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# Breaks in money demand.

I. Introduction

During the last twenty years TWENTY YEARS. The lapse of twenty years raises a presumption of certain facts, and after such a time, the party against whom the presumption has been raised, will be required to prove a negative to establish his rights.
2.
, beginning with the provocative paper by Goldfeld [5] that revealed the case of the "missing money," the question of whether money demand (the relationship between money, income, and an interest rate) is stable has been intensively investigated using a variety of econometric e·con·o·met·rics
n. (used with a sing. verb)
Application of mathematical and statistical techniques to economics in the study of problems, the analysis of data, and the development and testing of theories and models.
techniques. Currently, the most popular framework for examining the behavior of money demand is the cointegration framework. In this framework, the stationarity of money demand instead of the stability of money demand is evaluated. Earlier tests of the stability of money demand typically centered on whether the coefficient coefficient /co·ef·fi·cient/ (ko?ah-fish´int)
1. an expression of the change or effect produced by variation in certain factors, or of the ratio between two different quantities.

2.
estimates were stable, i.e. not subject to a structural break. These tests did not consider the underlying time series aspects of the variables in money demand or the time series properties of their joint relationship prior to estimation estimation

In mathematics, use of a function or formula to derive a solution or make a prediction. Unlike approximation, it has precise connotations. In statistics, for example, it connotes the careful selection and testing of a function called an estimator.
as is now common given the seminal work A seminal work is a work from which other works grow. The term usually refers to an intellectual or artistic achievement whose ideas and techniques have been adopted or responded to in later works by other people, either in the same field or in the general culture.  of Engle and Granger (1).

Since then, newer tests have focussed on the time series properties of the money demand variables and whether the joint relationship between the variables is stationary Stationary can mean:
• Fixed in position, or mode: immobile.
• Unchanging in condition or character.
• In statistics and probability: a stationary process.
• In mathematics: a stationary point.
• In mathematics: a stationary set.
, i.e., whether the variables are cointegrated. Engle and Granger [1] and Johansen and Juselius [10] offer cointegration estimation procedures that have been applied by numerous researchers to the money-income-interest rate relationship. The pervasive pervasive,
adj indicates that a condition permeates the entire development of the individual.
finding is that money demand is non-stationary (see section II, below). Structural stability has not typically been a facet facet /fac·et/ (fas´it) a small plane surface on a hard body, as on a bone.

fac·et
n.
1. A small smooth area on a bone or other firm structure.

2.
of investigation. However, the issues of stationarity and stability should not necessarily be treated independently. Failure to take account of structural change may bias the results in favor of upon the side of; favorable to; for the advantage of.

non-stationarity, as shown in Perron Per´ron

n. 1. (Arch.) An out-of-door flight of steps, as in a garden, leading to a terrace or to an upper story; - usually applied to mediævel or later structures of some architectural pretensions.
[16].(1)

History suggests that the economic environment and monetary institutions, regulations, and operating procedures have changed over time. In the early 1970s, the fixed exchange rate system collapsed when the gold exchange standard was abandoned and the U.S. dollar became a fiat currency In economics, fiat currency or fiat money is money backed by government demand for it as legal tender in payment of legal liabilities, such as taxes. It is often associated with paper money because legal liabilities are created and settled by documents which are usually . During that same time, the U.S. suffered an oil price shock that produced accelerating inflation and stagnant stagnant /stag·nant/ (stag´nant)
1. motionless; not flowing or moving.

2. inactive; not developing or progressing.
GDP GDP (guanosine diphosphate): see guanine.  growth--an outcome that had never before been experienced in post World War II U.S. economic history. In 1979, the Fed changed its operating procedure from primarily targeting interest rates to targeting monetary aggregates. This action combined with Fed chairman Volcker's commitment to fighting inflation has enabled the Federal Reserve's anti-inflation policy to become credible to the private market. In March 1980, the Depository Institutions Deregulation and Monetary Control Act Depository Institutions Deregulation and Monetary Control Act

The 1980 federal legislation that ended the regulation of the banking industry.
(the Monetary Control Act) was passed which phased out interest rate ceilings and reduced reserve requirements Reserve Requirements

Requirements regarding the amount of funds that banks must hold in reserve against deposits made by their customers. This money must be in the bank's vaults or at the closest Federal Reserve Bank.
on all types of accounts. This Act promoted competition amongst various types of financial institutions and may have been responsible for the disintermediation The elimination of the distributor and/or retailer (the middleman) when making a purchase. The term is used to refer to purchasing directly from a manufacturer's Web site, the benefits of which are convenience, fast turnaround time and sometimes lower prices.  that ensued.

From a policy perspective, it is important to know the behavior of money demand. Both the original Goldfeld [5] finding of the "case of the missing money" and later findings that money demand is non-stationary are troublesome since the ability of policymakers to prevent money market disruptions Market Disruption

A situation where markets cease to function in a regular manner, typically characterized by rapid and large market declines. Market disruptions can result from both physical threats to the stock exchange or a unusual trading (as in a crash).
hinges Hinges may refer to:
• Plural form of hinge, a mechanical device that connects two solid objects, allowing a rotation between them.
• Hinges, a commune of the Pas-de-Calais département, in northern France
on whether a money demand relationship that is predictable can be identified. If money demand is not stable, then proper policy conduct may ex post be misguided mis·guid·ed
Based or acting on error; misled: well-intentioned but misguided efforts; misguided do-gooders.

mis·guid
in light of a structural break and there may be a period of learning before policy is readjusted to its proper course. If money demand is non-stationary, then the Fed may not be able to use such a relationship to target money growth with much accuracy. In this case, the Fed's ability to, ex ante, prevent money market disequilibriums from affecting the economy would be curtailed. This idea follows Poole's [17] analysis. On the other hand, if the Fed's policy is to adjust, ex post, to movements in money demand, it will need to know whether the movements are permanent or transitory TRANSITORY. That which lasts but a short time, as transitory facts that which may be laid in different places, as a transitory action. . If they are permanent (i.e., money demand is non-stationary), then an adjustment that accommodates "base" drift in the money supply may be warranted. If money demand is stationary so that the movements are transitory, there may be no reason for the Fed to take action unless they desire to speed up (lean with the wind) or slow down (lean against the wind) the adjustment toward a constant equilibrium equilibrium, state of balance. When a body or a system is in equilibrium, there is no net tendency to change. In mechanics, equilibrium has to do with the forces acting on a body. .

