
Research Article


Analysis of the Neutrality of Money for the US Economy 

Afsin Sahin
and
Imdat Dogan



ABSTRACT

Background and Objective: Neutrality of money hypothesis is one of the widely researched topics in economics claiming that the effect of money supply on output is positive in the shortrun but disappears in the longrun. Besides this level effect, relationship between the volatilities of these two variables is also another interesting subject to investigate. This study aimed to discuss the neutrality of money hypothesis in terms of level and volatility effects of money supply. Materials and Methods: Data from the United States economy covers the period of 1959: 012016: 05. First, mean equation of EGARCH model is utilized to investigate for a lagged effect of the stationary variables of money supply growth on output growth in the shortrun. Second, Asymmetric Dynamic Conditional Correlation Model (ADCCEGARCH) is employed to analyze the dynamic relationship between shortrun volatilities of money supply growth and output growth. Last, Detrended Cross Correlation Analysis (DCCA) is applied to explore for a longrun relationship between nonstationary variables of money supply and output. Results: The lagged effect of money supply growth on output growth is positive in the shortrun according to the results of EGARCH’s mean equation. According to the ADCCEGARCH analysis’s dynamic cross conditional correlation results, the volatility of money supply growth and volatility of output growth vary substantially in the shortrun by time. Moreover, DCCA results indicated a positive simultaneous longrun relationship between money supply and output in levels. Conclusion: It is concluded that a nonneutrality of money in the shortrun and the dynamic conditional correlations vary over time.





Received: April 09, 2017;
Accepted: May 24, 2017;
Published: June 15, 2017
Copyright: © 2017. This is an open access article distributed under the terms of the creative commons attribution License, which permits unrestricted use, distribution and reproduction in any medium, provided the original author and source are credited.


