Economic growth, energy prices and technological innovation.

Joutz, Frederick L.

I. Introduction

Energy economists are repeatedly asked to analyze the short run and long run macroeconomic effects of energy price shocks. We examine the effect of energy prices in a dynamic model of economic growth as a function of capital, labor, energy prices, and technological innovation. Our approach extends earlier studies in two ways. First, we depart from the standard approach of modeling strictly in either levels or differences by using an error correction model. The advantage of this approach is that both short run and long run information is used in the model. Second, we construct a measure of technological innovation with patent filings. Typically, deterministic trends have been used to capture technological growth. The increase in energy efficiency since 1974 has been due to energy conservation and improvements in energy intensive capital stock and production processes. We try to simultaneously use energy prices and technological innovation in a model of macroeconomic growth.

If energy price symmetry is imposed, we conclude that the short run energy price effects are approximately half the long run energy price effects. When the restriction is relaxed short run price symmetry does not hold. In particular, short run price increases are associated with economic downturns while short run price declines have no significant impact on economic activity. Also, the results show that technological innovation, measured through the stock of patents, contributes both directly to economic growth and indirectly through improvements in the economy's capital stock.

Section II briefly reviews empirical and theoretical research on energy and economic activity. The use of patents as measures of technological innovation and their relationship to macroeconomic growth are discussed in section III. In section IV we present a model of macroeconomic growth with technological change and empirical results are presented in section V. The conclusion follows.

II. Energy and Macroeconomic Growth

The U.S. GDP to energy consumption ratio (billions of 1987$ to quadrillion BTUs) and the relative price of composite energy are plotted annually from 1949 to 1991 in Figure 1. (The data is described in Appendix A.) There are two distinct periods, pre- and post-1974. The efficiency of aggregate energy use rose in the first half of the 1950s, fell in 1955 and remained steady until 1966. At this point energy use increased relative to GDP until 1970, when it leveled off for three years. During the period 1949 to 1970 the relative energy price experienced no major fluctuations. Figure 2 contains plots of the level and growth rate of the relative energy price. Between the first oil price shock in late 1973 and 1982 the relative composite energy price increased 500%. Energy efficiency rose slowly; it took from 1974 to 1979, the second oil price shock, to reach the efficiency level of 1955. Since then aggregate energy efficiency has increased by 25%. The relative composite price started falling in 1983 with a major collapse of nearly 40% in 1986, the third oil price shock. Since then energy efficiency has remained steady.

Douglas Bohi [2] conducted a comprehensive study of energy price shocks and macroeconomic performance. His approach employed a traditional static model of growth and cross-section data. He tested whether the three energy price shocks of 1973, 1979, and 1986 had an important effect on output and employment in the United States and other industrialized countries. He finds little support for the conventionally assumed importance of energy prices in explaining aggregate economic performance. He concludes that energy's share of GNP is too small to account for the large fluctuations in economic activity and that macroeconomic stabilization policies may shoulder the blame.

John Tatom [28; 29; 30] tests the hypothesis that the effect of oil price declines are asymmetric to those of oil price increases. He begins by addressing the theory of economic effects of oil price shocks. He addresses the following issues (1) whether oil price shocks are transitory, (2) whether capital obsolescence is important, (3) whether adjustments are symmetric in response to price changes, and (4) role of domestic oil production.

On the aggregate supply side, Tatom finds that following an oil price increase the resulting effects go beyond a simple increase in the cost of output, as standard theory predicts. In addition, the shocks alter the incentives to employ energy resources and alter the optimal methods of production. These incentives are reversed during an oil price decrease leading to a symmetric analysis. The basic outcome when energy prices rise is a higher price level, lower output, lower real wages, and, over time, a reduced capital stock relative to labor.

He attacks the argument that firms react differently to an energy price cut than a price rise, because this view ignores maximizing behavior, a firm's self-interest in efficiency, and pressure from competitors. He states that at best any difference in a firms behavior is a matter of timing. In contrast, Hamilton [14] offers a theoretical rationale for asymmetric behavior in his paper on unemployment and the business cycle.

