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Abstract

The observed uneven distribution of economic activity across space is influenced by variation in exogenous geographical characteristics and endogenous interactions between agents in goods and factor markets. Until the past decade, the theoretical literature on economic geography had focused on stylized settings that could not easily be taken to the data. This article reviews more recent research that has developed quantitative models of economic geography. These models are rich enough to speak to first-order features of the data, such as many heterogeneous locations and gravity equation relationships for trade and commuting. At the same time, these models are sufficiently tractable to undertake realistic counterfactual exercises to study the effect of changes in amenities, productivity, and public policy interventions such as transport infrastructure investments. We provide an extensive taxonomy of the different building blocks of these quantitative spatial models and discuss their main properties and quantification.
观察到的经济活动在空间上的不均匀分布受到外生地理特征和商品及要素市场中介之间内生互动的影响。直到过去十年,关于经济地理学的理论文献一直关注那些难以应用于数据的典型化设置。本文回顾了最近的研究,这些研究已经发展了经济地理学的定量模型。这些模型足够丰富,可以描述数据的一阶特征,如许多异质地点和贸易及通勤的引力方程关系。同时,这些模型足够可处理,可以开展现实反事实练习,研究便利设施、生产力和公共政策干预(如交通基础设施投资)变化的影响。我们提供了这些定量空间模型不同构建块的广泛分类,并讨论了它们的主要特性和量化。

Keyword(s): agglomerationcitieseconomic geographyquantitative modelsspatial economics
关键词:集聚,城市,经济地理学,定量模型,空间经济学
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/content/journals/10.1146/annurev-economics-063016-103713
2017-08-02
2024-09-21

Quantitative Spatial Economics

    Stephen J. Redding; Esteban Rossi-Hansberg

fn1aJEL codes: F10, F14, R12, R23, R41

 

The observed uneven distribution of economic activity across space is influenced by variation in exogenous geographical characteristics and endogenous interactions between agents in goods and factor markets. Until the past decade, the theoretical literature on economic geography had focused on stylized settings that could not easily be taken to the data. This article reviews more recent research that has developed quantitative models of economic geography. These models are rich enough to speak to first-order features of the data, such as many heterogeneous locations and gravity equation relationships for trade and commuting. At the same time, these models are sufficiently tractable to undertake realistic counterfactual exercises to study the effect of changes in amenities, productivity, and public policy interventions such as transport infrastructure investments. We provide an extensive taxonomy of the different building blocks of these quantitative spatial models and discuss their main properties and quantification.
观察到的经济活动在空间上的不均匀分布受到外生地理特征和商品及要素市场中介之间内生互动变化的影响。在过去的十年中,关于经济地理学的理论文献主要关注那些难以直接应用于数据的典型化设置。本文回顾了最近的研究,这些研究已经发展了经济地理学的定量模型。这些模型足够丰富,可以描述数据的一阶特征,如许多异质地点和贸易及通勤的引力方程关系。同时,这些模型也足够易于处理,可以开展现实的反事实练习,以研究便利设施、生产力和公共政策干预(如交通基础设施投资)变化的影响。我们提供了这些定量空间模型不同构建块的广泛分类,并讨论了它们的主要特性和量化。

Keywords 关键词
 

Economic activity is highly unevenly distributed across space, as reflected by the existence of cities and the concentration of economic functions in specific locations within cities, such as Manhattan in New York and the Square Mile in London. The relative strengths of the agglomeration and dispersion forces that underlie these concentrations of economic activity are central to a range of economic issues. The delicate balance between these two sets of forces helps to determine, for example, the incomes of mobile and immobile factors, the magnitude of investments, and both city and aggregate productivity. The impact of public policies differentiated by location (place-based policies) and of transport infrastructure investments, local taxation, and land regulation is crucially determined by how these policies affect the equilibrium balance between these centripetal and centrifugal forces.
经济活动在空间上的分布高度不均,这体现在城市的存在以及城市特定地点经济功能的集中,如纽约的曼哈顿和伦敦的一平方英里。支撑这些经济活动集中的集聚力和分散力的相对强度是众多经济问题的关键。这两组力量之间的微妙平衡有助于决定,例如,流动和固定因素的收入、投资的规模以及城市和总体生产力。由地理位置差异化的公共政策(基于地点的政策)、交通基础设施投资、地方税收和土地管理的影响,关键取决于这些政策如何影响这些向心力和离心力之间的平衡。

The complexity of modeling spatial interactions between agents has meant that the theoretical literature on economic geography has traditionally focused on stylized settings—such as a small number of symmetric locations—that cannot easily be taken to the data. More recent research has developed quantitative models of the spatial distribution of economic activity. These models are rich enough to incorporate first-order features of the data, such as large numbers of locations with heterogeneous geography, productivity, amenities, and local factors, as well as trade and commuting costs. They are also able to incorporate key interactions between locations, such as trade in goods, migration, and commuting. At the same time, these models are sufficiently tractable to enable quantitative counterfactuals to evaluate empirically meaningful policies and counterfactual scenarios. In this article, we review this recent body of research on quantitative spatial economics, highlighting the key new theoretical and empirical insights and discussing remaining challenges and potential areas for further research. We provide an extensive taxonomy of the different building blocks of quantitative spatial models used in the literature and discuss their properties.
模型中代理之间空间交互的复杂性意味着,传统上经济地理学的理论文献集中于一些经过简化的设置——例如数量有限且对称的位置——这些设置难以直接应用于数据。最近的研究已经发展了经济活动空间分布的定量模型。这些模型足够丰富,可以包含数据的一阶特征,如大量具有异质地理、生产力、便利设施和地方因素的地点,以及贸易和通勤成本。它们还能够包含地点之间的关键交互,如商品贸易、移民和通勤。同时,这些模型足够易于处理,能够进行定量反事实分析,以评估经验上具有意义的政策和反事实情景。在本文中,我们回顾了定量空间经济学领域最近的研究成果,突出了关键的新理论和实证洞察,并讨论了剩余的挑战和进一步研究的潜在领域。 我们提供了文献中使用的不同定量空间模型构建块的广泛分类,并讨论了它们的性质。

We interpret the field of economic geography as the study of the interactions between economic agents across geographic space. This field, in contrast to the study of international trade, typically assumes economic agents to be geographically mobile. Early theoretical research on new economic geography [as synthesized by Fujita et al. (1999), Fujita & Thisse (2002), and Baldwin et al. (2003)] concentrated on formalizing mechanisms for agglomeration and cumulative causation, including forward and backward linkages between economic activities. This literature stressed the combination of love of variety, increasing returns to scale, and transport costs as a mechanism for agglomeration. This mechanism provided a fundamental theoretical explanation for the emergence of an uneven distribution of economic activity even on a featureless plain of ex ante identical locations and highlighted the potential for multiple equilibria in location choices. However, the complexity of these theoretical models limited the analysis to stylized spatial settings such as a limited number of locations, a circle, or a line. Therefore, although this early theoretical literature stimulated a wave of empirical research, much of this empirical research was reduced form in nature. As a result, the mapping from the model to the empirical specification was often unclear, and it was difficult to give a structural interpretation to the estimated reduced-form coefficients. In the absence of such a structural interpretation, the coefficients of these reduced-form relationships need not be invariant to policy intervention (e.g., the Lucas critique). Furthermore, the extent to which theoretical results for stylized spatial settings would generalize qualitatively and quantitatively to more realistic environments is unclear (for reviews of the earlier theoretical and empirical literature on new economic geography, see, e.g., Overman et al. 2003; Redding 2010, 2011).
我们解读经济地理学为研究经济主体在地理空间中的相互作用。这一领域与国际贸易研究相比,通常假定经济主体具有地理流动性。关于新经济地理学早期理论研究[如 Fujita 等人(1999 年)、Fujita 和 Thisse(2002 年)、Baldwin 等人(2003 年)综合]集中于形式化聚集和累积因果机制,包括经济活动之间的前向和后向联系。这一文献强调将多样性、规模报酬递增和运输成本作为聚集的机制。这一机制为经济活动在事先相同位置的无特征平原上出现不均匀分布提供了基本的理论解释,并突出了位置选择中多重均衡的潜力。然而,这些理论模型的复杂性限制了分析到有限的地点、圆形或线等风格化的空间设置。 因此,尽管这一早期的理论文献激发了一波实证研究,但其中大部分实证研究在本质上都是简化的。结果,从模型到实证设定的映射往往不清楚,对估计的简化形式系数进行结构解释很困难。在没有这种结构解释的情况下,这些简化形式关系的系数不需要对政策干预(例如,卢卡斯批判)保持不变。此外,理论结果对于风格化的空间设置在定性和定量上推广到更现实的环境中的程度尚不清楚(关于新经济地理学早期理论和实证文献的综述,参见,例如,Overman 等,2003;Redding,2010,2011)。

Following the introduction of quantitative models of international trade [in particular that of Eaton & Kortum (2002)], research in economic geography has developed a quantitative framework that connects closely to the observed data. In contrast to the previous theoretical work, this research does not aim to provide a fundamental explanation for the agglomeration of economic activity, but rather to provide an empirically relevant quantitative model to perform general equilibrium counterfactual policy exercises. Agglomeration in these models is simply the result of exogenous local characteristics augmented by endogenous economic mechanisms. These frameworks can accommodate many asymmetric locations that can differ from one another in terms of their productivity, amenities, and transport and mobility connections to one another. The analysis can admit many sectors with different factor intensities and observed input–output linkages between them. Furthermore, the same quantitative framework can be derived from an entire class of theoretical models of economic geography, highlighting the robustness of this framework to perturbations in theoretical assumptions. These theoretical models differ in assumptions (e.g., monopolistic competition versus perfect competition) and mechanisms (e.g., technological versus pecuniary externalities), in the structural interpretations of some reduced-form coefficients (e.g., whether the elasticity of trade with respect to trade costs corresponds to the elasticity of substitution or the dispersion of productivity), and in some of their predictions (e.g., when factors are mobile across locations, trade cost reductions have different effects on the spatial distribution of economic activity in models of constant versus increasing returns to scale). Nonetheless, these models are isomorphic to one another for a series of predictions (e.g., the gravity equation for bilateral trade and commuting, in which interactions between two locations increase with the product of their size and decrease with the distance between them).
在引入国际贸易的定量模型[特别是 Eaton & Kortum(2002)的模型]之后,经济地理学的研究发展了一个与观察数据紧密相连的定量框架。与先前的理论研究不同,这项研究并不旨在为经济活动的集聚提供根本性解释,而是提供具有经验相关性的定量模型以进行一般均衡反事实政策实验。在这些模型中,集聚仅仅是外生本地特征与内生经济机制增强的结果。这些框架可以容纳许多不对称的位置,这些位置在生产力、便利设施以及彼此之间的运输和流动性连接方面可能各不相同。分析可以接受许多具有不同要素强度和彼此之间观察到的投入产出联系的部门。此外,可以从整个经济地理学理论模型类别中推导出相同的定量框架,突显了该框架对理论假设扰动的鲁棒性。 这些理论模型在假设(例如,垄断竞争与完全竞争)和机制(例如,技术外部性与货币外部性)上存在差异,在结构解释某些简化形式系数(例如,贸易成本弹性与替代弹性或生产率分散性是否对应)以及某些预测(例如,当要素在不同地点之间流动时,贸易成本降低对规模报酬不变与规模报酬递增模型中经济活动空间分布的影响不同)方面存在差异。尽管如此,这些模型在一系列预测(例如,双边贸易和通勤的引力方程,其中两地之间的互动随着它们规模的乘积增加而增加,随着它们之间距离的增加而减少)上是同构的。

The close connection between model and data in this quantitative research has a number of advantages. First, by accommodating many regions and a rich geography of trade costs, these models provide microfoundations for central features of the data. Second, by allowing for many regions that can differ in their productivity and amenities, as well as a number of other characteristics, these models are sufficiently rich to explain the observed data as an equilibrium of the model. These models are typically exactly identified, such that there exists a one-to-one mapping from the observed data on the endogenous variables of the model (e.g., employment and wages) to the exogenous primitives or structural fundamentals of the model (e.g., productivity and amenities). Therefore, this mapping can be inverted to identify the unique values of the estimated structural fundamentals that exactly rationalize the observed data as an equilibrium. Having recovered these estimated structural fundamentals, the observed variation in the data can be decomposed within the model into the contributions of each of the fundamentals. Inevitably, this analysis is conditional on the assumed model, and different models generally imply different estimated structural fundamentals and decompositions.
该定量研究中模型与数据之间的紧密联系具有多个优势。首先,通过容纳许多地区和丰富的贸易成本地理,这些模型为数据的中心特征提供了微观基础。其次,通过允许许多地区在生产力、便利设施以及其他一些特征上存在差异,这些模型足够丰富,可以解释观察到的数据作为模型的均衡。这些模型通常是精确识别的,即存在从模型内生变量(例如,就业和工资)的观察数据到模型外生原始或结构基础(例如,生产力和便利设施)的一对一映射。因此,这种映射可以被反转,以识别唯一的结构基础估计值,这些值恰好合理地解释观察到的数据作为均衡。在恢复这些估计的结构基础后,数据中的观察到的变化可以在模型中分解为每个基础因素的贡献。 不可避免地,这项分析基于所假设的模型,而不同的模型通常意味着不同的估计结构基础和分解。

The cost of enriching theoretical models to connect more closely to the data is typically a loss of analytical tractability. However, a major contribution of this quantitative economic geography literature has been to preserve sufficient analytical tractability to provide conditions under which there exists a unique spatial equilibrium distribution of economic activity and to permit some analytical comparative statics (see, in particular, Allen & Arkolakis 2014, Allen et al. 2015). Another central advantage of this structural empirical approach relative to the earlier reduced-form empirical literature is the ability to undertake counterfactuals for policy interventions or other out-of-sample changes in model primitives. For these exercises to be valid, one must assume that the identified structural fundamentals are stable and invariant to the analyzed policy interventions (for a general review of structural estimation approaches in urban economies, see Holmes & Sieg 2015). Under this assumption, these counterfactuals yield general equilibrium predictions for the spatial distribution of economic activity, which take full account of all the complex spatial interactions between locations. 1 These interactions and general equilibrium effects are typically not identified in reduced-form difference-in-differences approaches because differencing between the treatment and control group eliminates any effect that is common to both groups. Thus, a key implication of this analysis is that locations are not independent observations in a cross-sectional regression but rather are systematically linked to one another through trade, commuting, and migration flows. Not recognizing this interdependence in reduced-form empirical analysis can lead to significant biases and substantial heterogeneity in treatment effects that threaten the external validity of the results (see, e.g., Monte et al. 2015). Finally, the use of the model's structure makes it possible to compute the counterfactual change in welfare, which is usually unobservable in reduced-form approaches and yet is typically the object of ultimate interest for policy intervention.
理论模型丰富化以更紧密地与数据连接的成本通常是分析可处理性的损失。然而,这一数量经济地理文献的主要贡献在于保留了足够的分析可处理性,以提供存在唯一空间均衡分布的经济活动条件,并允许进行一些分析比较静态(参见,特别是,Allen & Arkolakis 2014,Allen et al. 2015)。与早期简化形式实证文献相比,这种结构实证方法的另一个核心优势是能够对政策干预或其他模型原初的样本外变化进行反事实分析。为了使这些练习有效,必须假设所识别的结构性基本要素是稳定的,并且对所分析的政策干预保持不变(关于城市经济中结构估计方法的一般综述,参见 Holmes & Sieg 2015)。 在此假设下,这些反事实产生了关于经济活动空间分布的一般均衡预测,充分考虑了所有地点之间复杂的空间相互作用。 1 这些相互作用和一般均衡效应通常在简化形式的差分差异方法中无法识别,因为处理组和对照组之间的差分消除了两组共有的任何效应。因此,这一分析的关键含义是,地点在横截面回归中不是独立的观察值,而是通过贸易、通勤和移民流动系统地相互联系。在简化形式的经验分析中未能认识到这种相互依赖性可能导致显著的偏差和治疗效果的实质性异质性,从而威胁到结果的外部有效性(参见,例如,Monte 等人,2015 年)。最后,利用模型的结构可以计算福利的反事实变化,这在简化形式的方法中通常是不可观察的,但通常是政策干预的最终目标。

Quantitative spatial models share many similarities with the earlier theoretical literature on economic geography. The mechanisms are typically the same, although there is greater scope to combine multiple mechanisms within a single framework. The broad questions are also largely the same. For example, how important is physical geography (e.g., mountains, coasts) versus economic geography (the location of agents relative to one another)? What is the impact of reductions in transport costs on the spatial distribution of economic activity? However, there are three key differences in focus and specificity relative to the earlier theoretical research. First, this new research connects in a meaningful way with the observed data and thus provides quantitative rather than qualitative answers to these questions. The emphasis is therefore on combining, measuring, and quantifying existing theoretical mechanisms. Second and relatedly, this work identifies the key structural parameters that need to be estimated to undertake such quantification. Third, the meaningful connection with the data permits specificity in addressing counterfactual questions of interest to policy makers: For example, if a railroad is built between these cities in this country at this time, what is the quantitative effect on these particular regions, sectors, and factors of production? Not only can this specificity address important policy questions, but the ability to contrast the model's predictions with real-life policy allows us to gauge the empirical importance of different theoretical mechanisms.
定量空间模型与早期关于经济地理学的理论文献有许多相似之处。机制通常是相同的,尽管在单一框架内结合多个机制有更大的空间。广泛的问题也大致相同。例如,物理地理(例如,山脉、海岸)与经济地理(行为者之间的相对位置)哪个更重要?运输成本降低对经济活动空间分布的影响是什么?然而,与早期理论研究相比,在关注点和具体性方面有三个关键差异。首先,这项新研究以有意义的方式与观察到的数据相联系,因此对这些问题的回答是定量的而不是定性的。因此,重点在于结合、衡量和量化现有的理论机制。其次,与此相关,这项工作确定了进行此类量化所需估计的关键结构参数。 第三,与数据的实质性联系使得在处理政策制定者感兴趣的反事实问题时具有了具体性:例如,如果在这个国家、在这个时间在这些城市之间修建一条铁路,这对这些特定地区、部门和生产力因素会产生什么样的定量影响?这种具体性不仅能够解决重要的政策问题,而且将模型的预测与现实生活中的政策进行对比的能力,使我们能够评估不同理论机制的经验重要性。

In addition to the quantitative evaluation of specific counterfactuals and policy exercises, the existing research on quantitative spatial models has yielded two main sets of general insights that are not present in the earlier literature on economic geography. The first set of general insights are methodological. These include an improved understanding of the conditions for the existence and uniqueness of equilibrium in economic geography models, the conditions under which these models can be inverted to separate out the contributions of physical and economic geography, and methods for undertaking counterfactuals to evaluate comparative statics with respect to changes in the model's parameters. Perhaps even more important is that the literature has provided a set of model components that allow us to introduce, in a unified theoretical framework, a large variety of agglomeration and congestion forces in a simple and practical way. Together, these insights facilitate the quantification and measurement that are at the heart of this body of research.
除了对特定反事实和政策实验的定量评估之外,现有关于定量空间模型的研究产生了两套主要的普遍见解,这些见解在早期关于经济地理学的文献中并不存在。第一套普遍见解是方法论方面的。这包括对经济地理模型中均衡存在和唯一性的条件、这些模型在何种条件下可以逆转以分离出物理地理和经济地理的贡献,以及进行反事实以评估模型参数变化比较静态的方法的改进理解。也许更重要的是,文献提供了一套模型组件,使我们能够在统一的理论框架中以简单实用的方式引入大量聚集和拥堵力量。这些见解共同促进了这一研究领域的量化与测量,而这正是该领域研究的核心。

