Urbanization, Growth and Structural Change

Transcription

1 Urbanization, Growth and Structural Change Fabian Eckert and Michael Peters Yale University PRELIMINARY AND INCOMPLETE February 14, 2016 Abstract The process of economic growth has many non-balanced features. Of particular importance are employment changes across sectors of production and population changes across space. This paper makes two contributions. First of all, we systematically document these patterns across many countries of the world using detailed micro data. Secondly, we explore wether a parsimoniously parametrized model of trade and geography featuring demand non-homotheticities can explain the comovement between workers moving out of agricultural production and across space. We thank participants at the Yale International Lunch for very helpful comments. We are particularly thankful to Costas Arkolakis, Treb Allen, Sam Kortum, Giuseppe Moscarini and Aleh Tsyvinki for their suggestions. We also thank Tavis Leighton for outstanding research assistance. 1

2 1 Introduction Economic growth is accompanied by substantial changes in the way production is organized. The economic literature has focused on two. There is a large literature on structural change, referring to the process by which different sectors gain and lose) in importance. There is also a large literature on change across space, whereby the distribution of production and living) localities gets concentrated as countries develop. We will refer to this process loosely as urbanization, even though this will - strictly speaking - not be a paper about the emergence of cities. Casual empiricism suggests that these processes are related. Two basic regularities of these forces are i) a decline in the employment share in agriculture and ii) population movement from rural to urban areas. As far as quantitative economic models go, however, these process have so far been treated independently. There is a large quantitative macroeconomic literature on structural change. This literature is entirely about time-series properties. There is also a recent literature on quantitative trade-and geography models. While this literature has a rich microstructure on the spatial dimension, it is mostly static in nature. In this paper, we try to bring these two literatures together to have a quantitative framework that can speak to the joint time-series properties of mobility across space and across sectors of production. Related Literature On the empirical side there is a big literature on the reallocation process of workers across sector lines widely referred to as structural tranformation. Authors such as Kuznets [1957] and Chenery [1960] 2

3 have been early observers of the striking downward trend in the aggregate agricultural employment share and the simultaneous increase in manufacturing employment in the United States. Later the same facts were documented across developed countries by Herrendorf et al. [2013]. Eventually manufacturing employment peaked in the United States in the mid-70s ushering in a secular decline in the manufacturing employment share, with an ever larger fraction of US workers earning their wages in the service industry. This development completed the set of facts today widely known as strucutral change. The first key empirical contribution of our paper is to zoom in on these aggregate developments and to rigorously document the regional heteorgeneity and patterns that underlie it. For a global sample of countries in both the developed and developing world, we analyze the comovement of regional labour shares and population denities. As economic models take the spatial distribution of economics acitvity more and more seriously we hope to add to the hard empirical facts that any spatial model of growth needs to match. Recent work by Hornbeck and Moretti and David et al. [2013] has begun to highlight some of these local facts, focussing on the effect of spatially disaggregated TFP shocks on local labour markets. Additionally, there is an extensive literature in the field or urban and regional economics dealing with the phenomenon of the increasing spatial agglomeration of economic activity, in particular in cities. This literature has sought to document and understand the various agglomeration and dispersion forces that govern the spatial distribution of economic activity in coutries. In a second contribution our paper adds to this literature by doc- 3

4 umenting for regions across the world how the combination of structural change combined with regional comparative advantages quite naturally exert powerful forces on the reallocation of people across land. In particular we document how the particular direction of structural change systematically pushes people out of agricultural regions into denser urban localities. On the theoretical side, exploting techniques borrowed from the field of trade [Allen and Arkolakis, 2014] in a recent important contribution showed how to rigorously integrate spatial linkages into a general equilibrium model of regions. A simplified version of their model without local amenities and without production spillovers serves as the basic spatial structure underlying our model. As far as stuctural change is concerned, the seminal article by Baumol [1967] began a series of attempts at writing down models that could rationalize the asymmetric reallocation of workers first from the agriculural to the manufacturing sector and later into services. These early models already established the two key mechanisms by which structural change of this form can occur: either via demand non-homotheticity that would shift sectoral demand as nations grew richer, or technological change that is biased towards a particular sector allowing it to shed workers to the benefit of another. All these early models however faced a severe drawback: while they could rationalize the occurence of setoral reallocation of workers throughout the growth process, ie could speak to the so-called Kuznet facts, this came the expense of being unable to match the Kaldor facts. In an important contribution then Kongsamut et al. [2001] were the first authors to write down 4

