The growth episodes of the US economy: Evidence from Metropolitan Areas

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The growth episodes of the US economy: Evidence

from Metropolitan Areas

Master Thesis

MSc in International Economics and Business

8

th

_{January, 2018}

Author : H.G.E.C. (Frank) Groothedde

E-mail : frankgroothedde@hotmail.com

Student ID : 2375931

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Abstract:

The existing literature on growth patterns, and growth episodes in particular, has so far focused primarily on national performance, masking substantial differences in growth across metropolitan areas within the same country. Using a panel dataset of 382 metropolitan areas over the period 2002-2015 we employ a wide-range set of explanatory variables to explain metropolitan area growth patterns. First, this research shows that U.S. metropolitan areas follow widely diverging growth trajectories, with some metropolitan areas prospering whereas others are increasingly falling behind. The results indicate that richer metropolitan areas exhibit higher rates of growth, are more likely to experience growth episodes and are more resilient to economic shocks than their poorer counterparts. Second, the results indicate that factors associated with getting growth may be different from factors associated with the ability to sustain growth. Interestingly, the effect of these factors varies substantially across metropolitan areas with different income levels. Finally, this research contributes by linking the contribution of metropolitan areas to aggregate growth. The results clearly indicate the existence of Power-Law behaviour, in which the majority of aggregate growth is increasingly driven by the disproportionate contribution of a few large metropolitan areas. The main relevance of this research lies in applying the taxonomy of growth episodes to metropolitan areas and linking their contribution to aggregate performance. Despite these strong results the majority of growth and growth episodes remains unexplained and, hence, further research is needed.

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1. Introduction

Why are some metropolitan areas rich and others poor? Why do some metropolitan areas experience persistent levels of growth whereas others remain trapped in poverty? The past decades have seen an enormous range of research aimed at understanding the process and determinants of economic growth. Over time, economists have sought to identify the key sources of economic growth and tried to provide a model which accounts for regional differences in levels of income. Following the work of Romer (1986) and Lucas (1988), a vast literature has emerged that analyses the patterns and drivers of long-run national growth performance. The extensive focus on long-run national growth, however, masks deep differences in growth across time and regions. By now, it is well established that national growth performance masks widely diverging growth trajectories across regions within the same country. In the U.S. for instance, cities like New Orleans are increasingly falling behind whereas cities like Austin are prospering. Recent work has therefore begun to examine the factors associated with differential growth trajectories across regions within countries. So far there is relatively little systematic evidence on interregional differences in income and growth. This paper aims to contribute to this debate by analysing growth patterns at the level of metropolitan areas.

This research contributes to three different strands of literature by investigating growth episodes and trajectories at the level of metropolitan areas. Our paper is most closely related to the literature on growth episodes. The existing literature has exclusively analysed factors associated with growth episodes at the national level. Examining growth episodes at the sub-national level, however, adds an extra level of granularity because it allows for the inclusion of regional determinants. Our results indicate that factors associated with getting growth may be different from factors associated with the ability to sustain growth. These findings contribute to a better understanding of the local determinants associated with sustained growth and provides valuable information on how to enhance sustained growth and growth episodes at the level of metropolitan areas.

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Finally, this paper speaks to the existing literature by analysing regional contributions to aggregate growth. Previous work analyses both regional and aggregate growth performance but largely fails to take into account the macro implications of regional growth. In this study we combine both strands of literature by linking the contribution of metropolitan areas to aggregate growth performance. The corresponding findings reveal valuable insights into the main drivers of national growth performance. The results clearly indicate the existence of Power-Law behaviour, which means that the majority of aggregate growth is increasingly driven by the disproportionate contribution of a few large metropolitan areas. The ten largest contributing metropolitan areas amounted to more than 40 percent of aggregate U.S. growth during the period 2002-2015, further increasing to about 53 percent in the post-crisis period.

The following section provides a literature review on the different strands of growth literature. Then in section 3, the theoretical framework will be demonstrated, section 4 will state the data and descriptive analysis. Section 5 will discuss growth patterns across metropolitan areas, section 6 will present the regression results of the models and their interpretations, and section 7 will discuss the contribution of metropolitan areas to aggregate growth. Finally, section 8 will contain the conclusion of our research on this topic. In addition, an annex will be provided which contains additional information.

2. Literature Review

This review aims to provide insight into the main strands of literature related to this research. Our paper is most closely related to the literature on growth transitions and growth episodes in particular, which will be reviewed first. Moreover, this paper speaks to the literature on regional growth patterns, which will be reviewed subsequently. The final strand of literature reviewed is related to the contribution of individual regions to aggregate economic growth.

2.1 Taxonomy of growth episodes

By now, it is well established that economic growth tends to be highly unstable and can be characterized by large shifts in growth rates across periods. Since the early 1990s, a large body of research has focused on explaining cross-country differences in long-run growth rates, such as the divergence in growth paths between East Asia and Latin America (De Gregorio, 2004). This fixation on long-run growth averages across countries often masks distinct episodes of success and failure, underestimating the importance of persistent growth in economic development. The overwhelming majority of countries have experienced both growth miracles and failures over some periods, suggesting that growth within countries is a “start-stop” process (Jones, 2008). Most countries follow output paths that look more like mountains, cliffs, and plains than steady “hills” (Pritchett, 2000). Thus, in order to understand the patterns of long-run economic growth, attempting to explain differences in long-term growth rates may be misleading. It might instead be more promising to analyse what factors initiate or halt episodes of growth, or what influences the characteristics of growth episodes. Until recently, however, the economics literature provided little guidance on this issue.

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themselves, the country characteristics that are considered determinants of growth are highly persistent over time. As a result, they find that shocks within countries, rather than differences in country characteristics, play an important role in explaining growth variations. This point has been discussed further by the seminal paper of Pritchett (2000), who shows that economic growth is characterized by large shifts in growth rates across periods, especially in developing countries. These shifts lead to frequent transitions across growth regimes and distinct patterns of economic growth. Pritchett has qualitative categorized countries with steady growth as “hills”, rapid growth followed by stagnation as “plateaus”, rapid growth followed by decline as “mountains”, catastrophic falls as “cliffs”, continuous stagnation as “plains” and steady decline as “valleys”. These distinct patterns of economic growth indicate that growth rates across countries are highly unstable. In addition, the results show that growth rates are highly volatile, with developing countries having a much higher standard deviation than developed countries. Building on the insight that countries typically experience frequent transitions in growth regimes, the literature has recently begun to examine the determinants of growth episodes. Following Pritchett (2000), there is a large empirical literature that aims to identify the timing and characteristics of growth episodes. Over the years, different studies have explored the characteristics of different types of episodes.

