Endogenous Structural Breaks and the Stability of the Money Demand Function in Saudi Arabia

In this study, an endogenous investigation of the long run relationship between the demand for money, narrow definition of money (M1), and its determinants in Saudi Arabia was conducted. A structural break date was estimated by applying the Andrews (1993) and Andrews and Ploberger (1994) methods. These tests illustrated that there is evidence of a structural break for all of the variables, namely money demand, real income and nominal short-term interest rates when they are considered together. The results of the Hansen stability test support the idea that the instability of money demand could be related to the structural breaks. Since there is evidence of a structural break, the Gregory and Hansen procedure was used to test for the cointegrating equation of money demand. This test allows for a one time structural break in the relationship among the money demand variable, real income and nominal short-term interest rates. The results of this test affirm stable money demand in Saudi Arabia. The monetary aggregate in Saudi Arabia seems to be an appropriate indicator in the formulation of monetary policy.


Introduction
The relationship between money demand and its determinants is a crucial concern for policymakers, since it enables them to formulate appropriate monetary policies and increase the level of accuracy in targeting money growth. The issue of the stability of the money demand function in the long run has received extensive attention in the past. However, the results are not found to be conclusive, as some money demand studies indicate that it is unstable, while others claim it is stable. Goldfeld (1976) claimed that money demand was unstable in the United States (US) during the 1970s, while Stock and Watson (1993) claimed that the M1 demand was unstable during the post-world war ΙΙ. However, when the sample period investigated by Stock and Watson was extended to 1996 by Ball (2001), the results showed stability of M1. Furthermore, Choi and Jung (2009) found that M1 demand in the US is unstable during the period of 1959Q1 through 2000Q4. However, when Choi and Jung estimated the unknown structural break points in the money demand function and tested to see if a long run relationship existed in each sub-sample period of the structural break points, while they did find evidence of stability within each sub-sample, they did not find this evidence for the entire sample.
Some studies attribute the instability of the money demand function to structural changes arising from innovations in the financial sector and financial deregulation (Breuer & Lippert, 1996;Ericsson, Hendry, & Prestwish, 1998;Chio & Jung, 2009). Haug and Lucas (1996) illustrated that the stability of the money demand function depends on the type of cointegration tests used and the combination of money and interest rates. Gregory and Hansen (1996) found that data frequency can play an important role when testing for stability, while Cheong (2003) infers that the instability of the money demand function could be caused by a misspecification in dynamic models, error correction models (ECM), which omits important lags.
for structural breaks.
The purpose of this paper is to empirically evaluate the money demand function in Saudi Arabia, focusing on two primary issues. The first is to test whether or not the money demand function in Saudi Arabia is stable in the long run using the Hansen (1992) test for parameter stability. The second is to investigate the long run relationship between money demand and its determinants, real income and short-term interest rates, using the Gregory and Hansen (1996) cointegration test. The Gregory and Hansen (GH) cointegration test incorporates structural breaks. Therefore, this test allows one to empirically investigate the stationarity of the money demand function after allowing for a one time structural break in the relationship among the money demand variable, real income and nominal short-term interest rates.
What distinguishes this paper from the previous work is that this paper endogenously deals with the structural breaks. (Enders,p. 106) indicates that even if it is possible to determine the exact date of a structural break, the full effect of this structural break would not occur instantly.
The motivation for evaluating the stability of the money demand function in Saudi Arabia is that Saudi Arabia has experienced reforms in the financial sector and many severe economic crises, including the oil crisis in 1986 and the global financial crisis in 2008. The effects of these reforms and financial crises on the stability of the money demand function are rarely endogenously investigated. Consequently, these reforms and financial crises likely created structural breaks that need to be accounted for in the estimation of the long run money demand function.

