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    INSTITUTE OF DEVELOPING ECONOMIES

    IDE Discussion Papers are preliminary materials circulatedto stimulate discussions and critical comments

    Keywords : cointegration, DOLS, India, money demand JEL classification: E41, E52

    * Institute of Developing Economies ([email protected]).** Faculty of Economics, Kobe University ([email protected]).

    IDE DISCUSSION PAPER No. 166

    An Empirical Analysis of the MoneyDemand Function in India

    Takeshi INOUE * andShigeyuki HAMORI **

    September 2008

    Abstract This paper empirically analyzes Indias money demand function during the period of 1980 to

    2007 using monthly data and the period of 1976 to 2007 using annual data. Cointegration test

    results indicated that when money supply is represented by M1 and M2, a cointegrating vector is

    detected among real money balances, interest rates, and output. In contrast, it was found that

    when money supply is represented by M3, there is no long-run equilibrium relationship in the

    money demand function. Moreover, when the money demand function was estimated using

    dynamic OLS, the sign conditions of the coefficients of output and interest rates were found to be

    consistent with theoretical rationale, and statistical significance was confirmed when moneysupply was represented by either M1 or M2. Consequently, though Indias central bank presently

    uses M3 as an indicator of future price movements, it is thought appropriate to focus on M1 or

    M2, rather than M3, in managing monetary policy.

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    The Institute of Developing Economies (IDE) is a semigovernmental,

    nonpartisan, nonprofit research institute, founded in 1958. The Institutemerged with the Japan External Trade Organization (JETRO) on July 1, 1998.

    The Institute conducts basic and comprehensive studies on economic and

    related affairs in all developing countries and regions, including Asia, the

    Middle East, Africa, Latin America, Oceania, and Eastern Europe.

    The views expressed in this publication are those of the author(s). Publication does

    not imply endorsement by the Institute of Developing Economies of any of the viewsexpressed within.

    INSTITUTE OF DEVELOPING E CONOMIES (IDE), JETRO

    3-2-2, W AKABA , M IHAMA -KU , C HIBA -SHI

    C HIBA 261-8545, JAPAN

    2008 by Institute of Developing Economies, JETRO

    No part of this publication may be reproduced without the prior permission of theIDE-JETRO.

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    An Empirical Analysis of the Money Demand Function in India

    Inoue Takeshi

    (Institute of Developing Economies)

    and

    Shigeyuki Hamori

    (Faculty of Economics, Kobe University)

    Abstract

    This paper empirically analyzes Indias money demand function during the period of 1980 to

    2007 using monthly data and the period of 1976 to 2007 using annual data. Cointegration test

    results indicated that when money supply is represented by M1 and M2, a cointegrating vector

    is detected among real money balances, interest rates, and output. In contrast, it was found that

    when money supply is represented by M3, there is no long-run equilibrium relationship in the

    money demand function. Moreover, when the money demand function was estimated using

    dynamic OLS, the sign conditions of the coefficients of output and interest rates were found to

    be consistent with theoretical rationale, and statistical significance was confirmed when money

    supply was represented by either M1 or M2. Consequently, though Indias central bank

    presently uses M3 as an indicator of future price movements, it is thought appropriate to focus

    on M1 or M2, rather than M3, in managing monetary policy.

    JEL classification : E41; E52

    Keywords : Cointegration; DOLS; India; Money Demand

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    1

    1. Introduction

    In India, financial sector deregulation was undertaken beginning in the mid-1980s, when

    steps like the introduction of 182-day Treasury bills, lifting of the call money interest-rateceiling, and the introduction of certificates of deposit and commercial paper were taken in a bid

    to make the government securities market and the money market more efficient (Sen and Vaidya

    1997 [18]). Furthermore, with the balance of payments crisis in 1991, there began an

    intermittent series of more systematic financial sector reforms that continues even today. For

    example, the reform of the Indian interest-rate structure, which had been strictly managed by the

    Reserve Bank of India (RBI), began with the April 1992 deregulation of deposit rates and has

    progressed to the point where commercial banks are now permitted to freely set term deposit

    rates and lending rates for loans above Rs.2 lakh. 1 Moreover, the RBI, which had long been

    constrained by the Indian government's fiscal management, entered into an agreement with the

    government in September 1994 to limit the issuance of 91-day ad hoc Treasury bills, which

    were used to finance fiscal deficits, and eventually eliminated these securities altogether in April

    1997, greatly reining in the central bank's automatic monetization of fiscal deficits. 2

    The above are just a few examples of how interest-rate structure deregulation and the

    introduction of new financial products have progressed in India over the past 20 years.

