Money Supply, Interest Rate, Liquidity and Share Prices: A Test of Their Linkage. Using Panel Data of G-7 Countries. Abstract. This paper reports new evidence ...
Money Supply, Interest Rate, Liquidity and Share Prices: A Test of Their Linkage Using Panel Data of G-7 Countries
Abstract This paper reports new evidence of a liquidity effect on share prices from money supply changes. Money supply impacts on interest rate and liquidity were first proposed in 1969 and there is evidence that money supply increase leads to interest rate declines. Yet the proposition that money supply increase should lead to liquidity surges – thus to credit expansion – has yet to receive unanimous empirical support. Using panel quarterly data over 1968-2011 for G-7 countries, our results from a two-stage simultaneous solution of a system of equations indicate that money supply changes lead to a positive liquidity effect, as per the theory prediction. By extending the liquidity equation to asset prices, we also show that liquidity change has a significant positive effect on share prices, after controlling the effects of earnings, policy regime changes and global financial crisis. These findings, obtained after solutions to serious econometric issues of existing studies, appear to provide a clear verification of theory on the money supply effect on liquidity and on asset price. JEL Classification: E41 and E44 Key words: Liquidity, Money supply, System of equations, Causality test, Share prices, Interest rate, Two-stage least squares, Panel data, Unit Root tests, Structural break
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Money Supply, Interest Rate, Liquidity and Share Prices: A Test of Their Linkage Using Panel Data of G-7 Countries
1.
Introduction
Friedman’s (1969) suggestion of a negative money supply effect on interest rate has been verified in a number of studies while his suggestion of a positive money supply effect on liquidity has yet received unanimous support. 1 Hamilton (1997) attempted to show a liquidity effect by using daily observations, others (Pagan and Robertson, 1995; Goodfriend, 1997, and Lepper and Gordon, 1992; Edmond and Weill, 2005; and Thornton, 2007) have not been successful in verifying this proposition in their empirical reports. This paper is therefore an attempt first to verify the untested money-to-liquidity proposition by carefully specifying a relevant model by using a number of refinements to remove statistical and econometric problems and then applying a system of equations to test if the money-to-liquidity effect is evident. By using quarterly panel time series data of G-7 countries over 1968 and 2011 and by specifying controls for regime changes (shifts from monetary targeting to inflation targeting) and the global financial crisis for structural breaks in the variables, this research paper is able to verify a liquidity effect that has evaded detection. An innovation of this study is the extension of the money supply theory on liquidity to include liquidity effect on share prices. As a robustness test of our hypotheses, we provide causality tests linking money supply to liquidity as well as share prices and earnings. This paper is organised as follows. The readers will find in section 2 a very brief discussion of the money supply theory, also its variations, while focusing the discussion on (i) liquidity and (ii) share price effect. The next section 3 is devoted to explaining the data preparation 1
The empirical literature on the liquidity effect dates back at least to Cagan and Gandolfi (1969), Gibson (1970a,b), Leeper and Gordon (1992), Goodfriend (1997), Pagan and Robertson (1995), Christiano, Eichenbaum and Evans (1996), Hamilton (1997), Thornton (2001) Carpenter and Demiralp (2006) and Thornton (2007).
2
steps (to correct for stationarity, multicollinearity, serial correlations, heteroscedasticity, Hausman tests on use of random Vs fixed effects), the test models for causality tests, the system of equations and the regression models. The findings are presented and discussed in section 4 before the paper ends with relevant comments in section 5. In our opinion, this paper’s contribution is the verification of the old proposition by Friedman op cit of a money supply impact on liquidity after controlling the interest rate effect. Two further contributions of this paper are: money supply is directly related to liquidity, and by extension, liquidity changes lead to share price changes. The use of simultaneous equations modelling on panel data of G-7 countries provides new insight to existing literature and previous research.
2.
Monetary Supply, Interest Rate, Liquidity and Share Price
A brief review of literature is provided in this section. First, we describe the liquidity effect proposition which remains unconfirmed to-date. The link between liquidity and asset (stock) prices is then explored before considering the endogenous money supply equation. 2.1
Liquidity Effect
The phrase liquidity effect was introduced by Friedman (1969) to describe the first of three effects on interest rates caused by an unexpected exogenous change in the money supply: the other two effects are income and inflation expectations effects. While there is controversy (Bryant et al., 1988) as to whether changes in money supply do lead to negative interest rate changes as some authors conclude (Laidler, 1985). The linkage between money supply and interest rates has been recognized among policy makers on the basis of evidence of interest
3
rate effect. 2 The money stock is itself an asset in the portfolio of wealth-holders. Increases in the stock of money will cause decreases in the benefits of holders from the last dollar of money held. Changes in the supply of money are, therefore, a proxy for changes in the return on money. 3 The risk-free interest rate has been assumed to be a function of the long-term bond rate. Alternately, it is proposed that the demand for money is a function of, among other interest rates, the yield on equities. Any increase in the supply of money will tend to cause all interest rates across the board in the demand for money to fall. The speed with which yield on other assets respond depends on the rate at which excess holdings of money balances could be reduced: this provides a clue on how the central bank uses reserves to influence this to happen. The reaction rate of prices of different assets in turn depends upon the responsiveness of their potential purchasers to changes in the excess holdings of money. If those potential purchasers such as institutions, dealers, and wealthy individuals with the bulk of the floating supply of corporate stock are responsive to changes in their money balances, then the returns on corporate stock will be affected. Thus, stock prices should be responsive to movements in money supply with a negative coefficient through this channel. Despite its prominent role in conventional theories of the monetary policy transmission mechanism, there has been very little evidence of a statistically significant or economically meaningful liquidity effect being confirmed in studies. 4 Since previous attempts to identify
2
The inability to find conclusive evidence has led researchers like Pagan and Robertson (1995) to suggest that this could be due to different i) definitions of money, ii) models, iii) estimation procedures and iv) sample periods. 3 Duca (1995) adds bond funds to M2 and finds the expanded M2 more explainable of the missing M2 from 1990:3 to 1992:4. As an alternative to this approach, Mehra (1997) suggested redefining the opportunity cost of M2 to include the long-term bond rate to capture the increased substitution of mutual funds for bank deposits. 4 A number of researchers including Bernanke and Blinder (1992), Christiano and Eichenbaum (1991, 1992a, b) and Goodfriend (1991) have argued that the lack of empirical support is due to the Fed’s attachment to interest rate targeting in one form or another. They argued that innovations to monetary aggregates, M1, reflect shocks to money demand rather than to money supply. Consequently, the inability to find the liquidity effect is due to inability to isolate a statistically significant variable that reflect the exogenous policy actions of the Fed.
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the liquidity effect have been unsuccessful because the use of low frequency data necessarily mixes together the effects of policy on economic variables with the effects of economic variables on policy, Hamilton (1997) sought to develop a more convincing measure of the liquidity effect by estimating the response of the federal funds rate to exogenous reserve supply shocks using daily data, i.e., by estimating the daily liquidity effect. Among other things, the failure to find evidence of the liquidity effect using low frequency monetary and reserve aggregates has been attributed to the response of nominal income or inflation expectations to money supply shocks or to the inability of researchers to isolate exogenous monetary shocks. Researchers have attempted to overcome these problems using, among other things, structural vector autoregressions (SVARs). SVAR models have been estimated using a variety of monetary and reserve aggregates. Pagan and Robertson (1995) show that it is difficult to find convincing evidence of a liquidity effect with these models. Generally, most economists believe that liquidity effects appear in the data for US economy, though the size of the effects is a subject of controversy, due largely to identification problems in statistical work. Lepper and Gordon (1992) for example felt that in the absence of strong identifying assumptions, there is no consistent evidence of liquidity effects in the US data. Others suggest that liquidity effects reflect part of the economy’s coordination on a particular equilibrium when multiple solutions are possible. Goodfriend (1997) suggests a model in which imperfectly competitive firms face kinked demand curves and so price sluggishness emerges endogenously creating real effects of monetary policy in which liquidity effects play a role.
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2.2
Stock Prices
The portfolio model of Cooper (1970) assumes that individuals could hold wealth in two forms, money and common stock. The marginal returns of stock assets determine the quantities of assets individuals will hold. A portfolio is said to be balanced when the marginal returns to holding these two assets are equal. 𝑀𝑁𝑃𝑆𝑡𝑀 − 𝑃� = 𝑀𝑁𝑃𝑆𝑡𝑆 + 𝑟̅𝑡𝑠
(1)
Where, using the term of the author, the left side is the return to money asset and the right side is the return to stock asset; 𝑃�𝑡 is anticipated percentage change in general price level ; 𝑟� ∗𝑡 is the anticipated real pecuniary return of stocks (dividend plus change in stock
prices); MNPSts is marginal pecuniary return to the j-th asset (the risk of j-th assets is incorporated into its pecuniary returns. MNPStM is implicitly a function of demand for money except for returns on alternative assets. An underlying assumption is that the positive income effect on MNPStM,S cancel each other. Thus, the difference between MNPStM and MNPStM,S is primarily a function of money. In this model, money changes induce portfolio adjustments through MNPSt schedules and prices. The result is that money supply leads to stock returns. By re-arranging this equation, it could be shown that the stock return is: 𝑟̅𝑡𝑠 = (𝑀𝑁𝑃𝑆𝑡𝑀 − 𝑃� ) − 𝑀𝑁𝑃𝑆𝑡𝑆
~
(2)
Thus, Cooper’s model is equivalent to the asset pricing model in finance. It would be interesting to examine the link between the liquidity effect from money supply affecting the stock prices, as proposed in this study. Friedman’s proposition could be extended as money supply having an influence on asset prices namely share prices in this study. The model of equity pricing used with this kind of effect is
6
P0 = ∑𝑁 𝑡=1
𝐷𝑜 (1+𝑔𝑡 ) t (1+𝑖𝑡 +𝑟𝑡 )𝑡
~
(3)
where Po is the current price of a share; Do is the dividend at time 0; g is the constant growth rate of dividends; i t is the risk-free rate at time t; and rt is the equity risk premium at time t.5 By noting the equation “D = EPS (payout)”, a relationship could be shown that stock prices are correlated with EPS or some proxy such as industrial output (IPI) as representing corporate earnings, since payout ratio tends to be constant in most economies. Share prices being a leading indicator of earnings (proxied by IPI), is expected to lead earnings. 6 The relationship of stock prices to money has been a subject of academic research for several decades from other approaches as well while there is renewed interest given the recent discovery of endogenous money theory. In the light of current perennial financial crisis in the world, liquidity impact of money supply on stock prices has become a hot topic in policy circles to understand what ails financial systems. Most of these studies use Monetary Portfolio (MP) model developed by Brunner (1961), Friedman and Schwartz (1963) and Cagan (1972) as their starting premise. An investor is assumed as reaching an equilibrium position in which, in general, she holds a number of assets including money in portfolio of assets. A monetary disturbance such as an unexpected increase (or decrease) in the growth rate of the money supply causes disequilibrium in asset portfolios. Investors attempt to rebalance their desired money positions, which are transmitted as monetary changes to the financial markets at large. By substituting EPS (payout ratio), the numerator may be replaced as EPSO (POR) (1 + 𝑔)𝑡 . Thus, a proxy to represent EPS could be used to test if PO is significantly affected by earnings. We chose the proxy as the Industrial Production Index. As IPI goes up, the EPS goes up: a high correlation is found between income and IPI series. 5
6
Chen et al. (1986) used some macroeconomic variables to explain stock returns in the US stock markets. The authors’ findings showed industrial production to be positively related to the expected stock returns, among others. Tainer (1993) is of the view that the industrial production index is pro-cyclical. It is typically used as a proxy for the level of real economic activity. Fama (1990) and Geske and Roll, (1983) hypothesized a similar positive relationship through the effects of industrial production on expected future cash flows. Stock and Watson (1989) has shown share prices to be a leading indicator of US economic activity as indicated by IPI and ICI in their study from 1958-1988.