INTRODUCTION
Economic output is affected from endogenous and exogenous events. Exogenous shocks such as Vietnam War (19651975), which is one of the major examples of military spending in US history increased the volatility in economic output^{1}. These kinds of shocks leading a high government spending usually create budget deficits and had been often financed by the Federal Reserve Bank of the United States (FED) through monetization in the past. During 1970’s, FED adopted an expansionary monetary policy by increasing liquidity, which along with ongoing recession led to a stagflation. According to Mervyn King^{2}, FED’s this action stimulated the independency of the central banks around the world.
Following 1980s, central banks as independent institutions have started to choose their instruments to achieve their policy goals. Concerning the success of monetary targeting as adopted in some countries, there should be a stable relationship between the target variable and the monetary aggregates^{3}. This relationship is outlined in two mainstream concepts. First, the neutrality of money concept, which points out that money supply does not have any real effects on real output^{4}. Moreover, it is called superneutrality of money if nominal money supply growth does not have any effect on real output. Second, longrun and shortrun effects of nominal money supply on economic output are investigated within monetary economics literature. Keeping these in mind, this study contributed to the empirical monetary economics literature in both ways by applying Asymmetric Dynamic Conditional Correlation Model (ADCCEGARCH)^{5} and Detrended CrossCorrelation Analysis (DCCA)^{6}.
Tobin^{7} rejected the superneutrality of money hypothesis, which is based on neoclassical models of Solow^{8 }and Swan^{9}. According to Tobin^{7}, money and real assets are substitutes and in the case of an increase in inflation, households will increase their demand for real assets and money demand will diminish. Therefore, Tobin^{7} claimed that an increase in inflation also stimulates the capital accumulation and economic growth. However, Sidrauski^{10} does not reject the neutrality of money hypothesis and claims that money supply does not have any longrun effect on capital accumulation and production. Algan and Ragot^{11} criticized Sidrauski^{10} and assert that the neutrality of money will not hold when the borrowing constrains are binding. On the other hand, according to Lucas^{12}, money is neutral in the longrun. Finally, Gimenez and Kirkby^{13} claimed that quantity theory of money is valid for the US in the longrun but not in the shortrun.
Besides the theoretical models, the relationship between money supply and output is analyzed in empirical sense. For instance, according to Dewald^{14} there is a longrun relationship between money supply growth and economic growth for the US economy. Berger and Osterholm^{15} investigated the impact of money growth on output growth in the US for 19602005 period and find an evidence that money Granger causes output. Aksoy and Piskorski^{16} explore that the money supply Granger causes inflation and output in the US for 19812005 period. However, Lu et al.^{17} as a recent study found no causality from money supply to GDP for the US economy. Besides for post2000 period, the initial effect of money supply on GDP is negative that is explained by an increasing financialization tendency. Darrata et al.^{18} employed the Johansen cointegration method and find a longrun relationship between money supply and output for the post1980 US economy. Ogunmuyiwa and Ekone^{19} investigated the impact of money supply on economic growth utilizing causality test and error correction model for 19802006 periodin Nigeria and cannot explored a significant relationship. Liu and Jin^{20} investigated longrun and shortrun effects of money supply on economic growth.
The purpose of this study was to contribute and advance new knowledge to the empirical monetary economics literature by adopting noncommon and nonlinear methodologies in the analysis of the effects of money supply on production dynamics. This study unveils a shortrun nonneutrality of money supply volatility on output volatility. The findings may guide researchers and monetary policy makers to uncover the effects of volatilities on the macrovariables while taking decisions. The main aim of this study was to investigate a relationship between volatilities of two variables rather than their means. Therefore, the neutrality of money hypothesis for the US economy over the post1959 period by using Asymmetric Dynamic Conditional Correlation Model (ADCCM) is analyzed. There are several papers estimating the effects of macroeconomic variable’s volatility on output in the literature. For instance, Fountas and Karanasos^{21} employed the univariate Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model to test the causal effect of real and nominal macroeconomic volatility on inflation and output growth for the G7 covering the 19572000 period. Wang and Han^{22} used the multivariate GARCH model (MGARCHBEKK) and explore a covolatility between money supply growth and economic growth for China.
MATERIALS AND METHODS Friedman and Schwartz^{23} claimed that there is a high correlation between the standard deviations of income and money supply and this high correlation varies over the time. The scatter diagram in Fig. 1 indicates that the relationship between M1 money supply growth and output growth is not clear. Moreover, as shown in Fig. 2, lagging and leading effects of M1 money supply growth on output growth has a cycling behavior and dynamic in the sense of a standard correlation analysis.
In this study, Asymmetric Dynamic Conditional Correlation (ADCCEGARCH) model, which allows to explore the relationship between volatilities of money and output, was employed. The US monthly data of seasonally adjusted M1 money supply and seasonally adjusted industrial production index (2012 = 100) from January, 1959 to May, 2016 was utilized. Both data are gathered from the database of Federal Reserve Bank of St. Louis Electronic Data System. Following Walsh^{24}, detrended log of seasonally adjusted industrial production (DETLOGIND) and detrended log of seasonally adjusted M1 money supply (DETLOGM1) were constructed by using HodrickPrescott filtering methodology.
The descriptive statistics of the data are provided in Table 1. Both variables are stationary according to Augmented Dickey Fuller Unit Root (ADF) test statistics. The distribution for industrial production is skewed to the left and money supply is skewed to the right. The thickness of the tales statistics about the distribution indicates nonnormality. JarqueBera (JB) statistics rejects the normal distribution. BreuschPaganGodfrey (BPG), ARCHLM test and white test indicate heteroscedasticity in the residuals for each of the variables. LjungBox Q statistics fails to reject the null of noautocorrelation. Autocorrelation functions statistics (AC) indicate a positive but low level of persistency. The DCC methodology is initially developed by Engle^{5} and has been used for modelling volatility relationships in the sense of multivariate GARCH. An application of asymmetric DCC models are used in several areas in finance and economic research. Constant Conditional Correlation (CCC) can be found by Sahin and Dogan^{25}. Yin^{26} applied a DCCGARCH model to analyze the correlation between uncertainty and oil futures returns. Shaw et al.^{27} benefited from GARCHBEKK model to investigate the volatility transmission between future and spot interest rate markets.
Following Kim et al.^{28}, asymmetric DCCEGARCH (1,1) model is estimated by Eq. 14. The mean equations are as follows.
Model I mean Eq. 1: Model II mean Eq. 2: Constant is for the constant term in the Eq. 1. The β_{1} is the effect of DETLOGIND at time t1 on DETLOGIND at time t. The β_{2} is for the effect of DETLOGM1 at time t1 on DETLOGIND at time t. Mean Eq. 2 of the model II is provided as Eq. 2.  Fig. 1:  Scatter diagram of detrended logarithm of M1 money supply and detrended logarithm of industrial production 
 Fig. 2:  Dynamic standard correlations (1959: 012016: 05) 

