Long-Run Money Neutrality and Long-Run Super Neutrality
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06/06/19 Examples Reference this
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- Introduction
In the economic literature, the positive correlation between money supply and the price level is well accepted in economic literature. It roots from the quantity theory of money. The theory suggests that permanent and stochastic shocks in the money supply will increase the price level proportionally. Consequently, it has no effect on the real variable as time elapses. The theory also claims that the injection of money into the market will only affect nominal output, not the real output as the production and technology remain the same. In simpler words, money is claimed to be neutral – an idea that has been argued by economists, particularly in the short run. Lucas Jr (1996) described Long-Run Money Neutrality (LRN) as a situation where changes in the money supply will only change nominal variables such as nominal GDP, nominal exchange rate, and nominal wage, without making any changes in real variable such as investment, real consumption, and real output. Long-Run Super Neutrality (LRSN) of money is a situation where changes in the growth of the money supply will not cause any changes in real variables unless inflation occurs (Arintoko 2011).
There are few published papers that developed models to test the hypothesis of (super)neutrality of money in the long-run including Lucas (1988), Bullard (1994), Geweke (1986) and Bullard and Keating (1994). But, models developed by Fisher and Seater (1993) and King and Watson (1992) make use of the recent advancement in the theory of nonstationary regressors to develop test on the proposition of money (sper)neutrality (Serletis and Koustas 1998). In this paper, I will be using the framework published by Fisher and Seater (1993) to test the LRN and LRSN hypotheses. By LRN, Fisher and Seater (1993) meant that any permanent, exogenous money supply shock level will not have an impact towards real variable, and LRSN is defined as any permanent and exogenous money supply growth shock will not have an impact on real variables.
They formalized LRN and LRSN in the context of Autoregressive Integrated Moving Average (ARIMA) model. They showed that the restrictions imposed by LRN and LRSN depend critically on the order or integration of the money supply and the real variable. For example, money must be at least integrated of order one, otherwise, we cannot study the effect of a permanent change in the money supply simply because it does not exist. They also showed that money and real variable series should not have a stable long-run relationship between them to have a meaningful analysis of money (super)neutrality using this model. The model will be explained in detailed in section 3.
In this dissertation, I will attempt to study neutrality and superneutrality of money in the long-run, so the short-run dynamics of the economy resulting from monetary shocks will not be discussed in this paper since it is not relevant. The empirical study on the long-run money neutrality is important as it will determine if monetary policy is relevant and effective to be used in a country. Hence, it is crucial for monetary authorities to have prior knowledge of money neutrality of a country before making decisions on monetary policy.
This paper will test the hypothesis of long-run money neutrality using quarterly data of M1 and real GDP data from nine Organisation for Economic Co-operation and Development (OECD) countries namely Australia, Canada, Chile, Iceland, Israel, South Korea, Mexico, Turkey, and Switzerland. This paper is interesting because I include both developed and developing countries in the analysis, unlike other papers that usually focus only on one of the groups of countries. This assignment is organized as follows. Section 2 discusses the theory behind the neutrality of money and briefly describe the empirical findings in the past. Section 3 discusses the framework developed by Fisher and Seater (1993). I examine the order of integration and cointegration properties of the data used in the fourth section, ushering into the fifth section which discusses the empirical results for LRN. Section six presents the analysis of LRSN and the final section presents a concluding remark.
- Literature Review
2.1 Theoretical
MV=PY
Newcomb (1913) developed the famous version of the quantity theory of money (QTM). It started back then with the monetarist theorist Hume (1752) and popularized by Irving Fisher in the early of 19^{th} century. The right-hand side of the QTM describes the transfer of goods, services or securities while the left-hand side corresponds to the transfer of money (Friedman 1989). The equation shows the direct relationship between the nominal GDP
PYwith the money supply
M. So, the change in
Mwill either reflect in an increase in the real output or rise in the price. It is possible for velocity to decrease, but if we look at data, the velocity of transaction tends to be stable overtime. This is where the (non)neutrality of money plays a key role. If money is neutral, increasing money is not going to affect real output, thus increasing the price instead. Then it is not possible to use monetary policy as a tool to stimulate the economy-this is the classical theory. On the other hand, if the Keynesian economists are correct, that the price is sticky, then injecting money into the market might be able to increase the production capacity in the economy. Though, in this aspect, these theories do not totally contradict each other. Monetarists’ opinion is more accurate in the long-run, and Keynesians’ argument is true in the short-run as prices will take time to adjust.
The theory is mapped into the proposition of money neutrality. Few researchers such as Fisher and Seater (1993) and King and Watson (1992) have come up with models to test the hypothesis of money (super)neutrality. The model developed by Fisher and Seater (1993) will be used in this paper. The model formalized the classical concept of LRN and LRSN in the context of bivariate log-linear ARIMA framework and derived testable implications for both of proposition (Fisher and Seater 1993). The only assumption made in this model is that the money supply is exogenous in the long-run. King and Watson (1992) also used the same approach to test the proposition of LRN and LRSN, but without the assumption of long-run money exogeneity. King and Watson (1992) allowed money to be determined endogenously in the long-run.
