Modeling firms locational choice

Transcription

1 Modeling firms locational choice Giulio Bottazzi DIMETIC School Pécs, 05 July 2010

2 Agglomeration derive from some form of externality. Drivers of agglomeration can be of two types: pecuniary and non-pecuniary. Pecuniary: local final demand, intermediate market for input goods Non-pecuniary: technological spillovers, local knowledge (tacit), shared infrastructures, social and institutional framework (business associations) not sure: labor market (skilled labor can be "generic" skill OR specific "skill") Asses the relevance and compare the two tipes, empirically and theoretically

3 Agglomeration derive from some form of externality. Drivers of agglomeration can be of two types: pecuniary and non-pecuniary. Pecuniary: local final demand, intermediate market for input goods Non-pecuniary: technological spillovers, local knowledge (tacit), shared infrastructures, social and institutional framework (business associations) not sure: labor market (skilled labor can be "generic" skill OR specific "skill") Asses the relevance and compare the two tipes, empirically and theoretically

4 Agglomeration derive from some form of externality. Drivers of agglomeration can be of two types: pecuniary and non-pecuniary. Pecuniary: local final demand, intermediate market for input goods Non-pecuniary: technological spillovers, local knowledge (tacit), shared infrastructures, social and institutional framework (business associations) not sure: labor market (skilled labor can be "generic" skill OR specific "skill") Asses the relevance and compare the two tipes, empirically and theoretically

5 Agglomeration derive from some form of externality. Drivers of agglomeration can be of two types: pecuniary and non-pecuniary. Pecuniary: local final demand, intermediate market for input goods Non-pecuniary: technological spillovers, local knowledge (tacit), shared infrastructures, social and institutional framework (business associations) not sure: labor market (skilled labor can be "generic" skill OR specific "skill") Asses the relevance and compare the two tipes, empirically and theoretically

6 Agglomeration derive from some form of externality. Drivers of agglomeration can be of two types: pecuniary and non-pecuniary. Pecuniary: local final demand, intermediate market for input goods Non-pecuniary: technological spillovers, local knowledge (tacit), shared infrastructures, social and institutional framework (business associations) not sure: labor market (skilled labor can be "generic" skill OR specific "skill") Asses the relevance and compare the two tipes, empirically and theoretically

7 Agglomeration derive from some form of externality. Drivers of agglomeration can be of two types: pecuniary and non-pecuniary. Pecuniary: local final demand, intermediate market for input goods Non-pecuniary: technological spillovers, local knowledge (tacit), shared infrastructures, social and institutional framework (business associations) not sure: labor market (skilled labor can be "generic" skill OR specific "skill") Asses the relevance and compare the two tipes, empirically and theoretically

8 The Model Simulations Analytical result Location selection under dynamic externalities Modeling industrial evolution in geographical space with Dosi, Fagiolo and Secchi, JEG 7 (2007) pp N firms have to select among L locations Time is discrete: at each time step a firm is relocated (or entry/exit).

9 The Model Simulations Analytical result Location selection under dynamic externalities Modeling industrial evolution in geographical space with Dosi, Fagiolo and Secchi, JEG 7 (2007) pp N firms have to select among L locations Time is discrete: at each time step a firm is relocated (or entry/exit).

10 The Model Simulations Analytical result Location selection under dynamic externalities Modeling industrial evolution in geographical space with Dosi, Fagiolo and Secchi, JEG 7 (2007) pp N firms have to select among L locations Time is discrete: at each time step a firm is relocated (or entry/exit).

11 Firm decision The relevance of agglomeration economies The Model Simulations Analytical result Profit of firm i to locate in l = a l + b l n l + ɛ i,l n l the number of firms already there, ɛ i,l idiosyncratic component. Probabilistic discrete choice model (Thurstone (1927), Luce (1959)) Prob { firm i selects location l } a l + b l n l Occupancy vector n t = (n 1,t,..., n L,t ) describes the state of the economy.

