1
Money-Income Granger Causality
Reviewed: A Reinterpretation of
U.S. Pre- and Post-Crisis Data
Thomas Krom
Student 6145361
Amsterdam School
of Economics
-
University of
Amsterdam
Master program:
M. Sc. In Economics
Specialization:
Monetary Policy &
Banking
Thesis Supervisor:
Dr. Christian A.
Stoltenberg
Date:
12 November, 2014
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Money-Income Granger Causality Reviewed: A
Reinterpretation of U.S. Pre- and Post-Crisis Data
Thomas Krom
Amsterdam School of Economics, University of Amsterdam (UvA), the Netherlands 12 November 2014
Abstract.
I examine the extent to which fluctuations in the money stock Granger cause fluctuations in real and nominal output. Based on modified versions of Sims (1972) and Friedman and Kuttner (1992) various reduced form regressions and VAR models are estimated using data on the adjusted Monetary Base, M1, M2, M2 net of M1, income, prices and an interest rate differential. Covering U.S. data for 1949 – 2014 I find insignificant evidence regarding a contemporary stable and unidirectional Granger causal relationship between money and income and if such a relation would genuinely exist it contemporary favors an evaluation of 'reverse causal'. Subsequently, I argue that the evanescence of money’s predictive content is a result of deeper financial innovation and developments in transaction technologies.
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Table of Contents.
1. Introduction ... 4
2. Literature Review ... 7
2.1. Literature on the Money-Income Relation ... 7
2.2. The Commercial paper Rate versus the Treasury bill Rate ... 13
3. Data Description ... 14
4. Empirical Methodology ... 15
4.1. Econometric Analysis... 15
4.2. Lag length Selection... 16
4.3. Bivariate Regression Analysis: Sims’ Method ... 17
4.4. Multivariate VAR Analysis ... 18
5. Estimation Results ... 19
5.1. Decreasing Role of Money ... 19
5.2. Multivariate Autoregressive Evidence ... 22
5.3. Pre- and Post-Crisis Results ... 23
5.4. Robustness ... 25
5.4.1. Newey-West Standard Errors ... 26
5.4.2. Real GDP as Proxy for Economic Growth ... 27
5.5. Comparing the Results ... 28
6. Summary and Conclusion ... 31
6.1. Model Implications and Follow-up Research ... 32
7. Bibliography ... 34 8. Appendices ... 39 A. Data Appendix ... 39 B. Cross Correlations 1949q3 – 2014q2 ... 41 C. Regression Coefficients ... 42 D. VAR Results: 1949q3 – 1969q4 ... 43 E. VAR Results: 1949q3 – 1979q4 ... 45 F. VAR Results: 1980m1 – 1991m12... 47 G. VAR Results: 1992m1 – 2007m5 ... 49 H. VAR Results: 2007m6 – 2014m6 ... 51
I. Sims’ Results with Newey-West Standard Errors ... 53
J. VAR Results: 1992m1 – 2007m5 with Real GDP ... 54
K. VAR Results: 2007m6 – 2014m6 with Real GDP ... 55
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1. Introduction
One of the continuous and principal challenges to monetary economics remains the distinct confirmation or rejection of the commonly observed positive comovements between money – whatever defined – and economic activity. Although newly developed and improved models for monetary policy evaluation differ thoroughly in their details they often share a common feature by assigning only a minimal role for changes in the stock of money. Besides models that make no reference at all to any of the monetary aggregates, others, as for instance the cashless New Keynesian model (Woodford, 2003) do include nominal money but only to the extent of a money demand equation that conclusively serves to determine the amount of money that need to be supplied given the levels of output, inflation and an interest rates (Ireland, 2004, p. 969). In retrospect, certain academic literature favors the use of monetary aggregates as information variables in the context of a policy rule for the conduct of monetary policy. McCallum (1988; In: Feldstein & Stock, 1994) for instance proposes to use the Monetary Base (MB) to target nominal income growth. Similar policy rules demand strong performances of the aggregates, presupposing constant and stable predicting and/or causal relationships with the ultimate policy goals (Estrella and Mishkin, 1997, p. 280). Indeed, in such a potential application it is foremost important and necessary that the aforementioned aggregates have some value as information variables. For that reason, this paper evaluates the empirical validity of this condition by studying the Granger causal effects of fluctuations in the nominal money stock on economic activity.
Despite the relevance and the importance of the money-income relation, the conclusions that both historical and contemporary literature have reached are quite diverse. In terms of the former, Sims (1972) was among the first who scrutinized the predictive content of money by the use of F-tests on reduced form equations for output. Using U.S. postwar data until 1969, he found a unidirectional Granger causal relation from money (MB and M1) to income (Nominal GNP). Although subsequent research initially corroborated money’s predictive content it was not until the late 1980s that the vanishment of the solid relation was generally accepted (Friedman and Kuttner, 1992). Consequently, starting from 1990 onwards research has resulted in more mixed evidence due to the divergent treatment and use of monetary aggregates, sample periods and research methodologies. For instance, by adjusting the Monetary Base and M1 for respectively foreign holdings and inside money Aksoy and Piskorski (2006) and Hafer, Haslag and Jones (2007) conclude that money Granger caused output up until 1998. In contrast, by implementing a more structural approach Woodford (2008) and Andres, Lopez Salido and Nelson (2009) refute the former finding by estimating monetary policy models that provide little evidence for an active feedback role of money.
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Besides the genuine existence of comovements between money and income, the discussion also focusses on the specific direction of the relation. Opposed to classical economics and the argument of money neutrality, a unidirectional relation from money to income, as found by Sims (1972) could originally be explained by Keynesian models or monetary business cyclist who appealed to sticky wages and the failure of markets to clear. In short, when firms and workers agree on long-term contracts, which fix workers’ money wage in course of the contract, an unanticipated increase in the money growth rate will lead to higher inflation than expected. Hence, the induced fall in real wages incites firms to hire more workers, which raises the economy’s output (Shaghil, 1993, p. 14). In contrast, real business cycle theory originally encloses the concept of 'reverse causality'. For instance, for the transaction-services explanation of why money responds to real shocks, King and Plosser (1984) argued that the banking sector or more specific the 'credit service sector' produces transaction services that are, similarly to capital and labor, inputs for production. In that way, a real shock that enables workers or firms to produce more output in the near future will increase latter’s demand for transaction services. Since the flow of transaction services is promptly related to the banking sector’s stock of deposits, the increased demand of the former incites creditors to solicit additional funds (or reduce the stock of excess reserves) to increase deposits, which enlarges the quantity of inside money and so the money stock (Shaghil, 1993, p.17).1 Consequently, as indicated by Dyreyes, Starleaf and Wang (1980), a bidirectional Granger causal relation in which output (money) both causes and is caused by money (output) can then be explained by the mutual affective or the circuitous coexistence of both transmission mechanisms.
