The vintage effect in TFP-growth: An analysis of the age structure of capital

The age structure of capital plays an important role in the measurement of productivity. It has been argued that the slowdown in the 1970s can be ascribed to the aging of the stock of capital. In this paper, we incorporate the age structure in productivity measurement. One proposition proves that Nelson's [Nelson, R.R., 1964. Aggregate production functions and medium-range growth projections. American Economic Review 54 (September), 575–605] formula is only an approximation. Our final proposition shows that inclusion of the vintage effect prompts an upward correction of measured productivity growth in times of an aging stock of capital. Here capital ages if the investment/capital ratio falls short of the inverse of the capital age, as a first proposition shows. The analysis rests on a rigorous accounting for vintages. We translate the Bureau of Economic Analysis’ age of capital data into a measure of rates of obsolescence. Empirically, the correction of productivity growth for the vintage effect requires an estimate of the obsolescence and depreciation parameters on the basis of age data. The results indicate that the use of capital stock in efficiency units does cause some smoothing of total factor productivity growth over time. In the 1950s, when investment accelerated, the vintage-adjusted capital growth rate well exceeded the BEA growth rate, and vintage-adjusted TFP-growth is significantly lower than unadjusted TFP-growth. The measured productivity slowdown of the 1970s is somewhat ameliorated.     

CAPITAL AGGREGATION IN THE PRESENCE OF OBSOLESCENCE-INDUCING TECHNICAL CHANGE

The major question addressed is the treatment of capital embodied technical progress. Should Obsolescence be deducted to calculate a net stock, or should quality adjustments be made in each vintage of new capital, or both, or neither? In order to estimate the contribution of new investment to growth it is necessary to use a capital stock where different vintages are weighted in proportion to their marginal products. The commonly used gross capital measures do not do this, because they do not allow for the higher marginal product of more modern capital. Such an allowance for capital embodied technical progress can be made either by quality adjusting new capital or by incorporating obsolescence into the valuation of the old capital (but not both). However, even if new capital incorporates an allowance for improved quality, it will still be necessary to revalue the old capital. Frequently, a reasonable approximation to the net capital stock results from a linear decline in quasi-rents and can be approximated by published estimates of the stock of capital net of straight line depreciation. Steady technical progress will not lead to the commonly used exponential service decline functions. To avoid overestimating the return to investment when technology changes it will be necessary to use information on capital embodied technical change to revalue old capital, rather than to change the price indices for new capital.     

Undiscounted optimal growth with consumable capital and labor-intensive consumption goods

This paper presents a complete characterization of the optimal policy in a two sector undiscounted growth model. The model is an extension of the Leontief two sector model, which analyzes the optimal allocation of capital and labor to a consumption good sector and an investment good sector. The paper extends this framework to include consumable capital. Thus, the planner has preferences over the consumption good and the consumable capital. Future welfare levels are treated equally as current ones. Geometric techniques are applied to characterize the optimal policy if the consumption good is labor-intensive. The results suggest that if the initial capital stock is above a threshold level, that depends upon the consumption of capital, every optimal program is monotonic, converges to the golden rule stock in a finite number of periods, and undergoes either unemployment or excess capacity of capital.     

A METHOD FOR IMPROVED CAPITAL MEASUREMENT BY COMBINING ACCOUNTS AND FIRM INVESTMENT DATA

We propose a new method for estimating capital stocks at the firm level by combining business accounts information and investment data. The method also produces capital estimates at the sector or industry level by summing individual firms' capital stocks and appropriately inflating this sum to account for firms not included in the data set. Our approach has two major advantages compared with the much used Perpetual Inventory Method (PIM). First, long investment series are not necessary. Second, sector capital estimates are automatically adjusted for changes in the capital stock because of entry and exit of firms. While capital growth rates in Norwegian manufacturing were only 1 percent on average during 1993–2004 according to national accounts figures, our method yields much higher growth rates of 5.5 percent on average.     

