The elasticity of substitution in urban housing production: A VES approach

Many of the models which have been developed to explain urban spatial structure and land-use patterns rest on the properties of production functions. Differing factor price ratios within urban areas, particularly land prices, result in capital-land ratios exemplified by high-rise apartments and single-family dwellings. The purpose of this paper is to explore a new functional form for the housing production function. Specifically, a variable elasticity of substitution production function is proposed and some preliminary empirical evidence is provided using data for single-family housing.     

Capital-land substitution in urban housing: A survey of empirical estimates

Recent empirical studies of capital-land substitution in urban housing are examined to determine the best estimate of the elasticity of substitution parameter σ. Studies based upon a cross section of metropolitan areas produce a rather narrow range for σ. Studies of individual metropolitan areas produce a wide range of estimates for σ, suggesting that a may vary across metropolitan areas. However, all estimates of σ are probably biased toward zero by errors in the measurement of land values.     

WHAT DETERMINES THE ELASTICITY OF SUBSTITUTION BETWEEN CAPITAL AND LABOR? A LITERATURE REVIEW

This paper provides the first comprehensive review of the empirical and theoretical literature on the determinants of the elasticity of substitution between capital and labor. Our focus is on the two-input constant elasticity of substitution (CES) production function. We start by presenting four concise observations that summarize the empirical literature on the estimation of . Motivated by these observations, the main part of this survey then focuses on potential determinants of capital–labor substitution. We first review several approaches to the microfoundation of production functions where the elasticity of substitution (EOS) is treated as a purely technological parameter. Second, we outline the construction of an aggregate elasticity of substitution (AES) in a multi-sectoral framework and investigate its dependence on underlying intra- and inter-sectoral substitution. Third, we discuss the influence of the institutional framework on the extent of factor substitution. Overall, this survey highlights that the effective elasticity of substitution (EES), which is typically estimated in empirical studies, is generally not an immutable deep parameter but depends on a multitude of technological, non-technological, and institutional determinants. Based on these insights, the final section identifies a number of potential empirical and theoretical avenues for future research.     

保障性住房供给中民间资本引导--以天津市为例

民间资本具有逐利性，民间资本参与保障性住房供给必然要追逐利益，相应的制度设计必须尊重民间资本的逐利性，给予民间资本稳定、持续的利益激励，从而保证其稳定、持续地参与保障性住房供给。但基于民间资本的流动性，需要在制度设计中中断民间资本的逐利性，避免民间资本参与保障性住房过程中为追逐利益而偏离住房保障目标。对于具有较高获益性的保障性住房，天津市允许民间资本直接参与供给；而在获益性较低的保障性住房项目中，天津市采用保障性住房投资基金、保障性住房信托投资基金、住房公积金贷款等工具鼓励民间资本参与保障性住房供给，有效地兼顾了民间资本的逐利性和保障性住房的公益性，在结果上达到了双赢。     

Indeterminacy in discrete-time infinite-horizon models with non-linear utility and endogenous labor

We consider a discrete-time two-sector model with sector specific externalities in which the technologies are given by CES functions with asymmetric elasticities of capital–labor substitution, and the preferences of the representative agent are given by a CES additively separable utility function defined over consumption and leisure. We first show that when the labor supply is infinitely elastic, the steady state is always saddle-point stable, no matter what the elasticity of intertemporal substitution in consumption and the size of externalities are. We then prove that when the elasticity of intertemporal substitution in consumption is sufficiently large, local indeterminacy requires a low enough elasticity of the labor supply.     

Variable elasticity of substitution in urban housing production

The notion that the elasticity of substitution in urban housing production should vary with changing intensities of land use seems to be realistic and theoretically viable. Hence the variable elasticity of substitution production function has been proposed by some authors. However, it suffers from a serious shortcoming that the elasticity of substitution should not exceed unity. To allow for flexibility in the range of the elasticity of substitution, we explore a general functional form for the housing production function, the weak disposability of inputs production function in particular. Our empirical findings, based on the Santa Clara County single-family housing data, provide evidence that this general function is a more accurate specification of urban housing production than the variable elasticity of substitution function.     

我国新建住宅长期供给价格弹性估算——基于35个大中城市的实证研究

大多数住宅模型和政策分析,都直接或间接依赖于住宅供给价格弹性的估计值：为了应对市场需求冲击,是多供给住房还是提高住宅价格？基于Mayo（1981）构建的模型,估算了我国35个主要大中型城市的新建住宅供给价格弹性。根据流量模型,2000-2007年我国的新建住宅价格弹性系数在4-11之间,2008到2013年的价格弹性在5-13之间。而存量调整模型得到了截然不同的估算结果：2008-2013年我国的新建住宅供给价格弹性在1-6之间,更精确的估算出了我国新建住宅供给市场的价格弹性。     

Capital–labor substitution and equilibrium indeterminacy

This paper examines the quantitative relationship between the elasticity of capital–labor substitution in production and the conditions needed for equilibrium indeterminacy (and belief-driven fluctuations) in a one-sector growth model. With variable capital utilization, the substitution elasticity has little quantitative impact on the minimum degree of increasing returns needed for indeterminacy. However, when capital utilization is constant, a below-unity substitution elasticity sharply raises the minimum degree of increasing returns because it imposes a higher effective adjustment cost on labor hours. Overall, our results show that empirically-plausible departures from the Cobb–Douglas production specification can make indeterminacy more difficult to achieve.     

