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This paper investigates the effect of money on output in Taiwan with more robustness concerns. First, we employ different lag-length chosen criteria, such as AIC, BIC, FPE, SBC, SIC, and HJC for the lag length chosen for Granger causality. Second, we use the symmetric and asymmetric lag length models for further investigation. Third, we employ the simulated data and real data for comparison. Fourth, we further compare the results derived from short-term data with those derived from long-term period data. After surveying the relevant literature, we find that these concerns seem rarely concerned in the relevant studies. In addition, our empirical results reveal that the money indeed affects output even after taking the concerns mentioned above for robustness, implying that policymakers should adopt monetary policies with care in Taiwan.

Many economists have applied Granger causality tests to investigate causal relationships among variables since 1969. Thornton and Batten [

In addition, Keating [

We apply VAR models to examine the dynamic relationship between money and output with more robustness concerns. Since different criteria chosen for the optimal lag-length for VAR models might derivate from different results, whether six dissimilar lag-chosen criteria applied in the Granger causality tests will result in similar results is one of the main concerns in this paper. Additionally, while the empirical results are similar by applying different but qualified lag-length chosen criteria, we would regard them as empirical results with the concern of robustness. However, the empirical results might be doubtful, since the empirical results are far from singular when applying several but qualified lag-length chosen criteria.

In this study, the above concerns might induce several worthwhile topics for further research, and there are several question marks shown as follows. What are the important criteria to judge a good model? Should different cases apply different criteria to judge a good model? What are the most important criteria for the lag-length chosen criteria applied in Granger causality tests? Is it certain whether all different sample periods will show the same results? Are there any structure changes which exist during data period?

The empirical results which employed real data might be disturbed by uncertain events, so we use simulated data to reduce the disturbance of empirical studies which resulted from the real data. Therefore, we apply both real data and simulated data to examine whether empirical results will be different by employing different lag- chosen criteria for symmetric models and asymmetric models^{1}.

In summary, we design the following robustness concerns for this study as shown below. First, whether our empirical results are sensitive to different lag-length selection criteria, such as AIC^{2}, BIC^{3}, FPE^{4}, SBC^{5}, SIC^{6} and HJC^{7}? Second, whether the empirical results with concerning asymmetric lag-length would be different from those with concerning symmetric lag-length by using different lag-length chosen criteria? Third, whether the empirical results which used real data will be different from those which used simulated data. Fourth, whether the empirical results tested by short-term data will be different from those tested by long-term data. After concerning the above robustness issue for the empirical study, our empirical results demonstrate that money will still affect output, so policymakers in Taiwan should implement monetary policies with care.

This paper proceeds as follows. Section 1 introduces why we reinvestigate the effect of money on output for Taiwan with more robustness concerns. Section 2 surveys the relevant literature. Section 3 reports the empirical results of this study. Section 4 remarks the conclusion.

Thornton and Batten [

Hsiao [

Similarly, the study of Thornton and Batten [

However, the lag terms selected by the FPE criterion are inadequate for the purpose of testing the Granger causality as suggested by Kang [

Gredenhoff and Karlsson [^{8} performs well in most cases. In addition, Ozcicek and McMillin [

While surveying relevant literature, the traditional information criteria like the Bayesian Information Criterion (BIC) proposed by Rissanen [

Hacker and Hatemi-J [

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 [

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 [

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 [

Concerning business cycles issues, Basistha [

Furthermore, Gawin and Kydland [

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 [

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.

We obtain the monthly data of money (M2) and industrial production (IP) for Taiwan in the AREMOS database established by the Taiwan Economic Data Center for the period from January 1988 to December 2004. The M2 and industrial production are regarded as money variables and output variables respectively. The entire data period from January 1988 to December 2004 are tested. Meanwhile, two short-term data periods, January 1992 to December 2004 and January 1996 to December 2004, are tested in order to examine if different data periods will result in diverse empirical results.

