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.     

THE ELASTICITY OF CAPITAL–LAND SUBSTITUTION IN THE HOUSING CONSTRUCTION SECTOR OF A RAPIDLY URBANIZED CITY: EVIDENCE FROM TURKEY

This paper estimates the elasticity of capital-land substitution for the housing market in Ankara, the capital city of Turkey. Using constant elasticity of substitution (CES) and variable elasticity of substitution (VES) production functions and cross-section data, the paper provides new information to compare the housing supply elasticity of Ankara with that of the USA and the UK cases. Our regression results reveal that housing supply in Ankara is highly inelastic due to the uniform construction regime of local authorities. Moreover, we find that there is a considerable spatial differentiation of urban land density measures within the capital city. Because of the incomplete urbanization process, the elasticity of capital-land substitution is significantly higher in the outer parts of the city.     

Numerical solution of urban residential land-use models

Many recent papers have made drastic simplifications in urban residential land-use models, presumably for analytic tractability. In this one, numerical solutions to models embodying varying assumptions of substantive importance are obtained. These solutions are compared with estimated characteristics of 1950 residential population density functions. The comparisons suggest that a CES production function for housing with an elasticity of substitution of land for structures of 0.75 agrees more closely with observed 1950 characteristics than does the Cobb-Douglas function so commonly used for analytic simplicity. Assuming a constant marginal transport cost for commuters at all distances from the Central Business District (CBD), however, yields results agreeing somewhat better with 1950 characteristics used for comparison than does the more complicated model embodying congestion in commuter transport.     

Explaining economic growth in the Soviet Union, 1950–86

Production function estimates are provided for Soviet industrial production and gross national product for the period 1950–86. A variety of alternative specifications is tested, including Cobb-Douglas, constant elasticity of substitution and variable elasticity of substitution production functions, and an error correction mechanism is used to investigate the long-run properties of the estimated equation. The structural stability of the estimates is also examined. Constant-returns-to-scale Cobb-Douglas production functions suggest that the rate of total factor productivity growth in the Soviet economy has declined steadily over time, becoming negative sometime in the period between 1970 and 1980. However the extensive statistical tests can doubt on the validity of any production function estimated on Soviet data.     

Alternative functional forms for production,cost and returns to scale functions

We consider generalized production functions, introduced in Zellner and Revankar (1969), for output y=g(f) where g is a monotonic function and f is a homogeneous production function. For various choices of the scale elasticity or returns to scale as a function of output, differential equations are solved to determine the associated forms of the monotonic transformation, g(f). Then by choice of the form of f, the elasticity of substitution, constant or variable, is determined. In this way, we have produced and generalized a number of homothetic production functions, some already in the literature. Also, we have derived and studied their associated cost functions to determine how their shapes are affected by various choices of the scale elasticity and substitution elasticity functions. In general, we require that the returns to scale function be a monotonically decreasing function of output and that associated average cost functions be U- or L-shaped with a unique minimum. We also represent production functions in polar coordinates and show how this representation simplifies study of production functions' properties. Using data for the US transportation equipment industry, maximum likelihood and Bayesian methods are employed to estimate many different generalized production functions and their associated average cost functions. In accord with results in the literature, it is found that the scale elasticities decline with output and that average cost curves are U- or L-shaped with unique minima. © 1998 John Wiley & Sons, Ltd.     

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.     

The elasticity of substitution for land: The effects of measurement errors

The explanatory variable used in most previous studies of land-nonland substitution, assessed or appraised land value, is subject to considerable measurement error. There is evidence that this biases the substitution elasticity from a true value of unity to a measured value in the 0.5 to 0.8 range. An hedonic method of measuring land value is proposed and applied to the Chicago residential sales data developed by Berry and Bednarz. Substitution elasticities are estimated within a CES framework from the two measures of land value; after correction for a vintage effect, appraised land value indicates that the elasticity is 0.57 whereas the hedonic measure of land values supports a unitary substitution elasticity. Therefore, the errors-in-variables hypothesis is confirmed and the use of a Cobb- Douglas production function is suggested.     