12 Firm decision The relevance of agglomeration economies The Model Simulations Analytical result Profit of firm i to locate in l = a l + b l n l + ɛ i,l n l the number of firms already there, ɛ i,l idiosyncratic component. Probabilistic discrete choice model (Thurstone (1927), Luce (1959)) Prob { firm i selects location l } a l + b l n l Occupancy vector n t = (n 1,t,..., n L,t ) describes the state of the economy.

13 Firm decision The relevance of agglomeration economies The Model Simulations Analytical result Profit of firm i to locate in l = a l + b l n l + ɛ i,l n l the number of firms already there, ɛ i,l idiosyncratic component. Probabilistic discrete choice model (Thurstone (1927), Luce (1959)) Prob { firm i selects location l } a l + b l n l Occupancy vector n t = (n 1,t,..., n L,t ) describes the state of the economy.

14 The Model Simulations Analytical result Intrinsic Attractiveness - Economic Interpretation Intrinsic attractiveness a: perceived gains that a firm would obtain by choosing l net of any agglomeration effects. 1 sheer geographical aspects (a harbor or a river) including sticky man-made factors 2 enabling conditions and catalyzers like locally available skilled labor and knowledge spillover from thereby universities 3 externalities (suppliers or customers availability) that are endogenous to the location as a whole but exogenous to any particular small sector of activity

15 The Model Simulations Analytical result Agglomeration Economies - Economic Interpretation Strength of agglomeration economies b: measures the amount by which the advantages obtained by locating in l increases as a function of the number of firms already located there 1 technological externalities 2 sharing of fixed costs 3 local spin-off (entry/exit process)

16 The Model Simulations Analytical result 2 locations and No Agglomeration Feedbacks Set b 1 = b 2 = 0, a 1 = 1 and a 2 = 2. Location 1 average occupancy is a 1 /(a 1 + a 2 ) N=20 N=100 N= Probability density of the fraction of firms in location 1. for.

17 The Model Simulations Analytical result 3 Locations with equal Agglomeration Feedbacks a) 1 b) c) 1 d) a = 1 and a) b 1 = b 2 = b 3 = 0, b) b 1 = b 2 = b 3 = 0.3, c) b 1 = b 2 = b 3 = 1, d) b 1 = b 2 = b 3 = 5

18 The Model Simulations Analytical result 2 locations with diverse Agglomeration Feedbacks b 1 =0 b 1 =.1 b 1 =.5 b 1 = Probability density of the fraction of firms in location 1 for different values of b 1 with a 1 = 1, a 2 = 2 and b 2 = 0.

19 The Model Simulations Analytical result 3 Locations with Diverse Agglomeration Feedbacks a) 1 b) c) 1 d) a 1 = 1 and a 2 = a 3 = 2 a) b 1 = 0 b 2 = 0 b 3 = 0, b) b 1 = 0.1 b 2 = b 3 = 0, c) b 1 = b 2 = 0.1 b 3 = 0, d) b 1 = b 2 = 0.5 b 3 = 0.

20 The Model Simulations Analytical result Temporal Dynamics of Firms Shares 1 n 1 n 2 n Intrinsic attractiveness a 1 = 1 and a 2 = a 3 = 2 a) b 1 = 0 b 2 = 0 b 3 = 0 b) b 1 = 0.1 b 2 = b 3 = 0 c) b 1 = b 2 = 0.5 b 3 = 0 d) b 1 = b 2 = 2 b 3 = 0

21 The Polya Distribution The Model Simulations Analytical result This analytical framework admits a unique stationary distribution π(n; a, b). Assuming b l = b l the probability π(n; a, b) of finding n firms in a location with attractiveness a is ( ) N Γ(A/b) Γ(a/b + n) Γ((A a)/b + N n) π(n; a, n) =. n Γ(A/b + N) Γ(a/b) Γ((A a)/b)

22 The Polya Distribution The Model Simulations Analytical result This analytical framework admits a unique stationary distribution π(n; a, b). Assuming b l = b l the probability π(n; a, b) of finding n firms in a location with attractiveness a is ( ) N Γ(A/b) Γ(a/b + n) Γ((A a)/b + N n) π(n; a, n) =. n Γ(A/b + N) Γ(a/b) Γ((A a)/b)

23 The Polyit model The relevance of agglomeration economies Econometric specification The Data Results Imagine to have A set of location 1,..., L. A set of location-specific regressors X l. The number of economic unit n l in each location. Consider the specification p l (n, b) = X l β. Using the observed occupancy n l, maximize the likelihood of the Polya distribution L = log π (n; X l β, b) to obtain ( ˆβ, ˆb).