In the process of testing LRN, both models show that the test is possible only if both money and real variables series are non-stationary (at least integrated of order one). This is intuitive because if the money supply is integrated of order zero (stationary), then we cannot impose the test on the long-term effect of permanent, exogenous money supply shock to the real variable since the permanent shock is non-existing. On the other hand, if the real variable is integrated of order zero, then the series is stationary in the long-run and we can conclude without further analysis that money is neutral in the long-run. For the LRSN test, the integration of the real variable must be at least one plus the order of integration for the money supply. The LRSN test is only applicable for countries that satisfy the LRN. Empirical evidence found in the past will be reviewed in the next sub-section
2.2 Empirical
McCandless and Weber (1995) used data from 110 countries over three decades to examine long-run monetary facts. They found that the growth rate between money supply and price are highly correlated, the growth rate of money is independent of the growth rate of real output and inflation is uncorrelated with the real output growth. The first relationship exhibits a high correlation coefficient, 0.9 regardless of the type of money supply used. However, in all of the results presented, the authors did not display the standard errors for coefficients. This raises doubt about the reliability of the results produced.
Bae and Ratti (2000) investigated the hypothesis of LRN and LRSN in Argentina and Brazil, using Fisher and Seater (1993) model, authors make use of long, low-frequency data in the period of high rates of inflation in both countries due to bank insolvency. The neutrality of money in both countries hold by construction because the money growth is I(2) and real output series is integrated of order one (1), but the data does not support the hypothesis of superneutrality in both countries.
Leong and McAleer (2000) and Wallace and Cabrera-Castellanos (2006) examined the neutrality hypothesis in Australia and Guatemala respectively. In both papers, they use two different measure of money, M1, and M2. When M1 is used to test the money neutrality with respect to real output, they found that money is neutral, but when broad money[1] is used, the hypothesis of neutrality of money is rejected. This is true for both countries. Apart from the two papers, Noriega (2004) also performed the neutrality test on few countries including M1 and M2 from Mexico as a variable for money supply. She found out that money neutrality holds for M2 in Mexico, but not for M1. It shows that the conclusion of money neutrality is not robust to the type of money used in the analysis.
Few other papers used different models such as King and Watson (1992) to study the long-run (super)neutrality of money . Serletis and Koustas (1998) used data over a hundred years of yearly observation on money and real GDP for countries: Australia, Canada, Denmark, Germany, Italy. Japan, Norway, Sweden, the UK and the US. The results are mixed, but mostly supported the quantity theory of money where money is neutral. Hence, using monetary policy will not be effective if the purpose of the policy is to stimulate the economy.
Puah, Habibullah et al. (2006) study the LRN preposition in the context of Malaysian economy using Divisia M1 and M2 as the measure of money using quarterly data 1981: to 2004:4. They found that the proposition of money neutrality does not hold in both measurements of money. Later on, Chin-Hong, Muzafar Shah et al. (2009) used stock indexes to test the hypothesis and used M1 and M2 as the measurement of monetary aggregate. It confirms the earlier finding that: money is not neutral in Malaysia, regardless of the type of money used in the analysis. Just like both papers, I will be using Fisher and Seater (1993) model to test for LRN of money. The model will be explained in detail in the next section
- The Methodology
In this study, I will be using an econometric method derived by Fisher and Seater (1993) to test LRN and LRSN prepositions in nine OECD countries. The test is bivariate autoregressive integrated moving average (ARIMA) model in a reduced form that is convenient to test for the LRN and LRSN analysis. Both tests do not depend on the short-run dynamics of the economy, so, structural details are not relevant in this analysis and will not be addressed.
The main takeaway of Fisher and Seater (1993) model is that the restriction implied by the framework depends critically on the order of integration of our variables of interest, which in this case are money supply and real output. It is important due to two reasons. First, the consequence of a change in the money supply (growth) cannot be inferred if it has not occurred. So, the data of money supply (growth) must contain permanent stochastic change for us to make conclusions regarding LRN (LRSN). Second, restrictions implied by LRN and LRSN say that the conclusion of the analysis depends critically on the difference between the order of integration of the money supply (growth) and real output. This is crucial because we want to check the potential long-run response of real output to the long-run change in the money supply (growth). So, if the order of integration of the money supply (growth) is zero, which says that money is stationary, we cannot infer anything from the analysis since there is no permanent stochastic change in the money supply (growth). On the other hand, if there is permanent stochastic change in the money supply (money is at least integrated of order one), the restriction parameter implied by LRN depends on whether if there exist permanent stochastic change in real output.
In all discussion, I will follow the notations and descriptions from the author’s paper. The model is given by these equations:
aL∆<m>mt=bL∆<y>yt+ut
(1)
dL∆<y>yt=cL∆<m>mt+wt
(2)
where
mis money supply (M1),
yis the real output, and both variables are in natural logarithm. Let
mrepresent the order of integration for
m, and the same applies for
y. For example, if
m is
Iγ then 〈m〉 =
γ, the same applies for
y. The growth of the money supply is
∆mand
∆m= m-1. Let
∆≡1-L be the first difference and
aL, bL, cL,
dLbe the distributed lag polynomials in the lag operator
L. There is no restriction imposed
b0 and
c0 but
a0 = 1 and
d0 =1. Vector of
ut ,wt’is assumed to be independently and identically distributed overtime with (0,
Σ).