CONFORMISM AND STRUCTURAL CHANGE

Using a simple, multisector model of endogenous growth, we show that commodity‐specific consumption externalities can be a source of structural change. When the degrees of consumption externalities are different between goods, each sector grows at a different rate. However, the aggregate economy exhibits balanced growth in that capital stock and expenditure grow at the same constant rate. A three‐sector version of our model may reconcile Kaldor's stylized facts with empirically plausible profiles of industrial structure transformation.     

Comparing approaches to valuing sectoral net investments

In the literature of comprehensive national accounts, national net investments are used to indicate dynamic welfare improvement in an economy. A well-known approach associates national net investments with the shadow value of change in stock of capital assets in an economy. Following this capital stock approach, sectoral net investments can be defined as the shadow value of change in stock of capital assets owned by a sector in an economy. An alternative approach is based on future commodity flows to a sector. This commodity flow approach associates sectoral net investments with the present value of changes in future commodity flows to a sector. In the present paper, I compare these two approaches and prove that they coincide with each other only if the future commodity flows to the sector can be attributed to current stock of capital assets in the sector alone. In empirical studies, commodity flow approach can be a better alternative if the purpose is to estimate the contributions to national net investments of a recipient of future cash flows.     

The impact of public capital on the US private economy: new evidence and analysis

This paper presents new evidence on the impact of public capital on the productivity of the US private sector. Using a production function approach, we estimate the impact of public investment on private capital productivity, specifically addressing the empirical critiques of earlier studies. We find evidence of a cointegrating relationship in a dynamic specification of an empirical model that includes public infrastructure as a factor of production, indicating the existence of a long‐run relationship between the US public capital stock and the productivity of the private capital stock. The results are used to explore how the decline in the growth rate of the public capital stock would have affected the performance of the private sector.     

OPTIMAL TRANSITION DYNAMICS IN THE LEONTIEF TWO‐SECTOR GROWTH MODEL WITH DURABLE CAPITAL: THE CASE OF CAPITAL INTENSIVE CONSUMPTION GOODS*

We present results on undiscounted optimal policies in the Leontief two‐sector growth model with durable capital. Unlike the results with a labour intensive consumption goods sector, we show that a monotonic optimal programme is only one special case out of many richer possibilities of transition dynamics. Depending on the initial capital stock, and a key parameter ζ that could be interpreted as a marginal rate of transformation of capital between today and tomorrow, an optimal programme may converge to a period‐two cycle; and even when it converges to the golden rule stock, it can do so (damped) cyclically or with a “jump”.     

DEPRECIATION, OBSOLESCENCE, AND THE MEASUREMENT OF THE AGGREGATE CAPITAL STOCK OF THE UNITED STATES 1900–1962

This paper is concerned with the sensitivity of estimates of the aggregate capital stock of the United States to the statistician's choice of depreciation method. The usual depreciation charge can be shown to include allowances both for physical deterioration and for obsolescence. If one interprets the gross stock as the stock of surviving assets, then the various net stocks defined by depreciation accounting may be interpreted as a revaluation of these assets by means of an index of embodied technical change. Estimates of the United States capital stock were generated under eight sets of assumptions. These estimates are compared with respect to level, trend, and implications for other aggregate statistical indicators. The conclusion is reached that the assumptions which define a country's stock of tangible capital are of considerably greater importance than has often been supposed.     

Obsolescence and modernization in the growth process

In this paper, an endogenous growth model is built up incorporating Schumpeterian creative destruction and embodied technological progress. Under embodiment, long run growth is affected by two opposite effects: (i) obsolescence costs add to the user cost of capital, which have a negative effect on research efforts; and (ii) the modernization of capital increases the demand for investment goods, raising the incentives to undertake research activities. Applied to the understanding of the growth enhancing role of both capital and R&D subsidies, we conclude that the positive effect of modernization generally more than compensates the negative effect of obsolescence.     