    Theoretical research and empirical analyses, using primarily data on developed countries, have

    shown that the money demand function can become unstable as a result of such financial

    innovations and financial sector reforms. Partly because of instability in the money demand

    function, many central banks have in recent years switched from money supply targeting

    focused on monetary aggregates as the intermediate target, to inflation targeting, which seeks to

    stabilize prices by adjusting interest rates based on inflation forecasts. The RBI abandoned the

    flexible monetary targeting approach in favor of the multiple indicator approach in April 1998,

    putting an end to the use of money supply as the intermediate target, but retaining it as an

    important indicator of future prices. Consequently, examining the characteristics of the money

    demand function of India's financial sector, which has undergone significant change since the

    1980s, should bear significant meaning for present and future considerations of the RBIs

    monetary policy. This paper, therefore, uses annual data for the period of 1976 to 2007 and

    monthly data for the period of January 1980 to December 2007 to estimate India's money

    1 Except for bank savings deposits, non-resident deposits, loans for less than 200,000 rupees, andexport credit, interest rates have been greatly deregulated.2 Financial deregulation beginning in the 1990s also loosened requirements, like those requiringcommercial banks to keep central bank balances equal to a certain percentage of their own deposits

    and purchase government bonds and government-specified bonds, and the deregulation relaxedbarriers to entering the banking sector and opened stock markets to foreign participants.

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    demand function, which is derived from real money balances, interest rates, and output, and

    shed light on its characteristics.

    The next section of this paper consists of a review of relevant prior research and a discussion

    of the unique contributions of this paper. In the third section, the models are presented and in thefourth section, variables are defined, sources are provided, and data characteristics are explained.

    Moving into the fifth section, cointegration tests are performed using both monthly and annual

    data, the long-term stability of the money demand function is examined, and dynamic OLS

    (DOLS) is used to examine the sign conditions and significance of output and interest-rate

    coefficients. Lastly, analysis results are used to discuss the characteristics of India's money

    demand function and the implications for India's monetary policy.

    2. Literature Review

    India's money demand function has been the subject of numerous quantitative research efforts.

    Among these was the first study to explicitly consider the stationarity of, and cointegration

    relationships among, the variables of the money demand function. Moosa (1992) used three

    types of money supply cash, M1, and M2 to perform cointegration tests on real money

    balances, short-term interest rates, and industrial production over the period beginning with the

    first quarter of 1972 and extending through the fourth quarter of 1990. Results indicated that for

    all three types of money supply, the money balance had a cointegrating relationship with output

    and interest rates. However, greater numbers of cointegrating vectors were detected for cash and

    M1 than for M2, so Moosa (1992) states that narrower definitions of money supply are better

    for pursuing monetary policy.

    Bhattacharya (1995), like Moosa (1992), considered three types of money supply M1, M2,

    and M3 and used annual data for the period of 1950 to 1980 to analyze India's money demand

    function. Bhattacharya (1995) performed cointegration tests for real money balances, real GNP,

    and long-term and short-term interest rates, detected a cointegrating relationship among

    variables only when money supply was defined as M1, and clearly showed that long-term

    interest rates are more sensitive to money demand than are short-term interest rates. In addition,

    Bhattacharya (1995), after estimating an error correction model based on cointegration test

    results, found that, in the case of M1, the error correction term is significant and negative, and

    held that monetary policy is stable over the long term when money supply is narrowly defined.

