New dogs and old tricks: do money and interest rates still provide information content for forecasts of output and prices?

International Journal of Forecasting 16 (2000) 191–205www.elsevier.com/ locate / ijforecast

New dogs and old tricks: do money and interest rates still provideinformation content for forecasts of output and prices?

a b a ,*David C. Black , Paul R. Corrigan , Michael R. DowdaDepartment of Economics, The University of Toledo, Toledo, OH 43606, USA

bDepartment of Economics, Michigan State University, East Lansing, MI 48824, USA

Abstract

Out-of-sample forecasting experiments are used as an alternative to looking at F-statistics when examining whethermoney, interest rates or the commercial paper /T-bill spread provide information content for subsequent movements inoutput, real and nominal personal income, the CPI and the PPI. Here, a variable provides information if it improves theforecast of the explained variable. Employing this procedure we find that the paper-bill spread but not monetary aggregatesprovide information content for industrial production or real personal income when using data over the 1980–1997 period. Incontrast, we find that monetary aggregates provide information content for the CPI and nominal personal income but not thePPI. 2000 International Institute of Forecasters. Published by Elsevier Science B.V. All rights reserved.

Keywords: Macroeconomic forecasting: industrial production, personal income, inflation; Time series

JEL classification: E. Macroeconomics and monetary economics; E4. Money and interest rates

1. Introduction other important economic variables such asmonetary aggregates or interest rates. These

The Federal Reserve has at its disposal a variables may be used as intermediate targets iflimited set of instruments through which it can immediately subject to influence by policy andattempt to achieve its objectives of price stabili- if their movements affect output or prices. If thety and/or full employment output. Between the variable does not cause output or prices, it maytime a monetary instrument is adjusted and its still be useful as an information variable if itsultimate effect on economic activity has movements consistently lead movements in theoccurred there are observable movements in variables the Federal Reserve wishes to influ-

ence.Friedman and Kuttner (1992, 1993) sparked a

*Corresponding author. Tel.: 11-419-530-4603; fax:healthy debate as to which variables are good11-419-530-7844.candidates for intermediate targets or informa-E-mail address: [email protected] (M.R.

Dowd) tion variables. The candidates they considered

0169-2070/00/$ – see front matter 2000 International Institute of Forecasters. Published by Elsevier Science B.V. All rights reserved.PI I : S0169-2070( 00 )00035-2

192 D.C. Black et al. / International Journal of Forecasting 16 (2000) 191 –205

1to explain movements in industrial production clusions on in-sample estimates from F-tests.included a price index, a monetary aggregate Given the widely different results obtainedand the difference between the commercial using F-tests, this paper employs an alternativepaper rate and the treasury bill rate (the ‘paper- test of information content of candidate vari-bill spread’). Using F-statistics to determine ables, that of out-of-sample forecasting experi-whether a particular variable provided infor- ments. To this end, this paper follows the recentmation content, Friedman and Kuttner (1993, p. work of Thoma and Gray (1998) who214) concluded that the paper-bill spread was a forecasted industrial production in a three-vari-good candidate as it contained significant in- able vector autoregression with a price indexformation content for industrial production re- and alternative potential information candidatesgardless of sample: ‘[t]he spread is a predictor (paper-bill spread, federal funds rate or M2).of real economic activity, not prices, and of Employing monthly data from 1960:2 to 1995:4nominal magnitudes only to the extent that they and comparing the alternative model forecastsreflect real ones’. In contrast, they argued that to an autoregressive forecast of industrial pro-money is related to neither real nor nominal duction, Thoma and Gray (1998, p. 533) findincome fluctuations and concluded that money that ‘none of the financial variables is sys-is not a reasonable candidate as its information tematically useful in forecasting industrial pro-content broke-down in samples that included the duction’. In fact, like Emery (1996), they argue1980s. Monetary aggregates being ‘unreliable that the 1974 outlier may be the reason whyindicators of economic activity and as guides some studies have found that certain financialfor stabilizing prices’ has also been argued by market variables contain information content forAkhtar (1997, p. 4). industrial production while others have not.