It is possible that tests that find that money demand is non-stationary may be flawed flaw 1
n.
1. An imperfection, often concealed, that impairs soundness: a flaw in the crystal that caused it to shatter. See Synonyms at blemish.

2.
because the estimation procedures used have not considered a structural break. In our study, we use the econometric technique offered by Gregory and Hansen Han·sen , Gerhard Henrik Armauer 1746-1845.

Norwegian physician and bacteriologist who discovered (1869) the leprosy bacillus.
(G&H) [6] that allows for structural change in a cointegrating framework. We examine whether money demand is stationary in the long run after allowing for a one-time structural break in the money-income-interest rate relationship. The discussion above points to several possible breaks that may be significant for money demand.

We also use an error correction model with a structural break. Kremers, Ericcson and Dolado [11] find that an error correction model provides more power against the null-hypothesis of "no cointegration" than the standard augmented Dickey-Fuller cointegration test. The standard augmented Dickey-Fuller test In statistics and econometrics, an augmented Dickey-Fuller test (ADF) is a test for a unit root in a time series sample. It is an augmented version of the Dickey-Fuller test to accommodate some forms of serial correlation.  imposes a common factor restriction that reduces the information used in estimation relative to that used in an error correction specification. The common factor restriction imposes equality between the short and long run elasticities. Kremers, Ericcson, and Dolado [11] use a bivariate bi·var·i·ate
Mathematics Having two variables: bivariate binomial distribution.

framework to analyze the issue. However, they note that the conclusion holds for generalized gen·er·al·ized
1. Involving an entire organ, as when an epileptic seizure involves all parts of the brain.

2. Not specifically adapted to a particular environment or function; not specialized.

3.

We treat the structural breaks in two ways; (1) we pre-select the breakpoint The location in a program used to temporarily halt the program for testing and debugging. Lines of code in a source program are marked for breakpoints. When those instructions are about to be executed, the program stops, allowing the programmer to examine the status of the program  based on our priors, and (2) we let the data itself determine the breakpoint. In pre-selecting the breakpoints, the structural break is assumed to be caused by an exogenous Exogenous

Describes facts outside the control of the firm. Converse of endogenous.
shock to the money demand data generating process. A criticism of pre-selecting the breakpoint is that we may be data mining, especially if we have visually inspected the money demand relationship to determine an obvious breakpoint. The second treatment does not suffer from this criticism since the breakpoint is estimated endogenously en·dog·e·nous
1. Produced or growing from within.

2. Originating or produced within an organism, tissue, or cell: endogenous secretions.
. In this case, the structural break is modelled as a natural manifestation man·i·fes·ta·tion
n.
An indication of the existence, reality, or presence of something, especially an illness.

manifestation
(man´ifestā´sh
, albeit an outlier outlier /out·li·er/ (out´li-er) an observation so distant from the central mass of the data that it noticeably influences results.

outlier

an extremely high or low value lying beyond the range of the bulk of the data.
, of the data generating process itself. While the endogenous endogenous /en·dog·e·nous/ (en-doj´e-nus) produced within or caused by factors within the organism.

en·dog·e·nous
1. Originating or produced within an organism, tissue, or cell.
treatment does not suffer from "data mining," it is atheoretical a·the·o·ret·i·cal
Unrelated to or lacking a theoretical basis.
. Ideally, the endogenous estimation procedure will produce a breakpoint that maps into a recognizable historical event, but there is no assurance that this will happen. Moreover, the endogenous estimation procedure may find more than one breakpoint that has a test statistic statistic,
n a value or number that describes a series of quantitative observations or measures; a value calculated from a sample.

statistic

a numerical value calculated from a number of observations in order to summarize them.
big enough to surpass the critical value for rejecting "no cointegration." Since there are criticisms of each method, we present the results from both treatments.

We conduct tests for the stationarity of money demand subject to a structural break using three definitions of money: M1, M2, and credit. M1 and M2 have each been used as a target variable by the Fed and there has been debate over which measure is the appropriate one to use in conducting policy. While credit has not been used as a target variable, Friedman [3, 63] has suggested that it may contain information that "might provide some safeguard against false signals given by the monetary aggregates under conditions of instability affecting the public's demand for money." Our results indicate that a stationary money demand relationship exists after accounting for a structural break at 1980:Q1 for the credit money measure. We find tentative tentative,
adj not final or definite, such as an experimental or clinical finding that has not been validated.
evidence that M1 money demand is stationary subject to a structural break occurring in 1975:Q2. For the M2 money measure, we find, like most other studies, no evidence that money demand is stationary.

II. Literature Review

Numerous studies have examined money's relationship to income or income and an interest rate using the cointegration methodology. Money measures studied include: M1, M2, and credit. Conclusions from many of the studies point to structural instability as a problem in detecting a stationary money demand relationship, although none of the studies explicitly account for structural change through their estimation procedures. Miller [14] finds that M2, but not M1, retains a long run relationship with income and a short-term Short-term

Any investments with a maturity of one year or less.