Although the former research, among other work, differs in terms of outcomes it also shares a common feature in that it only examines money’s predictive content up until roughly 2000. Indeed, since the money stock has dramatically increased starting from 2007’s recession and is still extremely expansionary (see figure 1.1), it is particularly now of specific interest to evaluate latter’s conceivable consequences i.e. whether we can expect a boost in economic activity, solitary inflation, both or neither of the two. For that reason, the purpose of this paper is twofold. First, by verifying the sample period 1949 – 1991 I attempt to reach similar conclusions concerning money’s breakdown during the nineteen eighties in the U.S. Secondly, by using different model specifications I provide fresh pre- and post-crisis empirical estimates for the explicit feedback role of money on the dynamics of output and enquires whether the global financial crisis endorsed a structural break which 'brought money back'. In the light of the recent and continuous liquidity easing implemented by the Federal
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For an in-depth theoretical background on the 'wage price mechanism' and 'imperfect-information models' which entice money being prior to output please consult Blanchard (1987). In addition, for a deeper understanding of the 'transaction-services explanation' and the 'inside-outside money explanation' in favor of reverse causality please see Manchester (1989) or shaghil (1993).
6 -5.00% 0.00% 5.00% 10.00% 15.00% 20.00% 1947 1953 1959 1965 1971 1977 1983 1989 1995 2001 2007 2013 MB -5.00% 0.00% 5.00% 10.00% 1947 1953 1959 1965 1971 1977 1983 1989 1995 2001 2007 2013 M1 -5.00% 0.00% 5.00% 10.00% 1947 1953 1959 1965 1971 1977 1983 1989 1995 2001 2007 2013 M2 NM1M2
Figure 1.1. U.S. economy: Fluctuations (percentage change from previous month) of the adjusted MB, M1, M2, M2 net of M1, Industrial Production and Gross National Product. As can be seen from the graphs, monetary and economic variables were highly volatile during and shortly after the financial crisis of 2007-2008. Liquidity providing open market operations and expansionary monetary policy in general directly affected narrow money (base money) and to a smaller extent broader money (M1 and M2).
-10.00% -5.00% 0.00% 5.00% 10.00% 15.00% 1947 1953 1959 1965 1971 1977 1983 1989 1995 2001 2007 2013 IP GNP
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Reserve System in an attempt to dampen the real effects of the financial turmoil, the second aim is of the highest interest. Since the latter essentially presupposes constructive effects on output a reconsideration of money’s predictive or Granger causal role on real economic activity is clearly desirable. 2
The rest of this paper proceeds as follows: Section 2 functions as a literature review, where I discuss both historical and contemporary research with respect to the money-income relation. Furthermore, in section 3 and 4 I respectively describe the bivariate reduced form regressions and VAR specifications that are examined and the accompanying data. Consequently, I present the estimates of the regressions and Granger causality Wald tests in section 5. In essence, the results indicate that the stable Granger causal relation from money to output breaks down when U.S. data for the 1980s is included. Subsequently, based on VAR evidence I argue that if such a relation would genuinely exist at present it would tend to be defined as 'reverse causal'. In addition, based on the pre- and post-crisis sample estimates, up to 2014, I find insignificant evidence for a structural break in the Granger causal money-income relation after the financial crisis. Consequently, I argue that financial innovation, developments in transaction technologies or money’s lasting erratic velocity could potentially explain money’s changing predictive behavior from the 1980s onwards. Finally, section 6 concludes.
2. Literature Review
In this section, I extensively discuss the existing literature regarding the money-income relation. First, I describe the evolution of the latter relation during the historical timespan of 1950-1990 and subsequently for the sample period after 1990. In terms of the latter, I make a distinction between structural and reduced form model evidence. Consequently, a short section focuses on the effects of including an interest rate differential i.e. the paper-bill spread.
2.1. Literature on the Money-Income Relation
Whether the empirical relationship between money and income is a result of significant causal effects of the nominal money stock on real economic activity or vice versa remains a captivating question since the nineteen fifties. The work of Friedman and Schwartz (1963) represents one of the most influential studies on this area advocating the former interpretation of the data. The authors motivate their view by a key finding that in the U.S., fluctuations in monetary aggregates consisting
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However, the reader should bear in mind that Granger causality should clearly be differentiated from any deeper philosophical notion of causality (Holland, 1986, p.955).
8 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 j MB M1 M2
of primarily bank deposits and currencies, such as M1 or M2, systematically affect fluctuations in the real business cycle (Šustek, 2010, p. 451). 3 Although Friedman and Schwartz initiated the empirical research on money-income causality, the most significant contribution to this field was made by Sims (1972) with a practical application developed by Granger (1969) in order to identify 'causal' relationships. Since the appearance of Sims’ latter approach academics have often used this technique to scrutinize the (unidirectional) causal relationship between money and income
Figure 2.1. U.S. economy: Subsample cross correlations between monetary aggregates (MB, M1, M2) in quarter t+j and income (Real GDP) in quarter t. The cross correlations are based on logged data and prefiltered with the Hodrick-Prescott filter (𝜆=1600), using a periodicity of eight past and eight future quarters. Corresponding with Friedman and Schwartz (1963), the key point of this figure is that the MB and M1 (not M2) on average tend to lead real GDP as is presented by a more strongly positive correlation with future output than with past output.
(Thornton & Batten, 1985, p.164). 4 In addition, from Sims onwards, research on whether the money stock can effectively play a role in the monetary policy process has not just focused on whether variations in money help predict future variations in output but also on whether they help predict future variations in output which are not already foreseeable on the basis of variations of output itself. In particular, by using post-war U.S. data Sims (1972) evinced that Granger causality i.e. predictive causality is unidirectional from money (MB and M1) to income (Nominal GNP) for the sample period 1949q3 – 1968q4. Although the result was consistent with a variety of theories, the outcome was widely accepted as evidence that 'money matters' for economic activity. However, the
3
Figure 2.1 reflects a version of Friedman and Schwartz’ (1963) proposed empirical regularity covering U.S. data for the sample period 1949q3 – 1968q4. Other cross-correlation figures for the remaining sample periods can be consulted in Appendix B.
4
See, for example, Sims (1980a; 1980b), Hsiao (1981), McMillin, Douglas and Fackler (1984), Christiano and Ljungqvist (1988), Hayo (1999), Amato and Swanson (2001), Aksoy and Piskorksi (2006) and Reynard ( 2007).
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latter interpretation has been challenged in subsequent papers by Sims (1980a; 1980b) that indicate that money is no longer Granger causally prior to output when a short-term interest rate is included in a Vector Auto Regression (VAR) containing a price index, output and money (Litterman and Weiss, 1985, p.129). This observation is corroborated by among others Eichenbaum and Singleton (1986) and is particularly apparent in papers using data sets that encompass the 1980s. Conversely, by more systematically correcting for the unit root and trend characteristics of the data, Stock and Watson (1989) and Feldstein and Stock (1994) claimed to both resolve the interest rate aspect and the former money-income causality instability. The authors used a detrended log difference specification instead of Sims’ and Eichenbaum and Singleton’s formerly used detrended log levels approach and found yet again that monetary aggregates contained information for future output.