The debate sparked by Friedman and Kut- Like Thoma and Gray (1998), we testtners (1992, 1993) conclusions included an whether the inclusion of candidate variables forexamination of stationarity assumptions (Hafer intermediate targets or information variables& Kutan, 1997), presence of outliers in the data improve forecasts over an autoregressive model.(Emery, 1996), and the importance of error Using monthly data we conduct 12-step-a-headcorrection terms (Dotsey & Otrok, 1994). Hafer forecasts, continually updating the model esti-and Kutan (1997) found that difference-station- mates after each month. We then compute theary data produces results found in the literature mean absolute percentage error (MAPE) forwhile a trend–stationary assumption yields a each step-a-head forecast. If a model containingrelationship between money and output. Emery a candidate variable produces MAPEs lower(1996) argued that Friedman and Kuttner’s than the AR model, the candidate variable isconclusions regarding the paper-bill spread were said to contain information content for thedue mainly to outliers in the data in 1974 and in variable being forecasted. Our method of con-1980; for samples that exclude these outliers, tinually up-dating the data set provides a time-the spread provided no predictive content for moving measure of forecasting ability of po-industrial production. Dotsey and Otrok (1994)included an error correction term and foundmoney to provide information content for both

1nominal and real GDP. See Thoma and Gray (1998), Ohanian (1988), GrangerEach of the above mentioned responses to (1988), and Jacobs et al. (1979) for the drawbacks of using

Friedman and Kuttner’s work based their con- Granger F-tests to examine such relationships.

D.C. Black et al. / International Journal of Forecasting 16 (2000) 191 –205 193

tential candidate variables for intermediate system (e.g. authority over reserve requirements2targets or information variables. at all depository institutions). As the ability of

Instead of concentrating on the performance variables to explain economic activity may haveof one model specification over another, Thoma changed since 1980, our forecasting experi-and Gray (1998) focused on the question of ments which use only the later data set maywhether any financial variables provided in- capture the changes that took place as they wereformation content when forecasting economic not fed data from a pre-existing structuralactivity. Such a tact is eminently reasonable in model.the present context if the competing models do There are two additional differences betweennot perform better than an autoregressive model, the analysis here and that in Thoma and Grayas was shown in the results in Thoma and Gray (1998). First, we forecast nominal variables as(1998). We consider model comparisons be- well as real variables. This allows us to alsocause the extensions to their analysis here examine which variables are reasonable candi-provide insight into the workings of financial dates to provide information about movementsmarkets and the impact of monetary innova- in prices and nominal income. Second, wetions. include more than one financial market variable

This paper extends the Thoma and Gray in our VAR specification. This allows for an(1998) analysis in that we consider two sample examination of whether there is a synergy whenperiods: 1959:1–1979:10 and 1980:1–1997:3. both money and interest rates are included inThere are two reasons for considering two sub- the model specification to explain movements inperiods. First, the latter sample does not include output / income or in prices that could not bethe 1974 outlier found by Emery (1996) and detected in Thoma and Gray’s three-variableThoma and Gray (1998). Second, the sample VAR model.period used by Thoma and Gray, 1960–1995, Using this procedure we find, in contrast toinclude ‘several distinct periods characterizedby differences in the procedures used by the Fed

2Not surprisingly, the 1979 regime change at the Federalto implement monetary policy’ Walsh (1998, p.Reserve subsequently allowed much greater variations in31). Some of the procedural changes included athe federal funds rate, and the MCA contributed to thechange in the operating procedure at the Federalsubstantial innovations that have taken place in the US

Reserve in October of 1979 and the Depository financial system. For example, prior to the MCA theInstitutions Deregulation and Monetary Control relationship between reserves and checkable deposits wasAct of 1980 (MCA). In October 1979, the quite loose so that one could treat the money multiplier as

independent of Federal Reserve policy actions. That rela-Federal Reserve changed its operating proce-tionship has since tightened to the extent that the multiplierdure from targeting the federal funds rate tois no longer independent of policy actions (Garfinkel &targeting non-borrowed reserves. The MCA Thornton, 1991). Moreover, prior to 1980, changes in the

made depository institutions more competitive monetary base (and not in the money multiplier) primarilyby allowing them to introduce new financial determined the month-to-month changes in the US money

supply. However, since that time this relationship has beenmarket instruments (e.g. NOW and ATS ac-reversed (Gauger & Black, 1991). Black and Dowdcounts). In addition, it allowed these institutions(1994a,b) argued that the changes which occurred ingreater diversification of their earning asset1979–1980 brought about an increased sensitivity of the

portfolios. In exchange for these deregulations, currency to checkable deposits ratio (and, hence, thethe MCA gave greater control to the Federal money multiplier and the money supply) to changes inReserve over other features of the financial income.