_{y axis is for dynamic correlations between Yi and Mt+i. x axis shows the lags and leads} 
Table 1:  Descriptive statistics of the variables 
 Analysis are conducted by Eviews 9.0. pvalues are given in brackets, ***Statistical significance at 10% levels, respectively 
Constant is again for the constant term. The α_{1} parameter is for the effect of DETLOGIND at time t1 on DETLOGM1 at time t. The α_{2} parameter indicates the effect of DETLOGM1 at time t1 on DETLOGM1 at time t. Equations 3 and 4 are for the variance equations of the EGARCH model. Conditional variance equation (log h_{t}) is obtained from the asymmetric EGARCH (1,1) model and can be written by Kim et al.^{28}.
Model I variance Eq. 3: Model II variance Eq. 4: The parameter c_{1} is the constant of model I variance Eq. 3. The a_{1} is the ARCH parameter. The b_{1} is called the GARCH parameter and represents the effect of log h_{DETLOGIND} at time t1 on log h_{DETLOGIND} at time t. The parameter c_{2} is the constant of model II variance Eq. 4. The a_{2} is the ARCH parameter. The b_{2} is again called GARCH parameter and represents the effect of log h_{DETLOGM1} at time t1 on log h_{DETLOGM1} at time t. RESULTS
Panel B of Table 2 shows the specification results. The constant is shown by C in the variance equation. The ARCH parameter is given by A and GARCH parameter is shown by B. The parameter D indicates the coefficient for an asymmetry term. The parameters are estimated by RATS 8.1 computer programme. The asymmetry parameter is significantly positive indicating that unexpected negative monetary shocks to output growth affects the volatility more than the positive shocks which is a common finding in the economic and financial research literature a la leverage effect.
The parameters of the nonlinear model presented in Table 2 are used to obtain conditional covariances and conditional correlations. Conditional covariance is gathered from ADCCEGARCH (1,1). The H_{11} is the conditional variance for output. The h_{22} is the conditional variance for money supply. The H_{12} is the covariance between output and money supply. Figure 3 presents the timevarying conditional correlation graph obtained from ADCCEGARCH model I and II. Gray lines indicate NBER business cycle dates for US. Highest negative relationship between the volatilities of money supply growth and output growth exists during the recent 20082009 Global Financial Crisis and 1974, 1982, 1991 and 2001 recessions where the uncertainty increased and correlation coefficient is over 0.40 in absolute term.
Caveat: Analyzing the correlation of two nonstationary variables rather than the correlation between their first differences maybe aimed. At this stage, traditional correlation methods which are based on GaussMarkov’s assumptions cannot be benefited. Log of real income and log of money supply variables are not stationary and have increasing positive trends. Therefore, the standard correlation dynamics in Fig. 4 using levels of the variables would be biased. On the other hand, correlation analysis provided in Fig. 2 is detrended versions of these two variables and had given results for the shortrun dynamics. One may claim that cointegration analysis could be employed to overcome this problem for longrun relationships.
 Fig. 3:  Asymmetric DCCEGARCH graph 

_{y axis is for simultaneous dynamic conditional correlations between output growth volatility and money supply growth volatility. x axis indicates time} 
 Fig. 4:  Dynamic correlations using levels (1959: 012016: 05) 

_{y axis is for dynamic correlations between LOGINDi and LOGM1t+i. x axis shows the lags and leads} 
This view is widely adopted in the monetary economics literature, some of which were cited in text. To increase the contribution of the study to the existing related literature on the US economy, in this study, Zebende^{6} provided the methodology that may add another insight over the longrun neutrality of money debate.
Zebende^{6} developed a methodology to handle two nonstationary variables by crosscorrelation analysis. In this caveat section, the results of Detrended CrossCorrelation Analysis (DCCA) and its correlation coefficient (ρ_{DCCA}) are discussed to investigate the interaction between logarithm of money supply (LOGM1) and logarithm of output (LOGIND). The ρ_{DCCA} is calculated as^{29} in Eq. 5. One can also refer to Hussain et al.^{30} for an application of DCCA.
Table 2:  Asymmetric DCCEGARCH model results 
 ***Statistical significance at 10% levels, respectively, pvalues are presented in brackets. The asymmetry terms are normalized by one hundred 
Detrended Fluctuation Analysis (DFA) is presented by Peng et al.^{31} to analyze the longrange powerlaw correlations for the variables that are not stationary. For the advantage of DFA^{32}. The DFA lets one to interact root mean square fluctuation (F_{DFA}(n)) and the time scale n. If α>0.5 then there is a high correlation between variables:
F_{DFA}αn^{α}