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.     

超越对数函数要素替代弹性公式修正与估计方法比较

对超越对数函数要素替代弹性估计方法进行专门研究,修正了超越对数生产函数要素替代弹性公式错误,梳理超越对数成本函数各类替代弹性定义,综合考虑数据易得性、估计可靠性、定义合意性以判定各类估计方法的相对优劣。研究发现,受困于共线性难题,基于超越对数生产函数计算替代弹性效果不佳;基于超越对数成本函数计算替代弹性更具优势,影子替代弹性凭借出色的理论性质与强稳健性成为首选。     

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.     

Patent activity and technical change

As creations of the mind, intellectual property includes industrial property and copyrights. This paper presents an aggregate production function of the generalized Fechner–Thurstone (GFT) form to analyze the impact of an important component of intellectual industrial property, namely patent activity, on technical change in the USA for the period 1947–1981. Patents should alter isoquant maps, and measuring their elasticities is both intuitively and empirically appealing. We define a technology-changer as a variable that has an impact on the elasticity of the marginal rate of technical substitution (MRTS) between inputs of the GFT production function over time. Various types of US patent grant activity, specifically total, domestic, foreign, successful and unsuccessful patent applications, are used as instruments for the technology-changer. Using the GFT specification, the impacts of various technology-changers on the elasticity of the MRTS between inputs are estimated directly. It is found that granted (or successful) patents, patents granted to foreign companies and individuals, total patent applications, and even unsuccessful patent applications, have significant impacts on the rates at which inputs are substituted for each other over time in production.     

Wages and prices: Are workers fully compensated for cost of living differences?

This paper investigates the equilibrium relationship between wages and prices across labor markets. Of central interest is the extent to which workers receive higher wages to compensate for differences in the cost of living. According to the spatial equilibrium hypothesis, the utility of homogenous workers should be equal across labor markets. This implies that controlling for amenity differences across areas, the elasticity between wages and the general price level across areas should equal one, at least under certain conditions. I test this hypothesis and find that the predicted relationship holds when housing prices are measured by rents and the general price level is instrumented to account for measurement error. When housing prices are measured by housing values, however, the wage-price elasticity is significantly less than one, even using instrumental variables. Rents reflect the price paid for housing per unit of time and are arguably the superior measure. Thus, findings in this essay provide support for the full compensation hypothesis. These findings also have important implications for researchers estimating the implicit prices of amenities or ranking the quality of life across areas.     

中国城市住宅市场的结构差异性分析

市场价商品房、经济适用住房和廉租房构成了目前中国城市住宅市场的供应体系.依据中国30个主要城市的房地产开发统计数据,选择吸纳率作为评价住宅市场供需均衡状态的指标,利用固定影响变截距模型,重点研究了商品房和经济适用住房供给结构的城市差异性.研究发现,在城市住宅市场中,经济适用住房市场和商品房市场具有很强的相关性.作为具有政府资助性质的经济适用住房建设,存在典型的地域性特征,其政策的设定和实施会对整个住宅市场产生影响,地方政府应在利用比较全面的住宅市场指标体系进行综合分析基础上,制定适合本地的经济适用住房政策.     

Technical efficiency and region The U.S. manufacturing sector 1972–1977

In this paper we estimate the extent of technological bias in an interregional context for U.S. manufacturing during the period 1972–1977 using a factor augmenting production function approach. We present estimates of the elasticity of factor substitution for each of the 48 states in the sample using a variable elasticity of substitution production function. Next, we use these estimates to generate estimates of the rates of change in the efficiencies of capital and labor inputs and compare these estimates across states and census regions. We also examine and compare estimates of total factor productivity across states and regions. We ,find that the average annual rates of growth of capital efficiency during the period are 5.5 percent in the Northeast, 5.3 percent in the Northcentral, 5.6 percent in the West and 3.1 percent in the South. The rates of change of the efficiencies of labor are found to be negative across all regions except the South. The rates of change of total factor productivity are found to be 1.7 percent in the Northeast, 2.3 percent in the Northcentral, 2.4 percent in the West and 1.7 percent in the South. We also find that between 33 percent and 56 percent of the growth of output across regions is due to technical progress.     