5 a theoretical model which qualitatively matched both sets of empirical constraints in a neoclassical growth model augmented to allow for demand side driven structural change through Stone-Geary preferences. A few years on Ngai and Pissarides [2007] accomplished the same feat for supply side driven structural change, incorporating differential sectoral TFP growth within the framework of a neoclassical model of growth. The theoretical contribution of our paper is then to write down a model that combines a mechanism for structural change with spatial linkages in a general equilibrium model of regions. This allows us to study the joint movement of people across space and sector lines as we adjust our aggregte TFP parameter to match aggregate TFP growth observed in the time series. The remainder of the paper is structured as follows. Section 2 documents our empirical facts of regional structural change, populations and their comovement. and section 3 presents the theory, its empirical implications and the corresponding moments in the data. 2 Empirical Facts We document four facts about regional structural change using the decennial census data from Argentina between 1970 and 2011 made available by the National Institute of Statistics and Censuses of Argentina and downloaded from the Ipums International website. We are working on conducting a similar analysis for all countries in the Ipums International database for which data is available that covers a long enough period to observe struc- 5

6 Argentina Agricultural Employment Share Year Data: National Institute of Statistics and Censuses, Argentina Figure 1: Time series of the aggregate agricultural employment share tural transformation and offers a high enough regional resolution to make a regional analysis worthwhile. The following facts hold more or less tight for all countries we have analyzed thus far. Fact 1: The aggregate agricultural employment share has been falling steadily throughout the post World War II growth process. See Figure 1. Fact 2: The post World War II growth process has been accompanied by a reallocation of population across Argentina. In particular, there is an increase in concentration across space, whereby the most populous regions account for a larger of the population. See Figure 2. Fact 3: The regional agricultural employment share in 1970 is negatively correlated with population share growth from See Figure 3. 6

7 Argentina Population Share Year 90% least populous counties in % most populous counties in 1970 Data: National Institute of Statistics and Censuses, Argentina Figure 2: Time series of the population share attributable to top decile vs the remainder Next we construct a simple spatial model to speak to this set of empirical facts on structural change in the aggregate and across regions. 3 Theory We consider an economy with R distinct locations, which we denote by r = 1,..., R. There are two sectors of production, agriculture and nonagriculture, which we denote by s = A, N A. Population is perfectly mobile but there are dispersion forces, 1 ensuring each region is inhabited by a non- 1 The fact that esch region is equipped with a technology to produce a differentiated variety in each sector acts as a dispersion force. 7

8 Argentina Population Share Growth Agricultural Employment Share 1970 Trend Data: National Institute of Statistics and Censuses, Argentina Counties Figure 3: Regional agricultural employment shares and regional growth in population shares zero mass of agents. For now we consider a static economy and introduce dynamics by considering different cross sections of the model indexed by a changing sector-neutral TFP parameter. Importantly, we assume that are no inter-regional trade costs. The absence is trade-costs is extremely useful to get a streamlined treatment of both the macroeconomic literature on structural change and the literature on trade and geography. By dissociating the localities of production and consumption, we can express aggregate demand patterns simply as a function of aggregate prices P A and P NA. In particular, the distribution of people and hence income) across locations does not affect aggregate demand given prices. Intuitively, our economy admits aggregation on the consumer side. The patterns of aggregate supply across space, in contrast, will then 8

9 be determined by pattern of relative prices and comparative advantage. If non-homotheticities in demand change relative prices along the growth path, regional comparative advantage will evolve endogenously and in particular depend on changes in factor neutral technological progress. More specifically, we consider the following environment. Consumer preferences are given by where U = u C A, C M ), 1) C i = [ r ] σ y σ 1 σ 1 σ ir. 2) Hence, both agricultural and nonagricultural products are combined into a standard CES consumption bundle, with regional varieties being exogenously differentiated a la Armington. Final utility is then given from 1). At this point we do not need to specify the exact details of u.), but we obviously allow the demand stemming from 1) to be non-homothetic. Of course, all variables, should be indexed by time t. For notational simplicity we do not do so explicitly as long as there are no reasons for confusion. The respective varieties in sector s in region r are produced under constant returns according to Y rs = A rs L rs. Here L rs denotes total employment in sector s and region r and A rs denotes aggregate productivity. It is useful to express A rs as A trs = Z t M rs, i.e. productivity in time t depends on a time-varying aggregate TFP term Z t, which is common across sector-region cells and a term M rs, which parametrizes 9