保障性住房财政补贴模式效率评价——基于住房供给市场差异的研究

加大保障性安居工程财政补贴支持力度,确保财政补贴的高效运行成为推进安居工程建设的关键。依据住房供给弹性和住房过滤理论,从经济学角度分析了供方补贴和需方补贴的实施效率。基于不同城市的住房市场差异,考察我国11个典型城市的住房供给弹性和住房过滤,在识别本地区住房市场特性的基础上探讨适宜采取的补贴方式。研究表明,不同城市由于住房供给弹性和过滤情况的不同,保障性住房财政补贴的效率存在显著差异,采取合适的保障房补贴方式,能够优化资源配置,打破财政压力对推进保障房工作的限制。     

政府保障房供求补贴的不同效果

解决中低收入人群的基本住房问题是实现社会公平的基本国策之一。为了有效地实施保障性安居工程，通过构建数学模型研究在财政补贴率相同的条件下，住房消费补贴与住房供给补贴的成交价格、成交量与社会福利情况，可以发现这两者之间存在较大的差别，前者的成交价格、成交量和社会福利都高于后者，但前者比后者的财政补贴额更多。如果提高财政补贴率，那么前者成交价格会不断提高，而后者成交价格会不断降低，成交量都会呈现扩大趋势。成交价格、成交量和社会福利不但与财政补贴率及其补贴方式有关，也与住房的需求弹性和供给弹性有关。研究结论的政策意义在于，如果在政府财力有限、住房价格上涨压力较大的条件下，应当采用住房供给补贴；如果在政府财力相对宽松、住房价格上涨压力相对较小、依靠住房拉动经济增长的压力较大的条件下，则应当采用住房消费补贴，同时它还能实现公平与效率兼顾的目的。无论是采用住房消费补贴还是住房供给补贴，都应当增大供给弹性，减小需求弹性。     

Sources of downward bias in estimating the demand income elasticity for urban housing

Housing demand studies, whether relying upon individual or grouped data, have limited their observations to similar housing units and/or similar housing consumers to help control for product heterogeneity. Yet similar housing units tend to locate in clusters; tenants tend to segregate by race and income. The unintended results may be: (1) for grouped data, selection of a product subgroup with a supply price elasticity small enough to matter; (2) for individual data, selection of a consumer subgroup possessing a lower income elasticity than all housing consumers. Evidence is given that the supply price elasticity is sometimes small enough to matter when grouped data are used.     

Business cycle fluctuations and learning-by-doing externalities in a one-sector model

We consider a one-sector Ramsey-type growth model with inelastic labor and learning-by-doing externalities based on cumulative gross investment (cumulative production of capital goods), which is assumed, in accordance with Arrow (1962), to be a better index of experience than the average capital stock. We prove that a slight memory effect characterizing the learning-by-doing process is enough to generate business cycle fluctuations through a Hopf bifurcation leading to stable periodic orbits. This is obtained for reasonable parameter values, notably for both the amount of externalities and the elasticity of intertemporal substitution. Hence, contrary to all the results available in the literature on aggregate models, we show that endogenous fluctuations are compatible with a low (in actual fact, zero) wage elasticity of the labor supply.     

Production Technology Estimates and Balanced Growth

Capital‐labour substitution and total factor productivity (TFP) estimates are essential features of many economic models. Such models typically embody a balanced growth path. This often leads researchers to estimate models imposing stringent prior choices on technical change. We demonstrate that estimation of the substitution elasticity and TFP growth can be substantially biased if technical progress is thereby mis‐specified. We obtain analytical and simulation results in the context of a model consistent with balanced and near‐balanced growth (i.e. departures from balanced growth but broadly stable factor shares). Given this evidence, a constant elasticity of substitution production function system is then estimated for the US economy. Results show that the estimated substitution elasticity tends to be significantly lower using a factor‐augmenting specification (well below one). We are also able to reject conventional neutrality forms in favour of general factor augmentation with a non‐negligible capital‐augmenting component. Our work thus provides insights into production and supply‐side estimation in balanced‐growth frameworks.     

Inter-city wage differentials and intra-city workplace centralization

We explore the interaction of inter-city and intra-city wage differentials by occupation. The paper makes two main contributions. 1) We construct an occupation-specific index of workplace centralization that accounts for the difference between average employment density from the perspective of employees in each occupation and average employment density from the perspective of all employees. 2) We provide empirical evidence that relative wages of central to non-central occupations increase with city size, or equivalently, the elasticity of wages with respect to city size increases with occupational centrality. We conjecture that this empirical regularity arises because, as city size increases, workers in more central occupations face an increasingly less desirable locus of housing prices and commuting times relative to workers who have jobs in residential areas. The results are robust to the inclusion of individual-specific human capital variables and city-specific fixed effects.     