Fig. 5(ac): 
Crosscorrelation coefficient as a function of (n: months), 1959: 012016: 05, obtained from DCCA 
Detrended CrossCorrelation Analysis (DCCA) is similar to DFA and can be used to analyze the long range crosscorrelations if the variables are not stationarity^{33}. In this sense, we have a detrended covariance function F_{DFA }(n). According to Zebende et al.^{34}, if selfaffinity appears then a powerlaw exists in the crosscorrelation function where, λ is called as the longrange powerlaw crosscorrelation exponent:
In Panel A of Fig. 5, circle is the DFA analysis of LOGIND and square is the DFA analysis of LOGM1, α corresponds to the linear fit on the graph of Log FDFA in function of Log n and can be called as a DFA exponent. If the value of α is greater than 0.5, then we conclude that the time series are persistent and the autocorrelations are powerlaw. Note that in Panel A, there are two α for these two variables LOGIND and LOGM1 respectively. Panel B provides the λ_{DCCA} value as 19.94 that is a DCCA exponent. Panel C provides a graph of 1<ρ_{DCCA}< which is the DCCA crosscorrelation coefficient between LOGIND and LOGM1. Here, ρ_{DCCA} is a function of n where n is the time scale (months), thus 4<n<N(points)/4. ρ_{DCCA}, the correlation coefficients, point out that there is a change from a weak crosscorrelation to a strong crosscorrelation by the time being.
DISCUSSION Central banks being responsible from monetary policy are the major institutions, creating money and trying to affect the overall prices and production dynamics. They create an extensive amount of liquidity within the market through increasing money supply, especially during the economic recessions and crises. Since the consequences of these recessions were so extreme that the liquidity provision policy has not been sufficient to overcome the problems, policy makers have started to focus on the slope of the yield curve through quantitative easing. Therefore, central banks questioned the validity of nominal dichotomy in the economy. However, a change in money supply has negligible effects over real output in the longrun that is called neutrality of money but the effect in shortrun is apparent^{35}. For this purpose, money supply should be kept stable due to dynamic shortrun effects on the economy^{36}.
According to the results of this study, volatility of money supply growth affects the volatility of output growth in the shortrun. This finding is consistent with the Friedman and Schwarz^{23} hypothesis that standard deviation of money supply has a relationship between standard deviation of output. An increase of volatility in money supply, which is not desirable, gives a negative signal for the cost of production and supply side of the economy. Monetary uncertainty delays the production in the economy since firms would wait until the marginal cost of production stabilizes. On the other hand, labor would be indifferent between leisure and working. Labor supply will diminish and would have negative effects on the output volatility.
The DCCA findings in this paper is consistent by Westerlund and Costantini^{37}, Skare et al.^{38}, Ekomie^{39} in terms of finding longrun positive effects of money supply but contradicts with Serletis and Koustas^{40}, Asongu^{41} and Lee^{42} which indicated neutrality of money supply in the longrun.
CONCLUSION
This study employing ADCCEGARCH model concludes that money supply growth volatility has an effect on output growth volatility in the shortrun. The lagged effect of money supply growth on economic growth is also apparent in the shortrun. Moreover, money supply in levels has a positive effect on output in levels in the longrun according to the results of detrended cross correlation analysis. The results might shed some lights for monetary policy makers during their decision making process in conducting monetary operations. SIGNIFICANCE STATEMENTS
This study discovered that the lagged effect of money supply growth on output growth is positive in the shortrun. Moreover, the relationship between volatility of money supply growth and volatility of output growth is not always positive or negative in the shortrun. The results also indicate a positive simultaneous longrun relationship between money supply and output in levels. This study will help the researchers and Central Bankers to uncover the critical areas of neutrality of money that many researchers were not able to explore.
ACKNOWLEDGMENT
Author would like to thank Professor Gilney Figueira Zebende (Department of Physics, State University of Feira de Santana, Bahia, Brazil) for providing support in this study.