Emery (1996) but consistent with Friedman and (PY), MI and M2 monetary aggregates, theKuttner (1992, 1993), that both the spread and monetary base (BASE), consumer price indexM2 provide information content for both in- (CPI), producer price index (PPI), federal fundsdustrial production and real personal income in rate (FF), 3-month treasury bill rate and thesamples that exclude data from the 1980s and commercial paper rate. A paper-bill spread (SP)1990s. Also similar to Friedman and Kuttner’s is constructed by subtracting the treasury billconclusions, money loses its information con- rate from the commercial paper rate. As intent when forecasting industrial production or Friedman and Kuttner (1992, 1993), the analy-real personal income in a sample which includes sis below uses log-differences of all the seriesdata after 1980. However, in contrast to the except for the interest rate data. Dickey–Fullerconclusions of Thoma and Gray (1998), we find (DF) and augmented Dickey–Fuller (ADF) testssupport for the interest rate spread in forecasting report that the transformed series are stationary.industrial production when using 1980–1997 Six lags of each variable were used in thedata. analysis of each model considered. Forecasting

Results regarding the contribution of money experiments are conducted on the followingtowards forecasts of the CPI are very robust variables: industrial production, real personalacross the two samples. For the early sub-period income, nominal personal income, the consumera combination of money and the federal funds price index and the producer price index.rate improve forecasts of the CPI. For the later In Section 3 we report first the results fromsub-period, money continues to provide infor- forecasting experiments of real output / income.mation content for forecasts of the CPI (in This is followed by forecasts of nominal vari-contrast to the arguments by Friedman and ables in Section 4. In each case we consider anKuttner (1992, 1993) and Akhtar (1997)), but autoregressive model (AR) as the benchmarkthe contribution of the federal funds rate de- model to determine whether the inclusion ofteriorates substantially. The results from the candidate variables in five subsequent modelsforecasting experiments of the producer price reduces the forecast error. If it does, thisindex were substantially different from those of variable is considered as a reasonable candidateCPI forecasts: there is no support for the as an information variable.inclusion of any monetary aggregate in forecasts For each case we report the results from twoof the PPI for either sub-period. Forecasting series of forecasting experiments using vectorexperiments of nominal personal income indi- autoregression models. We also alternate monet-cate that the spread provides information con- ary aggregates, and measures of interest rate,tent with the early sample data but both money prices and output / income. The first set ofand the federal funds rate are reasonable candi- experiments used data from 1959:1 to 1979:10date variables when using the later data set. (sample A) with the forecast period from

1973:12 to 1979:10. The second set of experi-ments used data from 1980:1 to 1997:3 (sampleB) with the forecast period from 1991:5 to2. Data and model1997:3. As mentioned in the previous section,

As in Friedman and Kuttner (1992, 1993) we comparing the results from forecasting experi-obtained our data from Citibase. The data are in ments using these two samples allows us tomonthly form over the 1959:1–1997:3 period examine whether a change has occurred in theand include industrial production (IP), real information content provided by candidate vari-personal income (Y), nominal personal income ables.


We begin the description of our forecasting forecast output or price through combinations ofexperiments by an example of those conducted past values of price, output / income, monetaryusing sample B. To produce a sequence of 12 aggregate, and an interest rate measure. Theone-step-ahead forecasts each model was esti- variables chosen as possible explanatory vari-mated first using data from 1980:1 to 1991:4, ables were done so that the alternative modelsproducing 1- to 12-month ahead forecasts for here are consistent with those in the literature1991:5 through 1992:4. Each of the 12 forecasts cited above. The models take the form repre-are then compared to the corresponding histori- sented in Eq. (1):cal observation and the absolute percentage