short-term

1. Of or relating to a gain or loss on the value of an asset that has been held less than a specified period of time.
commercial paper rate from 1959:Q1-1987:Q4. Miller [14, 147] argues that structural changes over the sample period may make it more difficult to detect cointegration. Mehra [13] conducts Chow Tests The Chow test is an econometric test of whether the coefficients in two linear regressions on different data are equal. The Chow test is most commonly used in time series analysis to test for the presence of a structural break.  for error-correction equations of money (M1) demand and finds evidence of structural instability. He also finds mixed results regarding a long run relationship between money, income, and the interest rate. The results from his Chow tests in conjunction with mixed results about a stable long run money demand equation suggest that structural change may play a role in the findings. Hoffman and Rasche [9] use the Johansen-Juselius method to test for cointegration between real M1 and real personal income and between real base money and real personal income. They test three different sample periods: 1953:M1-1974:M12; 1953:M1-1981:M12, and 1953:M1-1988: M12. They uniformly fail to reject "no cointegration" even when a potential structural breakpoint and the subsequent sample period are omitted. However, their pre-selected truncation points may not correspond to the breakpoint that would be determined through estimation and this may affect their conclusions. When they amend their tests to include a short-term interest rate variable, they find strong evidence of co-integration though a longer term interest rate produced less robust results. Counter to Hoffman and Rasche [9], Hafer and Jansen [7] find no evidence of cointegration between money, income, and either a commercial paper rate or a corporate bond rate, over the same sample period, but using quarterly data. They use the Johansen-Juselius method. Their results are similar to Friedman and Kuttner's [4]. Hetzel and Mehra [8] document stability for an M2-demand equation from 1952:Q1-1988:Q4 but not for M1. They explain the instability for M1-demand by suggesting that the introduction of NOW accounts in 1981 made M1 more substitutable with other saving deposits and that financial institutions were slow to adjust the rate on NOW accounts to market rate changes. Each of these studies implicitly or explicitly ascribes to structural change a role in the findings.

III. Data and Methodology

Quarterly data spanning 1959:Q1-1990:Q4(2) are used to test for cointegration between money, income, and the interest rate. We use the following money demand specification where all variables except the interest rate are in logs.

(1) m - [Alpha] - [Beta]y + [Gamma]r = [Epsilon 1. (language) EPSILON - A macro language with high level features including strings and lists, developed by A.P. Ershov at Novosibirsk in 1967. EPSILON was used to implement ALGOL 68 on the M-220. ]

where m represents M1, M2, or credit in real terms; y is GNP GNP

See: Gross National Product
in 1982 dollars; and r is the six-month commercial paper rate. The Aaa corporate bond rate is also considered. Since equation (1) presents the most general money demand specification, a finding that money, income, and the interest rate are cointegrated provides evidence that money demand is stationary, while a finding of no cointegration provides evidence that money demand is not stationary.(3)

Before using the G&H method that permits a structural break, we apply the Engle-Granger [1] two-step cointegration test to the cointegrating regression regression, in psychology: see defense mechanism.
regression

In statistics, a process for determining a line or curve that best represents the general trend of a data set.
residual from equation (1):

(2) [MATHEMATICAL EXPRESSION A group of characters or symbols representing a quantity or an operation. See arithmetic expression.  NOT REPRODUCIBLE re·pro·duce
v. re·pro·duced, re·pro·duc·ing, re·pro·duc·es

v.tr.
1. To produce a counterpart, image, or copy of.

2. Biology To generate (offspring) by sexual or asexual means.
IN ASCII ASCII or American Standard Code for Information Interchange, a set of codes used to represent letters, numbers, a few symbols, and control characters. Originally designed for teletype operations, it has found wide application in computers. ]

The Engle-Granger method does not admit a break. The null hypothesis null hypothesis,
n theoretical assumption that a given therapy will have results not statistically different from another treatment.

null hypothesis,
n
is [Rho] = 1. MacKinnon [12] presents critical values. Rejection of the null hypothesis implies that [Epsilon] is stationary and that the variables under consideration are cointegrated without a structural break in the money demand relationship. Failure to reject the null hypothesis implies that [Epsilon] is non-stationary, i.e., the variables are not cointegrated.

It is possible that an inability to reject the null hypothesis of "no cointegration" based on the above specification may arise if there is an unaccounted for An inclusive term (not a casualty status) applicable to personnel whose person or remains are not recovered or otherwise accounted for following hostile action. Commonly used when referring to personnel who are killed in action and whose bodies are not recovered.  structural break in the money, income, interest rate relationship. Thus, these variables may bear a stationary relationship after accounting for a structural break. To test for this possibility, equation (1) is respecified to contain dummy variables This article is not about "dummy variables" as that term is usually understood in mathematics. See free variables and bound variables.

In regression analysis, a dummy variable
as in G&H. The specification is:

(3) m - [[Alpha].sub.1] - [[Alpha].sub.2]DU ([Tau]) + [[Beta].sub.1]yDU ([Tau]) + [[Gamma].sub.1]r + [[Gamma].sub.2]rDU ([Tau]) = [Epsilon].

DU ([Tau]) is a dummy variable which is equal to one for t [is greater than] TB, and 0 otherwise. TB is the date at which the break occurs, and [Tau] is used to index the dummy variable according to according to
prep.
1. As stated or indicated by; on the authority of: according to historians.

2. In keeping with: according to instructions.

3.
the date at which the breakpoint is estimated. The breakpoint can be imposed, a priori a priori

In epistemology, knowledge that is independent of all particular experiences, as opposed to a posteriori (or empirical) knowledge, which derives from experience.
, or estimated endogenously. The endogenous procedure estimates equation (3) sequentially for [Tau] = 2, ..., T - 1. Every sample date (except the start and endpoints) is estimated as a point of a potential structural break. The [Epsilon] from each regression is then passed through equation (2) and the [Rho] coefficient is computed. The breakpoint associated with the "maximum" (in absolute value) test statistic on [Rho] is conjectured to be that point at which the structural break occurs. Ideally, the estimated break-point that "maximizes" rejection of the hypothesis of no cointegration should correspond to an a priori breakpoint.

The sample breaks we selected are: the closing of the gold window in 1971:Q3; the oil price shock in 1973:Q2; the change in Fed operating procedure toward targeting monetary aggregates in 1979:Q4 (which may coincide with a market perception of an anti-inflation policy stance); and the passage of the Monetary Control Act in 1980:Q1. The structural changes that we consider are treated as having a permanent impact on money demand. The closing of the gold window coincides with the permanent dissolution Act or process of dissolving; termination; winding up. In this sense it is frequently used in the phrase dissolution of a partnership.