24 The Polyit model The relevance of agglomeration economies Econometric specification The Data Results Imagine to have A set of location 1,..., L. A set of location-specific regressors X l. The number of economic unit n l in each location. Consider the specification p l (n, b) = X l β. Using the observed occupancy n l, maximize the likelihood of the Polya distribution L = log π (n; X l β, b) to obtain ( ˆβ, ˆb).

25 The Polyit model The relevance of agglomeration economies Econometric specification The Data Results Imagine to have A set of location 1,..., L. A set of location-specific regressors X l. The number of economic unit n l in each location. Consider the specification p l (n, b) = X l β. Using the observed occupancy n l, maximize the likelihood of the Polya distribution L = log π (n; X l β, b) to obtain ( ˆβ, ˆb).

26 Sectoral analysis The relevance of agglomeration economies Econometric specification The Data Results Sectoral and geographical specificities in the spatial structure of economic activities with Dosi, Fagiolo and Secchi, SCED 19 (2008) Census of Manufacturers and Services (ISTAT) BU and employees are classified with respect to 784 geographical locations and ISIC industrial sectors. n j,l = # of firms or employees in location l sector j For each sector j consider the specification p j,l (n; b, β) = β n j,l β captures urbanization effects. (ˆb j, ˆβ j ) for each sector.

27 Sectoral analysis The relevance of agglomeration economies Econometric specification The Data Results Sectoral and geographical specificities in the spatial structure of economic activities with Dosi, Fagiolo and Secchi, SCED 19 (2008) Census of Manufacturers and Services (ISTAT) BU and employees are classified with respect to 784 geographical locations and ISIC industrial sectors. n j,l = # of firms or employees in location l sector j For each sector j consider the specification p j,l (n; b, β) = β n j,l β captures urbanization effects. (ˆb j, ˆβ j ) for each sector.

28 Sectoral analysis The relevance of agglomeration economies Econometric specification The Data Results Sectoral and geographical specificities in the spatial structure of economic activities with Dosi, Fagiolo and Secchi, SCED 19 (2008) Census of Manufacturers and Services (ISTAT) BU and employees are classified with respect to 784 geographical locations and ISIC industrial sectors. n j,l = # of firms or employees in location l sector j For each sector j consider the specification p j,l (n; b, β) = β n j,l β captures urbanization effects. (ˆb j, ˆβ j ) for each sector.

29 n = number of BUs Econometric specification The Data Results Metropolis Excluded Business Units - NO Metropolis beta b

30 Goodness of fit The relevance of agglomeration economies Econometric specification The Data Results 20 - Wood processing 33 - Precision instruments Observed Model 1 Model Observed Model 1 Model C 1 C 2 C 3 C 4 C 5 C 6 C 7 C 8 C 9 C 10 C 1 C 2 C 3 C 4 C 5 C 6 C 7 C 8 C 9 C 10 Occupancy class frequencies computed on observed data (white bars) and estimated without (red bars) and with (green bars) agglomeration effect.

31 Summarizing The relevance of agglomeration economies Econometric specification The Data Results Dynamic micro-economic model with choice under uncertainty: probabilistic notion of equilibrium. We used it to: disentangle location-specific and sector-specific forces of agglomeration. assess the relevance of sector-specific agglomeration economies produce empirically testable hypothesis on the whole spatial distribution of economic activities

32 Summarizing The relevance of agglomeration economies Econometric specification The Data Results Dynamic micro-economic model with choice under uncertainty: probabilistic notion of equilibrium. We used it to: disentangle location-specific and sector-specific forces of agglomeration. assess the relevance of sector-specific agglomeration economies produce empirically testable hypothesis on the whole spatial distribution of economic activities

