Actual Capital Stock Research Articles

Tobin's q and U.S. inflation

A smaller than 1 Tobin's q has been frequently observed for the postwar U.S. economy. In theory, Tobin's q less than 1 would discourage investment. However, actual capital stock has grown during this period. This paper proposes inflation besides Schumpeterian innovation as an explanation for this apparent paradox. A stylized IS-LM model along the lines of Tobin–Brainard shows that inflation affects Tobin's q. Employing U.S. data from 1953 to 2000, we find a negative strong relationship between Tobin's q and inflation. Vector error correction models (VECM) confirm the long-run relationship and suggest a very fast rate of adjustment to the steady-state in some specifications. Overall, price movements have a long-run negative impact on Tobin's q.

Soft computing applications to estimate the quantitative contribution of education on economic growth

First, this article softly categorizes a target system (a country or a region) according to the level of Science and Technology (S & T) progress. We calculate potential human capital stock and actual human capital stock in the same cluster, and set up the internal correlation between them (fuzzy reflection). Second, we conceptualize actual human capital as one production factor, joined with the other two production factors, land and technology, to set up the fuzzy mapping to economic growth. Finally, we obtain the economic contribution rate of education (ECRE) through two marginal rates, namely marginal economic growth to actual human capital stock, and marginal actual human capital to potential human capital. This method greatly reduces the bias in the ECRE that results from the indirect and lagged effects of education. It therefore identifies the effect of education on economic growth more explicitly. Based on the level of science and technology progress, 31 provinces in China could be classified into three clusters. The first cluster (Developed S & T) has an ECRE of 11.60%, and contains two provinces; the second cluster (developing S & T) has an ECRE of 8.84%, and contains 11 provinces; the third cluster (underdeveloped S & T) has an ECRE of 1.49% and contains 18 provinces.

A Hicksian multiplier-accelerator model with floor determined by capital stock

This article reconsiders the Hicksian multiplier-accelerator model with the “floor” related to the depreciation on actual capital stock. Through the introduction of the capital variable, a growth trend is created endogenously by the model itself, along with growth rate oscillations around it. The “ceiling” can be dispensed with altogether. As everything is growing in such a model, a variable transformation is introduced to focus relative dynamics of the income growth rate and the actual capital output ratio.

Estimation on Regional Benefit and Optimal Level of Road Capital Stock

This paper measures the regional benefit of road investment in Korea, using the translog cost functions of the manufacturing industry for the four macroregions of Seoul Metropolitan Area, South-Eastern Area, South-Western Area, and Central Area. This paper shows that the road capital contributes significantly to the productivity of the manufacturing industry in the sense that the magnitude of the road capital stock elasticity of the production cost at the national level is -0.0124. The net social rate of return for all regions is higher than the yield of corporate bonds, which implies that the road capital stock is undersupplied in Korea. The ratio of optimal to actual road capital stock declined from 1986 to 1991, and then increased in all regions except Seoul Metropolitan Area since 1992. In order to generate economic efficiency and regional equality, it is necessary to increase road capital investment in the less developed regions of Korea, such as the South-Western Area and the Central Area.

Economies of scale and optimal capital in nuclear and fossil fuel electricity production

This paper tests for economies of scale in the electric utility industry using a five-year panel data set that includes both fossil fuel and nuclear fuel electricity generation. In addition, a variable cost function is used as opposed to a total cost function because the assumption of cost-minimizing production inputs is not met. That is, electric utilities are overcapitalized. Therefore, the optimal capital stock is estimated, which is significantly less than the actual capital stock, and an estimate of economies of scale is generated. Evidence suggests that firms are operating on the negatively sloped portion of the long-run average cost curve near the trough. This indicates either slight economies of scale or no economies of scale.

Irreversible investment and the expected capital stock with stationary uncertainty

The paper analyses irreversible investment under stationary uncertainty in a competitive sector. It is shown that while future uncertainty reduces the desired capital stock, over time the expected actual capital stock is higher under uncertainty with irreversibility.