2.1.1 Decelerations and slumps

A part of the growth literature has focused on the negative implications of unsteady growth, such as decelerations and slumps. For instance, Hausmann et al. (2006) focus on the factors associated with the entry of countries into growth collapses as well as their duration. In their study, growth collapses are defined as periods that start when output per worker growth decelerates to negative rates and end when the value preceding the decline is attained again. Their sample encompasses 180 developing and developed economies over the period from 1960 until 2006, identifying a total of 535 growth collapses. Their results reveal that while countries can experience growth collapses due to multiple reasons, such as political transitions, export collapses and wars, the duration and depth differs substantially across countries and is particularly difficult to predict. The main factor that they find to be robustly associated with the duration of growth collapses is the density of a country’s alternative export basket, which is associated with a shorter crisis duration. Moreover, they find that although short-lived recessions are fairly common across all regions, long-lived recessions are much more prevalent in the developing world.

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distributed evenly across countries. The spread of duration, however, is very large: slumps in low-income countries are substantially deeper than in high-income (OECD) countries.

In a related paper Breuer and McDermott (2013) investigate the factors associated with economic depressions around the world. Their research differs from previous work because it is focused solely on depressions, which by definition are more severe than regular slumps. Economic depressions are defined as periods in which output per capita falls by at least 20 percent in total over at least four years. Their sample encompasses 161 developing and developed economies over the period from 1950 until 2009, identifying a total of 104 depressions in 85 countries. Thus, more than half of the countries have experienced a depression despite the conservative definition. The results are generally strong, indicating that the onset and exit of economic depressions is influenced by a large set of financial, economic, political and cultural variables. Economic liberalization in particular has a substantial impact on reducing the chance of economic depressions.

2.1.2 Accelerations and takeoffs

A related stream of literature focuses on accelerations and takeoffs. For instance, Hausmann et al. (2005) focus in their paper on growth accelerations, which is a rapid increase in economic growth over a sustained period of time. More specifically, the authors define a growth acceleration as an increase in GDP per capita growth of at least 2 percentage points, sustained for eight years or more. In addition, the post-acceleration growth rate has to be 3.5 percent during the entire spell. The sample encompasses 110 countries over the period from 1957 and 1992, allowing for the identification of 83 growth accelerations. This implies that, in any given year, two to three new growth accelerations are initiated worldwide. Several explanatory variables are used to predict the initiation and sustainability of growth accelerations. The results reveal that financial liberalization and positive trade shocks are associated with unsustained growth, while economic reforms and positive political regime changes increase the likelihood of sustained growth accelerations. The vast majority of growth accelerations, however, remains unexplained, underlining the need for further research.

In a subsequent paper, Hausmann et al. (2005) attempt to fill this gap by developing a unified framework for analysing and formulating growth strategies. Their goal is to develop a framework for growth diagnostics, that is, a strategy aimed at identifying and alleviating the most bindings constraints on economic growth. In their study, they show that growth accelerations are fairly easy to initiate and do not necessarily require a comprehensive set of economic reforms. Instead, identifying and alleviating the most binding constraints on economic activity is considerably more effective to initiate growth.

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episodes follow widely diverging growth paths. The average annual real GDP per capita growth is 2.3 percent for countries that experienced takeoffs, while economic growth remained stagnant for those that did not. The results show that takeoffs can be initiated by choosing the right policies, with de jure trade openness and capital account openness being positively correlated with takeoffs after stagnation.

2.1.3 Duration of growth episodes

In contrast, the ability to sustain growth over longer periods of time remains largely unexplained. Even though growth accelerations are fairly easy to initiate, sustaining the process of economic growth turns out to be more demanding (Hausmann et al., 2005; Rodrik, 2005). Over the last decades many developing countries have fundamentally reformed their economies. The results have generally been disappointing due to a lack of persistent growth (Rodrik, 2006). One conclusion from the literature discussed so far is that factors associated with getting growth may be different from what is important to keep growth going.

This issue is addressed by Berg et al. (2012) who investigate the factors associated with sustained growth. In order to identify growth spells they employ econometric structural break tests. Annual growth of GDP per capita must be at least two percent to be classified as growth spell. Their sample encompasses 140 developing and developed countries from 1950 until 2006, allowing for the identification of a large number of growth spells. The results reveal that countries are not different in the frequency of growth spells, but rather in the duration of growth spells. To design effective policies, it is therefore of great importance to understand the sources of sustainable economic growth. Using survival analysis, Berg et al. (2012) find that growth spells can be prolonged by good political institutions, trade liberalization and an equal income distribution. Moreover, an export or production structure that favours manufacturing and sophisticated products is conducive to longer growth, which is consistent with the existing literature (Hausmann et al., 2007; Hausmann et al., 2006). Also, growth is found to be significantly more persistent in advanced economies.

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2.2 Diverging growth trajectories across regions

Spatial differences in per capita income have motivated much of growth theory and development economics. Following the work of Romer (1986) and Lucas (1988) a vast literature has emerged that analyses the patterns and drivers of national growth performance. However, the extensive focus on country-level results hides deep differences in regional growth performance. Indeed, over the past decades regional income disparities have been increasing while there has been a steady reduction of income disparities across countries (OECD, 2016). The divergence within countries can for a large part be attributed to agglomeration economies, as economic activities increasingly tend to be concentrated in space. Generally speaking, workers in larger cities tend to be more productive. This can partly be explained by a greater share of highly-skilled and educated workers, but this is also due to “agglomeration economies” that arise from living and working in larger cities. Agglomeration economies result from three types of micro-foundations, based on sharing, matching and learning mechanisms (Duranton and Puga, 2004). Probably the simplest example of agglomeration through sharing occurs when large numbers of firms or workers benefit by drawing on a common pool of resources, such as public goods and infrastructure. Another source of scale economies through sharing relates to increased specialisation due to a larger number and variety of intermediate goods available. Additionally, large cities are home to a variety of workers and firms, thereby reducing the search and matching friction when looking for a potential employee or supplier. Lastly, large cities facilitate face-to-face contact. This provides more opportunities for people and firms to interact with each other, stimulating the exchange of tacit knowledge.

Given these self-reinforcing mechanisms it should be no surprise that regional income disparities within countries are increasing instead of decreasing. In their paper, Brakman and van Marrewijk (2008) decompose global income inequality and EU income inequality into a within-country and across-country component, revealing that within-country inequality has increased since the 1980s. This trend is also seen in the U.S., where wage convergence ended in 1980 and diverged from 1980 onwards (Giannone, 2017). However, a recent study by Garcilazo and Martins (2013) indicates that the forces of agglomeration are less dominant than one might think. Their results revealed that many rich regions grew faster than poorer ones, but also that many poor regions outperformed richer regions in terms of GDP per capita growth rates. This dispersion in regional growth rates indicates that there is tension between convergence and agglomeration forces. This effect appears to be largely driven by lagging regions. Some regions far away from the frontier are catching-up quite rapidly on the one hand, while on the other hand some lagging regions are increasingly falling behind the frontier.