33 Summarizing The relevance of agglomeration economies Econometric specification The Data Results Dynamic micro-economic model with choice under uncertainty: probabilistic notion of equilibrium. We used it to: disentangle location-specific and sector-specific forces of agglomeration. assess the relevance of sector-specific agglomeration economies produce empirically testable hypothesis on the whole spatial distribution of economic activities

34 Summarizing The relevance of agglomeration economies Econometric specification The Data Results Dynamic micro-economic model with choice under uncertainty: probabilistic notion of equilibrium. We used it to: disentangle location-specific and sector-specific forces of agglomeration. assess the relevance of sector-specific agglomeration economies produce empirically testable hypothesis on the whole spatial distribution of economic activities

35 Overview The relevance of agglomeration economies The static model The dynamic model Extending New Economic Geography (NEG) analysis including non pecuniary externality inside a tractable evolutionary model of firms location. Benchmark model (as Krugman, 1991) with increasing return and pecuniary externalities + immobile workers and mobile capital (Forlsid and Ottaviano 2003 use skilled labour ). Modified in three ways (see e.g. Frenken and Boschma, 2007): 1. Direct firms interaction via technological externalities 2. Explicit time dimension 3. Heterogeneity in firms locational preferences

36 Overview The relevance of agglomeration economies The static model The dynamic model Extending New Economic Geography (NEG) analysis including non pecuniary externality inside a tractable evolutionary model of firms location. Benchmark model (as Krugman, 1991) with increasing return and pecuniary externalities + immobile workers and mobile capital (Forlsid and Ottaviano 2003 use skilled labour ). Modified in three ways (see e.g. Frenken and Boschma, 2007): 1. Direct firms interaction via technological externalities 2. Explicit time dimension 3. Heterogeneity in firms locational preferences

37 Overview The relevance of agglomeration economies The static model The dynamic model Extending New Economic Geography (NEG) analysis including non pecuniary externality inside a tractable evolutionary model of firms location. Benchmark model (as Krugman, 1991) with increasing return and pecuniary externalities + immobile workers and mobile capital (Forlsid and Ottaviano 2003 use skilled labour ). Modified in three ways (see e.g. Frenken and Boschma, 2007): 1. Direct firms interaction via technological externalities 2. Explicit time dimension 3. Heterogeneity in firms locational preferences

38 Overview The relevance of agglomeration economies The static model The dynamic model Extending New Economic Geography (NEG) analysis including non pecuniary externality inside a tractable evolutionary model of firms location. Benchmark model (as Krugman, 1991) with increasing return and pecuniary externalities + immobile workers and mobile capital (Forlsid and Ottaviano 2003 use skilled labour ). Modified in three ways (see e.g. Frenken and Boschma, 2007): 1. Direct firms interaction via technological externalities 2. Explicit time dimension 3. Heterogeneity in firms locational preferences

39 Overview The relevance of agglomeration economies The static model The dynamic model Extending New Economic Geography (NEG) analysis including non pecuniary externality inside a tractable evolutionary model of firms location. Benchmark model (as Krugman, 1991) with increasing return and pecuniary externalities + immobile workers and mobile capital (Forlsid and Ottaviano 2003 use skilled labour ). Modified in three ways (see e.g. Frenken and Boschma, 2007): 1. Direct firms interaction via technological externalities 2. Explicit time dimension 3. Heterogeneity in firms locational preferences

40 Overview The relevance of agglomeration economies The static model The dynamic model Extending New Economic Geography (NEG) analysis including non pecuniary externality inside a tractable evolutionary model of firms location. Benchmark model (as Krugman, 1991) with increasing return and pecuniary externalities + immobile workers and mobile capital (Forlsid and Ottaviano 2003 use skilled labour ). Modified in three ways (see e.g. Frenken and Boschma, 2007): 1. Direct firms interaction via technological externalities 2. Explicit time dimension 3. Heterogeneity in firms locational preferences

41 The static model The dynamic model An evolutionary model of firms location with technological externalities Handbook of Evolutionary Economic Geography, 2010

42 NEG settings The relevance of agglomeration economies The static model The dynamic model 2 locations. I households per location, global consumers and local workers, demand for a bundle of manufacturing goods and one agricultural good. n 1 + n 2 = N firms, single input (labour) production with increasing return Transportation cost τ as iceberg cost.