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From a different perspective, using a pooled cross-section and time-series analysis – we prefer a system of equations approach as more effective to model complex structures involved - Brennan, Chordia, and Subrahmanyam (1998) report significant positive relation between expected share returns and illiquidity. Hence the relationship between the money supply and the stock prices discovered by Sprinkel (1964) plays an important role in money supply leading to asset prices such as common stock prices. However, studies by Cooper (1970), Pesando (1974), Kraft and Kraft (1977), and Rozeff (1974)) have questioned this linkage between stock prices and money supply. Over time, studying this issue has lapsed until the emergence of the Global Financial Crisis, which has been diagnosed as having been caused by liquidity surges that created imbalance in the financial sector and real sector: Ariff et al., (2012). 2.3
Money Supply Effect
The main channel of influence of the money supply on dividends is through the firm's current and expected earnings, especially as regards expectation of the money supply effect on dividends. Although the current prices of common stock will be affected by changing current dividends, the main effect of money supply is on the expected growth rate of dividends arising from permanent change in earnings of firms from positive NPV projects being chosen at lower cost of capital when interest rates fall after money supply increases. This also suggests that a proxy for earnings such as (industrial production index) IPI, is a better variable than dividends, which is a managed variable. Thus, the money supply and stock prices are positively related through this channel. The theoretical framework presented by monetarists for the relationship between the money supply and stock prices is from the quantity model or the more sophisticated portfolio theory. The quantity theory of money (Brunner, 1961; Friedman, 1961; and Friedman and Schwartz, 8
1963) states that an increase in the money supply results in a change in the equilibrium position of money with respect to non-money other assets, for example shares, in the portfolio balance of asset holders. This alters the demand for other assets that compete with money balances. Quantity Theory of Money states that M. V = P. Q
~
(4)
where, M is the total amount of money in circulation in an economy during the period, say a year; P the corresponding price level; P.Q is the nominal money value of output; V is the velocity of money in final expenditures; and Q is an index of the real value of final expenditures. An increase in money supply is expected to increase excess supply of money balance, which in turn leads to excess demand for shares. Share prices are expected to rise as a result. This channel of interaction has been described as a direct channel for the first time in Sprinkel (1964). He explicitly tested a model incorporating Simple Quantity Theory (SQT) in a model of asset pricing. As the supply of money expands, the portfolio of desired versus actual cash holding is thrown out of balance. Since the stock of money must be held by the agents, the prices of other assets and goods and services for consumption are bid up to a new equilibrium level. This theory is still in vogue although the question of how the money supply influences the asset prices has newer interpretations, as for example, in Effa et al., (2011). Therefore, the relationship between the money supply and stock prices is said to be positive in nature through this adjustment mechanism. In summary, the most plausible explanation for a relationship between money supply changes and stock returns conditional on liquidity effect seems to be a combination of the quantity theory of money and asset pricing model in a portfolio setting. Monetary theory is enhanced by the introduction of liquidity as the missing link between money and aggregate demand. 9
Increasing liquidity can be observed during business upturns strengthening investment and expanding the volume of money in account, thus enhancing financial activities. Research studies by post-Keynesian economists have provided new insights on money being endogenously rather than exogenously determined. In theoretical as well as in empirical finance, the role of liquidity has been highlighted in recent policy debates so it is an area of applied research with potential usefulness.
3.
Data Sources, Variables and Methodology
3.1
Hypotheses and Methodology
A system of equations comprising 2 simultaneous equations of stock returns (P) and liquidity (LQ), is developed to be solved endogenously as follows: 7 Pit = f [LQ+, MS+, IPI+, IPI(-1)+]
(5)
LQit = f [MS+, Y+, LR-]
(6)
MSit = f [LQ+, Y+, TBR-, P+, CPI+, CPI(1)+]
(7)
where Pit is aggregate share price index, LQit is liquidity as proxied by reserve money, MSit is money supply, IPI is industrial production index, Y is real GDP, LR is lending rate, TRB is Treasury bill rate and CPI is inflation. All variables are in log change ratios. It is hypothesized that money supply (MS) is endogenously determined (see Effa et al., 2011) by economic activity as mediated via the deposit-taking institutions. The literature on post-
7
The basis of the model in this section stems from Badarudin et al. (2011). Not all the variables used in that paper are used in this study because the focus of this study is on liquidity and stock prices, whereas in the cited paper, the objective was money supply effect on share prices.
10
Keynesian theory on endogenous money is extensive. 8 Economic activity is proxied by real gross domestic product (Y), liquidity (LQ) is endogenously determined by money supply (MS) and asset prices (P) from liquidity (LQ). Money supply (MS) is also determined by stock returns (P), inflation (CPI), real GDP (Y) and Treasury bill rate (TBR). Liquidity is determined by real GDP (Y), money supply (MS) and Lending rate (LR). Using the simultaneous equation model above, test models shown below will be used to test hypotheses 1 to 3: H1:
MS causes GDP (suggesting money is exogenous) or there is bidirectional causality. H11:
GDP causes MS or there is bidirectional causality between MS and GDP.
H12: There is bidirectional causality between money supply and real GDP (implying money is endogenous). This needs to be established first before analysis. H2:
MS causes Liquidity: this follows from Friedman’s proposition still not verified. H21:
Liquidity causes MS. This is to test the bi-directional causality.
H22: Share Prices causes Liquidity. Credit expansion from liquidity caused earnings to rise and that in turn causes share prices to rise. H3:
Liquidity causes Share Prices. This is to test the bi-directional causality.
It is hypothesised under hypotheses 1 there may be unidirectional or bidirectional causality from real GDP to money supply. The findings are tested against a VAR formulation to check for robustness and consistency. The model developed earlier has variables that are endogenous although these are exogenously or predetermined. The decision regarding exogeneity among variables is heavily criticized by Sims (1980). According to Sims (1980), if there is simultaneity among a number of variables, then all these variables should be treated in the same way. There should
8
Influenced greatly by Kaldor and Moore in 1988 developed the post-Keynesian view on money, which is today the cornerstone of the PK theory of endogenous money (Rochon, 2006). The core of this theory is that causality runs from bank lending to bank deposits, instead of the traditional notion that deposits create loans.
11
be no distinction between endogenous and exogenous variables. This means that each equation has the same set of regressors as in the class of VAR models. The VAR model has some very good characteristics: •
It is very simple, and there is no need to worry about endogenous or exogenous variables as is needed in system of equation models.
•
Estimation is very simple as each equation is estimated by the OLS procedure.
•
Forecasts obtained from VAR models are in most cases better than from simultaneous equations models (Mahmoud (1984) and McNees (1986)).
VAR results provided good diagnostic statistics that could be used as checks for robustness and interpretation. However, VAR model also suffers from the following shortfalls: •
They are a-theoretic since they are not based on any economic theory. With no restrictions on any of the parameters, everything causes everything.
•
Loss of degrees of freedom. A three-variable VAR with 12 lags for each variable will entail estimation of 36 parameters in each equation plus a constant. If the sample size is not large, loss of degrees of freedom will cause problems in estimation.
•
Obtained coefficients in VAR models are difficult to interpret since they lack any theoretical background, although sound theories guide our tests in this thesis. To overcome this, impulse response functions are developed which examines the response of the dependent variable in the VAR to shocks in the error terms. Granger causality, variance decomposition, innovation accounting and impulse response functions are the methodology in VAR models that replaces parameter estimates, identifying restrictions and hypothesis testing in classical econometrics.
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The use of the VAR model here, is to verify and separate the liquidity, income and price effects from a money supply increase using the impulse response functions. For a 2-equation VAR model with 2 lags: lnPt = a0+ a1lnPt-1+ a2lnPt-2 + a3lnLQt-1 +a4lnLQt-2 +a5lnRIPIt + a6lnRGDPt+ a7lnCPI+ a8TBR + a9LR
(8)
lnLQt = b0+ b1lnPt-1+ b2lnPt-2 + b3lnLQt-1 +b4lnLQt-2+b5lnRIPIt + b6lnRGDPt+ b7lnCPI+ b8TBR + a9LR
(9)
The econometric issues differentiating a simultaneous and VAR formulation of a system of equations can best be seen as follows: B0
Bj (j≥l)
SEM
x
x
VAR
x
cov (𝜀𝑡𝑧 ) x
Simultaneous-equation estimation and VAR methods address the issue of how to estimate the parameters of a system such as those in equations 5-7 using assumptions on “identification”. Each approach is widely discussed in the literature and involves some constraint upon the parameters in the matrices Bo, B1….. Bn and the covariance matrix of the errors 𝜀𝑡𝑧 . The Table
above summarizes the two main approaches discussed in this paper.
In the simultaneous methodology, cov ( 𝜀𝑡𝑧 ) was left unrestricted, but the Bj (j≥0) was
restricted using identification from theory. For models with lagged dependent variables, this often meant that lagged values of dependent variables, were omitted from the system to identify the coefficients attached to the endogenous variables remaining in the equations. Sims (1980) 9 condemned such exclusion on restrictions as “incredible”. Having decided that
9
Sims (1980) suggested using a recursive system. For this we need to restrict some of the parameters in LQt but not vice versa. That is, Pt is affected by both structural innovations of Pt and LQt while LQt is affected by its own structural innovation. This is a triangular decomposition also called Cholesky decomposition or the error
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no elements in Bj (j ≥ 1) could be restricted, that is, all lagged values appear in every equation, Sims was forced to adopt two other assumptions to estimate B0. First, he proposed that the structural errors cov(𝜀𝑡𝑧 ) have a diagonal covariance matrix, that
is, they were uncorrelated, so that a share price shock could be regarded as independent of a liquidity shock. Second, he chose to make B0 lower triangular. Together, these assumptions produced a Wold causal ordering, and that terminology is one frequently used in the literature. Thus, the ordering (p, lq, m ) means that pt can be determined as pt depends only on lagged values (predetermined) of
pt, lqt
and mt. The next variable in the ordering depends on
contemporaneous values of the previous variables in the ordering and lagged values of itself and the remaining variables (predetermined); for example, lqt depends on pt and lagged values of lqt, and mt. The implication of these assumptions is that the simultaneous system in the 2 equations (8) and (9) has been transformed to one that is recursive, making OLS the appropriate estimator of the unknown parameters in B0. 10 We derived a reduced form equation of the system of equation as below: lnP = α0+ α1lnLQ+α2MS+α3lnIPI
(10)
lnLQ1 = β0+ β1lnMS+β2lnRGDP + β3LR
(11)
From 10: lnP = α 0+ α 1(β 0+ β 1lnMS+ β 2lnRGDP + β 3LR) + α 2lnMS+ α 3lnIPI lnP = α0+ α1β0+ α1β1lnMS+ α 1β2lnRGDP + α 1β3LR + α2lnMS + α 3lnIPI lnP = α0+ α1β 0+ lnMS(α1β 1 + α 2)+ lnRGDP (α1β 2)+ α 1β3LR+ α 3lnIPI structure becomes lower triangular as explained in footnote 10. The cov(𝜀𝑡𝑧 ) shock doesn’t affect LQ directly but affects it indirectly through its lagged effect in VAR. -1 Sims found that cov(𝜀𝑡𝑧 ) and 𝛽 0 such that 𝛽̂0 + 𝑐𝑜𝑣 � ( 𝜀𝑡𝑧 ) (𝛽̂0′ ) = 𝑐𝑜𝑣 � (𝜀𝑡𝑧 ), where the right hand side is the estimated covariance matrix of reduced form (VAR) errors. Numerically, this can be derived from a choleski decomposition to the right hand side.
10
14
Reduced form equations for stock price and liquidity are: lnP = α0+ α1β 0+ lnMS(α1β 1 + α 2)+ lnRGDP (α1β 2)+ α 1β3LR+ α 3lnIPI
(12)
lnLQ1 = β0+ β1lnMS+β2lnRGDP + β3LR
(13)
3.2
Test Models
3.2.1
Causality Testing
A number of test models are developed to carefully examine the hypothesized relationship between liquidity and share prices as well as money supply. The first of these is the causality test. If cointegration can be identified between dependent and independent variables as presented in the results discussed in the last section, then it can be understood that there is at least a single aspect of causality (Granger, 1969). Causality refers to the ability of one variable to predict and thus cause the other. The Granger (1969) causality test for two variables xt (see equations 5-6) and yt (see equations 5-6) involves the following Vector AutoRegressive (VAR) model to be estimated: yt = 𝑎1 + ∑𝑛𝑖=1 𝛽𝑗 xt−i + ∑𝑚 𝑗=1 𝛾𝑗 y𝑡−𝑗 + 𝑒1𝑡
(14)
xt = 𝑎2 + ∑𝑛𝑖=1 𝜃 xt−i + ∑𝑚 𝑗=1 𝛿𝑗 y𝑡−𝑗 + 𝑒2𝑡
(15)
where it is assumed that both 𝑒1𝑡 and 𝑒2𝑡 are uncorrelated white-noise error terms.