Although the role of money in predicting output in the former specification is declining when data for the 1980’s is included, Stock and Watson argued that the difference in outcomes is due to the increased volatility of the data which resulted in more powerful test statistics, and the fact that increased sample sizes contain more observations resulting in more precise estimates (1989; In: Thoma, 1994, p. 280). Furthermore, a prominent paper by Friedman and Kuttner (1992) claimed that Stock and Watson’s results were important in that, contrary to the belief that the money-income relation has adjourned in the 1980’s, the latters’ outcomes present a significant relation by extending the data through 1985. However, they consequently prove that the Stock and Watson results are not robust by extending the sample through 1988, a result subsequently acknowledged by Friedman and Kuttner (1993), Estrella and Mishkin (1997) and Hayo (1999). In essence, it is generally accepted that money’s predictive role for output evaporated in the U.S. during the late 1980s.
Noticeable, the latter was almost concurrently accompanied with a switch in monetary policymaking after the inauguration of Paul Volcker as chairman of the Federal Reserve. Whereas in the pre-Volcker years monetary policy was passive, after the disinflation period during the tenure of Volcker and Greenspan, interest rate policy could be described as being active (Lubik and Schorfheide, 2004). 5 Opposed to the argument of policy mistakes on the side of the Fed, a passive interest rate setting (just as now with an active stance) was consistent with equilibrium determinacy and the achievement of minimizing macroeconomic volatility. Accordingly, the switch itself can be explained as a reaction of the monetary authority to either a higher value in asset market participation due to deregulation and financial innovation (Bilbiie and Straub, 2013) or a declining role of money in facilitating transactions (Kriwoluzky and Stoltenberg, 2014). During the passive
5 I.e. under the Taylor-principle, nominal interest rates are increased by more than one-to-one as a response to an
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regime at which output and inflation were negatively correlated 6, a decrease in the nominal interest rate resulted in an increase in the demand for real money balances since transaction frictions, as measured by the marginal cost saving effect of holding money balances, were significant. Hence, according to Kriwoluzky and Stoltenberg (2014) money served as an endogenous state variable for inflation and output in that an increase in real money balances amplified the effects of an exogenous shock by increasing households consumption possibilities and accordingly aggregate demand and supply. Subsequently, the authors decisively evince that an analogous New Keynesian monetary economy model with transaction frictions loses explanatory power from 1983 onwards. Given that innovations in transaction technologies have significantly reduced the real resource costs of transactions and so the motive for holding money balances, the latter perceived amplifying effect has significantly declined and hence output and inflation are not affected by the demand for money (Kriwoluzky and Stoltenberg, 2014). 7
Although the previous discussion has mainly focused on the historical timespan of 1950-1990, even today the topic receives particular attention due to the previously mentioned sideshow treatment of money in modern monetary business cycle models. 8 Consequently, the theoretical implications for the preclusion of money have been thoroughly investigated. Woodford (2003, p.51; 2008) for instance evinced that money plays a quantitatively unimportant role in the concerning models and argues that "with an interest rate rule (…) the equilibrium paths of inflation and output can be understood without reference to the implied path of the money supply or the determinants of money demand." Although knowledgeable, the dichotomy that these monetary models display is not only inconvenient to accept for quantity theory orthodoxy proponents but it is also inconsistent with the conflicting results of vast empirical literature and especially with a large body of VAR evidence. For instance, Meltzer (2001; In: Nelson, 2002, p. 688) has challenged the former specifications by arguing that these models neglect important channels of monetary policy. The author argues that: "Open market operations by a central bank affect both the nominal interest rate
6 To see why this is the case, consider a shock to government expenditures which crowds out private consumption
and increases the labor supply since the present value of taxes goes up in order to pay for the additional government spending. Accompanied with an increase in aggregate demand this endorses an increase in output. Consequently, a reversion to the steady state requires consumption growth to be positive, which postulates an increase in the real interest rate. In contrast to an active interest rate policy situation where the latter is achieved by an increase in inflation, with a passive interest rate policy an increase in the real interest rate necessitates a decrease in inflation accompanied with a decrease in the nominal interest rate. Hence, inflation and output are negatively correlated under an accommodative interest rate policy but positively correlated in the case of a restrictive interest rate policy (Kriwoluzky and Stoltenberg, 2014).
7
In essence, using Bayesian estimation techniques the latter alteration and money’s accompanying weakened predictive content are consistent with the authors’ finding that a cashless economy provides more explanatory power compared to a monetary economy from 1989 onwards.
8
Money does however play a prominent role in the euro area in the conduct of monetary policy. It essentially functions as a policy instrument with respect to the medium-term price level as is signaled by the statement of a quantitative reference value of 4.5% for the growth rate of the most broad monetary aggregate M3 (Karfakis, 2013, p. 488).
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and the central bank’s balance sheet – the liabilities side of which includes the monetary base. If prices are sufficiently sticky in the short run, these operations also affect both the short-term real interest rate and the Monetary Base". For that reason, Meltzer believes that the short-term real interest rate does not completely outline the effects of monetary policy actions and that fluctuations in the real monetary base produce direct or separate effects on aggregate demand. Meltzer successively demonstrates this proposition by finding empirical evidence by the use of quarterly U.S. data (2001; In: Nelson, 2002, p. 688). Finally, it is also noteworthy that the aforementioned models provide little foundation to evaluate the effects of credit and unconventional quantitative easing measures that the U.S. has recently initiated to dampen the persevering negative impacts of the 2007-2008 financial crisis (Canova and Menz, 2011, p.578).
More specific, in the case of McCallum (2001) and Woodford (2003) both authors calibrate New-Keynesian models in which money has a transaction role but find that disregarding liquidity premia is appropriate. In addition, by employing a structural backward looking macroeconomic model, Rudebusch and Svensson (1999; 2002) find that nominal money does neither affect inflation nor output for U.S. data up to 1990, which essentially corroborates the former. However, by using the same optimizing IS-LM model in the context of Rudebosch and Svensson but employing a different monetary aggregate Nelson (2002) concludes the opposite namely that real base money growth matters for real economic activity for a given short-term interest rate, the Federal Funds rate. Similar results are obtained by Hafer et al. (2007) when lagged values of real interest rates and the output gap are accounted for. On the contrary, Ireland (2004) and Andres, Lopez Salido and Nelson (2009) examine the role of money in three types of New-Keynesian forward looking models, varying in terms of separable and non-separable utility and money demand function. Using U.S. data for 1979-2003 they find little statistical evidence for the active feedback role of money. However, this evidence has recently been questioned by Favara and Giordani who argue that the potentially false restrictions in Ireland’s model force "estimates of the impact of money on other variables to zero" (2009, p. 420). By using a multivariate SVAR approach the authors test the prediction that monetary aggregates are trivial by means of impulse responses, i.e. as a result of an LM shock, responses of all variables except money in the SVAR have to be flat. Favara and Giordani, using U.S. data for the period 1966-2001, find that this prediction is incorrect because an LM shock in contrast indeed affects the dynamic behavior of output (2009, p. 420; 421). Finally, Castelnuovo (2012) also estimates a new-Keynesian model of the business cycle in order to find whether money played a time-varying role in the post War era. By conducting Bayesian estimations with a rolling window approach the author’s outcomes reveal that money as measured by M2 (although in declining importance) served as a relevant aggregate to understand U.S. output during 1966-2000.