Competitive equilibrium cycles with endogenous labor

In this paper, we study a two-sector optimal growth model with elastic labor supply. We show that the modified golden rule is saddle-point stable when the investment good is capital intensive. To characterize stability with a capital intensive consumption good, we focus on either additively separable or homothetic preferences. In the first specification, we show that optimal oscillations require the elasticity of intertemporal substitution in consumption to be high enough while the elasticity of labor needs to be low enough. At the same time, we prove that with a linear utility in leisure the modified golden rule is always saddle-point stable. In the second specification for preferences, we show that the local dynamic properties of the optimal path depend instead on the shares of consumption and leisure into total utility. We prove that endogenous fluctuations are even more likely with homothetic preferences.     

要素替代弹性、有偏技术进步对我国工业能源强度的影响

从要素替代弹性和有偏技术进步视角分析我国工业能源强度,通过采用标准化供给面系统方法,对1994~2008年工业行业数据进行实证估计,确定不同类型行业资本、能源与劳动的嵌套CES生产函数结构。结果表明,多数行业的技术进步是资本、能源偏向型技术进步,这是因为在多数行业内,资本和能源表现为互补关系。在此基础之上,进一步分析有效资本、有效能源和有效劳动在特定要素替代弹性条件下,通过影响能源份额进而影响能源强度的作用机制,并利用工业行业数据刻画这3种有效要素对能源强度的动态影响。     

The price responsiveness of housing supply in OECD countries

The responsiveness of housing supply to changes in prices bears important implications for the evolution of housing prices and the speed of adjustment of housing markets. Based on a stock-flow model of the housing market estimated within an error correction framework, this paper estimates the long-run price elasticity of new housing supply in 21 OECD countries. Estimates suggest that the responsiveness of housing supply to price changes varies substantially across countries. It is relatively more flexible in North America and some Nordic countries, while it is more rigid in continental European countries and in the United Kingdom. The responsiveness of housing supply depends not only on national geographical and urban characteristics but also on policies, such as land use and planning regulations.     

PRIVATIZED HOUSING AND THE DEVELOPMENT OF CONDOMINIUMS IN CENTRAL AND EASTERN EUROPE: THE CASES OF POLAND, HUNGARY, SLOVAKIA, AND ROMANIA

This paper looks at the housing sector reform in Central and Eastern Europe and examines the progress to date in housing privatization and policies aimed at improving the management and condition of the existing housing stock through the establishment and operation of the condominium form of ownership. The paper compares and analyzes approaches taken in four countries with regard to four issues: (I) the legal framework and implementation strategies; (2) the role of local government housing strategies in supporting the development of viable condominium associations; (3) property management of privatized housing; and (4) financing rehabilitation and capital repair projects for condominiums. Findings include the need for a clear legal framework, competition in the property management market, more supportive local government policies, and public sector support in tackling rehabilitation finance issues.     

How to optimize the allocation of research resources? An empirical study based on output and substitution elasticities of universities in Chinese provincial level

Although significant progress has been made in China's basic research in recent years, there remains a wide gap between research in China and that from developed countries. How to optimize the allocative efficiency of research resources is of great importance for increasing research output. In this paper, using the fixed effect stochastic frontier model based on the translog production function, we estimate output and substitution elasticities of research and development (R&D) inputs at universities in China's provincial level during 2009–2016. We find that the R&D technical efficiency of China's universities, after a rapid growth, has tended to become relatively stable. Improvements of internationalization degree and exogenous R&D capabilities are conducive to promoting R&D technical efficiency, whereas expenditures from government grants inhibit the promotion of R&D technical efficiency; the effects of R&D capital deepening and internet penetration are not evident. The output elasticity of R&D capital is much higher than that of R&D personnel, suggesting that R&D capital is the main driving force of research output. The substitution elasticity between R&D capital and personnel has experienced a change from substitution to complementary since 2014. To realize sustained growth of research output, we should increase R&D input with positive output elasticity or reduce R&D input with negative output elasticity, making the necessary trade-offs according to the substitution relationship between the two R&D inputs.     

WHAT HAVE WE LEARNED FROM THREE DECADES OF RESEARCH ON THE PRODUCTIVITY OF PUBLIC CAPITAL?

The last three decades have witnessed a great deal of research effort devoted to measuring the private output elasticity of public capital. The wide range of available estimates have precluded any consensus so far, however. This paper reconciles the empirical findings of the literature by quantitatively analyzing a sample of 578 estimates collected from 68 studies for the 1983–2008 period. Using meta‐regression analysis, we show how study design characteristics and publication bias can explain a large fraction of the variation across estimates. We find a short‐run output elasticity of public capital supplied at the central government level of 0.083, which increases to 0.122 in the long run. If, in addition, only core infrastructure at a regional/local level of government is considered, these estimates are almost doubled. The average output elasticity of public capital amounts to 0.106. Our results suggest that public capital is undersupplied in OECD economies.