Technical change and irreversible investment under risk

Abstract A stochastic dynamic model was constructed to analyze investment decisions of an individual farmer under risk in the presence of irreversibilities, embedded technical change and indivisible capital. An analytical solution was obtained and its local behavior studied by numerical methods. Optimal investment is obtained by regulating the difference between the desired and actual capital stocks between two barriers that define an inaction interval. While the desired capital drifts between the barriers, no action is taken. If the desired capital touches the upper barrier, the farmer invests pushing the average efficiency of the actual capital stock up. This in turn raises the desired capital even higher and contracts the inaction interval. If these effects are strong enough, the farmer will invest again until the potential gains of the technological package are exhausted. If the desired capital falls enough, the farmer disinvests, pushing down the average productivity and expanding the inaction interval. Disinvestment continues until it stops either because the inaction interval becomes so wide that it is no longer optimal to disinvest or because the actual capital stock is so small that it is no longer profitable to produce.

Technical change and irreversible investment under risk

AbstractA stochastic dynamic model was constructed to analyze investment decisions of an individual farme under risk in the presence of legibilities, embedded technical change and indivisible capital. An analytical solution was obtained and its local behavior studied by numerical methods. Optimal investment is obtained by regulating the difference between the desired and actual capital stocks between two barriers that define an inaction interval. While the desired capital drifts between the barriers, no action is taken. If the desired capital touches the upper barrier, the farmer invests pushing the average efficiency of the actual capital stock up. This in turn raises the desired capital even higher and contracts the inaction interval. If these effects are strong enough, the farmer will invest again until the potential gains of the technological package are exhausted. If the desired capital falls enough, the farmer disinvests, pushing down the average productivity and expanding the inaction interval. Disinvestment continues until it slops either because the inaction interval becomes so wide that it is no longer optimal to disinvest or because the actual capital stock is so small that it is no longer profitable to produce.

The Unique "Rent Defined" Capital Input Assumption in Investment Theory

Jorgenson [14; 15; 16; 17; 18; 19] and associates [10; 11; 12; 22], along with others [1; 2; 3; 6; 8; 9] have discussed a neoclassical investment theory in which there is a unique input of capital services. Investment is a function of the difference between the capital stock required to provide these services (usually considered proportional to the services to be provided) and the actual capital stock. The idea that there is an optimal capital input is derived from neoclassical factor demand theory in which profit maximizing firms constrained by a regular or strictly quasiconcave production function employ a single unique capital input for a particular set of factor prices and output. While the neoclassical investment theory is subject to many objections [1; 27]), this paper will concentrate on a very simple one that has not been discussed. It will be argued that there is not a single desired capital stock or input of capital services for the rent-based definition of capital services neoclassical writers use. This simple observation makes irrelevant both the research on the lag structure for the adjustment of the rent measured capital stock to its desired value and the research on the costs of adjusting the rent measured aggregate capital stock to the desired value.

The Long-Run Creditworthiness of Developing Countries: Theory and Practice

This paper analyzes the determinants of developing country long-run creditworthiness, focusing on the process of capital accumulation relative to external debt. Creditworthiness depends on the actual capital stock compared with a critical level, representing the gross wealth just sufficient to ensure that interest payments to foreigners never exhaust national output given expected gross inflows and existing outstanding debt. Hence, the probability of rescheduling is linked to debt service-capital, net inflows-capital, investment rates, and income levels. The empirical results, based on a probit analysis of historical rescheduling incidents, are quite robust and supportive of the theoretical framework.

