Thornton and Batten [1] and Kang [2] indicate that the empirical results of the Granger causality might be sensitive to the lag-length chosen in empirical models, and we also find several studies which mentioned about lag-length criteria issues in the relevant literature.

Hsiao [8] proposes the FPE criteria, which adopts a stepwise procedure based on Granger’s concept of causality. This criterion is suggested as a practical means to identify the order of lags for each variable in a multivariate autoregressive model. This model seems useful because it could serve as a reduced form formulation to avoid imposing spurious restrictions on the model.

Similarly, the study of Thornton and Batten [1] suggests that based on a standard, classical and hypothesis- testing norm, the FPE criterion performs well in selecting lag-length for a model, but the FPE criterion may not conform to all researchers’ prior beliefs about the appropriate trade-offs between bias and efficiency. Unlike Thornton and Batten’s findings [1] , the evidence of Jones [9] reveals that one of the ad hoc methods for lag- length determination is found to perform somewhat better than the statistical search methods in correctly assessing the causal relationships between money policy and inflation. These ad hoc methods are non-statistical in nature and include arbitrary lag specifications and rule-of-thumb lag-lengths.

However, the lag terms selected by the FPE criterion are inadequate for the purpose of testing the Granger causality as suggested by Kang [10] . In the Kang’s research, he reveals that the lag terms are selected optimally in the most efficient forecast equations obtained from both univariate variable analysis and transfer function analysis in order to test for the causality between the industrial production and the leading indicator of US data by his new procedure. In addition, he shows that the ARIMA analysis is better than using a pure AR process in the FPE criterion to achieve optimal models. Furthermore, Hall [11] finds considerable gains in the power of ADF tests from estimating p rather than fixing it at some relatively large number (i.e., he concludes that estimating the appropriate lag terms for the ADF tests will obtain power for the tests).

Gredenhoff and Karlsson [12] use simulated data to investigate how sensitive the lag-length estimation procedures are to the true model structure. They show that the commonly used procedure based on equal lag-length together with AIC and HQC⁸ performs well in most cases. In addition, Ozcicek and McMillin [4] are also concerned about lag-length selection by a Monte Carlo simulation approach, and the results imply that the AIC dominates for the symmetric lag models (i.e. the AIC is more frequently used for selecting the lag-length for a model than the other criteria).

While surveying relevant literature, the traditional information criteria like the Bayesian Information Criterion (BIC) proposed by Rissanen [13] shows that the autocorrelation of the process might be characterized by large negative components. In addition, the Shibata [14] criterion (SIC) is also employed in this study, since SIC converges to BIC as selecting lower orders for moderate MA parameters while the sample size increases. As for the AR coefficients, the SIC selects a higher order for small samples, but converge to the BIC as the sample size increases. Thus, both criteria are concerned as lag-chosen criteria in this paper.

Hacker and Hatemi-J [7] show that Schwarz’s Bayesian Criterion (SBC) performs well in choosing the optimal lag order, but there are some situations where the SBC might have a relatively high possibility to pick the right lag with a higher lag order, and then outperform the SBC will be not as good as other lag-chosen criteria. Therefore, Hatemi-J [6] applies a Monte Carlo simulation experiment to investigate the performance of the HJC for choosing the optimal lag order in stable and unstable VAR models, and finds the performance of HJC is quite efficient in both models.

From the above literature, the chosen lag-length seems to be quite important in relevant empirical research, since it will influence the results of empirical studies. Thus, we investigate whether empirical results will be different among the six different lag-length criteria while choosing between the different lag-length according to these different criteria. Additionally, we also investigate whether the empirical results will be different if we employ different time zones to test the effect of money on output, and it will be a worthwhile topic to reinvestigate this issue, since money seems to play an important role in the area of financial economics.