REFERENCES 
1: Gordon, R.J., 2012. Macroeconomics. 12th Edn., Pearson Education Limited, USA., ISBN13: 9780138014919, pp: 463464
2: King, M., 2016. The End of Alchemy: Money, Banking and the Future of the Global Economy. 1st Edn., W. W. Norton Publ., UK., ISBN13: 9780393247039, pp: 5
3: Mishkin, F., 2016. Monetary Targeting. In: The Economics of Money, Banking and Financial Markets, Mishkin, F.S. (Ed.). Pearson Education Limited, USA., pp: 4
4: Orphanides, A. and R.M. Solow, 1990. Money, Inflation and Growth. In: Handbook of Monetary Economics, Volume 1, Friedman, B.M. and F.H. Hahn (Eds.). Chapter 6, Elsevier Science Publishers, Netherland, ISBN13: 9780444880253, pp: 224259
5: Engle, R., 2002. Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models. J. Bus. Econ. Stat., 20: 339350. CrossRef  Direct Link 
6: Zebende, G.F., 2011. DCCA crosscorrelation coefficient: Quantifying level of crosscorrelation. Phys. A: Stat. Mech. Applic., 390: 614618. CrossRef  Direct Link 
7: Tobin, J., 1965. Money and economic growth. Econometrica, 33: 671684. Direct Link 
8: Solow, R.M., 1956. A contribution to the theory of economic growth. Quart. J. Econ., 70: 6594. CrossRef  Direct Link 
9: Swan, T.W., 1956. Economic growth and capital accumulation. Econ. Rec., 32: 344361. CrossRef  Direct Link 
10: Sidrauski, M., 1967. Rational choice and patterns of growth in a monetary economy. Am. Econ. Rev., 57: 534544. CrossRef  Direct Link 
11: Algan, Y. and X. Ragot, 2010. Monetary policy with heterogeneous agents and borrowing constraints. Rev. Econ. Dyn., 13: 295316. CrossRef  Direct Link 
12: Lucas, Jr. R.E., 1996. Nobel lecture: Monetary neutrality. J. Political Econ., 104: 161182. CrossRef  Direct Link 
13: Gimenez, J. and R. Kirkby, 2014. How to model money? Racing monetary frameworks against the quantity theory of money. Working Paper, January 8, 2014, pp: 145.
14: Dewald, W.G., 1998. Historical U.S. money growth, inflation and inflation credibility. Federal Reserve Bank of St. Louis, November/December 1998, pp: 1324.
15: Berger, H. and P. Osterholm, 2009. Does money still matter for U.S. output? Econ. Lett., 102: 143146. CrossRef  Direct Link 
16: Aksoy, Y. and T. Piskorski, 2006. U.S. domestic money, inflation and output. J. Monetary Econ., 53: 183197. CrossRef  Direct Link 
17: Lu, X., K. Guo, Z. Dong and X. Wang, 2017. Financial development and relationship evolvement among money supply, economic growth and inflation: A comparative study from the U.S. and China. Applied Econ., 49: 10321045. CrossRef  Direct Link 
18: Darrat, A.F., M.C. Chopin and B.J. Lobo, 2005. Money and macroeconomic performance: Revisiting divisia money. Rev. Financial Econ., 14: 93101. CrossRef  Direct Link 
19: Ogunmuyiwa, M.S. and A.F. Ekone, 2010. Money supplyeconomic growth nexus in Nigeria. J. Social Sci., 22: 199204. Direct Link 
20: Liu, L. and Y.H. Jin, 2005. Money supply, inflation and economic growth of ChinaThe experimental analysis based on cointegration analysis. Stat. Res., 3: 120. Direct Link 
21: Fountas, S. and M. Karanasos, 2007. Inflation, output growth and nominal and real uncertainty: Empirical evidence for the G7. J. Int. Money Finance, 26: 229250. CrossRef  Direct Link 
22: Wang, Q. and X.T. Han, 2011. Can Monetary Policy Target on Asset Price?Evidence from Chinese Real Estate Market. In: Studies on Financial Markets in East Asia, Susai, M. and S. Uchida (Eds.). World Scientific Publications, India, ISBN13: 9789814460699, pp: 4149