Thus, xt does not Granger cause yt if β1 = β2 =… . ..= βi = 0, where this hypothesis is tested using the F test. If no cointegration is found between variables, then the standard causality test (Granger, 1969) can be applied. If there is cointegration, then causality can be examined using the vector error-correction model (VECM) (Granger, 1988) as below: ∆ yt = 𝛼0 + ∑𝑛𝑖=1 𝛼1𝑖 ∆ y𝑡−1 + ∑𝑛𝑖=1 𝛼2𝑖 ∆ x𝑡−1 + ∑𝑛𝑖=1 𝛼3 ∆ EC 𝑡−𝑛 + 𝜀𝑡 15
(16)
The short-term causality of the VECM can be tested using the Wald test (χ2 test), and the long-term causality is tested by examining whether the error-correction coefficient 𝛼3 in the model is significantly different from zero. 3.2.2
System of Equations Structural Model
The effects to be observed may be represented as in the following equations: Pit = f [LQ+, MS+]
(5a)
LQit = f [MS+, P+]
(6a)
MSit = f [GDP+]
(7a)
where Pit is aggregate share price index, LQ it is liquidity as proxied by reserve money and MSit is money supply. All variables are in log change ratios. The use of the testable equations will be further elaborated later in this section. If two variables are cointegrated as discussed above, a vector error-correction model (VECM) and Granger causality test may also be used to test for causality between Share Price and Liquidity: equations (5a and 6a) will be employed since both these variables are simultaneously determined. Equation (7a) will also be used to test Hypothesis 1 on whether there is bidirectional causality between real GDP and money supply. Under hypotheses 2 to 3, share price is expected to Granger cause liquidity and liquidity is expected to Granger cause share price. By employing a VECM and Granger causality tests, equations (5a and 6a) may be useful in determining whether these hypotheses hold. Hypothesis 2, which suggests that there is either unidirectional or bidirectional causality between share price and liquidity, may be tested using a VECM and Granger causality test by applying equations (5a) and (6a). 16
Hypothesis 3, which suggests that there is a simultaneous relationship (or effect) between share price and liquidity and between liquidity and share price, may be tested by using equations (5a) and (6a). These empirical structural relationships will be tested using a system of equations. A simultaneous equations approach lends structure to the nature of the joint measurement errors, and has several desirable features. First, security price and liquidity variables are viewed as endogenous. The structural relationship is carefully derived to a reduced form equation as discussed in the previous section. Under this perspective, security price and liquidity are viewed as being jointly determined by a larger set of publicly available information, which is not explicitly captured in equations, (5a) and (6a). However, not all items of information are relevant to each variable, which is reflected in the residuals in each equation. In other words, liquidity could change for reasons not leading to price changes, and vice versa. Second, if either equations (5a) or (6a) were estimated in isolation, the coefficient estimates would be potentially subject to simultaneous equations bias. An empirical assessment of how much the coefficients from a single-equation approach differ from those provided by a simultaneous equations approach will be provided. Our view is that the estimated earnings response coefficient and the return response coefficient from a system of equations will be greater than under single-equation OLS estimation, because the bias will be reduced. By including all the variables discussed above, the structural equations for the system of equations is: ln Pit = a0+ a1 ln LQit + a2 ln MSit + a3 ln IPI it + eit
(17)
ln LQit = b0+ b1 ln MSit + b2 ln Yit + b3 LR it + vit
(18)
MSit = c0+ c1 ln INFit + c2 ln Yit + c3 TBR it + c4 ln Pit + c5 ln LQit + zit
(19)
17
3.3
Data and Variables
Data needed for all variables are from the Datastream database while the macroeconomic variables are verified against the International Financial Statistics (IFS) database of the International Monetary Fund (IMF) for consistency to ensure that there are no errors. The data are quarterly series for the period 1960:1 – 2011:2, where the number after colon refers to the quarter. Data for all seven G-7 countries are compiled and it is important to note that income is included as an explanatory variable in some equations specified above. Real gross domestic product is used as a proxy for income and since only quarterly data are available for income, the highest frequency is quarter. To specify a proxy for earnings, we searched the literature. The industrial production index (IPI) is highly correlated with income, which in turn is known to determine the earnings of firms in a modern economy. Hence, we use the log change of IPI as a proxy for earnings in the equation for asset pricing: if IPI goes up, the earnings of the firms go up. Liquidity is another difficult variable to specify. There are three alternative proxies: bid-ask spread used in market studies (Amihud and Mendelson, 1986); volume of transactions (Amihud, 2002; Chordia, Subrahmanyam and Anshuman 2001); reserve money (Gordon and Leeper, 2002). Using reserve money appears to be a right choice because, if the banking system has more money in the central bank, liquidity declines, and if it keeps less reserves, liquidity goes up. Hence, liquidity is inversely related to reserves. Data for money supply, M2, values are used. 11 The Treasury bill rate and the bank lending rate are the domestic 3-month Treasury-bill rate and lending rate respectively. The MSCI stock index values reported in Datastream is widely used for stock returns, P, computed as
11
The choice of monetary aggregate has been discussed earlier and its implications on the demand for money have been discussed in Pagan and Robertson (1995) and Duca (1995) on finding the liquidity effect and for the stock market in Parhizgari (2012) on the share price effect.
18
log change. The consumer price index is used as a proxy for inflation, INF. The bank lending rate, LR, deposit rates, TBR, and real gross domestic product, RGDP, are also obtained. All variables are seasonally adjusted where available and transformed to logarithmic form, with the exception of interest rates, which are the local 3-month Treasury bill rate, TBR and Lending Rate, LR. The asset pricing theory as discussed in section 2 suggests a relationship between share prices and corporate dividend streams growing at g-rate of growth. The g and dividends depend in the long run on earnings of the corporations, which directly depends on IPI. Although we are testing the relationship between liquidity and share prices, there is a need to control the effect of earnings changes in the system of equations. For this, we use the IPI after some initial tests using cointegration. Once the series are tested for stationarity, we ran a cointegration test with income RGDP and IPI: see Appendix A. As is evident from the test statistics, IPI is a good proxy for earnings. So, we specify this as a control in our liquidity equation for share prices. Please see Appendix on how this research dealt with the econometric issues. 12
4.
Findings
The results of these carefully run tests are presented in this section. After discussing the descriptive statistics, the data transformation test results are summarised and discussed. The causality test results are presented next before presenting the results of single equation and then the system of equations results. 4.1
Descriptive statistics
The Table 1 provides summary descriptive statistics of the variables used in the regression (single and system of equations). The variables are first differenced and computed by ratio 12
Extensive tests were done to ensure that the econometric problems are overcome in our study. These results are summarized in Appendix A to show to the reviewer that these tests ensure that the results are robust. Since this paper is lengthy, the materials in the appendix may be treated as additional materials for review purpose.
19
relative to prior observation. The Jarque-Bera (JB) test indicates that all variables are not normal. Most of these variables are skewed (> 0, for normality should be close to 0). A quick read of the values of these variables suggest that these are as one would expect in the panel of G-7 economies. For example, the Treasury rate over the test period of 44 years in the industrial economies of G-7 countries is 6.6 per cent and the lending rate is 8.1 per cent. These first moment values are as reported for the panel of G-7 countries. Another expected value within known ball park is inflation with a mean of 4 per cent. The mean of difference in LSPRICE or the share price returns is 0.02 per cent over 1960-2011. Table 1: Descriptive Statistics of the Panel Variables used in Tests S.D. is standard deviation. LSPRICE, LRM2, LRIPI, LRGDP, LCPI, TBR, LR and LRLQ are Stock price index, Money supply, Industrial production index, Income, Inflation, Treasury bill rate, Lending rate and Reserve money respectively. All variables are in logarithmic form except for TBR and LR. The data series are quarterly series TBR
3.36
∆LSPRICE 0.017
6.62
2.40
3.50
0.022
5.80
8.67
9.07
5.38
0.37
20.15
-0.44
-2.94
-0.77
1.03
-0.35
0.00
0.42
0.42
2.75
2.59
0.99
0.08
3.79
939 939
939939
939939
939 939
939939
939939
939 939
LCPI
LR
LRGDP
LRIPI
LRLQ
LRM2
LSPRICE
Mean
4.03
8.11
4.09
0.19
0.69
3.31
Median
4.26
7.39
4.17
0.03
-0.32
Maximum
4.83
23.27
4.67
1.78
Minimum
2.34
0.16
2.41
Std. Dev.
0.63
3.97
Obs
939
939 939
4.2
Causality test results
The Table 2 is a summary of bidirectional causality tests using all the variables, money supply, MS, income, GDP, and Liquidity, LRLQ. It is evident that all variables have bidirectional impact on one another except for the variable asset price (share price) to money supply and share price to liquidity, where money supply and liquidity leads share prices, as per expectations according to theory and empirical evidence. As is summarized in the table in Panel A, the bi-directional relationship is indicated by
while
shows
a
unidirectional relationship. Hence we accept these empirical results as the way the
20
relationships hold in our data set. For all other variables, finding bidirectional causality needs to be interpreted carefully. Finding bidirectional causality between money and income is as predicted by the endogenous money supply theory as reported in several studies since the famous paper by Moore (1989). Significant for the Friedman’s proposition of money effect on liquidity is confirmed in our tests: note that the money supply and liquidity effect is bidirectional. This is a new finding confirming the proposition that holds in the long run in our panel data of G-7 economies. The theoretical relationship is shown in Figure 1. Figure 1: Theoretical Relations Identified in our Models Monetarist MS
Accommodationist
Y
Y
MS
MS
LQ
MS
SP
LQ
SP
LQ
SP
Structuralist Y
MS
MS
SP
LQ
SP
Table 2: Summary of Causality Test Results Pairwise Granger Causality Tests Date: 12/22/11 Time: 10:55 Sample: 1960Q1 2011Q4 Lags: 2 Null Hypothesis:
Obs
F-Statistic
Prob.
LRGDP does not Granger Cause LRM2
1092
3.21319
0.0406
2.85053
0.0582
0.20880
0.8116
3.23185
0.0398
13.9188
1.E-06
3.96873
0.0192
LRM2 does not Granger Cause LRGDP LSPRICE does not Granger Cause LRM2
1158
LRM2 does not Granger Cause LSPRICE LRLQ does not Granger Cause LRM2
1053
LRM2 does not Granger Cause LRLQ
21
LSPRICE does not Granger Cause LRGDP
1299
LRGDP does not Granger Cause LSPRICE LRLQ does not Granger Cause LRGDP
1065
LRGDP does not Granger Cause LRLQ LRLQ does not Granger Cause LSPRICE
1082
LSPRICE does not Granger Cause LRLQ
16.6523
7.E-08
8.13256
0.0003
19.0515
7.E-09
2.42924
0.0886
3.07769
0.0465
1.80899
0.1643
All variables have bidirectional impact on one another except for LSPRICE to LRM2 and LSPRICE to LRLQ.
In view of the reported weakness of Granger causality test on bivariate relationships, a multivariate of 3 endogenous variables, LSPRICE, LRLQ AND LRM2 was conducted in a VECM framework. This can be seen in the table below which confirms the findings earlier of bidirectional causality between share prices and liquidity, share prices and money supply and liquidity and money supply. All the 3 panels showed that the variables tested displayed causality is significant at the 5% level. Since the causality is both ways, these can be interpreted as bidirectional causality. Although many of the central banks in the G-7 countries adopted monetary targeting in the 1970s, these were later abandoned in favor of inflation targeting and other instruments. The Central Bank of Canada abandoned monetary targeting in 1982 by changing its monetary policy to price stability by targeting inflation. The change could be prompted by practical reasons because the Central Bank of Canada failed to hit its monetary targets due to the endogeneity of money supply. The Bank of England adopted monetary targeting in late 1973 and due to difficulties in meeting those targets in 1976-79 abandoned monetary targeting (target for M3 was dropped in 1987) to inflation targeting. In the US, the Fed missed its M1 growth target in all three years of 1979-82. In Oct 1982, with inflation in check, the Fed began to deemphasize monetary aggregates and in February 1987 the Fed announced it would no longer even set M1 targets. Finally, in July 1993, Alan Greenspan testified in Congress that the Fed would no longer use any monetary targets, 22
including M2, as a guide for the conduct of monetary policy. Germany, engaged in monetary targeting for over 20 years starting at end 1974. In 1988, the Bundesbank switched targets from central bank money to M3, but the targets were flexible as the Bundesbank did not feel bound by the targets and allowed growth outside its target ranges for period of 2-3 years, and overshoots of its targets were subsequently reversed. The target ranges for money growth were missed on the order of 50 per cent of the time in Germany, in favor of other objectives like output and exchange rates.