The second set of general insights is substantive in terms of the quantitative importance of theoretical mechanisms. First, market access is an empirically relevant causal determinant of the spatial distribution of activity. This mechanism can account for the observed decline of approximately one-third in the relative size of West German cities close to the new border with East Germany following the division of Germany after World War II (Redding & Sturm 2008). Similarly, assuming that the railroads constructed up to 1890 had not been built, the value of agricultural land in the United States would have been reduced by approximately 60%, with limited potential for mitigating these losses through feasible extensions to the canal network (Donaldson & Hornbeck 2016). Second, canonical models of urban economics (e.g., Fujita & Ogawa 1982, Lucas & Rossi-Hansberg 2002) can account quantitatively for the observed gradients of economic activity within cities (e.g., Ahlfeldt et al. 2015). The estimated parameter values imply substantial and highly localized agglomeration externalities for both production and residential choices.
第二组一般性见解在理论机制的数量重要性方面具有实质性。首先,市场准入是活动空间分布的一个经验相关的因果决定因素。这一机制可以解释二战后德国分裂后,西德靠近东德新边界的城市相对规模下降约三分之一的现象(Redding & Sturm 2008)。同样,假设到 1890 年为止修建的铁路没有建设,美国农业土地的价值将减少约 60%,通过可行的运河网络扩展来缓解这些损失的可能性有限(Donaldson & Hornbeck 2016)。其次,城市经济学的经典模型(例如,Fujita & Ogawa 1982,Lucas & Rossi-Hansberg 2002)可以定量解释城市内部经济活动的梯度(例如,Ahlfeldt 等人 2015)。估计的参数值表明,生产和居住选择都存在实质性和高度局部化的聚集外部性。

Third, the local incidence of economic shocks is shaped in an important way by spatial linkages in goods and factor markets, which give rise to heterogeneous treatment effects of changes in the local economic environment (Monte et al. 2015) as well as heterogeneous aggregate implications of local shocks (Caliendo et al. 2014). Fourth, the distribution of economic activity across cities and regions is shaped in a quantitatively important way not only by productivity and amenity differences but also by a number of other spatial frictions, such as local infrastructure and governance (e.g., Desmet & Rossi-Hansberg 2013, Behrens et al. 2014). Fifth, the distribution of economic activity shapes the dynamics of local innovation and growth by determining the market size of firms. This link is quantitatively relevant for understanding the evolution of the spatial distribution of economic activity over time (e.g., Desmet & Rossi-Hansberg 2014) and the counterfactual dynamic response of the economy to global migration, trade policy changes, and global shocks such as climate change (e.g., Desmet & Rossi-Hansberg 2015, Desmet et al. 2016, Nagy 2016).
第三,经济冲击在地方上的发生方式在很大程度上受到商品和要素市场空间联系的影响,这导致了地方经济环境变化产生的异质处理效应(Monte 等人,2015 年)以及地方冲击的异质总体影响(Caliendo 等人,2014 年)。第四,经济活动在城市和地区之间的分布不仅在数量上受到生产力和便利性差异的影响,还受到许多其他空间摩擦的影响,如地方基础设施和治理(例如,Desmet & Rossi-Hansberg,2013 年,Behrens 等人,2014 年)。第五,经济活动的分布通过确定企业的市场规模来塑造地方创新和增长的动态。这一联系在理解经济活动空间分布随时间演变的演变(例如,Desmet & Rossi-Hansberg,2014 年)以及经济对全球移民、贸易政策变化和全球冲击(例如,气候变化)的逆事实动态反应方面具有定量相关性(例如,Desmet 等人,2015 年,Desmet 等人,2016 年,Nagy,2016 年)。

The remainder of this review is structured as follows. In Section 2, we outline a menu of building blocks or model components that can be combined in different ways in quantitative spatial models. We discuss the criteria for choosing between these building blocks and the trade-offs involved. In Section 3, we develop an example of such a quantitative spatial model based on a canonical new economic geography model. In this framework, a system of cities and regions is linked together through costly goods trade and labor mobility. We solve the model numerically and perform policy exercises that reduce external and internal trade costs. In Section 4, we provide another example based on the canonical urban model, which focuses instead on the internal structure of economic activity within a city. In both cases, we discuss the analytical characterization of the existence and uniqueness of the equilibrium, the inversion of the model to recover unobserved location characteristics from observed endogenous variables, and the use of the model to undertake counterfactuals for transport infrastructure improvements or other policy interventions. In Section 5, we review the empirical evidence on the predictions of these models. Section 6 concludes and discusses some potential areas for further research.
本综述的其余部分结构如下。在第 2 节中,我们概述了一系列构建模块或模型组件,这些组件可以在定量空间模型中以不同的方式组合。我们讨论了选择这些构建模块的标准以及所涉及的权衡。在第 3 节中,我们基于经典的新经济地理学模型开发了一个此类定量空间模型的例子。在这个框架中,城市和地区通过成本高昂的商品贸易和劳动力流动性相互联系。我们对该模型进行数值求解,并执行降低外部和内部贸易成本的政策实验。在第 4 节中,我们提供了另一个基于经典城市模型的例子,该模型专注于城市内部经济活动的内部结构。在这两种情况下,我们讨论了均衡存在性和唯一性的分析特征、将模型逆向来从观察到的内生变量中恢复未观察到的位置特征,以及使用该模型进行交通基础设施改善或其他政策干预的逆事实分析。 在第五节中,我们回顾了这些模型预测的经验证据。第六节总结并讨论了一些进一步研究的潜在领域。

 

Each of the quantitative spatial models considered in this review makes implicit or explicit assumptions about a number of building blocks or model components. In this section, we review the key building blocks and menu of assumptions in existing studies. In addition to preferences, production technologies, endowments, and market structure, these building blocks include the three main reasons why agents’ location relative to one another in geographic space matters: frictions for the movement of goods, ideas, and people. Combining different building blocks and assumptions allows researchers to capture different dimensions of the spatial economy. We discuss the criteria for selecting building blocks and choosing between assumptions for each block. We provide examples of existing studies that have selected particular items from the menu. In Sections 3 and 4, we pick particular combinations of building blocks and assumptions and show how the resulting framework can be used for the quantitative analysis of the spatial economy.
每个在本综述中考虑的定量空间模型都对一系列基本模块或模型组件做出了隐含或显式的假设。在本节中,我们回顾了现有研究中关键的基本模块和假设菜单。除了偏好、生产技术、禀赋和市场结构之外,这些基本模块还包括三个主要原因,即为什么地理空间中代理之间的相对位置很重要:商品、思想和人员的流动摩擦。结合不同的基本模块和假设,研究人员可以捕捉到空间经济的不同维度。我们讨论了选择基本模块和在每个模块之间选择假设的标准。我们提供了现有研究中选择菜单中特定项目的例子。在第 3 节和第 4 节中,我们选择特定组合的基本模块和假设,并展示如何使用由此产生的框架进行空间经济的定量分析。

2.1.   Preferences 偏好

Assumptions about preferences play a central role in shaping consumers’ location decisions. Five main sets of assumptions about preferences can be distinguished.
假设关于偏好的观点在塑造消费者位置决策中扮演着核心角色。可以区分出关于偏好的五组主要假设。

2.1.1.   Homogeneous versus differentiated goods.
2.1.1. 同质化与差异化商品。

Following Krugman (1991a,b), new economic geography models such as that of Helpman (1998) emphasize firm product differentiation and consumers’ love of variety. More recent research has shown that similar properties hold in models in which goods are homogeneous (e.g., Eaton & Kortum 2002) and labor is mobile (e.g., Rossi-Hansberg 2005, Redding 2016) or models in which goods are differentiated only by country of origin (e.g., Armington 1969) and labor is mobile (e.g., Allen & Arkolakis 2014).
根据克鲁格曼(1991a, b),新的经济地理学模型,如 Helpman(1998)的模型,强调企业产品差异化和消费者对多样性的喜爱。最近的研究表明,在商品同质化(例如,Eaton & Kortum 2002)和劳动力流动(例如,Rossi-Hansberg 2005,Redding 2016)的模型中,类似的性质仍然成立,或者在商品仅通过原产地进行差异化(例如,Armington 1969)和劳动力流动(例如,Allen & Arkolakis 2014)的模型中也是如此。

2.1.2.   Single versus multiple sectors.
2.1.2. 单一与多个部门。

To preserve analytical tractability, theoretical models of economic geography have often restricted attention to a single production sector (e.g., Helpman 1998) or distinguished between aggregate sectors such as agriculture and manufacturing (e.g., Krugman 1991b, Puga 1999). With the development of tractable quantitative models and efficient computational methods, researchers have become able to handle multiple disaggregated sectors (e.g., Caliendo et al. 2014). This introduction of multiple sectors permits the analysis of issues such as structural transformation and development, as in the work of Desmet & Rossi-Hansberg (2014), Fajgelbaum & Redding (2014), Coşar & Fajgelbaum (2016), and Nagy (2016).
为了保持分析的可行性,经济地理学的理论模型通常将注意力限制在单一的生产部门(例如,Helpman 1998)或者区分如农业和制造业等综合部门(例如,Krugman 1991b,Puga 1999)。随着可处理数量模型和高效计算方法的发展,研究人员能够处理多个细分部门(例如,Caliendo 等人 2014)。这种引入多个部门的做法使得分析诸如结构转型和发展等问题成为可能,如在 Desmet & Rossi-Hansberg(2014)、Fajgelbaum & Redding(2014)、Coşar & Fajgelbaum(2016)和 Nagy(2016)的研究中。

2.1.3.   Exogenous and endogenous amenities.
2.1.3. 外源性和内源性便利设施。

Early new economic geography models, such as that of Krugman (1991b), assumed a featureless plain in which locations were ex ante identical, and ex post differences in the spatial distribution of economic activity emerged endogenously. To incorporate real-world differences across locations (e.g., climate, access to water, and other characteristics of physical geography), quantitative models typically allow for exogenous differences in amenities across locations. In the spirit of the seminal work of Rosen (1979) and Roback (1982), amenities are understood as any characteristic that makes a location a more or less desirable place of residence, as examined empirically for US metropolitan areas by Albouy (2016). Several studies have also argued that, to match the response of the local economy to external shocks, it is important to allow for endogenous amenities (e.g., low crime rates) as well as exogenous amenities (e.g., scenic views), as in the work of Ahlfeldt et al. (2015) and Diamond (2016), among others.
早期的新经济地理学模型,如克鲁格曼(1991b)的模型,假设了一个无特征的平原,其中位置在事前是相同的,而在事后,经济活动的空间分布差异内生地出现。为了纳入地理位置之间的现实差异(例如,气候、水资源获取和其他自然地理特征),定量模型通常允许地理位置之间在便利设施上的外生差异。在罗森(1979)和罗巴克(1982)开创性工作的精神下,便利设施被理解为任何使一个地点成为更或更不理想的居住地的特征,如阿尔布伊(2016)对美国大都市区的实证研究所示。一些研究也认为,为了使地方经济对外部冲击的反应相匹配,允许内生便利设施(例如,低犯罪率)以及外生便利设施(例如,风景优美)是很重要的,正如阿夫费尔特等人(2015)和戴蒙德(2016)等人的工作中所做的那样。

2.1.4.   Fixed local factors in utility.
2.1.4. 修正了效用中的本地因素。

The presence of fixed factors in utility, such as residential land, acts as a congestion or dispersion force (see, e.g., Helpman 1998, Monte et al. 2015).
存在固定因素如住宅用地在效用中的存在,充当拥堵或分散力(参见,例如,Helpman 1998,Monte 等人 2015)。

2.1.5.   Common versus idiosyncratic preferences.
2.1.5. 常见与特殊偏好。

A standard benchmark in the quantitative spatial literature is the assumption that agents have common preferences and are perfectly mobile across locations. In this case, a no-arbitrage condition ensures that real wages are equalized across locations, and each location faces a perfectly elastic supply of labor at the common real wage. A tractable approach to departing from this benchmark is to allow agents to have idiosyncratic preferences for each location that are drawn from an extreme value distribution. In this case, individual agents pick their preferred location, and each of these locations faces a supply curve for labor that is upward sloping in real wages, as higher real incomes have to be paid to attract workers with lower idiosyncratic preferences. The elasticity of labor supply with respect to the real wage is determined by the degree of heterogeneity in agents’ preferences (see, e.g., Artuç et al. 2010, Grogger & Hanson 2011, Kennan & Walker 2011, Busso et al. 2013). Although much of the literature has focused on idiosyncratic differences in preferences across locations, models with idiosyncratic differences in worker productivity across locations have many similar properties, although with different predictions for wages (see, e.g., Galle et al. 2015).
一个在定量空间文献中的标准基准是假设代理人具有共同偏好,并且可以在各个地点完美流动。在这种情况下,无套利条件确保了实际工资在各个地点的均等化,每个地点都面临在共同实际工资下的完全弹性的劳动力供给。偏离这一基准的一个可处理的方法是允许代理人对每个地点具有独特的偏好,这些偏好来自极端值分布。在这种情况下,个别代理人选择他们偏好的地点,而这些地点都面临向上倾斜的实际工资的劳动力供给曲线,因为需要支付更高的实际收入来吸引具有较低独特偏好的工人。劳动力供给对实际工资的弹性由代理人偏好的异质性程度决定(参见,例如,Artuç等人 2010 年,Grogger & Hanson 2011 年,Kennan & Walker 2011 年,Busso 等人 2013 年)。 尽管大量文献关注了不同地区偏好中的独特差异,但具有地区间工人生产率独特差异的模型具有许多相似属性,尽管对工资的预测不同(例如,参见 Galle 等人 2015 年的研究)。

2.2.   Production Technology 生产技术

Assumptions about production technology critically influence firms’ location decisions. Four main sets of assumptions concerning production technology can be distinguished.
生产技术的假设对企业的区位决策产生关键影响。可以区分出关于生产技术的四组主要假设。

2.2.1.   Constant versus increasing returns.
2.2.1. 恒定回报与递增回报。

Following Krugman (1991a,b), the new economic geography literature assumes increasing returns to scale, which generates the potential for a self-reinforcing process of agglomeration (often termed cumulative causation) and the emergence of multiple equilibrium spatial allocations even on a featureless plain of ex ante identical locations. However, even under the assumption of constant returns to scale, agents’ locations relative to one another in geographic space have implications for prices and allocations. Indeed, there are conditions under which models of constant returns to scale and transport costs are isomorphic for endogenous outcomes of interest to those of models with local increasing returns to scale (see, in particular, Allen & Arkolakis 2014). Both Armington differentiation by location of origin (e.g., Armington 1969) and Ricardian technology differences (e.g., Eaton & Kortum 2002) can provide alternative mechanisms for specialization from the love of variety and increasing returns to scale in new economic geography models.
根据克鲁格曼(1991a, b),新经济地理学文献假设规模报酬递增,这产生了聚集(通常称为累积因果)的自我强化过程,即使在事先位置相同的无特征平原上,也能出现多个均衡的空间分配。然而,即使在规模报酬恒定的假设下,地理空间中代理人的相对位置对价格和分配也有影响。确实,存在一些条件,使得规模报酬恒定和运输成本模型与具有局部规模报酬递增模型的内生结果同构(参见艾伦和阿尔科拉基斯 2014 年的研究)。阿明顿根据原产地差异(例如,阿明顿 1969 年)和里卡多的技术差异(例如,伊顿和科尔图姆 2002 年)都可以为新经济地理学模型中的专业化提供替代机制,从对多样性的热爱和规模报酬递增的角度出发。

2.2.2.   Exogenous and endogenous productivity differences.
2.2.2. 外源性和内源性生产率差异。

Although early theoretical models of economic geography focused almost exclusively on endogenous production externalities (e.g., knowledge spillovers), a long intellectual tradition in international trade emphasizes exogenous productivity differences (e.g., mineral resources), and quantitative spatial models have typically found it necessary to allow for such exogenous differences across locations to rationalize the observed employment and income data (e.g., Allen & Arkolakis 2014, Caliendo et al. 2014, Ahlfeldt et al. 2015, Desmet et al. 2016).
尽管早期的经济地理学理论模型几乎完全关注内生生产外部性(例如,知识溢出),但国际贸易中的长期知识传统强调外生生产力差异(例如,矿产资源),而定量空间模型通常发现有必要允许这种外生差异在不同地区存在,以合理化观察到的就业和收入数据(例如,Allen & Arkolakis 2014,Caliendo et al. 2014,Ahlfeldt et al. 2015,Desmet et al. 2016)。

2.2.3.   Input–output linkages.
2.2.3. 输入-输出联系。

Input–output linkages play a key role in determining how productivity shocks in a particular sector or region spread through the wider economy and shape local multipliers (i.e., the extent to which an increase in expenditure in one sector leads to more than proportionate increases in overall expenditure through increased demand in other sectors). Such input–output linkages provide an additional mechanism for agglomeration (e.g., Krugman & Venables 1995), and the observed linkages between sectors in real-world input–output matrices can now be incorporated in a relatively tractable way into quantitative spatial models (following Caliendo et al. 2014).
输入-输出联系在确定特定部门或地区的生产力冲击如何通过更广泛的经济传播并塑造本地乘数(即一个部门支出增加导致其他部门需求增加而使总支出超过比例增加的程度)方面发挥着关键作用。这种输入-输出联系为聚集(例如,Krugman & Venables 1995)提供了额外的机制,并且现在可以将现实世界输入-输出矩阵中观察到的部门间联系以相对容易处理的方式纳入定量空间模型中(遵循 Caliendo 等人 2014 年的研究)。

2.2.4.   Fixed local factors in production.
2.2.4. 修正生产中的本地因素。

The presence of fixed local factors in production, such as commercial land, acts as a congestion force (e.g., Rossi-Hansberg 2005, Ahlfeldt et al. 2015).
生产中固定地方因素的存在,如商业用地,充当拥堵力量(例如,Rossi-Hansberg 2005,Ahlfeldt 等 2015)。

2.3.   Costs of Trading Goods
商品交易成本

Several mechanisms can explain the importance of the location of agents relative to one another in quantitative spatial models. The first of these mechanisms is the cost of trading goods. Four main sets of assumptions concerning the costs of trading goods can be delineated.
几种机制可以解释在定量空间模型中,代理相对于彼此的位置的重要性。这些机制中的第一种是交易商品的成本。可以区分出关于交易商品成本的四个主要假设集。

2.3.1.   Variable versus fixed trade costs.
2.3.1. 变量贸易成本与固定贸易成本。

A widespread assumption used for analytical tractability is that of iceberg variable transport costs, whereby >1 units of a good must be shipped from location to location for one unit to arrive (i.e., some of each unit melts in transit). 2 Combining assumptions about the functional form of trade costs with those about preferences and production technology generates predictions for bilateral trade. Arguably, any plausible quantitative spatial model should explain the gravity equation, a strong empirical feature in which bilateral trade increases with exporter and importer size and declines with geographical distance (e.g., surveyed in Head & Mayer 2014).
广泛用于分析可处理性的一个假设是冰山变量运输成本,即一个商品必须从位置 i 运送到位置 n≠i,其中 dni >1 单位,才能使一个单位到达(即,每个单位中的一些在运输过程中融化)。 2 将关于贸易成本函数形式的假设与关于偏好和生产技术的假设相结合,可以预测双边贸易。可以说,任何合理的定量空间模型都应该解释引力方程,这是一个强大的经验特征,即双边贸易随着出口商和进口商规模的增加而增加,随着地理距离的增加而减少(例如,Head & Mayer 2014 年调查过)。

2.3.2.   Asymmetric versus symmetric transport costs.
2.3.2. 非对称与对称运输成本。

Whether transport costs are symmetric or asymmetric (i.e., whether or not =) has implications both for the characterization of equilibrium and for patterns of trade and income (see Waugh 2010, Allen et al. 2015). Although transport costs are necessarily symmetric if they depend solely on geographic distance, departures from symmetry can arise from a variety of geographic and economic factors (e.g., land gradient and trade volumes).
运输成本是否对称或不对称(即 dni 是否等于 din)对均衡特征的描述以及贸易和收入模式都有影响(参见 Waugh 2010,Allen 等人 2015)。尽管如果运输成本仅取决于地理距离,则必然是对称的,但来自各种地理和经济因素(例如,土地坡度和贸易量)的偏差可能导致不对称。

