The Solow Residual
带门的成语A growth accounting exerci is intended to break down the growth of output into the growth of the factors of production--capital and labor-- and the growth of the efficiency in the utilization of the factors. The measure of this efficiency is usually referred to as Total Factor Productivity (TFP henceforth). For policy purpos it may matter whether output growth stems from factor accumulation or from increas in TFP.
Robert M. Solow (1957) t up the grounds for growth accounting. He considered a neoclassical production function
(1)
where is aggregate output, is the stock of physical capital, is the labor force and reprents TFP, which appears in a Hicks neutral way. After some simple transformations this equation can be written in terms of the growth rates of the variables. For simplicity, consider a Cobb-Douglas production function with. Then, taking natural logarithms and differentiating both sides of (1) with respect to time the growth rate of aggregate output can be expresd as
(2)
(For a variable the term stands for the derivative of with respect to time, and so stands for the growth rate.) Note that the growth rates of physical capital and labor are weighted by 作文素材网 and. As is well known, the weights correspond to the respective shares of rental payments for capital and labor in total income. With available data on and the growth rates for output, physical capital and labor, TFP growth can be computed from (2) as the residual. Accordingly, TFP growth is the so called Solow residual.黄藤素
Solow carried out this exerci for the US economy for the period 1909-49 where output per man hour approximately doubled. According to his estimates about one-eighth of the increment in labor productivity could be attributed to incread capital per man hour, and the remaining ven-eighths to the residual. The residual emed too big!
To be sure, TFP is conformed by a broad range of influences—a variety of technological, economic and cultural factors. Think of technological innovations, underemployed labor shifting from agriculture to more productive ctors, economic policies aimed at liberalization and competition, and changes in shopping habits --from tiny shops to department stores. Usually, the changes will increa TFP. Notwithstanding, TFP may go down for some other reasons such as trade unions restrictions, environmental regulations and safety measures that limit the u of production factors. (By way of example, suppo that for some weight-lifting exercis your gym requires a spotter; then, two people are needed for a single task and so this rule would decrea TFP.) Other factors that may influence TFP are frictions in financial markets, physical and human capital externalities, public expenditures or any other element that affect the aggr
失败与成功egate productivity of the economy.
Measurement is also crucial for comprehending the Solow residual. First, obrve that aggregate output is roughly the value of market goods and rvices produced in a society, but for most purpos this measure is too narrow as it leaves out many basic activities that enhance welfare. For instance, from the preceding example we can e that a safety measure will usually decrea output in the benefit of protecting human lives, and it should be clear that the beneficial effects of this rule will not affect output directly. Also, output and other aggregate variables may be measured with error; indeed, many internet activities are not satisfactorily treated in the National Accounts. Second, there is the problem of quality adjustment. Various goods and rvices (e.g., cars, cellular phones) did not exist in the past or are now of much better quality, but the quality improvements are not well recorded in the statistics. Third, there are lags in the process of innovation, learning and implementation of technologies. Some current investments will have most of their payoffs in a far future, and cannot be evaluated according to today’s productivity. For a period ranging from 1973 to 1989 the US and som
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e other Western economies experienced a slowdown in TFP growth. Presumably, this productivity slowdown happened becau the advanced economies were getting transformed to the era of information and communication technologies, and in the meantime productivity --as shown in the statistics -- was quite low.
In spite of the measurement problems, various works have analyzed the determinants of the Solow residual [e.g., Edward F. Denison (1962) and Dale W. Jorgenson and Zvi Griliches (1967)] with emphasis on embodied and dimbodied technological progress. Advances in technology may be embodied in the latest vintages of capital. Thus, new capital is better than old capital, not just becau old capital has suffered wear and tear, but also becau of the quality improvement that comes with new capital. Therefore, a part of technological progress is embodied in and failure to allow for this ri in quality may overstate the growth assigned to TFP. Similar considerations apply to labor: New generations entering the labor force are better educated and by all counts are more productive. Sizeable estimates have been reported for the contribution of embodied technological progress in physical capital to growth, but it ems puzzling that many cross-country studies [e.g., Lant Pritchett (2001)] have found that the estimates for human capital to growth are insignificant or do not have the desired sign. In contrast, dimbodied technological progress, included in TFP, will be associated with new modes of organization and operation of inputs as well as other improvements not incorporated in
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to the quality of factors of production. In practice, it has proved quite difficult to offer reliable estimates for the importance of embodied and dimbodied technological progress. 银行金卡
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