Σconsists of
σuw,
σuuand
σww. If the variable is stationary around a linear trend, the model treats it as
I0. Equation (1) and (2) are the formalisation of LRN and LRSN that focuses to which extent an exogenous money supply shock
utaffects
m, Δm, y and
Δy
Since LRN and LRSN analysis involve with level and first differences of variables, it is convenient to generalise LRD in term of
xt≡∆imt and
zt≡∆jyt where
i, jequal to 0 or 1. For example, when
iis 0, then
xt≡mt represents the level of money supply. If
iis 1, then
xt≡∆ mtrepresents the first difference (growth of money supply). The same applies for
y.
Fisher and Seater (1993) then define the LRN in term of Long-run Derivative (LRD) of real output due to a permanent change in the money supply as follows:
LRDz,x=limk→∞∂zt+k∂ut∂xt+k∂ut (3)
xt in the equation represent either
mfor LRN or
Δm for LRSN analysis.
LRDz,xmeasures the ultimate effect of stochastic and exogenous monetary shocks
uton
zrelative to its ultimate effect on
x. The denominator cannot equal to zero, otherwise, the equation will be undefined. Intuitively, if there is no permanent change in
m, we cannot investigate the effect of the change in
mon
yin the long run. So,
limk→∞∂xt+k∂ut≠0must be satisfied, otherwise, the proposition of LRN and LRSN cannot be tested and we simply infer that LRD as undefined.
LRD is defined as the limit of the ratio of two sequences of an exogenous monetary shock. The numerator tells the effect of an exogenous shock on real output. The denominator measures effect of the same money supply shock on itself (as
kgoes to infinity). In short, LRD expresses the ultimate effect of money supply shocks on real output relative to the ultimate effect of the same shock on itself.
By solving equation (1) and (2), we get:
xt=∆-<x>[αLut+βLwt]
(4)
zt=∆-<z>[γLut+λLwt]
(5)
Where
αL=dLaLdL-bLcL
γL=cLaLdL-bLcL
Then we can rewrite
LRDz,xby substituting he results of the derivation into the limits as follows:
LRDz,x=(1-L)<x>-<z>γ(L) L=1α1 (6)
Equation (6) shows that the order of integration matters in determining the
LRDz,x. It allows us to derive the relevant values of
LRDz,xthat depends on their respective order of integration. There are few cases to consider. First, when
x-z≥1, then
LRDz,x≡0. Second, if
x-z=0then
LRDz,x=γ1α1=c(1)d(1). Third, when
x-z=-1,
LRDz,x=(1-L)-1γ1α1 where the numerator is the sums of partial sum. Lastly,
x=z-1≥1. These four cases will be discussed in detail in the next sub-section.
- Long-Run Neutrality
Fisher and Seater (1993) defined LRN as
LRDy,m=λ, where
λ=1 if
yis nominal variable[2],
λ=0 if
yis real variable. In this paper, all
yis the log of real output. While
mis the log of money supply. There are four cases to consider under the system.
- When
m<1, then
LRDy,mis not testable as we established earlier, if there is no permanent stochastic change in the money supply, then LRN is not addressable
- When
m≥y+1≥1, then LRN can be confirmed. Let say
m=1, then
y=0. There is enough evidence to show that permanent stochastic shock in money supply does not change the real output in the long-run
- When
m=y≥1, as argued before,
LRDy,m=c(1)d(1). This is the case where we use the reduced form of equation (4) and (5) to analyse how the two series evolve over time.
- When
m=y-1≥1,
LRDy,m=(1-L)-1c1d1,
LRDy,m=c*1d1, where
c*1=(1-L)-1c1,it must be true that
c1=0. Otherwise, a permanent exogenous shock on money supply might affect the growth rate of the real output permanently. Let say
m=1,
y=2and
c1=0, then
∆y=1,
LRD∆y,m=c(1)d(1). It simply says that monetary shock does not have such effect on real output.
- Long-Run Super Neutrality
Money is super neutral in the long-run if
LRDy,∆m=μ, where
μ=1if
yis nominal variable and
μ=0, if
yis real variable.
∆mis the log of money supply growth and
yis the log of real output. The Long-run money neutrality is a necessary condition for the long-run superneutrality of money. So, the test on LRSN proposition only applies to data that implies LRN. We consider four possible values of
μwhere
LRDy,∆m=μ
- When
∆m<1, then
LRDy,∆mis not testable, there is no permanent stochastic change in the growth of money supply, then LRSN is not testable.
- When
∆m≥y+1≥1, LRSN holds. The intuition is when
∆m=1and
y=0, we cannot associate the permanent change in the growth of money supply with the permanent change in the real output simply because there is no permanent change in the real output.
- When
∆m=y≥1, as argued before,
LRDy,∆m=c(1)d(1)=μ. In this case, the LRSN is testable, but LRN is not falsifiable because as we mentioned earlier, the necessary condition of the LRSN test is that
LRDy,m=0must holds.