The dissolution of a contract is its Rescission by the parties themselves or by a court that nullifies its binding force and reinstates each
of the Bretton Woods Bretton Woods can refer to:
• Bretton Woods, New Hampshire
• The United Nations Monetary and Financial Conference, more commonly known as the "Bretton Woods Conference"
• Bretton Woods system, the international monetary system created at the conference
fixed exchange rate arrangement which may have influenced monetary policy. This may represent a structural break in the relationship between money, income, and interest rates. Similarly, the oil price shock of 1973 may have fundamentally changed the behavior of real GNP Noun 1. real GNP - a version of the GNP that has been adjusted for the effects of inflation
real gross national product

GNP, gross national product - former measure of the United States economy; the total market value of goods and services produced by all
and possibly its relationship to monetary aggregates. Also, the Fed's change in operating procedure in 1979 may have caused a change in the relationship between money, income, and the interest rate; it may have also been the point in time at which a credible (and ex post, lasting) commitment to fighting inflation was perceived by the market. The passage of the Monetary Control Act in 1980 may have permanently changed the environment in which banks conduct business and the way in which customers manage their deposits.

Since we model the structural change as having a permanent impact on money demand, the dummy variables in equation (3) are a sequence of zeros prior to TB and ones thereafter. This is the typical application of a dummy variable in a time-series context and has been referred to elsewhere as an innovation (or intervention A procedure used in a lawsuit by which the court allows a third person who was not originally a party to the suit to become a party, by joining with either the plaintiff or the defendant. ) outlier model. The innovation outlier model contrasts to an additive additive

In foods, any of various chemical substances added to produce desirable effects. Additives include such substances as artificial or natural colourings and flavourings; stabilizers, emulsifiers, and thickeners; preservatives and humectants (moisture-retainers); and
outlier model where the structural change is confined con·fine
v. con·fined, con·fin·ing, con·fines

v.tr.
1. To keep within bounds; restrict: Please confine your remarks to the issues at hand. See Synonyms at limit.
to one period and thus does not have a lasting impact [16; 20; 15].(4)

The use of the appropriate critical values is important to interpreting the test results correctly. G&H compute To perform mathematical operations or general computer processing. For an explanation of "The 3 C's," or how the computer processes data, see computer.  several critical values based on different specifications for the cointegrating regression. Not only do the critical values depend on the number of undummied regressors excluding the intercept intercept

in mathematical terms the points at which a curve cuts the two axes of a graph.
, they also depend on whether the intercept and/or slope dummies are included in the regression. For equation (3), the critical value is -5.50 at the 5 percent significance level and -5.23 at the 10 percent level.

We also derive an error correction model from equation (3). The error correction model is derived by rewriting re·write
v. re·wrote , re·writ·ten , re·writ·ing, re·writes

v.tr.
1. To write again, especially in a different or improved form; revise.

2.
[Epsilon] = (1 - [Delta]) [multiplied mul·ti·ply 1
v. mul·ti·plied, mul·ti·ply·ing, mul·ti·plies

v.tr.
1. To increase the amount, number, or degree of.

2. Mathematics To perform multiplication on.
by] [[Epsilon].sub. -1] where the value of [Delta] determines whether the money demand relationship is stationary (after accounting for a structural break). For [Delta] = 0, [Epsilon] is non-stationary and [m, y, r] are not cointegrated. The error correction model is:

(4) [Delta]m = [[Alpha]'.sub.1] + [[Alpha]'.sub.2]DU([Gamma]) - [Delta] [[Epsilon].sub.1] + [[Beta]'.sub.1][Delta]y - [[Beta]'.sub.1][Delta]yDU ([Gamma]) + [[Gamma]'.sub.1][Delta]r + [[Gamma]'.sub.2][Delta]rDU([Gamma]) + u.

In the error correction specification, all of the variables including the dummy variables become first-differenced.(5) The error correction model includes an "error correction term" which is the lagged value of [Epsilon] from equation (3). Up to four lags of [Delta]m were included in the estimation procedure to insure Insure can mean:
• To provide for financial or other mitigation if something goes wrong: see insurance or .
• Or you may be looking for ensure or inshore.
that u is white noise.(6) Breakdates are imposed exogenously, and an endogenous estimation procedure is also applied.

The error correction model explicitly reveals the short and long run dynamics in the money demand relationship. Also, the t-statistic on [Delta] can be used to test for "no cointegration." Kremers, Ericsson, and Dolado [11] show that the t-statistic is distributed approximately normal eve when the series are not cointegrated, i.e., the error correction term is non-stationary. In small samples, however, they advise that the augmented Dickey-Fuller test statistic be used to test for cointegration. While their work did not explicitly address the inclusion of dummy variables, it seems sensible to treat the dummy variables as additional regressors. Thus, the cointegration augmented Dickey Fuller statistic will be used where the number of variables in the cointegrating equation is seven (excluding the intercept and lags of [Delta]m). The critical values to test for the hypothesis of "no cointegration" are taken from MacKinnon [12]. MacKinnon reports critical values for up to a six-variable system. The critical variables for a six-variable system are -4.71 at the 5 percent significance level and -4.42 at the 10 percent significance level. Admittedly, a higher-variable system will have critical values that are larger in absolute value.

IV. Empirical Results

We first present results from the standard cointegration test where a one-time break is not incorporated. Thus, we apply equation (2) to the residuals estimated from equation (1) and include a time trend for each regression.(7) The Box-Pierce Q statistic at twelve lags is used to determine whether the Dickey-Fuller or augmented Dickey Fuller test is appropriate. MacKinnon's [12] critical values are used.

The standard cointegration test serves two purposes. First, the test determines whether or not [Epsilon] is stationary without considering a structural break. Second, the G&H method has been criticized because it lacks power against the alternative of "cointegration" and "cointegration subject to a structural break." The results from the standard cointegration test in conjunction with those from the G&H procedure will help distinguish between these two alternative hypotheses.

The results of the Engle-Granger two-step cointegration test are provided in Table I. There is no evidence of cointegration between [m, y, r] for any of the money measures at the 10 percent significance level or better. The results did not depend on whether the six-month commercial paper rate or the Aaa bond rate was used. However, as discussed in section III, the results may be masking mask·ing
n.
1. The concealment or the screening of one sensory process or sensation by another.