VEC Granger Causality/Block Exogeneity Wald Tests Date: 12/22/11 Time: 11:22 Sample: 1960Q1 2011Q4 Included observations: 1043
Dependent variable: D(LSPRICE) Excluded
Chi-sq
df
Prob.
D(LRLQ)
7.317190
2
0.0258
D(LRM2)
8.996897
2
0.0111
All
20.74760
4
0.0004
Dependent variable: D(LRLQ) Excluded
Chi-sq
df
Prob.
D(LSPRICE)
7.960217
2
0.0187
D(LRM2)
9.639466
2
0.0081
All
18.30939
4
0.0011
Dependent variable: D(LRM2) Excluded
Chi-sq
df
Prob.
D(LSPRICE)
13.14648
2
0.0014
D(LRLQ)
13.44641
2
0.0012
All
23.94142
4
0.0001
23
The evidence in statistics presented in Table 2 Panel B is a summary of tests results of pairs of variables for Granger causality tests. These statistics indicate bidirectional causality for all the variables, MS, GDP and Liquidity. All variables have bidirectional impact on one another except for share price to MS and share price to liquidity.
4.3
Single and Reduced Form Equation Results on Panel Data
We discuss the results from single equation and reduced form regressions first before presenting the results from running the system of equations. The statistics presented in Table 3 indicate that the dependent variable - share price - in the first equation is determined by reserve money (that is liquidity LQ), money supply MS and proxy for earnings IPI and IPI(1). All the variables are significant in terms of the t-statistics. The liquidity impact on money supply in the third equation is quite significant reflecting reserve increases will lead to a decline in money supply. In the second equation, liquidity is determined by money supply, income or real GDP and lending rate LR. All the variables except for money supply (LRM2) and lending rate (LR) are significant given their t-statistics at the same acceptance levels of 0.01, 0.05 and 0.10. Money supply in the third equation is determined by income (RGDP), reserve money (LQ), share price (P), Treasury bill rate (TBR) and inflation (CPI). The significant relation between LQ and money is as per Friedman’s proposition highlighted in Granger causality test. Except for inflation, all the variables are significant given t-statistics at the 0.01, 0.05 and 0.10 levels of acceptance. The income elasticity of money is greater than one, 1.63 per cent given we use M2: in endogenous money supply studies the use of M3 quasi money elicits a larger effect because M2 does not reflect the transaction demand for money.
24
Table 3: Results of Estimation Using Single Equation The numbers in square brackets are t-statistics and in parentheses are p-values. ***, **, * denote significance at the 1, 5 and 10 per cent levels respectively. α is a constant for each equation. P is stock price index, LQ is liquidity as proxy by reserve money, MS is M2 as proxy for money supply, IPI is industrial production index as proxy for earnings, Y is real GDP as proxy for income, TBR is Treasury bill rate, CPI is inflation and LR is lending rate. Dum(GFC) is added to take into account global crisis with D=1 for 2007:2-2009:4, otherwise D=0. Dum(REGIME) is added to take into account regime changes with for Canada: D1=1 for 1991:1-2007:1, otherwise D1=0; for UK: D1=1 for 1992:4-2006:2, otherwise D1=0; and for US: D1=1 for 1987:1-2007:1, otherwise D1=0.
Panel A: Results of First equation: Dependent Variable- Share Price __________________________________________________________________________ Variables Coefficients t-statistic __________________________________________________________________________ Equation 1 α 3.45 [96.81] *** LRLQ 0.04 [6.04]*** LRMS -0.02 [-2.20]** LRIPI 1.65 [1.83]* LRIPI(-1) -2.94 [-3.29]*** DUM(GFC) 1.31 [9.84]*** DUM1(REGIME) 0.70 [11.57]*** __________________________________________________________________________ R-squared Adjusted R-squared S.E. of regression Durbin-Watson stat Second-Stage SSR
0.585663 0.583305 0.661234 0.029095 460.8406
Mean dependent var S.D. dependent var Sum squared resid J-statistic Instrument rank
3.236034 1.024344 460.8406 3.60E-19 7.000000
__________________________________________________________________________ Panel A*: Results of First equation: Dependent Variable-Share Price (After Hausman test to use RE model __________________________________________________________________________ Variables Coefficients t-statistic __________________________________________________________________________ Equation 1 α 3.45 [96.81] *** LRLQ 0.04 [6.04]*** LRMS -0.02 [-2.20]** LRIPI 1.65 [1.83]* LRIPI(-1) -2.94 [-3.29]*** DUM(GFC) 1.31 [9.84]*** DUM1(REGIME) 0.70 [11.57]*** __________________________________________________________________________ R-squared Adjusted R-squared S.E. of regression Durbin-Watson stat Second-Stage SSR
0.585663 0.583305 0.661234 0.029095 460.8406
Mean dependent var S.D. dependent var Sum squared resid J-statistic Instrument rank
3.236034 1.024344 460.8406 3.60E-19 7.000000
__________________________________________________________________________
25
The results are estimated using GMM (see Appendix B for test procedures on this method) on fixed cross section and time period effects. A Hausman test was carried on all 3 equations (see Appendix 3) before the choice of fixed or random cross section effects were selected with GMM to estimate the panel of equations. Appendix B also report on the assumptions of the various panel estimators and a comparison of the results from the various estimators used to estimate panel data from pooled OLS, fixed effects, random effects and first difference using GMM. Both the Hausman and Breusch and Panel B: Results of Second equation: Dependent Variable- Liquidity ___________________________________________________________________________ Equation 2 α -28.8 [-10.2]*** LRM2 -0.23 [-4.7]*** LRGDP 6.08 [7.29]*** LR 0.58 [7.44]*** DUM(GFC) 0.45 [0.37] DUM(REGIME) -0.11 [-0.16] ___________________________________________________________________________ R-squared -0.379366 Mean dependent var 0.695915 Adjusted R-squared -0.386758 S.D. dependent var 2.750695 S.E. of regression 3.239238 Sum squared resid 9789.656 Durbin-Watson stat 0.032247 J-statistic 242.0781 Second-Stage SSR 2540.045 Instrument rank 7.000000
Panel B*: Results of second equation: Dependent Variable- Liquidity (After Hausman test to use Random Effect model) ___________________________________________________________________________ Equation 2 α -3.45 [-2.0]** LRM2 -0.56 [-11.9]*** LRGDP 1.80 [25.3]*** LR -0.06 [-9.6]*** DUM(GFC) -0.4 [-7.0]*** DUM(REGIME) -0.62 [-19.5]*** ___________________________________________________________________________ R-squared
0.662701
Mean dependent var
0.004875
Adjusted R-squared
0.660894
S.D. dependent var
0.416246
S.E. of regression
0.242392
Sum squared resid
54.81722
Durbin-Watson stat
0.168946
J-statistic
129.0067
Second-Stage SSR
7.579622
Instrument rank
7.000000
__________________________________________________________________________________________
26
Pagan tests are carried out to decide on the choice of estimators. It is worth reporting on the fixed effects estimator because of how unlikely it is for the random effects error terms to be uncorrelated with the explanatory variables. The G-7 countries are heterogeneous among themselves and researchers can control for the unobserved differences between countries by using fixed effect model. Prior studies show that this is likely to be correlated on the same variable in a previous time period with annual data. Panel C- Results of Third equation: Dependent Variable- Money Supply __________________________________________________________________________ Equation 3 α -1.98 [-1.9]** LRGDP 1.63 [4.6]*** LRLQ -0.11 [-3.5]*** LSPRICE -0.03 [-0.2] TBR 0.17 [6.3]*** LCPI 25.08 [3.2]*** LCPI (1) -25.76 [-3.3]*** DUM(GFC) 2.74 [5.8]*** DUM(REGIME) 2.64 [12.7]*** ___________________________________________________________________________ R-squared 0.231587 Mean dependent var 3.088611 Adjusted R-squared 0.225636 S.D. dependent var 2.553030 S.E. of regression 2.246614 Sum squared resid 5213.834 Durbin-Watson stat 0.022543 J-statistic 1.09E-09 Second-Stage SSR 5213.834 Instrument rank 9.000000
Panel C*: Results of Third equation: Dependent Variable- Money Supply (After Hausman test to use Fixed Effect model __________________________________________________________________________ Equation 3 α -0.25 [-1.3] LRGDP 0.41 [5.0]*** LRLQ 0.22 [5.2]*** LSPRICE 0.10 [4.9]*** TBR 0.005 [1.9] LCPI 0.29 [7.4]*** DUM(GFC) -0.03 [-0.8] ___________________________________________________________________________ R-squared
0.993564
Mean dependent var
3.088611
Adjusted R-squared
0.993489
S.D. dependent var
2.553030
S.E. of regression
0.206006
Sum squared resid
43.66910
Durbin-Watson stat
0.031916
J-statistic
6.79E-19
Second-Stage SSR
43.66910
Instrument rank
13.000000
_________________________________________________________________________ 27
A test using reduced form equation regression was carried out with Share Price as the dependent variable to test the liquidity effect and the results are as reported in Table 3a. The results indicate income, lending rate and earnings are important determinants of share price: greater the money supply, MS, the interest rate goes down with a negative impact on share prices significant with t-value of -3.8. The greater the growth in GDP, the greater is the share price with a significant t-value of 5.1. All the variables are significant in terms of the tstatistics except for the dummy variable (GFC). The R2 showed an improvement over the previous equation for share price, although the impact of money supply on share prices remained the same. Table 3a: Results of Estimation on Reduced Form Equation for Share Price Equation Panel A: Results of First Equation, Dependent Variable is Share Price __________________________________________________________________________ Variables Coefficients t-statistic __________________________________________________________________________ Equation 1 α -2.63 [-20.4] *** LRMS -0.02 [-3.8]*** LRGDP 1.63 [5.2]*** LR -0.05 [-15.9]*** LRIPI 2.59 [4.9]**** LRIPI(-1) -3.49 [-6.6]*** DUM(GFC) -0.05 [-0.8] DUM1(REGIME) -0.06 [-1.7]* ______________________________________________________________________ R-squared Adjusted R-squared S.E. of regression Durbin-Watson stat Instrument rank
0.881342 0.880489 0.347128 0.135877 8.000000
Mean dependent var S.D. dependent var Sum squared resid J-statistic
3.418911 1.004119 117.3647 1.75E-20
__________________________________________________________________________
4.4
Results from System of Equations
Table 4 is a summary of results of the GMM panel data estimation as proposed by Arellano and Bond (1991). Two important statistics are discussed first. From the results, the Arellano 28
and Bond (1991) test of the hypothesis that there is no second-order serial correlation based on the residuals of the first differenced equation is not rejected. This suggests that the GMM estimators are consistent. Secondly, the Sargan (1958) test statistic in Table 4 is 0.32 with a p value of 0.01. The Sargan test is used to test for over-identifying restrictions, that is, it determines whether any correlation between instruments and errors exists. For an instrument to be valid, there should be no correlation between instruments and errors. Table 4: Results of Estimation Using System of Equation for Equations 1 and 3 Numbers in square brackets are t-statistics and in parentheses are p-values. ***, **, * denote significance at the 1, 5 and 10 percent levels respectively. α is a constant for each equation. P is stock price index, LQ is liquidity as proxy by reserve money, MS is M2 as proxy for money supply, IPI is industrial production index as proxy for earnings, Y is real GDP as proxy for income, TBR is treasury bill rate, CPI is inflation and LR is lending rate.