6 6error of each forecast is recorded. The dataY 5 a 1O b Y 1O g Xsample is then extended to include the 1991:5 t i t2i i t2i

i51 i51sample observation, re-estimated and used to6 6generate 12 forecasts for the 1991:6–1992:5

1O f M 1O d R 1 u (1)i t2i i t2i tperiod. The absolute percentage error of each of i51 i51

these forecasts are then recorded. This processof updating the data set and computing forecast where Y is the variable being forecasted. Whenterrors was continued with data from 1980:1 to forecasting industrial production and real and1996:3 ultimately being used to generate fore- nominal personal income, X represents thetcasts of output for 1996:4 through 1997:3. This measure of price included (i.e. the CPI or theprocedure produces 60 sets of forecasts, each PPI). When forecasting the CPI or the PPI, Xtincluding forecasts from 1 to 12 months ahead represents the measure of output / income in-for the period 1991:5 to 1997:3. cluded (i.e. industrial production or real person-

The means of the absolute percentage errors al income). M and R are, respectively, thet t(MAPE) of each of the 12-step-ahead forecasts monetary aggregate and the interest rate mea-for the 5-year period are then calculated. Com- sure used. As described below, in models II andparing MAPEs of competing models allows for V, the f values are zero and in model III the da time-moving measure of forecasting ability. values are zero.This allows us to determine whether the inclu- For example, in the cases where industrialsion of a particular variable in the model production serves as the output variable and M2specification provides information content when serves as the monetary aggregate, the fiveforecasting output or prices. For example, con- alternative models are listed in Table 1. Assider two models to forecast CPI: the first being mentioned above, by comparing the forecastan AR model and the second uses lagged values error (MAPEs) generated by the AR model toof both CPI and M2 to forecast CPI. If the those generated by:MAPEs generated by the first model are greaterthan the MAPEs generated by the second • Model II indicates the information content ofmodel, we would infer that M2 provides in- the interest rate spread.formation content for forecasts of CPI. Compar- • Model III indicates of the information con-ing the MAPEs of competing models also tent of money.allows us to examine the relative advantage of • Model V indicates the information content ofincluding, say, the federal funds rate instead of the federal funds rate.the interest rate spread when forecasting output • Models I and IV indicates the advantage ofor prices. the including both money and a measure of

The five alternative models to the AR model interest.


Table 1 sistently lower than all other models, giving aAn example of the five alternative models in one of the clear indication of which candidate variablesaforecasting experiments provide information content for the variableAlternative Variables included being forecasted. Examples of this are Table 3models (sample B) and Table 4 (sample A). The sub-Model I IP CPI M2 SP sequent sections will also show cases where theModel II IP CPI SP results appear ‘mixed,’ with one model perform-Model III IP CPI M2 ing better over a given number of step-a-headModel IV IP CPI M2 FF forecasts while another model performs better atModel V IP CPI FF

others. In such cases we are reminded of thea In this example industrial production (IP) serves as the question raised by Thoma and Gray (1998): do

output variable, CPI as the measure of price, and M2 as the any financial market variables provide infor-monetary aggregate. The measure of interest alternatesmation content? For example, consider Table 3between the interest rate spread(SP) and the federal funds(sample A), where models that include therate (FF).federal funds rate produces the lowest MAPEs

Such comparisons will determine whether a in the early step-a-head forecasts of real person-variable is a good candidate as an information al income, only to have models that include thevariable. Comparing the MAPEs from models I, interest rate spread produce the lowest MAPEsII and III (or models III, IV and V) examines the in the later steps. While the results are mixed,relative contributions of money versus the inter- they support the argument that including aest rate spread (or money versus the federal measure of interest improves the forecasts offunds rate). Moreover, comparing the MAPEs real personal income over that sub-period.from model II and V and those from models I An explanation for mixed results for any ofand IV examines the relative contribution of the the forecasting experiments will depend on thefederal funds rate versus the interest rate spread. variable being forecasted and the candidate

