THE SOURCE OF TEMPORARY TECHNOLOGICAL SHOCKS

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1 IJER, Vol. 9, No. 1, January-June, 2012, pp THE SOURCE OF TEMPORARY TECHNOLOGICAL SHOCKS XIANMING MENG University of New England, School of Business, Economics and Public Policy, University of New England, Armidale, NSW, ABSTRACT The real business cycle model mimics the economic fluctuation very well, but its explanation relies heavily on the unimaginable temporary technological shocks, especially the negative technological shocks. Through introducing a finite consumption theorem in the preference and utility theory, this paper explains the permanent and temporary technological shocks. The paper also has constructed a production function and growth model including innovations and estimated it by employing US time series data and DOLS method. The estimation results have verified the validity of the proposed model. JEL Code: E23, E12. Keywords: Technological shock, Innovation, Economic growth, Utility, Consumption. 1. INTRODUCTION The real business cycle model developed by Kydland and Prescott (1982) 1 mimics the American economic fluctuation quite well, which demonstrated that business cycles could be generated by technique shocks. However, it faces two problems. One is that, to explain the model results, it relies on a substantial intertemporal-substitution effect on consumption, saving and labour supply, which contradicts the empirical studies. In the absence of intertemporal-substitution effect, they had to assume that the changes in technology are temporary rather than permanent. The concept of temporary technological changes contradicts our basic understanding about technology and conflicts with any economic growth model, which shows that technology has significant positive and permanent effect on the economic growth of a nation. The other problem the real business cycle model faces is that, to explain economic recessions, it relies on negative technological changes, which is even more beyond our understanding. For example, Mankiw (1989) argued: If society suffered some important adverse technological shock, we would be aware of it. My own reading of the newspaper, however, does not lead me to associate most recessions with some exogenous deterioration in the economy s productive capabilities. To advocate this theory, they had to put forward some far-reaching examples, such as a natural

2 54 Xianming Meng disaster, a war, an oil shock and even a tightened monetary policy. Obviously, they are negative shocks, but none of them actually affect the technology level in a society. Decades have passed since the advent of the real business model, but these two problems have never been solved. Providing a satisfactory answer to them would not only perfect the real business model, but also may unearth the factors affecting economic growth and business cycles. The purpose of this paper is to uncover the sources of temporary and permanent technological shocks and derive a production function embodying them. The remainder of the paper is organized as follows: the next section introduces a finite consumption theorem in the preference and utility theory. Based on this theorem, the demand limitation and innovation scarcity in an economy are discussed. Section 3 derives an aggregate production function and thus a growth model including innovations. Section 4 provided an empirical testing for the proposed growth model. The last section concludes. 2. FINITE CONSUMPTION, DEMAND LIMITATION AND INNOVATION SCARCITY In the preference and utility theory we assume that, for any economic good X, more is preferred to less during the same period, and that the marginal utility decrease as the consumed goods increase, so we have a concave utility curve or indifference map shown as Figure 1. This the more the better assumption is easily understood and works well in ordinary situations, but not for extreme cases. Without constraint, this assumption will lead to unlimited utility when the quantity of economic goods becomes infinite. This extreme case should be excluded in an economic system for two reasons. First, it is unrealistic that one economic good can provide unlimited utility: no one can consume an infinite quantity of goods and no one can have infinite Figure 1 Utility of a Representative Individual in Current Utility Theory

3 The Source of Temporary Technological Shocks 55 utility. Second, it creates a theoretical problem of utility comparison, which we explain with the aid of Figure 1. The left panel of Figure 1 shows the utility function of consuming one economic good X and the right panel shows the utility indifference map of consuming two goods X and Y. In the left panel, it is apparent that the individual s utility is infinite as X goes to infinite. So, if X is infinite, it makes no difference to the individual s utility if he (or she) chooses to consume other goods or not. The right panel makes this problem even clearer. As X and Y become infinite, an unlimited number of utility difference curves are added to the map and the individual s utility goes to infinite. For any given value of Y, the values of utility goes to infinite as X goes to infinite, so the individual s utility is independent of Y given that X is approaching infinity. However, according to the the more the better assumption, the higher the value of Y, the higher utility should be. To overcome the shortcomings of the more the better assumption, a finite consumption and utility axiom should be introduced. That is, an individual can only consume a finite amount of an economic good, and an economic good can only provide finite utility for an individual. In combining the the more the better assumption and the finite consumption and utility assumption, the utility indifference map will not expand unlimitedly. As Figure 2 shows, as the amount of good consumed reaches maximum level, the individual s utility maximizes at point A. Figure 2 Utility of a Representative Individual with Finite Consumption Incorporating the consumption limit into an individual s demand curve, a vertical line at the right side of the usual demand curve should be added to manifest the maximum quantity demanded (shown in the left and middle panels of Figure 3). For a market with a finite number of consumers, aggregating the demand curves of all consumers horizontally yields the market demand curve which should also have a quantity constraint (shown as the right panel of Figure 3).