- When
∆m=y-1≥1,
LRDy,∆m=(1-L)-1c1d1, or
LRDy,∆m=c*1d1, where
c*1=(1-L)-1c1,it must be true that
c1=0. Otherwise, a permanent exogenous shock on the growth money supply might affect the growth rate of the real output permanently. Also,
c1=0indicates the neutrality of money in the long-run. So, if LRN holds, LRSN requires that the numerator adjusts appropriately. In the case of where LRN does not hold, LRSN cannot hold.
- Identification and estimation
Fisher and Seater (1993) summarize the restrictions in the previous sub-section in the following way:
c1-πd1=0
(7)
Where
πtakes the value of either 1 or 0. This restriction involves equation (2):
dL∆<y>yt=cL∆<m>mt+wt (8)
aL∆<m>mt=bL∆<y>yt+ut (9)
Ordinary least squares (OLS) will consistently estimate equation (8) which can be used to test (7). The scheme imposes
c0=0which implies
∆<m>mtdoes not affect
∆<y>yt. This is intuitive because if, for example,
yis the real output and is not responsive to the current value of the money supply because the time frame to adjust accordingly is too short.
While the assumption of
b1=0 for equation (9) implies money supply is exogenous in the long run, and I will justify the validity of the assumption by conducting cointegration test between money supply and real variable. This is important to ensure the stochastic change in money is not affected by the change in real output.
We can get the coefficient of frequency-zero regression by regressing
∆<y>yon
Δ<m>m, the coefficient equals to
c1d1. Note that the individual parameters of
c(L)and
dLare not of interest, but
c1d1is the main part of the analysis in our study. The estimator of
c1d1is given by
limk→∞bkwhere
bkis the coefficient of the equation below:
∑j=0k∆<y>yt-j=αk+bk∑j=0kΔ<m>mt-j+ek,t
(10)
When
m=y=1, neutrality of money is testable. OLS will provide consistent estimates of
bkfrom the reduced equation:
yt-yt-k-1=ak+bkmt-mt-k-1+ek,t
(11)
If
∆m=y=1, the super neutrality of money can be tested, by obtaining
bkfrom the reduced equation:
yt-yt-k-1=ak+bkΔmt-Δmt-k-1+ek,t
(12)
The coefficient can be estimated by using OLS. The null hypotheses of LRN and LRSN are both
bk= 0. The alternative suggests that (super) neutrality of money does not hold in the long-run. Table 1 summarizes the restrictions discussed in this section. The next section will present the results of unit root to determine the order of integration of the money supply and the real output for each country of interest. Apart from that, cointegration test to justify the only assumption (money is exogenous in the long-run) in this model also will be presented in the next section.
Table 1: LRN and LRSN restrictions
LRN=LRDy,m=λ | LRSN=LRDy,∆m=µ | ||||
m=0 | m=1 | m=2 |
∆m=0 |
∆m=1 | |
y=0 | Undefined | LRN holds | LRN holds | Undefined | LRSN holds |
y=1 | Undefined | LRN is testable | LRN holds | Undefined | LRSN is testable |
Source: Fisher and Seater (1993)
- Unit Root and Cointegration tests
The data used consist of quarterly observations on narrowly defined money supply M1 and real output measured by real Gross Domestic Product (GDP) for nine OECD countries. The sample period for each country are as follows: Switzerland (1985q1 – 2009q3), Chile (1996q1 – 2018q1), Israel (1983q1 – 2018q1), Iceland (1960q1 – 2018q01 Australia (1975q1 – 2009q3), Mexico (1986q1 – 2009q4), South Korea (1960q1 – 2009q4), Canada 1955q1 -2018q1) and Turkey (1986q1 – 2009q4). The data were collected from various issues of Federal Reserve Economic data published by St. Louis Fed, data published by oecd.org and from International Financial Statistic published by International Monetary Fund. All variables were converted into the natural algorithm.
Since I have shown earlier from the Fisher and Seater (1993) model, LRN and LRSN tests critically depend on the order of integration of both, money supply and the real output. King and Watson (1992) also show in their model that the order of integration plays a crucial role in determining if a test on LRN and LRSN is meaningful or not. So, the step of finding unit root in data is indispensable before we proceed to the neutrality test.
In doing so, I was considering to use either Augmented Dicky Fuller (ADF) by Said and Dickey (1984) or modified Dickey-Fuller (DF-GLS) proposed by Elliott, Rothenberg et al. (1992). Essentially, these two are the same, but in DF-GLS, the time series is transformed via a GLS before performing the test. Elliott, Rothenberg et al. (1992) and few studies have shown that DF-GLS has greater power compared to standard ADF test. Note also that DF-GLS test is performed on GLS-detrended data. So, the possible alternative hypothesis is either the series is stationary around a linear time trend or around the non-zero mean. Because of this reason, I will use DF-GLS to test for the existence of unit roots in the series.
Table 2 presents the results (test statistic value) of unit root test for real output
(GDP), first difference of real output
(d.GDP), money supply
(M1)and the first difference of money supply
(d.M1)for Turkey, Switzerland, Australia, South Korea, and Mexico. Asterisk is used to mark the rejection of the null hypothesis of a unit root at a 5% significance level. The number in parenthesis is the critical value for the correspondent test statistic.