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Indeed, the latter overview has mainly focused on small-scale DSGE models while a vast amount of the empirical literature with respect to money-income Granger causality - the topic of this paper - is based on single-equations estimations and F-tests on reduced form equations. In short, the basic principle of Granger causality (Granger, 1969) is to test whether lagged values of a certain monetary aggregate help to predict or explain current and future values of output, which can be performed in three types of tests. Simple Granger causality tests, as in Sims (1972) are performed in a single equation with only two variables i.e. money and income including their lags and leads. In essence, when output is regressed on money and future values of the specific monetary aggregate have coefficients insignificantly different from zero while past values do not it can be stated that money Granger causes output. Secondly, multivariate causality tests, as in among others Hafer and Kutan (1997) take more variables besides money and output into consideration. As an example, the effect on output could in fact run through (a short-term) interest rate. The principle of Granger causality remains the same, except that in this way other variables can affect the test results and therefore not including the latters might erroneously allocate the causality effect to money (Hayo, 1999, p.1493; 1494). Finally, Granger causality tests can also be performed in VARs as in the case of Friedman and Kuttner (1992; 1993), Estrella and Mishkin (1997), Amato and Swanson (2001), Leeper and Roush (2003) and Smets (2003). In this case the multivariate model is extended to allow for simultaneity of all the included variables. To test for money’s predictive power the Granger causality test with respect to the lags of the monetary aggregate variable is then performed in the output equation only (p. 1494).9
An example of the latter approach is given by Aksoy and Piskorksi (2006). By using the exact specification of Friedman and Kuttner (1992) but substituting the MB variable for a 'corrected' domestic money variable the authors find that the perceived lack of a significant Granger causal relation between U.S. monetary aggregates and output is partly attributable to the presence of considerable and unstable foreign holdings of the U.S. dollars (2006, p. 184).10 Accordingly, the
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The specific definition of income or output differs substantially among academic papers and depends on the variable being used. E.g. Sims (1972) uses Nominal Gross National Product (GNP) as an indicator for output while Krol and Ohanian (1990) use Real Industrial Production (IP), Nelson (2002) focuses on consumption growth and Hafer, Haslag and Jones (2007) use Gross Domestic Product (GDP). The same holds for the definition of money. Sims (1972) focuses on the adjusted Monetary Base (MB) and M1 while Davis and Tanner (1997) particularly use M2, Estrella and Mishkin (1997) use M3, Aksoy and Piskorski (2006) focus on domestic money (currency corrected for foreign holdings of dollars) and Šustek (2010) on Money of Zero Maturity (MZM), a monetary aggregate that predominantly consists of zero-maturity deposits.
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The inclusion of 'domestic money' i.e. MB corrected for foreign holdings of U.S. dollars is based on the outcomes of Jefferson (2000). The author finds that the latter has more explanatory power for fluctuations in income compared with the 'regular' MB. Jefferson further mentions that it is important to know the amount and flow dynamics of the currency abroad so that its implications for the state of the real domestic economic and monetary environment can be assessed and evaluated. If these currency flows abroad are vast, unstable and not accounted for, the interpretation of domestic monetary conditions could turn out to be spurious. The increasing flow of U.S. dollars abroad, in an unstable way, is exactly what is perceived during the period 1965-1998. Also in the 1990s and 2000s
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adjusted MB is significant at the 1% level and consequently Granger causing output in the presence of the federal funds rate for the entire sample period of 1966-1998.11 Since a recurring matter in related research is how money is exactly measured Hafer et al. (2007) extend the work of Aksoy and Piskorski (2006) by testing whether movements in both inside and outside money i.e. the money multiplier component and the monetary base component of M2 respectively, fit the data better which turns out is indeed the case. 12 Finally, Psaradakis, Ravn and Sola (2005) propose a method for
analyzing the Granger causality link between monetary variables and output based on a VAR model with time varying parameters. By using U.S. quarterly data for the period 1959 - 2002 they find that causality patterns have significantly changed over the sample period for both independent variables taken into consideration i.e. M1 and M2. While fluctuations in M1 had predictive power for fluctuations in output during a seven year time span from 1976 to 1983 and around 1990’s recession, M2 growth Granger caused output at the beginning of the sample and in the interval from 1970-1983. Although some results differ compared with other research, it is noteworthy that the latter research corroborates the view that money has largely lost its predictive power at the end of the Volcker disinflation period as already indicated by Friedman and Kuttner (1992, p. 667). Finally, Psaradakis et al. find that there is a tendency for the money stock to gain predictive power during, or shortly before recessions. The latter could indicate that during recessions or shortly before, monetary policy is used more actively and successfully in order to prevent a downfall of the domestic economy (2005, p. 667).
2.2. The Commercial paper Rate versus the Treasury bill Rate
Following the work of Sims (1980a, 1980b) it has become common in tests for the effects of money on output to account for the effect of a specific interest rate. Consequently, whether money has a significant predictive effect on income is not only sensitive to whether the model includes an interest rate but also on the specific one. Although the former inclusion in empirical analyses is now standard enough, the latter question i.e. which short-term rate is the most appropriate, has gained little attention in contemporary literature. Despite two specific rates that are frequently being used: the Commercial paper Rate, see Sims (1980a), Friedman and Kuttner (1992; 1993) and Lee and Yang
the flows of U.S. currency abroad are significantly higher compared with the decades before (Jefferson, 2000; In: Aksoy and Piskorski, 2006, p. 185). For a model that estimates foreign holdings of US currency please see Anderson and Rasche (1999).
11
Unfortunately, by my knowledge no results exist for more recent sample periods that include domestic money.
12
The decision of the decomposement of M2 in inside money and outside money is not based on existing literature but merely founded on the note of Hafer et al. that "an interesting though often ignored question is whether there is something inherent to M2 that is systematically related to output" (2007, p. 952). The research covers the sample period of 1883-2000. Again, by my knowledge no evidence exists for more recent sample period.
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(2012) and the Treasury bill Rate, see Litterman and Weiss (1985), Stock and Watson (1989), Psaradakis et al. (2005) and Castelnuovo (2012) none of the above authors fully clarify their arguments in support of the selection made (Friedman and Kuttner, 1993, p.193).