To examine whether the information content explanatory variables considered. It may be thatprovided by a candidate variable is special to two candidate explanatory variables providethe particular variable being forecasted, we competing information for the variable beingrepeated the above analysis first substituting real forecasted. Alternatively, one or neither of thepersonal income (Y) for industrial production candidate explanatory variables may improve(IP). This is followed by forecasting experi- forecasts. For example, when comparing thements of nominal variables — nominal personal MAPEs from the alternative models to thoseincome (PY), the CPI and finally the PPI. To from the AR model in Table 2 (sample A), itexamine whether a change has taken place in appears that the inclusion of one measure ofthe information content provided by monetary interest (SP) improves forecasts of industrialaggregates, all of the above forecasting experi- production while the other measure of interestments were repeated first using M1 instead of (FF) does not. In other cases, such as that inM2 and then the monetary base instead of M2. Table 2 (sample B), the inclusion of eitherHowever, to conserve space we report in detail measure of interest will produce lower MAPEsthe results obtained using M2 and only summa- than the AR model at various step-a-headrize those obtained using M1 and the monetary forecasts (SP in eight of the 12 steps and FF inbase. the last six steps). In addition, patterns may

As the forecasting experiments reported in emerge, as in Table 3 (sample A) discussedsubsequent sections will show, there are cases above. So even when there is no clear su-where the MAPEs from one model are con- periority of one model specification over


Table 2Comparison of the means of the absolute percentage error (MAPEs) of forecasting industrial production with two sampleperiods

Step AR Alternative models

I II III IV VIP,CPI,M2,SP IP,CPI,SP IP,CPI,M2 IP,CPI,M2,FF IP,CPI,FF

Sample A: 1959:1 –1979:10. Forecast Horizon: 1973:12 –1979:10a1 0.502 0.716 0.680 0.581 0.584 0.581a2 1.030 1.343 1.271 1.171 1.186 1.219a3 1.578 1.757 1.679 1.631 1.661 1.759

a4 2.146 2.070 1.994 2.109 2.103 2.418a5 2.728 2.279 2.107 2.563 2.530 3.055a6 3.240 2.293 2.157 2.857 2.819 3.664a7 3.690 2.194 2.174 3.081 3.024 4.138a8 4.101 2.208 2.200 3.297 3.248 4.622

a9 4.478 2.432 2.459 3.523 3.439 5.031a10 4.845 2.759 2.940 3.746 3.612 5.375a11 5.169 3.176 3.385 3.974 3.833 5.727a12 5.463 3.547 3.823 4.312 4.140 6.120

Sample B: 1980:1 –1997:3. Forecast Horizon: 1991:5 –1997:3a1 0.304 0.332 0.321 0.322 0.340 0.327a2 0.448 0.476 0.465 0.501 0.520 0.469

a3 0.559 0.637 0.554 0.696 0.670 0.594a4 0.716 0.850 0.728 0.915 0.874 0.760a a5 0.827 1.064 0.827 1.069 1.035 0.863

a6 0.901 1.176 0.888 1.212 1.136 0.891a7 0.953 1.285 0.896 1.323 1.191 0.889

a8 1.002 1.417 0.867 1.438 1.258 0.902a9 1.054 1.608 0.866 1.574 1.352 0.894a10 1.107 1.825 0.860 1.701 1.466 0.935a11 1.214 2.021 0.914 1.833 1.581 1.013a12 1.332 2.176 0.994 1.936 1.677 1.124

a Indicates the model with the lowest MAPE for that particular step-a-head forecast.

aanother (given the set of explanatory variables), 2–5 and 7 the superscript ( ) indicates themixed results still can provide a strong indica- model with the lowest MAPE for that particulartion of the information content of candidate step-a-head forecast.) Two results stand outvariables. from these experiments. First, for sample A,

models that include the interest rate spread(models I and II) produce the lowest MAPEs in

3. Forecasts of real variables nine of the 12 steps. Similarly, model IIproduces MAPEs lower than those from model3.1. Forecasts of industrial productionV in ten of the 12 steps, indicating an incentive

The top portion of Table 2 reports the to include the interest rate spread rather than theMAPEs of the forecasts of industrial production federal funds rate in forecasts of industrialover the 1973:12–1979:10 period using the production for the 1959–1979 period. Second,1959:1–1979:10 sample A data set. (In Tables each of the models that include money (models


Table 3Comparison of the means of the absolute percentage error (MAPEs) of forecasting real personal income with two sampleperiods