Table 2: DF-GLS unit root test
*reject the null hypothesis of a unit root at 5% significance level
The optimum order of lags is determined by Ng and Perron (1995) provided in Stata result.
For real output in Turkey, Switzerland, Australia, South Korea, and Mexico, the results indicate that the null hypothesis of a unit root in the log level cannot be rejected at 5% significance level. In the first difference of the logs of real output, the null hypothesis of a unit root can be rejected at a 5% significance level. Hence, we can conclude for the log level of real output, the series is integrated of order one for these countries.
The null of a unit root cannot be rejected for the log level of money supply, and for the log of first difference series, the null hypothesis of a unit root can be rejected in all countries except Switzerland at 5% significance level. So, M1 for the four countries is said to have a unit root. For money supply in Switzerland, Canada and Iceland, we cannot reject the null of a unit root at first difference log levels, indicating money supply is integrated of order ≥ 1. So, according to the Fisher and Seater (1993), if the real output is integrated of order one, then the neutrality of money holds without further analysis. But we can test he LRSN proposition in these countries.
Table 3: Summary of unit root test
Turkey | Switzerland | Australia | South Korea | Mexico | Canada | Chile | Israel | Iceland | |
y | I(1) | I(1) | I(1) | I(1) | I(1) | I(1) | I(1) | I(1) | I(1) |
m | I(1) | I(2) | I(1) | I(1) | I(1) | I(2) | I(1) | I(1) | I(2) |
As stated before, Fisher and Seater (1993) model assume that money supply is exogenous in the long-run. To address this assumption, we can test the data for cointegration. Even though failure to reject the null hypothesis of no cointegration does not provide enough evidence for money supply exogeneity, but the rejection of null does provide direct evidence against money exogeneity in the long-run.
Meaningful test of money (super) neutrality can be conducted if there is no cointegration between real GDP and money supply, on top of the requirement for the order of integration for money supply to be at least equal to one. The reason behind these requirements is money must exhibit the property that when there is a permanent shock, the stochastic trend that drives money and real GDP are not correlated with each other in the long-run.
Table 4: Results of Johansen and Juselius (1990) Cointegration test
Countries | Maximum test statistic | Corresponding critical value* |
Australia | 9.7485 | 15.41 |
Mexico | 13.4109 | 16.87 |
South Korea | 6.8426 | 14.07 |
Turkey | 11.8652 | 16.87 |
Canada | 25.0707 | 25.32 |
Chile | 28.6611* | 25.32 |
Iceland | 15.9065 | 25.32 |
Israel | 20.2901 | 25.32 |
Switzerland | 13.8708 | 18.17 |
*at 5% significant level
I used Johansen and Juselius (1990) maximum likelihood cointegration test to study the long-run relationship between money supply and real GDP in each country. I determined the optimal number of lag used based on Schwert (1987) formula, where
l=4T100)0.25. As reported in Table M, we cannot reject the null of no cointegration for all countries except Chile. So, the necessary conditions of meaningful LRN test is fulfilled for the rest and we can proceed with the analysis of the neutrality test results in the next section.
- The Long-Run Neutrality Tests Results
The results of DF-GLS and Johansen tests suggest that LRN is testable using
c1d1in eight out of nine countries of interest since the money supply is at least is integrated of order one. The neutrality of money in three (Switzerland, Canada, Iceland) of the country can be inferred without further analysis because the money supply is integrated of order two, and the real output is integrated of order one. LRN is not testable in one of the country (Chile) because we cannot reject that there exist cointegration between money supply and real GDP. From Johansen and Juselius (1990) maximum likelihood cointegration test, there is evidence to reject the existence of cointegration between real output and money supply, supporting the assumption made in this model: money is exogenous in the long run in the rest of the countries. The countries are Australia, Turkey, South Korea, Israel, Switzerland, Canada, Iceland and Mexico.
(11) is used to test the money neutrality in the long run in five of the countries that have one unit root in their money series. The results are presented in Tables 5-9. I report the values of the coefficient, Newey and West (1987) standard errors, t-statistic of null hypothesis and p-value.
There is a mixture of empirical results of LRN. In Australia, we reject the null hypothesis of money neutrality in the long-run for
13>k>3. It shows that when the money supply is injected into the market, it will take times for the effect to take place, and after some period, the effect will disappear. Since our data is quarterly, the results say that it will take about a year for the effect to take place, and the effect will last for two years before prices start to adjust.
For Mexico, we reject the LRN proposition except when
k=6. Overall, we can conclude that money is not neutral in the long run for Mexico.
Moving to Turkey, we fail to reject the proposition of money neutrality since the coefficients of the slope are all significant. So, according to this result, any attempts by the central bank to stimulate the economy using monetary policy will not be effective.
In South Korea, we only fail to reject the proposition of money neutrality for
10>k>4. It shows that any monetary intervention has an immediate effect on the economy, and the effect will not be significant for a few periods before having a strong and significant effect afterwards.