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aim to promote sustainable and inclusive growth. The World Bank report, for instance, recommends to focus on a few large cities with the highest growth potential as main pillar of development. This means that development policies should be place neutral, allowing the forces of agglomeration to operate at full force. The OECD report on the other hand, advocates the dispersion of economic activities in order to spread the benefits of economic development. In this view, growth potential can be found in many different types of regions, and these should all contribute in the process of economic development. The underlying assumption is that the potential for catching up is present in all types of regions, but the policies to unlock and sustain growth are very different. So far there is relatively little systematic evidence on interregional (or within-country) differences in income and growth. (Acemoglu and Dell, 2010).

2.3 Regional contributions to aggregate growth

Despite the renewed interest in economic geography, the existing literature has largely ignored the contribution of regions to aggregate economic growth. The study of Garcilazo and Martins (2013) is, to the best of our knowledge, the first to investigate how different types of regions contribute to aggregate growth. Their study encompasses 816 OECD TL3 regions over the period from 1995 until 2007. Regional contributions are the product of two components: a size component and a growth component. Accordingly, their research approach takes into account the size of the regional economy in addition to regional rates of growth. Their results reveal that unweighted GDP and GDP per capita growth rates are normally distributed across all TL3 regions. In contrast, regional contributions to aggregate growth follow a Power-Law. This means that a few large regions contribute disproportionally to aggregate growth whereas most regions contribute only marginally. The disproportionate contribution of some regions to aggregate growth is largely driven by their sheer size and economic power rather than by exceptionally high rates of growth.

However, because the group of regions contributing only marginally represents the overwhelming majority, their cumulative contribution to aggregate growth remains dominant. According to the authors, policy makers therefore have to stimulate growth in the periphery and lagging regions since their cumulative contribution to aggregate growth remains dominant, while at the same time ensuring that the regions with the largest contribution keep competitive.

2.4 Contributions to existing literature

The existing literature on growth patterns clearly shows that economic growth tends to be erratic and can be characterized by large shifts in growth rates across periods. As Pritchett (2000) already pointed out, countries tend to follow distinct patterns of growth that can be characterized as hills, plateaus, cliffs, plains and valleys. The results from this literature are mixed. A wide-range set of factors is found to be significantly associated with the onset and/or duration of growth episodes on the one hand, while the majority of growth episodes remains unexplained on the other hand. Further research is therefore needed to shed light on the underlying mechanisms.

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structural headwinds (IMF, 2017). This underlines the need to apply the taxonomy of growth episodes also to developed nations. Furthermore, up until now growth trajectories have mainly been analysed for economies on aggregate, hiding deep differences in growth trajectories across metropolitan areas. Indeed, the existing literature indicates that over the past decades income disparities have been increasing within countries. Taking the U.S. as an example, cities like New Orleans are increasingly falling behind whereas cities like Austin are prospering. Even though the literature indicates that income disparities are increasing across metropolitan areas, little research has been conducted on the underlying growth patterns. There has also been limited research on the contribution of metropolitan areas to aggregate growth. This underlines the need to apply the taxonomy of growth patterns, and growth episodes in particular, to metropolitan areas rather than entire economies.

This paper speaks to both issues by applying the taxonomy of growth episodes to metropolitan areas within the U.S. This is, to the best of our knowledge, the first study to analyse growth episodes at the sub-national level. We add to the existing literature in three major ways. First, we analyse growth episodes and the factors associated with persistent growth at the level of metropolitan areas (i.e. sub-national) rather than the national level. Second, we analyse growth trajectories and agglomeration effects across metropolitan areas within the U.S. Third and finally, we combine both strands of literature by linking the contribution of metropolitan areas to aggregate growth performance.

3. Theoretical Framework and Estimation Methods

Following the literature review, a set of research questions is formulated to shape the focus of this paper. The main goal of this paper is to analyse growth patterns, and positive growth episodes in particular, across metropolitan areas within the U.S. This brings us to the first research question, which is formulated more broadly:

1. What are the main patterns in metropolitan area growth observed and to what extent are metropolitan areas within the U.S. following diverging growth trajectories?

The first research question is formulated more broadly in order to keep an open approach and situate the empirical context. The findings related to this research question serve a dual purpose: they are considered valuable results in themselves and will additionally serve as background information for the following analysis. The following set of research questions is subsequently formulated to analyse growth episode characteristics:

2. What factors are positively related to rates of growth at the metropolitan area level? 3. What factors are positively related to the occurrence of growth episodes at the

metropolitan area level?

4. What factors are positively related to the duration of growth episodes at the metropolitan area level?

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formulated three separate research questions. Each research question captures a different characteristic of growth and is analysed with a different econometric approach, which will be outlined later in this section. Finally, the research question below is formulated to link the contribution of metropolitan areas to aggregate growth performance:

5. What is the relative contribution of individual metropolitan areas to aggregate rates of growth?

Research questions one and five are analysed using descriptive analysis and discussed in sections five and seven resp., whereas research questions two, three and four are analysed using the theoretical framework outlined in this section and discussed in section six. Our theoretical framework is inspired by the approach of McGregor et al. (2015), who analyse growth episodes at the country level. In order to analyse the factors associated with metropolitan area growth rates we first estimate the following regression using annual data from 2002 until 2015:

(1) ΔRGDPit= αi + δXit + δZit + Ѱt + εit

Where ΔRGDPit is the annual growth rate of real GDP per metropolitan area. X is

considered the main variable of interest and represents a vector of explanatory variables capturing idiosyncratic, national and global factors. Z represents a vector of control variables. Finally, our analysis uses MSA (αi) and time (Ѱt) fixed effects.

As for the analysis of growth episodes, two complementary approaches are used. First, the following regression is estimated, which relates the probability that a given year is part of a growth episode to a number of explanatory and control variables.

(2) Episodeit = αi + δXit + δZit + Ѱt + εit

Where Episodeit is a dummy variable indicating whether a given year is part of a positive

growth episode per metropolitan area. X is considered the main variable of interest and represents a vector of explanatory variables capturing idiosyncratic, national and global factors. Z represents a vector of control variables. Finally, our analysis uses MSA (αi) and time (Ѱt)

fixed effects.

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Second, we analyse the relation between the duration of growth episodes and explanatory variables using survival analysis. Initially, the Kaplan Meier estimator is used to estimate the survival function of growth episodes. Subsequently, episode duration is related to a set of explanatory variables by using the Cox's proportional hazards regression model.

In general, the survival function gives the probability of surviving past time t, which can be written as: S(t)=Pr(T>t), where T is the actual survival time. The survival function is the complement of the cumulative distribution function of the actual survival time T, which can be written as: P(t)=Pr(T≤t). Finally, the hazard function gives the probability of failure at time t (i.e. exit from an episode of growth), conditional upon surviving until time t. This can be written as: λ(t)=𝑝(𝑡)

𝑆(𝑡), with p(t) being the probability density function. Note that all three functions are

interrelated. If one knows the survival function, its complement is the cumulative distribution function and the hazard function can be obtained by dividing the death density by the survival function.