10 both comparative advantage within region r and absolute advantage across regions. For now, we assume that Z t is the only thing, which varies over time. Importantly, we assume M rs to be constant over time in order to focus on structural change driven purely from the demand side. We will come back to this restriction below. The absence of trade costs implies that the supply side of the economy can be characterized by the usual relationship. Because people are mobile across both space and industries, wages are equalized across sectors within regions and we denote them as w r. Note that wages are not necessarily equalized across space, if there are dispersion forces 2. Utility, however, is equalized across space in any spatial equilibrium. Given equilibrium wages, prices for regional sector specific varities are given by p sr = w r A sr, and the price index for sector s is given by P s = r wr A rs ) 1 σ ) 1 1 σ. Importantly, P s is equalized across space because of the absence of trade costs. This directly implies that the share of total sectoral expenditure of consumers living in region r on sector s goods from region m is equal across destination regions r. In particular, 2 Beyond those induced by the ability of region to produce sectoral differentiated varities. Eg. Allen and Arkolakis [2014] add a regional agglomeration externality, which is a function of local population, which prevents wages from equalizing across space 10

11 π rsm = = psm P s ) 1 σ wm /A sm = ) 1 σ w m A ms w r r P s ) 1 σ A rs ) 1 σ = π sm. 3) Now consider the allocation of labor. Let L r be the number of people living in region r. The number of people in region r working in sector s is then given by L rs = A 1 rs Y rs = 1 A rs p rs Y rs p rs P s Y s P s Y s = 1 w r π sr P s Y s. 4) Here P s Y s denotes total spending on sector s goods and Yrsprs P sy s the share of total spending in sector s going to region r. = π sr is simply For now we do not specify the preferences in 1), but work directly with aggregate demand shifters. In particular, let total spending on sector s goods be given by P s Y s ϑ s P Y, 5) where ϑ s denotes the share of aggregate spending allocated towards sector s goods. With non-homothetic demand, ϑ s will not be constant across time because it will depend on aggregate income and hence aggregate TFP Z t. For now we will take [ϑ s,t ] t as given. Using 4) and 5) we therefore have that L rs = 1 w r π sr ϑ s P Y. 6) 11

12 We can also solve for the within-county-labor share in sector s. Note first that the number of people living in region r is given by L r = L rs = [ ] 1 π sr ϑ s P Y w s s r [ ] = 1 P Y ϑ s π sr. 7) w r Hence, the employment share in sector s in region r is given by s µ rs L rs L r = π sr ϑ s ŝ ϑ ŝ πŝr. 8) 8) is an important equation for us. In particular, using 3), it follows directly that µ rs = L rs L r = [ w r A rs ) 1 σ / r ŝ ϑ ŝ [ w r A rŝ ) 1 σ / r ) ] 1 σ w r A rs ϑ s ) 1 σ ]. 9) w r A rŝ Hence, the employment share in sector s in region r depends on the interaction between aggregate demand for sector s ϑ s ) and region r s comparative advantage relative to other regions. In particular, 9) implies that λ r L A,r L NA,r = π Ar π NAr ϑ A ϑ NA = = ArA A rna ) σ 1 m w r ) 1 σ A ra / m w r ) 1 σ A rna / m m ) σ 1 A mna w m A ma w m ) σ 1 ) 1 σ w m A ms ϑ A ) 1 σ w m ϑ NA A mna ϑ A ϑ NA, 10) where A and N A denotes the agricultural and non-agricultural sector respectively. We refer to λ r as sectoral specialization in region r. It is interesting 12

13 to note one direct implication of 10): λ r = L A,r/L NA,r = A ra/a rna ) σ 1 σ 1, 11) λ m L A,m /L NA,m A ma /A mna ) i.e. the relative degree of sectoral specialization in agriculture across counties only depends on technological comparative advantage - neither the distribution of wages [w r ] r, nor the allocation of people across space [L r ] r nor the aggregate demand patterns ϑ A ϑ NA. In a neoclassical model with constant technology M rs, this directly implies that λ r /λ m should be constant across time even though the economy as a whole might experience structural change in that the aggregate labor share in agriculture declines. We are going to test this implication for the case of Argentina below. To do so it is useful to also define the aggregate counterpart of 10), i.e. λ = L A L NA = r L A,r r L NA,r = 1 r w r 1 r w r π Ar π NAr ) ϑ A ϑ NA. 12) Note that this the only implication we can derive without imposing further assumptions, because it is the only implication, which does not need to take a stand on how people move across space and what equilibrium wages are. We are now going to put more restriction on that process. The benchmark of perfect mobility A natural benchmark is the case of perfect mobility and aggregate preferences 1) only defined over consumption goods. In this case, equilibrium wages have to be equalized across space, i.e. w r = w. 13) 13

