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The Phillips Curve: Evidence of a “lady or tiger dilemma”
The QuarterlyReviewof Economicsand Face, Vol. 34, No. 4, Winter, 1994, pages 333-345 Copylight 0 1994 Trustees of the Universityof Illinois AU rightsof reproductionin auy form resewed. ISSN 003S5797
The Phillips Curve: Evidence of a “Lady or Tiger Dilemma”
HEDAYEH SAMAVATI, DAVID A. DILTS and CLARENCE R. DEITSCH Indiana University and Ball State University
This study examines the relation between inflation and unemployment. Grange-r Causality was applied to U.S. data since the end of the Vietnam War. The results support the conclusion that there is a unidirectional causation ranningfiom inflation to unemployment. This result has important poliq and research implications. The natural rate hypothesis is not su@n-ted j&r the timeperiod examined. It cannot be determined, howeoer, whether the slope coefjcitmt for the Phillips Curve characteristic of this period is positive or negative. This result, together with the existence of policy lags, implies that there is inherent risk in any policy persniption. Furtb, the results suj@rt Irving Fisher’s specajication of regression models used to estimate posited relationsbetween inflation and unemployment.
Among the most heated of the debates in macroeconomic theory has been the controversy surrounding the existence of the Phillips or, perhaps, the Fisher curve. Irving Fisher (1926) and Phillips (1958) found that there was a statistical association between a real and a nominal aggregate economic variable. Fisher observed a correlation between price inflation and unemployment in the United States and Phillips discovered an association between nominal wage inflation and unemployment rates in the United Kingdom. Perhaps the most important
reason that the Phillips Curve relation stirred so
much controversy was that it purported to explain an observed relation between two important policy variables. The Phillips Curve relation provided policy-makers with a “cruel choice” (unemployment or inflation). The choice was one that was also easily understood by politicians and the general public, hence its popularity in certain circles. Subsequendy, it was argued that if inflation is fully anticipated then the Phillips Curve becomes vertical at the natural rate of unemployment. On the other hand, in the expectations-augmented Phillips Curve, if price changes are not fully anticipated then it is possible to observe a non-vertical short-run Phillips Curve (Friedman, 1968; Lucas, 1972a, 1972b, 1973; Phelps, 1967). Friedman (1977) discussed several situations in which a non-vertical Phillips Curve may be observed. Friedman postulated several circumstances in which a 333
334
QUARTERLY REVIEW OF ECONOMICS AND FINANCE
tradeoff
between unemployment
noise is introduced Friedman
and inflation could be observed, primarily when
into the price system by unanticipated
explained
shocks, such as inflation.
that in longer periods an observed negatively sloped Phillips
Curve may be due to structural transition in the economy, political unrest, or uncontrolled inflation. Price stability, of course is the best solution, but inflation if anticipated should eliminate the monetary sources of an observed Phillips Curve. If, on the other hand, the inflation rate is permitted to accelerate and decelerate in a random fashion, then the market pricing mechanisms creating bouts of unemployment.
result not in efficiency, but in uncertainty
Under these conditions,
tively sloped Phillips Curve if the government
one may observe a posi-
attempts to utilize the “cruel choice”
option to spend itself out of recession and if those recessionary forces are insensitive to monetary or fiscal policies. As Friedman stated, “. . . a positively sloped Phillips Curve over somewhat longer periods may occur as a transitional
phenomenon
that will
disappear as economic agents adjust not only their expectations but their institutional and political arrangements
to a new reality.” Policy makers face the possibility of the
lady or the tiger dilemma.’ A negatively sloped Phillips Curve rewards monetary policy advocates (the lady) during recession, but on the other hand, a non-negatively sloped Phillips Curve rewards the tiger with the policy maker foolish enough to attempt a reduction in unemployment
with monetary policy. Additionally, research has demon-
strated that the exploitation
of the short-run expectations
augmented Phillips Curve
to gain political popularity may not be a worthwhile exercise (Smyth, Washburn and Dua, 1989). Other macroeconomists For example,
according
have rejected the existence of the Phillips Curve relation.
to proponents
supply shocks, mainly technological
of the real business cycle theory, aggregate
disturbances and/or intertemporal
of leisure for income, are responsible for output (employment)
substitution
fluctuations. The real
business cycle theorists dismiss the short-run Phillips Curve relation because, they argue, nominal variables, such as money, cannot affect real variables such as output. Consequently, real business cycle theorists argue that the efficacy of monetary policy in controlling
the unemployment
rate is questionable
(e.g., Kydland and Prescott,
1982; Long and Plosser, 1983; King, Plosser and Rebel0 1988a, 1988b). The purpose of this study is to examine the relation between the rates of inflation and unemployment
to determine
whether
there is evidence
of a causal relation
between these variables. In other words, does the available evidence support the hypothesis of a non-vertical Phillips Curve for the U.S. economy since the end of the Vietnam War? Granger causality is applied to ascertain whether there is evidence of a causal relation between inflation and unemployment. will have implications “cruel choice”, determining
for economic
The evidence presented here
policy and the possibility of the existence of the
the trade-off between inflation
and unemployment.
Furthermore,
the causal relation, if any, between inflation and unemployment
an implication for the specification
of econometric
rates has
models. There is a controversy as
THE PHILLIPS CURVE to which variable should be specified as the independent Phillips controversy (Friedman,
335
variable; the Fisher versus
1975).