4 56 Xianming Meng Figure 3 Demand Curves for Commodity X For an economy with a finite number of markets, aggregating all the market demand curves with quantity constraints yields the aggregate demand curve which should have a vertical line at the right end (shown as AY* in Figure 4). Figure 4 Possible Deficiency of Aggregate Demand The existence of a demand limit means that the aggregate demand curve can always reach the horizontal axis (even if the Pigou effect 2 is taken into account), so that the deficiency of aggregate demand is guaranteed when the production capacity expand rapidly in modern economy. In Figure 3, if the aggregate supply curve (e.g., AS0) is at the left of the demand constraint, there is no deficiency of demand and thus the total products supply can expand until it reaches Y*. However, if the

5 The Source of Temporary Technological Shocks 57 production capacity expands over this limit for some reason (e.g., the aggregate supply curve shifts from AS0 to AS1), there is an overproduction or deficiency of demand (Y1 Y*). Since the total goods supply is more than the total demand, the total output Y1 is not sustainable and the economy has to retreat back to Y*. It looks like the demand deficiency does exist just as what Keynesian economists suggested, but it is not in the real sense. The aggregate demand curve with demand constraint is achieved through aggregating all the market demand curves under the assumption that there is only a finite number of commodities in an economy. This assumption is valid for any static moment in an economic system. But for a dynamic economic system, the number of commodities may increase over time due to product innovation. If product innovation is fast enough to increase the number of commodities significantly, the aggregate demand constraint may be lifted. However, the repeated occurrence of economic recessions indicates otherwise. So the demand deficiency actually reflects the low speed of innovation or, put differently, the essence of demand deficiency is the scarcity of innovation. 3. A PRODUCTION FUNCTION AND GROWTH MODEL INCLUDING INNOVATION Before we specify the production function and derive the growth model, it is necessary to consider innovation in more detail. There are many kinds of innovations. For economic growth, we consider two kinds of them. One is product innovation, which produces new products and expands aggregate demand. A certain speed of product innovation is required to break the demand constraint and thus keep the economy growing. The other kind is production innovation, which includes any innovations in the process of production, such as innovation in production procedure, machinery, and management. Production innovation contributes directly to the aggregate supply (or output level). But a sustainable output level is constrained by the level of aggregate demand, which is influenced by the speed of production innovation. Since both production innovation and product innovation are very important for an economy, they should be included in an aggregate production function. However, the neoclassical production function does not include any innovation but does include a technology level variable. The specification of the aggregate production function including both production and product innovations is based on the different effects of both innovations. Since the production innovation will lead to the direct and permanent increase in output, we call it the permanent technological shock or technological advance. In production function it can be reflected by the level of technology. On the other hand, the product innovation will influence output temporarily and indirectly through demand. Its effect on output depends on its speed. A high speed of product innovation can release the consumption constraint and thus promote production while a low production

6 58 Xianming Meng innovation rate may limit production and affect output negatively. Due to its temporary effect, it is suitable to call product innovation temporary technological shock, or simply technological shock. The rate of product innovation cannot influence labour and capital inputs directly, but it can confine or enlarge the effect of production innovation, so we introduce it in the neoclassical aggregate production function as the exponent of technology level, shown as follows: where N Y A N F( L, K) Y the total output A the technology level N the number of new products N the change of the number of new products L the labour input K the capital input This function shows that the total output level is determined by the level of technology, labour input and capital input, and the speed of innovation of new products. Due to the variation of the growth rate of new-product innovations, the effect of technology may be enlarged or reduced. Especially, since the change in the number of new products in different periods may be positive or negative, the effect of technology may be more or less than one and thus may magnify or lessen the effects of labour and capital. Moreover, the cyclical pattern of a new product innovation may generate the cyclical effect of technology change, which in turn results in cyclical economic fluctuations the business cycles. Based on the revised aggregate production function, we can derive the economic growth model. Using the log form of the production function and fully differentiating it, we have: N ln Yt ln A ln( F( L, K)) N N N 1 F( L, K) 1 F( L, K) dyt / Y da/ A (ln A) d dl dk N N F( L, K) L F( L, K) K N N (ln A) N N L F ( L, K) da/ A d / dl/ L N N N N F( L, K) L K F( L, K) dk/ K F( L, K) K