Panel A - Results of First Equation: Dependent Variable-Share Price _____________________________________________________________________ Variables Coefficients t-statistic _____________________________________________________________________ Equation 1 α 3.49 [92.8]*** LRLQ 0.04 [5.1]*** LRM2 0.05 [2.2]* LRIPI 2.21 [2.3]*** LRIPI(-1) -3.60 [-3.8]*** DUM(GFC) 1.08 [7.7]*** _____________________________________________________________________ R-squared Adjusted R-squared S.E. of regression Durbin-Watson stat Second-Stage SSR
0.532995 0.530782 0.701671 0.028599 6.87E-19
Mean dependent var S.D. dependent var Sum squared resid J-statistic Instrument rank
3.236034 1.02344 519.4203 6.87E-19 6.000000
Panel B: Results of Second Equation: Dependent Variable- Liquidity __________________________________________________________________________ Equation 2 α -10.31 [-12.8]*** LRM2 -0.11 [-3.6]*** LRGDP 2.25 [11.6]*** LR 0.27 [13.2]*** DUM(GFC) 0.23 [0.48] ___________________________________________________________________________ R-squared Adjusted R-squared S.E. of regression Durbin-Watson stat Second-Stage SSR
0.247141 0.243924 2.391507 0.009209 5353.270
Mean dependent var S.D. dependent var Sum squared resid J-statistic Instrument rank
0.692484 2.750356 5353.270 1.56E-27 5.000000
___________________________________________________________________
29
The summary results are from running a system of equations tests, as the best procedure to understand the dynamics of money supply and asset prices. The statistics indicate that the dependent variable share price, P, in the first equation, is determined by reserve money LQ (greater the use of reserve money, the greater is the share price, meaning liquidity has a positive impact on share prices), money supply MS has positive impact on share price, and earnings of firms IPI and IPI(-1) as read by the combined lag and non-lagged variable. All the variables are significant in terms of the t-statistics (example, t of 5.1for liquidity) at the levels normally used in hypothesis testing. In the second equation, money supply is determined by RGDP (proxy for income), reserve money (proxy for liquidity) LQ, share price P, Treasury bill rate TBR and inflation CPI (please see the t-values in the table). Panel C - Results of Third Equation, Dependent Variable is Money Supply (stand alone for comparison) ___________________________________________________________________ Equation 3 α -1.98 [-1.9]* LRGDP 1.63 [4.6]*** LRLQ -0.11 [-3.5]*** LSPRICE -0.03 [-0.2] TBR 0.17 [6.3]*** LCPI 25.08 [3.2]*** LCPI (1) -25.76 [-3.3]*** DUM(GFC) 2.74 [5.8]*** DUM(REGIME) 2.64 [12.7]*** ______________________________________________________________________ R-squared Adjusted R-squared S.E. of regression Durbin-Watson stat Second-Stage SSR
0.231587 0.225636 2.246614 0.022543 5213.834
Mean dependent var S.D. dependent var Sum squared resid J-statistic Instrument rank
3.088611 2.553030 5213.834 3.96E-20 9.000000
_______________________________________________________________________________
The results in Panel C are for money supply equation. Except for share price, LSPRICE, all the variables are significant given their probability of t-statistics at the 0.01, 0.05 and 0.10 acceptance levels. In the third equation, liquidity is determined by money supply, MS and real GDP (proxy for income), and the lending rate LR. All the variables are significant also at 30
the same acceptance levels given their respective t-statistics of 4.6 and 6.3. These test statistics are robust since panel regressions eliminate most of the econometric problems highlighted (in Appendix) as likely to affect single equations and OLS regressions in the majority of studies. Table 5 compares the signs that were expected for each coefficient and the actual sign obtained from the GMM panel data estimation (see Appendix B for a fuller detail on this procedure). All but few of the variables show the expected signs. Five signs were different from the expected sign: The money supply (MS) and lending rate (LR) in equation (6) and the liquidity (LQ), share price (P) and treasury bill rate (TBR) in equation (7). All other signs are as predicted by theory. Table 5: Expected and Actual Signs of Variables in GMM Estimation __________________________________________________________________________ Variables Expected Sign Actual Sign __________________________________________________________________________ Equation 5 __________________________________________________________________________ LQ + + MS + + IPI + + DUM(GFC) + + __________________________________________________________________________ Equation 6 __________________________________________________________________________ MS + Y + + LR + DUM(GFC) + + __________________________________________________________________________ Equation 7 __________________________________________________________________________ LQ + Y + + P + TBR + CPI + + CPI(+1) + DUM(GFC) + + DUM(REGIME) + + __________________________________________________________________________ 31
The dummy variables which represent monetary regime breaks in macroeconomic aggregates to inflation targeting (Canada: 1991:1 to 2007:1; UK: 1992:4 to 2006:2; US 1987:1 to 2007:1) and the effect of global financial crisis in 2007:2 to 2009:4 were found to be significant as per expectations: see Table 5a for a listing of these dummy controls. Leaving these uncontrolled in tests would have introduced spurious results, which eliminated in our tests in this report. So, with controls for regime change and crisis, we included these dummies in our equations in order to estimate reliable estimators. Table 5a: Changes in Monetary Policy Regime Country
Event
Start date
End date
Canada
Inflation targeting announced (Thiessen (1998))
1991:1
2007:1
United Kingdom
Chancellor wrote to the Chairman setting out new framework for monetary policy (BOE diary of events)
1992:4
2006:2
United States
Fed announced that it would no longer set M1 targets and moved away from borrowed reserve targets
1987:1
2007:1
The results obtained in this section from carefully building a system of equations and then testing by GMM panel regression methodology yield robust results on (i) money supply effect, (ii) liquidity effect and (iii) liquidity effect on share prices. Friedman’s theory predicted liquidity effect is supported as is also a liquidity effect on share prices. 7.
Conclusion
This paper is a report of an investigation on the (i) money supply effects on interest rate and (ii) liquidity as well as (iii) liquidity effect on asset (share) price. The literature on money supply effect has been widely followed in policy circles, yet the propositions (ii) and (iii) have yet been verified with unanimous support. By adopting all the econometric refinements 32
(see the appendices A and B) needed to obtain robust parameter estimates and by using system of equations developed for this study, the results reported in this paper are useful new findings on the money supply and asset pricing literature. As a further robustness test, we tested the reduced form equations as well. The panel data variables are transformed to ensure that there is no spurious parameter estimates as a means to improve on prior studies. Friedman’s 1969 propositions are used: we add an asset pricing equation to these propositions in order to extend the test for a liquidity– credit surge - effect on share prices. Further, we control monetary regime changes and the effect of global financial crisis by specifying dummy variables to correct structural breaks in the time series. The results appear to suggest that the already known evidence (see Badarudin et al., 2011) that money supply is endogenous is supported by results presented in this paper. Further, there is bidirectional causality from money to interest rate as already confirmed in studies on post-Keynesian endogenous money theory. The new findings reported here relate to (i) the effect of money supply on liquidity that has yet been confirmed and (ii) the liquidity effect on share prices. These results appear to support Friedman’s second proposition on money supply effect on liquidity: as a robustness test, we derived a reduced form equation and tested this again to verify the results. We extended Friedman’s proposition to asset prices to test if the liquidity effect on share prices produces results that credit surges may lead to asset (share) price increases. Our data limitation is simply that this research uses quarterly series since GDP data are only available as quarterly series although earnings proxy, which is available on an annual basis, is industrial production index. It would be useful to secure earnings series and extend this study with that variable as well to verify results reported in this paper.
33
Appendix A: Methodology Used to Overcome Econometric Problems Unit root tests Unit root tests are performed on the variables so as to prepare the data set for cointegration and causality tests. Cointegration analysis is valid if the unit root test establishes the order of integration of the variables of interest is I(1). Thus, we validate the stationarity properties of the variables prior to conducting the cointegration tests. For this, the Johansen cointegration equation is applied. 𝑝
∆ Xt = 𝑎0 + 𝑎1 Xt−1 + 𝑎2 t + ∑𝑖=2 𝑏𝑖 ∆ X𝑡−𝑖+1 + 𝑢𝑡
(A1)
where p is the number of lagged changes in Xt necessary to make 𝑢𝑡 serially uncorrelated.
Testing the null against the alternative hypothesis Ha: a1 < 0, the null hypothesis of the unit root is rejected if the observed t-statistic is sufficiently negative in the MacKinnon (1996) lower tail critical value. Two other tests needed are for the series to be characterised as an I(1) process with a drift or time trend: 𝑝
∆ Xt = 𝑎0 + 𝑎1 Xt−1 + ∑𝑖=2 𝑏𝑖 ∆ X𝑡−𝑖+1 + 𝑢𝑡 𝑝
∆ Xt = 𝑎1 Xt−1 + ∑𝑖=2 𝑏𝑖 ∆ X𝑡−𝑖+1 + 𝑢𝑡
~ ~
(A2) (A3)
In all three cases, the hypotheses tested are: H0: the series contain a unit root, against H1: the series is stationary. The test statistic below (Equation A4) is then tested against the critical values at the accepted level of significance: � 𝑎
1 Test statistic = 𝑆𝐸 � (𝑎� )
(A4)
1
Johansen cointegration tests
34
Cointegration results based on Johansen’s (1988) procedure are sensitive to the choice of lag length in VAR (Cheung and Lai, 1993). Thus, the optimum lag lengths of the VAR is determined by minimising the Schwarz (1978) Bayesian Information Criteria (SBC). This criterion is designed to select the model with maximum information available. The general concept of cointegration between variables suggests that there exists an equilibrium or a longrun relationship between two time series provided the series are integrated of the same order. This will be confirmed using the Phillips-Perron test. The rank of the coefficient matrix Γ represents the number of cointegrating vectors. The likelihood ratio test for the null hypothesis that there are at most r cointegration vectors is used as the Trace Test statistic: 𝑝 TraceTest = - T ∑𝑖=𝑟+1 ln(1 − 𝜆�𝚤 )
~
(A5)
where T is the sample size and 𝜆�𝚤 , K, 𝜆�𝑝 are the p-r smallest squared canonical correlations.
The MacKinnon, Haug and Michelis (1999) critical values are used to determine whether the null hypothesis that there are at most r cointegration vectors is rejected or not. The critical values differ depending on whether a linear trend is included or not and are summarised. Another restricted maximum likelihood ratio test is referred to as the Maximal Eigenvalue
Test statistic: Maximal Eigenvalue Test = T ∑𝑟𝑖=1 ln(1 − 𝜆̂∗𝑖 )/(1 − 𝜆̂𝑖 )
(A6)
where 𝜆̂∗𝑖 , K, 𝜆̂∗𝑟 are the r largest squared canonical correlations. Similar to the Trace Test, the Maximal Eigenvalue Test statistics will be compared against the MacKinnon, Haug and Michelis (1999) critical values as given in their paper. There are instances when there is a discrepancy between the results of the Trace Test and the Maximal Eigenvalue Test, where one test will indicate the presence of cointegration and the 35
other will not. In such cases, Johansen and Juselius (1990) suggest that the Trace Test may lack power relative to the Maximal Eigenvalue Test. Thus any discrepancies will be resolved through acceptance of the Maximal Eigenvalue Test. The three tests – namely, the unit root test, Johansen cointegration and the causality test discussed in this section and the former two sections – will be used to determine the validity of hypotheses 1 to 3. Hausman test for correlated random effects The ability of the random effects (RE) model to take into account variation between individuals as well as variation within individuals makes it an attractive alternative to fixed effects (FE) estimation. However, for the random effect estimator to be unbiased in large samples, the effects must be uncorrelated with the explanatory variables, an assumption that is often unrealistic. This assumption can be tested using the Hausman test. The Hausman test is a test of significance of the difference between the fixed estimates and the random effects estimates. Correlation between the random effects and the explanatory variables will cause these estimates to diverge; their will difference will be significant and it will be appropriate to use FE models. If the difference is not significant, there is no evidence of the offending correlation and then we can apply the RE model. The differences between the two sets of estimates can be tested separately using t-tests, or as a block using a χ2 – test, and are reported in Appendix 3. VIF Test for Multicollinearity This table provides summary measure of the variables tested for multi-collinearity. There is no multi-collinearity among the variables, money supply, share price index and liquidity because the VIF is less than 5.
36
VARIABLES LRM2 LSPRICE LRLQ
VIF 1.118 2.026 1.328
< 5 = no multicollinearity < 5 = no multicollinearity < 5 = no multicollinearity
Panel Unit Root Tests Using Phillips-Perron Fisher Tests This table summarizes the results of the Maddala and Wu (1999) and Choi (2001) Fisher tests. All variables are in logarithmic form except for TBR, the treasury bill rate and LR, the lending rate of banks. The hypotheses tested are: H0: each series in the panel contains a unit root, against H1: at least one of the individual series in the panel is stationary.