The last country for LRN analysis is Israel. The empirical result for Israel is interesting because it says that money supply is neutral for the first 16 periods before the effect of the intervention takes place. If Bank of Israel injects money into the market, the effect will only be seen after four years. So, we fail to reject the proposition of money neutrality in the first sixteen periods, but we strongly reject the proposition afterwards.
To summarize, we conclude that money in Mexico is not neutral[3] and money in Turkey is neutral. There is mixed of results in South Korea and Australia. For Australia, money is neutral except at
13>k>3, while in South Korea, money is neutral only at
10>k>4. For Israel, money is said to be neutral for
16>k.
Table 5: Australia (LRN)
Long-run regression of real output on M1
k | β_{k} | SE_{k} | t_{k} | p-value |
1 | -.0177361 | .0197221 | -0.90 | 0.370 |
2 | .0030715 | .0217575 | 0.14 | 0.888 |
3 | .0403905 | .0246553 | 1.64 | 0.104 |
4 | .1007221 | .0286838 | 3.51 | 0.001 |
5 | .0775334 | .0257318 | 3.01 | 0.003 |
6 | .0658924 | .025944 | 2.54 | 0.012 |
7 | .076948 | .0266898 | 2.88 | 0.005 |
8 | .0963117 | .0284547 | 3.38 | 0.001 |
9 | .0780853 | .0268082 | 2.91 | 0.004 |
10 | .068181 | .0264526 | 2.58 | 0.011 |
11 | .0675191 | .0272765 | 2.48 | 0.015 |
12 | .0719285 | .0287086 | 2.51 | 0.014 |
13 | .0559642 | .0275328 | 2.03 | 0.044 |
14 | .0440886 | .0273604 | 1.61 | 0.110 |
15 | .0406755 | .0279047 | 1.46 | 0.148 |
16 | .0405504 | .0293337 | 1.38 | 0.169 |
17 | .0304362 | .0281875 | 1.08 | 0.282 |
18 | .0209959 | .0275647 | 0.76 | 0.448 |
19 | 0152439 | .0278295 | 0.55 | 0.585 |
20 | .0173084 | .0286547 | 0.60 | 0.547 |
Table 6: Mexico (LRN)
Long-run regression of real output on M1
k | β_{k} | SE_{k} | t_{k} | p-value |
1 | -.1308131 | .0338932 | -3.86 | 0.000 |
2 | .053302 | .0207783 | 2.57 | 0.012 |
3 | -.0591502 | .0261658 | -2.26 | 0.026 |
4 | -.0363897 | .0177426 | -2.04 | 0.033 |
5 | -.0473131 | .0212397 | -2.23 | 0.028 |
6 | -.0125895 | .0164782 | -0.76 | 0.447 |
7 | -.0460744 | .0180304 | -2.56 | 0.012 |
8 | -.0383258 | .013475 | -2.84 | 0.006 |
9 | -.0540421 | .0159385 | -3.39 | 0.001 |
10 | -.0408873 | .0133745 | -3.06 | 0.003 |
11 | .0619308 | .0145493 | -4.26 | 0.000 |
12 | -.0587005 | .0111949 | -5.24 | 0.000 |
13 | -.0677573 | .0133636 | -5.07 | 0.000 |
14 | -.0567214 | .0116431 | -4.87 | 0.000 |
15 | -.0690954 | .0126634 | -5.46 | 0.000 |
16 | -.0660912 | .0102501 | -6.45 | 0.000 |
17 | -.0730103 | .0121189 | -6.02 | 0.000 |
18 | -.0642219 | .0107057 | -6.00 | 0.000 |
19 | -.073477 | .0115149 | -6.38 | 0.000 |
20 | -.0706741 | .0091346 | -7.74 | 0.000 |
Table 7: Turkey (LRN)
Long-run regression of real output on M1
k | β_{k} | SE_{k} | t_{k} | p-value |
1 | .1110874 | .2275847 | 0.49 | 0.628 |
2 | .1736699 | .2217279 | 0.78 | 0.438 |
3 | .0798759 | .128634 | 0.62 | 0.538 |
4 | .0500777 | .0507832 | 0.99 | 0.330 |
5 | .0585315 | .0993159 | 0.59 | 0.559 |
6 | .0754603 | .1204268 | 0.63 | 0.535 |
7 | .0425601 | .0838622 | 0.51 | 0.615 |
8 | .0331602 | .0432629 | 0.77 | 0.448 |
9 | .0469386 | .0794779 | 0.59 | 0.558 |
10 | .0663745 | .1027263 | 0.65 | 0.522 |
11 | .0340118 | .0802038 | 0.42 | 0.674 |
12 | .00598 | .0523897 | 0.11 | 0.910 |
13 | -.0060998 | .0849067 | -0.07 | 0.943 |
14 | -.0019134 | .1125989 | -0.02 | 0.987 |
15 | -.0371201 | .0956272 | -0.39 | 0.701 |
16 | -.0679851 | .0682048 | -1.00 | 0.327 |
17 | -.0520092 | .1026166 | -0.51 | 0.616 |
18 | .0032694 | .131267 | 0.02 | 0.980 |
19 | -.0182519 | .1027627 | -0.18 | 0.860 |
20 | -.0620864 | .0650276 | -0.95 | 0.349 |
Table 8: South Korea (LRN)
Long-run regression of real output on M1
