Evolution of money supply and gross domestic product are in a close relationship, inthis paper we analysis this relationship in order to construct a function which will explicit thisconnection for Romania. Evolution of gross domestic product is one with a seasonal component sofrom the data series we will be eliminating seasonality with the X-12 ARIMA method. Analyzing thedata of money supply (M3) and of GDP over ten years through the Augmented Dickey-Fuller weobtained that both series are non-stationary. Applying the co-integration analysis method Engle-Granger we conclude that the two series have a cointegration relationship between them. We willpropose a model explanation of the link between the two sets of data type, a DVAR model.money supply (M3), GDP, seasonality, stationarity, cointegration, DVAR.

Daniela Zapodeanu

Mihail Ioan Cociuba

English

Research Papers in Economics

Annales Universitatis Apulensis Series Oeconomica, 12(1), 2010 
  501
LINKING MONEY SUPPLY WITH THE GROSS  
DOMESTIC PRODUCT IN ROMANIA 
 
 
Daniela Zapodeanu 
1 
Mihail Ioan Cociuba 
2 
 
 
ABSTRACT: Evolution of money supply and gross domestic product are in a close relationship, in 
this paper we analysis this relationship in order to construct a function which will explicit this 
connection for Romania. Evolution of gross domestic product is one with a seasonal component so 
from the data series we will be eliminating seasonality with the X-12 ARIMA method. Analyzing the 
data of money supply (M3) and of GDP over ten years through the  Augmented Dickey-Fuller we 
obtained that both series are non-stationary. Applying the co-integration  analysis method Engle-
Granger we conclude that the two series have a cointegration relationship between them. We will 
propose a model explanation of the link between the two sets of data type, a DVAR model. 
 
Key words:  money supply (M3), GDP, seasonality, stationarity, cointegration, DVAR. 
 
JEL codes:G17, C51. 
 
 
  Fundamentals notions. 
  Starting from the well  known quantity theory of money of Irving Fisher: M*V=P*Q, where 
M is money, V - velocity of money, P - price level and Q - the quantity of goods and services from 
an economy, we try to analyze the relationship between GDP (value of goods and services in a 
country) and money.  Highlighting the long-term stable relationship between money  growth and 
inflation, usually indicates that monetary mass is within the increase in economic activity (GDP) 
[Zăpodeanu, 2002: 31]. 
  Analysis conducted in other countries showed that money demand function is a function 
which is not stable over time [Blundell-Wignall, 1984] -because of changes that may occur in the 
interest rate and inflation expectations,or either because of changes in function itself ( changing its 
on structure). Analyzing the demand for money in Austria [Hayo, 2000] through a VAR a model  
(vector autoregressive model) notes that the demand for money is stable, having an elastic monetary 
aggregate M1 uniform and independent on to GDP rate, while M1 and M2 monetary aggregates are 
influenced by income level and long-term interest rate (inverse relationship), for the euro zone 
[Brand et all, 2000] uses a structural cointegrated VAR model for the money demand (M3) and 
finds a relations between long-term interest rates and GDP. The analysis of demand for money in 
Venezuela [Cuevas, 2002]  shows that the best function used is VECM (vector error correction 
model), which achieves a positive subunit elasticity of demand for currency in relation with  GDP 
and  a  negative  subunit  elasticity  to  inflation.  Analyzing  the  demand  for  money  in  transition 
economies [Ozturk, Acaravci, 2008] using an feasible least squares model (FGLS) found a long-run 
positively connection with real GDP and an inverse relationship with inflation and real effective 
exchange rate. Analyzing the Czech Republic [Bednarik, Radek, 2010] use the VAR method for 
analyzing the relationship between money supply and GDP, using co-integration test notes that the 
                                            
1  University of Oradea, Faculty of Economics, danizapodeanu@yahoo.com 
2  University of Oradea, Faculty of Economics, cociuba@gmail.com Annales Universitatis Apulensis Series Oeconomica, 12(1), 2010 
  502
two series are not co-integrated, and for the Granger causality test they concluded that there isn't 
any causality between the two series. In conclusion to build money demand function it should be 
analyzed the data sets, using specific tests and then testing the obtained models. This paper will 
analyze the connection between the GDP and money series in order to build a capable function, 
which will correctly explicit monetary and economic realities. 
  We will define money as “non-bank agents all claims on the banking system”, it is formed 
according to the NBR
3 method from three monetary aggregates: the narrow money (M1) which 
comprises currency in circulation (notes and coins) and deposits immediately convertible into cash 
or which can be used for payments via bank transfer overnight deposits; intermediate money (M2) 
comprises narrow money in the (M1) and deposits with initial term of up to two years including 
deposits redeemable at notice up to 3 months including. The definition of M2 mirrors the interest in 
analyzing and monitoring a monetary aggregate which, apart from cash, includes deposits with high 
liquidity;  broad money  (M3)  comprises  intermediate money  (M2), plus  marketable instruments 
issued by monetary  financial institution's  sector; money market instruments, especially shares / 
units  of  money  market  funds  and  borrowings  from  repurchase  agreements  are  included  in  the 
aggregate (greater liquidity makes these instruments be substitutes for deposits). 
 