7 The Source of Temporary Technological Shocks 59 let we hav the following growth model: L F( L, K) K F( L, K) Sl, Sk, F( L, K) L F( L, K) K N N (ln A) N N dyt / Y da/ A d / Sl dl/ L Sk dk/ K. N N N N If we measure the differentiations of variables as the year-on-year changes, the above equation indicates the relationship among the percentage annual growth rates of output, new products, technology change, and labour and capital inputs. Given the data on the growth rates of output, new products, and labour and capital inputs, we can estimate the contribution of labour, capital and production innovation to the economy and, more importantly, the growth rate of technology (da/a) and the base technology level (ln A). 4. AN EMPIRICAL EVIDENCE There is difficulty in applying the growth model to empirical estimation: the number of new products is hard to measure. However, in a modern economy where production capacity is not an issue, the sales growth rate is a good indicator of market potential or, put in another way, market saturation. Since the influence of growth rate of product innovation in the aggregate production function is fulfilled through the restriction of market saturation (the low rate of product innovation will lead to market saturation), the sales growth rate is an ideal candidate to replace the growth rate of product innovations. Thus, the growth model becomes: S S(ln A) S S dyt / Y da/ A d / Sl dl/ L Sk dk/ K S S S S Given the data on the growth rates of output, sales, and labour and capital inputs, the contribution of independent variables can be estimated. From another perspective, the estimation may test out the validity of our production function. Based on the annual time series data from 1950 to 2008 in USA, we estimate the following model: where OUTPUT C1 C2 * CAPITAL C3 * LABOUR C4 * SALES C5 * DSALES OUTPUT the percentage annual growth rate of real output of business sector CAPITAL the percentage annual growth rate of capital input in business sector LABOUR the percentage annual growth rate of labour input in business sector

8 60 Xianming Meng SALES the percentage annual growth rate of sales to final demand DSALES the percentage annual growth rate of SALES The time series of growth rates of real output, labour input and capital input are from the Net Multifactor Productivity and Cost Table ( ) calculated by the Bureau of Labour Statistics (BLS) 3. The annual growth rates of final sales are from the GDP account provided by the Bureau of Economic Analysis (BEA) 4. The E-view software is used for the model estimation and testing. Since most macroeconomic time series data are non-stationary, unit root tests are performed. Before formal testing procedures are undertaken, the time series data are plotted to allow for visual inspection (see Appendix 1). All time series show no trends, but most of them have intercept, except DSALES. The Augmented Dickey- Fuller (ADF) tests are performed to check the stationarity of all time series. The results are listed in Appendix 2. With the exception of DSALES, the PP and ADF tests suggest first order integration for all variables at 5% level of significance. DSALES is found to be stationary. Since non-stationary time series are used, the cointegration test has to be performed. Johansen procedure (see Johansen, 1988; Johansen and Juselius, 1990) is used to test for cointegration among OUTPUT, CAPITAL, LABOUR and SALES. In implementing the tests, a deterministic linear trend and incept in the cointegration equation is included, so that the deterministic trends are removed from the cointegration relationship, and thus the test results are free from the distortion of deterministic trends. The trace test suggests 3 cointegration equations while the maxeigenvalue test suggests 2 cointegration equations (see appendix 3). However, the likelihood ratio (LR) tests in the Johansen procedure is derived from asymptotic property and the statistic inference may not be applicable to finite sample. Thus, many econometricians express concern about the problem of finite sample size in Johansen s LR tests for cointegration. Reinsel and Ahn (1988) suggest that a scaling factor, which is a simple function of T, n, and k (T is the sample size, n is the number of variables in the model and k is the number of lags), may be used to obtain finite-sample critical values from their asymptotic counterparts. Reimers (1992) claims that in finite samples the Johansen test statistics too often over-rejects the null hypothesis of noncointegration when it is true and suggests the application of the Reinsel-Ahn method to adjust Johansen s test statistics by a factor of (T nk)/t. Cheung and Lai (1993) use the surface analysis in Monte Carto experiments to estimate the finite-sample critical values for both trace and max-eigen value tests and find that the finite sample bias of Johansen s tests is a positive function of T/(T nk). Following this finding, they claim that since both n and k are of positive values, T/(T nk) is always greater than one for any finite T value, indicating that the tests are biased toward finding cointegration too often when asymptotic critical values are used. Furthermore, the finite-sample bias toward over-rejection of the no cointegration hypothesis magnifies with increasing values of n and k. (Cheung and Lai, 1993, p. 319).