As noted earlier, the Kaplan Meier estimator is used to estimate the survival function of growth episodes. An important advantage of the Kaplan Meier estimator is that the method allows to estimate the survival function in the presence of right-censored data. This is the case in our sample, as the study period ends in 2015 while the event of interest, exiting an episode of growth, can occur after the end-of-study. The Kaplan Meier estimator can be written as:

𝑠̂(𝑡) = ∏(1 −ⅆ𝑖 𝑛_𝑖)

𝑖:𝑡𝑖≤𝑡

,

With di being the number of deaths (i.e. exits from an episode of growth) at time t and ni being

the number of survivors still at risk just prior to time t.

Additionally, we employ the Cox proportional hazards model to relate the duration of growth episodes to a set of explanatory variables. The model can be written as follows:

𝜆(𝑡; 𝑥) = 𝜆𝑜(𝑡)к(𝐱)

𝜆𝑜(𝑡) is called the baseline hazard function whereas к

()

>0 is a positive function of 𝐱. The baseline hazard function is the hazard rate of growth episodes when all covariates affecting it take a value of zero. Essentially, it is the average hazard rate that is common to all episodes in our sample. Note that the equation shows that the individual hazard rate differs proportionately based on a function к

(

𝐱

)

of observed covariates. It is typically assumed that the hazard rate responds exponentially; each unit increase in 𝐱 results in proportional scaling of the hazard. The term к

()

is therefore parametrised as к

(

𝐱

)

= exp (𝐱

β)

. This results in the following equation:

𝑙𝑜𝑔𝜆(𝑡; 𝒙) = 𝑙𝑜𝑔𝜆𝑜(𝑡) + 𝐱𝜷

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This assumption is also known as the proportional hazards assumption, which imposes the restriction that the hazard ratio does not change over time for any individual. Thus, the proportional hazards assumption implies that the ratio of hazards between two groups, e.g. the treatment and baseline group, is constant over time. To see this, assume that we have two groups, with

x

being a dummy variable taking the value of zero for group 0 and one for group 1. The model can then be written as follows:

𝜆𝑜(𝑡; 𝑥)= 𝜆𝑜(𝑡) 𝜆𝑜(𝑡)exp(x𝛽)

The term 𝜆𝑜(𝑡) represents the risk in time 𝑡 for group 0 while 𝜆𝑜(𝑡)exp(x𝛽) represents the risk in time t for group 1. It can be seen that only the baseline hazard function 𝜆𝑜depends on time 𝑡. Note further that if 𝛽=0, then the hazard risks across both groups are identical.

4. Sources of data and descriptive analysis

This section describes the dataset compiled out of different sources to support the empirical implementation of the theoretical framework and provides the corresponding descriptive statistics.

4.1 Sources of data and variables

Our dataset combines several data sources. The first building block is represented by the BEA Regional Economic Accounts (BEA-REA). The methodology used to construct GDP by metropolitan area relies heavily on GDP by state and personal income information (BEA, 2015). The construction of GDP by metropolitan area starts by creating current-dollar statistics for each industry. Earnings at the metropolitan area level are used to assign activity that is measured at the state level to individual metropolitan areas. Once these industry statistics have been calculated, GDP levels across all industries are summed together to calculate the total current GDP by metropolitan area. In addition, Real GDP is an inflation-adjusted measure based on the national prices of the goods and services produced within that metropolitan area. It is derived by applying national chain-type price indexes to the current-dollar industry statistics for every individual metropolitan area using the Fisher Ideal Index. The standard methodology uses information on all 61 industries from the GDP by state accounts for years when this detail is available and information on all 21 industry sectors when the detailed industry information is not available. BEA-REA data of current and real GDP is available at the metropolitan area level from the year 2001 and onwards, enabling us to construct growth rates from the year 2002 and onwards. During the period 2002 until 2015 the total current GDP of all metropolitan areas combined equals 89.8 percent of the total current GDP of the entire U.S1_{. Data on current and}

real GDP levels and growth rates is obtained from this database. Additionally, sectoral shares in value added at current prices are constructed using BEA-REA data, as it contains annual data on both total current GDP and current GDP by industry at the metropolitan area level. Moreover, BEA-REA data is also used to construct a number of additional variables, including population size (POP), employment growth (ΔEmployment), per capita GDP relative to the U.S. (RELUS) and the tax rate on production and imports (TAXES). Note that the tax rate on

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production and imports is constructed at the state level due to a lack of data at the metropolitan area level.

The second building-block is represented by the Local Area Unemployment Statistics (LAUS) of the U.S. Bureau of Labor Statistics (https://www.bls.gov/data/#unemployment). Local Area Unemployment Statistics (LAUS) are constructed by the U.S. Bureau of Labor Statistics as follows. First, total employment is calculated with data from either the CES or Quarterly Census of Employment and Wages (QCEW). This information is complemented with employment components that are not represented in the establishment series, such as self-employed workers. Second, total unemployment is calculated by adding the amount of persons that receive UI benefits with an estimation of those that have already exhausted their benefits. As a third and final step the annual unemployment rate is constructed by dividing both measures for every subsequent year. The BLS Local Area Unemployment Statistics contains annual unemployment rates for all metropolitan areas in our dataset (UNPL). Note that unemployment rates are not seasonally adjusted since we are analysing growth on an annual basis.

The third building-block is represented by administrative data compiled by the U.S. Patent and Trademark Office (https://www.uspto.gov/learning-resources). Data from the U.S. Patent and Trademark Office provides information about the annual amount of utility patents granted per metropolitan area. Utility patents are by far the most common type of patents and protect inventions—either entirely new ideas or improvements to existing inventions. The origin is determined by the residence of the first-named inventor on the patent grant. Data on the amount of utility patents granted is available for more than 90 percent of total observations.

These disparate sources of data subsequently had to be harmonised to create an integrated dataset for the analysis. The first-building block, represented by the BEA-REA, defines coverage for all 382 metropolitan areas from 2002 until 2015. All the other sources of data had to fit accordingly. The data sources discussed above are useful to compile idiosyncratic (MSA-specific) variables. However, additional variables are needed to capture national and global shocks. In order to capture national shocks we included aggregate U.S. growth rates of real GDP in our dataset, retrieved from the BEA National Economic Accounts (BEA-NEA). The fifth and final building-bock is represented by the World Bank, which provides data about the Chinese growth rate of real GDP measured in Purchasing Power Parity (constant 2011 $) (https://data.worldbank.org/indicator/NY.GDP. MKTP.PP.KD? locations =CN). The data on Chinese growth rates allows us to capture global economic shocks which have potentially huge impact at the local level.

Throughout our paper we will use the classification of the National Bureau of Economic Research (NBER) which defines December 2007 as the onset of the global recession (http://www.nber.org/cycles/cyclesmain.html) . The period 2002-2007 is therefore considered pre-crisis while the period 2008-2015 is considered post-crisis.