METHOD AND DATA Clive Granger (1969) proposed a method to obtain statistical evidence of the direction ofcausality between economic variables. Granger’s causality test2 is applied to monthly price and unemployment
data in the United States for the period January
1974
through April 1990. The monthly unemployment and Consumer Price Index (CPI) data were drawn from the standard published sources. Both series were seasonally adjusted at the source. Granger (1969) defined “causality” in terms of a forecastability criterion. Pierce and Haugh (1977) described the criterion as follows: “a variable X causes another variable Y, with respect to a universe of information set that includes X andY, if present Y can be better predicted by using past values of X than by not doing so, all other information contained in the past of the universe being used in either case”. In this context, for example, if changes in prices improve the accuracy of predictions of the unemployment
rate, and the unemployment
rate fails to improve the accuracy of
predictions in changes in prices, then the evidence is consistent with the conclusion that there is a unidirectional causality from the inflation rate to the rate of unemployment. The common test procedures used to detect Granger causality in the literature base their conclusions on tests of significance of model parameters (tests of how well the model fits the in-sample data). In contrast, in this study, causality findings come from the comparison of forecasts from different forecasting models. As Granger stated (1980, p. 348)) “It is generally accepted that to find a model that apparently fits better than another is much easier than to fit one that forecasts better.” Thus, where the original Granger causality definition does require evidence of improved forecasts, the common methods of Granger causality testing are tests of goodness of fit. In the approach used here, the general guidelines suggested by Granger (1980) are followed. More specifically,
to make inferences
about causal orderings,
forecast
errors are
analyzed in a manner similar to that suggested by Ashley, Granger and Schmalensee (1980). This procedure is faithful to the original definition of Granger causality in that hypotheses are tested on the basis of out-of-sample forecasting performance. This method “ . . . does prevent evidence for spurious causation occurring because of data mining” (Granger 1980, p. 349). To test for differences in “post-sample” forecasting ability, the sample was partitioned into a modeling period (January of 1974 through December of 1986) and a forecast evaluation period consisting of forty observations (January of 1987 through April of 1990). To test whether changes in prices (inflation) are causally prior to the rate of unemployment, forty one-step ahead forecasts of the unemployment rate are generated from both univariate and bivariate ARMA (Autoregression Moving Aver-
336
QUARTERLY REVIEW OF ECONOMICS AND FINANCE
age) models. If inflation causes the unemployment models of unemployment mation)
will generate
(containing
rate, then the bivariate forecasting
both the inflation and unemployment
infor-
superior forecasts to those from the univariate forecasting
models of unemployment.
For each information
set, an ARMA model was estimateds
using the data through period t. The estimated model was used to obtain the forecast
fel. Next,
the data was updated by one observation and an ARMA model was fitted to
the data through period (t + 1). Then, the new model was used to produce the forecast
fH2.Repeating
the procedure thirty-eight times resulted in forty one-step ahead forecasts of the rate of unemployment for each information set. The forecast errors
were used to define new variables and to estimate the simple regression models as proposed by Ashley et al. (1980). The same procedure was employed to test whether unemployment causes inflation. To determine the superior set of forecasts, one can compare the mean square error (MSE) of the two forecast sets. However, no direct test for the significance of differences in forecast MSEs is available because forecast errors produced by models that contain several variables in common are likely to be cross-correlated, and autocorrelated
(Ashley et al., 1980).
The following indirect procedure to evaluate forecast accuracy was developed by Ashley et al. (1980). Let el be the set of the forecast errors of a model that uses the historical values of one variable, and let q be the set of the forecast errors of the bivariate model. It can be shown that: MSE(er) - MSE(a2) = [s*(4) -
s2(e2)l + [m(ed2-m(d21,
(1)
where s*( ei, and m( e,) are the sample variance and mean of the ei series, respectively. In addition, assume that: At=erl-~rand&=~,+~Pthen: MSE(el) - MSE(%) = [chA,,Ul
+ [Ned2 - m(ed21,
(2)
where c& and v& are the sample covariance and variance over the forecast period. As a test of whether MSE ( ei) is significantly greater than MSE (9) one can estimate the following ordinary least squares equation: AC= Pi + P2& - m(Ql
+ ut
(3)
then: t3t = m(el) -
m(e2)
(4)
/v&(&)
(5)
and: fis = &(A,,&)
Ifm(ei) and m(s) are both positive, and if p1 and p2 are significantly greater than zero, this implies that MSE(4) is significantly greater than MSE( q). In other words, if the forecasts of the bivariate models, (i.e., including both unemployment and
THE PHTLLWS CURVE
337
inflation rates) perform better than those of the univariate models, the null hypothesis, pr = p2 = 0, can be rejected in favor of the alternative that both are nonnegative and at least one coefficient is positive. If both coefficients are positive, an F-test of the null hypothesis that both parameters are zero can be performed. estimated coefficients judged
If one of the two
is significantly negative, then the bivariate models cannot be
to have given rise to better forecasts. If one coefficient
is not significantly
negative, a one-tailed &test on the other estimated parameter can be used.
THE ANALYSIS The plots of the unemployment
rate (UR) and monthly percentage inflation rate (IR)
multiplied by 10 appear in Figures 1 and 2. Preliminary data analysis, examination partial autocorrelation
of data plots, sample autocorrelation
and
functions, indicate that neither series were integrated proc-
esses.4 However, formal statistical tests of stationarity for both series were performed. One problem with analyzing nonstationary data is that the usual statistical properties of first and second sample moments do not hold. For example, those sample moments do not converge to their population parameters as sample size increases (Philips, 1985; Hendry, 1986). In addition, Dickey, Bell and Miller (1986) showed that the forecasts from the stationary model converge to the series mean and the forecast standard errors converge to the series standard deviation. However, the forecasts from the nonstation-
Time Figure 1.
338
QUARTERLY REVIEW OF ECONOMICS AND FINANCE
Time Figure 2.
ary model converge to a number different from the series mean and the forecast standard errors diverge to t m. Given the difficulties that arise from analyzing nonstationary data, one may conclude that examining differences of the data is a safe approach. Several authors have warned against this approach. For example, Hendry (1986) and Granger (198’7, 1988) argue that differencing economic time series data may result in the loss of all information about potential long-run relationships. The models will generally be mis-specified resulting in poor forecasts. In addition, if the two series are integrated of order one (have unit roots), they may be co-integrated and need to be analyzed using error correction models (Granger 1981, 1983, 1986, 1987, 1988; Engle and Granger 1987). Hakkio and Rush (1989) show that taking first differences of a bivariate relationship in order to induce stationarity may result in omitted variables bias, if the two variables are cointegrated. Because the decision of whether to difference
has implications for forecasts and
models, the formal statistical tests for unit roots are required. The results of those tests are presented in the following section. Empirical Results of Non-stationarity Tests
Tables 1 and 2 report results of non-stationarity tests for both the inflation rate (IR) and the unemployment rate (UR) series. Conventional Dickey-Fuller (DF) test results are presented in Table 1 and the results of the augmented Dickey-Fuller (ADF) tests appear in Table 2.
THE PHILLIP
CURVE
339
Table 1. DICKJ%FULLER TEST RE!XJLTs: NO,LAGS A P
AK A&
0.138 (0.031) 0.112 (0.087)
AURt
Std. JIrror of Estimate
d&l>
-0.271 (0.049) -0.033 (0.012)
rh Tfi
DW-D
0.234
-5.55*
2.18
0.230
-2.75
1.66
Note: Regressions are of the form AY, = p + (p,, - l)Y,_t + residual. ‘Standard emm” are in parentheses below coefficients. Sample size is 195 in both cases. The usual t statistic for the coefficient on Y&t is the ‘f,, statistic and can be read dire&y from the computer printout. Tbe statistic Q tests the null hypothesis (p-1) = 0 qamst the alternative (p-l) < 0. The rejection region ia the set of values of r,, less than -9.46 (-2.58) for a test of size 0.01 (0.10). Critical values of z,, are qxwted from percentiles for ‘1,, stati%ics table (Dickey 1976, pg. 53). *means significantly **means significantly
negative at the one percent level. negative at the ten percent
level.