9 The Source of Temporary Technological Shocks 61 In the case of this study, the sample size is 60 (T = 59 after adjustment); 5 variables are included in the model (n = 5); and the AIC indicates the proper lags for cointegration test is 3 (k = 3). So the finite-sample bias in the cointegration test tends to be large. Following the suggestion of previous studies, T/(T nk) is used to scale up the standard critic value. The adjusted critic values are shown in the column next to the standard critic value in Appendix 3). According to the adjusted critical values, the trace test suggests two cointegration relationships at 0.05 level while max-eigenvalue test suggests one cointegration. However, the trace test only marginally suggests the second cointegration, so we tend to conclude that there is only one cointegration among tested variables. Since the cointegration among I (1) variables is confirmed, it is valid to estimate the model using the dynamic ordinary least square (DOLS) developed by Saikkonen (1991) and generalised by Stock and Watson (1993): OUTPUT C1 C2 * CAPITAL C3 * LABOUR C4 * SALES C5 * DSALES t t t t t M ( A CAPITAL B LABOUR C SALES ) m M m t m m t m m t m t To minimize AIC, 3 leads and 3 lags are used in the estimation. The estimation results are as follows (we omit the coefficients on leads and lags because the purpose of the use of leads and lags is to increase the estimation efficiency). The complete results are shown in Appendix 4. OUTPUT CAPITAL LABOUR SALES DSALES t t t t t t Wald Stat s. t p-value R-squared = 0.985, adjusted R-squared = 0.973, D.W. = The Durbin Watson (D.W.) statistic suggests that there is no first order autocorrelation in the residuals, and the further LM test (up to 10 lags) show no autocorrelation at a p-value greater than 40%. The high (adjusted) R-squared value suggests that the model explains the dependent variable very well. Due to the nonstandard nature of the estimation when nonstationary time series are involved, the t-value and p-value produced by E-view are not valid for analysis. However, Stock and Watson (1993) demonstrate that the DOLS estimators have large-sample chi-squared distributions and thus the Wald test is applicable. Therefore, the above standard errors and the p-values from Wald tests are valid. The model passes all other diagnostic tests (The white heteroskedesticity test results: F (22, 29) = , p = ; The results of J.B. normality test are displayed in Appendix 5; The result of recursive coefficients and recursive residuals are shown in Appendix 6 and Appendix 7 respectively; For the results of CUSUM and CUSUM of square, please see Appendix 8).

10 62 Xianming Meng The DOLS estimators reveal the following interesting findings: First, all independent variables show positive contribution to the output, which is consistent with the prediction of the aggregate production function. Second, the growth rate of sales has tremendous positive effects on the growth of GDP. The large Wald statistic for the coefficient of sales growth rate demonstrates its importance. Since the sales growth rates reflect the product innovation rates, this results implies the important contribution of production innovation and the necessity to include it in an aggregate production function. Third, the labour input is significant at around 3% level, but the contribution of capital is found insignificant. The greater significance of labour input than capital input is consistent with the effect that much more income in the US economy goes to labour than to capital. Finally, the insignificance of DSALES is consistent with the theoretic production function. Referring to the production function, the coefficient of DSALES indicates the log value of technology level multiplied by the sales growth rate. The log value is quite small; the growth rate of final sales can be positive or negative, and very small in value (less than 8% as shown in appendix 1). As a result, the average value of the sum of the products should be close to zero as shown by the estimation results. For contrast and comparison, we also estimated the Solow growth model (omitting the variables SALES and DSALES in the above model and using the same dataset and estimation procedure). The estimation results are: OUTPUT CAPITAL 0.809LABOUR t t t t Wald Stat s. t p-value R-squared= 0.818, adjusted R-squared = 0.749, D.W. = The (adjusted) R-squared value decreased dramatically and the D.W. statistics show the existence of autocorrelation. Both of them indicate the misspecification of the model (having omitted important independent variables). The Wald statistics and the p-values of above estimation also show the significance of labour input and the insignificance of capital input, but the estimated coefficients for both labour and capital increase nearly 3 times, which manifests that omission of the innovation (or sales) variable exaggerates the contribution of both labour and capital. 5. CONCLUSION The preference and utility theory needs modification so as to avoid unlimited utility and unlimited consumption, which is unrealistic and problematic in a real economy.