Tatom claims that the argument asserting that the domestic oil industry impacts dominate other industries is overstated. This confusion arises as a result of the slow change in unemployment. The shock initially affects productivity and supply, which result in supply outracing demand changes. Thus, the inventory buildup/drawdown creates pressure on prices and cyclical pressure on unemployment.

Timothy Considine [6] develops a neoclassical model to look at the impact of the 1986 collapse in energy prices on the macroeconomy. The economic performance following the 1986 price drop challenged three existing paradigms of energy price interactions.

His first challenge was to the view that since world oil reserves are fixed and that as consumption rises oil prices will increase faster than overall inflation. Considine points out that real oil prices from 1859 to 1986 have resembled a random walk and argues the 1986 plunge was a correction to the price increases in 1979-1981.

The second challenge was to the idea that lower oil prices are unambiguously "good" for the U. S. economy. Based on numerous accepted studies showing higher energy prices leading to higher inflation, lower output, and higher unemployment, symmetry would call for lower oil prices to generate economic "benefits". With the data from 1986 showing only minor benefits Considine asks whether other factors offset the presumably stimulative effects of lower oil prices or is the macroeconomic response asymmetric? He concludes that other factors, like the fall in output and the unemployment increase in the energy sector offset the assumed positive effects. In 1986 the combination of a 3 percent fall in domestic petroleum's production, a 4 percent decline in natural gas' production, and the increase in the trade deficit's reduced the macroeconomic response to the energy price drop.

His third challenge is that large increases or decreases in energy prices impose adjustment costs on the economy. The common wisdom was that resource allocation may take time due to delays in obtaining information. As an example of informational delay laid off workers in the oil industry remained in the oil producing region(s) anticipating the layoff as a temporary downturn and expecting imminent rehiring. After the extended downturn and displacement, experienced workers were reluctant to return to the fields when the oil industry recovered, because they feared the upswing would be temporary. Similar bottlenecks were observed in investment resources. Considine classifies adjustments as either consumer spending, producer decisions, or wage and price adjustment and notes that these adjustments are intertwined with monetary and fiscal policies. He concludes that for offsetting reasons the adjustment costs are low.

Hamilton [15] finds that oil price "shocks" proceeded seven of the eight post World War II recessions by about three-quarters of a year. (If data through 1991 is added the record runs to eight of nine recessions.) He finds that the oil price shocks are best interpreted as events exogenous to the U.S. economy. Hamilton concludes that they are contributing factors to the duration and depth of the recession(s), but not necessary or sufficient conditions.

Mork [20] modifies Hamilton's choice of oil price to remove oil price control distortions and expands the sample to include the negative oil price shock in 1986. He continues to find a strong correlation between oil prices and macroeconomic activity. Furthermore, he finds evidence in favor of an asymmetric response; there is a relatively large negative response of output to positive price shocks and an insignificant response to price declines. Both authors estimate VAR models so that elasticities are not computable.

III. Patents, Technological Innovation, and Macroeconomic Growth

Griliches, Pakes, and Hall [13] and Schmookler [26] argue that patent applications are a valuable resource for the analysis of innovative activity. A brief discussion of the advantages and disadvantages in using patent data is provided in this section.

We feel it is a better proxy than just R&D expenditures for three main reasons. First, there is a measurement problem with the R&D data. Cordes [7] finds that reporting of R&D expenditures varies by company size and tax policy. Second, the expenditures are more properly thought of as inputs to technological change while patents are an output. Third, the applications data captures valuable economic information. Firms have decided to invest resources in developing a technology or modifying an existing one. Their initial investment has produced a product or innovation which they feel has economic value, thus they are willing to submit the application to earn the rents from their effort.

Griliches [12] agrees that patents (grants) are an imperfect indicator of inventive input or output. All inventions do not result in patents and patents vary considerably in their economic impact. We argue that the same holds true for R&D expenditures. He does argue that the aggregate count of patents can serve as a measure of shifts in technology.