k | β_{k} | SE_{k} | t_{k} | p-value |
1 | .0896909 | .035287 | 2.54 | 0.012 |
2 | .0987234 | .0381531 | 2.59 | 0.010 |
3 | .0901763 | .0433475 | 2.08 | 0.039 |
4 | .0731673 | .0462327 | 1.58 | 0.115 |
5 | .0530868 | .0454083 | 1.17 | 0.244 |
6 | .0404424 | .0455731 | 0.89 | 0.376 |
7 | .0112444 | .0472359 | 0.24 | 0.812 |
8 | -.0229216 | .0483224 | -0.47 | 0.636 |
9 | -.0483291 | .048241 | -1.00 | 0.318 |
10 | -.071999 | .0477961 | -1.51 | 0.134 |
11 | -.1058076 | .0479897 | -2.20 | 0.029 |
12 | -.1386605 | .047714 | -2.91 | 0.004 |
13 | -.1585404 | .0468138 | -3.39 | 0.001 |
14 | -.1757103 | .0460871 | -3.81 | 0.000 |
15 | -.1993996 | .0456067 | -4.37 | 0.000 |
16 | -.2209469 | .0450967 | -4.90 | 0.000 |
17 | -.2333233 | .044117 | -5.29 | 0.000 |
18 | -.2425184 | .0429781 | -5.64 | 0.000 |
19 | -.2576448 | .0424603 | -6.07 | 0.000 |
20 | -.2731231 | .0419926 | -6.50 | 0.000 |
Table 9: Israel (LRN)
Long-run regression of real output on M1
k | β_{k} | SE_{k} | t_{k} | p-value |
1 | -.0406284 | .0421366 | -0.96 | 0.338 |
2 | -.0392382 | .0342573 | -1.15 | 0.255 |
3 | -.0262023 | .0305422 | -0.86 | 0.393 |
4 | -.0036893 | .0289115 | -0.13 | 0.899 |
5 | .0133559 | .029161 | 0.46 | 0.648 |
6 | .0246739 | .0294897 | 0.84 | 0.405 |
7 | .0308016 | .0293415 | 1.05 | 0.297 |
8 | .0338928 | .0290174 | 1.17 | 0.246 |
9 | .035991 | .0290206 | 1.24 | 0.219 |
10 | .0369725 | .0290638 | 1.27 | 0.207 |
11 | .0395795 | .028742 | 1.38 | 0.173 |
12 | .0433263 | .0285264 | 1.52 | 0.133 |
13 | .0486648 | .0285778 | 1.70 | 0.093 |
14 | .0521022 | .0290589 | 1.79 | 0.077 |
15 | .0551176 | .0291394 | 1.89 | 0.063 |
16 | .0575693 | .0293684 | 1.96 | 0.054 |
17 | .0617681 | .0298544 | 2.07 | 0.042 |
18 | .069408 | .0301815 | 2.30 | 0.024 |
19 | .0776243 | .0301634 | 2.57 | 0.012 |
20 | .0866463 | .0300603 | 2.88 | 0.005 |
For Switzerland, Canada and Iceland, the long-run money neutrality proposition holds by construction according to Fisher and Seater (1993) model. This is because they have more than one unit root in their money series and a unit root in the real output series. So, the analysis in these countries will not be discussed in this section. These countries are eligible for LRSN analysis and we will address the superneutrality of money in the long run in the next section.
- The Long Run Super Neutrality tests result
Except for Canada, Iceland, and Switzerland, the LRSN test is not addressable in other countries because there is no permanent stochastic change in the money growth. So, we cannot study the impact of a permanent change in the growth of money simply because it does not exist.
The result of regression for equation
(12)is presented in table 10 – 12. For Canada, then we fail to reject the proposition superneutrality of money except for
4>k>1. It means by increasing the growth of money supply permanently, the effect can only be seen for short period of time (less than 4 periods or less than a year).
For Iceland, we reject the null hypothesis of
βk=0for
k>2as the slope are all statistically significant and positive. This result means LRSN of money does not hold for Iceland, so any increase in the growth of money supply permanently will have a positive impact on the economy.
Lastly, for Switzerland, we conclude that using Fisher and Seater (1993) model, we fail to reject the long-run money superneutrality proposition. This is because the coefficient of the regression is statistically significant except for few values of
k=10.
To summarize, money is said to be superneutral in the long-run for Switzerland (except
k=10) and for Canada (except for
4>k>1). While money is not superneutral in Iceland.