Table A1: Panel Unit Root Tests – Fisher Phillips-Perron tests Numbers in parentheses are p-values. ***, **denote significance at the 1 and 5 percent levelsrespectively. LSPRICE rice is stock price index, LRLQ is liquidity, LRGDP is real gross domestic product, LRM2 is money supply, LRIPI is industrial production index, LCPI is inflation, TBR is Treasury bill rate and LR is lending rate.
Fisher chi-square statistic
Choi Z-statistic
Variables
Level
Difference
Level
Difference
LSPRICE
5.496 (0.9776)
405.587*** (0)
2.858 (0.9979)
-18.323*** (0)
LRM2
17.835 (0.2144)
186.885*** (0)
0.025 (0.51)
-11.515*** (0)
LRLQ
8.628 (0.8541)
292.975*** (0)
3.074 (0.9989)
-14.863*** (0)
LRIPI
5.819 (0.9708)
440.749*** (0)
1.688 (0.9543)
-19.724*** (0)
TBR
39.455*** (0.0003)
LCPI
5.501 (0.8712)
176.706*** (0)
1.332 (0.9086)
-10.981*** (0)
LRGDP
6.119 (0.9634)
345.168*** (0)
3.330 (0.9996)
-16.714*** (0)
LR
28.319** (0.0129)
-4.057*** (0)
-1.830** (0.0336) 37
The results indicate that, besides TBR and LR, the null hypothesis that the series contains a unit root cannot be rejected for all variables at the one percent level of significance. For example, the Fisher chi-square statistic and Choi Z-statistic were 17.84 and 0.025 respectively for money supply, with p-values of 0.21 and 0.51. The p-values are above the 10 percent level of significance, indicating the null hypothesis cannot be rejected. The variables (except for TBR and LR) are then tested for stationarity in first differences. The results show that the null hypothesis that the series is non-stationary when first differenced is rejected for the same variables. This means that all variables (besides TBR and LR) are integrated of order one or I(1). For LR, both the Phillips-Perron Fisher tests based on Maddala and Wu (1999) and Choi (2001) reject the null hypothesis that the series contains a unit root, thus making the variable stationary. The Fisher chi-square statistic of 28.32 and Choi Z-statistic of -1.83 together with the p-value of less than 5 percent indicate that LR is stationary at level under both tests at the 5 percent level of significance. The results indicate that TBR and LR are I(0). Thus these variables are left in level form. As most of the variables are found to be integrated of order one (I(1)) as is also confirmed from other tests reported in the table below, the next step is to test these series to determine whether they are cointegrated. The panel cointegration test is based on Pedroni (1999, 2004) and the results are reviewed in the next section.
38
Table A2: Panel Unit Root Tests 1960-2011 Series LRM2 LRGDP LSPRICE LRLQ LRIPI TBR LR
∆LRM2 ∆LRGDP ∆LSPRICE ∆LRLQ ∆LRIPI ∆TBR ∆LR
LLC -2.654 (0.004)* -1.146 (0.126) 0.212 (0.584) 2.588 (0.995) -0.3331 (0.369) -0.397 (0.346) -0.353 (0.362)
Breitung 0.969 (0.834) 2.357 (0.991) 1.452 (0.927) 1.789 (0.963) -0.400 (0.344) -1.848 (0.032)* -1.679 (0.047)
IPS -0.229 (0.409) 0.489 (0.688) -0.488 (0.313) 0727 (0.767) 1.401 (0.919) -1.509 (0.066) -1.727 (0.042)
ADF 11.208 (0.669) 11.272 (10.084) 19.315 (0.153) 13.713 (0.471) 7.640 (0.907) 21.546 (0.088) 21.738 (0.084)
PP 11.857 (0.618) 10.084 (0.756) 15.618 (0.337) 47.274 (0.000)* 8.200 (0.879) 12.585 (0.559) 10.509 (0.724)
Hadri 14.697 (0.000)* 20.353 (0.000)* 12.741 (0.000)* 10.946 (0.000)* 11.113 (0.000)* 19.317 (0.000)* 15.959 (0.000)*
-7.044 (0.000)* -32.581 (0.000)* -15.280 (0.000)* -20.522 (0.000)* -6.959 (0.000) -8.321 (0.000)* -4.585 (0.000)*
-7.469 (0.000)* -9.478 (0.000)* -8.956 (0.000)* -10.303 (0.000)* -5.571 (0.000) -9.494 (0.000)* -6.255 (0.000)*
-15.277 (0.000)* -37.173 (0.000)* -16.920 (0.000)* -30.590 (0.000)* -10.103 (0.000) -13.879 (0.000)* -10.509 (0.000)*
212.099 (0.000)* 192.593 (0.000)* 256.69 (0.000)* 444.467 (0.000)* 126.224 (0.000) 196.394 (0.000)* 131.885 (0.000)*
-447.220 (0.000)* 482.908 (0.000)* 487.31 (0.000)* 430.208 (0.000)* 462.849 (0.000) 498.751 (0.000)* 331.782 (0.000)*
2.045 (0.020)* -0.047 (0.519) 2.089 (0.018)* 2.301 (0.011)* 6.867 (0.000) -2.192 (0.986) -1.882 (0.970)
Cointegration Tests for RIPI and RGDP for G-7 Countries This table summarizes the tests results of RIPI and RGDP for cointegration tests among panel data of the G-7 countries. They indicate that RIPI and RGDP are cointegrated in the long run and therefore, IPI can be used as a proxy for earnings. The number of lag truncations was set to four. The Pedroni tests are all one-sided. All statistics, with the exception of Panel rhoStatistic and Panel PP-Statistic is bigger than 1.64 which means we can reject the null hypothesis of no cointegration and conclude in favor of cointegration. Finally, the McCoskey and Kao LM test is again one-sided with a critical value of -1.64 (thus LM-statistic > -1.64
39
implies rejection of the null hypothesis of no cointegration and concluded in favor of cointegraton. Table A-3: Pedroni Residual Cointegration Test Null Hypothesis: No cointegration Trend assumption: Deterministic intercept and trend Lag selection: fixed at 4
Alternative hypothesis: common AR coefs. (within-dimension) Weighted Statistic
Prob.
Statistic
Prob.
Panel v-Statistic
1.770295
0.0832
4.925717
0.0000
Panel rho-Statistic
1.450482
0.1393
1.911497
0.0642
Panel PP-Statistic
-0.516121
0.3492
0.560359
0.3410
3.828551
0.0003
2.932268
0.0054
Panel ADF-Statistic
Alternative hypothesis: individual AR coefs. (between-dimension) Statistic
Prob.
Group rho-Statistic
3.077634
0.0035
Group PP-Statistic
2.606960
0.0133
Group ADF-Statistic
2.071175
0.0467
Kao Residual Cointegration Test Null Hypothesis: No cointegration Trend assumption: No deterministic trend Lag selection: fixed at 4 Newey-West bandwidth selection using Bartlett kernel t-Statistic
Prob.
ADF
-1.746509
0.0404
Residual variance
0.001111
HAC variance
0.000862
Pedroni Panel Cointegration Tests for Money Supply, Liquidity and Share Price Four lags are chosen as the optimal number of lag lengths as the series are quarterly data. The Pedroni (1997) panel cointegration test results are provided in Table 2-C. Like unit root tests, individual (country) cointegration tests suffer from low power. Even if the postulated economic relationship were generally true, a researcher would accept the non-cointegration
40
hypothesis far more often than should be done. The pooling used in panel cointegration tests can improve power relative to single country based tests. A good, recent survey of the panel cointegration published literature can be found in Banerjee (1999). We employ residualsbased tests of the null of no cointegration, as developed by Pedroni (1999), which are appropriate for heterogeneous panels in which both N and T are of moderately large dimension. Pedroni’s tests are of two types. One set, based on Levin and Lin (1993) and hereafter called ‘panel’ statistics, pools over the within dimension. Numerator and denominator components of the test statistics are summed separately over the N dimension. A second set – in the spirit of Im et al. (1997), and hereafter called ‘group’ statistics – pools over the between dimension, obtaining the ratio of numerator to denominator for each country prior to aggregating over the N dimension. In both cases, under the null hypothesis, the variables are not cointegrated for each panel member; the alternative asserts that a cointegrating vector exists for each individual, although this vector may be unique for each individual. However, the alternative hypotheses for the two types of test differ in the following way: The panel statistics test the null that the first order autoregressive coefficient ρi = 1 for all i against the alternative ρi = ρ < 1 for all i, whereas the group statistics test the null ρi = 1 for all i against the alternative ρi < 1 for all i. In other words, the alternative hypothesis for the panel test asserts that the autoregressive coefficient in the auxiliary ADF regression of the cointegrating residuals is the same for every individual. Maddala and Wu (1999) argue that this alternative is unreasonable and that the group statistics are more appropriate because their alternative hypothesis is less restrictive – simply that the autoregressive coefficient in the auxiliary regression is less than unity, although it may differ for each individual. The results for equation (4) show that the null of no cointegration is rejected for panel v, panel ADF, group rho and group ADF. The panel v-statistic was found to be 1.61, which is close to 41
the critical value of 1.64 and significant at the ten percent level. Similarly, the panel ADF, group rho and group ADF were found to be -1.47, 1.76 and -1.91 respectively. As the Pedroni (1997) statistics are one-sided tests and these statistics are smaller than the critical value of 1.64, the panel ADF and group ADF statistics are found to be significant at the one percent level of significance, while the group rho was found to be significant at the ten percent level. Table A-4: Panel Cointegration Results - Pedroni (1997) test ___________________________________________________________________________ Panel A: Within-dimension ___________________________________________________________________________ Eq A-4 Eq A-5 Eq A-6 ___________________________________________________________________________ Panel v-Statistic 1.61** 1.90* 1.98** Panel rho-Statistic 1.43 -0.65 0.18 Panel PP-Statistic 0.10 -5.17*** -5.22*** Panel ADF-Statistic -1.47* 0.76 0.68 ___________________________________________________________________________ ___________________________________________________________________________ Panel B: Between-dimension ___________________________________________________________________________ Eq 4 Eq. 5 Eq. 6 ___________________________________________________________________________ Group rho-Statistic 1.76* -1.25 0.44 Group PP-Statistic -0.31 -5.03*** -2.16*** Group ADF-Statistic -1.91*** 1.94*** 1.82*** ___________________________________________________________________________ Note: ***, **, * denote significance at the 1, 5 and 10 percent levels respectively. Pedroni (1997) tests are one-sided tests with critical values of 1.64 for the panel v-statistic and -1.64 for all others.
The equations are: LSPRICEit = f [ LRM2+ , LRLQ+ , LRIPI+]
(A4 )
LRM2it = f [LRLQ+, LRGDP+, TBR-, LCPI+]
(A-5)
LRLQit = f [LRM2+, LRGDP+, LR- ]
(A-6)
42
For equation (A5), the panel v statistics of 1.90 are above the critical value of 1.64. Furthermore, the group pp statistic shows a lower value than the critical value of -1.64, and group ADF show a higher value than the critical value of 1.64, and these statistics are significant at one percent level of significance. This shows that there is cointegration. In addition, for equation (A-6), the panel v and group ADF statistics are above 1.64, while the panel PP, and group PP statistics are all lower than -1.64 and significant at the one percent level of significance. This suggests that the null hypothesis of no cointegration is rejected based on these four statistics. As cointegration is present in the equations, the vector error-correction model can be used to test for long-run and short-run causality in the equations. This is discussed in the next section. Results of the VECM tests The Pedroni (1997) panel cointegration tests confirm that the variables in equations (4) to (5) are cointegrated. The resulting long-run coefficients as summarised in Table 2-D are obtained through the normalisation of the cointegrating vectors. It should be stressed that the VECM are individually run for each equation and that it is not run together as a system. This is because the purpose of this section is to determine whether the predetermined variables and the endogenous variables that are on the right hand side have a causal effect on the dependent variable. The evidence of cointegrating relations in Table A-5 shows that there is a positive relationship in equation (4) between share price index and illiquidity, a major concern of this thesis. Liquidity and share price are found to have a positive relationship for equations (4)
43
and (5), suggesting the presence of a bidirectional relationship similar to earlier results. There is a positive relationship between share price and money supply for equation (7). Table A-5: Cointegrating Relations Equations Pit = f [LQ+, MS+, IPI+] LQit = f [MS+, Y+, LR-] MSit = f [LQ+, Y+, TBR-, P+, CPI+, CPI(1)+]
(5) (6) (7)
Cointegrating relation 0.29LQ+2.98 0.76P-0.33MS-0.63 2.26P-2.96LQ-1.88
Note: Pit is aggregate share price index, LQit is liquidity as proxied by reserve money, MSit is money supply, IPI is industrial production index, Y is real GDP, LR is lending rate, TBR is Treasury bill rate and CPI is inflation. All variables are in in log change ratios.