The use of patent data in growth modeling is controversial. Archibugi [1] reviews the value of patents as an indicator of technological change. She concludes that, "Patents are a fascinating indicator because they lead the analyst into the process of invention and innovation. They can help to gather information on the intangible phenomenon that is knowledge: a fact which leads a growing number of scholars to optimism about their employment. As any indicator, patents are full of traps, some of which can be avoided by careful use. But it is difficult to persuade the platoons of skeptics on their validity. Their criticism is often bitter, but it plays an important role in preventing the misuse of the indicator and forces the analyst to test and improve the quality of their data. However in return, they are entitled to ask their critics to provide better measures, if they can."

In this paper we measure technological innovation using patent applications rather than patent grants by date of issue. A complete series of patents granted by date of application was unavailable. We try to avoid or account for trap(s) in the relationship between the capital stock and the technology stock in the model specified below.

The technology stock variable calculated using patent filings and real GDP are displayed in Figure 3. The two series move closely together throughout the sample. However, there appears to be a stronger relationship through 1970. Real GDP has increased nearly 270% from 1950 to 1991 while the technology stock has increased only 90% over the same period. This suggests a simple 3:1 relationship between real GDP and patent measure of technological innovation. Average annual GDP growth over the sample is slightly above 2.7 percent. Growth accounting studies by Denison [8] and Kendrick [18] suggest technological innovation contributes only about one per cent to economic growth.

IV. A Model of Output and Economic Growth

Saunders [24; 25] addresses the different paradigms between short and long run effects of energy shocks using a theoretical model. He contends that in the short run people generally consider an effect on the economy to be dramatic, resulting in "inflation, recession, unemployment, inertia in the capital stock, and myopia of economic agents." While in the long run a relatively weak effect is observed where these same economic agents have the foresight to adjust the capital stock, and balanced growth paths exist and optimal growth theory holds.

Saunders reconciles these dichotomous views by extending the usual two factor optimal growth theory to include energy as a factor of production and notes the bridge between the two paradigms is investment and factor competition. He shows the transition from short to long term through a simulation model. In this study we have taken Saunders basic model and tested it with the use of real data. We do not distinguish between price changes and price shocks.

We employ a traditional aggregate production function except we replace deterministic trends with the stock of technological change.

[Y.sub.t] = f ([L.sub.t], [K.sub.t] [Pe.sub.t], [A.sub.T]) (1)

where [Y.sub.t] is real GDP, [L.sub.t] is total civilian employment, [K.sub.t] is lagged real private and public capital stock, [Pe.sub.t] is the real composite price of energy, and [A.sub.t] is the lagged stock of total application filings at the U.S. Patent and Trademark Office. The real price term enters through a "first order condition" for energy "employment" as in papers by Rasche and Tatom [23], Tatom [28; 29; 30], and Bohi [2]. The stock of patent filings represents the stock of technological innovation in our model.(1) The output, capital stock, and relative composite energy price series are in 1987 dollars.

We propose the following functional form

[Mathematical Expression Omitted].

The last term is a random disturbance. An interactive term, [e.sup.[A.sub.t]][K.sub.t], is included to capture embodied technological change in the capital stock. This measures the relative quantity versus quality spill-over effects. If the coefficient, [[Beta].sub.3], is positive, there are quality spillovers. A negative sign suggests that quantity spillovers dominate. This implies that there is "double counting" in the capital stock variable. The later embodies technical innovations as firms invest in equipment and structures which are more efficient. Thus, there are direct and indirect effects from technological innovation. The diffusion and impact of technological change is assumed to be nonlinear.

Traditionally, the model is estimated by taking natural logarithms and applying ordinary or restricted least squares to impose constant returns to scale.

