The Economics of Density: Evidence from the Berlin Wall Gabriel M. Ahlfeldt London School of Economics and CEPR Stephen J. Redding Princeton University, NBER and CEPR Daniel M. Sturm London School of Economics and CEPR Nikolaus Wolf Humboldt University and CEPR 1 / 40 Motivation • Economic activity is highly unevenly distributed across space: – The existence of cities (e.g. 19 cities worldwide had a population greater than 10 million in 2007) – Concentrations of economic functions within cities (e.g. advertising agencies in mid-town Manhattan) • A key research objective is determining the strength of agglomeration and dispersion forces – Agglomeration: increasing returns – Dispersion: land scarcity and commuting costs • Determining the magnitude of these forces is central to a host of economic and policy issues: – Productivity advantages of cities – Cost-benefit analyzes of transport infrastructure – E ff ects of property taxation and regional policy 2 / 40
Empirical Challenges • Economic activities often cluster together because of shared locational fundamentals – What are the roles of agglomeration/dispersion forces versus shared natural advantages? – Historical natural advantages can have long-lived e ff ects through for example sunk costs or coordination e ff ects • One approach regresses productivity, wages or employment on the density of economic activity – Third variables can a ff ect both productivity and wages and density – Di ffi cult to find instruments that only a ff ect productivity or wages through density (with a few exceptions) • Little evidence on the spatial scale of agglomeration forces or separating them from congestion forces • Di ffi cult to find sources of exogenous variation in the surrounding concentration of economic activity 3 / 40 This Paper • We develop a quantitative model of city structure to determine agglomeration and dispersion forces, while also allowing empirically-relevant variation in: – Production locational fundamentals – Residential locational fundamentals – Transportation infrastructure • We combine the model with data for thousands of city blocks in Berlin in 1936, 1986 and 2006 on: – Land prices – Workplace employment – Residence employment • We use the division of Berlin in the aftermath of the Second World War and its reunification in 1989 as a source of exogenous variation in the surrounding concentration of economic activity 4 / 40
Road Map • Historical Background • Theoretical Model • Data • Reduced-Form Evidence • Structural Estimation 5 / 40 Historical Background • A protocol signed during the Second World War organized Germany into American, British, French and Soviet occupation zones • Although 200km within the Soviet zone, Berlin was to be jointly occupied and organized into four occupation sectors: – Boundaries followed pre-war district boundaries, with the same East-West orientation as the occupation zones, and created sectors of roughly equal pre-war population (prior to French sector) – Protocol envisioned a joint city administration (“Kommandatura”) • Following the onset of the Cold War – East and West Germany founded as separate states and separate city governments created in East and West Berlin in 1949 – The adoption of Soviet-style policies of command and control in East Berlin limited economic interactions with West Berlin – To stop civilians leaving for West Germany, the East German authorities constructed the Berlin Wall in 1961 6 / 40
The Division of Berlin 7 / 40 Theoretical Framework • We build on the urban model of Lucas and Rossi-Hansberg (2002), which has a number of attractive features – Models city structure in continuous two-dimensional space – Does not impose mono-centricity – But considers a symmetric circular city • We develop an empirically-tractable version of this model – Model the city as a large number of discrete blocks – Allow for di ff erences in production fundamentals, residential fundamentals and transport connections across blocks – As a result the model allows for a rich asymmetric distribution of economic activity within the city • The model remains tractable because of heterogeneity in workers’ commuting decisions, modeled following Eaton and Kortum (2002) • The model provides a quantitative framework that can also be used for analyzing other interventions (e.g. transport network) 8 / 40