I II III IV VY,CPI,M2,SP Y,CPI,SP Y,CPI,M2 Y,CPI,M2,FF Y,CPI,FF

Sample A: 1959:1 –1979:10. Forecast Horizon: 1973:12 –1979:10a1 0.352 0.401 0.408 0.353 0.342 0.330a2 0.562 0.587 0.559 0.556 0.518 0.511

a3 0.696 0.723 0.694 0.708 0.651 0.668a4 0.817 0.815 0.808 0.829 0.805 0.834

a5 0.952 0.873 0.870 0.949 0.927 0.984a6 1.081 0.953 0.940 1.100 1.068 1.169a7 1.174 1.051 1.030 1.217 1.178 1.289a8 1.284 1.120 1.112 1.308 1.281 1.425a9 1.396 1.268 1.263 1.432 1.401 1.575

a10 1.470 1.406 1.441 1.554 1.509 1.743a11 1.592 1.582 1.647 1.638 1.595 1.866

a12 1.714 1.753 1.835 1.743 1.698 1.986

Sample B: 1980:1 –1997:3. Forecast Horizon: 1991:5 –1997:3a1 0.685 0.698 0.690 0.697 0.707 0.714

a2 0.740 0.752 0.735 0.755 0.745 0.748a3 0.816 0.882 0.848 0.855 0.862 0.848a4 0.933 0.994 0.948 0.965 0.960 0.942a5 0.852 0.931 0.891 0.909 0.924 0.898a6 0.903 0.989 0.942 0.979 0.997 0.967a7 0.870 0.956 0.901 0.963 0.984 0.955a8 0.853 0.962 0.893 0.952 0.974 0.914a9 0.956 1.056 0.993 1.027 1.046 0.997a10 0.848 0.947 0.876 0.919 0.935 0.874a11 0.850 0.945 0.883 0.919 0.934 0.893a12 0.831 0.920 0.871 0.904 0.921 0.901

a Indicates the model with the lowest MAPE for that particular step-a-head forecast.

The lower portion of Table 2 reports theI, III, and IV) produce MAPEs that are lowerMAPEs of the forecasts of industrial productionthan those from the AR in nine of the 12 steps.over the 1991:5–1997:3 period obtained byThese results lead us to conclude that both theemploying the 1980:1–1997:3 sample B dataspread and M2 are reasonable candidate vari-set. As with the results from sample A, theables for intermediate targets or as information

3 interest rate spread continues to provide in-variables for this period.formation content for industrial production as

3A reasonable question is whether the MAPEs from the the MAPEs from model II are lower than thosefive alternative models are significantly different from from the AR model in eight of the 12 steps (andthose of the AR model. For example, confidence intervals tying in another step). In contrast to the resultscould be employed to test this but, as noted in Thoma and

from sample A, we conclude that money doesGray (1998, p. 531, fn. 8), there have been ‘recentlynot provide information content for industrialvoiced concerns about the theoretical foundations and

performance’ of the available procedures. production for this sample as each model that


Table 4Comparison of the means of the absolute percentage error (MAPEs) of 12-step-ahead forecasting experiments of theConsumer Price Index over two sample periods (The output / income variable is industrial production)


I II III IV VCPI,IP,M2,SP CPI,IP,SP CPI,IP,M2 CPI,IP,M2,FF CPI,IP,FF

Sample A: 1959:1 –1979:10. Forecast Horizon: 1973:12 –1979:10a a1 0.174 0.181 0.176 0.187 0.173 0.173a2 0.282 0.292 0.294 0.290 0.257 0.270a3 0.433 0.427 0.435 0.440 0.382 0.408a4 0.550 0.522 0.553 0.530 0.486 0.519a5 0.664 0.640 0.673 0.648 0.579 0.615a6 0.786 0.805 0.809 0.778 0.698 0.742a7 0.914 0.993 0.974 0.953 0.839 0.894a8 1.080 1.197 1.132 1.121 1.014 1.058

9 1.252 1.422 1.305 1.307 1.199* 1.241a10 1.437 1.638 1.463 1.486 1.395 1.427a11 1.633 1.843 1.613 1.673 1.565 1.594a12 1.851 2.042 1.787 1.862 1.724 1.759