As indicated by Friedman and Kuttner (1991; 1992, p. 247) several specific features of both rates e.g. the larger default risk on commercial paper, the superior liquidity of treasury bills and the differences in tax treatments distinguishes these rates in such a way that they are rather perceived as perfect complements than as perfect substitutes. As a result, these factors among others could reasonably account for the average spread between these two instrument’s respective rates which is being perceived over time. In a subsequent paper Friedman and Kuttner (1993) test for the specific relationship between the latter spread and output. They find that the paper-bill spread indeed has predictive content with respect to output at the 1% significance level even when the sample includes data for the 1980s. 13
3. Data Description
The data covers the period from September 1947 to June 2014. Among others the macroeconomic fundamentals that I use throughout this paper are much in line with those examined by Sims (1972), Stock and Watson (1989), Friedman and Kuttner (1992; 1993) Thoma (1994) and Amato and Swanson (2001) and contain Nominal Gross National Product (GNP), Real Gross Domestic Product, chained 2009 dollars (GDP) and the Industrial Production Index (IP). The financial variables taken into consideration to assess the fluctuations of the macroeconomic variables are the following: the Monetary Base adjusted for changes in reserve requirements (MB), M114, M215 and the non-M1 component of M2 (NM1M2). In addition, the Consumer Price Index including all items (CPI), the three month AA Financial Commercial Paper Rate i.e. the interest rate on short-term unsecured
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According to Friedman and Kuttner (1993), looking at the commercial paper rate and the Treasury bill rate separately, the former reflects financing cost corresponding to interest sensitive expenditure flows more directly compared with the latter rate. The authors argue that since interest rates matter for nonfinancial economic activity essentially because of its impact on spending behavior of private sector borrowers, any impact that causes the two rates to covary imperfectly will make the commercial paper rate more superior compared with the Treasury bill as a measure of this effect (p. 194).
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By definition of the Federal Reserve Bank of St. Louis: "M1 consists of funds that are readily accessible for spending, i.e. currency outside the U.S. Treasury, Federal Reserve Banks and the vaults of depository institutions; traveler’s checks of nonbank issuers; demand deposits and other checkable deposits (OCD’s), which consist primarily of negotiable order of withdrawals (NOW) account at depository institutions and credit union share draft accounts. Seasonally adjusted M1 is calculated by summing currency, traveler’s checks , demand deposits and OCD’s each seasonally adjusted separately" (Federal Reserve Bank of St. Louis, 2014).
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By definition of the Federal reserve Bank of St. Louis: "M2 consists of a broader set of financial assets that are held principally by households, i.e. M1; saving deposits (which include money market deposit account, MMDA’s); small-denomination time deposits (time deposits in amounts of less than $100.000; and balances in retail money market mutual funds (MMMF’s). Seasonally adjusted M2 is computed by summing savings deposits, small-denomination time deposits, and retail MMMF’s, each seasonally adjusted separately, and adding the result to seasonally adjusted M1" (Federal Reserve Bank of St. Louis, 2014).
15
borrowing by corporations (CP) and the three month Treasury bill Rate i.e. the analogous unsecured borrowing rate for the U.S. government (TB) are used in the second part of the research in order to concede potential omitted variable bias problems.16 The first part which is in line with the methodology of Sims (1972) makes use of quarterly data for GNP, MB, M1 and M2 and focuses on the complete research period. In contrast, the VAR analysis makes use of monthly data for the period 1980 to 2014 and uses the IP, GDP, MB, M1, M2, NM1M2, and the difference between the Commercial Paper Rate and the T-bill Rate (R).17 The mentioned monetary aggregates, among others, are computed by the Federal Reserve Bank of St. Louis. Although the latter also provides alternative monetary measures such as the Monetary Services Index or Divisia measures, I leave such an enlarged search for follow-up related studies. Finally, except for the T-bill Rate and the Commercial Paper Rate, all series were issued seasonally adjusted.18
4. Empirical Methodology
In this section, I elaborate on the specific methodology used in order to investigate the money-income Granger causal relation. The accompanying paragraphs respectively describe the lag-order selection procedure, the reduced form equations as in line with Sims (1972) and the multivariate VAR specifications as in line with Friedman and Kuttner (1992; 1993).
4.1. Econometric Analysis
In essence, the empirical analysis can be divided in two separate parts. In the first part Sims’ (1972) results are reproduced for the period 1949q3 – 1968q4 and 1949q3 – 1979q4 and successively broadened up to 2014q2 by focusing on three additional time periods namely 1980q1 – 1991q4, 1992q1 – 2007q2 and 2007q3 – 2014q2. Furthermore, the second part focusses specifically on VAR models including two, three or four variables and examines the (causal) relation between money and income by the use of Granger causality Wald tests. The latter test results serve as additional evidence that could either be used to solidify the results found under the first part or to demonstrate inconsistencies or certain impediments. Finally, whereas the first two time periods reflect the sample periods examined by respectively Sims (i.e.1949-1968) and Friedman and Kuttner (1992;1993), Feldstein and Stock (1994) and Thoma (1994) (i.e. 1980-1991) the latter two are not based on
16
The aggravation method chosen for the data is the end of period amount in favor of the average.
17
In contrast, due to a lack of sufficient data for the commercial paper rate during the sample period 1949q3 – 1968q4 and 1949q3 – 1979q4 only the three month Treasury Bill rate is included as an interest rate proxy. Including the T-bill solely is in line with the research of Litterman and Weiss (1985) and Psaradakis et al. (2005).
18
16
existing research. In order to investigate whether the money-income relation regained importance after the 2007 subprime crisis, two separate time periods are examined, one that start from 1992m1 (the period where formerly mentioned research mostly ended) to 2007m5 and 2007m6 (the period in which the fall of Lehman Brothers triggered the global financial crisis) to 2014m6.
4.2. Lag length Selection
Undoubtedly, an important matter in the money-income research is the determination of the appropriate lag length selection of the VAR. As indicated by Thornton and Batten (1985, pp.164-165; In: Hayo, 1999), a specific lag length choice could have a substantial effect on the test results and for that reason selecting different statistical criteria could produce contradictory conclusions regarding the Granger causal order between money and income. More specific, the authors find that simple ad hoc approaches such as examining a few arbitrary lag structures as in Hsiao (1981) and McMillen et al. (1984) and even 'rule of thumb' approaches could produce misleading results. Unfortunately, no generally correct or best method exists for choosing a specific lag length model. Therefore, for the time period 1980m1 -2014m6 the following approach, comparative to Hayo (1999, p.6) is taken into consideration: First, a VAR with twelve monthly lags is estimated, which for the greater part corresponds with the lag order in Stock and Watson (1989), Friedman and Kuttner (1993), Thoma (1994), Davis and Tanner (1997) and Aksoy and Piskorski (2006).19 Consequently, a Lagrange Multiplier (LM) test is performed at lags j ∈ (1,12) to test for autocorrelation in the residuals of the specific VAR model. If the null hypothesis of non-serial correlation cannot be rejected the specific lag-order is accepted. In contrast, if the latter hypothesis can be rejected at the 0.05 level the lag length is increased to sixteen lags whereupon a Hendry-type testing down procedure takes place until no autocorrelation is found (Hayo, 1999, p.6).