Because several authors (Dickey et al. 1986; Nelson and Rang 1981, 1984; Rang 1985) waned against preliminary removal of linear or non-linear trend, none of the regressions in Tables 1 and 2 include a time trend. The hypothesis of non-stationarity of the inflation rate is rejected at the one-percent level using both DF and ADF tests in Tables 1 and 2 respectively. The similar hypotheses regarding the UR are rejected at the ten-percent level. Given other evidence, it is concluded that both series are stationary. Thus, the series were used to estimate the univariate and bivariate forecasting models that generate forecasts to be used in Granger causality tests. The estimated univariate forecasting models for the inflation and unemployment rates over the period January 1974 through March 1990 are presented in Table 3. Table 4 presents the estimated residual autocorrelations of each model up to 12 lags respectively. Results reported in Table 4 indicate that for both models the residual autocorrelations are insignificant up to lag 12. One can conclude that the estimated univariate
Table 2.
A& AU&
NC&
AUGMENTED
DICKJW-
TEST RESULTS: FOUR LAGS
0.090 -0.184 -0.197 -0.187 -0.071 -0.121 (0.035)(0.058)(0.082)(0.081)(0.078)(0.074) 0.224 -0.031 -0.073 -0.136 -0.155 -0.248 (0.086)(0.012)(0.071)(0.070)(0.070)(0.071) Regressions
are of the form AU, = p + @,,-I )Y,_t + I$,
&AU,,
0.230
-3.15* 2.003 8.023
0.216
-2.64** 2.001 6.998
+ residual.
‘Standard ermrsL are in parentheses below coefficients. Sample size is I91 in both cases. 7be usual t statistic for the coefficient on Y+t isthe~)lstatisdcandcanbereaddirecdyfrom thecompurerprintour.Thesratistic~ thenull hypothesis (p-l) =Oagainstdwaltemate (p-1) < 0. Tbe rejection region is the set ofvalues of4 less than -2.88 (-2.58) for a test ofsize 0.05 (0.10). Critical values are reported from percentiles for ‘T,,statistic table (Dickey 1976, pg. 53). *means significantly “meuls
significandy
negative at the five percent negative at the ten percent
level. level
340
QUARTERLY REVIEW OF ECONOMICS AND FINANCE
Table 3. UNIVARWTE FORECASTING MODELS UNEMPLOYMENT RATES (January 1974-March 1990)
Residual Series
Note:
CNST
I&
1.40 (0.31)
W
0.21 (0.08)
Figures
in parentheses
are standard
Kl
W-1
0.73 (0.05) -
errors.
All
of the
OF INFLATION
coefficients
AND
Std. Error
m-5
-
-
2.32
1.12 (0.03)
-0.15 (0.03)
0.21
are significant
at the one percent
significance
level.
models are “appropriate” and thus can be used to forecast each variable. The estimated bivariate model for the period January 1974 through March 1990 is: IR, = 2.344 + 0.635IR,i (1.080)
- 0.477UR,5
(0.056)
UR,= 0.080 + l.O41UR,i (0.095)
- 0.1621Rfi5 + 0.29UR,5
(0.321)
(0.060)
+ 0.0141R,3 + 0.128UR,3
(0.048)
(0.005)
where values in parentheses matrix is:
(0.329)
- 0.91UR,5
(0.075)
(0.046)
are standard errors and the model’s error covariance
5.073 -.0594
. 0.439
I
Table 5 presents the diagnostic checking for the bivariate model. The Table indicates that auto and cross-correlations between residuals of the bivariate model are not significant up to lag 24 indicating the appropriateness
of the model.
As explained earlier, both univariate and bivariate forecasting models were used to generate one-step ahead forecasts of each variable. Forecast errors were computed and regression models according to Ashley et al. (1980) method were estimated. Table 6 presents the results of the regression models used to test the non-causality hypotheses.
Table
4.
INFLATION Lags
RESIDUAL AUTOCORRELATIONS AND UNEMPLOYMENT MODELS
1
2
ACF
-.lO
-.05
.12
-.Ol
.03
.09
St.E.
.07
.07
.07
.07
.07
.07
.07
ACF
-.08
-.03
.08
-.oo
.07
-.oo
.07
.07
.07
.07
St.E.
.07
.07
3
-.02 .07
4
5
6
7 -.03
FOR 8
THE 9
UNIVARIATE 10
11
12
.09
.16
.14
.12
.07
.07
.08
.08
.08
.05
.04
.03
-.Ol
.07
.07
.07
.07
-.02 .07
-.02
THEPHlLLIPs
Tabb 5.
AUTO AND CROSS-CORRELATIONS
Lags1 through 12 .. .. .. .. .. ..
CURVE
341
BETWEEN RESIDUAL TERMS
.. ..
.. ..
.. ..
.. ..
.. ..
+. . .
., ..
.. ..
.. ..
..
..
..
..
..
..
..
..
.
.. +.
Lags 13 through 24
..
Nde:
..
+.
The approximate + Denma -Denotes Denotes
std. error for the estimated
a value neater
a value less than -Vstd. a nonaignificanr
correlauons
above is l/sqn
(NOBE)
NOBE is the effective number
of oknations.
than P/std. error. error.
value based upon the above crirerion.
Regression Model 1, compares statistically two sets of forecasts of the unemployment rate. One set is based on the bivariate forecasting models of the unemployment rate and the other set on the univariate. Both coefficients are positive and the intercept is significant at the .Ol level. This result implies that forecasts of the bivariate models are superior to those of the univariate ones. In other words, past values of the inflation rate contained some unique information that was useful in predicting the unemployment rate. One may conclude, therefore that inflation “Granger causes” unemployment. Regression Model 2 tests whether forecasts of inflation, using both the unemployment and inflation rate histories are superior to those forecasts based on the history of inflation alone. Model 2 reveals that both the intercept and the slope coefficients are negative and the intercept is significant at the .Ol level. This result implies that the past values of unemployment do not help to improve forecasts of inflation. That is, the unemployment rate does not “Granger cause” the inflation rate. In short, the analysis provides evidence of unidirec tional causality that runs from inflation to the rate of unemployment.