4.2 Idiosyncratic, National and Global determinants

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Starting with the idiosyncratic variables, we first constructed a set of industry shares per metropolitan area. Industry shares can be calculated in terms of GDP (at current or constant prices), employment and ratio of income. All industry shares in our analysis are constructed in value added at current prices using BEA-REA data. For a number of industries there were too many missing values, which resulted in a final industry breakdown of seven sectors: Natural resources and Mining; Manufacturing; Retail Trade; Information services; Finance, insurance, real estate, rental, and leasing; Professional and business services and Government. The corresponding specification of NAICS codes is included in appendix E. Note that the descriptive statistics display the industry shares in natural log form. For example, a manufacturing share of 20 per cent is displayed in the descriptive statistics as LN(20)=2.9957. This was done to mitigate the effect of outliers, since some metropolitan areas are heavily specialized in one specific industry. It was also considered to include the squared value per industry share to account for non-linear effects. However, since all metropolitan areas within the U.S. are in a similar, advanced stage of economic development this did not prove useful.

Growth in employment (ΔEmployment) is included to capture the effect of changes in total employment. It is well established that total employment directly affects the level of real GDP: when more people are active in the labor market, the total size of the economy is expected to increase. Growth in total population was also considered as it encompasses workers who dropped out of the labor force. Although growth in employment provides better estimates, we acknowledge that our focus on employment has certain shortcoming such as ignoring the crucial role of volunteers in many communities. The amount of utility patents granted per metropolitan area per million population (LnPATENTS) is included as a proxy for innovation and capital stock. This was done because actual data on capital stock was not available at the metropolitan area level. In the literature, patents are generally considered a useful way to measure innovation and high-tech capital (Katila, 2000). This variable is transformed into natural log form due to large differences across metropolitan areas.

Moreover, taxes on production and imports (TAXES) are included to control for distortions. Annual tax rates on production and imports are constructed by dividing the total amount of taxes on production and imports minus subsidies by total current GDP. Tax rates are constructed at the state level rather than the metropolitan area level due to a lack of available data. Another idiosyncratic variable is population size in natural log form (LnPOP). Generally speaking, workers in larger cities tend to be more productive (Duranton and Puga, 2004). Population size is therefore included to capture the effect of agglomeration economies. Again, this variable is transformed into natural log form to control for large differences across metropolitan areas.

Turning to the variable capturing national effects, we included aggregate U.S. growth rates of real GDP in our dataset (U.S. ΔRGDP). The underlying intuition is easy to understand: when the U.S. economy on aggregate is performing well, this is likely to have a positive, albeit varying, effect on metropolitan area growth. In order to capture global effects, we included the Chinese growth rate of real GDP measured in 2011 $PPP (China ΔRGDP).

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by the U.S. average GDP per capita for every year. A value larger than one thus implies that a metropolitan area is richer than the U.S. average, whereas a value smaller than one implies that it is poorer. This captures the divergence and convergence effect. Finally, we included annual unemployment rates to control for metropolitan area business cycles (UNPL). Annual unemployment rates are displayed in a percentage relative to total employment. In addition we employ a fixed-effects regression model as an additional control measure to account for unobserved heterogeneity across metropolitan areas and time.

4.3 Construction of the Episode variable

Our empirical approach to analyse growth encompasses two dependent variables. First, the annual growth rate of real GDP is calculated for every year using BEA-REA data, starting with the year 2002 and ending with the year 2015. The second dependent variable is Episode, which is a dummy variable indicating whether a particular year is part of a positive growth episode. The current literature uses two distinct approaches to identify growth regimes and shifts across growth regimes. The first is a ‘filter-based’ approach that identifies growth regimes based on subjectively defined criteria. The second approach uses statistical structural break tests (Kar et al., 2013). Which method does a better job at identifying growth episodes? Both methods have their limitations. The limitation of the filter-based approach is well established – the use of criteria pre-determined by the researcher is ad-hoc, and results in a lack of consistency in the identification of growth regimes across papers. A major limitation of the statistical method on the other hand, is the low power of the Bai-Perron test, which results in the unjust rejection of true breaks. In addition, the statistical approach identifies all transitions, up breaks and down breaks, whereas we will solely focus on growth episodes (i.e. up breaks). Due to these limitations we will use a set of subjectively defined criteria to identify episodes of growth.

Each contribution using the filter-based approach has studied a single type of growth transition and defined them accordingly, rather than identifying growth episodes through a consistent set of economic criteria. For instance, Hausmann et al. (2005) focus in their paper on growth accelerations, which is defined as an increase in per-capita growth of at least two percentage points, sustained for eight years or more. In a more recent paper, Aizenman and Spiegel (2010) aim to identify factors associated with growth takeoffs, defined as a transition from economic stagnation to significant growth. Here, stagnation is defined as five-year periods with average growth per capita below one percent, whereas significant growth is defined as five-year periods with growth rates exceeding three percent. The paper most closely related to ours is that of McGregor et al. (2015), who define growth episodes through a simple set of economic criteria. They consider a year to be part of a positive growth episode when GDP per capita has been growing for two successive years.

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less than one percent and growth resumes in the subsequent year, that year is not treated as an interruption of growth.

Note that we use a somewhat stricter definition of growth episodes than McGregor et al. (2015) by using three growth years as criterium rather than two. This is due to the fact that we investigate growth episodes within a developed economy like the U.S., where growth tends to be more stable than in developing economies. We have however considered two growth years as criterium, which resulted in a disproportionally large number of growth episodes, and four and five years, which overlooked a substantial part of ongoing growth episodes.

4.4 Descriptive statistics

Table 1 reports unweighted descriptive statistics for the entire panel.

Table 1. Summary Statistics for the Growth Panel Dataset, 2002-2015.

Notes: ΔRGDP refers to the annual growth rate of real GDP in a given year, Episode is a dummy variable indicating whether a given year is part of a positive growth episode. Primary, MFC, Retail, IT, Finance, Prof. services and

Government capture the contemporaneous values of sectoral shares in current GDP per year in natural log form. ΔEmployment refers to the annual change in absolute employment in a given year. LnPatents captures the annual

number of utility patents granted per million population in natural log form, Taxes and Unemployment refer to the annual rates of taxes and unemployment. RELUS captures GDP per capita relative to the U.S. average in a given year, LnPopulation refers to the absolute population size in natural log form. Finally, U.S. ΔRGDP captures the aggregate growth rate of U.S. real GDP and China ΔRGDP captures the aggregate growth rate of Chinese real GDP in $PPP in every given year.

Variable N Mean SD Min Max

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The average growth rate of real GDP is 1.53% for all observations, with a standard deviation of 4.06%. The high level of standard deviation reveals substantial variation in growth rates that arises from variation across metropolitan areas and changes over time. Moreover, the table reveals that the probability of a given year being part of a positive growth episode is 60.3% across all observations. Since the variable EPISODE is a dummy variable, its standard deviation of 0.49 cannot be directly interpreted. Furthermore, it can be seen that the average industry share and the corresponding standard deviation differs substantially per industry group. For instance, the primary sector has on average a low industry share with a relatively high standard deviation, whereas finance has a much higher industry share with a relatively low standard deviation. These patterns will be discussed thoroughly in the next section(s).