In addition, as in line with among others Krol and Ohanian (1990), Swanson (1998) and VAR research in general, lag-order selection is also based on specific lag-order selection statistics. For that reason several information criteria i.e. Akaike’s Information Criterion (AIC), Schwarz’s Bayesian Information Criterion (SBIC) and Hannan and Quinn Information Criterion (HQIC) are consulted for the different two, three and four variable VARs. These information criteria measure the difference between the specified model and the true model which should indeed be minimized. When all three statistics agree, the selection for the specific VAR is clear. In the case of conflicting results the AIC is preferred over the SBIC and HQIC since the former tends to be more accurate in the case of monthly
19 Stock and Watson (1989), Thoma (1994) and Davis and Tanner (1997) also take a two, three, and four variable VAR
approach into consideration consisting of either 12 or 6 monthly lags on money and 12 lags on output, inflation and an interest rate. Aksoy and Piskorski (2006) however use the exact same autoregressive specification of Friedman and Kuttner (1992;1993) but use the equivalent number of quarterly lags i.e. four lags for all variables.
17
data (Ivanov and Kilian, 2005). For comparative reasons, a universal lag-order is chosen for all information criteria based regressions for the time range 1980m1 -2014m6. This is done by choosing the modus lag-order of all regressions. In summary, these two approaches demonstrate a solid and comprehensible preference for VAR models with respectively nine lags, based on the information criteria, and twelve lags which is indeed much in line with the majority of related research.
In contrast, for the time period 1949q3-1968q4 and 1949q3 – 1979q4 a different approach is considered. In order to provide reliable VAR evidence that corroborates or repudiates Sims’ (1972) results and which can be easily compared with the latter, the same amount of lags is used in the two, three and four variable autoregressive models namely eight quarterly lags. In addition, for comparative reasons the same models are also estimated with the respective equivalent amount of twelve monthly lags namely four quarters and nine months namely three quarters.
4.3. Bivariate Regression Analysis: Sims’ Method
Sims’ (1972) methodology of identifying causal directions is founded on a more advanced version of Tobin’s (1970) post hoc ergo propter hoc principle by including both past and future values of GNP or monetary aggregates in a simple linear regression (1972, p.543). As stated, it is generally possible to estimate a regression of Y on past, current and future values of X. However, in the case of causality running from X to Y it is expected that future values of X will not appear in the regression even if they are allowed for. For that reason, a practical and common statistical test for unidirectional money-income Granger causality can be carried out: Regress money-income on past and future values of money using a prefiltering technique to separate trend and cyclical components. When causality runs from money to income, future values of money in the regression should have coefficients insignificantly different from zero (p.545).
Following Sims and taking M2 also into consideration nine OLS regression are estimated, three in the form of GNP = f(M, 8 lags) where M respectively represent the adjusted MB, M1 and M2; three in the form of GNP = f(M, 4 leads, 8 lags) where M represent the same monetary variables MB, M1 and M2 and three in the form of M = f(GNP, 4 leads, 8 lags) where again, M represents the latter monetary aggregates. In addition, six F-tests are conducted on four future quarter coefficients to estimate the future effect of GNP on money and vice versa. This is first done for the period 1949q3 – 1968q4 (and 1949q3 – 1979q4) and successively for 1980q1 – 1991q4, 1992q1 – 2007q2 and 2007q3 – 2014q2. All variables in the regressions are measured as natural logs and prefiltered using Sims’ filter 1 − 1.5𝐿 + 0.5625𝐿2 i.e. each logged variable is substituted by 𝑥𝑡 = 1.5𝑥𝑡−1+ 0.5625𝑥𝑡−2 (1972, p.545).
18
4.4. Multivariate VAR Analysis
In essence, the specifications for real output fluctuations as measured by the industrial production index (∆𝑦) are respectively given by the following two, three and four variable models: 20
∆𝑦𝑡 = 𝛼 + ∑ 𝛽𝑖∆𝑦𝑡−𝑖 𝑛 𝑖=1 + ∑ 𝛾𝑖∆𝑚𝑡−𝑖 𝑛 𝑖=1 ∆𝑦𝑡 = 𝛼 + ∑ 𝛽𝑖∆𝑦𝑡−𝑖 𝑛 𝑖=1 + ∑ 𝛾𝑖∆𝑚𝑡−𝑖 𝑛 𝑖=1 + ∑ 𝛿𝑖∆𝑝𝑡−𝑖 𝑛 𝑖=1 ∆𝑦𝑡 = 𝛼 + ∑ 𝛽𝑖∆𝑦𝑡−𝑖 𝑛 𝑖=1 + ∑ 𝛾𝑖∆𝑚𝑡−𝑖 𝑛 𝑖=1 + ∑ 𝛿𝑖∆𝑝𝑡−𝑖 𝑛 𝑖=1 + ∑ 𝜖𝑖∆(𝑟𝐶𝑃− 𝑟𝑇𝐵) 𝑛 𝑖=1
where ∆𝑦, ∆𝑚, ∆𝑝, and ∆(𝑟𝐶𝑃− 𝑟𝑇𝐵) are the growth rates of industrial production (log first difference), the specific financial variable (log first difference), inflation (log first difference of CPI) and the change of the spread between the commercial paper rate and the T-bill rate (log first difference). Consequently, within each VAR system I conduct Granger causality Wald tests. Indeed, for the time period 1949 -1979 𝑛 reflects either three, four or eight quarters. In contrast, for the three sample periods in the time range of 1980-2014 𝑛 represents either nine or twelve months. For that reason the former nine lag analysis is similar to that of Feldstein and Stock (1994) and Estrella and Mishkin (1997). However, there are two main differences. First, I use monthly data instead of quarterly data. A second difference is related to the specific break in the data which is frequently identified as having been occurred during the late 1980s. My analysis focuses on the time period since 1980m1 as one in which the performance of the money-income relation is poor, rather than determining the exact timing of the break, which appears to be of more precedence for Feldstein and Stock.
Furthermore, the twelve month autoregressive specification for output fluctuations for the time period 1980-2014 almost exactly follows Stock and Watson (1990) and Friedman and Kuttner (1993). However, Stock and Watson argued for the inclusion of the 𝑓(𝑡) regressor based on their finding that money growth tends to be stationary about a small but statistically significant trend term (In: Friedman and Kuttner, p.191). Comparatively, this paper makes use of individually detrended variables for all sample periods, which is equivalent to including 𝑓(𝑡) in the regression. Following Ravn and Uhlig (2002), the former variables are computed by applying the Hodrick-Prescott (HP) filter with a default smoothing parameter (𝜆) of 129,600 for monthly data and 1600 for quarterly
20
For practical reasons I omit the general matrix notation of a VAR(p) and present the most important regression with output as dependent variables as an example. However, the same regressions are also estimated with either money, prices or the interest rate differential as left hand side variable.
19
data. The HP filter is desirable since it dismisses unit root trend components. Besides, it has no phase shift and by choosing an appropriate smoothing parameter it approximates the optimal filter which isolates solely components having cycle frequencies (Karfakis, 2013, p.490). As expected, after applying the filter and transforming the data to first differences all economic and financial series satisfy stationary properties.21
5. Estimation Results
In the accompanying section, I provide the estimation results on the Granger causal money-income relation for several sample periods. First, the results of Sims (1972) are replicated and consequently extended to 2014q2. In the second part, I provide the estimation results of the multivariate autoregressive models and subsequently conduct two robustness exercises. Finally, in the last paragraph I compare my test estimates with the existing literature and elaborate on money’s declining role since the 1980s, the contemporary revers causality pattern and money’s generally unaltered role during 2007’s recession.