[y.sub.t] = [[Beta].sub.0] + [[Beta].sub.1][l.sub.t] + [[Beta].sub.2][k.sub.t] + [[Beta].sub.3][k.sub.t][A.sub.t] + [[Beta].sub.4][pe.sub.t] + [[Beta].sub.5][a.sub.t] + [[Epsilon].sub.t] (3)

Lower case letters represent variables in natural logarithms and upper case are in levels. A white noise error term, [[Epsilon].sub.t], captures the unexplained movements in output. The classical statistical assumptions of stationary stochastic data generating processes are violated with most macroeconomic data and these series are no exception. Nelson and Plosser [21] have suggested that macroeconomic series are driven by stochastic trends. These processes are said to have a unit root in their autoregressive representation or to be integrated of order one, I(1). Simple first differencing of the data will remove the nonstationarity problem, but with a loss of generality about the long run relationships among the variables.

Engle and Granger [11] solve this filtering problem with the cointegration technique. They suggest that, if all or a subset of the variables are I(1), there may exist a linear combination of the variables which is stationary, I(0). Despite the fact that each of the series has no affinity for a mean value and trend away from their initial values, they may be linked together in long run relationships. When this is true, the variables are said to be cointegrated. The new series [z.sub.t], the estimated residual from equation (3), represents the deviation between the current level and the level based on the long-run relationship.

[z.sub.t] = [y.sub.t] - [[Beta].sub.0] - [[Beta].sub.1][l.sub.t] - [[Beta].sub.2][k.sub.t] - [[Beta].sub.3][k.sub.t][A.sub.t] - [[Beta].sub.4][pe.sub.t] - [[Beta].sub.5][a.sub.t] (4)

Series which are cointegrated can always be represented in an error correction model. The growth rate of output is a function of the growth rates in labor, capital stock, the technology embodied in the capital stock, energy prices, stock of technology, plus the error correction term. The latter represents the deviation of actual output from the predicted level from the production function.

[Delta][y.sub.t] = [[Pi].sub.0] + [[Pi].sub.1] [Delta][l.sub.t] + [[Pi].sub.2][Delta][k.sub.t] + [[Pi].sub.3][Delta][pe.sub.t] + [[Pi].sub.4][Delta][a.sub.t] + [[Pi].sub.5][z.sub.t-1] + [u.sub.t] (5)

Lags of the independent and dependent variables are often included to capture additional short and medium term dynamics of growth. The advantage of the model in this form over that in equation (3) is that the model is stationary so that estimation and statistical inference can be performed using standard statistical methods. The contemporaneous coefficients are interpreted as short run elasticities. The coefficient on the ECM term represents the speed of adjustment back to the long run equilibrium relationship among the variables.

V. Empirical Results

In this section, we present the empirical results from tests for stationarity, cointegration, the dynamic model, and tests for symmetry in the output elasticity with respect to energy prices. Plots of the data suggested that the series were nonstationary and could contain unit roots in their autoregressive representations. We follow Campbell and Perron's [4] rules (of thumb) for investigating whether these series contain unit roots. To begin, we estimate the following three forms of the augmented Dickey-Fuller (ADF) test where each form differs in the assumed deterministic component(s) in the series:

[Delta][Y.sub.t] = [[Alpha].sub.1][Y.sub.t-1] + [summation of] [[Beta].sub.i][Delta][Y.sub.t-i] where i=1 to p + [[Epsilon].sub.t] (6.1)

[TABULAR DATA FOR TABLE I OMITTED]

[Delta][Y.sub.t] = [[Alpha].sub.0] + [[Alpha].sub.1][Y.sub.t - 1] + [summation of] [[Beta].sub.i] [Delta][Y.sub.t-i] where i=1 to p + [[Epsilon].sub.t] (6.2)

[Delta] [Y.sub.t] = [[Alpha].sub.0] + [[Alpha].sub.1] [Y.sub.t-1] + [[Alpha].sub.2]t + [summation of] [[Beta].sub.i][Delta][Y.sub.t-i] where i=1 to p + [[Epsilon].sub.t]. (6.3)

The [[Epsilon].sub.t] is assumed to be a white noise disturbance. In the first equation there is no constant or trend. The second contains a constant but no trend. Both a constant and a trend are included in the third equation. The number of lagged differences, p, is chosen to insure that the estimated errors are not serially correlated.