5. Patterns of growth across U.S. metropolitan areas

5.1. Analysis of dispersion across U.S. metropolitan areas

We begin the analysis slicing the information reported in Table 1 into various dimensions. It is well established in the literature that economic development is closely linked to the process of structural change. Regions with different income levels are generally different in terms of their economic structure. We therefore begin the analysis of dispersion with Table 2 which reports the descriptive statistics for each of the variables per income quartile. These quartiles are constructed as follows: metropolitan areas are divided into income quartiles on a per-year basis from 2002 until 2015, based on their level of GDP per capita in every respective year. This means that in 2002 we constructed income quartiles for that year based on the level of GDP per capita in that year. In the following year we constructed new income quartiles based on the corresponding level of GDP per capita in that year and so on. This allows for metropolitan areas to change income quartiles across years when their relative income position changes. Metropolitan areas with high rates of growth are thus expected to move to higher quartiles of income during our sample period, whereas lagging metropolitan areas are expected to move to lower income quartiles.

A number of interesting patterns emerge when metropolitan areas are divided into income quartiles. The results in table 2 show that metropolitan areas belonging to different income quartiles are heterogeneous in terms of growth rates and episodes. Real GDP growth rates vary significantly across income quartiles, with growth rates being the lowest in the first quartile and the highest in the fourth quartile with values of 0.97% and 2.29% respectively. Additionally, the occurrence of growth episodes also increases with levels of income. The table reveals that the probability of a given year being part of growth episode is 72% in the highest quartile compared to just 50% in the lowest quartile. These findings suggest that regional income disparities are increasing within the United States, as richer metropolitan areas outperform poorer ones. These results suggest the presence of a large dispersion of economic growth across metropolitan areas with a tendency to increase in the period following the crisis (see tables A-2.1 and A-2.2 in appendix A).

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as retail, whereas higher income quartiles have higher shares in knowledge- intensive industries such as IT and Finance. This is consistent with the existing literature and will be thoroughly discussed in section 5.3. The differences in economic structure across income quartiles are clearly reflected by the variable LnPATENTS. The table reveals that higher income levels are associated with a larger amount of utility patents granted and hence innovation. This is consistent with the fact that R&D is particularly important for knowledge-based industries, which are more prevalent in higher income quartiles.

Table 2. Summary Statistics for the Growth Panel Dataset by Income Quartile, 2002-2015.

Notes: ΔRGDP refers to the annual growth rate of real GDP in a given year, Episode is a dummy variable indicating whether a given year is part of a positive growth episode. Primary, MFC, Retail, IT, Finance, Prof. services and

Government capture the contemporaneous values of sectoral shares in current GDP per year in natural log form. ΔEmployment refers to the annual change in absolute employment in a given year. LnPatents captures the annual

number of utility patents granted per million population in natural log form, Taxes and Unemployment refer to the annual rates of taxes and unemployment. RELUS captures GDP per capita relative to the U.S. average in a given year, LnPopulation refers to the absolute population size in natural log form.

Also noteworthy is the relationship between income per capita and population size. It can be seen that metropolitan areas with higher income levels are generally larger in terms of population size. Given that population size is displayed in natural log form, these differences are larger than one might initially expect. The table shows that the mean log population size of the lowest quartile translates into an absolute population size of about 183.000 (EXP(12.1174=183.029), whereas the absolute population size is about 657.000 (EXP(13.3953= 656908) in the fourth quartile. This reveals an almost fourfold increase in the mean log population size between the lowest and highest income quartile.

Lowest Quartile Second Quartile Third Quartile Fourth Quartile

Variable Mean SD Mean SD Mean SD Mean SD

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This is in line with previous research, which confirms that city standard of living (measured by GDP per capita levels) tends to increase with city size (OECD, 2016). The appendix contains two additional figures, which further highlight the link between population size, income levels and rates of growth (see B-0.1 and B-0.2 in appendix B). We will not discuss the details here, but the figures confirm that population size is positively and strongly associated with levels of GDP per capita. Moreover, population size appears to reduce the volatility of growth. The variable RELUS, which captures GDP per capita relative to the U.S. average, reveals that the large majority of metropolitan areas is poorer than the U.S. average. Only metropolitan areas in the highest income quartile are richer than the U.S. average, with an average RELUS value of 1.1107, whereas the remaining three income quartiles have average values that are all lower than 1. Because the average weighted value of RELUS by definition has to be 1 for the U.S. on aggregate, this indicates that the regions with above average levels of GDP per capita are relatively large, which is consistent with our previous findings. Finally, it can be seen that unemployment rates decrease for higher income levels, whereas tax rates are about similar across income quartiles.

5.2. The geography of the patterns of growth

Table 3 shows the growth rate and occurrence of growth episodes disaggregated by region, structured along Northeast, Midwest, South and West, and income quartile.

Table 3. Growth and Growth Episodes by Income Quartile and Region, 2002-2015. Region Variable Lowest

Quartile Second Quartile Third Quartile Fourth Quartile Northeast ΔRGDP 0.7260 0.7412 0.7857 1.5704 EPISODE 0.5564 0.4910 0.4892 0.7200 N=686 0.1939 0.2434 0.2711 0.2915 Midwest ΔRGDP -0.3221 0.7410 1.3484 2.0931 EPISODE 0.3854 0.5128 0.5965 0.7184 N=1288 0.1491 0.2120 0.3137 0.3253 South ΔRGDP 0.9427 1.4110 2.0977 2.5382 EPISODE 0.4984 0.6110 0.6608 0.7268 N=2184 0.2784 0.2990 0.2349 0.1877 West ΔRGDP 1.6880 1.8904 1.5098 2.6922 EPISODE 0.5474 0.5896 0.6211 0.7475 N=1190 0.3454 0.2109 0.1908 0.2529

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As expected, metropolitan areas with higher income levels exhibit higher rates of growth and are more likely to experience episodes of growth. This pattern is consistent across all regions. Interestingly, tables A-3.1 and A-3.2 in appendix A indicate that this pattern is even stronger in the post-crisis period than in the pre-crisis period. Note that the probability of being in an episode of growth decreased only modestly for metropolitan areas in the highest quartile in the wake of the crisis, while it more than halved for metropolitan areas in the lowest quartile. This suggests that richer metropolitan areas are more resilient to economic shocks. Moreover, table 3 reveals that geographic regions are heterogeneous in terms of growth rates and episodes. Metropolitan areas belonging to the South and West region exhibit somewhat higher rates of growth than metropolitan areas in the Northeast and Midwest region across all income quartiles. However, a clear-cut pattern does not emerge.

The figures below shed some extra light on the findings in table 3 by showing growth patterns at the metropolitan area level along the geographical dimension. Figure 1 shows the level of GDP per capita in 2002, which is the first year observed in our dataset. This visualization clearly reveals that metropolitan areas located in the eastern part of the U.S. are on average richer than metropolitan areas located in the western part of the U.S. Also noteworthy are the large regional income disparities, even across metropolitan areas within the same state.