Hausman Test on Fixed Vs Random Effects The Hausman test is formulated to assist in making a choice between the fixed effects and random effects approaches. Hausman (1978) adapted a test based on the idea that under the hypothesis of no correlation, both OLS and GLS are consistent but OLS is inefficient while under the alternative OLS is consistent but GLS is not. For the panel data the appropriate choice between the fixed effects and the random effects methods investigates whether the regressors are correlated with the individual effect. Given a panel data model where fixed effects would be appropriate, the Hausman test investigates whether random effects estimation could be almost as good. The Hausman test uses the following test statistic: H = (𝛽̂ FE- 𝛽̂ RE)' [ Var (𝛽̂ FE − 𝑉𝑎𝑟(𝛽̂RE) ]-1 (𝛽̂ FE- 𝛽̂ RE)
~
χ 2 (k) (A-8)
If the value of the statistic is large then the difference between the estimates is significant, so we reject the null hypothesis that the random effect model is consistent and we use the fixed effects estimators. In contrast, a small value of the Hausman statistic implies that the random effects estimator is more appropriate. First equation: Pit = f [LQ-, MS+, IPI+, IPI(-1)+] 44
(A-8)
Table A-6: Hausman Test Results Correlated Random Effects - Hausman Test Equation: Untitled Test cross-section random effects Test Summary
Chi-Sq. Statistic
Chi-Sq. d.f.
Prob.
0.000000
5
1.0000
Cross-section random
* Cross-section test variance is invalid. Hausman statistic set to zero. Cross-section random effects test comparisons: Variable
Fixed
Random
Var(Diff.)
Prob.
LRLQ
0.874632
0.234924
0.004048
0.0000
LRM2
0.567389
0.297203
0.003342
0.0000
LRIPI
19.063341
35.588380
-0.691613
NA
LRIPI(-1)
-20.226909
-36.877843
-0.682555
NA
0.459397
1.451244
0.000294
0.0000
Coefficient
Std. Error
t-Statistic
Prob.
DUM
Cross-section random effects test equation: Dependent Variable: LSPRICE Method: Panel Generalized Method of Moments Date: 12/25/11 Time: 22:25 Sample: 1 1456: Periods included: 198 Cross-sections included: 7 Total panel (unbalanced) observations: 1059 2SLS instrument weighting matrix Instrument list: C LRLQ LRM2 TBR LRIPI DUM
C
1.167543
0.161093
7.247623
0.0000
LRLQ
0.874632
0.065445
13.36430
0.0000
LRM2
0.567389
0.061073
9.290374
0.0000
LRIPI
19.06334
1.706850
11.16873
0.0000
LRIPI(-1)
-20.22691
1.698962
-11.90545
0.0000
DUM
0.459397
0.109364
4.200611
0.0000
Effects Specification Cross-section fixed (dummy variables) R-squared
0.755492
Mean dependent var
3.233679
Adjusted R-squared
0.752923
S.D. dependent var
1.023859
S.E. of regression
0.508927
Sum squared resid
271.1805
Durbin-Watson stat
0.815866
J-statistic
Second-Stage SSR
144.9970
Instrument rank
45
1.45E-20 12.000000
Conclusion: Accept Ho because χ 2 is small and p-value > 0.05, therefore there is no correlation between the explanatory variable and the random effects. More appropriate to use Random Effect models in this case We proceed to test the second equation which yielded the following results. Table A-7: Second Equation: LQit = f [MS+, Y+, LR-]
(A-9)
Equation: Untitled Test cross-section random effects Test Summary
Chi-Sq. Statistic
Chi-Sq. d.f.
Prob.
3.163090
5
0.6749
Random
Var(Diff.)
Prob.
-0.562980
0.000015
0.3291
Cross-section random Cross-section random effects test comparisons: Variable LRM2
Fixed -0.559222
LRGDP
1.796646
1.802984
0.000029
0.2417
LR
-0.060955
-0.061002
0.000000
0.9211
DUM
-0.398604
-0.400509
0.000016
0.6305
DUM1
-0.613913
-0.615067
0.000005
0.5978
Cross-section random effects test equation: Dependent Variable: LRLQ Method: Panel Generalized Method of Moments Date: 12/25/11 Time: 22:33 Sample: 1 1456: Periods included: 198 Cross-sections included: 7 Total panel (unbalanced) observations: 939 2SLS instrument weighting matrix Instrument list: C LRLQ LRM2 LRIPI LRIPI(-1) DUM DUM1 Coefficient
Std. Error
t-Statistic
Prob.
C
-4.175158
0.189821
-21.99524
0.0000
LRM2
-0.559222
0.047568
-11.75625
0.0000
LRGDP
1.796646
0.071427
25.15369
0.0000
LR
-0.060955
0.006404
-9.518856
0.0000
DUM
-0.398604
0.057091
-6.981925
0.0000
DUM1
-0.613913
0.031590
-19.43387
0.0000
Effects Specification Cross-section fixed (dummy variables)
46
R-squared
0.992345
Adjusted R-squared
0.992254
S.D. dependent var
2.750695
S.E. of regression
0.242087
Sum squared resid
54.32779
Durbin-Watson stat
0.169885
J-statistic
Second-Stage SSR
7.601849
Instrument rank
Conclusion: Accept Ho because χ
2
Mean dependent var
0.695915
129.7110 13.000000
is small and p-value > 0.05, therefore there is NO
correlation between the explanatory variable and the random effects. More appropriate to use RE effect models. The final test is done on Equation 3: Table A-8: Third Equation: MSit = f [LQ+, Y+, TBR-, P+, CPI+, CPI(1)+] (A-10) Correlated Random Effects - Hausman Test Equation: Untitled Test cross-section random effects Test Summary
Chi-Sq. Statistic
Chi-Sq. d.f.
Prob.
Cross-section random
142308.600855
6
0.0000
Random
Var(Diff.)
Prob.
** Warning: estimated cross-section random effects variance is zero. Cross-section random effects test comparisons: Variable
Fixed
LRGDP
0.407506
2.373013
0.005528
0.0000
LRLQ
0.220569
-0.152625
0.001801
0.0000
LSPRICE
0.104898
0.209514
0.000119
0.0000
TBR
0.005145
0.099665
0.000003
0.0000
LCPI
0.292862
-0.688682
0.001019
0.0000
DUM
-0.033248
1.361938
0.000054
0.0000
t-Statistic
Prob.
Cross-section random effects test equation: Dependent Variable: LRM2 Method: Panel Generalized Method of Moments Date: 12/25/11 Time: 22:42 Sample: 1 1456: Periods included: 199 Cross-sections included: 7 Total panel (unbalanced) observations: 1042 2SLS instrument weighting matrix Instrument list: C LRLQ LSPRICE TBR LRGDP LCPI LCPI(1) DUM Coefficient
Std. Error
47
C
-0.247549
0.184775
-1.339733
0.1806
LRGDP
0.407506
0.080965
5.033114
0.0000
LRLQ
0.220569
0.042523
5.187025
0.0000
LSPRICE
0.104898
0.021011
4.992451
0.0000
TBR
0.005145
0.002708
1.899938
0.0577
LCPI
0.292862
0.039789
7.360409
0.0000
DUM
-0.033248
0.042838
-0.776138
0.4378
Effects Specification Cross-section fixed (dummy variables) R-squared
0.993564
Mean dependent var
3.088611
Adjusted R-squared
0.993489
S.D. dependent var
2.553030
S.E. of regression
0.206006
Sum squared resid
43.66910
Durbin-Watson stat
0.031916
J-statistic
0.083617
Second-Stage SSR
43.66910
Instrument rank
Conclusion: Reject Ho because because χ
2
14.000000
is large and p-value < 0.05, therefore there is
correlation between the explanatory variable and the random effects. Use FE effect models in this case. Appendix B: A Comparison of Different Panel Estimators on G-7 Countries In this appendix, we summarize the results from other tests done and not reported in the body of the paper. Overall, these results further show that the results reported in the body of the paper are verified by these extension tests. The assumptions of the models are shown first:
Table B-1: Equations and Assumptions
Methods
Equation
Assumptions
For Pooled OLS: cluster errors
LnYit = βXit + uit
Cov(Xit, uit) = 0
For CX=FE: iid errors
LnYit = βXit +ai+vit
Cov (Xit, aj) ≠0
48
Cov (Xit, vis) = 0
For CX=RE: iid errors
LnYit = βXit +ai+vit
For CX=FE, Y=FE: iid errors
LnYit = βXit +ai+dt+wit Cov(Xit, ai) ≠ 0, Cov (Xit, dt) = 0 Cov (Xit, wis) = 0
For CX=FE, Y=FE: cluster errors
LnYit = βXit +ai+dt+wit Cov(Xit, ai) ≠ 0, Cov (Xit, dt) ≠ 0 Cov (Xit, wis) = 0
For CX=N, Y=FE: cluster errors
∆LnYit = β∆Xit +∆dt+∆wit Cov (Xit, dt) ≠ 0 Cov (Xit, wis) = 0
Cov(Xit, ai) = 0,
Cov (Xit, vis) = 0
Table B-2: Results of Applying Estimators to Panel Data LSPRICE
OLS +cluster
CX=FE Y=N
CX=RE Y=N
CX=FE Y=FE
3.49 (61.77)*** 0.038 (9.62)*** 0.027 (3.29)*** 1.24 (1.06) -2.67 (-2.27)*** 1061
CX=FE Y=FE +cluster 1.15 0.74 2.29 2.29 (9.23)*** (4.46)*** (16.83)*** (14.19)*** 0.83 0.51 0.32 0.32 (16.75)*** (17.23)*** (4.87)*** (3.49)*** 0.57 0.67 0.28 0.28 (11.99)*** (21.12)*** (6.28)*** (6.71)*** 4.61 4.24 1.78 1.78 (8.54)*** (7.87)*** (2.89)*** (2.45)*** -5.83 -5.41 -2.45 -2.45 (-10.9)*** (-10.1)*** (-4.01)*** (-3.37)*** 1061 1061 1061 1061
CX=N Y=FE +cluster 0.02 (11.57)*** -0.03 (-0.61) 0.04 (-0.29)*** 0.31 (2.02)** -0.16 (-1.16) 1061
C
LRM2
OLS +cluster
CX=FE Y=N
CX=RE Y=N
CX=FE Y=FE
C
-5.39 (-1.11) 2.67 (0.98) -0.17 (-0.45) 0.14 (0.15) 0.13 (0.71)
-0.26 (-1.38)*** 0.41 (5.04)*** 0.22 (5.08)*** 0.10 (4.87)*** 0.006 (1.94)***
-0.47 (-0.27) 0.41 (5.11)*** 0.21 (5.10)*** 0.10 (4.99)*** 0.005 (1.97)***
-0.68 (-1.57)*** 0.44 (4.13)*** 0.26 (4.77)*** 0.05 (1.52) 0.005 (1.05)
CX=N Y=FE +cluster 0.02 (10.59)*** -0.01 (-0.29) -0.03 (-0.87) 0.02 (0.68) 0.002 (1.23)
LRLQ LRM2 LRIPI LRIPI(-1) OBS
LRGDP LRLQ LSPRICE TBR
49
CX=FE Y=FE +cluster -0.67 (-2.11)** 0.44 (3.89)*** 0.26 (3.38)*** 0.05 (1.85)* 0.005 (0.87)***
LCPI
25.49 (1.34) -26.30 (-1.29) 1061