43 NEG settings The relevance of agglomeration economies The static model The dynamic model 2 locations. I households per location, global consumers and local workers, demand for a bundle of manufacturing goods and one agricultural good. n 1 + n 2 = N firms, single input (labour) production with increasing return Transportation cost τ as iceberg cost.

44 NEG settings The relevance of agglomeration economies The static model The dynamic model 2 locations. I households per location, global consumers and local workers, demand for a bundle of manufacturing goods and one agricultural good. n 1 + n 2 = N firms, single input (labour) production with increasing return Transportation cost τ as iceberg cost.

45 NEG settings The relevance of agglomeration economies The static model The dynamic model 2 locations. I households per location, global consumers and local workers, demand for a bundle of manufacturing goods and one agricultural good. n 1 + n 2 = N firms, single input (labour) production with increasing return Transportation cost τ as iceberg cost.

46 Household and Firms The static model The dynamic model Household maximize CES utility for a demand log c = σ + (...) log p Firm in l i faces cost function v(y) = (βy + α li ) w li, y = output w = wages β constant and α location specific.

47 Household and Firms The static model The dynamic model Household maximize CES utility for a demand log c = σ + (...) log p Firm in l i faces cost function v(y) = (βy + α li ) w li, y = output w = wages β constant and α location specific.

48 Market structure The relevance of agglomeration economies The static model The dynamic model Agricultural sector is global (zero transport cost): wages are equal in both locations and set to 1. Assuming monopolistic competition for firms, equality of wages imply p = σ/(σ 1)β. No α li : same price in both locations.

49 Market structure The relevance of agglomeration economies The static model The dynamic model Agricultural sector is global (zero transport cost): wages are equal in both locations and set to 1. Assuming monopolistic competition for firms, equality of wages imply p = σ/(σ 1)β. No α li : same price in both locations.

50 Market structure The relevance of agglomeration economies The static model The dynamic model Agricultural sector is global (zero transport cost): wages are equal in both locations and set to 1. Assuming monopolistic competition for firms, equality of wages imply p = σ/(σ 1)β. No α li : same price in both locations.

51 The static model The dynamic model Economic (location-by-location) equilibrium Determine prices and quantities given n 1 and and n 2 : Consumer budget constraint and CES function determine demanded quantities in both locations. Equating global demand and supply determines firms production. Output price and cost structure set the level of profits in the two locations

52 The static model The dynamic model Economic (location-by-location) equilibrium Determine prices and quantities given n 1 and and n 2 : Consumer budget constraint and CES function determine demanded quantities in both locations. Equating global demand and supply determines firms production. Output price and cost structure set the level of profits in the two locations

53 The static model The dynamic model Economic (location-by-location) equilibrium Determine prices and quantities given n 1 and and n 2 : Consumer budget constraint and CES function determine demanded quantities in both locations. Equating global demand and supply determines firms production. Output price and cost structure set the level of profits in the two locations

54 The static model The dynamic model Economic (location-by-location) equilibrium Determine prices and quantities given n 1 and and n 2 : Consumer budget constraint and CES function determine demanded quantities in both locations. Equating global demand and supply determines firms production. Output price and cost structure set the level of profits in the two locations

55 Short-run profits The relevance of agglomeration economies The static model The dynamic model Set x = n 1 /N. Profits per location read π 1 (x) = I ( 1 Nσ x + (1 x)τ σ 1 + τ σ 1 ) xτ σ 1 α 1, + (1 x) π 2 (x) = I ( 1 Nσ xτ σ 1 + (1 x) + τ σ 1 ) x + (1 x)τ σ 1 α 2. Endowment Local Dem. Foreign Dem. Costs

56 Traditional model The relevance of agglomeration economies The static model The dynamic model Assumption Fixed costs are constant across sectors and locations, α 1 = α 2 = α. From the equation above xπ 1 (x) + (1 x)π 2 (x) = 2I Nσ α Long run equilibrium gives N 2I σ α