Figure 1. Initial level of GDP per Capita in 2002

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of U.S. Commuting Zones to Chinese imports. U.S. Commuting Zones heavily exposed to Chinese imports appear to be located at relatively similar places as the metropolitan areas that are lagging economically in Figures 2 and B-2.1.

Figure 2. Annual growth rate of real GDP 2002-2015

Lastly, figure 3 shows the probability that a year is part of a positive growth episode per metropolitan area for the period from 2002 until 2015. The pattern in this figure indicates that metropolitan areas in the eastern part of the U.S. and the east coast in particular are more likely to be in an episode of growth. Appendix B contains two additional figures, B-3.1 and B-3.2, that show the likelihood of growth episodes in the period before and after the economic crisis. These figures reveal that growth episodes were very common across all metropolitan areas in the period preceding the crisis. Many metropolitan areas however, saw an end to their growth episodes in the period after the crisis. Interestingly, a small group of metropolitan areas kept growing almost unhindered, of which most were located in the eastern part of the U.S. and the east coast in particular. One of the main take away points of these three figures is that the eastern part of the U.S. seems to be more resilient to economic shocks. Even though the South and West region were converging to the frontier in the period before the crisis, their growth performance has significantly weakened in the period after the crisis.

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Using the approach developed by Broadberry et al. (2017), we show that the growth rate reported in Table 3 for each metropolitan area is a combination of four factors: (1) the annual frequency with which a metropolitan area grows, f(+), (2) the growth rate when growing, g(+), (3) the annual frequency with which a metropolitan area shrinks, f(-), and (4) the shrinking rate when shrinking, ). Thus, the overall growth g is defined as: g = {f(+) g(+)} + {f(-) g(-)}.Growth years are defined as years in which real GDP growth is greater than or equal to zero, whereas shrinking years are defined as years in which real GDP growth is smaller than zero. The frequency of growing and shrinking by geographic region and income quartile is calculated by dividing the number of growing and shrinking years by the total number of years observed for each subgroup.

Table 4. Annual Growing and Shrinking by Region and Income Quartile, 2002-2015.

Frequency of growth (1) Average growth rate (2) Contribution of growing (3)=(1)*(2) Frequency of shrink (4) Average shrinking rate (5) Contribution of shrinking (6)=(4)*(5) GDP Growth (3)+(6) North- Q1 0.6316 2.1761 1.3744 0.3684 -1.7599 -0.6484 0.7260 east Q2 0.6168 2.2767 1.4042 0.3832 -1.7299 -0.6630 0.7412 Q3 0.6075 2.5261 1.5347 0.3925 -1.9083 -0.7490 0.7857 Q4 0.7400 2.8808 2.1318 0.2600 -2.1591 -0.5614 1.5704 Mid- Q1 0.5208 2.4184 1.2596 0.4792 -3.3009 -1.5817 -0.3221 West Q2 0.6374 2.7231 1.7356 0.3626 -2.7427 -0.9946 0.7410 Q3 0.6955 3.0780 2.1409 0.3045 -2.6032 -0.7925 1.3484 Q4 0.7780 3.4584 2.6908 0.2220 -2.6930 -0.5977 2.0931 South Q1 0.6069 3.3453 2.0303 0.3931 -2.7667 -1.0876 0.9427 Q2 0.6723 3.1715 2.1321 0.3277 -2.2005 -0.7211 1.4110 Q3 0.7368 3.7980 2.7986 0.2632 -2.6632 -0.7008 2.0978 Q4 0.7805 4.3332 3.3820 0.2195 -3.8442 -0.8438 2.5382 West Q1 0.6594 3.9595 2.6107 0.3406 -2.7090 -0.9228 1.6879 Q2 0.7171 3.5194 2.5239 0.2829 -2.2393 -0.6334 1.8905 Q3 0.6916 3.7183 2.5717 0.3084 -3.4436 -1.0619 1.5098 Q4 0.8073 4.2477 3.4292 0.1927 -3.8246 -0.7370 2.6922

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The results in table 4 show that the frequency of growing years is higher for metropolitan areas in higher income quartiles. In addition, it can be seen that metropolitan areas in higher income quartiles experience higher rates of both growing and shrinking. Interestingly, the results reveal that growing and shrinking rates tend to move in tandem across all income quartiles. Metropolitan areas in lower quartiles of income typically experience lower growing rates when growing and lower shrinking rates when shrinking, whereas metropolitan areas in higher income quartiles typically experience higher rates of both growing and shrinking. The above results are consistent across all geographic regions.

In order to calculate the net growth performance per subgroup, we first calculate the net contribution of growing and shrinking to growth separately and combine them subsequently. The net contribution of growing is calculated by multiplying the frequency of growing years with the average growing rate, whereas the net contribution of shrinking is calculated by multiplying the frequency of shrinking years with the average shrinking rate. Column 3 and 6 show the net contribution of growing and shrinking to economic performance. We can see that the net contribution of growing is larger for metropolitan areas with higher income levels, which is expected as both the frequency of growing years and growth rate is higher. Interestingly, the net contribution of shrinking is lower for metropolitan areas with higher income levels. This indicates that the higher shrinking rates of metropolitan areas with higher income levels are more than offset by the lower frequency of shrinking years.

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5.3. Industry patterns of growth

Table 5 shows the sectoral composition disaggregated by region and income quartile.

Table 5. Sectoral Composition by Region and Income Quartile, 2002-2015.

Region Industry Lowest

Quartile Second Quartile Third Quartile Fourth Quartile Northeast Primary 0.4488 -0.0410 -0.1401 -1.2137 Manufacturing 2.7798 2.8010 2.2808 2.2584 Retail 2.1016 2.0315 1.9028 1.7189 IT 0.8912 0.9734 1.0631 1.3782 Finance 2.4245 2.5000 2.7710 3.0549 Prof. Services 1.7984 2.0476 2.1506 2.3992 Government 2.8865 2.6958 2.7014 2.6017 Midwest Primary 0.3842 0.3610 0.5684 -0.1289 Manufacturing 2.9108 2.9718 2.8591 2.8312 Retail 2.1055 1.9840 1.9126 1.7263 IT 0.6908 0.8537 0.9474 1.0448 Finance 2.4666 2.5182 2.6278 2.8851 Prof. Services 1.8268 1.8853 1.9989 2.2272 Government 2.7097 2.5814 2.6105 2.3014 South Primary 0.5295 0.3531 0.4755 0.3911 Manufacturing 2.3888 2.5811 2.4042 2.5340 Retail 2.1931 1.9931 1.9235 1.7263 IT 0.6927 0.7664 0.9158 1.1110 Finance 2.4680 2.5373 2.7092 2.6945 Prof. Services 1.8832 1.9487 2.0936 2.2931 Government 2.8309 2.8916 2.7296 2.4178 West Primary 1.5803 0.9602 0.8575 0.3622 Manufacturing 2.2112 2.1560 2.0055 2.1282 Retail 2.1167 2.0558 2.0157 1.7586 IT 0.7527 0.9114 1.0512 1.3545 Finance 2.5542 2.6733 2.8431 2.8193 Prof. Services 1.7834 1.9492 2.2973 2.2379 Government 2.9448 2.9511 2.7040 2.6037

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The primary sector share is the largest for metropolitan areas in the lowest quartile and decreases for higher income quartiles. This is consistent with the literature, which indicates that regions with a revealed comparative advantage in primary products are at a distinct disadvantage (McMillan and Rodrik, 2011). The problem with a large primary sector is that it has a very limited capacity to generate substantial employment, contrary to manufacturing industries and related services. Therefore, in metropolitan areas with a comparative advantage in natural resources, the positive contribution of productivity-enhancing structural change to economic growth is expected to be limited.