Table I presents the unit root test results following equations (6.1), (6.2), and (6.3). Real GDP, employment, and the capital stock are difference stationary with a constant term included. Equation (6.2) appears to be the relevant model for output. The F-test for an insignificant constant and lagged level (row 3 - column 3) is rejected with a value 32.29. The t-ratio for the coefficient on the lagged level, -1.86, is not less than the critical value, therefore, the null hypothesis of a unit root cannot be rejected. Labor and the capital stock also appear to follow a random walk with drift. The relative price of energy, the capital stock of innovations, and interaction term follow random walks without drift or trend.

The cointegration test procedure follows the maximum likelihood approach recommended by Johansen and Juselius [16]. We begin by modeling all the variables in a VAR system:

[x.sub.t] = [[Pi].sub.0] + [[Pi].sub.1] [x.sub.t-1] + . . . + [[Pi].sub.k][x.sub.t-k] + [[Epsilon].sub.t]. (7)

In this case x is a (p x 1), where p = 6, vector of nonstationary I(1) variables and the [[Pi].sub.i] are (p x p) coefficient matrices at different lags. [[Pi].sub.0] is a (p x 1) vector of constant terms; it could include other deterministic components like trend terms. The disturbances are assumed to be white noise. The system in levels can be transformed to one in differences and the error correction term without loss of generality.

[Delta][x.sub.t] = [[Pi].sub.0] + [[Gamma].sub.1] [Delta][x.sub.t-1] + . . . + [[Gamma].sub.k - 1] [Delta][x.sub.t-k+1] + [Pi][x.sub.t-k] + [[Epsilon].sub.t],

where

[[Gamma].sub.i] = - I + [[Pi].sub.1] + . . . + [[Pi].sub.i]; [for every]i = 1, . . ., k-1,

and

[Pi] = - I + [[Pi].sub.1] + . . . + [[Pi].sub.k] (8)

Table II. Cointegration Analysis on the system of y, l, k, pe,
[e.sup.A] x k, and a

p - r [Lambda] maximal eigenvalue trace statistic

0 0.65 43.02 100.72
1 0.55 32.95 57.69
2 0.29 14.27 24.74
3 0.19 9.07 10.47
4 0.03 1.40 1.40
5 0.2e - 3 0.007 0.007

The number of cointegrating vectors in the hypothesis tests are
given by p, the number of variables, minus r, the reduced
dimension of the system.

The rank of the matrix for the level terms, [Pi], is of reduced rank when cointegrating relationships exist. In that case it can be partitioned as [Pi] = [Alpha][Beta][prime] where [Alpha] is the (p x r) matrix of speed of adjustment coefficients and [Beta] is the (p x r) matrix of cointegrating vectors or long run relationships. Cointegration testing and the maximum likelihood estimation of [Beta] is derived from a series of regressions and reduced rank regressions. Linear hypotheses on the cointegrating vector(s) like constant returns to scale or price elasticities can be conducted using the [[Chi].sup.2]-distribution.

Table II presents the results from a multivariate cointegration test on the six variables employed in our study: y, l, k, pc, [e.sup.A] x k and a. We employ the Johansen procedure to test for cointegration. One lag in differences were used in the model; the system lag length was determined by the Schwartz Criterion and the Akaike Information Criterion. The first column gives the null hypotheses of more than p - r = 0, 1, 2, 3, 4, or 5 cointegrating vectors. When there are no cointegrating vectors, p - r = 0, the model in differences is appropriate. The results from the maximum eigenvalue and trace statistics indicate the presence of a single cointegrating relation based on the critical values from Osterwald-Lenum [22, Table 1].