Table 10: Canada (LRSN)
Long-run regression of real output on M1
k | β_{k} | SE_{k} | t_{k} | p-value |
1 | -.0415922 | .035643 | -1.17 | 0.244 |
2 | -.1337163 | .0500918 | -2.67 | 0.008 |
3 | -.2764028 | .0674333 | -4.10 | 0.000 |
4 | -.2252957 | .0726363 | -3.10 | 0.002 |
5 | -.2256265 | .0886661 | -2.54 | 0.012 |
6 | -.2105167 | .1069526 | -1.97 | 0.050 |
7 | -.1528771 | .1111935 | -1.37 | 0.171 |
8 | -.0970114 | .1223009 | -0.79 | 0.429 |
9 | -.0968078 | .1393587 | -0.69 | 0.488 |
10 | -.0868881 | .1455914 | -0.60 | 0.551 |
11 | -.0768588 | .1521153 | -0.51 | 0.614 |
12 | -.1370832 | .152159 | -0.90 | 0.369 |
13 | -.1620757 | .1511121 | -1.07 | 0.285 |
14 | -.1541828 | .1663285 | -0.93 | 0.355 |
15 | -.1577759 | .177134 | -0.89 | 0.374 |
16 | -.1143118 | .1820497 | -0.63 | 0.531 |
17 | -.1142654 | .1955836 | -0.58 | 0.560 |
18 | -.1203746 | .1953015 | -0.62 | 0.538 |
19 | -.0954435 | .1897604 | -0.50 | 0.616 |
20 | -.0774966 | .2146637 | -0.36 | 0.718 |
Table 11: Iceland (LRSN)
Long-run regression of real output on M1
Table 12: Switzerland (LRSN)
Long-run regression of real output on M1
k | β_{k} | SE_{k} | t_{k} | p-value |
1 | -.0002648 | .0079436 | -0.03 | 0.973 |
2 | -.005512 | .0143041 | -0.39 | 0.701 |
3 | -.0209437 | .0179758 | -1.17 | 0.247 |
4 | -.0576535 | .0327559 | -1.76 | 0.073 |
5 | -.0527826 | .0289136 | -1.83 | 0.071 |
6 | -.0641569 | .0344667 | -1.86 | 0.066 |
7 | -.0592614 | .0350503 | -1.69 | 0.094 |
8 | -.0847947 | .0484557 | -1.75 | 0.085 |
9 | -.0825878 | .0449014 | -1.84 | 0.069 |
10 | -.1003671 | .0501092 | -2.00 | 0.048 |
11 | -.0913381 | .0491458 | -1.86 | 0.067 |
12 | -.1403001 | .0629424 | -1.79 | 0.070 |
13 | -.0929489 | .0567458 | -1.64 | 0.105 |
14 | -.1010598 | .0640943 | -1.58 | 0.119 |
15 | -.0924466 | .062596 | -1.48 | 0.144 |
16 | -.1406306 | .0783909 | -1.79 | 0.077 |
17 | -.0904663 | .0626567 | -1.44 | 0.153 |
18 | -.1095393 | .067641 | -1.62 | 0.109 |
19 | -.1061894 | .0650701 | -1.63 | 0.107 |
20 | -.1488999 | .0852348 | -1.75 | 0.085 |
- Conclusion
In this dissertation, the classical proposition of LRN and LRSN of money that originates from the quantity theory of money has been tested using the model developed my Fisher and Seater (1993). I used the model to test the propositions of LRN and LRSN sing nine OECD countries namely Australia, Switzerland, Canada, Israel, Mexico, Chile, South Korea, Turkey, and Iceland. This is the first paper that attempts to study the proposition of (super) neutrality of money in this group of countries. The properties of non-stationarity and cointegration of the data have been given special emphasis as it plays a crucial role in determining if the test is meaningful using Fisher and Seater (1993) model. We found evidence that money is integrated of order one for all the countries except Iceland, Canada, and Switzerland. Even though Chile has one unit root in the money series, neither test on LRN or LRSN can be conducted since the money supply and the real output common trend. In another word, we cannot reject the null hypothesis that these series are cointegrated with each other.
Our results show that money does not matter for Turkey and Australia. While money matters for Mexico, Israel, and South Korea in the long-run. We found evidence against money superneutrality in Iceland, and evidence supporting the proposition in Canada and Switzerland. So, a permanent growth of the money supply can affect the real economic performance in Iceland, but not in Canada and Switzerland.
The important take away from this paper is the monetary authorities should have prior knowledge about the relationship between money and real output before manipulating monetary policy in order to influence economic performance. For countries in which LRN and LRSN do not hold, injection of money might affect the real output. Otherwise, it will only increase the inflation as prices start to adjust.
Table 13: Summary of the results
Country | Series | Order of Integration | LRN | LRSN |
Australia | Y
M1 |
I(1)
I(1) |
Holds | Not addressable |
Canada | Y
M1 |
I(1)
I(2) |
Holds | Holds |
Israel | Y
M1 |
I(1)
I(1) |
Holds | Not addressable |
Chile | Y
M1 |
I(1)
I(1) |
Not informative | Not informative |
Mexico | Y
M1 |
I(1)
I(1) |
Fails | Not addressable |
South Korea | Y
M1 |
I(1)
I(1) |
Fails | Not addressable |
Iceland | Y
M1 |
I(1)
I(1) |
Holds | Fails |
Turkey | Y
M1 |
I(1)
I(1) |
Holds | Not addressable |
Switzerland | Y
M1 |
I(1)
I(2) |
Holds | Holds |
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[1] M2
[2] In this case, the variable is output, but it could be other real variables such prices, etc.
[3] Except when k=6
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