Model Setup • We consider a city embedded within a larger economy, which provides a reservation level of utility ( ¯ U ) • The city consists of a set of discrete blocks indexed by i , with supply of floor space depending on the density of development ( j i ) • There is a single final good which is costlessly traded and is chosen as the numeraire • Markets are perfectly competitive • Workers choose a block of residence, a block of employment, and consumption of the final good and floor space to max utility • Firms choose a block of production and inputs of labor and floor space to max profits • Floor space within each block optimally allocated between residential and commercial use • Productivity depends on fundamentals ( a i ) & spillovers ( Υ i ) • Amenities depend on fundamentals ( b i ) & spillovers ( Ω i ) • Workers face commuting costs 9 / 40 Consumption • Utility for worker w residing in block i and working in block j : ◆ b ✓ ` ij ◆ 1 � b ✓ c ij U ij w = B i z ij w , 0 < b < 1, 1 � b d ij b – Consumption of the final good ( c ij ), chosen as numeraire ( p i = 1) – Residential floor space ( ` ij ) – Residential amenity B i – Commuting costs d ij – Idiosyncratic shock z ij w that captures idiosyncratic reasons for a worker living in block i and working in block j • Indirect utility U ij w = z ij w B i w j Q b � 1 i , d ij • The idiosyncratic shock to worker productivity is drawn from a Fr´ echet distribution: F ( z ij w ) = e � T i E j z � e ij w , T i , E j > 0, e > 1, 10 / 40
Commuting Decisions • Probability worker chooses to live in block i and work in block j is: ⌘ � e ⇣ d ij Q 1 � b ( B i w j ) e T i E j ( B r w s ) e ⌘ Φ ij i p ij = Φ . ⌘ � e ⇣ d rs Q 1 � b ∑ S r = 1 ∑ S s = 1 T r E s r • Residential and workplace choice probabilities p ij = ∑ S S S p ij = ∑ S j = 1 Φ ij i = 1 Φ ij ∑ ∑ p Ri = , p Mj = . Φ Φ j = 1 i = 1 • Conditional on living in block i , the probability that a worker commutes to block j follows a gravity equation: E j ( w j / d ij ) e p ij | i = s = 1 E s ( w s / d is ) e , ∑ S 11 / 40 Commuting Market Clearing • In the model, workplace employment in block j equals the sum across all blocks i of residence employment times the probability of commuting from i to j : ( w j / d ij ) e S d ij = e kt ij . ∑ H Mj = s = 1 ( w s / d is ) e H Ri , ∑ S i = 1 • In our data, we observe workplace employment ( H Mj ), residence employment ( H Ri ) and bilateral travel times ( t ij and hence d ij ) • Given these observed data, we can solve for the wages for which the observed values of workplace and residence employment are an equilibrium of the model • Commuting equilibrium above provides a system of S equations that determines unique values of the S unknown wages { w j } 12 / 40
Consumer Equilibrium • Expected utility # 1 / e " S S ⌘ � e ⇣ d rs Q 1 � b ( B r w s ) e = ¯ ∑ ∑ E [ U ] = g U , T r E s r r = 1 s = 1 • Residential amenities ( B i ) from residential choice probabilities: ◆ 1 e Q 1 � b B i T 1 / e ✓ H Ri i i = , ¯ W 1 / e U / g H i S E s ( w s / d is ) e , d is = e kt is . ∑ W i = s = 1 • Residential amenities are influenced by both fundamentals ( b i ) and spillovers ( Ω i ) " ◆# S ✓ H Rs b i = B i Ω � h e � rt is ∑ , Ω i ⌘ . i K s s = 1 13 / 40 Production • A single final good (numeraire) is produced under conditions of perfect competition, constant returns to scale and zero trade costs with a larger economy: � a ( q j L j ) 1 � a , � X j = A j 0 < a < 1, H Mj • H Mj is workplace employment • L j is total floor space • q j is the fraction of floor space allocated to commercial use • Productivity ( A j ) depends on fundamentals ( a j ) and spillovers ( Υ j ): " ◆# S ✓ H Ms A j = a j Υ l e � dt is ∑ j , Υ j ⌘ , K s s = 1 • d is the rate of decay of spillovers • l captures the relative importance of spillovers 14 / 40
Producer Equilibrium • Firms choose a block of production, e ff ective employment and commercial land use to maximize profits taking as given goods and factor prices, productivity and the locations of other firms/workers • Productivity ( A j ) from profit maximization and zero profits: ✓ a a ◆ 1 1 � a q j = ( 1 � a ) 1 � a A . j w j • Production fundamentals ( a j ) and spillovers ( Υ j ) follow from the production technology: ◆# � l " S ✓ H Ms a j = A j Υ � l e � dt is ∑ , Υ j ⌘ . j K s s = 1 15 / 40 Land Market Clearing • Utility max and pop mobility imply demand residential floor space: 1 H Ri ¯ U 1 � b ( 1 � q i ) L i = . b 1 b 1 � b B 1 � b 1 � b b v ¯ i i • Profit max and zero profits imply demand commercial floor space: ✓ w i 1 ◆ 1 � a q i L i = H Mi . a A i • Floor space L supplied by a competitive construction sector using geographic land K and capital M as inputs L i = j i K 1 � µ j i = M µ , i , i • Density of development ( j i ) from land market clearing: = ( 1 � q i ) L i + q i L i L i j i = K 1 � µ K 1 � µ i i 16 / 40
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