Table 6. REGRESSION CAUSALITY Alternative Hypothesis
RESULTS FOR TESTING GRANGER
Intercept
Slope
Durbii-Watson (d)
(1) Inflation causes Unemployment
0.034
0.025
(8.020)
(1.390)
1.421
(2) Unemployment causes Inflation Note:
Figures in parentheses
-0.283
-0.007
(-5.501)
(-0.522)
are ktatistics.
1.175
342
QUARTERLY REYIEW OF ECONOMICS AND FINANCE
DISCUSSION AND CONCLUSIONS During the period examined, January 1974 to April 1990, the evidence reported in Table 6 suggests that there is a unidirectional to the rate of unemployment.
causal relation from the inflation rate
If, the Phillips Curve were vertical over this sixteen year
period, one should have observed no causality between the unemployment the rate of inflation
rate and
(the natural rate hypothesis, i.e., any rate of inflation can be
associated with the natural rate of unemployment).
The empirical findings reported
here, however, suggest a non-vertical Phillips Curve. Whether anticipated or not, the rate of inflation has, over the period examined, “Granger caused” unemployment. theoretical
and one pragmatic.
specification
This finding has two significant implications,
one
There is also a point to be made concerning
the
of empirical models used to test the Phillips Curve relation.
The theoretical implication is that the evidence presented here is inconsistent with the real business cycle paradigm. Real business cycle theorists postulate that variations in money, which are associated with variations in inflation, are unimportant to aggregate output and employment fluctuations. The evidence presented here supports the conclusion that a monetary phenomenon, ment, a real phenomenon.
inflation, causes unemploy-
The pragmatic implication of inflation causing unemployment is that there is a serious policy dilemma. The “cruelest choice” for economic policy makers is to decide whether or not to use discretionary expansionary policy to bring the economy out of recession. Such economic policy has an inherent risk. In other words, to act (not act) and to see what resides behind the door-a lady or a tiger. The results indicate that inflation does affect the unemployment do not conclusively demonstrate
rate. The causality tests themselves, however,
that there exists a tradeoff between unemployment
and inflation. The results of the causality tests can be interpreted
to support either a
negatively or positively sloped Phillips Curve. For the sixteen years examined, the result is consistent with the Irving Fisher analysis of the trade-off between inflation and unemployment.
On the other hand, the finding is also consistent with Friedman’s
“stage three” positively sloped Phillips Curve. The “cruelest choice dilemma” is simply to determine
the sign of the slope coefficient
for the Phillips Curve that will be
observed when the policy adjustments impact the economy. If the slope coefficient
is
negative then the traditional “cruel choice” phenomenon is what faces policy makers. If, however, the slope coefficient is positive, then expansionary fiscal or monetary policy will simply increase both the rates of inflation and unemployment. The “lady or tiger dilemma” for policy makers is “to act or not to act!” In other words, if the policy makers employ expansionary measures to mitigate unemployment, they are presuming that they can exploit a stable, negatively sloped Phillips Curve. If this presumed exploitable negative relation is, in reality, a positively sloped Phillips Curve then policy makers face the potential danger of combined inflation and high unem-
THEPHlLLIPs
CURVE
343
ployment. The re fore, it appears that Friedman’s views concerning monetary rules may be a rational policy option for risk averse policy makers. Finally, the results reported here suggest the proper specification of the empirical models used to test the Phillips Curve relation. Friedman argued that the proper specification of the regression equations used to estimate the Phillips Curve relation is of significance (both theoretically and empirically). “The truth of 1926 and the error of 1958” (as Friedman argued) is supported by the evidence presented in this paper. The statistical evidence presented here supports Friedman’s claim that inflation is properly specified as the independent variable in “Phillips Curve” analyses. That is, rather than the specification proposed by A. W. Phillips (1958)) the proper specification is that proposed by Irving Fisher (1926) as asserted by Friedman, This finding is of significance to those researchers using ordinary least squares to examine relations between
inflation
Friedman’s inflation
and unemployment.
well known theoretical and unemployment,
Irving Fisher’s specification
arguments
hence,
concerning
his taste for inflation
posited
is consistent relations
with
between
as the independent
vati-
able.
NOTE!3 Direct all correspondence and Management
to: Hedayeh Samavati, Indiana University, School of Business
Sciences, Department of Economics and Finance, Fort Wayne, IN 46805
1499. *
The authors acknowledge helpful comments from William W. Baden, Clive Granger,
Lawrence J. Haber and Tony Loviscek. 1. The Frank R. Stanton story (1884) of the lady or the tiger is that an accused young man was given the option by his king to select a door to prove his guilt or innocence.
Behind one
door was a hungry tiger that would leap upon him and tear him apart. Behind the other door was a fair young lady as compensation for the false accusation. Stanton leaves the story with a question, “Which came out of the opened door-the 2.
lady or the tiger?”
Some authors have stressed causality in a philosophical
context
(See for example,
Zellner 1979 and 1988). Here, however, we use causality as a statistical concept; that is, Granger causality. 3.
The univariate ARMA forecasting models were estimated using the Box-Jenkins (1970)
method. The bivariate ARMA models were estimated using the method proposed by Tiao and Box (1981). In each case the three stages of model building; tentative identilication, estimation, and diagnostic checking were repeated until an “appropriate model” was found. A model is considered appropriate if it reduces the series to white noise process with the least number of estimated parameters (most parsimonious). 4.
The sample autocorrelation
sample partial autocorrelation
functions of both series die down exponentially and the
functions cut off after lag 1.