股票期权与企业绩效关系的实证研究综述

股票期权作为企业家人力资本分享企业剩余索取权的典型模式在国外企业中普遍实行,国内也有近百家上市公司进行了试点。股票期权多大程度上激励了企业家人力资本,多大程度上带来了企业绩效的提高,是中外研究者实证研究一直关注的焦点问题。本文在对国内外学术界有关股票期权与企业绩效的实证研究进行综述的基础上,提出对相关问题的思考。     

Ramsey Equilibrium in a Two-Sector Model with Heterogeneous Households

We prove an existence theorem for a stationary perfect foresight equilibrium under borrowing constraints in a two-sector model with infinitely lived heterogeneous agents. The most patient agent holds all the capital in this solution. We also show that if the capital goods sector is capital intensive and capital income is increasing in the aggregate capital stock, then the aggregate capital stock eventually is monotonic and converges to the steady state stock. If the consumption goods sector is more capital intensive and capital income is increasing in aggregate capital we prove convergence to the steady state under more restrictive conditions. Periodic equilibria are shown to exist under weaker hypotheses. Journal of Economic Literature Classification Numbers: D52, D90, E13.     

On Terms of Trade and Capital Accumulation

This paper studies, within an OLG general equilibrium framework, the role of relative factor intensities in determining the relationship between the terms of trade and the capital stock. It shows that a diversified production equilibrium can be characterized by a positive association between these two variables if the investment sector is more labor-intensive and sector technologies are relatively dissimilar. Therefore, capital accumulation and terms-of-trade improvements do not require an import sector growing faster than the export sector when the latter is more capital-intensive. Large Stolper–Samuelson effects on factor incomes drive the results.     

An estimate of the capital stock for the Belgian industrial sector

The paper submitted for publication considers the conditions for and the construction of a capital stock series, consistent with all macroeconomic relations. A careful study of the literature has shown that most existing and widely used capital stock series do not meet that requirement. A generative method with a general model for the real sector is proposed. The choice of the parameters of this model was decided upon the general consistency with the main macroeconomic aggregates. The results are compared with existing series of capital stock. What was obtained was a capital stock series that gives non-diverging results for the macroeconomic series when using the capital stock in alternative specifications. The main conclusions on depreciation rate, capital stock, technological change, return on capital and share of capital are condensed in a set of tables and diagrams.     

ESTIMATES OF CAPITAL STOCK BY INDUSTRIES IN THE FEDERAL REPUBLIC OF GERMANY

The main purpose of this paper is to discuss some of the measurement problems in connection with the perpetual inventory method applied for estimates of capital stock. In the Federal Republic of Germany, highly aggregated capital stock data by business sector are compiled by the Federal Statistical Office within its national accounts calculations, while more detailed capital stock estimates by industrial sectors are published by the German Institute of Economic Research (DIW) in Berlin. Because of various gaps in the statistical sources, the accuracy of the capital stock calculations is not yet entirely satisfactory. Aside from the problem of establishing long time series for gross fixed capital formation in constant prices for all sectors, it is difficult to obtain reliable data on the inter-sectoral transactions in secondhand capital goods. In addition, there are problems of determining price indices and service life distributions of the fixed assets in the various parts of the economy. This paper shows a way to arrive at a reasonably close approximation to the latter problem.     

Regional productivity variation and the impact of public capital stock: an analysis with spatial interaction,with reference to Spain

In this article, we examine whether variations in the level of public capital across Spain's Provinces affected productivity levels over the period 1996 to 2005. The analysis is motivated by contemporary urban economics theory, involving a production function for the competitive sector of the economy (‘industry’) which includes the level of composite services derived from ‘service’ firms under monopolistic competition. The outcome is potentially increasing returns to scale resulting from pecuniary externalities deriving from internal increasing returns in the monopolistic competition sector. We extend the production function by also making (log) labour efficiency a function of (log) total public capital stock and (log) human capital stock, leading to a simple and empirically tractable reduced form linking productivity level to density of employment, human capital and public capital stock. The model is further extended to include technological externalities or spillovers across provinces. Using panel data methodology, we find significant elasticities for total capital stock and for human capital stock, and a significant impact for employment density. The finding that the effect of public capital is significantly different from zero, indicating that it has a direct effect even after controlling for employment density, is contrary to some of the earlier research findings which leave the question of the impact of public capital unresolved.     