5.1. Decreasing Role of Money
Focusing on the time period 1949q3 – 1968q4 one can see from Table 5.1 that the regression of money on four leads and eight lags of GNP as well as the regression of GNP on eight lags of money are significant. In addition, while future values of the MB, M1 and M2 are not significant in explaining GNP, future values of GNP on the latter money variables were highly significant (Table 5.2). Indeed, this is not completely the case for M2, however the results are generally in line with Sims (1972, p.546-547).22 Besides, as can be seen from Appendix C it seems that for the GNP on money regressions the largest individual coefficients appear on the lags while the coefficients on future leads appear to be small and as mentioned not significantly different form zero. Furthermore, the coefficients in the latter regressions tend to be positive at first but successively change sign beyond
21
Both Phillips-Perron and (Engle Granger) Augmented Dickey Fuller tests reject the null hypothesis stating the presence of a unit root at the 0.01 significance level. The latter holds for all the indicated first difference series’ specification under the VAR analysis and for both the complete data set as well as for all sample periods.
22
Although close, the estimates for the sample period 1949q3 – 1968q4 (as well as other regression outcomes) are not exactly the same as in Sims (1972). As an example, I find F = 2.44 for GNP = f(M1, 8 lags) compared with Sims’ F = 2.24. As stated by Amato and Swanson (2001, p3), the reason for these small deviations can be found in periodic redefinitions of data on monetary aggregates presumably to improve their connection, to some extent, to measures of output. Noteworthy, with respect to M2 there have been six redefinitions of the series between 1980 and 2000. In addition, besides redefinitions, monetary aggregates or money data in general is also revised on a regular basis due to seasonal factor adjustments or incomplete data collections from depository institutions. Finally, a last type of change involves rebenchmarking which are typically made each February following the Federal Reserve’s publication of Money Stock Revision. In essence, rebenchmarking involves series revisions because of additional source data collection by the Federal Reserve after the completion of near term revisions (Amato and Swanson, 2001, pp. 6-7).
20
the fourth lag (Appendix C). This is not only in line with Sims but also with Friedman and Schwartz’ (1963) notion that aggregates, on average, tend to positively lead Real GDP. Indeed, I also indicated this in figure 2.1. In essence, the former results corroborate Sims (1972) and tend to reject the hypothesis of money being purely passive i.e. money is not influencing but merely responding to GNP in favor of the hypothesis that GNP is purely passive.
In contrast, prolonging the analysis towards 1979q4 shatters the latter results. Although the test statistics on future values of GNP on money are still much stronger than vice versa, I find that all F-statistics are extremely significant and hence no clear conclusion can be drawn in terms of a unidirectional money-income relation. This is certainly not in line with present literature that indicates that money had a significant marginal predictive value for income, and not vice versa, until roughly the 1980s, that is until just before a new monetary policy procedure was adopted by the Federal Reserve System (Friedman and Kuttner, 1993, p.192). Furthermore, iterating the same analysis for 1980q1 – 1991q4 one can discern familiar results. Although again the test statistics on future values of GNP on money are much stronger than vice versa and statistically significant at the respective 0.05, 0.01 and 0.05 level, I find no clear evidence for a unidirectional causal relation. For instance, the regression of GNP on the adjusted MB seems significant at the 0.05 level (F=2.83) however the same also holds for the inclusion of future leads in the regression (F=2.56).
Remarkably, the estimates for the sample periods 1992q1 – 2007q2 and 2007q3 – 2014q2 don’t give a clear picture either. While the outcomes of the former are to some extent in line with the period 1980q1 – 1991q4 i.e. regressions with both MB lags and leads are significant at the 0.05 level (F=4.69; F=3.20) they differ severely in the F-statistics on four future leads. In essence, the results for the latter sample tend to provide evidence for a shift in the money-income relation.23 For instance, table 5.1 indicates that regressions with future leads of money tend to have more explanatory power – but not necessarily significant – compared with regressions without leads. This is especially the case for the Monetary Base (F=3.75 vs F=0.26). The latter is corroborated by the perceived shift of significance in table 5.2 i.e. future values of MB tend to explain GNP (F=3.06) while the opposite is not true (F=0.24). However, a similar analysis does not hold for M1 and M2.
In summary, when considering the sample period 1949q3 – 1968q4 my results for the reduced form regressions are generally in line with the existing literature, which favors a unidirectional relation from money (MB and M1) to output (GNP). However, this is not the case for the remaining sample periods that signify a bidirectional relation when data up to 1979q4 is included and no univocal causal pattern for the rest of the samples up to 2014q2.
23
That is, if such a causal relation truly exists since the data fits the model relatively diminutive for the latter period. In essence, for the sample period 2007q2 – 2014q2 one can certainly see that the fraction of the sample variance of the regressand that is explained by the independent variable, expressed by the adjusted R2 tends to diminish severely.
