GEOGRAPHICAL ECONOMICS

(1)

GEOGRAPHICAL ECONOMICS

(2)

(3)

(4)

ELTE Faculty of Social Sciences, Department of Economics

Geographical Economics

week 12

AGGLOMERATION AND PRODUCTIVITY Authors: Gábor Békés, Sarolta Rózsás

Supervised by Gábor Békés

June 2011

(5)

week 12 Gábor Békés

Agglomeration and the productivity of rms

Ciccone-Hall (1996): US Ciccone (2002):

EU

Outline

1 Agglomeration and the productivity of rms Ciccone-Hall (1996): US

Ciccone (2002): EU

(6)

EU

Agglomeration and the productivity of rms

Ciccone, A., and R. E. Hall (1996), Productivity and the density of economic activity, American Economic Review, 86: 5470.

Start-up - dierences 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 productive 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

(7)

EU

Ciccone-Hall (1996)

At which level?

output, input: state level, density: county level Results: capital accounts for some of the dierences in productivity but leaves most of the variation unexplained The density of economic activity is crucial for explaining the variation of productivity

There is no rst geography, evenly distributed space Simple production function (labor and land, but no capital)

f(_n,q,a) =_n^α^q a

(λ−1)/λ

(1) quantity of goods produced on an area of 1km² space in a given county; n denotes labor, q represents total output of the county and a is the size of the county

(8)

EU

Theoretical model

The labor employed in a county c, n_c, is distributed equally among all the km² in the county. Total output in the county:

q_c=_a_c n_c

a_c

αq_c a_c

(λ−1)/λ

(1a) Technology in the county:

q_c a_c =

n_c a_c

γ

(2) where γ=αλis the product of the production elasticity (α), and the elasticity of the externality (λ);

α the eect of congestion λ the eect of agglomeration

γ the common eect of two opposite forces - this can be identied in the data

(9)

EU

Theoretical model

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

Q_s =

∑

c∈Cs

n^γ_ca^−(γ_c ⁻¹⁾ (3) Let N_s be the number of workers in the particular state (=∑_c∈Csn_c), then the average labor productivity in the state:

Productivity is a function of density:

Q_s N_s =

∑

c∈Cs

n_c a_c

γ a_c N_s =

∑

c∈Cs

n^γ_ca^−(γ−_c ¹⁾/N_s =_D_s(γ) ₍₄₎

(10)

EU

Theoretical model

D_s(γ) factor density index

Ds the average number of workers per km²in a particular state D the average number of workers per km²in the US

d_c the average number of workers per km²in a particular county

Ds(γ) =_D^γ⁻¹ D_s

D γ−1

c

∑

∈Cs

nc d_c

D_s γ−1

/Ns (5) In a given state the eect of density is the product of three factors

national eect

state eect (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 eects

Externality is positive, if the agglomeration eect outweigh congestion

(11)

EU

Ciccone-Hall (1996)

The paper contains another model, where IRS arises from the greater variety of intermediate products

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

c

γ

(12)

EU

Estimation

A simple equation to estimate

log Q_s/N_s =_logφ+_{log D}_s+_u_s ₍₆₎ logφderiving from the production function, a constant Data: US states and counties

Result: 5.2%

(13)

EU

Agglomeration and the productivity of rms 2

Ciccone, A. (2002), Agglomeration eects in Europe, European Economic Review, 46: 21337.

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

(14)

EU

Theoretical model

The model extension

The rm is replaced by space. It can be said that each km² equals one rm.

Production function of a given km²: in region s and state c q=Ω_scf(nH,k;Q_sc,A_sc) =Ω_sc

(nH)^βk¹⁻^βαQ_sc A_sc

(λ−1)/λ

(7) q denotes output produced on 1km² of land

n - the number of workers employed on the km² H - human capital, k - physical capital,

Ω - index of total factor productivity (TFP) in the region Q_sc - total output of the region, A_sc - the size of the region Q_sc/A_sc →spatial externality - IFλ>₁

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

(15)

EU

Theoretical model

Labor and capital are distributed equally within the region N_sc - totalemployment in the region, H_sc - the average level of human capital of workers in the region, K_sc - the total amount of physical capital used in the region,

Production function in the region:

Q_sc =_A_sc_q=

=A_scΩ_sc

(N_scH_sc/A_sc)^β(K_sc/A_sc)¹⁻^β^α Q_sc

A_sc

(λ−1)/λ

(8) Labor productivity:

Q_sc

N_sc =Ω_sc

(H_sc^β(^K^sc N_sc)¹⁻^β

αλN_sc A_sc

αλ−1

(9)

(16)

EU

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: K_sc = ^α(¹_r⁻^β)

c Q_sc Labor productivity:

Q_sc

N_sc =_Λ_c_Ω_sc_H_sc

N_scH_sc A_sc

θ

(10) θ measures the eect of the regional density of employment and human capital on regional productivity.

θ= ^αλ−1

1−αλ(1−β) ⁽¹¹⁾

Λ_c country FE - estimated

(17)

EU

Agglomeration eect

θ = the eect of the regional density of employment and human capital on regional productivity,θ= ₁_−αλ(^αλ−₁¹_−β)

=Agglomeration eect

Recall: α- marginal products of labor and capital,λ - spatial (positive) externalities in the region

If the two eects 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 eect 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 inow of physical capital (assuming free ow of capital) This eect will become stronger as the role of capital (1−β) becomes greater.

(18)

EU

Empirical model

Estimation

log Q_sc−log N_sc=

=_log_Λ_c+θ(_{log N}_sc−_{log A}_sc) + (θ+₁)_H_sc+vlogΩ_sc (12)

log Q_sc−_{log N}_sc =_DUM_c+θ(_{log N}_sc−_{log A}_sc) +_δF_sc+_u_sc (13) DUM country and NUTS2 dummy, F - the fraction of workers with tertiary education

u_sc - dierences between total factor productivity in region and the country that contains those region;

+ the eect of neighboring regions +φ(_{log N}_scn−_{log A}_scn)

(19)

EU

Empirical model

Diculty: θ is the common agglomeration eect

in order to be an externality (^λ−_λ¹) 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)

(20)

EU

Estimation

Estimation 1. OLS

If regional/country xed eects do not capture exogenous dierences 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 dierences in employment density (administrative shocks), not aected by modern dierences in exogenous total factor productivity

US (Ciccone-Hall) - IV

1850 population of the state

railroad dummy, distance from the eastern seaboard of the US

(21)

EU

Results

(22)

EU

Results

Eect: OLS - 5.1% , 2SLS - 4.5%

NUTS1,2 dummies do not modify (compare US above - 5.2%)

Dierences in agglomeration eect across countries can be tested: there are no signicant dierences (the US may dier) The value of the capital-income share: 30%, income share of land: 1.5%,θ=₄.5%

The eect of externality: ^λ⁻_λ¹=₄.4%

Doubling the number of workers leads to 4.4% higher productivity