344
QUARTERLY
REVIEW OF ECONOMICS
AND FINANCE
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THEPHILLIPSCURVE
345
(1972b). “Expectations and the Neutrality of Money.” Journal ofEconomic Thzxny, 4(April): 103-124. (1973). “Some International Evidence on Output-Inflation Tradeoffs.” American [261 -. Economic R&w, 63(June): 326-334. [27] Nelson, Charles R. and Heejoon Eang. (1981). “Spurious Periodicity in Inappropriately Detrended Time Series.” Econometrica, 49: 741-751. -. (1984). “Pitfalls in the Use of Time as an Explanatory Variable in Regression.” WI Journal of Business and Economic Statistics, 2: 73-82. [29] Phelps, Edmund S. (1967). “Phillips Curves, Expectations of Inflation, and Optimal Unemployment Over Time.” Economica, (August): 254-281. [30] Phillips, A. W. (1958). “The Relation between Unemployment and the Rate of Change of Money Wage Rates in the United Kingdom, 1861-1957,” Economica, (November): 283-299. [31] Philips, P. C. B. (1985). “Understanding Spurious Regressions in Econometrics.” Cowles Foundation discussion paper, #757. [32] Pierce, D.A. and L. D. Haugh. (1977). “Causality in Temporal Systems: Characterization and a Survey.” Journal of Econometrics, i(May): 265-293. [33] Smyth, David J., Susan R. Washburn and Pami Dua. (1989). “Social Preferences, Inflation, Unemployment and Political Business Cycles: Econometric Evidence for the Reagan Presidency.” Southern Economic Journal, 56(0ctober): 336-348. [34] Tiao, G. C. and G. E. Box. (1981). “Modeling Multiple Time Series with Application.” Journal of the American Statistical Association, (December): 802-816. [35] Zellner, Arnold. (1979). “Causality and Economics.” Pp. 9-54 in Three Aspects of Policy and Policy Making. Carnegie-Rochester Conference Series on Public Policy, Vol. 10, edited by , K. Bnmner and A. H. Meltzer. Amsterdam: North-Holland. (1988). “Causality and Causal Laws in Economics.” Journal of Econometrics, 39: [36] -. 7-21.
r251 -.
The Phillips Curve: Evidence of a “Lady or Tiger Dilemma”
HEDAYEH SAMAVATI, DAVID A. DILTS and CLARENCE R. DEITSCH Indiana University and Ball State University
This study examines the relation between inflation and unemployment. Grange-r Causality was applied to U.S. data since the end of the Vietnam War. The results support the conclusion that there is a unidirectional causation ranningfiom inflation to unemployment. This result has important poliq and research implications. The natural rate hypothesis is not su@n-ted j&r the timeperiod examined. It cannot be determined, howeoer, whether the slope coefjcitmt for the Phillips Curve characteristic of this period is positive or negative. This result, together with the existence of policy lags, implies that there is inherent risk in any policy persniption. Furtb, the results suj@rt Irving Fisher’s specajication of regression models used to estimate posited relationsbetween inflation and unemployment.
Among the most heated of the debates in macroeconomic theory has been the controversy surrounding the existence of the Phillips or, perhaps, the Fisher curve. Irving Fisher (1926) and Phillips (1958) found that there was a statistical association between a real and a nominal aggregate economic variable. Fisher observed a correlation between price inflation and unemployment in the United States and Phillips discovered an association between nominal wage inflation and unemployment rates in the United Kingdom. Perhaps the most important
reason that the Phillips Curve relation stirred so
much controversy was that it purported to explain an observed relation between two important policy variables. The Phillips Curve relation provided policy-makers with a “cruel choice” (unemployment or inflation). The choice was one that was also easily understood by politicians and the general public, hence its popularity in certain circles. Subsequendy, it was argued that if inflation is fully anticipated then the Phillips Curve becomes vertical at the natural rate of unemployment. On the other hand, in the expectations-augmented Phillips Curve, if price changes are not fully anticipated then it is possible to observe a non-vertical short-run Phillips Curve (Friedman, 1968; Lucas, 1972a, 1972b, 1973; Phelps, 1967). Friedman (1977) discussed several situations in which a non-vertical Phillips Curve may be observed. Friedman postulated several circumstances in which a 333
334
QUARTERLY REVIEW OF ECONOMICS AND FINANCE
tradeoff
between unemployment
noise is introduced Friedman
and inflation could be observed, primarily when
into the price system by unanticipated
explained
shocks, such as inflation.
that in longer periods an observed negatively sloped Phillips
Curve may be due to structural transition in the economy, political unrest, or uncontrolled inflation. Price stability, of course is the best solution, but inflation if anticipated should eliminate the monetary sources of an observed Phillips Curve. If, on the other hand, the inflation rate is permitted to accelerate and decelerate in a random fashion, then the market pricing mechanisms creating bouts of unemployment.
result not in efficiency, but in uncertainty
Under these conditions,
tively sloped Phillips Curve if the government
one may observe a posi-
attempts to utilize the “cruel choice”
option to spend itself out of recession and if those recessionary forces are insensitive to monetary or fiscal policies. As Friedman stated, “. . . a positively sloped Phillips Curve over somewhat longer periods may occur as a transitional
phenomenon
that will
disappear as economic agents adjust not only their expectations but their institutional and political arrangements
to a new reality.” Policy makers face the possibility of the
lady or the tiger dilemma.’ A negatively sloped Phillips Curve rewards monetary policy advocates (the lady) during recession, but on the other hand, a non-negatively sloped Phillips Curve rewards the tiger with the policy maker foolish enough to attempt a reduction in unemployment
with monetary policy. Additionally, research has demon-
strated that the exploitation
of the short-run expectations
augmented Phillips Curve
to gain political popularity may not be a worthwhile exercise (Smyth, Washburn and Dua, 1989). Other macroeconomists For example,
according
have rejected the existence of the Phillips Curve relation.
to proponents
supply shocks, mainly technological
of the real business cycle theory, aggregate
disturbances and/or intertemporal
of leisure for income, are responsible for output (employment)
substitution
fluctuations. The real
business cycle theorists dismiss the short-run Phillips Curve relation because, they argue, nominal variables, such as money, cannot affect real variables such as output. Consequently, real business cycle theorists argue that the efficacy of monetary policy in controlling
the unemployment
rate is questionable
(e.g., Kydland and Prescott,
1982; Long and Plosser, 1983; King, Plosser and Rebel0 1988a, 1988b). The purpose of this study is to examine the relation between the rates of inflation and unemployment
to determine
whether
there is evidence
of a causal relation
between these variables. In other words, does the available evidence support the hypothesis of a non-vertical Phillips Curve for the U.S. economy since the end of the Vietnam War? Granger causality is applied to ascertain whether there is evidence of a causal relation between inflation and unemployment. will have implications “cruel choice”, determining
for economic
The evidence presented here
policy and the possibility of the existence of the
the trade-off between inflation
and unemployment.
Furthermore,
the causal relation, if any, between inflation and unemployment
an implication for the specification
of econometric
rates has
models. There is a controversy as
THE PHILLIPS CURVE to which variable should be specified as the independent Phillips controversy (Friedman,
335
variable; the Fisher versus
1975).