    Bahmani-Oskooee and Rehman (2005) analyzed the money demand functions for India and

    six other Asian countries during the period beginning with the first quarter of 1972 and ending

    with the fourth quarter of 2000. Using the ARDL approach described in Pesaran et al. (2001),

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    they performed cointegration tests on real money supplies, industrial production, inflation rates,

    and exchange rates (in terms of US dollar). For India, cointegrating relationships were detected

    when money supply was defined as M1, but not M2, so they concluded that M1 is the

    appropriate money supply definition to use in setting monetary policy.Contrasting with the above, there is also prior research that uses money supply defined

    broadly in holding that India's money demand function is stable. In one example, Pradhan and

    Subramanian (1997) employed cointegration tests, an error correction model, and annual data

    for the period of 1960 to 1994 to detect relationships among real money balances, real GDP, and

    nominal interest rates. They estimated an error correction model using M1 and M3 as money

    supply definitions and found the error correction term to be significant and negative. Their

    position, therefore, was that the money demand function is stable not only with M1 but also

    with M3.

    Das and Mandal (2000) considered only the M3 money supply in stating that India's money

    demand function is stable. They used monthly data for the period of April 1981 to March 1998

    to perform cointegration tests and detected cointegrating vectors among money balance,

    industrial production, short-term interest rates, wholesale prices, share prices, and real effective

    exchange rates. Their position, therefore, was that long-term money demand relevant to M3 is

    stable. Similarly, Ramachandran (2004), too, considered only the M3 money supply in using

    annual data for the period of 1951/52 to 2000/01 to perform cointegration tests on nominal

    money supply, output, and price levels. Because stable relationships were discovered among

    these three variables, Ramachandran (2004) states that, over the long term, it is possible to use

    an increase in M3 as a latent indicator of future price movements.

    As is the case with the studies referred to above, prior research in general states that India's

    money demand function is stable. 3 Furthermore, studies performed using multiple money

    supply definitions have tended to draw the conclusion that because India's money demand

    function is more stable when money supply is defined narrowly, the central bank should adopt

    cash or M1 as the narrow definition of money supply when determining monetary policy.

    Contrasting with that position, however, other studies have concluded that the money demand

    function is stable when money supply is broadly defined. Views on what definition of money

    supply to use for monetary policy, therefore, differ.

    This paper uses both monthly and annual data, considers three types of money supply M1,

    M2, and M3, and comprehensively estimates India's money demand functions for each case. It

    3 Nag and Upadhyay (1993), Parikh (1994), Rao and Shalabh (1995), Rao and Singh (2006), andothers as well have also performed quantitative analyses of Indias money demand function.

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    also discusses the implications of empirical results for the RBIs monetary policy formation. In

    contrast with prior studies, this paper, after performing cointegration tests on money supply,

    output, and interest rates as money demand function variables, applies DOLS and sheds light on

    the characteristics of India's money demand function through examinations of the signconditions and statistical significance of variable coefficients.

    3. Models

    There are various theories concerning the money demand function. For example, Kimbrough

    (1986a, 1986b) and Faig (1988) came up with the following money demand function as a result

    of explicitly considering transaction costs.

    ( , )t t t t

    M L Y R

    P = 0Y L > , 0R L < (1)

    In this formula, t M represents nominal money supply for period t ; t P represents the price

    index for period t ; t Y represents output for period t ; and t R represents the nominal

    interest rate for period t . Increases in output bring increases in money demand, and increases

    in interest rates bring decreases in money demand.

    We use two models corresponding to equation (1) in order to conduct an empirical analysis.

    Model 1: 0 1 2ln( ) ln( ) ln( )t t t t t M P Y R u = + + + , 1 20, 0 > < (2)

    Model 2: 0 1 2ln( ) ln( ) ln( ) ln( )t t t t t M P Y R u = + + + , 1 20, 0 > < (3)

    Both Models (2) and (3) are log linear models, but Model (2) uses the level of interest rates and

    Model (3) uses the logarithm value of interest rates.

    4. Data

    This paper uses both monthly data and annual data for empirical analysis. For monthly data,

    we use data over the period of January 1980 to December 2007. The data source for the

    industrial production index (seasonally adjusted by X12) and the wholesale price index is IMF

    (2008). We obtained M1, M2, and M3 from various issues of the RBI Bulletin. We deflate these

    monetary aggregates by the wholesale price index, and we use the call rate as the interest rate.