Below we focus only on the output equation, because the employment, capital stock and relative energy price series appear to be weakly exogenous. There is marginal evidence rejecting weak exogeneity for the stock of innovation. Granger causality tests using all the variables found feedback between output and the technology stock. In that case the hypothesis of strong exogeneity of the technology stock is rejected. This result is consistent with Schmookler's findings that invention and innovation are demand driven [26]. Also, it reflects the supply and demand interpretations attributed to technological innovations (stock of patent activity) with GDP. The long run model estimates for the period 1950-1991 are:

[Mathematical Expression Omitted].

Variables in lower case are in natural logarithms, upper case are in levels. T-statistics are reported in parentheses. While we cannot draw much inference from this model there are several interesting points. The assumption of constant returns to scale is rejected. However, the ratio of the labor coefficient to the capital coefficient is "close" to the 2:1 ratio often found in the conventional models.

The long run elasticity of output with respect to energy price is slightly higher than that found by Tatom [30] and other authors, minus 7 percent vs. minus 6 percent. The interactive term with technology embodied capital stock is negative. This is consistent with the hypothesis that greater efficiency or technological diffusion decreases the capital input requirements given labor and energy. The effect of technological innovation falls between estimates by Denison [8] of 1% and Jorgenson [17] of 0.7%.

The estimated residuals from the cointegrating regression above are used as the ECM in a model of short run economic growth. In this model, there is a single price change variable, in effect symmetry is imposed. The estimated residuals from models using a depreciation rate of 15% and 4% are plotted in Figure 4. There are no significant differences in the model fit or coefficient estimates, suggesting the results are fairly robust. We reduced the first order autoregressive distributed lag model to the following by deleting insignificant variables.

[Mathematical Expression Omitted]

(di denotes the growth rate of the variable i)

[RBAR.sup.2] = 0.7463 SE = 1.16 D.W. = 1.93

LM Chi-Square Statistic for Serial Correlation with 12 lags is 9.49 with 12 dof

Heteroskedasticity tests (p-values in parentheses)

Breusch-Pagan Godfrey test = 6.0 with 6 dof (0.42)

Harvey test = 3.9 with 6 dof (0.69)

Glejser test = 4.6 with 6 dof (0.60)

ARCH test (4 lags) = 0.48 with 1 dof (0.99)

Jarque-Bera Asymptotic LM Normality Test Chi-Square 0.9655 with 2 dof

The ECM term is negative as theory predicts. A deviation from long run growth this period is corrected by about 30% in the next year. The immediate impact of changes in employment growth and capital stock growth are positive. There is a slowdown in the following year, but the overall effect on output is positive. The output elasticity effect of a change in the relative energy price is about half that of the long run impact. Technological innovation in the short run does not have an immediate effect on output growth.

The growth model's predictive power denoted by [RBAR.sup.2] is a respectable 0.75. Tests for autocorrelation of the residuals at lag one through lag twelve are rejected. The null hypothesis of no heteroskedasficity cannot be rejected using the Breusch-Pagan-Godfrey, Harvey, Glejser, and ARCH tests. The recursive Chow test procedure did not reveal any structural breaks in the model at 5 percent, but there appears to be some model instability at 10 percent between 1974 and 1980.

When we divided the price variable into a positive price change vector, dpup, and a negative price change vector, dpdown, the symmetry hypothesis is rejected. The likelihood ratio statistic of 7.8 with one degree of freedom is significant at one percent. We tested if the growth in the innovation and technology, Ak and a, contributed to the short run model's fit by adding the current and lagged values.(2) The null hypothesis of no explanatory power could not be rejected using either the Wald Chi-square test or the individual t-statistics. Below are the results.