57 Traditional model The relevance of agglomeration economies The static model The dynamic model Assumption Fixed costs are constant across sectors and locations, α 1 = α 2 = α. From the equation above xπ 1 (x) + (1 x)π 2 (x) = 2I Nσ α Long run equilibrium gives N 2I σ α

58 Traditional model The relevance of agglomeration economies The static model The dynamic model Assumption Fixed costs are constant across sectors and locations, α 1 = α 2 = α. From the equation above xπ 1 (x) + (1 x)π 2 (x) = 2I Nσ α Long run equilibrium gives N 2I σ α

59 Profit functions The relevance of agglomeration economies The static model The dynamic model τ= x τ=0.5 π 1 π 2 π 1 π x τ=0.7 π 1 π x τ=0.2 π 1 π x

60 Geographical equilibrium: The static model The dynamic model Theorem There always exists only one symmetric geographical equilibria for x = 0.5. The border distribution x1 = 1 and x 0 = 0 are never equilibria.

61 Non-pecuniary externalities The static model The dynamic model Assumption Fixed costs are locally shared α l = α N 2 n l Fixed costs are a function of firms concentration: knowledge spillover, access to specific skilled labor pool, use of service or infrastructure. Same long run equilibrium N 2I σ α

62 Non-pecuniary externalities The static model The dynamic model Assumption Fixed costs are locally shared α l = α N 2 n l Fixed costs are a function of firms concentration: knowledge spillover, access to specific skilled labor pool, use of service or infrastructure. Same long run equilibrium N 2I σ α

63 Non-pecuniary externalities The static model The dynamic model Assumption Fixed costs are locally shared α l = α N 2 n l Fixed costs are a function of firms concentration: knowledge spillover, access to specific skilled labor pool, use of service or infrastructure. Same long run equilibrium N 2I σ α

64 Profit functions The relevance of agglomeration economies The static model The dynamic model τ= x τ=0.5 π 1 π 2 π 1 π x τ=0.7 π 1 π x τ=0.2 π 1 π x

65 Geographical equilibrium The static model The dynamic model Theorem There always exists two, and only two, geographical equilibria given by the border distribution x1 = 1 and x 0 = 0. In particular, the unique distribution where profits are equal, x = 0.5, is never an equilibrium.

66 Entry-Exit process The relevance of agglomeration economies The static model The dynamic model Out of equilibrium process: one firm at a time is randomly selected (uniformly) and updates its location choice. Firm i maximizes perceived profit Payoff i = π li + ε i,li. Choice is probabilistic with p l = but π i depends on choice of all other firms. e π l e π 1 + e π 2, l {1, 2}. (1)

67 Entry-Exit process The relevance of agglomeration economies The static model The dynamic model Out of equilibrium process: one firm at a time is randomly selected (uniformly) and updates its location choice. Firm i maximizes perceived profit Payoff i = π li + ε i,li. Choice is probabilistic with p l = but π i depends on choice of all other firms. e π l e π 1 + e π 2, l {1, 2}. (1)

68 Entry-Exit process The relevance of agglomeration economies The static model The dynamic model Out of equilibrium process: one firm at a time is randomly selected (uniformly) and updates its location choice. Firm i maximizes perceived profit Payoff i = π li + ε i,li. Choice is probabilistic with p l = but π i depends on choice of all other firms. e π l e π 1 + e π 2, l {1, 2}. (1)

69 The static model The dynamic model Towards a dynamic geographical equilibrium With p l linear in x l the equilibrium distribution can be computed. Theorem Denote linearized profits around x = 0.5 as c l, and the number of firms in location l as n l. They read c l = a + bn l, l = 1, 2, where intrinsic profit a and marginal profit b are a = 1 4ατ σ 1 (1 + τ σ 1 ) 2, b = 4α2 στ σ 1 I(1 + τ σ 1 ) 2.