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    The call rate was obtained from RBI (2006) over the period of January 1980 to December 2005,

    RBI (2007a) and RBI (2008) over the period of January 2006 to December 2007.

    For annual data, we use data over the period of 1976 to 2007. Real GDP and the GDP deflator

    were taken from IMF (2008). We obtained M1, M2, and M3 from various issues of the RBIBulletin. We deflate these monetary aggregates by the GDP deflator, and we use the call rate as

    the interest rate. The call rate was obtained from RBI (2007b) and RBI (2008). Logarithm

    values are used for money supply, price levels, and output (industrial production and GDP).

    Interest rates are analyzed in two ways, taking a logarithm in one case and not in the other.

    As a preliminary analysis, we carried out the augmented Dickey-Fuller tests for the logs of

    real money balances, output, and interest rates (Dickey and Fuller 1979). As a result, the level of

    each variable was found to have a unit root, whereas the first difference of each variable was

    found not to have a unit root. Thus, we can say that each variable is a nonstationary variable

    with a unit root.

    5. Empirical Results

    5.1 Monthly Data

    First, we analyzed the money demand function in relation to the use of M1 using the monthly

    data over the period of January 1980 to December 2007. For that analysis, we conducted

    Johansen cointegration tests for the money demand function (Johansen 1991). There are two

    kinds of Johansen-type tests: the trace test and the maximum eigen-value test.

    Table 1 shows the results of cointegration tests for Model 1 and Model 2. Model 1 includes

    the logs of real money balances, the logs of industrial production, and the interest rate; whereas

    Model 2 includes the logs of real money balances, the logs of industrial production, and the logs

    of interest rates. As is evident from Table 1, the null hypothesis of no cointegrating relation is

    rejected at the 5% significance level for both models. As the existence of the cointegrating

    relation was supported, we estimated the money demand function using dynamic OLS (DOLS). 4

    Table 2 shows the estimation results with respect to Model 1. As is evident from this table, the

    output coefficient is significantly estimated to be at positive values (1.1484 for K=1, 1.1498 for

    K=2, and 1.1556 for K=6). The interest rate coefficient is significantly estimated to be at

    negative values (-0.0043 for K=1, -0.0049 for K=2, and -0.0050 for K=6). Thus, the sign

    condition of the money demand function holds for all cases. Table 3 shows the estimation

    results with respect to Model 2. As is evident from this table, the sign condition of the money

    demand function holds for all cases. The output coefficient was significantly estimated at

    4 Standard errors are calculated using the method of Newey and West (1987).

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    positive values (1.1432 for K=1, 1.1437 for K=2, and 1.1478 for K=6), while the interest rate

    coefficient was significantly estimated at negative values (-0.0480 for K=1, -0.0548 for K=2,

    and -0.0595 for K=6). As is evident from the above results, it became clear that a cointegrating

    relation was supported and that the existence of a money demand function with respect to M1was statistically supported.

    Next, we considered the money demand function when using M2 for the money supply

    component. Table 4 indicates the results of cointegration tests for Model 1 and Model 2. As is

    evident from the table, the null hypothesis of no cointegration is rejected at the 5% significance

    level for both models. As the existence of the cointegrating relation was supported, we

    estimated the money demand function using DOLS. Table 5 shows the estimation results with

    respect to Model 1. As is evident from this table, the sign condition of the money demand

    function holds. The output coefficient was significantly estimated at positive values of 1.0966

    for K=1, 1.0977 for K=2, and 1.1023 for K=6, while the interest rate coefficient was

    significantly estimated at negative values of -0.0049 for K=1, -0.0055 for K=2, and -0.0059 for

    K=6. Table 6 shows the estimation results with respect to Model 2. As is evident from this table,

    the sign condition of the money demand function holds. The output coefficient was significantly

    estimated at positive values of 1.0907 for K=1, 1.0908 for K=2, and 1.0934 for K=6, while the

    interest rate coefficient was significantly estimated at negative values of -0.0543 for K=1,

    -0.0617 for K=2, and -0.0685 for K=6. As is evident from the above results, it became clear that

    a cointegrating relation was supported and that the existence of a money demand function with

    respect to M2 was statistically supported.