Recent Studies on Money Demand in Saudi Arabia
There have been several empirical studies on the stability of the money demand function in Saudi Arabia (Al-Kswani & Al-Twaijari, 1999;Lee, Chang, & Chen, 2008;Bahmani, 2008;Masih & Algahtani, 2008;Abdulkheir, 2013). These studies use different econometric techniques to empirically investigate the stability of the long and short run relationship between money demand and its determinants. This section provides a brief review of some of the recent studies on the stability of the money demand function in Saudi Arabia (Table 1).
Al-Kswani and Al-Twaijari (1999) conducted a Johansen and Juselius (1990) cointegration test to examine the long run relationship between M1 demand and its determinants, real income, interest rate, expected inflation rate, and real exchange rate using annual data from the period of 1977 to 1997. The results indicate the existence of a long run relationship between M1 demand and its determinants. In addition, they examined the stability of the money demand function in the short run using an error correction model (ECM). The results of the ECM illustrate that M1 demand is stable. The long run income elasticity is 1.72 which is not closer to unity as suggested by the quantity theory of money. This finding indicates that the Saudi economy is becoming monetized.
Furthermore, Lee, Chang and Chen (2008) employed the panel cointegrated technique developed by Larsson, Lyhagen, and Lothgren (2001) to determine the panel cointegrated relationship between money demand, M1, and its determinants in six selected Gulf Cooperation Councils (GCC) using annual data from 1979 to 2000. The individual country by country trace statistics indicate that there is a long run relationship between M1 demand and its determinants, GDP, the interest rate, and the nominal exchange rate in Saudi Arabia. However, when the scale variable was changed from real GDP to private consumption, the results of the individual trace statistics show that the M1 money demand is unstable. The results of the panel test suggest that the demand for money, M1, is stable in GCC countries.
Using annual data for the period of 1971 through 2004, Bahmani (2008) examined the stability of the M2 demand for money in fourteen countries: Saudi Arabia, Qatar, Syria, Tunisia, Turkey, Kuwait, Lebanon, Libya, Morocco, Oman, Bahrain, Egypt, the United Arab Emirates, and Jordan. The Persaran (2001) cointegration test and the CUSUM and CUSUMSQ parameter instability tests were applied. The results of the cointegration and the stability tests support the idea that the demand for money, M2, in Saudi Arabia is stable in both the long and short run. Masih and Algahtani (2008) evaluated the money demand function in Saudi Arabia using annual data for the period from 1986 to 2004. Using both the cointegration technique developed by Pesaran and Shin (2002) and the CUSUM and CUSUMSQ instability tests, the authors tested for the long and short run relationships between real M2 and M3 demand for money and their determinants. The results from the cointegration and instability tests suggest that M2 and M3 are stable.
Abdulkheir (2013)  Joselius (1990) technique to test for the long and short run relationships between the M2 demand and its determinants, namely the inflation rate, real GDP, the interest rates, and real exchange rates. The results suggest that M2 demand is stable in both the long and short run.

The Model and the Data
This study uses annual Saudi Arabia data from 1980 to 2012 to test whether there is cointegration between money demand and its determinants, real income and interest rates. All data were obtained from the International Financial Statistics website. The monetary aggregate was deflated by the price level, CPI. The money demand specification can be written as: where: m denotes the real money supply, M1. In Equation (1), y is real GDP, i is US treasury bills and є is the error term. All variables are in natural logs, except the nominal interest rates. The expected signs of the coefficients in Equation (1) are positive for income elasticity and negative for interest rate semi-elasticity (e.g., λ 2 > 0, and λ 3 < 0). In addition, the properties of the error sequence (є) are an integral part of the theory. If (є) has a stochastic trend, then the deviation from the money market equilibrium will not be eliminated (Enders,p. 357). This theory assumes that the εt sequence is stationary.

Structural Break Tests
The Andrews (1993) and Andrews and Ploberger (1994) methods are used to check for one unknown structural break in both individual time-series and the model as a whole. These methods estimate the structural breaks endogenously; therefore, they do not require a priori knowledge of the dates of the structural breaks. Both methods are computed on the basis of the Wald test; they test the null of no structural break. The existence of a structural break implies that the linear relationship between money demand and its determinants does not hold. The Andrews test is computed as: where: Ft/T is considered to be the F-test statistic. The Andrews and Ploberger (1994) is computed as: where: L 1 and L 2 denote the trimmed region [0.15T, 0.85T], respectively. According to Hansen (2000), the ExpF is considered a more powerful test than SupF that has almost a zero size distortion. Since both tests assume that all variables are stationary, the first difference data are used.

Unit Root Test
This paper utilizes Phillips and Perron (1988) and Zivot and Andrews (1992) to test unit roots. The Zivot and Andrews (1992) test allows for one unknown structural break in the series. According to the procedure of Zivot and Andrews, a break point is endogenously determined. Zivot and Andrews (ZA) use three models to test for a unit root.