2.3.3.   Geographic versus economic frictions.
2.3.3. 地理与经济摩擦。

Both geographic frictions (e.g., mountains) and economic frictions (e.g., borders, road and rail networks) can influence bilateral transport costs. With the diffusion of geographic information system data and software, advances have been made in the detailed modeling of observed determinants of transport costs (e.g., mountains, rivers, and coastlines) using algorithms that determine the lowest-transport-cost path, such as the Djikstra or Fast Marching algorithm used by Allen & Arkolakis (2014), Ahlfeldt et al. (2015), Donaldson & Hornbeck (2016), Desmet et al. (2016), Donaldson (2016), and Nagy (2016).
地理摩擦(例如,山脉)和经济摩擦(例如,边界、公路和铁路网络)都可以影响双边运输成本。随着地理信息系统数据和软件的扩散,在详细建模运输成本观察到的决定因素(例如,山脉、河流和海岸线)方面取得了进展,使用了确定最低运输成本路径的算法,如 Allen & Arkolakis(2014)、Ahlfeldt 等(2015)、Donaldson & Hornbeck(2016)、Desmet 等(2016)、Donaldson(2016)和 Nagy(2016)使用的 Dijkstra 或快速行进算法。

2.3.4.   Role of nontraded goods.
2.3.4. 非交易商品的作用。

Nontraded goods can typically be thought of as the limiting case in which iceberg trade costs for a particular good are infinite (→∞). These non-traded goods play an important role in shaping input–output linkages and local multipliers (see, e.g., Moretti 2011b, Caliendo et al. 2014). A given productivity difference in the traded sector has a larger proportionate impact on overall employment with nontraded goods because the relocation of workers in the traded sectors shifts around demand and thus employment for nontraded goods.
非贸易商品通常可以被视为一个极限情况,即特定商品的冰山贸易成本无限大(dni →∞)。这些非贸易商品在塑造投入产出联系和地方乘数方面发挥着重要作用(参见,例如,Moretti 2011b,Caliendo 等人 2014)。贸易部门中生产率的差异对非贸易商品的整体就业的影响比例更大,因为贸易部门中工人的重新分配会改变需求,从而影响非贸易商品的就业。

2.4.   Technology for Idea Flows
技术流思想

The second mechanism explaining the importance of the location of agents relative to one another in quantitative spatial models is friction in idea flows. Three main sets of assumptions concerning the technology of idea flows are considered.
第二机制解释了在定量空间模型中,代理相对位置的重要性,即思想流动的摩擦。关于思想流动技术的三个主要假设集被考虑。

2.4.1.   Knowledge externalities and diffusion.
2.4.1. 知识外部性和扩散。

An externality arises whenever an economic agent takes an action that affects another economic agent without internalizing this effect when evaluating the cost and benefits of the action. In the flow of ideas, such externalities can be the result of the lack of a market or can be mediated by prices, as in the case of pecuniary externalities. An obvious example would be a case in which ideas discovered by a researcher or firm in one location diffuse to other researchers and firms in the same location or in different locations. The standard approach to modeling such knowledge externalities is to assume that they are a function of the distance-weighted sum of employment in surrounding locations (see, e.g., Fujita & Ogawa 1982, Lucas & Rossi-Hansberg 2002). This reduced-form specification can be derived from alternative microfoundations. The standard classification of these microfoundations is that of Marshall (1920), which distinguishes between knowledge spillovers, externalities due to thick labor markets, and backward and forward linkages. More recently, Duranton & Puga (2004) propose sharing, matching, and learning as three different classes of mechanisms that can result in similar reduced-form specifications. Other research has sought to measure and distinguish between these and other microeconomic mechanisms (see Jaffe et al. 1993, Ellison et al. 2010, Comin et al. 2013). Most empirical studies find that these externalities are highly localized and decay rapidly with geographical, technological, or economic proximity (e.g., Arzaghi & Henderson 2008, Rossi-Hansberg et al. 2010, Ahlfeldt et al. 2015). A key question in setting up spatial models is whether these externalities are present only within the spatial unit of analysis (e.g., Allen & Arkolakis 2014) or across spatial units, as well (e.g., Rossi-Hansberg 2005).
外部性产生于经济主体采取的行动影响其他经济主体,而评估该行动的成本和收益时未将此影响内部化的任何时候。在思想流动中,这种外部性可能是由于市场缺失的结果,也可能是通过价格进行调节,如在货币外部性的情况下。一个明显的例子是,一个研究者或某地企业发现的思想扩散到同一地点或不同地点的其他研究者和企业。对这种知识外部性的标准建模方法是假设它们是周围地区就业加权总和的函数(参见,例如,Fujita & Ogawa 1982,Lucas & Rossi-Hansberg 2002)。这种简化形式的规范可以从替代的微观基础中推导出来。这些微观基础的标准化分类是马歇尔(1920 年)的分类,它区分了知识溢出、由于劳动力市场密集而产生的外部性以及前向和后向联系。 最近,Duranton & Puga(2004)提出了共享、匹配和学习作为导致类似简化形式规范的三种不同机制类别。其他研究试图衡量和区分这些以及其他微观经济机制(参见 Jaffe 等,1993;Ellison 等,2010;Comin 等,2013)。大多数实证研究发现,这些外部性高度局部化,并且随着地理、技术或经济邻近性的增加而迅速衰减(例如,Arzaghi & Henderson,2008;Rossi-Hansberg 等,2010;Ahlfeldt 等,2015)。在建立空间模型时的一个关键问题是,这些外部性是否仅存在于分析的空间单元内(例如,Allen & Arkolakis,2014),还是也跨越空间单元(例如,Rossi-Hansberg,2005)。

2.4.2.   Innovation. 2.4.2. 创新。

Spatial models must also determine whether the level of local productivity is constant and exogenous or the result of intentional investments in innovation. The incentives to undertake these investments depend critically on the ability to appropriate the returns from the development of ideas and, thus, the speed with which these ideas diffuse to other agents. Most research in economic geography is concerned with the static spatial distribution of economic activity at a point in time; however, innovation is an inherently dynamic activity. Modeling these dynamics is challenging because of the high dimensionality of the state space across locations and over time. However, tractable quantitative models of spatial innovation and the corresponding evolution of economic activity have recently been developed by Desmet & Rossi-Hansberg (2015), Desmet et al. (2016), and Nagy (2016). In these frameworks, the spatial economy influences the profitability of local innovations by determining the market size of firms and, therefore, the extent to which the cost of innovation can be shared among consumers. The key to the tractability of these frameworks is the fact that a competitive market for land, together with local diffusion of technology, implies that future returns from an innovation are fully capitalized in land rents.
空间模型还必须确定当地生产力的水平是恒定和外部性的,还是创新有意投资的成果。进行这些投资的激励取决于从思想发展中获取回报的能力,以及这些思想扩散到其他行为者的速度。大多数经济地理学的研究关注的是某一时间点的经济活动的静态空间分布;然而,创新本质上是一种动态活动。由于空间和时间上状态空间的高维性,对这些动态进行建模具有挑战性。但是,Desmet & Rossi-Hansberg(2015 年)、Desmet 等人(2016 年)和 Nagy(2016 年)最近开发了可处理的定量空间创新模型及其相应的经济活动演变模型。在这些框架中,空间经济通过确定企业的市场规模来影响当地创新的盈利性,从而决定了创新成本在消费者之间共享的程度。 土地市场的竞争性以及技术的本地扩散意味着创新未来的回报完全体现在土地租金中,这是这些框架可处理性的关键。

2.4.3.   Transferability of ideas.
2.4.3. 思想的可迁移性。

Another important factor is the extent to which ideas developed in one location can be costlessly transferred to other locations. In the international trade literature, several studies have explored the implications of frictions that reduce the productivity of ideas when transferred to other countries through foreign direct investment (see, in particular, Arkolakis et al. 2014). Within countries, a firm that enters and develops a blueprint for production in one location may face costs when transferring that blueprint to other locations, as shown by Fajgelbaum et al. (2015).
另一个重要因素是,在某一地点发展起来的想法能够无成本地转移到其他地点的程度。在国际贸易文献中,有几项研究探讨了通过外国直接投资将想法转移到其他国家时,摩擦降低想法生产力的含义(参见,特别是 Arkolakis 等人 2014 年的研究)。在国家内部,一家进入并在一个地点发展生产蓝图的企业,在将该蓝图转移到其他地点时可能会面临成本,正如 Fajgelbaum 等人(2015)所展示的。

2.5.   Costs of Moving People
人员迁移成本

The third mechanism that explains the importance of the spatial location of agents relative to one another in quantitative spatial models is friction in the movement of people. In this section, four main sets of assumptions are described.
第三种解释在定量空间模型中代理相对空间位置重要性的机制是人们在运动中的摩擦。在本节中,描述了四组主要假设。

2.5.1.   Migration costs. 2.5.1. 移民成本。

The first assumption relates to frictions in the migration of people. Such frictions provide an alternative explanation for real wage differences across locations, in contrast to the idiosyncratic differences in preferences discussed in Section 2.1. This raises the question of the extent to which observed urban–rural wage differentials within countries reflect migration frictions, nonrandom selection of worker productivity, the cost of land and other nontraded goods, and amenity differences (see, e.g., Young 2013, Bryan & Morten 2015). Although these migration frictions can exist within countries, they are typically thought to be much larger between countries. To the extent that these migration frictions involve sunk costs, agents’ location decisions again become inherently dynamic. In this case, these location decisions depend not only on current real wages, but also on expected continuation values, as analyzed by Artuç et al. (2010), Caliendo et al. (2015), and Morten & Oliviera (2016). Desmet et al. (2016) measure the moving costs at the origin and the destination that rationalize the observed net population flows across regions of the world using a dynamic spatial model.
关于人口迁移的摩擦是第一个假设。这种摩擦为不同地区实际工资差异提供了另一种解释,与第 2.1 节中讨论的偏好差异的个性差异形成对比。这引发了这样一个问题:观察到的国家内部城乡工资差异在多大程度上反映了迁移摩擦、工人生产力的非随机选择、土地和其他非贸易商品的成本以及便利性差异(参见,例如,Young 2013,Bryan & Morten 2015)。尽管这些迁移摩擦可以在国家内部存在,但通常认为它们在国家之间要大得多。在迁移摩擦涉及沉没成本的情况下,代理人的位置决策再次具有内在的动态性。在这种情况下,这些位置决策不仅取决于当前的实际工资,还取决于预期的持续价值,正如 Artuç等人(2010 年)、Caliendo 等人(2015 年)和 Morten & Oliviera(2016 年)所分析的那样。Desmet 等人(2016 年)使用动态空间模型来衡量迁移成本,这些成本合理化了观察到的全球各地区净人口流动。

2.5.2.   Commuting. 2.5.2. 上班通勤。

A second assumption concerns whether agents can separate their workplace and residence by commuting between them. In the canonical monocentric city of urban economics, all production activity is assumed to occur at the center of the city, and commuting costs play the key role in determining the land price gradient with respect to distance from the center of the city (see Alonso 1964, Mills 1967, Muth 1969, Lucas 2000). An important contribution of more recent research has been to allow for nonmonocentric patterns of economic activity within cities; in the nonmonocentric case, the interaction of agglomeration forces and commuting costs remains central to determining internal city structure (see Fujita & Ogawa 1982, Lucas & Rossi-Hansberg 2002, Ahlfeldt et al. 2015, Brinkman 2016). In models of systems of cities, the efficiency of the commuting technologies within each city is an important determinant, alongside the amenities and productivities of each city, in shaping the distribution of city sizes (see Desmet & Rossi-Hansberg 2013, Behrens et al. 2014). In the literature on local labor markets, many studies have examined the impact of local shocks and policy interventions on local employment (for reviews, see Moretti 2011a, Kline & Moretti 2014b, Neumark & Simpson 2015). However, relatively little attention has been devoted to commuting and the resulting distinction between employment by workplace and employment by residence. When locations are connected by bilateral commuting flows, a shock to one location can spill over to other locations (see Monte 2015), and a given local shock can have heterogeneous employment effects across locations depending on commuting networks (see Monte et al. 2015).
关于代理人是否可以通过通勤在工作和居住地之间进行分离的第二个假设。在城市经济学的经典单中心城市中,所有生产活动都被假定为发生在城市中心,通勤成本在确定距离城市中心的地价梯度中起着关键作用(参见 Alonso 1964,Mills 1967,Muth 1969,Lucas 2000)。近期研究的一个重要贡献是允许城市内部存在非单中心的经济活动模式;在非单中心的情况下,集聚力量和通勤成本之间的相互作用仍然是决定城市内部结构的关键(参见 Fujita & Ogawa 1982,Lucas & Rossi-Hansberg 2002,Ahlfeldt 等 2015,Brinkman 2016)。在城市的系统模型中,每个城市通勤技术的效率是一个重要决定因素,与每个城市的便利性和生产力一起,塑造城市规模的分布(参见 Desmet & Rossi-Hansberg 2013,Behrens 等 2014)。 在关于地方劳动力市场的文献中,许多研究探讨了地方冲击和政策干预对地方就业的影响(参见 Moretti 2011a,Kline & Moretti 2014b,Neumark & Simpson 2015)。然而,相对较少的关注被投入到通勤以及由此产生的在工作场所就业和居住地就业之间的区别。当两个地点通过双边通勤流相连时,一个地点的冲击可能会溢出到其他地点(参见 Monte 2015),并且一个特定的地方冲击可能会根据通勤网络在不同地点产生异质性的就业影响(参见 Monte 等人 2015)。

2.5.3.   Skills and heterogeneity.
2.5.3. 技能与异质性。

For both migration and commuting decisions, a third modeling factor is whether agents have common or idiosyncratic preferences/productivities across locations. Under the assumption of extreme value–distributed idiosyncratic preferences/productivities, quantitative spatial models imply gravity equation relationships for migration or commuting (e.g., McFadden 1974, Kennan & Walker 2011, Ahlfeldt et al. 2015, Monte et al. 2015, Allen et al. 2016). Empirically, there is strong evidence that both migration and commuting flows are characterized by such gravity equation relationships, in which bilateral flows increase with origin and destination size and decline with geographical distance (see, e.g., Fortheringham & O'Kelly 1989). Whether agents are assumed to have common or idiosyncratic preferences/productivities, an additional modeling decision is whether to allow for multiple type of agents (e.g., workers with different observed levels of skills). In the presence of multiple types of agents who value location characteristics differentially, the equilibrium distribution of economic activity is typically characterized by spatial sorting, in which agents of a given type endogenously self-select into locations with a particular set of characteristics (see, e.g., Davis & Dingel 2015, Gaubert 2015, Redding & Sturm 2016).
对于迁移和通勤决策,第三个建模因素是代理人在不同地点是否具有共同或独特的偏好/生产力。在极端值分布的独特偏好/生产力假设下,定量空间模型暗示了迁移或通勤的引力方程关系(例如,McFadden 1974,Kennan & Walker 2011,Ahlfeldt 等人 2015,Monte 等人 2015,Allen 等人 2016)。经验上,有强有力的证据表明,迁移和通勤流量都表现出这种引力方程关系,其中双边流量随着起点和终点规模的增长而增加,随着地理距离的增加而减少(参见,例如,Fortheringham & O'Kelly 1989)。无论假设代理人具有共同或独特的偏好/生产力,另一个建模决策是是否允许存在多种类型的代理人(例如,具有不同观察到的技能水平的工人)。 在存在多种不同价值地理位置特性的代理人的情况下,经济活动的均衡分布通常表现为空间排序,即特定类型的代理人内生性地自我选择进入具有特定特征集合的位置(参见,例如,Davis & Dingel 2015,Gaubert 2015,Redding & Sturm 2016)。

2.5.4.   Congestion in transportation.
2.5.4. 交通运输拥堵。

A fourth specification choice is the extent to which increased flows of people lead to greater congestion and higher travel costs and whether these can be relieved by transport infrastructure provision. Duranton & Turner (2011) provide evidence in support of a fundamental law of highway congestion [originally suggested by Downs (1962)], according to which increased provision of highways leads to a proportionate increase in vehicle kilometers traveled with no reduction in congestion. Anderson (2014) finds that public transit plays an important role in alleviating congestion during peak travel times. Using hourly data on traffic speeds for all major Los Angeles freeways, Anderson finds that a 2003 strike by Los Angeles County Metropolitan Transportation Authority workers led to an abrupt increase in average delays of 47% (0.19 minutes per mile) during peak travel periods.
第四个选择是人口流动增加导致交通拥堵加剧和出行成本上升的程度,以及这些是否可以通过交通基础设施的提供来缓解。Duranton & Turner(2011)提供了支持公路拥堵基本法则的证据[最初由 Downs(1962)提出],根据该法则,公路供应的增加会导致行驶里程的成比例增加,而不会减少拥堵。Anderson(2014)发现,公共交通在缓解高峰时段的拥堵中发挥着重要作用。利用洛杉矶所有主要高速公路的交通速度的每小时数据,Anderson 发现,2003 年洛杉矶县大都会交通管理局工人的罢工导致高峰时段平均延误突然增加了 47%(每英里 0.19 分钟)。

2.6.   Endowments 捐赠基金

The above choices about preferences; production technology; and the costs of the movement of goods, ideas, and people need to be combined with choices on the endowments of the economy.
上述关于偏好、生产技术和商品、思想及人员流动成本的抉择,需要与关于经济禀赋的抉择相结合。

2.6.1.   Population and skills.
2.6.1. 人口与技能。

A minimal endowment would be homogeneous labor alone, as in an Armington model (e.g., Allen & Arkolakis 2014). More generally, different types of labor can be distinguished, some of which may be more mobile across locations than others and some of which may have different skills or levels of wealth.
一个最小的禀赋将是同质劳动力,如在 Armington 模型中(例如,Allen & Arkolakis 2014)。更普遍地,可以区分不同类型的劳动力,其中一些可能比其他劳动力在地理位置上更具流动性,而另一些可能具有不同的技能或财富水平。

2.6.2.   Spatial scope and units.
2.6.2. 空间范围与单位。

In most cases, geographically mobile labor is combined with geographically immobile land, such that the model yields predictions for the prices of immobile factors of production (see, e.g., Rossi-Hansberg 2005, Redding 2016, among many others). Two further decisions are the spatial scope of the model and the spatial units for which it is quantified. Is the model concerned with a single city, a system of cities, a set of rural and urban regions within a country or group of countries, or the global economy as a whole? Is space ordered along one dimension (e.g., latitude) or two dimensions? Data are typically available for discrete spatial units. How disaggregated are these units? Are they points on a latitude and longitude grid, city blocks, municipalities, counties, commuting zones, metropolitan areas, states or provinces, regions, or countries as a whole? Clearly these two decisions are interrelated because the choice of spatial scope may limit the level of spatial disaggregation of the units for which data are available.
在大多数情况下,地理上流动的劳动力与地理上固定的土地相结合,从而使模型能够预测生产中固定要素的价格(例如,参见 Rossi-Hansberg 2005,Redding 2016 等)。另外两个决策是模型的空间范围和它所量化的空间单位。模型是关注单一城市、城市体系、一个国家或多个国家内的城乡区域,还是整个全球经济?空间是沿着一个维度(例如,纬度)还是两个维度有序排列?数据通常适用于离散的空间单位。这些单位是如何细分的?它们是经纬度网格上的点、街区、市镇、县、通勤区、大都市区、州或省、地区,还是整个国家?显然,这两个决策是相互关联的,因为空间范围的选择可能会限制可用数据的单位的空间细分程度。

2.6.3.   Capital and infrastructure.
2.6.3. 资本与基础设施。

Other mobile factors of production, such as physical capital that is used in a construction sector (see, e.g., Epple et al. 2010, Combes et al. 2016, Ahlfeldt et al. 2015), can be introduced. Incorporating physical production capital that fully depreciates every period, as do Desmet & Rossi-Hansberg (2013), is also simple. However, incorporating, over time, local capital investments that do not depreciate fully introduces a dynamic forward-looking problem, with the whole distribution of capital across space as a state variable, that has not been tackled in the literature. 3 More generally, depending on the assumptions made about the costs of the movement of goods, ideas, and people, the economy's endowments can also include transport infrastructure networks, which up to now have largely been treated as exogenous in quantitative spatial models.
其他生产要素的移动因素,例如在建筑部门使用的物质资本(参见,例如,Epple 等,2010 年,Combes 等,2016 年,Ahlfeldt 等,2015 年),也可以引入。像 Desmet & Rossi-Hansberg(2013 年)那样,将完全折旧的物质生产资本纳入,也是简单的。然而,随着时间的推移,将不完全折旧的地方资本投资纳入,引入了一个动态的前瞻性问题,整个空间资本分布作为一个状态变量,这在文献中尚未得到解决。 3 更一般地说,根据对商品、思想和人员流动成本的假设,经济的禀赋还可以包括运输基础设施网络,到目前为止,这些在定量空间模型中大多被处理为外生变量。