Sample B: 1980:1 –1997:3. Forecast Horizon: 1991:5 –1997:3a1 0.041 0.056 0.058 0.051 0.059 0.061a2 0.099 0.112 0.134 0.103 0.118 0.127a3 0.151 0.182 0.214 0.159 0.174 0.185

a4 0.205 0.222 0.289 0.190 0.212 0.235a5 0.264 0.267 0.359 0.214 0.240 0.272a6 0.321 0.293 0.420 0.224 0.252 0.308a7 0.382 0.304 0.484 0.230 0.266 0.345a8 0.453 0.328 0.556 0.255 0.291 0.398a9 0.530 0.352 0.636 0.271 0.307 0.457a10 0.611 0.378 0.718 0.280 0.330 0.517a11 0.697 0.399 0.804 0.303 0.360 0.582a12 0.789 0.427 0.899 0.332 0.383 0.654

a Indicates the model with the lowest MAPE for that particular step-a-head forecast with this output / income variable.

includes money (I, III, and IV) produces higher the MAPEs from model I are smaller than thoseMAPEs than does the AR model in every step. of model III in eight of the 12 steps as well.

Third, model II produces lower MAPEs thandoes the AR model in nine of the 12 steps.3.2. Forecasts of real personal incomeHence, the inclusion of the paper-bill spread

The top portion of Table 3 reports the does appear to improve forecasts of real person-MAPEs when forecasting real personal income al income for this sample.using Sample A. As to whether the paper-bill To compare measures of the interest rate,spread contains information content for real consider the MAPEs from models II and V.personal income for the 1959:1–1979:10 period, These models differ in the inclusion of thenote first that model I, which includes M2 and spread in model II and the federal funds rate inthe spread, produces lower MAPEs than does model V. Since model II produces lowerthe AR model in eight of the 12 steps. Second, MAPEs than does model V in nine steps, it


Table 5Comparison of the means of the absolute percentage error (MAPEs) of 12-step-ahead forecasting experiments of theConsumer Price Index over two sample periods (The output / income variable is real personal income)


I II III IV VCPI,Y,M2,SP CPI,Y,SP CPI,Y,M2 CPI,Y,M2,FF CPI,Y,FF

Sample A: 1959:1 –1979:10. Forecast Horizon: 1973:12 –1979:10a1 0.174 0.173 0.163 0.176 0.161 0.160

a2 0.282 0.282 0.282 0.278 0.250 0.256a3 0.433 0.401 0.416 0.422 0.387 0.395a4 0.550 0.510 0.540 0.533 0.502 0.523a5 0.664 0.615 0.650 0.649 0.605 0.637a6 0.786 0.756 0.761 0.790 0.718 0.760a7 0.914 0.935 0.901 0.964 0.842 0.884a8 1.080 1.131 1.061 1.107 0.977 1.014a9 1.252 1.320 1.199 1.261 1.116 1.132

a10 1.437 1.507 1.325 1.401 1.273 1.262a11 1.633 1.673 1.429 1.527 1.409 1.379a12 1.851 1.820 1.537 1.677 1.537 1.496

Sample B: 1980:1 –1997:3. Forecast Horizon: 1991:5 –1997:3a1 0.041 0.089 0.098 0.091 0.094 0.090a2 0.099 0.181 0.206 0.180 0.189 0.186a3 0.151 0.244 0.291 0.236 0.235 0.232a4 0.205 0.289 0.356 0.258 0.258 0.274

a5 0.264 0.318 0.405 0.260 0.263 0.286a6 0.321 0.354 0.471 0.294 0.276 0.316a7 0.382 0.367 0.532 0.313 0.284 0.368a8 0.453 0.401 0.621 0.342 0.323 0.435a9 0.530 0.446 0.716 0.377 0.355 0.509a10 0.611 0.477 0.809 0.413 0.391 0.577a11 0.697 0.500 0.899 0.446 0.432 0.641a12 0.789 0.526 0.996 0.467 0.440 0.715

a Indicates the model with the lowest MAPE for that particular step-a-head forecast with this output / income variable.

appears that the spread is a ‘better’ interest rate MAPEs are lower than those from the ARmeasure. model in eight of the 12 steps.