Model (B): A trend shift
Model (C): Both a mean and a trend shift In Equations (4) through (6)

Cointegration Test
Gregory and Hansen's (1996) cointegration test is used to test for a long run relationship between money demand and its determinants. This test allows for an unknown regime shift in the intercept, either alone or in both the intercept and the coefficient vector. It can take on the following regression forms: Level shift (GH1): Level shift with trend (GH2): Regime shift (GH3): In Equations (7) through (9), Y t is the dependent variable, X t is the independent variable, λ 1 and λ 2 are the intercept and the slope coefficients before the structural break, respectively, λ 11 and λ 22 are the intercept and the slope coefficients after the structural break, respectively. The time trend is t, where DU tb = 1 if t > b and DU tb = 0 if t ≤ b, while b is the date at which the structural break occurs. Gregory and Hansen (GH) propose the ADF* = inf t є T ADF (t), which is a modified version of the Engle and Granger (1987) cointegration test. The smallest value of this test is considered to be the break point. The null hypothesis of the GH test is that there is no cointegration with a structural break, while the alternative is that there is cointegration with a structural break. It is easy to extend these three models to include more than one explanatory variable.

Structural Break Test Results
The results of the Quandt-Andrews and Andrews-Ploberger tests for one unknown structural break are presented in

Parameter Stability Test Results
The results of Hansen test for parameter instability are presented in Table 3, together with their probabilities. The results illustrate signs of instability. The three test statistics of Lc, MeanF, and SupF indicate that the null hypothesis of cointegration, for M1 demand, is rejected at the 5 percent significance levels. According to these results, there is strong evidence that the demand for money, M1, in Saudi Arabia is unstable.  indicated that Hansen's test can perform well when there is no structural break. Breuer and Lippert (1996) mentioned that tests of the stability of money demand only focus on whether the coefficient estimates are stable over time, without taking into account the structural break.

Phillips-Perron (PP) Unit Root Test Results
The results of the PP test are presented in Table 4. The results indicate the presence of non stationarity of all variables at levels. Thus, the null hypothesis of a unit root is not rejected. For the first difference of the series, the null hypothesis of a unit root is rejected at the 1% level for all variables. Therefore, the results show that M1, y, and i are integrated of order (1).

Zivot and Andrews Unit Root Test Results
The results of the Quandt-Andrews and Andrews-Ploberger tests and the Hansen test suggest that a structural break is important and needs to be taken into account when testing for a unit root. Perron (1989) shows that if researchers ignore a structural break in the data series, then they may falsely accept the null hypothesis of a unit root. Therefore, we apply the ZA unit root test, which examines a unit root in the presence of a single endogenous structural break in the data series.
The results of the ZA unit root test are presented in Tables 5 and 6, respectively. The results illustrate that M1 is not stationary in levels in the A and C models; however, it is stationary in levels in the B model. Moreover, the results of the ZA test indicate that the y is non-stationary in levels. Thus, the null hypothesis of a unit root is not rejected. The results of all the models of a ZA test suggest that the interest rate variable, i, is stationary in levels.
For the first difference of the series, the null hypothesis of a unit root is rejected at the 1% level. The results show that M1 and y are integrated of order (1), while i is integrated of order (0). Since we obtained mixed results, it is worth performing cointegration tests on the demand of M1. Testing for cointegration is still necessary and valid, despite the variables not being from the same order. Harris (1995) points out that it is common to test for cointegration when the variables are not from the same order, because unit root tests, in most cases, suffer from statistical power problems and size distortions.
The ZA break dates correspond with the oil price crash of 1986 and the low oil price beginning in late 1997 due to the East Asian economic crises. In addition, the break date of 1999 corresponds with the high oil price beginning in 1999. In 2004, the oil prices increased dramatically, which led to high revenues. The break date of 2007 refers to the oil shock of 2007-2008. www.ccsen Table 6. ZA **,*** denot

Gregor
The result ADF* sta hypothesis demand fo The break Trade Org   structural break tests indicate the existence of structural breaks in the model. However, given the specification of the model and the dataset, the results of the Gregory and Hansen (GH) cointegration test, which allows for one unknown structural break, suggest that M1 demand is stable in the long run.
Since there was evidence from the GH cointegration test that a long run relationship exists between M1 demand and its determinants for Saudi Arabia, it is possible for policymakers to conduct money targeting using M1 for the control of monetary policy.
For future research, I would suggest using econometric techniques which incorporate more than one unknown structural break in order to investigate the stability of money demand function in Saudi Arabia. In addition, the future work on this issue should depart from linear models and use nonlinear models since most of the previous research focused on linear models of money demand.