2.7.   Equilibrium 平衡

Given the above assumptions about preferences; production technology; endowments; and the technologies for the movement of goods, ideas, and people, a final set of assumptions concerning the equilibrium conditions of the model must be considered.
考虑到上述关于偏好的假设、生产技术、禀赋以及商品、思想和人员流动的技术,必须考虑关于模型均衡条件的最终假设集。

2.7.1.   Market structure.
2.7.1. 市场结构。

Two main market structures have been considered in the literature on quantitative spatial models. Models of constant returns to scale, such as those based on the work of Armington (1969) and Eaton & Kortum (2002), typically assume perfect competition (see, e.g., Allen & Arkolakis 2014, Caliendo et al. 2014). In contrast, models of increasing returns to scale, such as those in the new economic geography literature, typically assume monopolistic competition (see, e.g., Helpman 1998, Monte et al. 2015, Redding 2016). One reason for this assumption is the fact that internal increasing returns to scale require the assumption of imperfect competition because otherwise, according to Euler's theorem, factor payments would more than exhaust the value of output. Of the possible forms of imperfect competition, monopolistic competition is particularly tractable, and its assumption of free entry ensures zero equilibrium profits, which implies that all revenue is ultimately paid to factors of production.
两种主要的市场结构在定量空间模型文献中被考虑。规模报酬不变的模型,如基于 Armington(1969 年)和 Eaton & Kortum(2002 年)工作的模型,通常假设完全竞争(参见,例如,Allen & Arkolakis 2014,Caliendo 等 2014)。相比之下,规模报酬递增的模型,如新经济地理学文献中的模型,通常假设垄断竞争(参见,例如,Helpman 1998,Monte 等 2015,Redding 2016)。这种假设的一个原因是,内部规模报酬递增需要假设不完全竞争,否则,根据欧拉定理,要素支付将超过产出的价值。在不完全竞争的可能形式中,垄断竞争特别易于处理,其自由进入的假设确保了零均衡利润,这意味着所有收入最终都支付给了生产要素。

2.7.2.   General versus partial equilibrium.
2.7.2. 一般均衡与局部均衡。

A central feature of quantitative spatial models is the discipline and internal consistency imposed by the equilibrium conditions of the model. However, researchers must choose the level at which these equilibrium conditions are imposed. If the model is of the internal structure of economic activity within a single city, the equilibrium conditions may hold within the city, which can be embedded within a larger economy that provides a reservation level of utility taken as given by the city. If the model is of a single country, these equilibrium conditions may hold within the country, which is assumed to face exogenous prices or levels of expenditure on a world market. At the most general level, if the model is of the global economy, the equilibrium conditions must be specified for the world as a whole. But if some factors are immobile across countries or some goods are nontraded, some of the equilibrium conditions will hold within each country separately.
一个中心特征是定量空间模型受到模型均衡条件所强加的纪律性和内部一致性。然而,研究人员必须选择这些均衡条件施加的层次。如果模型是单个城市内经济活动的内部结构,均衡条件可能在该城市内成立,该城市可以嵌入一个更大的经济体中,该经济体提供城市视为既定的保留水平效用。如果模型是单个国家的,这些均衡条件可能在该国内成立,假设该国面临世界市场的外生价格或支出水平。在最一般层次上,如果模型是全球经济,均衡条件必须为整个世界指定。但如果某些因素在国家间不可流动或某些商品不可交易,一些均衡条件将分别在每个国家内成立。

2.7.3.   Land ownership and the distribution of rents.
土地所有权和地租分配。

If land is used for either residential or production purposes, then it will generate rents to its owners. Thus, specifying who are the owners of land in the different locations modeled is essential for the welfare properties of the model and can be important for the determination of the equilibrium allocation. The urban economics literature has a long tradition of abstracting from land rents by postulating the existence of absentee landlords who receive all the rents but are not explicitly modeled. This assumption, although sometimes convenient, eliminates the ability of the model to incorporate full general equilibrium effects. This limitation is particularly important because many changes in policy or productivity effects of innovation will ultimately be capitalized in land rents and therefore will be accrued to landowners. Of course, simply allowing for a land market where agents can buy and sell land would be ideal. However, it necessarily requires incorporating location-specific wealth effects. For example, if a region receives a positive productivity shock, its land will appreciate, which will make current owners richer and owners everywhere else relatively poorer. Although perhaps realistic, keeping track of these changes in individual wealth in a model with migration is extremely challenging. The key complication is that incorporating location-specific wealth effects makes agents heterogeneous as a function of their location history. The literature has devised three main methods of incorporating land rents into the analysis, and thus accounting for general equilibrium effects, without generating these types of heterogeneous wealth effects. The first is to introduce a global portfolio that aggregates the land rents of the whole economy and to give agents shares in this portfolio (see, e.g., Desmet & Rossi-Hansberg 2014). The second is to distribute land rents locally to current residents (see, e.g., Redding 2016). This second option generates inefficiencies because moving across locations imposes an externality on the rents received by other agents. One can also combine both to account for trade deficits, as do Caliendo et al. (2014). Finally, the third method assumes the presence of local immobile landlords who consume all their land income locally. Then, local consumption will simply add up to total labor income (see, e.g., Monte et al. 2015).
如果土地用于住宅或生产目的,那么它将为所有者产生租金。因此,明确不同位置模型中土地的所有者是谁对于模型的社会福利属性至关重要,并且对于确定均衡分配也很重要。城市经济学文献有着长期从土地租金中抽象出来的传统,通过假设存在收取所有租金但未在模型中明确表示的缺席地主。这种假设虽然有时方便,但消除了模型纳入完全一般均衡效应的能力。这种限制尤其重要,因为许多政策变化或创新的生产力效应最终将体现在土地租金中,并因此累积到土地所有者手中。当然,简单地允许存在一个可以买卖土地的房地产市场是理想的。然而,这必然需要纳入特定位置的财富效应。例如,如果一个地区受到正的生产力冲击,其土地将增值,这将使当前所有者变得更富有,而其他地方的所有者相对较穷。 尽管可能现实,但在一个包含迁移的模型中追踪个人财富的变化极具挑战性。关键复杂性在于,将特定位置的财富效应纳入考虑使得代理人在其位置历史方面变得异质。文献中提出了三种将土地租金纳入分析的方法,从而考虑一般均衡效应,而不产生这些类型的异质财富效应。第一种是引入一个全球投资组合,汇总整个经济体的土地租金,并给代理人分配该投资组合的股份(例如,参见 Desmet & Rossi-Hansberg 2014)。第二种是将土地租金在本地分配给当前居民(例如,参见 Redding 2016)。第二种选择会产生低效率,因为跨地区迁移会对其他代理人的租金产生外部性。还可以将两者结合起来以考虑贸易赤字,如 Caliendo 等人(2014)所做的那样。最后,第三种方法假设存在本地不可移动的地主,他们将在本地消费所有土地收入。然后,本地消费将简单累加到总劳动收入(例如,参见 Monte 等人)。 2015).

2.7.4.   Trade balance. 2.7.4. 贸易差额。

In any spatial model, one must choose the spatial unit for which trade is balanced. In quantitative trade models, this is often a country, although country trade accounts clearly exhibit long-lasting and persistent trade imbalances (see, e.g., Reyes-Heroles 2016). The decision is even more relevant when one focuses on smaller spatial units such as states, commuting zones, counties, or even zip codes or census tracks. The narrower the spatial unit, the less likely it is that trade is balanced for each location because agents can commute or migrate, taking with them their wealth balances, and regions can have accumulated assets and debts in other regions that result in future permanent trade flows. Even so, the assumption of trade balance at the local level is common in the quantitative spatial literature. Another popular option is to acknowledge the possibility of deficits, calibrate them using data, but keep them invariant in the counterfactual exercises (see, e.g., Allen & Arkolakis 2014). Yet another possibility is to calculate a baseline counterfactual economy without deficits from which all other counterfactual exercises are computed (thereby ameliorating the fact that deficits are fixed). In static models, a final possibility is to model changes in deficits as resulting from variations in the rents accrued to land owners (see, e.g., Caliendo et al. 2014). A full quantitative dynamic spatial model that endogenizes the consumption–savings decisions that determine whether a location saves and borrows over time has, to our knowledge, not been developed.
在任何空间模型中,必须选择贸易平衡的空间单元。在定量贸易模型中,这通常是一个国家,尽管国家贸易账户明显显示出长期和持续的贸易失衡(例如,参见 Reyes-Heroles 2016)。当人们关注如州、通勤区、县甚至邮政编码或人口普查区等更小的空间单元时,这一决策更为重要。空间单元越窄,贸易在每个地点平衡的可能性就越小,因为代理人可以通勤或迁移,带着他们的财富平衡,而地区可能在其他地区积累了资产和债务,导致未来永久性的贸易流动。即便如此,在定量空间文献中,假设地方层面的贸易平衡是常见的。另一个流行的选择是承认赤字的可能性,使用数据校准它们,但在反事实实验中保持它们不变(例如,参见 Allen & Arkolakis 2014)。 另一种可能性是计算一个无赤字的基线反事实经济,所有其他反事实练习都基于此(从而改善赤字固定的事实)。在静态模型中,还有一种可能性是将赤字的变化建模为来自土地所有者获得的租金的变化(例如,参见 Caliendo 等人 2014 年的研究)。据我们所知,尚未开发出一个完全的定量动态空间模型,该模型内生化了决定一个地区是否随时间储蓄和借贷的消费-储蓄决策。

2.8.   Criteria for Menu Choice
菜单选择标准

Having outlined the modules or building blocks that can be used to create quantitative spatial models, we now discuss some of the possible criteria for choosing among these modules.
概述了可用于创建定量空间模型的模块或构建块后,我们现在讨论一些在选择这些模块时可能适用的标准。

2.8.1.   Tractability. 2.8.1. 可行性。

The first criterion includes both analytical and computational tractability. Traditionally, theoretical models of economic geography have focused on a small number of symmetric regions to preserve analytical tractability. Technical advances have now made it possible to obtain analytical results for the existence and uniqueness of equilibrium and for comparative statics even for large numbers of asymmetric locations connected by real-world transport networks (see, in particular, Allen & Arkolakis 2014, Allen et al. 2015). Other technical innovations have permitted analytical characterizations of the dynamics of the distribution of economic activity across space (see Desmet & Rossi-Hansberg 2013, Desmet et al. 2016). Related methodological improvements have developed a set of standard techniques for tractably undertaking counterfactuals in a class of theoretical models using the observed values of variables in an initial equilibrium (see Dekle et al. 2007). At the same time, advances in computing power and computational methods have made it possible to solve systems of nonlinear equations for large numbers of locations over realistic computational time periods. 4
第一个标准包括分析和计算的可处理性。传统上,经济地理学的理论模型专注于少数对称区域以保持分析的可处理性。技术进步现在使得即使对于通过现实世界交通网络连接的大量非对称位置,也能获得关于均衡存在性和唯一性以及比较静态的分析结果(参见 Allen & Arkolakis 2014,Allen et al. 2015)。其他技术创新允许对空间经济活动分布的动态进行分析描述(参见 Desmet & Rossi-Hansberg 2013,Desmet et al. 2016)。相关方法论改进开发了一套标准技术,在理论模型中使用初始均衡中变量的观测值来可处理地进行反事实分析(参见 Dekle et al. 2007)。同时,计算能力和计算方法的发展使得在现实计算时间内解决大量位置的非线性方程组成为可能。 4

2.8.2.   Structural assumptions.
2.8.2. 结构假设。

A second criterion involves the choice of structural parameters and exogenous location characteristics that are invariant to policy interventions. When a quantitative spatial model is used to undertake a counterfactual for the impact of a place-based policy or transport infrastructure improvement, the researcher must decide which components of the model are invariant to this intervention. Are productivity and amenities exogenous? Or are there agglomeration externalities for productivity and amenities such that only certain components of these location characteristics are fundamentals that are invariant to the intervention? Is there an outside level of utility in a wider economy that is constant? Or are there exogenous prices or expenditures in world markets? Answers to questions such as these will influence the selection of building blocks from the list outlined above. Only when the assumed structural parameters and locational fundamentals are indeed constant will the analysis not be subject to the Lucas critique.
一个第二标准涉及选择对政策干预不变的结构参数和外生位置特征。当使用定量空间模型对基于地点的政策或交通基础设施改进的影响进行反事实分析时,研究人员必须决定哪些模型成分对此干预不变。生产力和便利设施是否外生?或者,生产力和便利设施存在集聚外部性,只有这些位置特征的某些成分是基本且对干预不变的?在更广泛的经济体中是否存在一个恒定的效用水平?或者,在世界市场上存在外生价格或支出?对这些问题的回答将影响从上述列表中选择构建块。只有当假设的结构参数和位置基本要素确实保持不变时,分析才不会受到卢卡斯批评的影响。

2.8.3.   Connection between model and data.
2.8.3. 模型与数据之间的联系。

A third criterion relates to the question being asked, the level of detail at which an answer is required, and what is observed in the data. Is the question about the aggregate effects of a policy or the impact on the distribution of economic activity across disaggregated spatial units? To what extent is understanding the distributional impact at the disaggregated level relevant for evaluating the aggregate effect? What are the spatial units for which the data are recorded? What types of data are available? These include the levels of the endogenous variables of the model for each location (e.g., population, wages); endogenous bilateral flows (e.g., trade and commuting flows); frictions in the movements of goods, ideas, and people (e.g., mountains and borders); and changes in the endogenous variables of the model for each location (e.g., changes in population or wages). Different types of data can sometimes be substitutes for one another. For example, quantitative models can typically be solved using either data on endogenous bilateral flows (e.g., bilateral trade) or data on exogenous frictions (e.g., the costs of traversing mountains and water). Do the data available permit a structural estimation of the model's parameters? Or will the model be calibrated using values of the model's parameters from elsewhere? Or can a subset of the parameters be estimated and the remaining parameters borrowed from other studies? When the model is taken to the data, is it exactly identified such that it has enough degrees of freedom to exactly explain the observed data as an equilibrium outcome? If so, is the model invertible such that there exists a one-to-one mapping from the parameters and observed data to the unobserved location characteristics or structural residuals? What overidentification checks can be undertaken using moments not used in the calibration or estimation to provide a check on the validity of the model's predictions?
一个第三标准与所提问题、所需答案的详细程度以及数据中的观察结果有关。问题是关于政策的总体效应还是对经济活动在不同空间单元中的分布的影响?在多大程度上,理解在细分层面的分布影响对于评估总体效应是相关的?数据记录的空间单元是什么?有哪些类型的数据可用?这包括每个位置的模型内生变量的水平(例如,人口、工资);内生双边流动(例如,贸易和通勤流动);商品、思想和人员流动的摩擦(例如,山脉和边界);以及每个位置模型内生变量的变化(例如,人口或工资的变化)。不同类型的数据有时可以相互替代。例如,定量模型通常可以使用内生双边流动的数据(例如,双边贸易)或外生摩擦的数据(例如,穿越山脉和水的成本)来解决。 数据是否允许对模型参数进行结构估计?或者模型将使用来自其他地方的模型参数值进行校准?或者是否可以估计参数的子集,而将剩余参数从其他研究中借用?当模型应用于数据时,它是否恰好识别,以便它有足够的自由度来精确解释观察到的数据作为均衡结果?如果是这样,模型是否可逆,即存在从参数和观察数据到未观察到的位置特征或结构残差的唯一映射?可以使用哪些未在校准或估计中使用的矩来执行过度识别检验,以提供对模型预测有效性的检查?

 

In this section, we outline a canonical quantitative spatial model that corresponds to a multiregion version of the new economic geography model of Helpman (1998). To study the determinants of the spatial distribution of economic activity across a set of regions connected by goods trade and factor mobility, we select the following items from the menu of building blocks above:
在这一节中,我们概述了一个与 Helpman(1998)提出的新经济地理学模型的多区域版本相对应的规范量化空间模型。为了研究经济活动在由商品贸易和要素流动性连接的一系列区域中的空间分布的决定因素,我们从上述构建模块菜单中选择以下项目:

  1. 1.  From Section 2.1, we select love of variety, single traded sector, no amenities, residential land use, and common preferences.
    1. 从 2.1 节中,我们选取了喜新厌旧、单一交易领域、无便利设施、住宅用地和共同偏好。
  2. 2.  From Section 2.2, we select increasing returns to scale, exogenous productivity, no input–output linkages, and no commercial land use.
    2. 从 2.2 节中,我们选取规模报酬递增、外生生产力、无投入产出联系以及无商业土地利用。
  3. 3.  From Section 2.3, we select iceberg variable trade costs, symmetric trade costs, economic and geographic frictions, and no nontraded goods besides residential land use.
    3. 从第 2.3 节中,我们选取冰山变量贸易成本、对称贸易成本、经济和地理摩擦,以及除了住宅用地之外没有非贸易商品。
  4. 4.  From Section 2.4, we select no knowledge externalities or diffusion, no innovation, and no transferability of ideas.
    4. 从 2.4 节中,我们选取无知识外部性或扩散、无创新以及无思想可转移性。
  5. 5.  From Section 2.5, we select perfectly costless migration, no commuting, single worker type with no heterogeneity, and no congestion in transportation.
    5. 从第 2.5 节,我们选择完美无成本的迁移、无通勤、单一工人类型且无异质性的情况,以及无交通拥堵。
  6. 6.  From Section 2.6, we select homogeneous labor, exogenous land endowments in regions within a single country, and no capital.
    6. 从第 2.6 节中,我们选取同质劳动力、单一国家内地区的外生土地禀赋,以及无资本。
  7. 7.  From Section 2.7, we select monopolistic competition, general equilibrium with a single country, land rents redistributed to residents, and balanced trade in each location.
    7. 从第 2.7 节中,我们选取了垄断竞争、单一国家的总体均衡、土地租金重新分配给居民以及每个地点的平衡贸易。

This model has been widely used in empirical work, including work by Hanson (2005) and Redding & Sturm (2008).
此模型已被广泛应用于实证研究中,包括 Hanson(2005)和 Redding & Sturm(2008)的研究工作。

We consider an economy consisting of a set of regions indexed by . Each region is endowed with an exogenous quality-adjusted supply of land (). The economy as a whole is endowed with a measure of workers, where each worker has one unit of labor that is supplied inelastically with zero disutility. Workers are perfectly geographically mobile, and thus, in equilibrium, real wages are equalized across all populated regions. Regions are connected by a bilateral transport network that can be used to ship goods subject to symmetric iceberg trade costs, such that =>1 units must be shipped from region in order for one unit to arrive in region , where =1. 5
我们考虑一个由 N 个地区组成的集合 N,这些地区由 N 进行索引。每个地区都拥有一个外生质量调整后的土地供应量(H)。整个经济体系拥有一个 的工人数量,其中每个工人提供一单位劳动力,该劳动力供应无弹性且无负效用。工人具有完美的地理流动性,因此,在均衡状态下,所有人口地区的实际工资相等。地区通过一个双边运输网络相连,可以用来运输商品,并受到对称的冰山贸易成本的影响,即从地区 i 运输 dini >1 单位商品才能使一单位商品到达地区 n≠i,其中 dnn =1。 5

3.1.   Consumer Preferences
3.1. 消费者偏好

Preferences are defined over goods consumption () and residential land use () and are assumed to take the Cobb-Douglas form: 6
偏好定义在商品消费(Cn)和住宅土地利用(hn)上,并假定其采用 Cobb-Douglas 形式: 6

1. 

The goods consumption index is defined over consumption () of each horizontally differentiated variety from the endogenous measures supplied by each region. This consumption index and its dual price index, , are given by
商品消费指数 Cn 是在每个地区提供的内生度量 M 的基础上,定义了每个水平差异化的品种 j 的消费 cni(j)。该消费指数及其对偶价格指数 Pn 由以下公式给出

2. 