    Finally, we considered the money demand function when using M3 for the money supply

    component. Table 7 indicates the results of cointegration tests for Model 1 and Model 2. As is

    evident from this table, the null hypothesis (in which there is no cointegrating relation) is not

    rejected at the 5% significance level for either of the models. It became clear that a

    cointegrating relation was not supported and thus that the existence of a money demand

    function with respect to M3 was not statistically supported.

    5.2 Annual Data

    We also analyzed the money demand function in relation to the use of M1 using the annual

    data over the period from 1976 to 2007. Since industrial production does not necessarily reflect

    the total level of output in the Indian economy, it is worthwhile to analyze the money demand

    function using annual data, which enables us to use the GDP data. Table 8 shows the results of

    cointegration tests for Model 1 and Model 2. As is evident from Table 8, the null hypothesis of

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    no cointegrating relation is rejected at the 5% significance level for both models. As the

    existence of the cointegrating relation was supported, we estimated the money demand function

    using DOLS. Table 9 shows the estimation results with respect to Model 1. As is evident from

    this table, the output coefficient is significantly estimated to be positive (1.0037 for K=1, 0.9812for K=2, and 0.9769 for K=3). The interest rate coefficient is significantly estimated to be

    negative (-0.0366 for K=1, -0.0260 for K=2, and -0.0242 for K=3). Thus, the sign condition of

    the money demand function holds for all cases. Table 10 shows the estimation results with

    respect to Model 2. As is evident from this table, the sign condition of the money demand

    function holds for all cases. The output coefficient was significantly estimated to be positive

    (1.0020 for K=1, 1.0011 for K=2, and 1.0624 for K=3), while the interest rate coefficient was

    significantly estimated to be negative (-0.3399 for K=1, -0.2321 for K=2, and -0.2378 for K=3).

    As is evident from the above results, it became clear that a cointegrating relation was supported

    and that the existence of a money demand function with respect to M1 was statistically

    supported.

    Next, we considered the money demand function when using M2 for the money supply

    component. Table 11 indicates the results of cointegration tests for Model 1 and Model 2. As is

    evident from the table, the null hypothesis of no cointegration is rejected at the 5% significance

    level for both models. As the existence of the cointegrating relation was supported, we

    estimated the money demand function using DOLS. Table 12 shows the estimation results with

    respect to Model 1. As is evident from this table, the sign condition of the money demand

    function holds. The output coefficient was significantly estimated at positive values of 0.9402

    for K=1, 0.9173 for K=2, and 0.9132 for K=3, while the interest rate coefficient was

    significantly estimated at negative values of -0.0397 for K=1, -0.0295 for K=2, and -0.0278 for

    K=3. Table 13 shows the estimation results with respect to Model 2. As is evident from this

    table, the sign condition of the money demand function holds. The output coefficient was

    significantly estimated at positive values of 0.9381 for K=1, 0.9374 for K=2, and 0.9988 for

    K=3, while the interest rate coefficient was significantly estimated at negative values of -0.3669

    for K=1, -0.2648 for K=2, and -0.2715 for K=3. As is evident from the above results, it became

    clear that a cointegrating relation was supported and that the existence of a money demand

    function with respect to M2 was statistically supported.

    Finally, we considered the money demand function when using M3 for the money supply

    component. Table 14 indicates the results of cointegration tests for Model 1 and Model 2. As is

    evident from this table, the null hypothesis (in which there is no cointegrating relation) is not

    rejected at the 5% significance level in three out of four cases. It became clear that a

    cointegrating relation may not be supported and thus that the existence of a money demand

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    function with respect to M3 may not be statistically supported.

    Our empirical results using annual data are consistent with those using monthly data. Thus,

    the cointegrating relation for the money demand function is statistically supported for M1 and

    M2, but not for M3 for both monthly and annual data.