  Data used and methodology 
  The data used are gross domestic product (GDP) and broad money (M3) and the monetary 
aggregates M1 and M2, the series of data were obtained from monthly reports NBR for M1, M2, 
M3 and the base of Eurostat for GDP They span the period between 1999 - 2010,  the data used are 
quarterly, the number of observations is 45
4.  In the research has been used the open source software 
for econometric analysis Gretl (GNU regression, Econometrics and Time-series Library). 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Fig. no 1.-  Methodology of Granger causality test  
(Sursa : Pop Silaghi, M.I. , Exports-Economic growth causality: Evidence from CEE Countries, pg.108, Romanian 
                                            
3   The same methodology is applied to the ECB. 
4   The data used are given in The Appendix. Annales Universitatis Apulensis Series Oeconomica, 12(1), 2010 
  503
Journal of Economic Forecasting,pg. 108, no. 2/2009,http://www.ipe.ro/rjef.htm) 
The research carried out has the following structure: a graphical analysis of data series, 
seasonality  analysis  for  GDP  (and  elimination),  stationary  series  analysis  (ADF  test),  testing 
cointegration, proposed models, causality analysis. 
   
Fig. no 2 - Graphical analysis of time series GDP, M1, M2, M3 
 
Representation  of  data  series  shows  that  GDP  has  a  strong  seasonality,  which  will  be 
removed using the X-12 ARIMA methodology used by the U.S. Bureau of Statistics, on the broad 
money supply and monetary aggregates M1,M2 series is noted that this are no stationary series; in 
order  to  make  them  stationary  they  need  to  be  differentiated.  The  money  aggregates  have  a 
continuous growth rate, except for M1, the explanation for the narrow monetary aggregate decline 
lies in the fact that due to economic crisis the revenues decreased, and also the decline in circulation 
cash.  
 Annales Universitatis Apulensis Series Oeconomica, 12(1), 2010 
  504
Fig. no 3 - GDP Seasonality 
 
Analyzing the series stationarity 
  The stationarity concept was defined in the work of Box-Jenkins [1984], stationarity implies 
that the process is invariably if analyzed in time, these conditions must be met: the average of time 
series  are  constant  and  series  variance  is  constant..[Codirlasu,  2008]  If  a  stationary  process  is 
affected by a stochastic shock effect, in time it  will disappear, because of non-persistent errors 
property. [Mester, 2007]
 For analyzing stationarity the most used test is the Augmented Dickey 
Fuller test, which is a test that estimated by the method of least squares the equation: 
 
Δ yt = δ yt-1 + Σ γj *Δ yt-j +α+β*t+vt. 
 
It will test the hypotheses: H0 :  δ=1 and  H1 :  δ<1  
 
Table no. 1 
ADF Tests 
Series 
Name 
F- Statistic  Probability  Stationary 
series 
GDP
5  −0.4262    0.90  No 
M3  −1.786      0.71  NO 
d_GDP
6  −1.829      0.06  Yes, P>90% 
d_M3  −3.290     0.02  Yes, P>95% 
 
According to tests conducted we conclude that M3 and GDP series are not stationary, but their 
first difference, or d_M3 d_GDP, are stationary and so further analysis will be made to see whether 
the series are cointegrated. 
 
   
                                            
5  Gross domestic product is tested by eliminating seasonality 
6  It tests the first difference of variables GDP and M3 Annales Universitatis Apulensis Series Oeconomica, 12(1), 2010 
  505
Testing cointegration 
Cointegration is a statistical property of time series, if two or more series are not integrated 
individually, but a linear combination of them has a lower order of integration, then the series are 
said  to  be  co-integrated.  Co-integration  is  a  methodology  of  testing  hypotheses  about  the 
relationship between two variables having unit roots, the test is: testing stationarity series. First we 
use a  series  of  linear regression  between money  supply and  gross  domestic  product  using the 
method of least squares, then testing stationarity for residuals, this is achieved by applying the ADF 
test on the residuals, if they are stationary then the series are co-integrated , or otherwise they are 
not co-integrated. 
 
Step 1: cointegrating regression 
OLS, using observations 1999:1-2010:1 (T = 45) 
Dependent variable: GDP_d11 
                coefficient     std. error        t-ratio     p-value  
  ----------------------------------------------------------------------- 
  const      16662.6        1824.68         9.132       1.26e-11 *** 
  M3         0.647050      0.0186637     34.67       4.61e-33 *** 
Step 2: testing for a unit root in uhat (ADF test) 
including one lag of (1-L)uhat 
sample size 43 
unit-root null hypothesis: a = 1 
   model: (1-L)y = b0 + (a-1)*y(-1) + ... + e 
   1st-order autocorrelation coeff. for e: 0.029 
   estimated value of (a - 1): -0.0967796 
   test statistic: tau_c(2) = -1.76596 
   asymptotic p-value 0.647 
   