Tax Incentives, Stabilization Policy, and the Proportional Replacement Hypothesis: Some Negative Conclusions

analyzed gross investment as the sum of two components: 1) net investment by which firms adjust their actual capital stock toward a desired level and 2) replacement investment proportional to the actual capital stock.1 There has now been substantial discussion about the specification of the desired capital stock and about the dynamics of adjustment to this desired capital stock (e.g., [1; 2; 4; 6; 8; 10; 15; 21; 25]). The current paper deals instead with the second component of aggregate investment demand, the replacement investment. The proportional replacement hypothesis (P.R.H.) incorporated in previous studies has important implications about the response of gross investment to tax incentives. By definition it indicates that an initial increase in net investment is followed immedi-

A Disequilibrium Neoclassical Investment Function

M ODERN investment functions, springing from the work of Jorgenson,' differ from earlier investment functions in that they start with an explicit assumption about the economy's aggregate production function. In particular, Jorgenson assumes a Cobb-Douglas production function. Starting with an explicit production function means that it is possible to calculate algebraically the impact of factors, such as interest rates, that could not be isolated in earlier investment functions. Choosing the correct production function is important in estimating partial effects, but the proper definition of the cost of capital variable is also central to their correct estimation. Formulations other than those of Jorgenson are possible. If one had priors about the differences in the opportunity cost of capital under the Duesenberry supply of funds hypothesis,2 the cost of capital could be defined to embody these priors. Doing so would lead to different estimates of the partial effects of tax rates, interest rates, and depreciation policies. Thus, the partial effects that emerge from a modern investment function are a product of the initial specifications of the production function and the cost of capital variable. In addition to choosing the correct production function and the correct definition of the cost of capital, there are other directions in which the modern investment function can be modified. In Jorgenson's neoclassical equilibrium world the cost of capital and the marginal product of capital are always identical. Thus, the desired capital stock at any moment of time is equal to output divided by the marginal product of capital (the cost of capital) multiplied by the elasticity of output with respect to capital. Thus, the only problems are ones of correct data measurement and estimation of the lag structure. This formulation has some theoretical problems. Introducing lags means that the economy is not in equilibrium. actual capital stock lags behind the desired capital stock. Therefore, the cost of capital and the marginal product of capital are not equal. Even if they were equal, the marginal product of capital will differ before and after expansion of the capital stock. Thus output should be divided by the expected cost of capital rather than the actual cost of capital to determine the desired capital stock.3 In a disequilibrium world, the cost of capital and the marginal product of capital can diverge. Profit maximizing firms invest to eliminate the gap between the marginal product of capital and the cost of capital. investment necessary to eliminate this gap depends upon the economy's production function. This paper investigates a disequilibrium investment function based on a Cobb-Douglas production function and Jorgenson's definition of the cost of capital. I was led to investigate such a model in the process of attempting to use the Jorgenson investment function.4 Several problems emerged in addition to those investigated elsewhere.5 (1) Although the Jorgenson investment function fit quarterly time series data for producers' * author would like to thank the referee for many useful comments. 'Dale W. Jorgenson, Anticipations and Behavior, in J. S. Duesenberry, E. Kuh, G. Fromm, and L. R. Klein (editors), Brookings Quarterly Econometric Model of the United States (Chicago: Rand McNally, 1965). Rational Distributed Lag Functions, Econometrica, XXXIV (Jan. 1966), 135-149. With Calvin D. Siebert, A Comparison of Alternative Theories of Corporate Behavior, American Economic Review, XVIII (Sept. 1968). Optimal Capital Accumulation and Corporate Behavior, Journal of Political Economy, LXXVI (Nov./Dec. 1968), 1123-1151. With J. A. Stephenson, The Time Structure of Behavior in United States Manufacturing, 1947-60, this REvIEw, XLIV (Feb. 1967), 16-27. Investment Behavior in U.S. Manufacturing, 1947-60, Econometrica, XXXV (April 1967), 169-220. 2J. Duesenberry, Business Cycles and Economic Growth (New York: McGraw-Hill, 1968), 87-112. 3This was pointed out to me by my colleague Duncan Foley. 'Anyone wishing the detailed econometric results of my attempts to fit the Jorgenson model to producer's durable equipment and nonresidential structures can have them by writing to me. 'Robert Eisner and M. I. Nadiri, Investment Behavior and Neoclassical Theory, this REvIEw, L (Aug. 1968).