3.2.   Production 3.2. 生产

Varieties are produced under conditions of monopolistic competition and increasing returns to scale. To produce a variety, a firm must incur a fixed cost of units of labor and a constant variable cost in terms of labor that depends on a location's productivity . Therefore, the total amount of labor, (), required to produce () units of a variety in location is
品种在垄断竞争和规模报酬递增的条件下产生。为了生产一个品种,企业必须承担 F 单位劳动力的固定成本以及与地点 i 的生产力 A 相关的劳动力的常数变动成本。因此,在地点 i 生产品种 j 的 x(j)单位所需的劳动力总量 l(j)是

3. 

Profit maximization and zero profits imply that equilibrium prices are a constant markup over the marginal cost of supplying a variety to a market,
利润最大化与零利润意味着均衡价格是市场供应某种商品边际成本的一个常数加成

4. 

and equilibrium output of each variety is equal to a constant that depends on location productivity, namely,
并且每种品种的均衡产出等于一个依赖于地理位置生产力的常数,即,

5. 

which implies that equilibrium employment for each variety is the same for all locations, so
这表明每种品种的均衡就业在所有地点都是相同的,因此

6. 

Given this constant equilibrium employment for each variety, labor market clearing implies that the total measure of varieties supplied by each location is proportional to the endogenous supply of workers choosing to locate there:
考虑到每种品种的恒定均衡就业,劳动力市场出清意味着每个地点提供的品种总供应量与选择在该地定居的工人的内生供应量成比例:

7. 

3.3.   Price Indices and Expenditure Shares
3.3. 价格指数和支出份额

Using equilibrium prices (Equation 4) and labor market clearing (Equation 7), one can express the price index dual to the consumption index (Equation 2) as
使用均衡价格(方程式 4)和劳动力市场均衡(方程式 7),可以将与消费指数(方程式 2)相对应的价格指数表示为

8. 

Using the constant elasticity of substitution (CES) expenditure function, equilibrium prices (Equation 4), and labor market clearing (Equation 7), the share of location ’s expenditure on goods produced in location is
利用常弹性替代(CES)支出函数、均衡价格(方程 4)和劳动力市场均衡(方程 7),位置 N 在位置 i 生产的商品上的支出份额是

9. 

The model therefore implies a gravity equation for goods trade, where the bilateral trade between locations and depends on both bilateral resistance (bilateral trade costs ) and multilateral resistance (trade costs to all other locations ), as in the work of Anderson & van Wincoop (2003). Together, Equations 8 and 9 imply that each location's price index can be written in terms of its trade share with itself, so
该模型因此暗示了一个关于货物贸易的重力方程,其中 N 和 i 之间的双边贸易取决于双边阻力(双边贸易成本 dni)和多边阻力(对所有其他地点的贸易成本 k dnk),正如 Anderson 和 van Wincoop(2003)的研究所示。8 号和 9 号方程共同意味着每个地点的价格指数可以用其与自身的贸易份额来表示,因此

10. 

3.4.   Income and Population Mobility
收入与人口流动性

Expenditure on land in each location is redistributed in a lump sum to the workers residing in that location. Therefore, trade balance at each location implies that per capita income in each location equals labor income plus per capita expenditure on residential land, (1−α), namely,
各地点的土地支出以总额形式重新分配给该地点居住的工人。因此,每个地点的贸易平衡意味着每个地点的人均收入 vn 等于劳动收入 wn 加上人均住宅土地支出(1−α)vn,即,

11. 

Land market clearing implies that the supply of quality-adjusted land, , equals the demand for land, . By combining this market clearing condition with the first-order condition of the consumer problem, we obtain the result that land rents, , are given by
土地市场出清意味着质量调整后的土地供应量 Hn 等于土地需求量 Lnhn。将这一市场出清条件与消费者问题的第一阶条件相结合,我们得到土地租金 rn 的表达式为

12. 

Population mobility implies that workers receive the same real income in all populated locations, thus
人口流动性意味着工人在所有人口密集地区都能获得相同实际收入,因此

13. 

By using the price index (Equation 10), the assumption that trade is balanced at each location such that income equals expenditure (Equation 11), and land market clearing (Equation 12) in the population mobility condition (Equation 13), one determines that real wage equalization implies that the population and domestic trade share π of each location must satisfy
通过使用价格指数(公式 10),在人口流动性条件(公式 13)下,贸易在每个地点平衡的假设(收入等于支出,公式 11)和土地市场出清(公式 12),可以确定实际工资均等化意味着每个地点的人口 Ln 和国内贸易份额πnn 必须满足

14. 

Therefore, the population share of each location ( ) depends on its productivity , supply of land , and domestic trade share π relative to those of all other locations,
因此,每个地点的人口份额( )取决于其生产率 An、土地供应 Hn 以及相对于所有其他地点的国内贸易份额πnn

15. 

where each location's domestic trade share π summarizes its market access to other locations.
每个位置的国内贸易份额πnn 概括了其对其他地点的市场准入。

3.5.   General Equilibrium 一般均衡

The properties of the general equilibrium of the model can be characterized analytically by combining the trade share (Equation 9), price index (Equation 8), and population mobility condition (Equation 13). Under the assumption that trade costs are symmetric (=), one can follow the arguments of Allen & Arkolakis (2014) to show that these three sets of relationships reduce to the following system of equations in the populations of each location:
模型的总体均衡性质可以通过结合贸易份额(方程 9)、价格指数(方程 8)和人口流动性条件(方程 13)进行解析性描述。在贸易成本对称(dni = din)的假设下,可以遵循 Allen & Arkolakis(2014)的论证,表明这三组关系简化为每个地点 N 个人口中的 N 个方程组:

16. 

where the scalar is determined by the requirement that the labor market clears ( ) and
在满足劳动力市场出清( )的要求下确定标量

Wages in turn are implicitly determined by
工资反过来是由...隐含决定的

17. 

where ξ is a scalar that normalizes wages. Allen & Arkolakis (2014) use this argument, together with the mathematical results for fixed points of systems of equations of the form given by Equation 16 (Fujimoto & Krause 1985), to show that there exists a unique for each that satisfies Equation 16 as long as γ∈(0, 1). Thus, given the land area and productivity parameters {, } and symmetric bilateral trade frictions {} for all locations , , there exists a unique equilibrium as long as this parametric restriction is satisfied. Furthermore, if γ∈(0, 1), then one can also guarantee that a solution to Equation 16 can be found by iteration from any initial distribution of populations. 7
ξ是一个标准化工资的标量。Allen & Arkolakis(2014)使用这个论点,结合方程 16(Fujimoto & Krause 1985)给出的方程组不动点数学结果,来证明对于每个 n 存在唯一的 Ln,只要γ2/γ1∈(0, 1),它就满足方程 16。因此,给定所有位置 n,i∈N 的土地面积和生产率参数{Hn, An}以及对称的双边贸易摩擦{dni},只要满足这个参数限制,就存在唯一的均衡。此外,如果γ2/γ1∈(0, 1),还可以保证可以从任何初始人口分布通过迭代找到方程 16 的解。 7

The parameter restrictions that guarantee that an equilibrium exists and is unique amount to imposing conditions that guarantee that congestion forces always dominate agglomeration forces. In our simple model, a sufficient condition for γ∈(0, 1) is σ(1−α)>1. Intuitively, as population concentrates in a location, the measure of varieties produced there expands, which, in the presence of trade costs, makes that location a more attractive residence (an agglomeration force). However, as population concentrates in a location, this also bids up land prices (a dispersion force). The higher the elasticity of substitution (σ), the weaker is the agglomeration force. The higher the share of land (1−α), the stronger is the dispersion force. For parameter values for which σ(1−α)>1, the dispersion force dominates the agglomeration force, and a unique equilibrium distribution of economic activity exists.
参数限制保证存在且唯一的均衡,相当于施加条件以保证拥堵力量始终支配聚集力量。在我们的简单模型中,γ2/γ1∈(0, 1)的充分条件是σ(1−α)>1。直观地说,随着人口在某一地点集中,该地点生产的品种数量增加,这在存在贸易成本的情况下,使该地点成为更吸引人的居住地(聚集力量)。然而,随着人口在某一地点集中,这也推高了土地价格(分散力量)。替代弹性的弹性(σ)越高,聚集力量越弱。土地份额(1−α)越高,分散力量越强。对于σ(1−α)>1 的参数值,分散力量支配聚集力量,存在唯一的经济活动均衡分布。

The existence of such a unique equilibrium is important because it ensures that counterfactuals for transport infrastructure improvements or other public policy interventions have determinate implications for the spatial distribution of economic activity. Although this is a convenient property of the model for quantitative empirical work, a central feature of the theoretical literature on new economic geography was the presence of multiple equilibria [as in the original core–periphery model of Krugman (1991b)], and assuming σ(1−α)>1 excludes this possibility. Thus, for the range of parameters where σ(1−α)>1, the model cannot generate agglomerations when space is perfectly homogeneous; it can generate agglomerations only as a result of initial differences across locations. Of course, in this general class of models, the vector of initial differences can be multidimensional and quite rich, as discussed in the context of a richer model with many sources of heterogeneity across locations by Desmet et al. (2016).
该独特均衡的存在具有重要意义,因为它确保了关于交通基础设施改善或其他公共政策干预的假设情景对经济活动空间分布的确定影响。尽管这是模型进行定量实证研究的一个便利属性,但新经济地理学理论文献的一个中心特征是存在多个均衡[如克鲁格曼(1991b)的原核-外围模型],而假设σ(1−α)>1 排除了这种可能性。因此,在σ(1−α)>1 的参数范围内,模型在空间完全同质的情况下不能产生集聚;它只能通过不同地点的初始差异产生集聚。当然,在这个一般模型类中,初始差异向量可以是多维的,相当丰富,正如 Desmet 等人(2016)在讨论具有许多地点异质性来源的更丰富模型时所指出的。

At a more philosophical level, whether a model is characterized by multiple equilibria may depend on its level of abstraction. On the one hand, a model may exhibit multiple equilibria because it omits the relevant idiosyncratic factors that determine one allocation rather than another in the data. On the other hand, if a model includes all such idiosyncratic factors, it ceases to be a model and becomes a descriptive representation of reality. One possible interpretation of such idiosyncratic factors is as random realizations of a stochastic error that is drawn from a parameterized distribution. At smaller spatial scales (e.g., blocks within cities), one might expect such random idiosyncratic factors to be more important relative to the systematic deterministic components of a model (e.g., natural resource abundance) than at larger spatial scales (e.g., across regions or countries).
在更哲学的层面上,一个模型是否具有多重均衡可能取决于其抽象程度。一方面,一个模型可能表现出多重均衡,因为它省略了决定数据中某一分配而非另一分配的相关独特因素。另一方面,如果一个模型包括了所有这样的独特因素,它就不再是模型,而变成了对现实的描述性表征。对这种独特因素的一种可能的解释是它们是随机实现,这些随机实现是从参数化分布中抽取的随机误差。在较小的空间尺度上(例如,城市内的街区),人们可能会预期这种随机的独特因素相对于模型中系统的确定性成分(例如,自然资源丰富度)在较大空间尺度上(例如,跨区域或国家)更为重要。

Throughout this section, we focus on a canonical new economic geography model with increasing returns to scale and monopolistic competition. However, similar properties hold in a wider class of models. Allen & Arkolakis (2014) demonstrate an isomorphism to a perfectly competitive Armington trade model (in which goods are differentiated by location of origin), extended to incorporate labor mobility and external economies. Allen & Arkolakis (2014) and Redding (2016) show that similar properties also hold in a perfectly competitive Ricardian trade model following Eaton & Kortum (2002) with labor mobility and external economies of scale.
在整个本节中,我们关注一个具有规模报酬递增和垄断竞争的典型新经济地理模型。然而,类似的性质也存在于更广泛的模型类别中。Allen & Arkolakis(2014)证明了与一个完全竞争的 Armington 贸易模型(其中商品通过原产地进行区分)的同构性,并将其扩展到包含劳动力流动和外部经济。Allen & Arkolakis(2014)和 Redding(2016)表明,在遵循 Eaton & Kortum(2002)的完全竞争 Ricardian 贸易模型中,也具有类似的性质,该模型具有劳动力流动和规模经济的外部性。

3.6.   Model Inversion 模型反演

In this section, we describe how the quantitative spatial model can be used to rationalize observed data. We suppose that a researcher has estimates of the model's two key parameters: the share of residential land in consumer expenditure (α) and the elasticity of substitution between varieties (σ). The researcher is also assumed to have parameterized symmetric bilateral trade costs (), for example, by assuming that they are a constant elasticity function of distance, and to observe an endogenous population, {}, and nominal wages, {}. One can show that there is a one-to-one mapping from the model's parameters and the observed data to the unobserved values of quality-adjusted land {} and productivities {} (up to a normalization constant). That is, the model can be inverted to recover the unique values of unobserved quality-adjusted land and productivities that rationalize the observed data as an equilibrium outcome of the model.
在这一节中,我们描述了如何使用定量空间模型来合理化观察到的数据。我们假设研究者已经估计了模型的两个关键参数:住宅用地在消费支出中的份额(α)和品种之间的替代弹性(σ)。研究者还被假设已经对对称的双边贸易成本(dni)进行了参数化,例如,假设它们是距离的常数弹性函数,并观察到内生人口{Ln}和名义工资{wn}。可以证明,从模型的参数和观察到的数据到未观察到的质量调整后土地{Hn}和生产力{An}的值之间存在一一对应的关系(直到归一化常数)。也就是说,可以通过逆模型来恢复未观察到的质量调整后土地和生产力唯一值,这些值可以合理化观察到的数据,作为模型均衡结果的体现。

Inverting the model amounts to using Equations 16 and 17 to solve for {, } given {, }. This is exactly the opposite of what we do when we solve for an equilibrium of the model, where we solve for {, } given {, }. To guarantee that there exists a unique set of values {, } that rationalize the observed data (up to a normalization or choice of units), we can proceed as follows. Using Equation 17, we can solve for and substitute this solution in Equation 16. The resulting equation can then be solved for {} using information on {, }. To show that such a solution exists and is unique, we can again use the mathematical theorems that guarantee solutions to these type of equations [e.g., those of Fujimoto & Krause (1985) for discrete space or Zabreyko et al. (1975) for continuous space]. As in the previous section, a solution exists if, after substituting for , the exponent of the term inside the sum is smaller than the exponent of the term outside the sum. In our example, this is guaranteed if σ(1−α)>1. We can then recover {} using Equation 17.
将模型进行逆运算相当于使用方程 16 和 17 求解{An, Hn},给定{Ln, wn}。这与我们在求解模型平衡时的做法正好相反,在求解模型平衡时,我们给定{An, Hn}求解{Ln, wn}。为了保证存在一组唯一的值{An, Hn}来合理化观察到的数据(直到归一化或选择单位),我们可以按以下步骤进行。使用方程 17,我们可以求解 Hn,并将此解代入方程 16。然后,可以使用{Ln, wn}的信息求解{An}。为了证明这样的解存在且唯一,我们可以再次使用保证这类方程解的数学定理[例如,Fujimoto & Krause(1985)的离散空间定理或 Zabreyko 等(1975)的连续空间定理]。与上一节一样,如果将 Hn 代入后,求和式中 A 项的指数小于求和式外的 An 项的指数,则存在解。在我们的例子中,这由σ(1−α)>1 保证。然后,我们可以使用方程 17 恢复{Hn}。

Having recovered the unobserved productivities {}, these can be used, together with the parameterization of trade costs () and observed wages () in the trade shares (Equation 9), to generate predictions for unobserved bilateral trade shares (π) in the equilibrium observed in the data. Related arguments hold if the researcher directly observes bilateral trade shares (π) instead of having to assume values for bilateral trade costs (). In this case, unobserved quality-adjusted land supplies (), productivities (), and bilateral trade costs () can be recovered from the observed data (up to a normalization or choice of units).
已恢复未观察到的生产率{An},这些可以与贸易成本的参数化(dni)和观察到的工资(wn)在贸易份额(方程 9)中一起使用,以生成对数据中观察到的均衡状态下未观察到的双边贸易份额(πni)的预测。如果研究者直接观察到双边贸易份额(πni)而不是必须假设双边贸易成本(dni)的值,相关的论点仍然成立。在这种情况下,可以从观察到的数据中恢复未观察到的质量调整后的土地供应(Hn)、生产率(An)和双边贸易成本(dni)(直至归一化或单位选择)。

These arguments imply that the model is exactly identified, in the sense that it has the same number of degrees of freedom (unobserved location characteristics in the form of the quality-adjusted land supplies and productivities for each location) as observed endogenous variables (population and wages ). Therefore, the model's ability to explain the observed data cannot be used as a test of the model because the unobserved quality-adjusted land supplies and productivities are free parameters that can be adjusted so as to ensure that the model exactly matches the data. Note also that, because denotes quality-adjusted land, it cannot be directly compared to observations on total land supply in a location. Doing so would simply yield a measure of the average quality of land in that region (which is related to its residential amenities). Furthermore, the observed data on wages and populations cannot be used to estimate the model's structural parameters, α and σ. Given any value for these parameters, quality-adjusted land supplies and productivities can be adjusted so as to ensure that the model exactly rationalizes the data. Therefore, any change in the value of the structural parameters can be offset by changes in these unobserved location characteristics such that the model continues to explain the data.
这些论点意味着模型在精确识别的意义上,具有与观察到的内生变量(人口 Ln 和工资 wn)相同的自由度(以每个位置的质量调整后的土地供应 Hn 和生产率 An 形式存在的未观察到的位置特征)。因此,模型解释观察到的数据的能力不能作为对模型的检验,因为未观察到的质量调整后的土地供应和生产率是自由参数,可以调整以确保模型与数据完全匹配。注意,由于 Hn 表示质量调整后的土地,它不能直接与某个位置的总体土地供应的观察值进行比较。这样做只会得到该地区土地平均质量的度量(这与它的居住便利性有关)。此外,观察到的工资和人口数据不能用来估计模型的结构参数α和σ。对于这些参数的任何值,都可以调整质量调整后的土地供应和生产率,以确保模型能够完全合理化数据。 因此,结构参数值的任何变化都可以通过这些未观察到的位置特征的变化来抵消,从而使模型继续解释数据。

Nonetheless, the model's ability to exactly explain the data implies that it provides a framework that can be used to decompose the observed variation in endogenous variables (e.g., population and wages) into the contribution of different exogenous determinants (e.g., trade costs and exogenous determinants of productivity and quality-adjusted land). Note that the recovered exogenous fundamentals do not explain the variation in endogenous variables but simply account for it according to the model. Furthermore, additional data not used for the quantification of the model or exogenous shocks to the economy (e.g., natural experiments from history) can be used to provide overidentification checks (tests of the model's external validity) or to estimate the model's structural parameters. We consider several empirical studies in Section 5 that have sought to provide such overidentification checks or undertake such structural estimation.
尽管如此,模型精确解释数据的能力意味着它提供了一个框架,可以用来将内生变量(例如人口和工资)观察到的变化分解为不同外生决定因素(例如贸易成本和生产力及质量调整后的土地的外生决定因素)的贡献。请注意,恢复的外生基本因素并不能解释内生变量的变化,而只是根据模型对其进行解释。此外,未用于模型量化或对经济的外生冲击(例如历史中的自然实验)的额外数据可以用来提供过度识别检验(对模型外部有效性的检验)或估计模型的结构参数。我们在第 5 节中考虑了几项实证研究,这些研究试图提供这样的过度识别检验或进行这样的结构估计。

3.7.   Counterfactuals 反事实

In this section, we show how our quantitative spatial model can be used to undertake counterfactuals for the effects of public policy interventions, such as transport infrastructure improvements. We show that these counterfactuals can be undertaken using the observed values of the endogenous variables of the model in an initial equilibrium without having to solve for the unobserved location characteristics, as in the work of Dekle et al. (2007). We denote the (unknown) value of variables in the counterfactual equilibrium with a prime (′) and the relative value of variables in the counterfactual and observed equilibria by a hat ( ). We suppose that the researcher observes population (), wages (), and trade shares (π) in the initial equilibrium and can parameterize the change in bilateral trade costs as a result of the transport infrastructure improvement ( ). From the trade share (Equation 9), price index (Equation 10), income equal to expenditure (Equation 11), land market clearing (Equation 12), and population mobility (Equation 13), we obtain the following system of equations that can be used to solve for the counterfactual changes in wages, trade shares, and population shares ({ , , }) given only the observed wages, trade shares, and population shares in the initial equilibrium ({, π, λ}):
在这一节中,我们展示了如何使用我们的定量空间模型来对公共政策干预的影响进行反事实分析,例如交通基础设施的改善。我们表明,这些反事实分析可以使用模型内生变量的初始均衡观测值进行,而无需解决未观测到的位置特征,正如 Dekle 等人(2007 年)的研究所示。我们用撇号(x′)表示反事实均衡中变量的(未知)值,用帽子( )表示反事实和观测均衡中变量的相对值。我们假设研究者观察到初始均衡中的人口(Ln)、工资(wn)和贸易份额(πni),并且可以将双边贸易成本的变动参数化为运输基础设施改善的结果( )。从贸易份额(方程 9)、价格指数(方程 10)、收入等于支出(方程 11)、土地市场出清(方程 12)和人口流动性(方程 13),我们得到以下方程组,可用于求解在初始均衡中仅给定观察到的工资、贸易份额和人口份额时,工资、贸易份额和人口份额的逆事实变化({ }):

18. 