14 Note that 13) directly implies that π sr = Aσ 1 rs m Aσ 1 ms, i.e. π sr is fully determined from technology. Labor market clearing requires that Lr = L L r = L ra + L rna. We also have good market clearing region-by-region or balanced trade), i.e. wl r = Total income in region r = π A,r P A Y A + π NA,r P NA Y NA = π Ar ϑ A + π NAr ϑ NA ) P Y. 14) We can pick one normalization for our economy. It is useful to normalize aggregate income to unity, i.e. P Y = wl = 1. 15) Combining 14) and 15) yields a tractable expression for the allocation of people across space, i.e. L r L = π Arϑ A + π NAr ϑ NA = A σ 1 ) ra ϑ A + m Aσ 1 ma A σ 1 ) rna ϑ NA 16) m Aσ 1 mna Hence, the share of people in region r are simply a demand weighted average of region r s relative technology. In particular: 1. regions with an absolute advantage will have a higher population density, 14

15 2. regions with a comparative advantage in agriculture, i.e. a large π A,r /π NA,r, will have a higher population density as long as aggregate demand puts a lot of weight on agricultural goods. In particular, 16) directly implies that d dt ) Lr dϑ A dϑ NA = π Ar + π NAr L dt dt = π Ar π NAr ) dϑ A dt. 17) As the aggregate agricultural expenditure share declines, the share of people living in region r will decline if and only if region r has a comparative advantage in agriculture, i.e. π Ar > π NAr. 17) is a crucial equation for us because it imposes tight restrictions on the comovement between changes in population density and changes in agricultural employment. To implement 17) empirically, we can express it in terms of observables. Using 6) we also get that L ra = 1 w π Ar ϑ A. 18) Hence, the aggregate employment share in agriculture is indeed simply given by L A L = r L ra L = r π Ar ϑ A = ϑ A. 19) Using 16) and 19) it therefore follows directly that L r L = π NA,r + π Ar π NA,r ) L A L. 20) Hence, declines in the aggregate agricultural share over time will increase decrease) population density in region r if region r has a comparative advantage in agriculture non-agriculture). 15

16 Finally the models makes tight predictions about the relationship between agricultural employment shares and the share of people or population density) in region r. Using 18) and 20) we get that L ra = L π Ar ϑ A 1 = L L r π π L NA,r A,r = L r L r L r π Ar π NA,r π A,r π Ar π NA,r ) L 1 π NA,r L r = π A,r π Ar π NA,r π A,rπ NA,r π Ar π NA,r Lr L ) 1 21) Hence, there is linear relationship between the agricultural employment share in region r and the inverse of the population share in region r! In particular, wether the correlation between regional population and agricultural employment is negative depends on comparative advantage. In particular, π A,r π NA,r π Ar π NA,r = Empirical implications 1 1 π NA,r 1 > 0 iff π A,r > π NA,r. π A,r The model with perfect mobility has four predictions, which we can take to the Argentinian data. 1. The regional pattern of sectoral specialization should be constant over time. More precisely, using 11) and 12) it follows directly that where π Ar π NAr λ r = π Ar π NAr λ, 22) is constant over time. Hence, as far as regional specialization is concerned, each region moves [ one-to-one with the aggregate. { } ] R λ The time series patterns of [λ t ] t and rt λ t are contained in Fig- r=1 ure 4. In particular, we plot the evolution of λ t and the median of λrt While it is indeed the case that the aggregate degree of specialization declines at a faster rate than then "typical" county, the relative degree 16 t λ t.

17 Argentina Year Normalized quantities to 1 in Aggregate Lambda Median Regional/Aggregate Lambda Data: National Institute of Statistics and Censuses, Argentina Figure 4: Time series of λ and the median across regions of λr λ. Normalized 1970 in each group to 1. of specialization λ rt /λ t is not constant as our benchmark model predicts. Below, we will therefore incorporate additional features into the theory. 2. The changes in regional population density in response to sector reallocation in the aggregate is given from 20) as d L r /L) dt = π Ar π NA,r ) d L A/L) dt Note that 22) implies that ) πar d LA /L) = π NA,r 1 π NA,r dt 23) π Ar π NA,r = λ r λ, 24) which should be constant. Hence, regions whose degree of specialization exceeds the aggregate in 1970, are predicted to have declining popula- 17