70 The static model The dynamic model Towards a dynamic geographical equilibrium With p l linear in x l the equilibrium distribution can be computed. Theorem Denote linearized profits around x = 0.5 as c l, and the number of firms in location l as n l. They read c l = a + bn l, l = 1, 2, where intrinsic profit a and marginal profit b are a = 1 4ατ σ 1 (1 + τ σ 1 ) 2, b = 4α2 στ σ 1 I(1 + τ σ 1 ) 2.

71 The static model The dynamic model Geographical equilibrium distribution Bottazzi et al. (2007), Bottazzi and Secchi (2007) Theorem The model admits a unique stationary distribution π(n) = N!C(N, a, b) Z(N, a, b) 2 l=1 1 n l! ϑ n l (a, b), where ( C(N, a, b) = 2a N ) bn, (2) ϑ n (a, b) = { n h=1 [a + b(h 1)] n > 0 1 n = 0 (3) and Z(N, a, b) is a normalization factor.

72 Recovering different phases The static model The dynamic model The push toward symmetry of pecuniary externalities increases (decreases) with transportation cost (τ). Theorem When the marginal profit is bigger than the intrinsic profit, b > a, the equilibrium distribution of the entry-exit process is bimodal with modes in x = 0 and x = 1, when b < a the equilibrium distribution is unimodal with mode in x = 0.5, and when a = b the equilibrium distribution is uniform.

73 Recovering different phases The static model The dynamic model The push toward symmetry of pecuniary externalities increases (decreases) with transportation cost (τ). Theorem When the marginal profit is bigger than the intrinsic profit, b > a, the equilibrium distribution of the entry-exit process is bimodal with modes in x = 0 and x = 1, when b < a the equilibrium distribution is unimodal with mode in x = 0.5, and when a = b the equilibrium distribution is uniform.

74 The static model The dynamic model Simulations and stationary distributions τ=0.95 τ= τ=0.95 τ=

75 The static model The dynamic model Comparative dynamics: Number of households 1 3 AGGLOMERATION A B C 0.9 A B C τ EQUIDISTRIBUTION I x

76 The static model The dynamic model Comparative dynamics: Fixed costs AGGLOMERATION C B A A B C τ EQUIDISTRIBUTION α x

77 Footloose capital The relevance of agglomeration economies The model Equilibria Walfare Analysis Localized technological externalities and the geographical distribution of firms with P.Dindo, LEM W.P. 2008/11 As before, households are local workers and global consumers. Traditional good trade at no cost and is produced at constant return to scale. Modern goods pay transportation cost τ and are produced with increasing returns. Households are global investors endowed with one unit of capital. They invest it in location 1 or 2. Capital is mobile and trade at no cost.

78 Inter-regional spillovers The model Equilibria Walfare Analysis Firm in l i {1, 2} faces cost function v(y i ) = βy i + α li, y = output β constant and α location specific α l = plus it need one unit of capital. Nα n l + λ(n n l ), Two essential parameter: commercial openness τ and technological openness λ.

79 Capital rent differences The model Equilibria Walfare Analysis 8 >< >: r 1(x) = r 2(x) = 1 + R(x) «µl 2L Nσ 1 + R(x) «µl 2L Nσ 1 x + (1 x)τ σ xτ σ 1 + (1 x) + where total rent of the economy is x 2µL Nασ R(x) = N(xr 1(x) + (1 x)r 2(x)) = σ µ «τ σ 1 xτ σ 1 + (1 x) «τ σ 1 x + (1 x)τ σ 1 x+λ(1 x) + 1 x (1 x)+λx α x + λ(1 x) α (1 x) + λx,.

80 Geographical equilibria The model Equilibria Walfare Analysis Geographical equilibria decided by (x) = r 1 (x) r 2 (x) Border equilibrium x = 0 if (0) < 0 (or x = 1 if (1) > 0): Agglomerated (AG) economies. Interior equilibrium x (0, 1) if (x) = 0 and d (x) dx = (x) < 0: Non agglomerated (NAG) economies if x = 1/2 or Partially agglomerated (PAG) economies otherwise.