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 (

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 ^{9}.^{}

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

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

Equation One^{11}: GIP = f (MG_{t}_{−a}, GIP_{t}_{−b}),

H_{1}: F value

which a and b indicate the lag lengths chosen for the money variable and output variable^{12} for the GIP equation, and H_{1} is the hypothesis for the MG Granger-cause GIP. If the F value is significant, it means that the MG Granger-cause GIP.

. Abbreviations defined for criterion and variables.

AIC | Akaike’s Information Criterion |
---|---|

BIC | Bayesian Information Criterion |

FPE | Final Prediction Error Criterion |

SBC | Schwarz’s Bayesian Criterion |

SIC | Shibata Criterion |

HJC | Hacker and Hatemi-J’s Criterion |

M2 | Money |

IP | Industrial Production |

MG | Money Growth |

GIP | Growth of Industrial Production |

. Statistics of M2, IP, MG and GIP.

Variable | Data Period: 1988.1-2004.12 | |||
---|---|---|---|---|

Mean | Standard Deviation | Minimum | Maximum | |

M2 | 131677.34 | 57416.44 | 39524.44 | 230006.00 |

IP | 94.17 | 15.78 | 59.70 | 131.72 |

MG | 0.0088 | 0.0094 | −0.0084 | 0.0384 |

GIP | 0.007 | 0.0933 | −0.2249 | 0.3299 |

. Unit root tests for M2 and IP.

Panel A: Data Period (I): 1988.1-2004.12 | |||||||
---|---|---|---|---|---|---|---|

Variable | Trend | ADF(t) | DF(t) | APP(t) | PP(t) | ||

Level | M2 | No | 0.46 | 0.52 | 0.54 | 0.52 | |

Yes | −2.01 | −2.56 | |||||

IP | No | −0.34 | −3.47 | −2.42 | −3.49 | ||

Yes | −2.53 | −9.04* | |||||

Log Difference | M2 | No | −5.60* | −11.72* | −11.92* | −11.77* | |

Yes | −8.22* | −13.55* | |||||

IP | No | −8.87* | −23.08* | −30.84* | −23.20* | ||

Yes | −8.85* | −30.84* | |||||

Panel B: Data Period (II): 1992.1-2004.12 | |||||||

Variable | Trend | ADF(t) | DF(t) | APP(t) | PP(t) | ||

Level | M2 | No | −1.21 | −0.70 | −0.72 | −0.70 | |

Yes | −2.15 | −2.40 | |||||

IP | No | −0.36 | −3.79* | −3.02 | −3.79* | ||

Yes | −2.03 | −7.53* | |||||

Log Difference | M2 | No | −5.23* | −10.23* | −10.23* | −10.23* | |

Yes | −7.79* | −26.23* | |||||

IP | No | −7.14* | −20.55* | −11.25* | −20.55* | ||

Yes | −7.77* | −26.11* | |||||

Panel C: Data Period (III): 1996.1-2004.12 | |||||||

Variable | Trend | ADF(t) | DF(t) | APP(t) | PP(t) | ||

Level | M2 | No | −0.41 | −0.23 | −0.22 | −0.23 | |

Yes | −2.00 | −2.46 | |||||

IP | No | −0.47 | −3.17 | −2.48 | −3.17 | ||

Yes | −2.13 | −7.47* | |||||

Log Difference | M2 | No | −5.70* | −8.39* | −8.23* | −8.39* | |

Yes | −5.86* | −23.38* | |||||

IP | No | −6.63* | −17.53* | −8.23* | −17.53* | ||

Yes | −6.60* | −23.28* | |||||

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 Two^{13}: MG = f (MG_{t}_{−c}, GIP_{t}_{−d}),

H_{2}: F value

in which c and d mean the lag lengths chosen for the money variable and output variable for the MG equation, and H_{2} 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.