2. An opaque covering used to camouflage the metal parts of a prosthesis.
a significant one-time structural break. We examine this possibility next.
```Table I. Engle-Granger Two-step Cointegration Tests: 1961:Q2-90:Q4

[[Epsilon].sub.t] = [Eta]  + [Rho][[Epsilon].sub.t-1] +
[summation][[Theta].sub.i]
[[Delta].sub.[[Epsilon].sub.t-i]]
+ [Delta]time + [u.sub.t]

Specification                             Six-month Commercial
Paper Rate

[[Epsilon].sub.t] = m - [Alpha]            Q(12)     DF/ADF   [Rho]
- [Beta]y + [Gamma]r

M1                                         29.49(*)   -2.33   0.92
M2                                         18.69(*)   -2.49   0.84
Credit                                     24.02(*)   -1.79   0.95

Specification                             Aaa Corporate Bond Rate

[[Epsilon].sub.t] = m - [Alpha]           Q(12)    DF/ADF     [Rho]
- [Beta]y + [Gamma]r

M1                                         8.67     -1.97      0.94
M2                                        18.49     -2.26      0.91
Credit                                     7.18     -1.99      0.96
```

Note: The critical value for the Box-Pierce Q statistic is 18.55 at the 10 percent marginal significance level. When the Q(12) statistic is significant, the augmented Dickey-Fuller test statistic (using four lags) is reported. MacKinnon's critical values are -4.12 (5 percent level) and -3.83 (10 percent level).

(*) indicates significance at the 10 percent marginal significance level.

Panel A of Table II presents the results for the G&H procedure for the estimated sample period 1961:Q2-90:Q4 where the six-month commercial paper rate is used. Results for M1, M2, and credit are reported. We report the test statistics for cointegration at the estimated breakpoint, for comparison, the test statistics achieved for pre-selected breakpoints. The values for [Rho] from equation (2) are also reported. No evidence of cointegration is reported for M1, M2, or credit using the G&H procedure. The results suggest that there is no long run relationship between money, income, and the six-month commercial paper rate.

Table II. Gregory and Hansen Specification for a Cointegrating Money, Income, Interest Rate Relationship 1961:Q2-90:Q4
```
[[Epsilon].sub.t] = [Eta]  + [Rho][[Epsilon].sub.t-1] +
[summation][[Theta].sub.i]
[[Delta].sub.[[Epsilon].sub.t-i]]
+ [Delta]time + [u.sub.t]

Null Hypothesis: [Rho] = 1.0

[Epsilon] = m - [Alpha] - [Alpha]dum
- [[Beta].sub.1]y                    IMPOSED
Estimated
- [[Beta].sub.2]ydum                TIMEBREAK
Breakpoint
+ [[Gamma].sub.1]r
Estimated      Test
+ [[Gamma].sub.2]rdum           71:Q3     73:Q2

Panel A: Money Demand with 6-month Commercial Paper Rate

M1                                          -3.39    -3.42
([Rho])                                     (0.86)   (0.84)
M2                                          -2.84    -2.76
([Rho])                                     (0.80)   (0.81)
Credit                                      -2.64    -3.38
([Rho])                                     (0.86)   (0.83)

[Epsilon] = m - [Alpha] - [Alpha]dum
- [[Beta].sub.1]y                   IMPOSED
- [[Beta].sub.2]ydum               TIMEBREAK
+ [[Gamma].sub.1]r
+ [[Gamma].sub.2]rdum            79:Q4     80:Q1

Panel A: Money Demand with 6-month  Commercial Paper Rate

M1                                          -2.94      -3.10
([Rho])                                     (0.86)     (0.89)
M2                                          -2.78      -2.78
([Rho])                                     (0.78)     (0.78)
Credit                                      -4.46      -4.31
([Rho])                                     (0.67)     (0.68)

[Epsilon] = m - [Alpha] - [Alpha]dum
- [[Beta].sub.1]y                            Estimated
- [[Beta].sub.2]ydum                         Breakpoint
+ [[Gamma].sub.1]r             Estimated     Test
+ [[Gamma].sub.2]rdum          Breakpoint    Statistic

Panel A: Money Demand with 6-month Commercial Paper Rate

M1                                         1975:Q2        -4.42
([Rho])                                                   (0.71)
M2                                         1990:Q1        -3.28
([Rho])                                                   (0.77)
Credit                                     1976:Q4        -5.18
([Rho])                                                   (0.58)

[Epsilon] = m - [Alpha] - [Alpha]dum
- [[Beta].sub.1]y                    IMPOSED
Estimated
- [[Beta].sub.2]ydum                TIMEBREAK
Breakpoint
+ [[Gamma].sub.1]r
Estimated      Test
+ [[Gamma].sub.2]rdum           71:Q3     73:Q2

Panel B: Money Demand with Aaa Bond Rate

M1                                          -2.82    -3.80
([Rho])                                     (0.89)   (0.82)
M2                                          -2.87    -2.48
([Rho])                                     (0.85)   (0.89)
Credit                                      -2.58    -3.10
([Rho])                                     (0.89)   (0.87)

[Epsilon] = m - [Alpha] - [Alpha]dum
- [[Beta].sub.1]y                   IMPOSED
- [[Beta].sub.2]ydum               TIMEBREAK
+ [[Gamma].sub.1]r
+ [[Gamma].sub.2]rdum            79:Q4     80:Q1

Panel B: Money Demand with Aaa Bond Rate

M1                                          -2.93      -2.07
([Rho])                                     (0.89)     (0.93)
M2                                          -2.71      -3.15
([Rho])                                     (0.88)     (0.78)
Credit                                      -3.71      -5.86(*)
([Rho])                                     (0.49)     (0.53)

[Epsilon] = m - [Alpha] - [Alpha]dum
- [[Beta].sub.1]y                            Estimated
- [[Beta].sub.2]ydum                         Breakpoint
+ [[Gamma].sub.1]r             Estimated     Test
+ [[Gamma].sub.2]rdum          Breakpoint    Statistic

Panel B: Money Demand with Aaa Bond Rate

M1                                          1975:Q4        -4.26
([Rho])                                                    (0.62)
M2                                          1981:Q2        -4.11
([Rho])                                                    (0.67)
Credit                                      1980:Q1        -5.86(*)
([Rho])                                                    (0.53)
```

Note: The critical values are -5.50 at the 5 percent significance level and -5.23 at the 10 percent significance level. See Gregory and Hansen [6, Table 1B].

(*) indicates significance at the 5 percent level.