Recently, Cheung and Fujii [15] examine the implications of conditional heteroskedasticity for testing the effect of money on output, and they find that the presence of ARCH effects could be attributed to uncertainties in monetary policy and output. In addition, their results highlight the possibility of the presence of conditional heteroskedasticity shown in their models. Hafer and Kutan [16] investigate the empirical relationships among money, interest rates, and output across several industrialized and developing countries. The results suggest that money often plays a significant role in explaining the fluctuations of real output. Across the different countries examined, money accounts for more of the variance in real output than normal interest rates in about half of these countries. Moreover, Moroney [17] develops a long-run approach to examine the quantity of money growth, real GDP growth, and inflation. The results show that money growth and GDP growth are nearly orthogonal, consistent with long-run monetary super neutrality. In Das’ [18] paper, he tries to explore the short-run relationships among money, price and output, exploits the characteristics of these variables by Vector Autoregressive and Moving Average models (VARMA models), and shows money has a significant effect on output in his empirical study. Berger and Osterholm [19] investigate whether money growth Granger-causes output growth in the United States. They find that the Granger-causal role of money appears to have vanished completely after the “great moderation”. Caraiani [20] examines the relationship between money and output using quarterly data from the US economy. He finds evidence of a weaker relationship within the Great Moderation as well as a stronger relationship during the Great Recession. Gefang [21] explores money-output causality within the context of a logistic smooth transition vector error correction model, and obtain strong support for nonlinear Granger causality from money to output. Haug and Dewald [22] study how fluctuations in money growth correlate with fluctuations in real output growth and inflation. They find that money growth does not lead or affect real output growth in the longer run.

All cited papers propose that money has a causal effect on output. However, we doubt if relationships can still go on by concerning different lag-length selection criteria used in VAR models. In this paper, the relationships between money and output are retested with more robustness concerns. In addition, we list six different criteria proposed by several scholars as shown in the relevant literature, but few papers cover these different lag-chosen criteria in their empirical studies. So, we wonder that their empirical findings might be based on special lag-chosen criteria. Thus, if all different criteria will produce similar empirical results, the empirical results will be more reliable by taking more robustness concerns into account.

Some central banks in the world might adopt stable monetary policies such as the constant growth rate of money per month or per year; the money volatilities might not be high under such a circumstance. If the low money volatilities would not cause the fluctuation of output, it seems better to adopt stable monetary policies. On the contrary, adjusted money policies might be appropriate if the economy of a country should be stabilized by monetary policy instruments. Since money-output issues seem to be related to monetary policy, transmission mechanisms, and business cycles, we then address more literature for the above issues.

As for the monetary policy, Isik and Acar [23] investigate the relationship between openness and the effectiveness of monetary policy on output by using annual data for the period of 1990-2000 for a panel of 42 countries. Their empirical results support the theoretical expectations that the more open the economy, the smaller the output effects of a given change in the money supply. Mojon [24] provides evidence about how US monetary policy contributes to the drop in the volatilities of US output fluctuations and to the decoupling of household investment from the business cycle. The results show that changes in the size of monetary policy shocks will affect both the correlation between output components and their volatility. Luporini [25] presents evidence on the channel of the monetary policy for the Brazilian economy of the 1990s. He analyzes the effects of an un-

expected change in the baseline interest rate on output in a VAR system, and his empirical results show that a tightening in the monetary policy affects economic activity immediately, reducing the rate of growth of real GDP.

As for the transmission mechanisms, Boivin and Giannoni [26] determine whether the reduction in output and inflation variability has been associated with a change in the transmission of monetary policy, and conclude that the reduced effect of monetary policy shocks is mainly due to a more effective systematic behavior of monetary policy. Ireland [27] proposes that the monetary transmission mechanism describes how policy actions taken by the central bank induce changes in the short-term nominal interest rate or the nominal money stock in order to influence macroeconomic activity, since the central bank controls the monetary base, and is able to increase or decrease the money supply through open market operations, like buying or selling government bonds. Chih- Hsiang et al. [28] study the effects of money supply on real output and inflation in China between 1993 and 2008. The result reveals that real GDP growth in China responds to negative money supply shocks but not positive money supply shocks. Serletis and Rahman [29] investigate the effects of money growth uncertainty on real economic activity, and find evidence that money growth volatility has significant negative effects on output growth.

Concerning business cycles issues, Basistha [30] proposes that stabilization of business cycles is one of the primary goals of monetary policy. The US economy did not experience any recessions or significant inflationary regimes in 1992-2000. One of the potential explanations for this phenomenon is a better monetary policy adopted by the US government. However, Pedersen and Elmer [31] study the connection between the business cycle and economic growth by comparing dates of the business cycle turning point, and find that there might be a connection between the business cycle and economic growth.

Furthermore, Gawin and Kydland [32] find changes in the money supply have effects on the cyclical nature of nominal variables. Booth and Booth [33] also find that the presidential cycle has explanatory power beyond business conditions. Korenok and Radchenko [34] analyze the effect of a monetary policy shock on the business cycle and the extent to which a shift in a monetary policy affects the dynamics of the business cycle. The results reveal that monetary policy shocks have a small but significant impact on persistent and transitory parts of the cycle. From the above literature studies, we find that relevant research about monetary policy instruments, transmission mechanisms and business cycles are mentioned in previous studies.