CAPITAL APPROPRIATIONS AND BUSINESS FIXED INVESTMENT IN MANUFACTURING: AN ECONOMETRIC ANALYSIS*

THE PURPOSE OF THIS STUDY is to examine a model of business fixed-investment spending in the context of a fully specified econometric model of income determination. Investment decisions are measured by appropriations for capital spending rather than by capital expenditures themselves. Although data on appropriations are restricted to the 1,000 largest manufacturing firms, this important subset accounts for virtually all of the variation of capital spending in manufacturing and a substantial portion of the variation of all business fixed-investment expenditures. The relationship between expenditures and appropriations is treated separately from the relationship between appropriations and the determinants of investment decisions. Appropriations are assumed to be determined in an internal (to the firm) market for investment funds. This view incorporates both accelerator and internal-funds theories of capital spending into the theoretical structure used to explain investment decisions. The relationship between expenditures and appropriations is treated as a simple linear distributed lag. The resulting two-equation investment system was estimated by ordinary least squares using annual first differences for total manufacturing and several constituent manufacturing industries. The results indicated fairly general support for the theoretical structure. Expansion requirements (the difference between desired and actual capital stock) and the subjective or internal cost of funds consistently appeared as significant determinants of appropriations. The long-term interest rate was not generally a significant determinant of appropriations, but did appear important in some individual industries. The results of the distributed-lag estimations indicated that it takes about three years for a dollar of appropriations to be fully realized in expenditures, though well over half of each appropriation dollar is phased into expenditures within a year and a half of the formal commitment. A set of estimated equations for total manufacturing which included the appropriations equation, the distributed-lag equation, and several linking equations was introduced into the University of Michigan Econometric Model of the U.S. Economy. The Michigan model was then used to generate ex post forecasts of important measures of economic activity for the period 1960 through 1965. The results indicated that the incorporation of the estimated investment system substantially improved the forecasting accuracy of the full system when compared with forecasts which relied solely on businessmen's anticipations of capital spending for projections of business fixed investment. Even though a measure of capital appropriations was available for only the 1,000 largest manufacturing firms, the accuracy in the prediction of capital expenditures in this important subset of firms was sufficient to improve the overall forecasts of economic activity.

A Stock-Adjustment Investment Model

Firms' investment in plant and equipment is explained by a stock-adjustment model in which the coefficient of adjustment is allowed to vary. It is assumed that firms partially close the gap between desired and actual capital stock, but that the speed of adjustment depends on the firm's ability to procure funds at reasonable cost. A panel of individual firm responses to the McGraw-Hill plant and equipment survey is the principal data source, supplemented by financial statement information for the firms and two indices representing costs of debt and equity financing. The predictions generated by the regressions are aggregated for comparison with the observed aggregates. 1. A STOCK-ADJUSTMENT INVESTMENT MODEL THE PURPOSE of this paper is to develop and test a model to explain firms' investment in plant and equipment. The model incorporates features which recent research on the investment decision suggests are significant. The basic framework is a stock-adjustment model, in which each year the firm moves partially toward its desired position, with the coefficient of adjustment (reaction coefficient) allowed to vary by firm and year. The model has the form

On a New Method of Capacity Estimation

Abstract Capacity is defined as that output which can be produced at minimum average total cost, given the existing stock of plant and equipment and existing techniques and factor prices. The level of capacity is inferred from observed investment behavior. Regression methods are used to estimate a relationship between desired capital stock and several explanatory variables including output, relative prices and time, on the hypothesis that net investment occurs in proportion to the excess of desired over actual stock. The relationship between desired capital stock and output is then inverted to yield a corresponding relationship between capacity and actual capital stock for given prices and techniques. The method is used to calculate aggregate capacity annually for 1949–60 and the properties of the resulting estimates are discussed. New estimates of capacity and its utilization in manufacturing are also presented and compared with those of other investigators.