19. 

20. 

Given our assumptions of σ(1−α)>1 and symmetric trade costs, there exists a unique general equilibrium in the model, which ensures that these counterfactuals yield determinate predictions for the impact of the transport infrastructure improvement or another public policy intervention on the spatial equilibrium distribution of economic activity.
鉴于我们假设σ(1−α)>1 和对称的贸易成本,模型中存在一个唯一的一般均衡,这确保了这些反事实能够对运输基础设施改善或另一项公共政策干预对经济活动空间均衡分布的影响做出确定的预测。

3.8.   Welfare 3.8. 福利

A further implication of this class of quantitative spatial models is that the welfare effects of public policy interventions that change trade costs can be expressed solely in terms of empirically observable sufficient statistics. Consider a transport infrastructure improvement that reduces trade costs between an initial equilibrium (indexed by 0) and a subsequent equilibrium (indexed by 1). Perfect population mobility implies that the transport infrastructure improvement leads to reallocations of population across locations until real wages are equalized. Using the population mobility condition (Equation 14), the changes in the domestic trade share (π) and population () for any one location are sufficient statistics for the welfare impact of the transport infrastructure improvement on all locations:
这一类定量空间模型的一个进一步含义是,改变贸易成本的公共政策干预的福利效应可以仅用经验上可观察的充分统计量来表示。考虑一种运输基础设施的改善,它降低了初始均衡(以 0 为指数)和随后均衡(以 1 为指数)之间的贸易成本。完美的人口流动性意味着运输基础设施的改善导致人口在不同地点之间的重新分配,直到实际工资均等化。使用人口流动性条件(方程 14),任何地点国内贸易份额(πnn)和人口(Ln)的变化是运输基础设施改善对所有地点福利影响的充分统计量:

21. 

Given our assumption of σ(1−α)>1, a larger reduction in a location's domestic trade share must be offset by a larger increase in its population to preserve real wage equalization. Intuitively, if the transport infrastructure improvement decreases trade costs for one location more than for other locations (and thus reduces the domestic trade share of this location), the resulting upwards pressure on its real wage induces a population inflow until the price of the immobile factor land is bid up to restore real wage equalization. This implication is a direct analog of the result found by the international trade literature that the domestic trade share is a sufficient statistic for the welfare gains from trade in a class of trade models (see Arkolakis et al. 2012). In an economic geography model in which an immobile factor of production, such as land, is used residentially or commercially, changes in the distribution of mobile factors of production across locations must also be taken into account (see Caliendo et al. 2014, Redding 2016).
鉴于我们假设σ(1−α)>1,一个地区国内贸易份额的更大减少必须通过其人口的更大增加来抵消,以保持实际工资均等化。直观地说,如果交通基础设施的改善使一个地区的贸易成本比其他地区降低更多(从而减少了该地区的国内贸易份额),那么对其实际工资产生的向上压力将导致人口流入,直到不可移动的生产要素土地的价格被推高以恢复实际工资均等化。这一推论是国际贸易文献中发现的直接类比结果,即国内贸易份额是一类贸易模型中贸易福利收益的充分统计量(参见 Arkolakis 等人,2012 年)。在一个生产要素如土地等不可移动的生产要素被用于居住或商业用途的经济地理模型中,还必须考虑生产要素在地区间的分布变化(参见 Caliendo 等人,2014 年,Redding,2016 年)。

3.9.   Quantitative Illustration
定量说明

In this section, we outline a quantitative illustration of the model for which accompanying MATLAB code is available. We show how the quantitative model can be used to evaluate the impact of trade frictions (both between countries and between regions within countries) on the spatial distribution of economic activity and welfare. We consider a model economy on a 30×30 latitude and longitude grid. We assume that this economy consists of two countries, one occupying the western half of the grid (West) and the other occupying the eastern half (East). We assume that labor is perfectly mobile across locations within each country but perfectly immobile across countries. Following Donaldson (2016), we compute a measure of lowest-cost-route effective distance, which minimizes the cumulative cost of traveling between each origin and destination. In particular, this measure assigns a cost (or weight) to traveling across each point on the grid of δ. For a pair of neighboring points and , the effective distance for an orthogonal link between these locations (moving vertically or horizontally across the grid) is . In contrast, the effective distance for a diagonal link between these locations (moving diagonally across the grid) is . For any origin and destination, the effective distance is the sum across all of the links between neighboring locations along the lowest-cost route. We assume that the cost (weight) is the same for each location on the grid (δ=δ) and normalize this common distance weight to one.
在这一节中,我们概述了一个模型的定量说明,并提供了相应的 MATLAB 代码。我们展示了如何使用定量模型来评估贸易摩擦(国家间和国内地区间)对经济活动和福利空间分布的影响。我们考虑了一个在 30×30 纬度和经度网格上的模型经济。我们假设这个经济由两个国家组成,一个占据网格的西部一半(西部),另一个占据东部一半(东部)。我们假设劳动力在每个国家内部的位置之间可以完全流动,但在国家之间完全不可流动。遵循 Donaldson(2016)的方法,我们计算了一个最低成本路线有效距离的度量,该度量最小化了每个起点和目的地之间旅行的累积成本。特别是,这个度量将成本(或权重)分配给网格上每个点 N 的δn。对于相邻的点 N 和 i,这两个位置之间正交链接的有效距离(在网格上垂直或水平移动)是 。 与这些地点之间的对角线链接的有效距离(在网格上斜向移动)为 。对于任何起点和终点,有效距离是沿着最低成本路线,在相邻位置之间的所有链接上的总和。我们假设网格上每个位置的成本(权重)相同(δn = δ = δ),并将这个共同距离权重归一化为一。

We allow productivity to differ randomly across locations. For each location, we draw a realization for productivity {} from an independent standard log normal distribution. displays the realization of productivities for the 900 locations in our grid. In this realization, there are two clusters of high-productivity areas, one northwest of the border and another southeast of it. Other, more isolated, high-productivity areas are also evident. Of course, in this example the location of high-productivity areas is purely random.
我们允许生产率在不同地区随机差异。对于每个地区,我们从独立的标准对数正态分布中抽取一个生产率{An}的实现值。图 1 显示了我们网格中 900 个地点的生产率实现值。在这个实现中,有两个高生产率区域的集群,一个位于边界西北部,另一个位于东南部。其他更孤立的高生产率区域也很明显。当然,在这个例子中,高生产率区域的地理位置完全是随机的。

Realization of random local productivity for the 900 locations in our grid. Cold () colors correspond to lower values, and hot () colors correspond to higher values.
实现网格中 900 个位置的随机局部生产力。冷(蓝色)颜色对应较低值,热(黄色)颜色对应较高值。
 

For simplicity, we assume that each location has the same quality-adjusted land area () of 100 km2. We choose central values for the model's parameters based on the existing empirical literature. First, we set the share of land in residential consumption expenditure (1−α) to 25%, which is in line with the housing expenditure share of Davis & Ortalo-Magne (2011). Second, we set the elasticity of substitution (σ) equal to 5, which implies an elasticity of trade flows with respect to trade costs of σ−1=4, in line with the estimates of Simonovska & Waugh (2014). Third, we assume that trade costs are a constant elasticity function of effective distance ( ), which implies an elasticity of trade flows with respect to effective distance of −(σ−1)ϕ [because trade flows depend on ]. We choose the parameter ϕ to match the elasticity of trade flows with respect to distance in gravity equations using interregional trade data of −(σ−1)ϕ=−1.5, which, for our assumed value for σ−1, implies ϕ=0.375.
为简化起见,我们假设每个地点具有相同的质量调整后土地面积(Hn)为 100 平方公里 2 。我们根据现有的实证文献选择模型参数的中央值。首先,我们将土地在住宅消费支出中的份额(1−α)设定为 25%,这与 Davis & Ortalo-Magne(2011)的住房支出份额一致。其次,我们将替代弹性(σ)设定为 5,这意味着贸易流量对贸易成本的弹性为σ−1=4,与 Simonovska & Waugh(2014)的估计一致。第三,我们假设贸易成本是有效距离( )的常数弹性函数,这意味着贸易流量对有效距离的弹性为−(σ−1)ϕ[因为贸易流量取决于 ]。我们选择参数ϕ以匹配重力方程中贸易流量对距离的弹性,使用区域间贸易数据得到−(σ−1)ϕ=−1.5,对于我们的σ−1 假设值,这意味着ϕ=0.375。

In addition to these geographical frictions from transport costs, we consider two forms of economic frictions to trade between locations. First, we assume a proportional internal tax on trade with other locations of 100% (τin=2), which is paid whenever a good flows from one location to another. Second, we assume a proportional external tax on trade between the two countries of 100% (τout=2), which is paid whenever a good crosses the border between the two countries (between latitude 15 and 16). For simplicity, we assume that the revenue from both taxes is wasted, and thus both correspond to real resource costs. In , we display the log level of economic activity across locations in the initial equilibrium with both taxes. Areas of high productivity have large population concentrations ( ), high wages ( ), and high land prices ( ). As expected, the log of the price index ( ) is a smooth surface with the gradient governed by trade costs. Prices are lower in areas that produce a large variety of goods, for example, at the two large cities close to the border. The largest agglomerations in this economy are most clearly appreciated in this panel. Panel also clearly exhibits the border effect created by the tariff between the two countries.
除了这些由运输成本引起的地理摩擦外,我们还考虑两种形式的经济摩擦来分析不同地点之间的贸易。首先,我们假设对与其他地点的贸易征收 100%比例的内部税(τ in =2),每当商品从一个地点流向另一个地点时支付。其次,我们假设对两国之间的贸易征收 100%比例的外部税(τ out =2),每当商品跨越两国边境(在纬度 15 和 16 之间)时支付。为了简化,我们假设这两种税收的收入都被浪费了,因此两者都对应于实际资源成本。在图 2 中,我们展示了在两种税收的初始均衡状态下,不同地点的经济活动对数水平。高生产力的地区有大量人口聚集(图 2a),高工资(图 2b)和高土地价格(图 2c)。正如预期的那样,价格指数的对数(图 2d)是一个平滑的表面,其梯度由贸易成本控制。在生产和多种商品的地区,价格较低,例如在靠近边境的两个大城市。 在这个经济体的最大聚集地在这张面板中表现得最为明显。面板 d 也清楚地展示了两个国家之间关税产生的边界效应。

Initial equilibrium, showing () log population, () log wages, () log land prices, and () log price index. Cold () colors correspond to lower values, and hot () colors correspond to higher values.
初始均衡,显示(a)对数人口,(b)对数工资,(c)对数地价和(d)对数价格指数。冷色(蓝色)对应较低值,暖色(黄色)对应较高值。
 

In , we display the log relative changes in population ( ), wages ( ), land prices ( ), and price indices ( ) as a result of the removal of the proportional tax on trade between the two countries. As trade costs between the two countries fall, economic activity reallocates toward the border between them. The areas that benefit the most are the ones close to but on the opposite side of the border from the large cities. These locations can now trade more cheaply with the large market in those cities and thus experience the largest increases in population ( ), wages ( ), and land rents ( ) and the largest reductions in the price index ( ). In contrast, the largest agglomerations lose relative to these up and coming locations. In the first row of , we report the resulting impact on the common level of welfare across locations within each country. We find that this external trade liberalization raises welfare in West and East by around 0.2% and 0.3%, respectively.
在图 3 中,我们展示了由于两国间贸易比例税的取消,人口( )、工资( )、土地价格( )和价格指数( )的相对变化。随着两国间贸易成本的降低,经济活动重新分配到两国边境。受益最大的地区是靠近但位于大城市对面的地区。现在,这些地区可以以更低的成本与那些城市的大市场进行贸易,因此人口(图 3a)、工资(图 3b)和土地租金(图 3c)的增长最大,价格指数(图 3d)的降幅也最大。相比之下,最大的聚集地相对于这些新兴地区有所下降。在表 1 的第一行中,我们报告了这种外部贸易自由化对每个国家内部各地点的福利水平的影响。我们发现,这种外部贸易自由化使西部和东部的福利分别提高了约 0.2%和 0.3%。

External liberalization, showing the ratio of counterfactual to initial values, : () log relative population, () log relative wages, () log relative land rents, and () log relative price index. Cold () colors correspond to lower values, and hot () colors correspond to higher values.
外部自由化,显示反事实值与初始值的比率, :(a)相对人口的对数,(b)相对工资的对数,(c)相对地租的对数,以及(d)相对价格指数的对数。冷(蓝色)颜色对应较低值,热(黄色)颜色对应较高值。
 

Welfare gains from external and internal liberalization
外部和内部自由化带来的福利收益

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External liberalization 外部自由化0.2%0.3%
Internal liberalization 内部自由化1.4%2.3%

In , we present an alternative counterfactual experiment where we remove all internal trade costs but leave international trade costs as in the initial equilibrium. The figure presents relative changes with respect to the initial equilibrium. The implications of an internal reduction in trade costs are clearly quite different than the ones from an external trade cost reduction. The main effect of the internal liberalization is to reduce the size of the two large cities in favor of rural areas, thereby making economic activity more dispersed ( ). As trade costs decline, the home market effect reducing local price indexes in large cities weakens, so that prices fall everywhere but less so in areas with larger populations ( ). Wages and land rents also fall in large agglomerations, whereas they increase in all other regions ( ). The second row of reports the welfare impact of the removal of the internal tax on trade with other locations. We find that this internal trade liberalization raises welfare in West and East by around 1.4% and 2.3%, respectively, more than five times the effects of the external trade liberalization.
在图 4 中,我们提出了一种替代的逆事实实验,其中我们消除了所有内部贸易成本,但保留与国际贸易成本相同的初始均衡。该图展示了相对于初始均衡的相对变化。内部贸易成本降低的影响与外部贸易成本降低的影响明显不同。内部自由化的主要影响是减少两个大城市规模,有利于农村地区,从而使经济活动更加分散(图 4a)。随着贸易成本的下降,减少大城市本地价格指数的国内市场效应减弱,因此价格在所有地方都下降,但在人口较多的地区下降较少(图 4d)。工资和土地租金在大城市群中也会下降,而在其他所有地区则会上升(图 4b,c)。表 1 的第二行报告了取消与其他地点贸易的内部税收对福利的影响。我们发现,这种内部贸易自由化使西部和东部的福利分别提高了约 1.4%和 2.3%,超过外部贸易自由化效果的五倍。

Internal liberalization, showing the ratio of counterfactual to initial values, : () log relative population, () log relative wages (truncated), () log relative land rents, and () log relative price index (truncated). Cold () colors correspond to lower values, and hot () colors correspond to higher values.
内部自由化,显示反事实值与初始值的比率, :(a)相对人口的对数,(b)相对工资(截断),(c)相对地租的对数,和(d)相对价格指数(截断)。冷(蓝色)颜色对应较低值,热(黄色)颜色对应较高值。
 

Intuitively, trade is much larger between regions than between countries, highlighting the greater importance of internal trade frictions relative to external trade frictions.
直观上看,地区间的贸易规模远大于国家间的贸易,突显了内部贸易摩擦相对于外部贸易摩擦的重要性。

Although our quantitative analysis in this section is inevitably stylized, particularly because we started from a random productivity distribution, it highlights the power and flexibility of this class of quantitative spatial models. Simply adding population data for a region would allow us to obtain real-world productivity estimates and would make this exercise quite informative about the region's economy and policy options. Although the particular quantitative model considered in this section abstracts from a number of real-world features, such as multiple traded sectors and input–output linkages, it could be further enriched to incorporate these and other salient features of the economy.
尽管本节中的定量分析不可避免地具有风格化,尤其是因为我们从随机生产力分布开始,但它突出了这类定量空间模型的力量和灵活性。简单地为一个地区添加人口数据就能使我们获得现实世界的生产力估计,这将使这项练习对该地区的经济和政策选择具有很高的信息量。尽管本节考虑的特定定量模型抽象了许多现实世界的特征,如多个贸易部门和投入产出联系,但它可以进一步丰富,以纳入这些以及其他显著的经济特征。

 

In this section, we show that the same quantitative methods used to analyze the distribution of economic activity across regions in the previous section can be used to study the internal structure of economic activity within cities. We outline a canonical quantitative urban model following Lucas & Rossi-Hansberg (2002) and Ahlfeldt et al. (2015), in which the agglomeration forces are external economies and the dispersion forces are an inelastic supply of land and commuting costs. To incorporate these features, we select the following items from the menu of building blocks outlined above:
在这一节中,我们表明,与上一节中分析地区间经济活动分布相同的定量方法可以用来研究城市内部经济活动的结构。我们概述了一个遵循 Lucas & Rossi-Hansberg(2002)和 Ahlfeldt 等人(2015)的典型定量城市模型,其中聚集力是外部经济,而分散力是非弹性的土地供应和通勤成本。为了纳入这些特征,我们从上述构建块菜单中选择以下项目:

  1. 1.  From Section 2.1, we select homogeneous goods, single traded sector, endogenous amenities, residential land use, and idiosyncratic preferences.
    1. 从第 2.1 节中,我们选取同质商品、单一贸易部门、内生性便利设施、住宅土地利用和异质性偏好。
  2. 2.  From Section 2.2, we select constant returns to scale, endogenous productivity, no input–output linkages, and commercial land use.
    2. 从 2.2 节中,我们选取规模报酬不变、内生生产率、无投入产出联系和商业土地利用。
  3. 3.  From Section 2.3, we select no trade costs and no nontraded goods besides residential and commercial land use.
    3. 从第 2.3 节中,我们选择了没有贸易成本,除了住宅和商业土地利用之外,没有非贸易商品。
  4. 4.  From Section 2.4, we select knowledge externalities, no innovation or dynamics, and perfect transferability of ideas.
    4. 从第 2.4 节中,我们选取知识外部性、无创新或动态,以及思想的完全可转移性。
  5. 5.  From Section 2.5, we select perfectly costless migration, costly commuting, single worker type with heterogeneity, and no congestion in transportation.
    5. 从第 2.5 节,我们选取了无成本的迁移、有成本的通勤、具有异质性的单一工人类型以及无交通拥堵。
  6. 6.  From Section 2.6, we select homogeneous labor, blocks within a single city, and no capital.
    6. 从第 2.6 节,我们选择同质劳动力、单一城市内的区块,以及无资本。
  7. 7.  From Section 2.7, we select perfect competition, equilibrium within a city given prices and utility in an outside economy, absentee landlords, and trade balanced within the city.
    7. 从第 2.7 节中,我们选取了完全竞争、给定价格和外部经济中的效用下的城市内部均衡、缺席房东以及城市内部贸易平衡。

We show how the model can be used to quantify the role of productivity and amenities in determining internal city structure and used to evaluate the impact of transport infrastructure improvements.
我们展示了如何使用该模型量化生产力和便利性在决定城市内部结构中的作用,并用于评估交通基础设施改善的影响。