81 Capital rent profile The relevance of agglomeration economies The model Equilibria Walfare Analysis (0)>0, (1/2)<0 (0)>0, (1/2)=0 (0)>0, (1/2)>0 (x) 0 (x) 0 (x) x (0)=0, (1/2)<0 0.5 x (0)=0, (1/2)=0 x x + x (0)=0, (1/2)>0 (x) 0 (x) 0 (x) x (0)<0, (1/2)<0 0.5 x (0)<0, (1/2)=0 0.5 x (0)<0, (1/2)>0 (x) 0 (x) 0 (x) 0 x x + x 0.5 x (x) for all the sign combinations of the coefficients (1/2) and (0). 0.5 x

82 The model Equilibria Walfare Analysis Geographical equilibria in the plane (λ, τ) 1 AG τ PAG τ NAG AG-NAG τ b τ a 0 0 λ 1 λ Parameters are L = 400, N = 150, σ = 3, µ = 0.5, α = 0.4.

83 Core is better than periphery The model Equilibria Walfare Analysis W 1 (x) = I(x) P 1 (x) W 2 (x) = I(x) P 2 (x), I(x) = income P (1,2) (x) = price index W 1 (x) W 2 (x) is negative in x = 0, zero in x = 1/2 and positive in x = 1: agglomeration favors local households but also increase aggregate income. Consider W T (x) = min {W 1 (x), W 2 (x)}.

84 Welfare maximizing equilibria The model Equilibria Walfare Analysis 1 AG * AG τ PAG τ NAG * AG-NAG * τ b τ a τ w 0 0 λ 1 λ are geographical equilibria which are also total welfare maximizers.

85 Policies The relevance of agglomeration economies The model Equilibria Walfare Analysis Policy g change aggregate welfare W T (x) g = W 1(x) g = 1 I(x) P 1 (x) g + W 1(x) λ λ g + W 1(x) τ τ g assume costs for improving both openness is equal λ g = τ g then gradient analysis tells which policy is best.

86 Best local policy The relevance of agglomeration economies The model Equilibria Walfare Analysis 1 τ b τ a λ + AG τ PAG τ NAG AG-NAG 0 0 λ 1 λ Welfare gradient: arrows point to the best policy.

87 Tractable model with static and dynamic geographical equilibria Technological externality strong (too strong?) source of agglomeration In an heterogeneous framework, idiosyncrasies reduce core-periphery likelihood. Agglomeration is a meta-stable phenomenon In General Equilibrium setting, increasing technological openness: leads to smoother τ-transition between equilibria (no hysteresis) decreases welfare gaps and the social cost of globalization policies

88 Tractable model with static and dynamic geographical equilibria Technological externality strong (too strong?) source of agglomeration In an heterogeneous framework, idiosyncrasies reduce core-periphery likelihood. Agglomeration is a meta-stable phenomenon In General Equilibrium setting, increasing technological openness: leads to smoother τ-transition between equilibria (no hysteresis) decreases welfare gaps and the social cost of globalization policies

89 Tractable model with static and dynamic geographical equilibria Technological externality strong (too strong?) source of agglomeration In an heterogeneous framework, idiosyncrasies reduce core-periphery likelihood. Agglomeration is a meta-stable phenomenon In General Equilibrium setting, increasing technological openness: leads to smoother τ-transition between equilibria (no hysteresis) decreases welfare gaps and the social cost of globalization policies

90 Tractable model with static and dynamic geographical equilibria Technological externality strong (too strong?) source of agglomeration In an heterogeneous framework, idiosyncrasies reduce core-periphery likelihood. Agglomeration is a meta-stable phenomenon In General Equilibrium setting, increasing technological openness: leads to smoother τ-transition between equilibria (no hysteresis) decreases welfare gaps and the social cost of globalization policies

91 Tractable model with static and dynamic geographical equilibria Technological externality strong (too strong?) source of agglomeration In an heterogeneous framework, idiosyncrasies reduce core-periphery likelihood. Agglomeration is a meta-stable phenomenon In General Equilibrium setting, increasing technological openness: leads to smoother τ-transition between equilibria (no hysteresis) decreases welfare gaps and the social cost of globalization policies