We examine the robustness of the results from equation (3) by using an alternative interest rate measure, the Aaa corporate bond rate. These results are presented in Panel B of Table II. In this case, we find one instance of cointegration using the G&H procedure. There is evidence of a break at 1980:Q1 that is significant for reestablishing a stable relationship between credit, income, and the Aaa bond rate. This breakdate corresponds to the passage of the Monetary Control Act which began the phaseout phase·out
n.
of interest rate constraints CONSTRAINTS - A language for solving constraints using value inference.

["CONSTRAINTS: A Language for Expressing Almost-Hierarchical Descriptions", G.J. Sussman et al, Artif Intell 14(1):1-39 (Aug 1980)].
and expanded both the sources and uses of funds. The date of the breakpoint also comes one quarter after the Fed change in operating procedure to targeting monetary aggregates. Lags in the reaction to the policy or lags in policy implementation may explain the timing of this breakpoint. The endogenous estimation procedure also picks out this date as the candidate affording the most power to the alternative of "stationary about a trend" with a one-time break. The finding is reassuring re·as·sure
tr.v. re·as·sured, re·as·sur·ing, re·as·sures
1. To restore confidence to.

2. To assure again.

3. To reinsure.
since the endogenous estimation procedure produces a breakdate that corresponds to a recognizable historical event.

None of the other pre-selected breakpoints: the closing of the gold window, the first oil price shock, or the change in Fed operating procedure to targeting monetary aggregates were found to be important in reestablishing a stable relationship for any of the money measures with income and the six-month commercial paper rate or the Aaa corporate bond rate when the G&H procedure is used.

Table III presents the results for the error-correction model of equation (4). Only results from the endogenous estimation procedure are presented. Reported are the breakdates at which the test statistic on [Delta] is maximized in absolute value. Panel A presents the results using the six-month commercial paper rate; Panel B presents the results using the Aaa bond rate. There is tentative evidence that M1 is cointegrated with income and the six-month commercial paper rate when account of a structural break is taken at 1975:Q2. The result should be interpreted with caution since the critical value for [Delta] has not been established for a higher-variable system. A lower bound of -4.71 for the critical value, however, is taken from MacKinnon [12] for a six-variable system. A comparison of the maximized breakdate in Table II and Table III for M1 shows that the date selected by the error correction model is the same as that selected by the cointegrating regression. In no other cases did the test statistic on [Delta] lead to rejection of the null hypothesis of "no cointegration."(8)
```Table III. Error Correction Model with Dummy Variables

[Delta]m = [[Alpha]'.sub.1] + [[Alpha]'.sub.2] +
[[Beta].sub.1][Delta]y + [[Beta].sub.2][Delta]ydum
+ [[Gamma]'sub.1][Delta]r + [[Gamma]'sub.2][Delta]rdum
+ [[Delta].sub.[[Epsilon].sub.-1]] + [[summation].sub.i]
= 1 [[Theta]'.sub.i][Delta]m + u

Panel A
Six-month Commercial Paper Rate

M1          M2            Credit
[[Alpha].sub.1]       0.002        0.012(**)     0.004(**)
[[Alpha].sub.2]      -0.915       -0.673        -2.402(**)
[[Beta].sub.1]        0.217(*)     0.185(**)     0.183(**)
[[Beta].sub.2]        0.117        0.091         0.304(**)
[[Gamma].sub.1]      -0.000       -0.001(**)    -0.003
[[Gamma].sub.2]      -0.005(**)   -0.005(**)    -0.003(**)
[Delta]              -0.163       -0.177        -0.113
[t.sub.[Delta]=0]    -5.382       -4.145        -3.667
break(a)             1975:Q2      1980:Q3       1981:Q4
#lags                      2            1             4

Panel B
Aaa Bond Rate

M1         M2          Credit
[[Alpha].sub.1]      -0.004      0.005       0.001
[[Alpha].sub.2]      -0.661      0.270      -1.153
[[Beta].sub.1]        0.290(**)  0.166       0.221(**)
[[Beta].sub.2]       -0.072     -0.231       0.150
[[Gamma].sub.1]      -0.000     -0.337       0.000
[[Gamma].sub.2]      -0.010(**) -0.005(*)   -0.004(**)
[Delta]              -0.105     -0.053      -0.130
[t.sub.[Delta]=0]    -3.246     -1.105      -3.729
break(a)             11975:Q1    1982:Q1     1981:Q4
#lags                       2          1           4
```

Note: The critical values [t.sub.[Delta]=0] for a six-variable system are -4.71 at the 5 percent significance level and -4.42 at the 10 percent significance level. The critical values are taken from MacKinnon [12] for m = 6 variable system (excluding the intercept). The critical values may be different since the error correction model is a seven variable system (excluding the intercept and lags of [Delta]m) and an endogenous estimation procedure is used.

(*) indicates significance at the 5 percent level.

(**) indicates significance at the 1 percent level.

(a.) The row presents the breakdate at which [t.sub.[Delta]] is at its maximum (absolute) value.

Since M1 satisfies the criteria for cointegration, we can draw inferences about the point estimates. For M1, the dummy variable on the six-month commercial paper rate is significant, negative, and small suggesting a low interest elasticity of money demand. The coefficient on income is significant and positive but rather small. The test statistic for [[Beta].sub.1] = 1 is -7.06 which means that short run unitary unitary

pertaining to a single object or individual.
income elasticity is rejected. The value of [Delta] implies an adjustment parameter (1) Any value passed to a program by the user or by another program in order to customize the program for a particular purpose. A parameter may be anything; for example, a file name, a coordinate, a range of values, a money amount or a code of some kind.  of 0.84 which implies a half-life half-life, measure of the average lifetime of a radioactive substance (see radioactivity) or an unstable subatomic particle. One half-life is the time required for one half of any given quantity of the substance to decay.  of 4 quarters.(9) This means that in one year, only half of money demand's deviation DEVIATION, insurance, contracts. A voluntary departure, without necessity, or any reasonable cause, from the regular and usual course of the voyage insured.
2.
from equilibrium has been removed.

