effect across countries can be tested: there are no significant differ- ences (the US may differ)

• The value of the capital-income share: 30%, income share of land: 1.5%,θ=4.5%

• The effect of externality: ^λ−1_λ =4.4%

• Doubling the number of workers leads to 4.4% higher productivity