The symmetric lag models indicate the same lags chosen for each variable in each equation of the symmetric lag models, but the asymmetric lag models depict different lags chosen for each variable in each equation of the asymmetric lag models.

In this section, we employ the real data series for investigating the relationship between money and output. As shown in the table below, we put all of the information in

In the symmetric VAR models, the F values shown in Grange causality tests selected by the AIC and the SBC lag-length chosen criteria are significant in the both data periods from Jan. 1988 to Dec. 2004 and from Jan. 1992 to Dec. 2004, which means that there exists significant feedback effects between MG and GIP. In addition, in the data period from Jan. 1996 to Dec. 2004, the F values shown in the Grange causality tests selected by the AIC and the SBC lag-length chosen criteria are also significant in the first Granger causality tests, which show unidirectional significant effects from MG to GIP.

While separating the 2 by 2 VAR models into two OLS equations, each OLS equation could select the different lag-length for money and output by employing these lag-length chosen criteria. Similar to symmetric models, the feedback effects also exist between MG and GIP by using AIC, FPE, SBC and SIC lag-chosen criteria. It means that money affects output and output affects money in both data periods from Jan. 1988 to Dec. 2004 and from Jan. 1992 to Dec. 2004.

In the data period Jan. 1996 to Dec. 2004, the feedback effects exist between MG and GIP by using the AIC, FPE, SBC, SIC and HJC criteria, which also means that money affects output and output affects money.

In this section, we simulate the money series by Monte Carlo methods^{14} and compare whether the simulated data will differ from the real data by employing three time zones data.

In the first Granger causality tests, the F tests are significant by employing AIC and SBC criteria in the data period (II). It indicates that money affects output and that the output affects money. However, it also reveals that money affects output only in the data period (III) (

Similar to the symmetric models, the feedback effects also exist between MG and GIP by applying the AIC, SBC, SIC and HJC criteria (i.e. this means that MG affects GIP and GIP affects MG).

. Granger causality for symmetric and asymmetric models for real data.

Period | Data Period (I): 1988.1-2004.12 | Data Period (II): 1992.1-2004.12 | Data Period (III): 1996.1-2004.12 | |||
---|---|---|---|---|---|---|

Criteria | Symmetric Models | Asymmetric Models | Symmetric Models | Asymmetric Models | Symmetric Models | Asymmetric Models |

AIC | (1) (3, 3) H_{1}: 13.08** (2) (15, 15) H_{2}: 11.56* | (1) (12, 24) H_{1}: 4.54* (2) (11, 11) H_{2}: 8.22* | (1) (3, 3) H_{1}: 10.44* (2) (3, 3) H_{2}: 9.13* | (1) (14, 23) H_{1}: 3.76* (2) (12, 12) H_{2}: 4.44* | (1) (1, 1) H_{1}: 12.47* (2) (1, 1) H_{2}: 0.35 | (1) (12, 24) H_{1}: 3.46* (2) (1, 3) H_{2}: 13.80* |

BIC | (1) (1, 14) H_{1}: 2.97* (2) (2, 15) H_{2}: 14.92* | (1) (1, 13) H_{1}: 2.47 (2) (1, 15) H_{2}: 13.29* | (1) (1, 13) H_{1}: 2.71 (2) (1, 24) H_{2}: 7.58* | |||

FPE | (1) (24, 24) H_{1}: 2.83* (2) (24, 24) H_{2}: 2.56* | (1) (22, 21 ) H_{1}: 2.97* (2) (18, 24) H_{2}: 3.02* | (1) (16, 13) H_{1}: 2.19* (2) (2, 24 ) H_{2}: 7.31* | |||

SBC | (1) (3, 3) H_{1}: 13.08** (2) (15, 15) H_{2}: 11.56* | (1) (1, 14) H_{1}: 2.97* (2) (2, 11) H_{2}: 16.73* | (1) (3, 3) H_{1}: 13.08** (2) (3, 3) H_{2}: 11.56* | (1) (1, 13) H_{1}: 2.47* (2) (1, 3) H_{2}: 18.75* | (1) (1, 1) H_{1}: 12.47* (2) (1, 1) H_{2}: 0.35 | (1) (1, 13) H_{1}: 2.71* (2) (1, 3) H_{2}: 13.80* |