0.52 (0.71) -0.23 (-0.31) 1061
0.29 (7.31)***
0.39 (5.15)***
0.39 (3.59)***
-0.69 (-5.21)***
1061
1061
1061
1061
LRLQ
OLS +cluster
CX=FE Y=N
CX=RE Y=N
CX=FE Y=FE
C
-10.36 (-17.33)*** -0.11 (-8.41)*** 2.27 (17.69)*** 0.26 (11.43)*** 1061
-2.72 (-26.1)*** -0.15 (-4.39)*** 0.99 (22.55)*** -0.02 (-7.05)*** 1061
-1.89 (-1.53) -0.15 (-4.41)*** 0.99 (22.6)*** -0.02 (-7.04)*** 1061
LCPI(1) OBS
LRM2 LRGDP LR OBS
CX=FE Y=FE +cluster -7.58 -7.59 (-23.7)*** (-28.6)*** -0.02 -0.02 (-0.7)*** (-0.73) 2.03 2.03 (25.09)*** (28.26)*** 0.005 0.005 (1.23) (1.27) 1061 1061
CX=N Y=FE +cluster 0.004 (0.003)** -0.067 (-0.55) 0.42 (5.32)*** -0.0002 (-0.09) 1061
Table B-3: Results of G-7 Countries Using Single Equation Estimates Share Price (Equation 1) Canada Eq 1: DV is Share Price
Panel A G-4 Countries Japan UK
USA
Panel B G-3 Countries France Germany
Coefficients with t-statistics in brackets 1.76*** -0.99*** -1.42*** 1.67*** 1.74*** -0.81 (11.53) (-56.06) (-34.53) (11.71) (7.11) (-8.93)*** LRM2 0.65*** 2.52*** 1.05*** 0.07*** -0.86*** 2.09*** (34.45) (84.00) (23.92) (1.36) (-3.03) (127.97) LRIPI 5.05*** 3.58*** 1.67*** 3.83*** 2.78 5.90*** (4.14) (4.66) (2.76) (3.38) (2.04) (5.90) LIPI (-1) -6.49*** -4.59*** -1.80*** -4.26*** -4.57 -5.76*** (-5.76) (-6.07) (-2.97) (-3.71) (-3.47) (-5.80) DUM (GFC) -0.32 0.07 0.48*** (-1.71) (0.63) (2.8) DUM (Regime) 0.57 -0.34 0.31*** 0.81*** (4.51) (-5.11) (5.38) (9.34) _________________________________________________________________________________________ Model Parameters Adjusted R2 0.8755 0.9148 0.9742 0.9278 0.8980 0.8189 Std Error 0.2999 0.3077 0.1862 0.2829 0.2490 0.2615 Mean 3.4245 3.8128 2.7749 3.0151 3.2193 3.3033 SD of dep var 0.8503 1.0544 1.1580 1.0530 0.7792 0.6145 Sum of Square Res14.3923 18.1777 5.6146 15.3724 5.0178 10.1876 _________________________________________________________________________________________ LRLQ
Liquidity (Equation 2)
Canada
Panel A G-4 Countries Japan
Italy 0.59 (2.94) -0.32 (-0.46) 1.88 (1.06) -3.73*** (-2.14)
0.8877 0.3414 2.9075 1.0186 10.723
Panel B G-3 Countries
UK
USA
50
France
Germany Italy
Eq 1: DV is Liquidity
Coefficients with t-statistics in brackets
LRM2
-0.67*** (-12.32)
1.49*** (16.33)
-0.07*** (2.78)
-0.20* (-1.87)
-0.32*** (-5.06)
1.13*** (26.52)
1.35*** (10.51)
LRGDP
1.09*** (10.50)
-0.03 (-10.79)
-0.32*** (-23.49)
0.61*** (5.63)
1.22*** (23.94)
-0.36 (-16.24)
1.14*** (-16.92)
LRate
0.002 (0.62)
-0.22*** (-27.22)
0.005 (1.05)
-0.034*** (-9.74)
-0.007** (-2.98)
-0.02*** (-4.74)
0.03*** (13.36)
DUM (GFC)
0.31*** (6.35)
0.005*** (0.05)
0.42*** (7.42)
0.42***
DUM (Regime) -0.12 -0.14 0.15*** 0.03 (-4.19) (-2.29) (3.57) (0.74) _________________________________________________________________________________________ Model Parameters Adjusted R2 0.6775 0.9629 0.4180 0.8747 0.9166 0.9062 Std Error 0.1038 0.1528 0.1401 0.1200 0.0447 0.0875 Mean -1.065 -1.1765 -1.2699 1.5060 3.9729 0.4514 SD of dep var 0.1828 0.7927 0.1837 0.3391 0.1549 0.2856 Sum of Square Res 1.7356 4.4809 3.2207 2.7949 0.1629 0.6349 _________________________________________________________________________________________
-0.8905 0.0692 8.6046 0.0504 0.3019
Money Supply (Equation 3) Panel A Panel B G-4 Countries G-3 Countries Canada Japan UK USA France Germany Italy Eq 1: DV is Money Supply Coefficients with t-statistics in brackets LRGDP 1.92*** 0.02*** 0.05 1.41*** 1.94 -0.14* -0.54 (37.94) (8.44) (1.75) (62.62) (10.39) (-1.86) (-3.24) LRLQ -0.53*** 0.29*** 1.21*** -0.07 -0.82*** 0.62*** 0.47*** (-11.79) (12.56) (10.67) (-2.33) (-5.46) (25.94) (7.92) LSPRICE -0.32*** 0.09*** 0.64*** -0.10*** 0.03 0.17*** 0.04 (-13.72) (2.65) (15.47) (-9.63) (0.81) (7.51) (1.78) TBRate 0.002 -0.02 -0.006 -0.02*** -0.004 0.01*** -0.006 (-0.95) (-1.48) (-0.78) (-8.92) (-1.13) (4.81) (-2.24) LCPI -2.56* -1.65 -0.30 1.62 1.83 -1.15* -2.11* (-2.78) (-1.97)** (-0.26) (3.53) (1.28) (-1.55) (-1.97) LCPI(1) 2.77*** 1.70 0.46 -1.98 -2.20 1.49** 2.26** (2.95) (2.04)** (0.41) (-4.28) (-1.49) (1.99) (2.03) DUM (GFC) 0.12*** -0.32 0.08*** (2.80) (-5.44) (3.31) DUM (Regime) 0.04 -0.15 -0.07 0.01 (1.12) (-3.27) (1.04) (0.85) _________________________________________________________________________________________ Model Parameters 0.9759 0.9592 0.9845 0.1221 0.9728 0.4803 Adjusted R2 0.9773 Std Error 0.0455 0.1206 0.1502 0.0353 0.0544 0.0725 0.0431 Mean 8.8203 1.0641 0.9613 3.7247 3.5558 1.6558 2.3673 SD of dep var 0.4396 0.7771 0.7437 0.3197 0.0581 0.4397 0.0598 Sum of Square Res0.3258 2.7476 3.6323 0.3017 0.2339 0.7732 0.1302 _________________________________________________________________________________________
51
Table B-4: G-7 Countries – Results of Reduced Form Equation Estimates Share Price (Equation 4) Panel A Panel B G-4 Countries G-3 Countries Canada Japan UK USA France Germany Italy Eq 1: DV is Share Price Coefficients with t-statistics in brackets LRM2 -1.40*** 0.64*** 0.63*** -4.19*** -0.36 0.30* 0.76* (-17.18) (4.78 ) (9.24 ) (-15.29) (-0.80) (1.70) (1.98) LRGDP 3.67*** 0.03*** 0.70*** 4.70*** 1.41*** 0.88*** 0.75 (23.55) (10.81) (21.64) (18.05) (3.84) (11.49) (3.69) LRate 0.0005 0.22*** -0.03*** -0.08** -0.09*** -0.11*** -0.12*** (0.10) (25.67) (-3.77) (-13.09) (-6.16) (-5.44) (-11.50) LRIPI 1.62*** 3.53*** 2.96*** 4.75*** 0.30 -1.05 0.96 (2.20) (4.36) (4.15) (5.01) (0.21) (-0.57) (0.69) LRIPI (-1) -2.39*** -3.98*** -3.49*** -3.87*** -1.94 -1.52 -0.41 (-3.8) (-4.83) (-4.88) (-4.14) (-1.39) (-0.82) (-0.30) DUM (GFC) -0.07 -0.18* 1.08*** (-0.86) (1.49 ) (10.57) DUM(Regime)0.28*** -0.38*** 0.15*** 0.56*** (4.21) (-4.4) (2.3) (7.83)
_________________________________________________________________________________________ Model Parameters 0.9213 0.9675 0.9596 0.9036 0.9003 0.8871 Adjusted R2 0.9677 Std Error 0.1563 0.2970 0.2108 0.2156 0.2419 0.2087 0.1768 Mean 3.4708 3.8082 2.8053 3.0625 3.2193 3.8332 3.4933 SD of dep var 0.8703 1.0588 1.1700 1.0727 0.7792 0.6608 0.5261 Sum of Square Res0.1563 0.2970 7.2882 9.1576 4.6817 4.0070 1.8747 _________________________________________________________________________________________ Liquidity (Equation 5) Panel A Panel B G-4 Countries G-3 Countries Canada Japan UK USA France Germany Italy Eq 1: DV is Liquidity
Coefficients with t-statistics in brackets
LRM2
-0.67*** 1.49*** -0.07*** -0.20* -0.32*** 1.13*** 1.35*** (-12.32) (16.33) (2.78) (-1.87) (-5.06) (26.52) (10.51) LRGDP 1.09*** -0.03 -0.32*** 0.61*** 1.22*** -0.36 1.14*** (10.50) (-10.79) (-23.49) (5.63) (23.94) (-16.24) (-16.92) LRate 0.002 -0.22*** 0.005 -0.034*** -0.007** -0.02*** 0.03*** (0.62) (-27.22) (1.05) (-9.74) (-2.98) (-4.74) (13.36) DUM (GFC) 0.31*** 0.005*** 0.42*** 0.42*** (6.35) (0.05) (7.42) DUM (Regime) -0.12 -0.14 0.15*** 0.03 (-4.19) (-2.29) (3.57) (0.74) _________________________________________________________________________________________ Model Parameters 0.9629 0.4180 0.8747 0.9166 0.9062 -0.8905 Adjusted R2 0.6775 Std Error 0.1038 0.1528 0.1401 0.1200 0.0447 0.0875 0.0692 Mean -1.065 -1.1765 -1.2699 1.5060 3.9729 0.4514 8.6046 SD of dep var 0.1828 0.7927 0.1837 0.3391 0.1549 0.2856 0.0504
52
Sum of Square Res 1.7356 4.4809 3.2207 2.7949 0.1629 0.6349 0.3019 _________________________________________________________________________________________ Money Supply (Equation 6) Panel A Panel B G-4 Countries G-3 Countries Canada Japan UK USA France Germany Italy Eq 1: DV is Money Supply Coefficients with t-statistics in brackets LRGDP 1.92*** 0.02*** 0.05 1.41*** 1.94 -0.14* -0.54 (37.94) (8.44) (1.75) (62.62) (10.39) (-1.86) (-3.24) LRLQ -0.53*** 0.29*** 1.21*** -0.07 -0.82*** 0.62*** 0.47*** (-11.79) (12.56) (10.67) (-2.33) (-5.46) (25.94) (7.92) LSPRICE -0.32*** 0.09*** 0.64*** -0.10*** 0.03 0.17*** 0.04 (-13.72) (2.65) (15.47) (-9.63) (0.81) (7.51) (1.78) TBRate 0.002 -0.02 -0.006 -0.02*** -0.004 0.01*** -0.006 (-0.95) (-1.48) (-0.78) (-8.92) (-1.13) (4.81) (-2.24) LCPI -2.56* -1.65 -0.30 1.62 1.83 -1.15* -2.11* (-2.78) (-1.97)** (-0.26) (3.53) (1.28) (-1.55) (-1.97) LCPI(1) 2.77*** 1.70 0.46 -1.98 -2.20 1.49** 2.26** (2.95) (2.04)** (0.41) (-4.28) (-1.49) (1.99) (2.03) DUM (GFC) 0.12*** -0.32 0.08*** (2.80) (-5.44) (3.31) DUM (Regime) 0.04 -0.15 -0.07 0.01 (1.12) (-3.27) (1.04) (0.85) _________________________________________________________________________________________ Model Parameters 0.9759 0.9592 0.9845 0.1221 0.9728 0.4803 Adjusted R2 0.9773 Std Error 0.0455 0.1206 0.1502 0.0353 0.0544 0.0725 0.0431 Mean 8.8203 1.0641 0.9613 3.7247 3.5558 1.6558 2.3673 SD of dep var 0.4396 0.7771 0.7437 0.3197 0.0581 0.4397 0.0598 Sum of Square Res 0.3258 2.7476 3.6323 0.3017 0.2339 0.7732 0.1302 ________________________________________________________________________________________
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