The first step of the test is to achieve a type of linear regression y = a * x + uhat, in this cae 
GDP variable is considered dependent and the explanatory variable is the money series. Residuals 
values are then analyzed using the ADF test, where it appears that they are not integrated of order 
zero I (0), with a probability of  over 64%. Same test also shows that there  is a possibility of 
integration of order one I (1) of uhat (residuals) series. The model will be one of the types of vector 
model  DVAR,  autoregressive  the  difference.  VAR  model  allows  symmetrical  treatment  of  all 
variables in the model, implicitly assumes that a certain variable is not exogenous and it is intended 
to be used when the one doesn't know for sure if a variable is exogenous.  
  In a VAR model with two variables the evolution of x variable will be influenced by past 
values (lag-s) of x, and current and previous values of y. Also, we assume that y is affected by 
lagged values of him, and current or previous values of x. Therefore, the system bi-variate simple 
(primitive form of the system) is described as follows: 
 
 
 
-where it is  assumed  that both  x  and  y are stationary  variables  and εxt and  εzt  are  white  and 
uncorrelated noise (also true in general for a VAR model).  
Model is obtained as: Annales Universitatis Apulensis Series Oeconomica, 12(1), 2010 
  506
VAR system, lag order 6 
OLS estimates, observations 2000:4-2010:1 (T = 38) 
Equation 1: d_M3 
                              coefficient       std. error     t-ratio      p-value 
  ---------------------------------------------------------------------------- 
  const                    1681.84         1848.51        0.9098     0.3716  
  d_M3_1               0.652607        0.209131     3.121       0.0045  *** 
  d_M3_2             −0.164053        0.297057    −0.5523    0.5857  
  d_M3_3             −0.196033        0.244194    −0.8028    0.4297  
  d_M3_4               0.414031        0.215361      1.923       0.0660  * 
  d_M3_5             −0.270799        0.233454    −1.160       0.2570  
  d_M3_6               0.499477         0.313375     1.594       0.1235  
  d_GDP_d11_1     0.0772018       0.460433     0.1677     0.8682  
  d_GDP_d11_2   −0.0116218       0.442275   −0.02628   0.9792  
  d_GDP_d11_3     0.258799         0.356250     0.7265     0.4743  
  d_GDP_d11_4     0.00828416     0.347111     0.02387    0.9811  
  d_GDP_d11_5   −0.905393         0.554954   −1.631       0.1153  
  d_GDP_d11_6     0.251037         0.584566     0.4294      0.6713 
 
Equation 2: d_GDP_d11 
                                 coefficient         std. error        t-ratio        p-value  
  ------------------------------------------------------------------------------------------ 
  const                      3139.31         809.627              3.877     0.0007   *** 
  d_M3_1                 0.465694       0.0915971          5.084     3.00e-05 *** 
  d_M3_2                 0.109037       0.130108            0.8381   0.4099   
  d_M3_3                 0.255453       0.106954            2.388     0.0248   ** 
  d_M3_4              −0.00486469     0.0943254      −0.05157   0.9593   
  d_M3_5              −0.343428       0.102250          −3.359       0.0025   *** 
  d_M3_6                0.111044       0.137254            0.8090      0.4261   
  d_GDP_d11_1      0.176880       0.201664            0.8771      0.3888   
  d_GDP_d11_2    −0.0195679      0.193711         −0.1010      0.9203   
  d_GDP_d11_3      0.0168844      0.156033           0.1082      0.9147   
  d_GDP_d11_4    −0.412313       0.152031          −2.712        0.0119   ** 
  d_GDP_d11_5    −0.201157       0.243063          −0.8276      0.4157   
  d_GDP_d11_6    −0.540244       0.256033          −2.110        0.0450   ** 
 
From the results we can conclude that the monetary aggregates (M3) are influenced only by 
it's lags, respectively lag 1 and 4; the evolution of  GDP is influenced by M3 lags and also by 
previous values of GDP, the rest of the coefficients not being representative at the usual 5-10% level 
of confidence.      
 
  Conclusion   
Based on the analysis of knowledge and theories in the field we performed an analysis of the 
relationship that exists between the GDP and money supply. We made stationarity and cointegration 
tests, which showed that the analyzed series are non-stationary and we analyzed the co-integration 
between them, the conclusion reached is that the best model explicating the link between the two 
variables vector model DVAR autoregressive in its difference.  
 
 Annales Universitatis Apulensis Series Oeconomica, 12(1), 2010 
  507
The two equations are then: 
 
d_M3    = 0.65* d_M3-1+ 0.41* d_M3-4  + εt 
d_GDP  = 3139.31 + 0.46* d_M3-1 +0.25*  d_M3-3 -0.34* d_M3-5 - 0.41*d_GDP-4 -0.54* d_GDP-6 
 
Further research will be conducted and tests will be made on this type of model. Changes in 
GDP is explained much more consistent with a model type DVAR than the M3, also analyzing M3 
series we  note that the variation does not depend on gross domestic product but on its previous 
levels, thus an autoregressive(ARMA or ARCH ) model can be deployed in future. Further we 
propose the development and testing DVAR model and ARIMA model for the money series. 
 
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LINKING MONEY SUPPLY WITH THE GROSS DOMESTIC PRODUCT IN ROMANIA

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