SIC | (1) (14, 24) H_{1}: 4.16* (2) (24, 24) H_{2}: 2.56* | (1) (20, 24) H_{1}: 2.43* (2) (24, 24) H_{2}: 2.13* | (1) (24, 23) H_{1}: 2.32* (2) (24, 23) H_{2}: 2.08* | |||

HJC | (1) (1, 14) H_{1}: 2.97 (2) (2, 11) H_{2}: 16.73* | (1) (1, 13) H_{1}: 2.97* (2) (1, 3) H_{2}: 18.75* | (1) (1, 3) H_{1}: 15.30* (2) (1, 3) H_{2}: 13.80* |

1) Star (*) means significant at 5% level; 2) The criteria for BIC, SIC, and FPE are selected by equation by equation. The symmetric lag models will select the same lag length for each variable in each equation. Therefore, the empty spaces are due to the above reason.

. Granger causality for symmetric and asymmetric models for simulated data.

Period | Data Period (I): 1988.1-2004.12 | Data Period (II): 1992.1-2004.12 | Data Period (III): 1996.1-2004.12 | |||
---|---|---|---|---|---|---|

Criteria | Symmetric Models | Asymmetric Models | Symmetric Models | Asymmetric Models | Symmetric Models | Asymmetric Models |

AIC | (1) (15, 15) H_{1}: 0.89 (2) (15, 15) H_{2}: 1.40 | (1) (1, 24) H_{1}: 8.05* (2) (11, 11) H_{2}: 12.89* | (1) (3, 3) H_{1}: 10.44* (2) (3, 3) H_{2}: 9.13* | (1) (24, 23) H_{1}: 2.53* (2) (12, 12) H_{2}: 4.44* | (1) (1, 1) H_{1}: 12.47* (2) (1, 1) H_{2}: 0.35 | (1) (12, 24) H_{1}: 3.46* (2) (1, 3) H_{2}: 13.80* |

BIC | (1) (1, 13) H_{1}: 5.55* (2) (24, 3) H_{2}: 12.89* | (1) (1, 13) H_{1}: 2.47 (2) (1, 15) H_{2}: 13.29* | (1) (1, 13) H_{1}: 2.71 (2) (1, 11) H_{2}: 9.34* | |||

FPE | (1) (24, 24) H_{1}: 1.17 (2) (24, 24) H_{2}: 2.30* | (1) (17, 24 ) H_{1}: 2.41* (2) (18, 24 ) H_{2}: 3.02* | (1) (16, 12) H_{1}: 3.07* (2) (2, 24) H_{2}: 7.31* | |||

SBC | (1) (15, 15) H_{1}: 0.89 (2) (15, 15) H_{2}: 1.40 | (1) (1, 13) H_{1}: 5.55* (2) (24, 3) H_{2}: 12.89* | (1) (3, 3) H_{1}: 13.08** (2) (3, 3) H_{2}: 11.56* | (1) (1, 13) H_{1}: 2.47* (2) (1, 3) H_{2}: 18.75* | (1) (1, 1) H_{1}: 12.47* (2) (1, 1) H_{2}: 0.35 | (1) (1, 13) H_{1}: 2.71* (2) (1, 3) H_{2}: 13.80* |

SIC | (1) (1, 24) H_{1}: 8.05* (2) (24, 3) H_{2}: 12.89* | (1) ( 20, 24) H_{1}: 2.43* (2) (24, 24) H_{2}: 2.13* | (1) (24, 23) H_{1}: 2.32* (2) (24, 23) H_{2}: 2.08* | |||

HJC | (1) (1, 13) H_{1}: 5.55* (2) (24, 1) H_{2}: 20.12* | (1) (1, 13) H_{1}: 2.47* (2) (1, 3) H_{2}: 18.75* | (1) (1, 13) H_{1}: 2.71* (2) (1, 3) H_{2}: 13.80* |

1) Star (*) means significant at 5% level; 2) The criteria for BIC, SIC, and FPE are selected by equation by equation. The symmetric lag models will select the same lag length for each variable in each equation. Therefore, the empty spaces are due to the above reason.