    6. Some Concluding Remarks

    If an equilibrium relationship is observed in the money demand function, financial authorities

    can employ appropriate money supply controls to maintain a reasonable inflation rate. This

    paper empirically analyzed India's money demand function over the period of 1980 to 2007

    using monthly data and the period of 1976 to 2007 using annual data. Results supported the

    existence of an equilibrium relation in money demand when money supply was defined as M1

    or M2, but no such relation was detected when money supply was defined as M3. These results

    were obtained for both monthly and annual data, so they were not affected by data intervals and

    were robust in this sense.

    What are the implications of these results for India's monetary policy? In the mid-1980s, the

    RBI adopted monetary targeting focused on the medium-term growth rate of the M3 money

    supply. Monetary targeting was used as a flexible policy framework to be adjusted in

    accordance with changes in production and prices, rather than as a strict policy rule. However,

    amid ongoing financial innovations and financial sector reforms, the RBI announced in April

    1998 that it would switch to the multiple indicator approach in order to be able to consider a

    wider array of factors in setting policy. Under this new policy framework, the M3 growth rate is

    used as one reference indicator.

    In general, a reference indicator, as an indicator of future economic conditions, is used as

    something between an operating instrument and a final objective, and no target levels are set, as

    is the case, for example, with intermediate targets. However, in India, where it is used as a

    reference indicator, the forecast growth rate for the M3 money supply is publicly announced on

    an annual basis, and it is focused on as a measure of future price movements. Consequently,

    Indian financial authorities, despite the fact that they have changed their policy framework,

    continue to pay significant attention to M3 movements. The empirical results of this paper,

    though, suggest that the RBI would be able to more appropriately control price levels if it would

    refer to the M1 and M2, rather than the M3, money supplies in managing monetary policy.

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    Table 1 Cointegration Tests (M1, Monthly data)

    * indicates that the null hypothesis is rejected at the 5% significance level.

    Model

    Hypothesized

    Number of

    Cointegration

    Equations

    Maximum Eigen-

    Value TestTrace Test

    Model 1 0 60.8885* 75.5725*

    At most 1 13.9371 14.6841

    At most 2 0.7470 0.7470

    Model 2 0 62.6358* 77.4240*

    At most 1 14.0725 14.7883

    At most 2 0.7157 0.7157

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    Table 2 Dynamic OLS (M1, Monthly data, Model 1)

    0 1 2log( 1 ) log( ) log( ) log( )K K

    t t t t yi t ri t t i K i K m p y r y r u

    = = = + + + + +

    Lead and

    LagVariable Coefficient SE t-Statistic P-value 2 R

    1K = Constant 2.9533 0.0741 39.8611 0.0000 0.9911

    log( )t y 1.1484 0.0158 72.4935 0.0000

    t r -0.0043 0.0012 -3.5416 0.0005

    2K = Constant 2.9478 0.0626 47.0700 0.0000 0.9923

    log( )t y 1.1498 0.0135 85.2199 0.0000

    t r -0.0049 0.0012 -4.0843 0.0001

    6K = Constant 2.9130 0.0539 54.0741 0.0000 0.9947

    log( )t y 1.1556 0.0107 108.2575 0.0000

    t r -0.0050 0.0015 -3.3923 0.0008

    Note: SE is the Newy-West HAC Standard Error (lag truncation=5).

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    13

    Table 3 Dynamic OLS (M1, Monthly data, Model 2)

    0 1 2log( 1 ) log( ) log( ) log( ) log( ) log( )K K

    t t t t yi t ri t t i K i K m p y r y r u

    = = = + + + + +

    Lead and

    LagVariable Coefficient SE t-Statistic P-value 2 R

    1K = Constant 3.0363 0.0894 33.9515 0.0000 0.9911

    log( )t y 1.1432 0.0164 69.6620 0.0000

    t r -0.0480 0.0134 -3.5715 0.0004

    2K = Constant 3.0445 0.0755 40.3038 0.0000 0.9924

    log( )t y 1.1437 0.0138 82.8285 0.0000

    t r -0.0548 0.0127 -4.3211 0.0000

    6K = Constant 3.0247 0.0655 46.2015 0.0000 0.9950

    log( )t y 1.1478 0.0104 109.8776 0.0000

    t r -0.0595 0.0144 -4.1434 0.0000

    Note: SE is the Newy-West HAC Standard Error (lag truncation=5).