We consider a city embedded within a larger economy that provides a reservation level of utility ( ). The city consists of a set of discrete blocks indexed by , ={1, …, }. Each block has a supply of floor space () that depends on geographical land area () and the density of development (φ). There is a single final good that is costlessly traded within the city and to the larger economy and is chosen as the numeraire (=1 for all ). 8 Markets are perfectly competitive. The final good is produced from labor and commercial floor space according to a Cobb-Douglas production technology with the following unit cost function,
我们考虑一个嵌入在更大经济体中的城市,该城市提供一定水平的效用( )。该城市由一系列离散的区块组成,区块由 n 索引,i={1, …, S}。每个区块拥有一定量的地面空间(H),这取决于地理土地面积(K)和开发密度(φ)。存在一种单一最终商品,在城内以及向更大经济体进行无成本交易,并被选为计价单位(对于所有 i,p=1)。 8 市场是完全竞争的。最终商品根据以下单位成本函数,通过劳动和商业地面空间按照 Cobb-Douglas 生产技术生产,

22. 

where denotes the wage and is the price of commercial floor space. Productivity () in each location can depend on production externalities (e.g., knowledge spillovers) and production fundamentals (e.g., access to natural water). Production externalities are modeled as depending on the travel time–weighted sum of workplace employment density in surrounding blocks, so that
w 表示工资,q 表示商业地价。每个地点的生产力(A)可能取决于生产外部性(例如,知识溢出)和生产基础(例如,自然水源的获取)。生产外部性被建模为依赖于周边地块工作场所就业密度加权总和的旅行时间,因此

23. 

where / is workplace employment density per unit of geographical land area, production externalities decline with travel time (τ) through the iceberg factor , δ determines their rate of spatial decay, and μ controls their relative importance in determining overall productivity.
LMs/Ks 为每单位地理土地面积的职场就业密度,生产外部性通过冰山因素 随旅行时间(τis)下降,δ决定其空间衰减速率,μ控制其在决定总体生产力中的相对重要性。

Workers decide whether or not to move to the city before observing idiosyncratic utility shocks for each possible pair of residence and employment locations within the city. If a worker decides to move to the city, she observes these realizations for idiosyncratic utility and picks the pair of residence and employment locations within the city that maximizes her utility. The preferences of a worker residing in location and working in location are defined over consumption of the final good; consumption of residential floor space; residential amenities (), which capture common characteristics that make a block a more or less attractive place to live (e.g., leafy streets and scenic views); the disutility of commuting from residence to workplace ); and the idiosyncratic preference shock (), which captures the fact that individual workers can have idiosyncratic reasons for living and working in different parts of the city. Preferences are assumed to take the Cobb-Douglas form with the following indirect utility function:
工人观察城市内每个可能的居住地和就业地组合的独特效用冲击之前,决定是否搬到城市。如果工人决定搬到城市,她会观察这些独特效用的实现,并选择城市内最大化她效用的居住地和就业地组合。居住在 N 地、工作在 i 地的工人的偏好定义为对最终商品的消费;居住空间的消费;居住便利设施(Bn),它捕捉使一个街区更或更吸引人居住的常见特征(例如,绿树成荫的街道和风景优美的景观);从居住地 N 到工作地点 i 通勤的不便(κni);以及独特偏好冲击(znio),它捕捉到个体工人可能因居住和工作的不同城市区域而有独特原因的事实。假设偏好采用 Cobb-Douglas 形式,以下为间接效用函数:

24. 

where is the wage at the worker's place of employment , is the residential price of floor space at the worker's place of residence , and the iceberg commuting cost increases with the travel time (τ) between and .
w 为工人工作地点 i 的工资,Qn 为工人居住地 N 的居住面积价格,而冰山通勤成本 随着 N 和 i 之间的旅行时间(τni)增加而增加。

Residential amenities () in each location can depend on residential externalities (e.g., crime or local public goods) and residential fundamentals (e.g., scenic views). Residential externalities are modeled symmetrically to production externalities depending on the travel time–weighted sum of residential employment density in surrounding blocks. Thus,
住宅便利设施(Bn)在每个地点可能取决于住宅外部性(例如,犯罪或当地公共物品)和住宅基本面(例如,风景景观)。住宅外部性根据周边地块住宅就业密度的旅行时间加权总和对称地建模为生产外部性。因此,

25. 

where / is residence employment density per unit of land area, residential externalities decline with travel time (τ) through the iceberg factor , ρ determines their rate of spatial decay, and η controls their relative importance in overall residential amenities.
LRr /Kr 为每单位土地面积的居住就业密度,居住外部性通过冰山因素 随旅行时间(τnr)下降,ρ决定其空间衰减率,η控制其在整体居住便利性中的相对重要性。

Idiosyncratic preferences for each pair of residence location and workplace location are drawn from an independent Fréchet distribution,
每个居住地 N 和工作地点 i 的独特偏好是从独立的弗雷歇分布中抽取的,

26. 

where the scale parameter >0 determines the average utility derived from living in location , the scale parameter determines the average utility derived from working in location , and the shape parameter ϵ>1 controls the dispersion of idiosyncratic utility.
在 Tn >0 的尺度参数决定居住在位置 N 的平均效用,尺度参数 E 决定在位置 i 工作的平均效用,形状参数ϵ>1 控制特有效用的分散程度。

Using the Fréchet distribution for idiosyncratic preferences, one finds that the probability that a worker chooses to live in location and work in location depends on the desirability of as a residence (amenities , the Fréchet scale parameter and residential floor prices ), the attractiveness of as an employment location (the Fréchet scale parameter and the wage ), and the cost of commuting between and (as determined by the iceberg commuting cost κ), relative to the attractiveness of all other possible pairs of residence and employment , namely,
使用弗雷歇分布来分析特殊偏好,发现工人选择在 N 地居住并在 i 地工作的概率取决于 N 地作为居住地的吸引力(设施 Bn、弗雷歇尺度参数 Tn 和住宅楼层价格 Qn),i 地作为就业地点的吸引力(弗雷歇尺度参数 E 和工资 w),以及 N 地和 i 地之间通勤的成本(由冰山通勤成本κni 决定),相对于所有其他可能的居住地 r 和就业地 s 的吸引力,即,

27. 

Therefore, bilateral commuting exhibits a gravity equation where the flow of commuters between locations and depends on both bilateral resistance (bilateral commuting costs κ) and multilateral resistance (commuting costs between all other locations and ).
因此,双边通勤表现出一个重力方程,其中从位置 n 到 i 的通勤流量取决于双边阻力(双边通勤成本κni)和多边阻力(所有其他位置 r 和 s 之间的通勤成本 r)。

Population mobility implies that the expected utility from moving to the city must equal the expected utility in the larger economy ( ). Using the Fréchet distribution for idiosyncratic preferences, this population mobility condition implies that
人口流动性意味着迁移到城市的预期效用必须等于更大经济体的预期效用( )。使用弗雷歇分布来表示异质偏好,这一人口流动性条件意味着

28. 

where is the expectations operator and the expectation is taken over the distribution for the idiosyncratic component of utility; and Γ(·) is the Gamma function.
是期望算子,期望是对效用的特异成分的分布取值; 和Γ(·)是伽马函数。

Commuting market clearing requires that the measure of workers employed in location () equals the sum across locations of the measure of workers residing in () times the probability of commuting to conditional on residing in , which can be written as
通勤市场出清要求在位置 i(LMi)就业的工人数量等于 N 个位置上居住的工人数量(LRn)的总和乘以在 N 居住条件下通勤到 i 的概率,这可以表示为

29. 

where λ is the probability of commuting to location conditional on residing in location ; labor market clearing implies =∑ λ and =∑ λ , where is the total measure of workers that choose to live in the city. Expected residential income conditional on living in location ( ) differs from the wage in location because of commuting to work in other locations :
λni|n 为居住在 N 地条件下通勤到 i 地的概率;劳动力市场出清意味着 LMi = ∑ =1 ∑ n=1λni L,LRi = ∑ =1 ∑ n=1λni L,其中 L 为选择居住在城市中的工人总数量。在居住在 N 地条件下( )的预期居住收入与 N 地的工资不同,因为通勤到其他地点 i 工作:

30. 

The no-arbitrage condition across alternative land uses implies that floor space is used entirely commercially ( ), used entirely residentially ( ), or allocated to both uses if the commercial price of floor price () equals the residential price of floor space () net of the tax equivalent of land use regulations ( ). The observed price of floor space ( ) in the data is assumed to equal the maximum of the prices of commercial and residential floor space. Therefore, for blocks that are incompletely specialized in commercial and residential activity, observed floor prices equal commercial floor prices ( ). Similarly, for blocks that are completely specialized in commercial activity, observed floor prices again equal commercial floor prices ( ). In contrast, for blocks that are completely specialized in residential activity, observed floor prices equal residential floor prices ( ).
无套利条件在替代土地利用之间意味着楼层空间完全用于商业(q>ξQ),完全用于住宅(q<ξQ),或者如果楼层价格的商业价格(q)等于楼层空间的住宅价格(q)减去土地利用规定的税等价(q=ξQ),则分配给两种用途。数据中观察到的楼层空间价格( )假定等于商业和住宅楼层空间价格的最大值。因此,对于不完全专业化的商业和住宅活动的地块,观察到的楼层价格等于商业楼层价格( )。同样,对于完全专业化的商业活动地块,观察到的楼层价格再次等于商业楼层价格( )。相反,对于完全专业化的住宅活动地块,观察到的楼层价格等于住宅楼层价格( )。

As was the case for the quantitative spatial model in Section 3, analytical results can be provided for the model considered here, including the existence and uniqueness of equilibrium, the ability to invert the model to recover unobserved fundamentals from observed endogenous variables, and the potential to undertake model-based counterfactuals. In the absence of production and residential externalities (μ=η=0), there are no agglomeration forces in the model, and thus the congestion forces of commuting costs and an inelastic supply of land ensure the existence of a unique equilibrium, as shown by Ahlfeldt et al. (2015). In the presence of production and residential externalities (μ≠0 or η≠0), there is the potential for multiple equilibria in the model, depending on the strength of these agglomeration forces relative to the exogenous differences in characteristics across locations. This potential multiplicity implies that the mapping from the model's parameters and exogenous location characteristics to its endogenous variables is not unique. Nonetheless, given sufficient data on these endogenous variables, some observed location characteristics, and model parameters, the mapping to the remaining unobserved location characteristics can be unique. In this case, the unobserved location characteristics (such as production and residential fundamentals) again correspond to structural residuals that exactly rationalize the observed data as an equilibrium of the model, as shown by Ahlfeldt et al. (2015). Intuitively, given sufficient data, the equilibrium conditions of the model, such as utility maximization, profit maximization, and market clearing, can be used to solve for unique values of fundamentals consistent with the observed equilibrium.
与第 3 节中的定量空间模型情况相同,可以为这里考虑的模型提供分析结果,包括均衡的存在性和唯一性、将模型反转以从观察到的内生变量中恢复未观察到的基本因素的能力,以及进行基于模型的反事实分析的可能性。在没有生产和居住外部性(μ=η=0)的情况下,模型中没有集聚力量,因此通勤成本和土地供应缺乏弹性的拥堵力量确保了唯一均衡的存在,如 Ahlfeldt 等人(2015)所示。在存在生产和居住外部性(μ≠0 或η≠0)的情况下,模型中存在多重均衡的可能性,这取决于这些集聚力量相对于地理位置特征外生差异的强度。这种多重性的可能性意味着从模型的参数和外生地理位置特征到其内生变量的映射不是唯一的。 尽管如此,在拥有足够这些内生变量、观察到的地理位置特征和模型参数的数据的情况下,可以将这些数据映射到剩余未观察到的地理位置特征,并且这种映射是唯一的。在这种情况下,未观察到的地理位置特征(如生产和居住基础)再次对应于结构残差,这些残差恰好合理地解释了观察到的数据作为模型均衡的情况,正如 Ahlfeldt 等人(2015)所展示的。直观上,在拥有足够数据的情况下,模型的均衡条件,如效用最大化、利润最大化和市场出清,可以用来求解与观察到的均衡一致的基本面唯一值。

Using a similar approach as that in Section 3, the model in this section can be used to undertake counterfactuals for the impact of public policy interventions, such as transport infrastructure improvements, on the spatial distribution of economic activity. For parameter values for which the model has a unique equilibrium, these counterfactuals yield determinate predictions for the impact of the public policy intervention on the spatial distribution of economic activity. For parameter values for which the model has multiple equilibria, counterfactuals can be undertaken assuming an equilibrium selection rule; for example, the initial values from the observed equilibrium can be used to select the closest counterfactual equilibrium.
采用与第 3 节类似的方法,本节中的模型可用于进行关于公共政策干预(如交通基础设施改善)对经济活动空间分布影响的反事实分析。对于模型具有唯一均衡的参数值,这些反事实分析可以给出公共政策干预对经济活动空间分布影响的确定性预测。对于模型具有多个均衡的参数值,可以通过假设均衡选择规则来进行反事实分析;例如,可以使用观察到的均衡的初始值来选择最近的反事实均衡。

Although for simplicity we have developed separate quantitative models of goods trade across cities or regions (Section 3) and commuting within a city (Section 4), both sources of spatial linkages are likely to be important in practice. To incorporate both sources of linkages, Monte et al. (2015) develop a unified quantitative model in which a system of regions are connected in both goods markets, through trade, and factor markets, through migration and commuting. Within this unified framework, the effect of changes in the local economic environment on employment depends critically on the ability to attract both migrants and commuters. Although a large literature on local labor markets has sought to estimate a representative local employment elasticity, a key implication of this framework is that the local employment elasticity is heterogeneous across locations. Therefore, an elasticity estimated in one context need not be generalizable to another context.
尽管为了简化,我们已分别开发了城市或地区间商品贸易的定量模型(第 3 节)和城市内部的通勤模型(第 4 节),但在实践中,这两种空间联系来源都可能很重要。为了纳入这两种联系来源,Monte 等人(2015)开发了一个统一的定量模型,其中区域系统在商品市场通过贸易和要素市场通过迁移和通勤相互连接。在这个统一框架内,当地经济环境变化对就业的影响在很大程度上取决于吸引移民和通勤者的能力。尽管大量关于当地劳动市场的文献试图估计代表性的当地就业弹性,但这一框架的关键含义是当地就业弹性在不同地区是异质的。因此,在一个背景下估计的弹性不一定可以推广到另一个背景。

 

We have shown how general equilibrium spatial models are typically exactly identified and can be quantified to rationalize the observed data as an equilibrium of the model. We now turn to the empirical literature that has used additional data, assumptions, or sources of variation to provide evidence on the mechanisms in these models, to test their quantitative predictions, and to structurally estimate their parameters. We first discuss the empirical evidence on the role of market access in determining the spatial distribution of economic activity across countries and regions. We next turn to the empirical evidence on productivity and the density of economic activity. Finally, we consider the empirical literature on path dependence and the dynamics of the spatial distribution of economic activity over time.
我们展示了如何典型地精确识别一般均衡空间模型,并量化以合理化观察到的数据作为模型均衡。现在我们转向使用额外数据、假设或变异来源的实证文献,以提供关于这些模型机制的证据,检验它们的定量预测,并结构性地估计它们的参数。我们首先讨论关于市场接入在决定国家间和地区间经济活动空间分布中所起作用的实证证据。接下来,我们转向关于生产率和经济活动密度的实证证据。最后,我们考虑关于路径依赖性和经济活动空间分布随时间动态变化的实证文献。

5.1.   Market Access 市场准入

One line of empirical research has examined a key implication of quantitative spatial models, namely, that both wages and population depend on market access. 9 We illustrate this prediction in the context of the quantitative spatial model developed in Section 3. Using CES demand, one finds that profit maximization (Equation 4) and zero profits (Equation 6) imply that the free-on-board price () charged for each variety by a firm in each location must be low enough to sell the quantity and cover the firm's fixed production costs, so that
一条实证研究线考察了定量空间模型的一个关键含义,即工资和人口都取决于市场准入。我们在第 3 节开发的定量空间模型背景下说明了这一预测。使用 CES 需求,可以发现利润最大化(方程 4)和零利润(方程 6)意味着每个地点 i 的厂商对每种品种收取的离岸价格(p)必须足够低,以便销售数量 并覆盖公司的固定生产成本,从而

31. 

We define the weighted sum of market demands faced by firms as firm market access (FMA), following Redding & Venables (2004), such that
我们定义企业面临的市场需求加权总和为企业市场准入(FMA),遵循 Redding & Venables(2004)的研究,即

32. 

where ξ≡[(σ−1)]−1/σ(σ−1)/σ collects together earlier constants. Thus, wages are increasing in both productivity () and firm market access (FMA).
在ξ≡[F(σ−1)] −1/σ (σ−1)/σ汇集了早期常数。因此,工资在生产力(A)和企业市场准入(FMA)方面都在增加。

Market access also affects the price index (Equation 8), which depends on consumers’ access to tradeable varieties, as captured by the measure of varieties () and their free-on-board prices () in each location , together with the trade costs of shipping the varieties from locations to (). We summarize this access to tradeable varieties using the concept of consumer market access (CMA):
市场准入也影响价格指数(公式 8),该指数取决于消费者对可交易品种的获取,这通过品种(M)及其在每个位置 i 的离岸价格(p)来衡量,以及将品种从位置 i 运送到 N 的贸易成本(dni)。我们使用消费者市场准入(CMAn)的概念来总结这种对可交易品种的获取。

33. 