Based on the above empirical results, we try to compare the difference between the real data and the simulated data^{16}. We then find that the empirical results are similar in employing either the real data or the simulated data, which are summarized in

^{17} and the real-business-cycle theory^{18} 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.

This paper employs M2 and IP data from January 1988 to December 2004, and three time zones, January 1988

. The summary of evidence for all sample periods.

Period Model Data | Data Period (I) (1988.1-2004.12) | Data Period (II) (1992.1-2004.12) | Data Period (III) (1996.1-2004.12) | |||
---|---|---|---|---|---|---|

Symmetric Models | Asymmetric Models | Symmetric Models | Asymmetric Models | Symmetric Models | Asymmetric Models | |

MG & GIP (real data) | . The summary of evidence for all sample periods. | . The summary of evidence for all sample periods. | . The summary of evidence for all sample periods. | . The summary of evidence for all sample periods. | . The summary of evidence for all sample periods. | . The summary of evidence for all sample periods. |

MG & GIP (simulated data) | . The summary of evidence for all sample periods. | . The summary of evidence for all sample periods. | . The summary of evidence for all sample periods. | . The summary of evidence for all sample periods. | . The summary of evidence for all sample periods. |

1)

to December 2004, January 1992 to December 2004 and January 1996 to December 2004, are investigated. The simulated data and real data are tested respectively in symmetric models and the asymmetric models by six different lag-chosen criteria are used to investigate whether the money will still affect the output.

In the empirical study, even though both symmetric models and asymmetric models employ six different lag- length selection criteria, the empirical results still reveal that feedback effects exist between money and output by applying different lag-length chosen criteria. Therefore, these empirical results prove that the monetary- business-cycle theory and the real-business-cycle theory exist.

However, the results show somewhat different outcomes between the real data and the simulated data in symmetric models for the data period from Jan. 1988 to Dec. 2004, since the feedback effects exist between the money and output by using the real data, and no relationship exists between the money and output by using the simulated data. It might infer that the symmetric models employed simulated data that might not be appropriate, since the real data might be more reliable than the simulated data.

In addition, this paper has the following concerns which are different from the relevant literature. First, one of the concerns is that the Granger causality results are sensitive if the lag-length chosen criteria for testing Granger causality by employing different lag-length chosen criteria, such as AIC, BIC, FPE, SBC, SIC, and HJC are applied. Second, whether the empirical results used by asymmetric lag length models are different from those used by symmetric lag length models is examined. Third, whether the empirical results applied by simulated data might vary with those applied by real data is also covered in this study. Fourth, whether empirical results applied with the short-term data are different from those applied with the long-term data is also examined. Although the empirical results show little difference for the symmetric model in the data period from Jan. 1988 to Dec. 2004, most of empirical results show that money and output may have significant feedback effects. It implies that the policymakers need to cautiously stabilize monetary policies to avoid economic fluctuation in Taiwan.

Since empirical studies might be based on special models and special criteria, the empirical study might be necessary to have more robustness concerns in order to make the reader trustworthy. In this paper, we obtain more robustness results from Taiwan’s evidence, and hope that these robustness concerns can be achieved in other countries for future study. These concerns, when applying different lag-length chosen criteria, for the symmetric models and asymmetric models, by real data and stimulated data, investigated the empirical results by data from different time zones. These findings are important concerns for further empirical study.

We thank the editor and anonymous reviewers for giving precious suggestions.