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    14

    Table 4 Cointegration Tests (M2, Monthly data)

    * indicates that the null hypothesis is rejected at the 5% significance level.

    Model

    Hypothesized

    Number of

    Cointegration

    Equations

    Maximum Eigen-

    Value TestTrace Test

    Model 1 0 25.3333* 39.3050*

    At most 1 11.8306 13.9716

    At most 2 2.1411 2.1411

    Model 2 0 26.2955* 39.6353*

    At most 1 11.0450 13.3398

    At most 2 2.2948 2.2948

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    15

    Table 5 Dynamic OLS (M2, Monthly data, Model 1)

    0 1 2log( 2 ) log( ) log( ) log( )K K

    t t t t yi t ri t t i K i K m p y r y r u

    = = = + + + + +

    Lead and

    LagVariable Coefficient SE t-Statistic P-value 2 R

    1K = Constant 3.2129 0.0760 42.2970 0.0000 0.9899

    log( )t y 1.0966 0.0165 66.5934 0.0000

    t r -0.0049 0.0012 -3.9508 0.0001

    2K = Constant 3.2096 0.0655 49.0098 0.0000 0.9913

    log( )t y 1.0977 0.0143 76.7408 0.0000

    t r -0.0055 0.0012 -4.5206 0.0000

    6K = Constant 3.1817 0.0583 54.5536 0.0000 0.9938

    log( )t y 1.1023 0.0117 94.5821 0.0000

    t r -0.0059 0.0015 -3.8277 0.0002

    Note: SE is the Newy-West HAC Standard Error (lag truncation=5).

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    Table 7 Cointegration Tests (M3, Monthly data)

    * indicates that the null hypothesis is rejected at the 5% significance level.

    Model

    Hypothesized

    Number of

    Cointegration

    Equations

    Maximum Eigen-

    Value TestTrace Test

    Model 1 0 20.4033 27.3507

    At most 1 5.2173 6.9474

    At most 2 1.7301 1.7301

    Model 2 0 19.4088 25.9354

    At most 1 5.0979 6.5266

    At most 2 1.4287 1.4287

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    18

    Table 8 Cointegration Tests (M1, Annual data)

    * indicates that the null hypothesis is rejected at the 5% significance level.

    Model

    Hypothesized

    Number of

    Cointegration

    Equations

    Maximum Eigen-

    Value TestTrace Test

    Model 1 0 29.0382* 40.3709*

    At most 1 8.8912 11.3327

    At most 2 2.4415 2.4415

    Model 2 0 31.2939* 42.7403*

    At most 1 8.9359 11.4464

    At most 2 2.5105 2.5105

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    19

    Table 9 Dynamic OLS (M1, Annual data, Model 1)

    0 1 2log( 1 ) log( ) log( ) log( )K K

    t t t t yi t ri t t i K i K m p y r y r u

    = = = + + + + +

    Lead and

    LagVariable Coefficient SE t-Statistic P-value 2 R

    1K = Constant 4.0407 0.2939 13.7502 0.0000 0.9716

    log( )t y 1.0037 0.0768 13.0640 0.0000

    t r -0.0366 0.0099 -3.7002 0.0014

    2K = Constant 3.8224 0.1669 22.9069 0.0000 0.9944

    log( )t y 0.9812 0.0448 21.9224 0.0000

    t r -0.0260 0.0058 -4.4821 0.0005

    3K = Constant 3.7578 0.1312 28.6378 0.0000 0.9952

    log( )t y 0.9769 0.0470 20.7860 0.0000

    t r -0.0242 0.0048 -5.0189 0.0010

    Note: SE is the Newy-West HAC Standard Error (lag truncation=5).

