Empirical study of causality between Real GDP and Monetary variables. Presented by : Hanane Ayad

overview Since the early 60’s, the literature concerning the interaction between monetary variables and real income, especially in U.S, have taken an new direction. Many of those models have been constructed to take into consideration some sophisticated channels through which money can influence Real Income. However, the empirical results gathered so far still do not lead to a clear path as to whether monetary variables do have a direct or whatever kind of effect on the real GDP.

Chronology of literature The earliest study dealing with the causal relationship between money and GDP was performed by Freidman and Schwartz (1963). Nine Years later, Sims(1972) came to argue that it is quite inappropriate to distinguish between cause and effect based only on correlation pattern. Eight years later (1980),Sims suggested a vector auto regression process that takes into consideration the eventual effect of additional controlling macroeconomic variables.

Chronology of literature The causality between money and GDP that Sims found in (1972) disappered as soon as he included a short term interest rate as a controlling variable. Others later found a strong evidence of causality when they use log level data and no significant effect of money on income when they adopt first difference data Stock and Watson (1989) adopted a first differenced log data, they found that M1 growth affects GDP growth when they included a Trend function, this monetary effect vanished once they increased the sample size, and added interest rate as an explanatory variable Dufour and Tessier (1997)came up with a more ingenious and logically coherent specification VARMA- Echelon.

Objectives of the empirical study Establish a causal link between monetary variables(m1 interest rate) and real GDP. Investigate the “nature” of the dynamic of this relationship. Detect a long run relationship and the speed of convergence into equilibrium (if there any)

methodology The most commonly used test for causality is the standard granger causality test. The best method that can be used to test the causality of cointegrated variables is the ECM procedure. The main advantage of this methodology: it does not only detect the causality effect, but also gives an idea about the long run relationship between the variables. If the variables are not cointegrated, the ECM is inappropriate, the best alternative in this case is the use of a VAR in difference process.

In this paper, I intended to test the causality between between some Monetary variables: m1, interest rate, CPI, and the real GDP using the ECM procedure. Before using the ECM, we need to make sure that all the four time series have the same unit roots. If it is the case, we then test for cointegration among the four variables, if they are cointegrated, we then can proceed to the second step of ECM, and run the long run regression: D(RGDP)=a+b1D(RGDP t-1 )+ b2D(M1t- 1+b3D(INTRTt - 1 )+b4D(CPI t-1 )+b5Ut-1+et In the case of no cointegration, we, use the VAR differenced, and test for the significance of the lagged independent variables. If the variables do no have the same unit roots, we just use the standard Granger causality test

Econometrics analysis Simulations reveals that the four variables are all I(1)for example of the real M1: ADF (M1 LEVEL ) ADF Test Statistic % Critical Value* % Critical Value % Critical Value ADF M1 (FIRST DIFFERENCE) ADF Test Statistic % Critical Value* % Critical Value % Critical Value

Econometrics analysis ADF RES2 (LEVEL) ADF Test Statistic % Critical Value* % Critical Value % Critical Value The residuals have a unit root of more than o, hence, the variables are not cointegrated, in this case, the use of ECM procedure is inappropriate. The best method than can be adopted in the absence of cointegration is the VAR in difference

cointegration We say that Xt and Yt are cointegrated if there is a long run relationship between Xt and Yt. If we have two non-stationary time series that have the same unit roots, let say X t = T(t) + e (x)t, and Y t = z(t) +e (y)t, where T(t), Z(t) are trend terms, e (x)t and e (y)t are white noise. If these two series can be written as a linear combination so that the trend terms cancels out, then we can say that X t and Y t are cointegrated. This can be done through testing the unit root for the residuals resulting from regressing Yt on Xt (Xt and Yt ) has the same unit root. The residual should have unit root less than that of the variable. Less say X t →I(b) and Y t → I(b) If Ut → I(d) where d is less than b. Them we can say that Xt and Yt are cointegrated.

Unit Root Y t = a + b t + U t where U t is the white noise and t is the trend factor. Y t-1 = a + b( t-1 ) + U t-1 ∆Y = a + Ut - U t -1. If we manage to cancel out the trend factor by differentiating only one time this means that Yt has one unit root. The DF test is done as follows: H0: THE VARIABLES HAS 1 UNIT ROOTHa: b < 0. ADF test done the same way, but we just add other lag difference terms of the dependent variable. So that we can control for higher order correlation. If ADF is less than ADF critical value we don’t reject the null.

Var in Difference ∆Y t = C 1 + a 11 ∆Y t-1 + a 12 ∆X t-1 + U 1 t ∆X t = C 2 + a 21 ∆Y t-1 + a 22 ∆X t-1 + U 2t We notice that the dependent variables are different but the set of the independent variables are the same.

Results of the VAR After analyzing the VAR in difference results, it seems plausible( Based on t-statistics) that: Interest rate has a direct effect on M1 M1 has a direct effect on CPI CPI has a direct effect on GDP Overall Even though M1 does not have a direct effect on RGDP, it affects RGDP indirectly through CPI

conclusion This paper dealt first with detecting if there is a long relationship between variables: unit rot testing was used to achieve this objective. Econometrics results reveals that monetary variables have an impact and a causal relationship on real GDP, but there were no evidence that they play any statistical significant role in the determination of real GDP in the long run.