Equilibrium dynamics in discrete-time endogenous growth models with social constant returns

The existing literature establishes possibilities of local determinacy and dynamic indeterminacy in continuous-time two-sector models of endogenous growth with social constant returns. The necessary and sufficient condition for local determinacy is that the factor intensity rankings of the two sectors are consistent in the private/physical and social/value sense. The necessary and sufficient condition for dynamic indeterminacy is that the final (consumable) good sector is human (pure) capital intensive in the private sense but physical (consumable) capital intensive in the social sense. This paper re-examines the dynamic properties in a discrete-time endogenous growth framework and finds that conventional propositions obtained in continuous time need not be valid. It is shown that the established necessary and sufficient conditions on factor intensity rankings for local determinacy and dynamic indeterminacy are neither sufficient nor necessary, as the magnitudes of time preference and capital depreciation rates both play essential roles. We have benefitted from discussion with Robert Becker, Eric Bond, Michael Kaganovich, Karl Shell and participants of the Midwest Macroeconomic Conference in Chicago and the Midwest Economic Theory and International Trade Meetings at Indiana University. The fourth author acknowledges financial support from the Institute of Economics and Business Administration of Kobe University and the Institute of Economic Research of Kyoto University to enable this international collaboration.     

THE CASE FOR PAY-AS-YOU-GO PENSIONS IN A SERVICE ECONOMY

The elderly consume more labour‐intensive services than young individuals. This makes them vulnerable to rising costs of services due to higher wages, which can be caused by increased capital accumulation. This paper shows that in a model with a service sector, the golden‐rule capital stock is lower and dynamic inefficiency is more likely to occur than in the conventional one‐sector model. This implies that in many cases, a positive Pay‐As‐You‐Go tax maximises long‐run welfare in a service economy. Calculations based on data from the United Kingdom and the Netherlands show that the long‐run optimal degree of funding coincides with the current situation in these countries.     

人力资本与经济增长:对中国的实证分析

本文利用北卡罗来那大学Chapel Hill分校和中国预防医学会营养与食品卫生研究所的调查数据，估计出1990年～2000年我国的工资方程和人力资本增长率。结合该时期经济增长，资本存量和劳动投入数据，我估算出中国20世纪90年代的全要素生产率，以及各因素对经济增长的贡献。此外，本文还详细讨论了统计年鉴中产出、资本和劳动数据存在的问题，在对以往的研究进行详细比较的基础上选择了适当的纠正方法。     

Skilled–unskilled wage inequality,product variety,public input and increasing returns: A static general equilibrium analysis

The paper develops a four sector small open economy model with two traded final good sectors, a public intermediate good producing sector and a nontraded good sector producing varieties of intermediate goods. There are three primary factors: capital, skilled labour and unskilled labour. Industrial sector producing a traded good uses capital, intermediate goods and skilled labour as inputs. Intermediate goods producing sector also uses capital and skilled labour. Public input producing sector and the agricultural sector producing the other traded good use capital and unskilled labour as inputs. It is shown that, if production technologies are the same for the agricultural sector and the public input producing sector and if the scale elasticity of output is very low, then an increase in capital stock (unskilled labour endowment) raises (lowers) the skilled–unskilled wage ratio. However, an increase in skilled labour endowment does not produce any unambiguous effect. On the other hand, an increase in the tax rate on industrial output and/or an increase in the price of the agricultural product, armed with the same set of assumptions, lowers the skilled–unskilled wage ratio.