11 The Source of Temporary Technological Shocks 63 The demand constraint implied by finite consumption theorem reflects the scarcity of innovation. To ensure economic growth, innovations must be encouraged by all means. For an economy, there are two kinds of important innovations and they work differently. The product innovation expands aggregate demand so it affects output indirectly while the production innovation increases aggregate supply directly. The revised neoclassical production function in this paper embodies the effects of both innovations. The estimation results confirm the suitability of the proposed production function and demonstrate the important contribution of innovations and labour input in the US economy. APPENDIX 1 Graphs of Time Series

12 64 Xianming Meng APPENDIX 2 Results of Unit Root Tests* Variable Level of test t-statistics (ADF test) Conclusion of ADF test OUTPUT Level unit root First difference No unit root CAPITAL Level unit root First difference No unit root LABOUR Level unit root First difference No unit root SALES Level unit root First difference No unit root DSALES Level No unit root First difference 6.16 No unit root * The number of lags is chosen to minimize AIC. APPENDIX 3 Results of Cointegration Tests* 0.05 Adjusted 0.05 Adjusted Trace critical critical Max-Eigen critical critical No. of CE(s) statistic value value No. ofce(s) statistic value value None * a None * a At most 1 * a At most 1* At most 2 * At most At most At most At most At most * denotes rejection of the hypothesis at the 0.05 level according to the standard critical value. a denotes rejection of the hypothesis at the 0.05 level according to the adjusted critical value. 3 lags are chosen to minimize AIC.

13 The Source of Temporary Technological Shocks 65 Dependent Variable: Method: OUTPUT Least Squares Sample (adjusted): Included observations: 52 after adjustments APPENDIX 3 Results of DOS Estimation Coefficient Std. Error t-statistic Prob. C CAPITAL LABOR SALES DSALES D(CAPITAL(1)) D(LABOR(1)) D(SALES(1)) D(CAPITAL(-1)) D(LABOR(-1)) D(SALES(-1)) D(CAPITAL(2)) D(LABOR(2)) D(SALES(2)) D(CAPITAL(-2)) D(LABOR(-2)) D(SALES(-2)) D(CAPITAL(3)) D(LABOR(3)) D(SALES(3)) D(CAPITAL(-3)) D(LABOR(-3)) D(SALES(-3)) R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic)

14 66 Xianming Meng APPENDIX 5 The Result of J.B. Normality Test APPENDIX 6 The result of Recursive Coefficients

15 The Source of Temporary Technological Shocks 67 APPENDIX 7 The Result of Recursive Residuals APPENDIX 8 The Result of CUSUM and CUSUM of Square NOTES 1. For the further development of the real business cycle model please also see Prescott (1986) and Plosser (1989) 2. For Pigou effect please see Pigou (1943). 3. These data are available from BLS website. Historical multifactor productivity measures (SIC linked to NAICS )

16 68 Xianming Meng 4. The data are a vailable from BEA website. Selected=Y, Table Percent Change From Preceding Period in Real Gross Domestic Product, Real Gross Domestic Purchases, and Real Final Sales to Domestic Purchasers. REFERENCES Cheung Y-W., and Lai K. S., (1993), Finite-Sample Sizes of Johansen s Likelihood Ratio Tests for Cointegration, Oxford Bulletin of Economics and Statistics, Vol. 55, pp Johansen S., (1988), Statistical Analysis of Cointegration Vectors, Journal of Economic Dynamics and Control, Vol. 12, pp Johansen S., and Jueslius K., (1990), Maximum Likelihood Estimation and Inference on Cointegration With Applications to the Demand for Money, Oxford Bulletin of Economics and Statistics, Vol. 52, pp Kydland F. E., and Prescott E. C., (1982), Time to Build and Aggregate Fluctuations, Econometrica, Vol. 51, pp Mankew N. G., (1989), Real Business Cycles: A New Keynesian Perspective, Journal of Economic Perspectives, Summer. Pigou A. C., (1943), The Classical Stationary State, Economic Journal, (December), pp Plosser C. I., (1989), Understanding Real Business Cycles, Journal of Economic Perspectives, Summer. Prescott E. C., (1986), Theory Ahead of Business Cycle Measurement, Federal Reserve Bank of Minneapolis Quarterly Review, Fall. Reimers H-E., (1992), Comparisons of Tests for Multivariate Cointegration, Statistical Papers, Vol. 33, pp Saikkonen P., (1991), Asymptotically Efficient Estimation of Cointegration Regressions, Econometric Theory, Vol. 7, pp Stock J. H., and Watson M. W., (1993), A Simple Estimator of Cointegrating Vectors in Higher Order Integrated Systems, Econometrica, Vol. 61, pp