Manufacturing shares seem to be quite similar across all income levels, with the second quartile having the highest share and gradually decreasing thereafter. The retail and government sector exhibit a similar pattern, in which the importance is highest for metropolitan areas in the lowest income quartile and gradually decreases with levels of income. Conversely, IT, finance and professional services have the highest share in metropolitan areas with high levels of income, whereas the share is lower in lower income quartiles. The results thus reveal that metropolitan areas across income quartiles are heterogeneous in terms of their economic structure, with lower quartiles having higher shares in traditional industries such as retail whereas higher quartiles have higher shares in knowledge -intensive industries such as IT and Finance. Overall, these findings indicate that there is a positive relationship between economic development and the share of knowledge-intensive services industries. This is consistent with the existing empirical evidence on economic development and skill-based structural change (Buera et al., 2015).

Finally, table 6 establishes the contribution of growing and shrinking to economic performance per industry. The approach developed by Broadberry et al. (2017) is applied again to decompose industry growth into growing and shrinking components. It can be seen that industries are substantially different in terms of their rate and frequency of growing and shrinking. Interestingly, industry growth patterns are remarkably consistent across all geographic regions. The results show that the frequency of shrinking years is the highest for the primary and IT sector, followed by manufacturing , finance and retail. Professional services and government have the lowest frequency of shrinking years. This pattern is similar before and after the onset of the crisis (see tables A-6.1 and A-6.2 in appendix A). There is, however, one important exception. In the post-crisis period the frequency of shrinking years became the highest in the IT sector, even higher than the primary sector.

A similar, but not identical, pattern emerges for the rates of growing and shrinking. Note that growing and shrinking rates again move in tandem. Industries with high growing rates also typically have high shrinking rates, while, conversely, industries with low growth rates typically also shrink at a lower rate. The primary and IT sector have the highest rates of both growing and shrinking, followed by manufacturing, finance and professional services. Perhaps unsurprisingly, retail and government have exhibited the lowest rates of both growing and shrinking. The above findings are consistent across all geographic regions.

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shrinking to economic performance. The results reveal that the primary sector has the highest net GDP growth in all geographic regions, indicating that the high frequency of shrinking years is more than offset with high growing rates. Professional services, IT and Finance also tend to have relatively high rates of net GDP growth, whereas the government sector, manufacturing and retail only contribute modestly to economic performance in terms of net GDP growth rates.

Table 6. The contribution of Growing and Shrinking to economic performance by Industry, 2002-2015.

Notes: Growth years are defined as years in which real GDP growth is greater than or equal to zero, Shrinking years are defined as years in which real GDP growth is smaller than zero. The average growth rate captures the growth rate when growing, whereas the average shrinking rate captures the shrinking rate when shrinking. Primary,

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Manufacturing, Retail, IT, Finance, Professional Services and Government capture the contemporaneous values

of sectoral shares in current GDP per year in natural log form.

5.4 Agglomeration effects

Metropolitan area GDP growth varies in accordance to the level of development, geography and reflects the dual effect of creative-destruction, reflected by growing-shrinking patterns. We now make the case that growth varies in accordance to size. An important line of thinking argues that regional divergence in economic growth can be linked to the forces of agglomeration within countries (Duranton and Puga, 2004). Essentially, this means that large metropolitan areas are considered main drivers of regional and national productivity and growth, at the cost of increased regional disparities. However, this picture does not apply to all cities. To see this, we constructed Figure 4, which shows the relationship between initial GDP per capita in 2002 and its subsequent growth rate over the period 2002-2015.

Figure 4. Initial level of GDP per capita and annual growth in the period 2002-15.

Had agglomeration forces dominated, the relation between initial GDP per capita and subsequent growth rates would have been positive, and quadrants (I) and (III) would have been most populated. Conversely, had catching-up forces dominated, the relation between initial GDP per capita and subsequent growth rates would have been negative, and quadrants (II) and (IV) would have been densely populated. Figure 4 does not provide such a regular trend, indicating a tension between convergence and agglomeration forces. Even though a clear-cut pattern does not appear, it can be seen that quadrants (I) and (III) are more densely populated than quadrants (II) and (IV), indicating that agglomeration forces dominate. Given that the majority of large metropolitan areas (defined as a population of >2.5 million) reside in quadrant 1, the agglomeration effects on aggregate growth are larger than one might think. The regional contributions to aggregate growth are discussed further in section 7.

I II IV III -2% 0% 1% 2% 3% 4% 5% 6% -1% A nn ua l ave rag e rea l G D P gr ow th rat e 20 02 -15 20,000 40,000 60,000 80,000 100,000 120,000 140,000

Initial GDP per capita 2002

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An interesting insight is to examine whether the size-growth nexus has been altered by the crisis. Figure 5 shows the relationship between Pre- and Post-Crisis growth rates per metropolitan area. Note that the growth rates of real GDP are centered by substracting the mean growth rate in every year. This was done to create an equal baseline for both periods, as Pre-Crisis growth rates are on average substantially larger than Post-Pre-Crisis growth rates.

Figure 5. Real GDP growth (centered) Pre- and Post-Crisis, 2002-15.

Figure 5 reveals that Pre-Crisis growth rates are a poor predictor of Post-Crisis growth rates. Had growth rates been similar during both periods, the relationship between Pre- and Post-Crisis growth rates would have been positive, and quadrants (I) and (III) would have been most populated. Conversely, had growth rates not sustained, the relationship between Pre- and Post-Crisis growth rates would have been negative, and quadrants (II) and (IV) would have been most populated. In contrast, the figure reveals that all quadrants appear to be about equally populated. This indicates that many metropolitan areas with above average rates of growth in the Pre-Crisis performed below average in the Post-Crisis period and vice versa. This pattern is consistent for metropolitan areas with both high and low levels of income (see figure B-5.1 in appendix B). IV III I II -6% -4% -2% 0% 2% 4% 6% 8% 10% G D P g ro w th P re -C ri si s (ce n te re d ) -4% -2% 0% 2% 4% 6% 8% 10% 12%

GDP growth Post-Crisis (centered)

Large MSA Regular MSA

The growth episodes of the US economy: Evidence from Metropolitan Areas