CES technology and business cycle fluctuations

We contribute to an emerging literature that brings the constant elasticity of substitution (CES) specification of the production function into the analysis of business cycle fluctuations. Using US data, we estimate by Bayesian-Maximum-Likelihood methods a standard medium-sized DSGE model with a CES rather than Cobb–Douglas (CD) technology. We estimate a elasticity of substitution between capital and labour well below unity at 0.15–0.18. In a marginal likelihood race CES decisively beats the CD production and this is matched by its ability to fit the data better in terms of second moments. We show that this result is mainly driven by the implied fluctuations of factor shares under the CES specification. The CES model performance is further improved when the estimation is carried out under an imperfect information assumption. Hence the main message for DSGE models is that we should dismiss once and for all the use of CD for business cycle analysis.     

Testing the Technology of Human Capital Production: A General‐to‐Restricted Framework

Studies of childhood development have suggested human capital is accumulated in complex and nonlinear ways. Nonetheless, empirical analyses of this process often impose a linear functional form. This paper investigates which technology assumptions matter in quantitative models of human capital production. I propose a general‐to‐restricted procedure to test the production technology, placing constraints on a modified McCarthy function, from which transcendental, constant elasticity of substitution, log‐linear and linear models are obtained as special cases. Applying the procedure to data on child height from the Young Lives surveys, as well as cognitive skills, I find that the technology of human capital production is neither log‐linear nor linear‐in‐parameters; rather, past and present inputs act as complements. I recommend that maintained hypotheses underlying functional form choices should be tested on a routine basis.     

Factor substitution,employment density and suburbanization

A model of an urban area producing one good for export is presented and solved to yield the employment density function. The production technology is a constant elasticity of substitution (σ) production function, unlike other models which use a Cobb-Douglas function. The shape of the employment density function proves to be sensitive to the elasticity of substitution and can diverge markedly from the usually assumed negative exponential form. The employment density function is a constant when σ = 0; always declines for positive σ but at an increasing rate if $\text{σ ≤}\text{1}\text{2}$; at either an increasing rate near the city center and decreasing thereafter or always at a decreasing rate if $\text{1}\text{2}\text{< σ < 1}$; and at a decreasing rate if σ ≥ 1. When the employment density function is differentiated with respect to σ, the sign of the derivative is positive near the city center and generally negative in the outer regions; the city seems to centralize. A decline in transport costs does not always suburbanize employment; it is contingent on the nature of the production technology.     

The price elasticity of the supply of single-family detached urban housing

Past attempts to estimate the price elasticity of the supply of housing have erred by using aggregate data. Many houses are built in areas where the volume of residential construction is low. Consequently, the influence of observations from higher-volume areas where costs may be higher is diminished. This problem is eliminated by using cross-sectional data from 61 different American urban areas, for a total of 223 observations from 1976 to 1981, to estimate a translog cost function for housing. The supply elasticity is found to be infinite.     

The industrial demand for energy

This paper uses a constant elasticity of substitution production function to examine the extent of factor substitutability in the production of industrial goods. Subsequently, the degree of interfuel substitution is estimated and it is demonstrated that all energy sources are substitutable. Finally, the stability of the demand for various energy sources is empirically tested for and it is concluded that over the period of investigation the demand has in fact remained unaltered.     

中国工业行业资本-劳动替代弹性估计及影响因素研究

基于超越对数生产函数的随机前沿模型估计2001—2015年中国工业行业的资本-劳动替代弹性,并对其影响因素进行分析,结果表明：劳动密集型行业的资本-劳动替代弹性普遍高于技术密集型行业,而后者又普遍高于资本密集型行业;行业开放程度、研发密度、产权属性、资本-劳动比、资产负债率、《劳动合同法》实施以及金融危机等因素都会影响资本-劳动替代弹性。