Using data on a cross section of countries, Redding & Venables (2004) find a strong correlation between wages and these measures of market access. Using data on counties within the United States, Hanson (2005) finds a similarly strong relationship between wages and market access. However, establishing that these relationships are causal is more challenging. For example, Redding & Venables (2004), Hanson (2005), and Bartelme (2016) all report instrumental variable specifications, but it is difficult to definitively establish that the exclusion restriction of the instruments only affecting wages through market access is satisfied. One line of research has used trade liberalization as a natural experiment that changes the relative market access of regions (see, e.g., Hanson 1996, 1997). 10 Although this evidence from trade liberalization has strengthened the case for a causal interpretation of the role of market access, a remaining concern is that trade liberalization reforms could be endogenous to domestic political economy concerns.
使用国家横截面数据,Redding & Venables(2004)发现工资与市场准入的这些指标之间存在强烈的关联。使用美国县级行政区数据,Hanson(2005)发现工资与市场准入之间存在类似强烈的关联。然而,确立这些关系是因果的更具挑战性。例如,Redding & Venables(2004)、Hanson(2005)和 Bartelme(2016)都报告了工具变量设定,但很难明确地确立工具变量的排除限制仅通过市场准入影响工资得到满足。一条研究线已经使用贸易自由化作为改变地区相对市场准入的自然实验(参见,例如,Hanson 1996,1997)。尽管贸易自由化的证据已经加强了市场准入作用因果解释的论据,但一个持续的担忧是贸易自由化改革可能是国内政治经济问题的内生性。

Another line of research has sought to use transport infrastructure as a source of variation in market access. In this case, the key endogeneity concern is that transport infrastructure is unlikely to be randomly assigned. Therefore, a growing reduced-form literature has sought exogenous sources of variation in transport infrastructure, including from routes planned for strategic reasons, historical exploration routes, and inconsequential places that are connected to transport infrastructure merely because they lie along the route between two other locations (for a review, see Redding & Turner 2015). A smaller number of studies have sought to estimate structurally the impact of transport infrastructure improvements within a quantitative spatial model. Donaldson (2016) undertakes a quantitative evaluation of the construction of India's vast railroad network and finds that there is a strong and statistically significant estimated effect of railroads on real income levels but that this effect becomes statistically insignificant after controlling for the model's sufficient statistic of a region's own trade share. This pattern of results is consistent with the view that the estimated effects of railroads are in fact operating through the market access mechanism in the model. In a similar vein, Donaldson & Hornbeck (2016) investigate the impact of the expansion of the railroad network on the agricultural sector and show that the overall impact on each location can be captured in terms of its market access. Increases in market access from the expansion in the railroad network from 1870 to 1890 are found to substantially increase county agricultural land values.
另一条研究线试图将交通基础设施作为市场接入差异的来源。在这种情况下,关键的内生性问题在于交通基础设施不太可能被随机分配。因此,越来越多的简化形式文献寻求在交通基础设施中的外生变异来源,包括出于战略原因规划的路线、历史勘探路线以及仅仅因为它们位于两个其他地点之间路线上的无关紧要的地方(参见 Redding & Turner 2015 年的综述)。少数研究试图在定量空间模型中结构性地估计交通基础设施改善的影响。Donaldson(2016)对印度庞大的铁路网络建设进行了定量评估,发现铁路对实际收入水平有强烈且统计上显著的估计效应,但这一效应在控制了模型中一个地区的贸易份额这一充分统计量后变得统计上不显著。 这种结果模式与观点一致,即铁路的估计效应实际上是通过模型中的市场准入机制发挥作用的。在这方面,Donaldson & Hornbeck(2016)研究了铁路网络扩张对农业部门的影响,并表明每个地点的总影响可以用其市场准入来衡量。发现从 1870 年到 1890 年铁路网络扩张带来的市场准入增加,显著提高了县农业土地价值。

To provide further evidence of a causal role for market access, Redding & Sturm (2008) use the division of Germany after World War II as a natural experiment that provides plausibly exogenous variation in market access. The division of Germany has a number of attractive features for isolating the role played by market access across West German cities depending on their proximity to the new border with East Germany. First, in contrast to cross-country studies, there is no obvious variation in institutions across cities within West Germany. Second, there are no obvious changes in natural advantage, such as access to navigable rivers or coasts, climatic conditions, or disease environment. Third, the change in market access following German division is much larger than what is typically observed in other contexts, and the effects can be observed over a long period of time. Fourth, the drawing of the border dividing Germany into East and West Germany was based on military considerations that are unlikely to be correlated with the predivision characteristics of cities. 11
为了进一步证明市场准入的因果作用,Redding & Sturm(2008)利用第二次世界大战后德国的分裂作为自然实验,该实验提供了市场准入的合理外生变化。德国的分裂具有许多吸引人的特征,可以隔离市场准入在靠近新边界与东德的城市中发挥的作用。首先,与跨国研究相比,在西德城市之间没有明显的制度差异。其次,没有明显的自然优势变化,如可通航河流或海岸的接入、气候条件或疾病环境。第三,德国分裂后市场准入的变化远大于其他环境中通常观察到的变化,其影响可以在长时间内观察到。第四,将德国划分为东西德边界的划定是基于军事考虑,这些考虑与城市在分裂前的特征不太可能相关。 11

In the quantitative model from Section 3, the treatment effect of division on border cities relative to those further from the new border depends on two parameter combinations that capture () the strength of agglomeration and dispersion forces [σ(1−α)] and () the elasticity of trade with respect to distance [(σ−1)ϕ, where ϕ is the elasticity of trade costs with respect to distance]. Redding & Sturm (2008) undertake a quantitative analysis of the model and show that, for plausible values of these parameter combinations that satisfy the condition σ(1−α)>1 for a unique equilibrium, the model can account quantitatively for both the average treatment effect of division and the larger treatment effect for small than for large cities.
在第三节的定量模型中,相对于远离新边界的城市,分割对边境城市的影响效果取决于两个参数组合,这两个参数组合捕捉了(a)聚集和分散力的强度[σ(1−α)]和(b)贸易相对于距离的弹性[(σ−1)ϕ,其中ϕ是贸易成本相对于距离的弹性]。Redding & Sturm(2008)对模型进行了定量分析,并表明,对于满足σ(1−α)>1 以实现唯一均衡的这些参数组合的合理值,模型可以定量解释分割的平均影响效果以及相对于大城市,分割对小城市的影响效果更大。

5.2.   Productivity and Density
生产率与密度

A large body of empirical literature finds that wages, land prices, productivity, employment, and employment growth are positively correlated with population density (for a survey, see Moretti 2011a). In their survey of this empirical literature, Rosenthal & Strange (2004) report that the elasticity of productivity with respect to the density of economic activity is typically estimated to lie within the range of 3–8%. 12 However, establishing that this correlation is indeed causal remains challenging, and a relatively small number of studies have sought exogenous sources of variation in the surrounding concentration of economic activity. For example, Rosenthal & Strange (2008) and Combes et al. (2010) use geology as an instrument for population density, exploiting the idea that tall buildings are easy to construct where solid bedrock is accessible. Greenstone et al. (2010) provide evidence on agglomeration spillovers by comparing changes in total factor productivity among incumbent plants in winning counties that attracted a large manufacturing plant and losing counties that were the new plant's runner-up choice.
大量实证文献发现,工资、土地价格、生产力、就业和就业增长与人口密度呈正相关(参见 Moretti 2011a 中的综述)。在他们对这一实证文献的综述中,Rosenthal & Strange(2004)报告称,通常估计生产率对经济活动密度的弹性值在 3-8%之间。然而,确立这种相关性确实是因果关系仍然具有挑战性,并且相对较少的研究寻求在经济活动集中度周围的变异的外生来源。例如,Rosenthal & Strange(2008)和 Combes 等人(2010)将地质学作为人口密度的工具变量,利用了在坚固基岩易于建造高层建筑的观点。Greenstone 等人(2010)通过比较吸引大型制造工厂的获胜县和作为新工厂备选选择的新败县的总要素生产率的变化,提供了关于集聚溢出的证据。

Several recent studies have used exogenous variation from natural experiments to examine whether estimated agglomeration economies are consistent with the predictions of quantitative spatial models. Combining data from an urban revitalization program in Richmond, Virginia, between 1999 and 2004 with a structural model of residential externalities, Rossi-Hansberg et al. (2010) estimate substantial and highly localized housing externalities. Land prices in neighborhoods targeted for revitalization rose by 2–5% more per annum than those in a control neighborhood. With every 1,000 ft of distance from the subsidized area, housing externalities are estimated to decline by around one-half. 13
一些近期研究利用自然实验的外生变化来检验估计的集聚经济是否与定量空间模型的预测一致。将弗吉尼亚州里士满 1999 年至 2004 年的一项城市复兴计划的数据与住宅外部性的结构模型相结合,罗西-汉斯伯格等人(2010 年)估计了显著且高度局部化的住房外部性。目标复兴地区的土地价格每年比控制地区的土地价格高出 2-5%。从补贴区域每增加 1,000 英尺距离,住房外部性预计将减少约一半。 13

Using the Tennessee Valley Authority (TVA) as a natural experiment and a structural model, Kline & Moretti (2014a) provide evidence on the long-run effects of one of the most ambitious regional development programs in US history. Using as controls authorities that were proposed but never approved by Congress, Kline & Moretti (2014a) found that the TVA led to large gains in agricultural employment that were eventually reversed when the program's subsidies ended. In contrast, gains in manufacturing employment were found to intensify well after federal transfers had lapsed, consistent with agglomeration economies in manufacturing.
以田纳西河谷管理局(TVA)作为自然实验和结构模型,克莱因和莫雷蒂(2014a)提供了关于美国历史上最雄心勃勃的区域发展计划之一的长期影响的证据。使用国会提出但从未获得批准的机构作为控制变量,克莱因和莫雷蒂(2014a)发现,TVA 导致了农业就业的大幅增长,当该计划的补贴结束时,这些增长最终被逆转。相反,制造业就业的增长被发现是在联邦转移支付结束后才加剧的,这与制造业的集聚经济一致。

Using the division of Berlin following World War II and its reunification after the fall of the Iron Curtain as an exogenous source of variation in the surrounding density of economic activity, Ahlfeldt et al. (2015) structurally estimate the parameters of the quantitative spatial model explained in Section 4. Following the city's division, there was a reorientation of the gradient in land prices and employment in West Berlin away from the main pre-war concentration of economic activity in East Berlin, whereas the city's reunification led to a reemergence of these gradients. The model's parameters are identified from the assumption that the systematic change in the pattern of economic activity in West Berlin following division and reunification is explained by the mechanisms of the model (changes in commuting access and production and residential externalities) rather than by systematic changes in the pattern of structural residuals (production and residential fundamentals).
利用第二次世界大战后柏林的分裂及其在铁幕倒塌后的重新统一作为周围经济活动密度变化的内生来源,Ahlfeldt 等人(2015)对第 4 节中解释的定量空间模型的参数进行了结构估计。在城市的分裂之后,西柏林的土地价格和就业梯度发生了重新定位,远离了东柏林战前经济活动的主要集中区域,而城市的重新统一导致了这些梯度的再次出现。模型的参数是通过以下假设来确定的:西柏林在分裂和重新统一后经济活动模式系统性的变化是由模型机制(通勤可达性、生产和居住外部性变化)解释的,而不是由结构残差(生产和居住基本面)模式系统性的变化解释的。

Both productivity and amenities are found to exhibit substantial and highly localized agglomeration externalities. The estimated elasticities of productivity and amenities with respect to the surrounding densities of workplace employment and residence employment are μ=0.07 and η=0.15, respectively. Undertaking counterfactuals for the impact of division and reunification, one finds that the special case of the model without agglomeration forces (μ=η=0) is unable to account quantitatively for the observed reallocations of economic activity in the data. In contrast, for the estimated values of production and residential externalities, the model is successful in matching the observed impacts of division and reunification, both qualitatively and quantitatively.
生产力与便利设施均被发现存在显著且高度局部化的聚集外部性。生产力和便利设施相对于工作场所就业密度和居住就业密度的弹性估计值分别为μ=0.07 和η=0.15。对分割和重聚的影响进行反事实分析,发现模型在没有聚集力(μ=η=0)的特殊情况下,无法定量解释数据中观察到的经济活动重新分配。相比之下,对于生产和居住外部性的估计值,模型在定性和定量上均成功匹配了分割和重聚的观察影响。

Other research, such as that of Bernard et al. (2016), has examined the role of urban property rights in influencing internal city structure in a developing-country context. Further quantitative evidence on the role of residential externalities in influencing the spatial distribution of economic activity is provided by Diamond (2015). From 1980 to 2000, the rise in the US wage gap between college and high-school graduates coincided with increased geographic sorting as college graduates concentrated in high-wage, high-rent cities. A structural spatial equilibrium model is used to evaluate the causes and welfare consequences of this increased skill sorting. Although local labor demand changes fundamentally caused the increased skill sorting, it was further fueled by endogenous increases in amenities (residential externalities) within higher-skill cities. Changes in cities’ wages, rents, and endogenous amenities increased inequality between high-school and college graduates by more than would be suggested by the increase in the college wage gap alone.
其他研究,如 Bernard 等人(2016)的研究,探讨了在发展中国家背景下城市产权在影响城市内部结构中的作用。Diamond(2015)提供了更多关于住宅外部性在影响经济活动空间分布中作用的定量证据。从 1980 年到 2000 年,美国大学毕业生与高中毕业生之间的工资差距扩大与地理上的排序增加相一致,大学毕业生集中在高工资、高租金的城市。使用结构空间均衡模型来评估这种技能排序增加的原因和福利后果。尽管地方劳动力需求的基本变化是导致技能排序增加的根本原因,但它进一步受到高技能城市内部便利性(住宅外部性)内生增加的推动。城市工资、租金和内生便利性的变化使得高中毕业生与大学毕业生之间的不平等程度超过了仅由大学工资差距增加所暗示的程度。

Several of the above studies find evidence of residential externalities; the microeconomic determinants of these externalities and their implications remain interesting areas for further research.
一些上述研究发现了居住外部性的证据;这些外部性的微观经济决定因素及其影响仍然是进一步研究的有趣领域。

5.3.   The Evolution of the Spatial Distribution of Economic Activity
经济发展空间分布的演变

Motivated in part by models with multiple equilibria, one line of empirical research on changes in the spatial distribution of economic activity over time has set out to look for evidence of path dependence, defined as temporary shocks permanently affecting the distribution of economic activity. Davis & Weinstein (2002, 2008) use Japanese war-time bombing as such an exogenous temporary shock and find little evidence of path dependence for either the distribution of population as a whole or employment in individual industries (for other research exploiting war-time bombing as an exogenous shock, see, e.g., Bosker et al. 2007, 2008; Miguel & Roland 2011). Subsequent studies have provided a number of apparent examples of path dependence using a variety of alternative sources of exogenous variation. Redding et al. (2011) find path dependence for the location of Germany's air hub using the natural experiment of Germany's division and reunification. 14 Bleakley & Lin (2012) find, using variation from portage sites in the United States, that a temporary historical advantage had permanent effects on the spatial distribution of population. Hornbeck & Keniston (2014) find long-lived effects of the Boston fire through the potential for large-scale rebuilding using plot-level data on land values. Michaels & Rauch (2016) report results consistent with path dependence using data on Roman cities.
部分受多均衡模型启发,一条关于经济活动空间分布随时间变化的经验研究路线试图寻找路径依赖的证据,定义为暂时性冲击永久性地影响经济活动的分布。戴维斯和韦恩斯坦(2002,2008)将日本战争时期的轰炸视为此类外生暂时性冲击,并发现对于整体人口分布或单个产业就业分布几乎没有路径依赖的证据(关于利用战争时期轰炸作为外生冲击的其他研究,参见,例如,Bosker 等人 2007,2008;Miguel 和 Roland 2011)。后续研究通过多种外生变化来源提供了许多路径依赖的明显例子。雷丁等人(2011)利用德国分裂和统一的自然实验发现德国航空枢纽位置的路径依赖。布莱克利和林(2012)发现,利用美国港口遗址的变化,一个暂时性的历史优势对人口空间分布产生了永久性影响。 霍恩贝克和肯尼斯顿(2014)通过土地价值的地块级数据发现波士顿火灾的长期影响,通过大规模重建的可能性。迈克尔和劳奇(2016)报告了与路径依赖一致的结果,使用罗马城市的数据。

Although we now have strong evidence of path dependence in the distribution of economic activity, the interpretation of these empirical results remains open to question. In particular, findings of path dependence do not necessarily imply multiple equilibria. If historical advantages lead to investments in local technology and infrastructure and better institutions, dynamic agglomeration effects can lead to maintained investments in these locations. These investments can serve as new sources of local advantages even after the original historical advantage has become obsolete or irrelevant. This is the case in the dynamic models of Desmet & Rossi-Hansberg (2015) and Desmet et al. (2016). The latter article shows that these dynamic agglomeration effects have significant predictive power over long periods. In particular, using only information for the year 2000 and running the dynamics backwards, Desmet et al. (2016) find a correlation between actual and predicted country population levels in 1950 as high as 0.74. In these models, the equilibrium is unique, and so the evolution of the distribution of economic activity is uniquely determined by initial conditions. In that sense, any shock or change in fundamentals in a given period will affect the future evolution and the balanced-growth path of the world economy. Empirical and theoretical research on the dynamic evolution of the distribution of economic activity is reviewed by Desmet & Henderson (2015).
尽管我们现在有关于经济活动分布路径依赖的强烈证据,但这些经验结果的解释仍然存在疑问。特别是,路径依赖的发现并不一定意味着存在多重均衡。如果历史优势导致对当地技术和基础设施的投资以及更好的制度,动态集聚效应可以导致对这些地点的投资持续。这些投资甚至可以在原始历史优势变得过时或不相关后,成为新的地方优势来源。这是 Desmet 和 Rossi-Hansberg(2015 年)以及 Desmet 等人(2016 年)的动态模型中的情况。后一篇文章表明,这些动态集聚效应在长期内具有显著的预测能力。特别是,Desmet 等人(2016 年)仅使用 2000 年的信息,逆向运行动态,发现实际和预测的 1950 年国家人口水平之间的相关性高达 0.74。在这些模型中,均衡是唯一的,因此经济活动分布的演变由初始条件唯一确定。 在这个意义上,任何给定时期的冲击或基本面的变化都将影响世界经济未来的演变和平衡增长路径。Desmet 和 Henderson(2015)回顾了关于经济活动分布动态演变的实证和理论研究。

Clearly, more theoretical and empirical work on the role of shocks and initial conditions in determining the evolution of economic activity is needed. Perhaps this will be one of the more fruitful areas for future research on quantitative spatial economics.
显然,需要更多关于冲击和初始条件在决定经济活动演变中作用的理论和实证研究。或许这将是未来定量空间经济学研究较为富有成效的领域之一。

 

The development of quantitative spatial models has been a major breakthrough in our understanding of the determinants of the spatial distribution of economic activity. Relative to earlier theoretical research, these models connect in an empirically meaningful way with the observed data, thereby permitting the quantification of key theoretical mechanisms and specificity in evaluating the counterfactual effects of policy interventions in particular settings. These models have also delivered both methodological and substantive general insights. The methodological insights include a list of components that can be used to incorporate a variety of agglomeration and congestion mechanisms in a unified spatial framework. Within this framework, they also include the conditions for the existence and uniqueness of equilibrium, the conditions under which these models can be inverted to separate out the contributions of physical and economic geography, and methods for undertaking counterfactuals to evaluate comparative statics with respect to changes in the model's parameters. The substantive insights include the empirical relevance of market access, the strength of agglomeration and dispersion forces within cities, and the importance of the dynamic forces shaping the evolution of the spatial distribution of economic activity over time.
经济发展活动空间分布的决定因素的理解上,定量空间模型的发展是一个重大突破。与早期的理论研究相比,这些模型以经验上有意义的方式与观察到的数据相联系,从而允许量化关键理论机制和特定性,以评估特定政策干预的逆事实效应。这些模型还提供了方法论和实质性的普遍见解。方法论上的见解包括一个可以用来在一个统一的空间框架中整合各种聚集和拥堵机制的组件列表。在这个框架内,它们还包括了均衡存在和唯一性的条件,以及在这些模型中可以逆推以分离出物理地理和经济地理贡献的条件,以及进行逆事实分析以评估模型参数变化比较静态的方法。 实质性见解包括市场准入的实证相关性、城市内部集聚和分散力量的强度,以及塑造经济活动空间分布随时间演变的动态力量的重要性。

This literature on quantitative spatial models has already achieved much. Nonetheless, there remain many areas where further research is needed. First, most research has continued to be concerned with the production and trade of goods, whereas much economic activity today is concentrated in services, whether tradable or nontradable. Second, most of the main frameworks in the literature are static and abstract from the effect of spatial frictions on the evolution of the spatial distribution of economic activity and growth. Third, although there have been several influential studies of the sorting of heterogeneous workers and firms across geographic space, there remains scope for further work. Fourth, the economic analysis of the geography of firm and worker networks remains underexplored. We expect much progress in these and other dimensions over the coming decades.
这一关于定量空间模型的文献已经取得了许多成果。然而,仍有许多领域需要进一步研究。首先,大多数研究仍然关注商品的生产和贸易,而今天的经济活动大多集中在服务领域,无论是有形服务还是无形服务。其次,文献中的大多数主要框架都是静态的,并且抽象化了空间摩擦对经济活动空间分布和增长演变的影响。第三,尽管有几项关于异质工人和企业在地理空间中排序的有影响的研究,但仍有许多工作可以进一步开展。第四,对企业和工人网络地理空间的经济分析仍处于探索阶段。我们预计在未来的几十年里,在这些和其他方面将取得重大进展。

 

The authors are not aware of any affiliations, memberships, funding, or financial holdings that might be perceived as affecting the objectivity of this review.
作者未披露任何可能影响本综述客观性的关联、会员资格、资金或财务持股。

 

We thank the International Economics Section and Princeton University for research support. We are grateful to colleagues and coauthors from other research, including Lorenzo Caliendo, Klaus Desmet, Dave Donaldson, Pablo Fajgelbaum, Gene Grossman, Ferdinando Monte, Eduardo Morales, Henry Overman, Daniel Sturm, Tony Venables, and Nikolaus Wolf, for insightful comments and discussion. Responsibility for any views, errors, or omissions lies with the authors alone.
我们感谢国际经济学部和普林斯顿大学的研究支持。我们对来自其他研究领域的同事和合著者,包括洛伦佐·卡利安多、克劳斯·德斯梅特、戴夫·唐纳森、帕布洛·法杰尔鲍姆、吉恩·格罗斯曼、费德里南多·蒙特、埃德华多·莫拉莱斯、亨利·欧弗曼、丹尼尔·斯特姆、托尼·文莱布斯和尼古劳斯·沃尔夫的宝贵评论和讨论表示感谢。对于任何观点、错误或遗漏,责任完全由作者承担。

 
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