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    20

    Table 10 Dynamic OLS (M1, Annual data, Model 2)

    0 1 2log( 1 ) log( ) log( ) log( ) log( ) log( )K K

    t t t t yi t ri t t i K i K m p y r y r u

    = = = + + + + +

    Lead and

    LagVariable Coefficient SE t-Statistic P-value 2 R

    1K = Constant 4.4896 0.3875 11.5861 0.0000 0.9738

    log( )t y 1.0020 0.0772 12.9872 0.0000

    t r -0.3399 0.0873 -3.8949 0.0009

    2K = Constant 4.0882 0.2591 15.7774 0.0000 0.9942

    log( )t y 1.0011 0.0524 19.1028 0.0000

    t r -0.2321 0.0615 -3.7765 0.0020

    3K = Constant 3.8970 0.1522 25.6072 0.0000 0.9944

    log( )t y 1.0624 0.0446 23.8410 0.0000

    t r -0.2378 0.0532 -4.4676 0.0021

    Note: SE is the Newy-West HAC Standard Error (lag truncation=5).

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    21

    Table 11 Cointegration Tests (M2, Annual data)

    * indicates that the null hypothesis is rejected at the 5% significance level.

    Model

    Hypothesized

    Number of

    Cointegration

    Equations

    Maximum Eigen-

    Value TestTrace Test

    Model 1 0 29.4465* 40.2924*

    At most 1 8.9430 10.8459

    At most 2 1.9029 1.9029

    Model 2 0 31.8685* 42.6966*

    At most 1 8.9294 10.8281

    At most 2 1.8988 1.8988

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    22

    Table 12 Dynamic OLS (M2, Annual data, Model 1)

    0 1 2log( 1 ) log( ) log( ) log( )K K

    t t t t yi t ri t t i K i K m p y r y r u

    = = = + + + + +

    Lead and

    LagVariable Coefficient SE t-Statistic P-value 2 R

    1K = Constant 4.3669 0.2886 15.1317 0.0000 0.9676

    log( )t y 0.9402 0.0760 12.3674 0.0000

    t r -0.0397 0.0098 -4.0638 0.0006

    2K = Constant 4.1610 0.1650 25.2232 0.0000 0.9936

    log( )t y 0.9173 0.0443 20.7286 0.0000

    t r -0.0295 0.0057 -5.1387 0.0002

    3K = Constant 4.1007 0.1311 31.2843 0.0000 0.9948

    log( )t y 0.9132 0.0478 19.1190 0.0000

    t r -0.0278 0.0049 -5.7213 0.0004

    Note: SE is the Newy-West HAC Standard Error (lag truncation=5).

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    23

    Table 13 Dynamic OLS (M2, Annual data, Model 2)

    0 1 2log( 1 ) log( ) log( ) log( ) log( ) log( )K K

    t t t t yi t ri t t i K i K m p y r y r u

    = = = + + + + +

    Lead and

    LagVariable Coefficient SE t-Statistic P-value 2 R

    1K = Constant 4.8505 0.3788 12.8058 0.0000 0.9702

    log( )t y 0.9381 0.0757 12.3845 0.0000

    log( )t r -0.3669 0.0857 -4.2806 0.0004

    2K = Constant 4.4693 0.2556 17.4837 0.0000 0.9935

    log( )t y 0.9374 0.0511 18.3566 0.0000

    log( )t r -0.2648 0.0613 -4.31665 0.0007

    3K = Constant 4.2862 0.1556 27.5495 0.0000 0.9938

    log( )t y 0.9988 0.0463 21.5558 0.0000

    log( )t r -0.2715 0.0541 -5.0207 0.0010

    Note: SE is the Newy-West HAC Standard Error (lag truncation=5).

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    24

    Table 14 Cointegration Tests (M3, Annual data)

    * indicates that the null hypothesis is rejected at the 5% significance level.

    Model

    Hypothesized

    Number of

    Cointegration

    Equations

    Maximum Eigen-

    Value TestTrace Test

    Model 1 0 20.7221 31.4139*

    At most 1 6.7122 10.6918

    At most 2 3.9796 3.9796

    Model 2 0 18.0444 28.3185

    At most 1 6.5157 10.2741

    At most 2 3.7584 3.7584

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