The results from both the cointegrating regression and the error correction model for M2 are particularly surprising since M2, being one of the broader monetary aggregates, has recently become the focal point focal point
n.
See focus.
of policy. These results suggest that M2 retains no stable long run relationship with income and the interest rate over time.(10) Thus, a policy based A decision made by any software application that is based on the policy (rules and regulations) of the organization. See policy and COPS.  on an M2 target may be misguided.

V. Summary and Conclusions

This study incorporates the use of a structural break in cointegration tests of the long-run relationship between money, income, and the interest rate. Breakpoints were treated two ways: they were pre-selected and thus treated as an exogenous event; and they were estimated and treated endogenously. In one instance, the endogenous treatment produced a breakdate which corresponded to a well-known event and which allowed for rejection of the null hypothesis of "no cointegration." When a structural break between money, income, and the Aaa bond rate is considered, we find evidence of cointegration when money is measured as credit. The breakpoint that maximized rejection of "no cointegration" occurred at 1980:Q1--the time of the passage of the Monetary Control Act and one quarter after the change in Fed operating procedure. This finding may be interpreted as evidence that credit demand is stable after taking account of a structural break. While the finding coincides with the date at which the Monetary Control Act was passed, the finding may also emerge due to lags in the reaction to or implementation of the Fed's change in operating procedure. We also find tentative evidence that M1 is cointegrated with income and the six-month commercial paper rate when a structural break at 1975:Q2 is permitted. The breakdate is very close to the time at which the "case of the missing (M1) money" arose.

The findings may be considered strong in light of the short historical span of data that is used. In general, cointegration becomes more difficult to detect as the data series is shortened short·en
v. short·ened, short·en·ing, short·ens

v.tr.
1. To make short or shorter.

2.
. However, this also means that our findings for M2 must be interpreted with caution. A failure to detect cointegration with income and the interest rate for M2 does not necessarily mean that a cointegrating relationship does not exist; the data set may be too small and/or the long run adjustment parameter too slow to discern dis·cern
v. dis·cerned, dis·cern·ing, dis·cerns

v.tr.
1. To perceive with the eyes or intellect; detect.

2. To recognize or comprehend mentally.

3.
an equilibrium relationship between the variables. The difference in results across M1, M2, and credit suggest that the assets included in M2 but not M1 may impart a non-stationary behavior to M2 demand with respect to a short-term interest rate; also the assets included in credit but not M2 may impart a stationary behavior to credit demand with respect to a long-term Long-term

Three or more years. In the context of accounting, more than 1 year.

long-term

1. Of or relating to a gain or loss in the value of a security that has been held over a specific length of time. Compare short-term.
interest rate. Thus, use of a medium-term interest rate and/or careful analysis of the components of M2 may be revealing.

Some general conclusions may be drawn about the money-income-interest-rate relationship. First, evidence of cointegration between money, income, and the interest rate depends on the money measure used. We identified a cointegrating relationship for credit and for M1 but not for M2.

Second, our results indicate that the relationship between money, income, and the interest rate may be sensitive to the interest rate used. Whereas we found evidence that credit was cointegrated with income and the Aaa bond rate, the results were overturned when the six-month commercial paper rate was used and vice-versa for M1. It is not surprising that credit, which is based on a broad money measure that includes time deposits, is cointegrated with a long-term interest rate and not with a shorter-term rate and that M1 which is a narrower money measure is cointegrated with a short-term interest rate.

Third, the estimated breakpoints that "maximize" rejection of the null hypothesis of "no cointegration" may not necessarily correspond to a pre-selected breakpoint. This may be trouble-some to some researchers since there may be no easy economic interpretation for the date selected by the search procedure. However, in our study, the endogenous estimation procedure produced one instance in which the estimated breakpoint allowed for rejection of the null hypothesis of "no cointegration" and corresponded to a reasonable date. We found a significant breakpoint at 1980:Q1 which coincides with the deregulation Deregulation

The reduction or elimination of government power in a particular industry, usually enacted to create more competition within the industry.

Notes:
Traditional areas that have been deregulated are the telephone and airline industries.
of the banking industry and arises one quarter after the Fed change in operating procedure to target monetary aggregates. For M1, the estimated breakpoint is close to the time during which the case of the missing (M1) money occurred.

There are several policy implications that emerge from our findings. Since no evidence was found that M2 was cointegrated with income and an interest rate, i.e., M2 demand is not stable, we question the usefulness of M2 as a policy instrument. However, our finding that credit demand is stationary means that credit could play a more important role in the conduct of monetary policy. Since credit is such a broad measure, it may not be useful as a target variable, but perhaps it could be relied upon to provide the Fed important, accurate information on the state of the economy. The authors would like to thank, without implicating im·pli·cate
tr.v. im·pli·cat·ed, im·pli·cat·ing, im·pli·cates
1. To involve or connect intimately or incriminatingly: evidence that implicates others in the plot.

2.
, Stan STAN Stanchion
STAN Stärke- und Ausrüstungsnachweis (German)
Stan Standard Man (human patient simulator)
STAN SEMCIP Technical Assistance Network
STAN System Trace Audit Number
STAN Star Trek Area Network
Black, Michael Ferrantino, Pierre Siklos, Myles Wallace Wal·lace , Alfred Russel 1823-1913.

British naturalist who developed a concept of evolution that paralleled the work of Charles Darwin.
, Mark Wohar, and three anonymous referees. Any errors that remain are the authors's responsibility.

(1.) Perron's [16] work applies structural break methodology to a univariate univariate adjective Determined, produced, or caused by only one variable  time series, but it has direct bearing for a cointegrating regression residual. (2.) We are grateful to Friedman and Kuttner for making their dataset available to us.

(3.) Prior to testing for cointegration, m, y, and r tested for unit root behavior using the augmented Dickey-Fuller (ADF (1) (Application Development Facility) An IBM programmer-oriented mainframe application generator that runs under IMS.

(2) (Automatic Document Feeder) A paper stacker that feeds one sheet of paper at a time into the unit.
) test. Unit root behavior could not be rejected for any of the series.

(4.) In additive outlier model, the dummy variable takes on the value of zero everywhere except at TB.

(5.) The dummy variables thus become a series of zero everywhere except at the breakdate where the dummy variable takes on the value of one. The cointegrating regression with the dummy variables is thus transformed from an innovation outlier model to an additive model.