[Mathematical Expression Omitted]

(the constant was included, but was insignificant)

[RBAR.sup.2] = 0.7922 SE = 1.05 D.W. = 2.11

LM Chi-Square Statistic for Serial Correlation with 12 lags is 11.2 with 12 dof

Heteroskedasticity tests (p-values in parentheses)

Breusch-Pagan Godfrey test = 10.9 with 7 dof (0.14)

Harvey test = 3.8 with 7 dof (0.80)

Glejser test = 6.9 with 7 dof (0.43)

ARCH test (4 lags) = 3.0 with 1 dof (0.89)

Jarque-Bera Asymptotic LM Normality Test Chi-Square 1.37 with 2 dof

The labor and capital coefficients are barely changed. The lagged capital growth rate is slightly more positive and significant. The ECM coefficient is the same as in the case where symmetry is imposed. However, the output elasticity with respect to price increases, dpup, is minus 7.9 percent, numerically larger than the long run elasticity, although not statistically. The response to negative price shocks is insignificant from zero. Output falls in the short run in response to energy price increases, but is not affected by energy price declines. The Wald Chi-square statistic that the coefficients are equal and of opposite sign is 4.13 with a p-value of 0.042.

The [RBAR.sup.2] is higher and the variance from this model is significantly lower than the model where symmetry is imposed. Thus, based on variance, the model with asymmetric price responses variance dominates the first model. There continues to be no problem with heteroskedasticity or autocorrelation. Furthermore the recursive Chow tests for model stability are not rejected at 10 percent. This model provides a better fit and is more robust than the model where symmetry is imposed. This result is similar to that found by Mork [19; 20].

VI. Conclusion

Economic growth is modeled as a function of labor, capital stock, energy prices, and technology stock. An ECM approach is used to depart from the standard approach of modeling strictly in either levels or differences. The advantage of the ECM approach comes from the ability to incorporate both short run and long run information in the model. Also, a measure of technological innovation is constructed using patent data to replace deterministic trends. Efficient estimates of output elasticities are obtained.

We find that the short run output elasticities with respect to energy price are half the long run price effects when a symmetric response is imposed. However, we conclude that the output response to energy price increases and decreases is asymmetric in the short run. Positive price shocks lead to a slowdown in economic growth while energy price declines have no significant impact on aggregate output.

The stock of patents contributes directly to economic growth and indirectly through the economy's capital stock. Our estimate of the output elasticity with respect to technological innovation is 0.9 per cent. The estimate is consistent with previous research.

Our model of economic growth does not include government policy and international trade. These two factors may account for the lack of response as suggested by Bohi [2]. Future research can examine the issues relating to human capital and technology and the output-technology stock feedback relationship.

Appendix A. Description of the Data

We use annual data from 1949 through 1991 in this study. The macroeconomic data series in this study are GDP, total civilian employment, capital stock. All nominal series are converted to real 1987 dollars using the GDP implicit price deflator. The GDP and employment data came from Citibase [5] and The Economic Report of the President [9].

The capital stock is published in the Survey of Current Business (October, 1992) [27]. We use the sum of both public and private total capital stock. The share of private capital stock as a percentage of total stock increased from 52% to 65% over the sample.

The total energy consumption series is measured in quadrillion Btu. The composite nominal price of total energy consumption is also deflated by the 1987 GDP implicit price index. The source for the quantity and price energy data is the U.S. Energy Information Administration's Annual Energy Review - 1991 [10, 25, 69].

Patent and R&D data came from the U.S. Patent and Trademark Office [31; 32]. Patent fillings and patent grants starting in 1837 to 1991 are used to construct technology stock variables. They are created using an assumed 15% depreciation factor in the following form:

[Stock.sub.t] = [(New Filings).sub.t] + [Stock.sub.t-1] x (1 - d) where d = 0.15.

1. We tried several capital stock measures using different depreciation rates. The reported results are based on the assumption of a 15% declining balance formula used by Griliches [12, 1701). In addition we used a 4% depreciation rate reported by Cabellero and Jaffee [3]. However, they estimate that depreciation rates had increased over time and were in the 12-15% range during the 1980s. The 15% depreciation rate suggests that the stock of knowledge is doubling every 7 years. Gus Mastrogianis from the U.S. Patent and Trademark Office claims this is consistent with anecdotal evidence.

2. Recall that the levels of the capital stock and technological stock variables are already lagged one period to reflect the stock(s) in place.

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