METHOD AND DATA Clive Granger (1969) proposed a method to obtain statistical evidence of the direction ofcausality between economic variables. Granger’s causality test2 is applied to monthly price and unemployment
data in the United States for the period January
1974
through April 1990. The monthly unemployment and Consumer Price Index (CPI) data were drawn from the standard published sources. Both series were seasonally adjusted at the source. Granger (1969) defined “causality” in terms of a forecastability criterion. Pierce and Haugh (1977) described the criterion as follows: “a variable X causes another variable Y, with respect to a universe of information set that includes X andY, if present Y can be better predicted by using past values of X than by not doing so, all other information contained in the past of the universe being used in either case”. In this context, for example, if changes in prices improve the accuracy of predictions of the unemployment
rate, and the unemployment
rate fails to improve the accuracy of
predictions in changes in prices, then the evidence is consistent with the conclusion that there is a unidirectional causality from the inflation rate to the rate of unemployment. The common test procedures used to detect Granger causality in the literature base their conclusions on tests of significance of model parameters (tests of how well the model fits the in-sample data). In contrast, in this study, causality findings come from the comparison of forecasts from different forecasting models. As Granger stated (1980, p. 348)) “It is generally accepted that to find a model that apparently fits better than another is much easier than to fit one that forecasts better.” Thus, where the original Granger causality definition does require evidence of improved forecasts, the common methods of Granger causality testing are tests of goodness of fit. In the approach used here, the general guidelines suggested by Granger (1980) are followed. More specifically,
to make inferences
about causal orderings,
forecast
errors are
analyzed in a manner similar to that suggested by Ashley, Granger and Schmalensee (1980). This procedure is faithful to the original definition of Granger causality in that hypotheses are tested on the basis of out-of-sample forecasting performance. This method “ . . . does prevent evidence for spurious causation occurring because of data mining” (Granger 1980, p. 349). To test for differences in “post-sample” forecasting ability, the sample was partitioned into a modeling period (January of 1974 through December of 1986) and a forecast evaluation period consisting of forty observations (January of 1987 through April of 1990). To test whether changes in prices (inflation) are causally prior to the rate of unemployment, forty one-step ahead forecasts of the unemployment rate are generated from both univariate and bivariate ARMA (Autoregression Moving Aver-
336
QUARTERLY REVIEW OF ECONOMICS AND FINANCE
age) models. If inflation causes the unemployment models of unemployment mation)
will generate
(containing
rate, then the bivariate forecasting
both the inflation and unemployment
infor-
superior forecasts to those from the univariate forecasting
models of unemployment.
For each information
set, an ARMA model was estimateds
using the data through period t. The estimated model was used to obtain the forecast
fel. Next,
the data was updated by one observation and an ARMA model was fitted to
the data through period (t + 1). Then, the new model was used to produce the forecast
fH2.Repeating
the procedure thirty-eight times resulted in forty one-step ahead forecasts of the rate of unemployment for each information set. The forecast errors
were used to define new variables and to estimate the simple regression models as proposed by Ashley et al. (1980). The same procedure was employed to test whether unemployment causes inflation. To determine the superior set of forecasts, one can compare the mean square error (MSE) of the two forecast sets. However, no direct test for the significance of differences in forecast MSEs is available because forecast errors produced by models that contain several variables in common are likely to be cross-correlated, and autocorrelated
(Ashley et al., 1980).
The following indirect procedure to evaluate forecast accuracy was developed by Ashley et al. (1980). Let el be the set of the forecast errors of a model that uses the historical values of one variable, and let q be the set of the forecast errors of the bivariate model. It can be shown that: MSE(er) - MSE(a2) = [s*(4) -
s2(e2)l + [m(ed2-m(d21,
(1)
where s*( ei, and m( e,) are the sample variance and mean of the ei series, respectively. In addition, assume that: At=erl-~rand&=~,+~Pthen: MSE(el) - MSE(%) = [chA,,Ul
+ [Ned2 - m(ed21,
(2)
where c& and v& are the sample covariance and variance over the forecast period. As a test of whether MSE ( ei) is significantly greater than MSE (9) one can estimate the following ordinary least squares equation: AC= Pi + P2& - m(Ql
+ ut
(3)
then: t3t = m(el) -
m(e2)
(4)
/v&(&)
(5)
and: fis = &(A,,&)
Ifm(ei) and m(s) are both positive, and if p1 and p2 are significantly greater than zero, this implies that MSE(4) is significantly greater than MSE( q). In other words, if the forecasts of the bivariate models, (i.e., including both unemployment and
THE PHTLLWS CURVE
337
inflation rates) perform better than those of the univariate models, the null hypothesis, pr = p2 = 0, can be rejected in favor of the alternative that both are nonnegative and at least one coefficient is positive. If both coefficients are positive, an F-test of the null hypothesis that both parameters are zero can be performed. estimated coefficients judged
If one of the two
is significantly negative, then the bivariate models cannot be
to have given rise to better forecasts. If one coefficient
is not significantly
negative, a one-tailed &test on the other estimated parameter can be used.
THE ANALYSIS The plots of the unemployment
rate (UR) and monthly percentage inflation rate (IR)
multiplied by 10 appear in Figures 1 and 2. Preliminary data analysis, examination partial autocorrelation
of data plots, sample autocorrelation
and
functions, indicate that neither series were integrated proc-
esses.4 However, formal statistical tests of stationarity for both series were performed. One problem with analyzing nonstationary data is that the usual statistical properties of first and second sample moments do not hold. For example, those sample moments do not converge to their population parameters as sample size increases (Philips, 1985; Hendry, 1986). In addition, Dickey, Bell and Miller (1986) showed that the forecasts from the stationary model converge to the series mean and the forecast standard errors converge to the series standard deviation. However, the forecasts from the nonstation-
Time Figure 1.
338
QUARTERLY REVIEW OF ECONOMICS AND FINANCE
Time Figure 2.
ary model converge to a number different from the series mean and the forecast standard errors diverge to t m. Given the difficulties that arise from analyzing nonstationary data, one may conclude that examining differences of the data is a safe approach. Several authors have warned against this approach. For example, Hendry (1986) and Granger (198’7, 1988) argue that differencing economic time series data may result in the loss of all information about potential long-run relationships. The models will generally be mis-specified resulting in poor forecasts. In addition, if the two series are integrated of order one (have unit roots), they may be co-integrated and need to be analyzed using error correction models (Granger 1981, 1983, 1986, 1987, 1988; Engle and Granger 1987). Hakkio and Rush (1989) show that taking first differences of a bivariate relationship in order to induce stationarity may result in omitted variables bias, if the two variables are cointegrated. Because the decision of whether to difference
has implications for forecasts and
models, the formal statistical tests for unit roots are required. The results of those tests are presented in the following section. Empirical Results of Non-stationarity Tests
Tables 1 and 2 report results of non-stationarity tests for both the inflation rate (IR) and the unemployment rate (UR) series. Conventional Dickey-Fuller (DF) test results are presented in Table 1 and the results of the augmented Dickey-Fuller (ADF) tests appear in Table 2.