18 Year Median Population Share A Comparative Adv Regions Median Population Share NA Comparative Adv Regions Comparative Advantage based on 1970 lambdas. Normalized quantities to 1 in Data: National Institute of Statistics and Censuses, Argentina Figure 5: Time series of the median of Lr L median λ r ) λ and λ r λ λr over the regions for which > λ < median λ r λ ). Normalized 1970 in each group to 1. tion density if the the aggregate agricultural share declines. Conversely, regions that already specialized in non-agricultural goods in 1970 will see an increase in population density if the economy undergoes structural change induced by demand side changes. In Figure 5 we depict the time series properties of population density across space for each region {L rt /L)} R r=1 [ ]. In particular, we distinguish regions according to t condition 24). We see that the distribution of comparative advantage in 1970 is a predictor for relative population growth: while regions with a comparative advantage in agriculture see their population share decline, regions, who were initially relatively specialized in manufacturing expand. 3. We can also look at the distribution of agricultural shares across space. 18

19 Argentina Agricultural Employment Share Data: National Institute of Statistics and Censuses, Argentina Figure 6: Density plot of regional employment shares at different points in time Is it the case that some regions increase their agricultural share even though agricultural employment declines in the aggregate? The answer is a clear no. To see this, note that 21) and 23) imply that d L ra /L r ) = π ) 2 A,rπ NA,r Lr d L r /L) dt π Ar π NA,r L dt ) 2 Lr d L A /L) = π A,r π NA,r. L dt 25) Hence, all regions should see their agricultural shares declining if the aggregate employment share shrinks. In Figure 6 we depict the crosssectional density of regional agricultural shares for different years. It is clearly seen that the entire distribution shifts in as expected from the theory. 4. Finally, we can look at the comovement between changes in agricultural 19

20 employment and changes in population density at the regional level. As seen from 25), we get that d L ra /L r ) dt = π A,rπ NA,r π Ar π NA,r ) 2 Lr d L r /L). L dt Hence, if the entirety of population mobility was explained by demanddriven structural change we should see the following pattern: for counties with an comparative advantage in agriculture according to 24), we see a positive relationship between population density and agricultural employment, and for regions with a comparative advantage in non-agriculture, the opposite is true. Because the first second) group will see declining increasing) population densities, all counties will see falling agricultultural employment shares as seen in 25)). In the data, we find the pattern depicted in Figure 7. While the gradient between changes in agricultural employment and changes in population growth is indeed flatter for regions with a comparative advantage in agriculture, it is still negative. Below, we will incorporate additional features into our theory to be able to speak to this fact in the data. Finally, we depict the regional comovement of changes in agriculture shares and changes in population density in Figures 8 and 9. Two features stand out. First, there is ample heterogeneity, with the changes in agricultural shares ranging from -200% to +70% The same is true for the changes in population density. Secondly, there is a correlation between these two phenomena, as also seen in Figure 7. In particular, regions with a fast decline in agricultural employment shaded light in Figure 8) tend to be regions with a large increase in their population density shaded dark in Figure 9). 20

21 Agricultural Share Growth Population Growth Comparative Advantage: A Comparative Advantage: NA CA: A, Trend CA: NA, Trend Comparative Advantage based on 1970 lambdas. Data: National Institute of Statistics and Censuses, Argentina Figure 7: Agricultural Share Growth and Population Growth by comparative advantage group 21

22 Legend Argentina ASHARE Figure 8: Map of the agricultural employment share change between in Argentina 22

23 Legend Argentina PSCHANGE Figure 9: Map of the population share change between in Argentina 23

24 References Treb Allen and Costas Arkolakis. Trade and the topography of the spatial economy. Technical report, Quarterly Journal of Economics, William J Baumol. Macroeconomics of unbalanced growth: the anatomy of urban crisis. The American economic review, pages , Hollis B Chenery. Patterns of industrial growth. The American Economic Review, 504): , H David, David Dorn, and Gordon H Hanson. The geography of trade and technology shocks in the united states. The American Economic Review, 1033): , Berthold Herrendorf, Richard Rogerson, and Ákos Valentinyi. Growth and structural transformation. Technical report, National Bureau of Economic Research, Richard Hornbeck and Enrico Moretti. Who benefits from productivity growth? the local and aggregate impacts of local tfp shocks on wages, rents, and inequality. Technical report. Piyabha Kongsamut, Sergio Rebelo, and Danyang Xie. Beyond balanced growth. The Review of Economic Studies, 684): , Simon Kuznets. Quantitative aspects of the economic growth of nations: Ii. industrial distribution of national product and labor force. Economic Development and Cultural Change, pages 1 111,

25 Rachel Ngai and Christopher A Pissarides. Structural change in a multisector model of growth