(6.) We applied an iterative it·er·a·tive
1. Characterized by or involving repetition, recurrence, reiteration, or repetitiousness.

2. Grammar Frequentative.

Noun 1.
procedure to determine the lag length necessary to insure that u us white noise.

(7.) See Schwert [18] and Engle and Yoo [2] for a discussion of the sensibility sensibility /sen·si·bil·i·ty/ (sen?si-bil´i-te) susceptibility of feeling; ability to feel or perceive.

deep sensibility
if including a time trend.

(8.) It is puzzling puz·zle
v. puz·zled, puz·zling, puz·zles

v.tr.
1. To baffle or confuse mentally by presenting or being a difficult problem or matter.

2.
that the more powerful error correction test for cointegration does not reject "no cointegration" when the G&H method does.

(9.) The adjustment parameter for M1 from the cointegrating regression is estimated to be 0.86 which also implies a half life of approximately four quarters.

(10.) In contrast, Siklos [19] finds cointegration for M2, per capita [Latin, By the heads or polls.] A term used in the Descent and Distribution of the estate of one who dies without a will. It means to share and share alike according to the number of individuals.  permanent income, and a short-term interest rate for the U.S. for 1880-1986.

References

[1.] Engle, Robert F. and C. W. J. Granger, "Cointegration and Error Correction: Representation, Estimation, and Testing." Econometrica, March 1987, 251-76.

[2.] -- and Sam (1) (Security Accounts Manager) The part of Windows NT that manages the database of usernames, passwords and permissions. A SAM resides in each server as well as in each domain controller. See PDC and trust relationship.  Yoo. "Forecasting and Testing in Co-integrated Systems," in Long-run Economic Relationships, edited by R. F. Engle and C. W. J. Granger. New York New York, state, United States
New York, Middle Atlantic state of the United States. It is bordered by Vermont, Massachusetts, Connecticut, and the Atlantic Ocean (E), New Jersey and Pennsylvania (S), Lakes Erie and Ontario and the Canadian province of
: Oxford University Press, 1991, pp. 113-30.

[3.] Friedman, Benjamin M., "Lessons on Monetary Policy from the 1980s." Journal of Economic Perspectives, Summer 1988, 51-72.

[4.] -- and Kenneth N. Kuttner, "Money, Income, Prices, and Interest Rates." American Economic Review, June 1992, 472-92.

[5.] Goldfeld, Stephen M., "The Case of the Missing Money." Brookings Papers on Economic Activity, 1976. 683-730.

[6.] Gregory, Allan W. and Bruce Bruce, Scottish royal family descended from an 11th-century Norman duke, Robert de Brus. He aided William I in his conquest of England (1066) and was given lands in England.  E. Hansen. "Residual-based Tests for Cointegration in Models with Regime Shifts." Rochester Center for Economic Research, Working Paper No. 335, November 1992.

[7.] Hafer, R. W. and Dennis W. Jansen, "The Demand for Money in the United States United States, officially United States of America, republic (2005 est. pop. 295,734,000), 3,539,227 sq mi (9,166,598 sq km), North America. The United States is the world's third largest country in population and the fourth largest country in area. : Evidence from Cointegration Tests." Journal of Money, Credit, and Banking, May 1991, 155-68.

[8.] Hetzel, Robert L. and Yash P. Mehra, "The Behavior of Money Demand in the 1980s." Journal of Money, Credit, and Banking, November 1989, 455-63.

[9.] Hoffman, Dennis L. and Robert H. Rasche, "Long-run Income and Interest Elasticities of Money Demand in the United States." The Review of Economics and Statistics, November 1991, 665-74.

[10.] Johansen, Soren, and Katarina Juselius, "Maximum Likelihood Estimation and Inference (logic) inference - The logical process by which new facts are derived from known facts by the application of inference rules.

on Cointegration--With Application to the Demand for Money." Oxford Bulletin of Economics and Statistics, May 1990, 169-210.

[11.] Kremers, Jeroen, Neil Ericsson, and Juan Dolado, "The Power of Cointegration Tests." Oxford Bulletin of Economics and Statistics, August 1992, 325-48.

[12.] MacKinnon, James G. "Critical Values for Cointegration Tests," in Long-run Economic Relationships, edited by R. F. Engle and C. W. J. Granger. New York: Oxford University Press, 1991, pp. 267-76.

[13.] Mehra, Yash P., "In Search of a Stable, Short-run M1 Demand Function." Economic Review of the Federal Reserve Bank of Richmond The Federal Reserve Bank of Richmond is the headquarters of the Fifth District of the Federal Reserve located in Richmond, Virginia . It covers the District of Columbia, Maryland, Virginia, North Carolina, South Carolina and most of West Virginia. , May/June 1992, 9-23.

[14.] Miller, Stephen M., "Monetary Dynamics: An Application of Cointegration and Error-Correction Modeling." Journal of Money, Credit, and Banking. May 1991, 139-54.

[15.] Mills, Terence C. Time Series Techniques for Economists New York: Cambridge University Press Cambridge University Press (known colloquially as CUP) is a publisher given a Royal Charter by Henry VIII in 1534, and one of the two privileged presses (the other being Oxford University Press). , 1992.

[16.] Perron, Pierre, "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis." Econometrica, November 1989, 1361-1401.

[17.] Poole, William, "Optimal Use of Monetary Policy Instruments in a Simple Stochastic By guesswork; by chance; using or containing random values.

stochastic - probabilistic
Macro Model." Quarter Journal of Economics, May 1970, 197-216.

[18.] Schwert, William, "Effects of Model Specification on Tests for Unit Roots in Macroeconomic mac·ro·ec·o·nom·ics
n. (used with a sing. verb)
The study of the overall aspects and workings of a national economy, such as income, output, and the interrelationship among diverse economic sectors.
Data." Journal of Monetary Economics, July 1987, 73-103.

[19.] Siklos, Pierre, "Income Velocity and Institutional Change: Some New Time Series Evidence, 1870-1986." Journal of Money, Credit, and Banking, August 1993, 377-92.

[20.] Zivot, Eric and Donald W. K. Andrews, "Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit Root Hypothesis." Journal of
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