23: Friedman, M. and A.J. Schwartz, 1963. Money and business cycles. Rev. Econ. Stat., 45: 3264. CrossRef  Direct Link 
24: Walsh, C.E., 2010. Monetary Theory and Policy. 3rd Edn., The MIT Press, Cambridge, USA., ISBN13: 9780262013772, pp: 48
25: Sahin, A. and I. Dogan, 2017. Relationship between the Istanbul chamber of wholesale general price index and its components: Asymmetric conditional correlation analysis on Turkey, 19682015. J. Yasar Univ., (In Press).
26: Yin, L., 2016. Does oil price respond to macroeconomic uncertainty? New evidence. Empir. Econ., 51: 921938. CrossRef  Direct Link 
27: Shaw, F., F. Murphy and F. O'Brien, 2016. Interest rate dynamics and volatility transmission in the European short term interest rate market. J. Econ. Finance, 40: 754772. CrossRef  Direct Link 
28: Kim, H.S., H.G. Min and J.A. McDonald, 2016. Returns, correlations and volatilities in equity markets: Evidence from six OECD countries during the US financial crisis. Econ. Modell., 59: 922. CrossRef  Direct Link 
29: Filho, A.M., M.F. da Silva and G.F. Zebende, 2014. Autocorrelation and crosscorrelation in time series of homicide and attempted homicide. Physica A: Stat. Mech. Applic., 400: 1219. CrossRef  Direct Link 
30: Hussain, M., G.F. Zebende, U. Bashir and D. Donghong, 2017. Oil price and exchange rate comovements in Asian countries: Detrended crosscorrelation approach. Phys. A: Stat. Mech. Applic., 465: 338346. CrossRef  Direct Link 
31: Peng, C.K., S.V. Buldyrev, S. Havlin, M. Simons, H.E. Stanley and A.L. Goldberger, 1994. Mosaic organization of DNA nucleotides. Phys. Rev. E, 49: 16851689. CrossRef  Direct Link 
32: Moret, M.A., G.F. Zebende, E. Nogueira Jr. and M.G. Pereira, 2003. Fluctuation analysis of stellar Xray binary systems. Phys. Rev. E, Vol. 68, No. 4. CrossRef  Direct Link 
33: Podobnik, B. and H.E. Stanley, 2008. Detrended crosscorrelation analysis: A new method for analyzing two nonstationary time series. Phys. Rev. Lett., Vol. 100, No. 8. CrossRef  Direct Link 
34: Zebende, G.F., M.F. da Silva and A.M. Filho, 2013. DCCA crosscorrelation coefficient differentiation: Theoretical and practical approaches. Phys. A: Stat. Mech. Appl., 392: 17561761. CrossRef  Direct Link 
35: Bekaert, G.J. and R.J. Hodrick, 2014. International Financial Management. 2nd Edn., Pearson Education Ltd., UK., ISBN13: 9781292021393, pp: 157158
36: Su, C.W., J.J. Fan, H.L. Chang and X.L. Li, 2016. Is there causal relationship between money supply growth and inflation in China? Evidence from quantity theory of money. Rev. Dev. Econ., 20: 702719. CrossRef  Direct Link 
37: Westerlund, J. and M. Costantini, 2009. Panel cointegration and the neutrality of money. Empir. Econ., 36: 126. CrossRef  Direct Link 
38: Skare, M., M. Benazic and D. Tomic, 2016. On the neutrality of money in CEE (EU member) states: A panel cointegration analysis. Acta Oeconomica, 66: 393418. CrossRef  Direct Link 
39: Ekomie, J.J.T., 2013. A multivariate longrun money neutrality investigation: Empirical evidence for CAMEU. Mod. Econ., 4: 384390. CrossRef  Direct Link 
40: Serletis, A. and Z. Koustas, 2015. Monetary neutrality. Working Papers 201506, Department of Economics, University of Calgary, Canada.
41: Asongu, S.A., 2014. A note on the longrun neutrality of monetary policy: New empirics. Eur. Econ. Lett., 3: 16. Direct Link 
42: Lee, J., 2012. Nonparametric testing for longrun neutrality with applications to US money and output data. Comput. Econ., 40: 183202. CrossRef  Direct Link 