THE PHILLIP
CURVE
339
Table 1. DICKJ%FULLER TEST RE!XJLTs: NO,LAGS A P
AK A&
0.138 (0.031) 0.112 (0.087)
AURt
Std. JIrror of Estimate
d&l>
-0.271 (0.049) -0.033 (0.012)
rh Tfi
DW-D
0.234
-5.55*
2.18
0.230
-2.75
1.66
Note: Regressions are of the form AY, = p + (p,, - l)Y,_t + residual. ‘Standard emm” are in parentheses below coefficients. Sample size is 195 in both cases. The usual t statistic for the coefficient on Y&t is the ‘f,, statistic and can be read dire&y from the computer printout. Tbe statistic Q tests the null hypothesis (p-1) = 0 qamst the alternative (p-l) < 0. The rejection region ia the set of values of r,, less than -9.46 (-2.58) for a test of size 0.01 (0.10). Critical values of z,, are qxwted from percentiles for ‘1,, stati%ics table (Dickey 1976, pg. 53). *means significantly **means significantly
negative at the one percent level. negative at the ten percent
level.
Because several authors (Dickey et al. 1986; Nelson and Rang 1981, 1984; Rang 1985) waned against preliminary removal of linear or non-linear trend, none of the regressions in Tables 1 and 2 include a time trend. The hypothesis of non-stationarity of the inflation rate is rejected at the one-percent level using both DF and ADF tests in Tables 1 and 2 respectively. The similar hypotheses regarding the UR are rejected at the ten-percent level. Given other evidence, it is concluded that both series are stationary. Thus, the series were used to estimate the univariate and bivariate forecasting models that generate forecasts to be used in Granger causality tests. The estimated univariate forecasting models for the inflation and unemployment rates over the period January 1974 through March 1990 are presented in Table 3. Table 4 presents the estimated residual autocorrelations of each model up to 12 lags respectively. Results reported in Table 4 indicate that for both models the residual autocorrelations are insignificant up to lag 12. One can conclude that the estimated univariate
Table 2.
A& AU&
NC&
AUGMENTED
DICKJW-
TEST RESULTS: FOUR LAGS
0.090 -0.184 -0.197 -0.187 -0.071 -0.121 (0.035)(0.058)(0.082)(0.081)(0.078)(0.074) 0.224 -0.031 -0.073 -0.136 -0.155 -0.248 (0.086)(0.012)(0.071)(0.070)(0.070)(0.071) Regressions
are of the form AU, = p + @,,-I )Y,_t + I$,
&AU,,
0.230
-3.15* 2.003 8.023
0.216
-2.64** 2.001 6.998
+ residual.
‘Standard ermrsL are in parentheses below coefficients. Sample size is I91 in both cases. 7be usual t statistic for the coefficient on Y+t isthe~)lstatisdcandcanbereaddirecdyfrom thecompurerprintour.Thesratistic~ thenull hypothesis (p-l) =Oagainstdwaltemate (p-1) < 0. Tbe rejection region is the set ofvalues of4 less than -2.88 (-2.58) for a test ofsize 0.05 (0.10). Critical values are reported from percentiles for ‘T,,statistic table (Dickey 1976, pg. 53). *means significantly “meuls
significandy
negative at the five percent negative at the ten percent
level. level
340
QUARTERLY REVIEW OF ECONOMICS AND FINANCE
Table 3. UNIVARWTE FORECASTING MODELS UNEMPLOYMENT RATES (January 1974-March 1990)
Residual Series
Note:
CNST
I&
1.40 (0.31)
W
0.21 (0.08)
Figures
in parentheses
are standard
Kl
W-1
0.73 (0.05) -
errors.
All
of the
OF INFLATION
coefficients
AND
Std. Error
m-5
-
-
2.32
1.12 (0.03)
-0.15 (0.03)
0.21
are significant
at the one percent
significance
level.
models are “appropriate” and thus can be used to forecast each variable. The estimated bivariate model for the period January 1974 through March 1990 is: IR, = 2.344 + 0.635IR,i (1.080)
- 0.477UR,5
(0.056)
UR,= 0.080 + l.O41UR,i (0.095)
- 0.1621Rfi5 + 0.29UR,5
(0.321)
(0.060)
+ 0.0141R,3 + 0.128UR,3
(0.048)
(0.005)
where values in parentheses matrix is:
(0.329)
- 0.91UR,5
(0.075)
(0.046)
are standard errors and the model’s error covariance
5.073 -.0594
. 0.439
I
Table 5 presents the diagnostic checking for the bivariate model. The Table indicates that auto and cross-correlations between residuals of the bivariate model are not significant up to lag 24 indicating the appropriateness
of the model.
As explained earlier, both univariate and bivariate forecasting models were used to generate one-step ahead forecasts of each variable. Forecast errors were computed and regression models according to Ashley et al. (1980) method were estimated. Table 6 presents the results of the regression models used to test the non-causality hypotheses.
Table
4.
INFLATION Lags
RESIDUAL AUTOCORRELATIONS AND UNEMPLOYMENT MODELS
1
2
ACF
-.lO
-.05
.12
-.Ol
.03
.09
St.E.
.07
.07
.07
.07
.07
.07
.07
ACF
-.08
-.03
.08
-.oo
.07
-.oo
.07
.07
.07
.07
St.E.
.07
.07
3
-.02 .07
4
5
6
7 -.03
FOR 8
THE 9
UNIVARIATE 10
11
12
.09
.16
.14
.12
.07
.07
.08
.08
.08
.05
.04
.03
-.Ol
.07
.07
.07
.07
-.02 .07
-.02
THEPHlLLIPs
Tabb 5.
AUTO AND CROSS-CORRELATIONS
Lags1 through 12 .. .. .. .. .. ..
CURVE
341
BETWEEN RESIDUAL TERMS
.. ..
.. ..
.. ..
.. ..
.. ..
+. . .
., ..
.. ..
.. ..
..
..
..
..
..
..
..
..
.
.. +.
Lags 13 through 24
..
Nde:
..
+.
The approximate + Denma -Denotes Denotes
std. error for the estimated
a value neater
a value less than -Vstd. a nonaignificanr
correlauons
above is l/sqn
(NOBE)
NOBE is the effective number
of oknations.
than P/std. error. error.
value based upon the above crirerion.