21 Table 5.1
Summary of OLS Regressions
Period: 1949q3 - 1968q4 1949q3 - 1979q4 1980q1 - 1991q4 1992q1 - 2007q2 2007q3- 2014q2
F-statistic R² F-statistic R² F-statistic R² F-statistic R² F-statistic R²
GNP = f(MB, 8 lags) 2.44** 0.8177 7.01** 0.9434 2.83* 0.7859 4.69** 0.9215 0.26 0.3306 GNP = f(MB, 4 leads; 8 lags) 1.49 0.8131 4.74** 0.9423 2.56* 0.8000 3.20** 0.9186 3.75* 0.7167 GNP = f(M1, 8 lags) 2.13* 0.8203 6.86** 0.9430 2.06 0.7609 0.27 0.8683 0.25 0.3201 GNP = f(M1, 4 leads; 8 lags) 1.65 0.8176 4.64** 0.9419 1.86 0.7688 0.52 0.8686 0.71 0.0900 GNP = f(M2, 8 lags) 1.69 0.8193 6.72** 0.9426 1.55 0.7409 0.40 0.8709 0.26 0.3295 GNP = f(M2, 4 leads; 8 lags) 1.91* 0.8095 4.39** 0.9408 1.10 0.7226 1.53 0.8933 1.17 0.3175 MB = f(GNP, 4 leads; 8 lags) 4.43** 0.8524 17.86** 0.9666 0.77 0.8821 2.68** 0.5170 1.21 0.0694 M1 = f(GNP, 4 leads; 8 lags) 2.96** 0.7922 10.03** 0.9373 2.26* 0.6705 2.08* 0.3243 0.84 0.1876 M2= f(GNP, 4 leads; 8 lags) 3.12** 0.9760 6.88** 0.9830 1.62 0.7572 4.07** 0.9293 1.30 0.4111 The F-statistic represents the null hypothesis that all right hand side (independent) variables have zero coefficients * Significant at 0.05 level
** Significant at 0.01 level
Table 5.2
F-tests and accompanying P-values on Four Future Quarters’ Coefficients
Period: 1949q3 - 1968q4 1949q3 - 1979q4 1980q1 - 1991q4 1992q1 - 2007q2 2007q3- 2014q2
F-statistic R² F-statistic R² F-statistic R² F-statistic R² F-statistic R²
GNP on MB 1.29 0.8129 10.31** 0.9360 1.37 0.7274 0.72 0.8890 3.06* 0.4865 GNP on M1 0.59 0.8028 7.73** 0.9316 1.37 0.7273 1.00 0.8911 1.19 0.3174 GNP on M2 0.49 0.8019 5.61** 0.9274 0.6 0.7084 3.46* 0.9064 4.13* 0.5500 MB on GNP 3.32* 0.8217 26.50** 0.9515 3.32* 0.9074 3.17* 0.4777 0.24 0.0666 M1 on GNP 5.23** 0.7983 20.37** 0.9264 3.8** 0.6585 0.32 0.1521 0.58 0.3038 M2 on GNP 6.21** 0.9768 20.65** 0.9835 3.31* 0.7815 0.94 0.8830 0.42 0.3106 * Significant at 0.05 level
22
5.2. Multivariate Autoregressive Evidence
The first three rows in table 5.3 describe the test results for the respective two, three and four variable VARs for the sample period 1949q3 – 1968q4 for both lag orders i.e. eight and four quarterly lags. In particular, each of the four subparts of table 5.3 reports the sample period, the amount of variables in the VAR i.e. two, three or four, the amount of lags, the monetary aggregate taking into consideration (far left i.e. MB, M1, M2 and NM1M2) and the significance probability, the p-value of the Wald test that the coefficients on all lags of the independent variable (column: either money or income) are jointly zero. This corresponds to testing the hypothesis that the column variable does not Granger cause the omitted counter variable. 2425 For instance, using the sample period 1949q3 – 1968q4 one can see that in the two variable VAR(8) case the Monetary Base tends to Granger cause output (p=0.000) while output does not Granger cause the Monetary Base (p=0.229).26
Indeed, the results for the Granger causality Wald tests are much in line with the outcomes of Sims (1972) and tend to corroborate the hypothesis of a unidirectional causal relationship from money to income. In particular, both the adjusted MB and M1 Granger cause output in all specifications at the 0.01 significance level (an exception is M1 on GNP for the two variable VAR(8) case where p=0.013) while the opposite is certainly not true. In contrast, the same doesn’t hold for M2. The broad monetary aggregate seems to Granger cause output in the four variables VAR(8) case (p=0.015) however the same does not hold for the VAR(4) case where output tends to lead money (p=0.014).27 This indefinite relation between M2 and GNP was also perceived in the previous section therefore it seems that for this specific time period no clear relation between the two existed. Extending the analysis to 1949q3 – 1979q4 I practically find the same results for the adjusted MB but not for M1 and M2. For practical reasons the test estimates can be found under Appendix E. Whereas four lags of M1 tend to Granger cause GNP in the two and three variable case (p=0.013; p=0.002)
24
The Granger causality test results for the VAR(3) specifications are essentially the same as the VAR(4) case and hence for the sake of convenience omitted.
25
For all VAR specification several postestimation test were conducted to strengthen the validity of the observed results. First, Jarque-Bera goodness-of-fit test estimates cannot reject the null hypothesis that the disturbances in the VARs are normally distributed at the 0.05 significance level. For that reason, I essentially find strong evidence that the sample data has the skewness and kurtosis equivalent to a normal distribution. In addition, for the far majority of the VAR specifications Lagrange Multiplier (LM) test for autocorrelation cannot reject the null hypothesis that there is no autocorrelation at lag j with j ∈ (1,12). Therefore, almost without exceptions the test outcomes give no hint for the presence of model misspecification. Finally, when testing for the stability condition of each VAR specification I find that the modulus of each eigenvalue are strictly less than 1, which means that the estimates satisfy the eigenvalue stability condition.
26 For a complete overview with all Granger causality Wald test estimates for money, income, inflation and the
interest rate differential for the sample period 1949q3 – 1968q4, please consult Appendix D.
27
In the sample period under investigation (1949q3 – 1968q4), the correlation between Gross National Product and other measures of income such as Real GDP, National GDP and Industrial Production are respectively: 0.9853, 1.000 and 0.9931. For that reason, the test results reported in the first subpart of table 5.3 are robust with respect to one’s choice of output measure.
23
similar results are missing for all other specifications. Similarly, eight lags of M2 tends to lead output when accounted for inflation and the Treasury bill rate (p=0.009; p=0.009) but not in any other model.
As mentioned in the previous section, the VAR specifications for the remaining sample periods make use of monthly data and consist of either twelve or nine lags. Starting with data on 1980m1 – 1991m12 the second subpart in table 5.3 describe some interesting results. In the two variable VAR(12) and VAR(9) models, output, approximated by Industrial Production, tends to Granger cause money, whatever defined. 28 The evidence for the former inference is quite strong as most Granger causality Wald tests are significant at the 0.01 level. Indeed, the opposite that money fluctuations lead output fluctuations certainly does not hold. Remarkably, the proposition of a one-directional shifted relationship from output to money is corroborated by the test results of the three variable estimations. Correspondingly, the estimates suggest that the hypothesis that money does not Granger cause output cannot be rejected for all specifications not even at the 0.10 significance level. Contrary, the same hypothesis but this time for output on money can structurally be rejected when accounted for the MB, M1, M2 or M2 net of M1. Table 5.3 also describes the Granger causality Wald test estimates for the four variable VARs. Although the test estimates for the adjusted MB are in line with the former results, the effect of M1, M2 and NM1M2 are more ambiguous. Economic growth tends to lead M2 and NM1M2 in the VAR(12) case (p=0.000; p=0.000) but not in the nine month specification (p=0.055; p=0.103). Finally, For M1 and output the relation seems to be bidirectional for the twelve-month specification and not existing for the nine-month case. In summary, the test estimates indicate that the former perceived unidirectional Granger causal relation from money to output does not hold when data for the sample period 1980m1 – 1991m12 is included. In contrast, I find weakly significant evidence for a general reverse causal relation between the adjusted MB, M2 or NM1M2 and output. Indeed, the latter does not strictly hold for M1 since the test estimates fail to verify a univocal relation with nominal income.
5.3. Pre- and Post-Crisis Results
In the third and fourth sub section of table 5.3 I provide the estimation results of the money-income relation for the pre-and post-crisis time periods 1992m1 – 2007m5 and 2007m6 – 2014m6. In essence, in contrast with the former sample period, data for 1992m1 – 2007m5 indicates that the
28
Again, correlations between Industrial Production and GNP or Real GDP are relatively high (0.9821; 0.9910) but lower for Nominal GDP (0.9530) for the sample period 1980m1 – 1991m12 . For that reason, the test results reported in the second subsection of table 5.3 are robust with respect to one’s choice of output measure.