In this paper, we also apply symmetric and asymmetric lags for the VAR and SUR models in order to distinguish if there exists any differences between the VAR and SUR models. Furthermore, we find that few articles employed by both real data and simulated data in empirical studies. In addition, some scholars like Fung and Kasumovich [35] study the effects of monetary shocks in VAR models for the G6 countries by using the real data. Others like Ozcicek and Mc Millin [4] use simulated data generated by Monte Carlo approach to study the performance of alternative lag-length chosen criteria for symmetric lag and asymmetric lag VAR models. Thus, our empirical study compare the empirical results for both symmetric lag models and asymmetric lag models with concerning different lag-length criteria by employing both actual data and simulated data.

Finally, we summarize what we are doing in this paper as follows: First of all, our empirical study concerns different lag-length selection criteria such as AIC, BIC, FPE, SBC, SIC and HJC. Second, we examine whether concerning asymmetric lag-length are different from concerning symmetric lag-length by employing the six mentioned lag-length chosen criteria. Third, the empirical results which employed simulated data are different from those that employed real data. Fourth, whether the empirical results employed short-term data are different from those employed long-term data.

Since several variables and lag-length selection criteria are mentioned many times in this paper, we, therefore

assign abbreviations for these variables and criteria terms as shown below (Table 1 & Table 2).

Table 2 displays the statistics for M2, IP, MG and GIP, including the means, standard deviations, minimums, and maximums for the M2, IP, MG and GIP. In Table 1, the means for the MG and GIP are 0.0088 and 0.007, and the standard deviations for the MG and GIP are 0.0094 and 0.0933 respectively.

We employ stationary tests to avoid the spurious results before the time series models are set up. Thus, we use unit roots test which test the stationary for the M2 and IP. In Table 3, the Augmented Dickey-Fuller (ADF) and the Augmented Phillips-Perron (APP) values for the level of the M2 and IP are not significant at the 5% level. Thus, differencing series are necessary, and we find the DF, ADF, PP, and APP tests for the log differencing M2 (MG) and log differencing IP (GIP) are all significant, implying that these series are stationary. Additionally, the meanings of log differencing variables for money and output have their economic meaning, since these two variables could be regarded as monetary policy and economic growth variables. Finally, we don’t find cointegration relationships between M2 and IP as shown in the cointegration tests⁹.

Because the presentation of the contents of empirical results for this paper are quite complicated, we therefore put all of the required information together in Table 4 to help readers understand the findings.

In addition, the meaning of equation one and equation two as shown as follows:

Equation One¹¹: GIP = f (MG_t−a, GIP_t−b),

H₁: F value

which a and b indicate the lag lengths chosen for the money variable and output variable¹² for the GIP equation, and H₁ is the hypothesis for the MG Granger-cause GIP. If the F value is significant, it means that the MG Granger-cause GIP.

1) DF(t) means the value of Dickey-Fuller test, ADF(t) means the value of Augment Dickey-Fuller test, PP(t) means the value of Phillips-Perron test, and APP(t) means the value of Augmented Phillips-Perron test; 2) The lag-length of ADF and that of APP are chosen by the AIC criteria; 3) Star (*) means significant at 5% level.

Equation Two¹³: MG = f (MG_t−c, GIP_t−d),

H₂: F value

in which c and d mean the lag lengths chosen for the money variable and output variable for the MG equation, and H₂ is the hypothesis of whether the GIP Granger-cause MG. If the F value is significant, then it implies that the GIP Granger-cause MG.

Based on the above empirical results, we try to compare the difference between the real data and the simulated data¹⁶. We then find that the empirical results are similar in employing either the real data or the simulated data, which are summarized in Table 6.

Table 6 shows the empirical results for symmetric models and asymmetric models by employing real data and simulated data in three time zones. The empirical results for asymmetric models show that feedback effects exist between money and output by applying six different lag-length chosen criteria, which seem to prove the monetary-business-cycle theory¹⁷ and the real-business-cycle theory¹⁸ in our empirical study. However, the results of the symmetric models are somewhat different from those of the asymmetric models by employing the simulated data. The results reveal unidirectional effects from money to output in the data period from Jan. 1996 to Dec. 2004. In addition, the empirical results show no significant relationship between money and output in the data period from Jan. 1988 to Dec. 2004 by applying the simulated data.

Since it doesn’t reveal some structure change for the data period, it implies that symmetric models which employed simulated data are not appropriate, i.e. asymmetric models would be more appropriate than symmetric models in this study.