Regression Model 1, compares statistically two sets of forecasts of the unemployment rate. One set is based on the bivariate forecasting models of the unemployment rate and the other set on the univariate. Both coefficients are positive and the intercept is significant at the .Ol level. This result implies that forecasts of the bivariate models are superior to those of the univariate ones. In other words, past values of the inflation rate contained some unique information that was useful in predicting the unemployment rate. One may conclude, therefore that inflation “Granger causes” unemployment. Regression Model 2 tests whether forecasts of inflation, using both the unemployment and inflation rate histories are superior to those forecasts based on the history of inflation alone. Model 2 reveals that both the intercept and the slope coefficients are negative and the intercept is significant at the .Ol level. This result implies that the past values of unemployment do not help to improve forecasts of inflation. That is, the unemployment rate does not “Granger cause” the inflation rate. In short, the analysis provides evidence of unidirec tional causality that runs from inflation to the rate of unemployment.
Table 6. REGRESSION CAUSALITY Alternative Hypothesis
RESULTS FOR TESTING GRANGER
Intercept
Slope
Durbii-Watson (d)
(1) Inflation causes Unemployment
0.034
0.025
(8.020)
(1.390)
1.421
(2) Unemployment causes Inflation Note:
Figures in parentheses
-0.283
-0.007
(-5.501)
(-0.522)
are ktatistics.
1.175
342
QUARTERLY REYIEW OF ECONOMICS AND FINANCE
DISCUSSION AND CONCLUSIONS During the period examined, January 1974 to April 1990, the evidence reported in Table 6 suggests that there is a unidirectional to the rate of unemployment.
causal relation from the inflation rate
If, the Phillips Curve were vertical over this sixteen year
period, one should have observed no causality between the unemployment the rate of inflation
rate and
(the natural rate hypothesis, i.e., any rate of inflation can be
associated with the natural rate of unemployment).
The empirical findings reported
here, however, suggest a non-vertical Phillips Curve. Whether anticipated or not, the rate of inflation has, over the period examined, “Granger caused” unemployment. theoretical
and one pragmatic.
specification
This finding has two significant implications,
one
There is also a point to be made concerning
the
of empirical models used to test the Phillips Curve relation.
The theoretical implication is that the evidence presented here is inconsistent with the real business cycle paradigm. Real business cycle theorists postulate that variations in money, which are associated with variations in inflation, are unimportant to aggregate output and employment fluctuations. The evidence presented here supports the conclusion that a monetary phenomenon, ment, a real phenomenon.
inflation, causes unemploy-
The pragmatic implication of inflation causing unemployment is that there is a serious policy dilemma. The “cruelest choice” for economic policy makers is to decide whether or not to use discretionary expansionary policy to bring the economy out of recession. Such economic policy has an inherent risk. In other words, to act (not act) and to see what resides behind the door-a lady or a tiger. The results indicate that inflation does affect the unemployment do not conclusively demonstrate
rate. The causality tests themselves, however,
that there exists a tradeoff between unemployment
and inflation. The results of the causality tests can be interpreted
to support either a
negatively or positively sloped Phillips Curve. For the sixteen years examined, the result is consistent with the Irving Fisher analysis of the trade-off between inflation and unemployment.
On the other hand, the finding is also consistent with Friedman’s
“stage three” positively sloped Phillips Curve. The “cruelest choice dilemma” is simply to determine
the sign of the slope coefficient
for the Phillips Curve that will be
observed when the policy adjustments impact the economy. If the slope coefficient
is
negative then the traditional “cruel choice” phenomenon is what faces policy makers. If, however, the slope coefficient is positive, then expansionary fiscal or monetary policy will simply increase both the rates of inflation and unemployment. The “lady or tiger dilemma” for policy makers is “to act or not to act!” In other words, if the policy makers employ expansionary measures to mitigate unemployment, they are presuming that they can exploit a stable, negatively sloped Phillips Curve. If this presumed exploitable negative relation is, in reality, a positively sloped Phillips Curve then policy makers face the potential danger of combined inflation and high unem-
THEPHlLLIPs
CURVE
343
ployment. The re fore, it appears that Friedman’s views concerning monetary rules may be a rational policy option for risk averse policy makers. Finally, the results reported here suggest the proper specification of the empirical models used to test the Phillips Curve relation. Friedman argued that the proper specification of the regression equations used to estimate the Phillips Curve relation is of significance (both theoretically and empirically). “The truth of 1926 and the error of 1958” (as Friedman argued) is supported by the evidence presented in this paper. The statistical evidence presented here supports Friedman’s claim that inflation is properly specified as the independent variable in “Phillips Curve” analyses. That is, rather than the specification proposed by A. W. Phillips (1958)) the proper specification is that proposed by Irving Fisher (1926) as asserted by Friedman, This finding is of significance to those researchers using ordinary least squares to examine relations between
inflation
Friedman’s inflation
and unemployment.
well known theoretical and unemployment,
Irving Fisher’s specification
arguments
hence,
concerning
his taste for inflation
posited
is consistent relations
with
between
as the independent
vati-
able.
NOTE!3 Direct all correspondence and Management
to: Hedayeh Samavati, Indiana University, School of Business
Sciences, Department of Economics and Finance, Fort Wayne, IN 46805
1499. *
The authors acknowledge helpful comments from William W. Baden, Clive Granger,
Lawrence J. Haber and Tony Loviscek. 1. The Frank R. Stanton story (1884) of the lady or the tiger is that an accused young man was given the option by his king to select a door to prove his guilt or innocence.
Behind one
door was a hungry tiger that would leap upon him and tear him apart. Behind the other door was a fair young lady as compensation for the false accusation. Stanton leaves the story with a question, “Which came out of the opened door-the 2.
lady or the tiger?”
Some authors have stressed causality in a philosophical
context
(See for example,
Zellner 1979 and 1988). Here, however, we use causality as a statistical concept; that is, Granger causality. 3.
The univariate ARMA forecasting models were estimated using the Box-Jenkins (1970)
method. The bivariate ARMA models were estimated using the method proposed by Tiao and Box (1981). In each case the three stages of model building; tentative identilication, estimation, and diagnostic checking were repeated until an “appropriate model” was found. A model is considered appropriate if it reduces the series to white noise process with the least number of estimated parameters (most parsimonious). 4.
The sample autocorrelation
sample partial autocorrelation
functions of both series die down exponentially and the
functions cut off after lag 1.
344
QUARTERLY
REVIEW OF ECONOMICS
AND FINANCE
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PI I31 [41 [51 Kl
[71 Bl PI WI Vll [I21 [I31 [I41 [I51 Ml [I71
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