Comparing the MAPEs from models I, III, An abrupt change in the information contentand IV to those from the AR model examines of these candidate variables occurred acrossthe relative contribution of M2 to the forecasts samples A and B. During the 1980–1997of real personal income. Model III, which period, neither money nor measures of theincludes money but not a measure of the interest interest rate can be considered reasonable candi-rate, produces MAPEs lower than those from date variables when forecasting real personalthe AR model in only two of the 12 steps. income during the later period. As shown in theHowever, when money is combined with a lower portion of Table 3, for this sample the ARmeasure of interest, as in models I and IV, the model is clearly the superior specification rela-


Table 6tive to the other five models, producing the4 A summary of the forecasts of the consumer price indexlowest MAPEs in 11 of the 12 steps.

reported in Tables 4 and 5 and those not previouslyreported using M1 and then the monetary base as the

amonetary aggregate

4. Forecasts of nominal variables MAPE Summary of forecasts of the CPI withcomparison three monetary aggregates

4.1. Forecasts of the consumer price indexPercentage of cases where MAPEcomparison at left is trueTable 4 provides the results from the fore-Experi- Experi- Experi-casts of the CPI which uses M2 as the monetaryments ments mentsaggregate and industrial production as the out-using M2 using M1 using Baseput / income variable. Table 5 does the same forA B A B A Bwhen real personal income is the measure of

output / income. These forecasting experiments AR,I 58 46 4 100 38 100were then duplicated using first MI and then the AR,II 42 100 42 100 42 100

AR,III 58 29 4 62 4 75monetary base in place of M2 in the variousAR,IV 0 33 0 46 0 46model specifications. The results from theseAR,V 0 42 0 42 0 42experiments are discussed below and are sum- I,IV 0 17 17 0 0 0

marized in Table 6. II,V 0 4 0 4 0 4The top portion of Table 4 shows that for III,IV 0 67 0 12 0 8

III,V 0 92 67 12 62 8sample A the AR model produces lowerIV,V 79 88 96 54 100 8MAPEs than those from models I and II in nine

aand ten of the 12 steps, respectively. This The values in columns headed sample ‘A’ and sample‘B’ indicate the percentage of cases for their respectiveappears to remove the interest rate spread as asample that the MAPE Comparison on the left is truereasonable candidate variable for forecasts ofsummed over the forecasts of the CPI using industrialthe CPI for this period. In contrast, notice thatproduction and then real personal income, and substituting

while both models that include the federal funds the various monetary aggregates indicated in this table.rate (models IV and V) produce lower MAPEsthan those from the AR model in all cases,

Using the same sample A period, the fore-model IV which includes both money and thecasting experiments of the CPI with real person-federal funds rate is clearly the superior modelal income produced the same general conclu-specification in this case — producing thesions as those with industrial production as thelowest MAPEs in 12 of the 12 steps (tyingmeasure of output / income. The top portion ofmodel V in the first step).Table 5 shows that model IV is the superiormodel specification. The only notable difference

4 in the results from the alternative measures ofWe found support for Emery’s (1996) claim of an outlieroutput / income is that there is support for bothin the 1980 data. Using a 1981:1–1997:3 sample we found

model V to be the superior model-producing the lowest measures of interest as candidate variables whenMAPEs in nine of the 12 steps. Moreover, model II real personal income is used, but the federalproduces lower MAPEs than those with the AR model in funds rate is again the superior measure ofhalf of the cases. However, consistent with the results

interest.using the 1980:1–1997:3 sample, we found that M2 doesThe lower portions of Tables 4 and 5 reportnot provide information content using the 1981:1–1997:3

sample. the results from the forecasts of the CPI for the


later sample B period when industrial product- both MI and the monetary base (but not M2)ion and then real personal income are used as and the federal funds rate are strong candidatesthe output / income variable. When forecasting as information variables when forecasting thethe CPI using the 1980:1–1997:2 (sample B) CPI during the sample A data period.data, model III (IV) is the superior specification Table 6 shows that an abrupt change appearswhen industrial production (real personal in- to have taken place across these two samples ascome) is used as the measure of output / income to which monetary aggregate provides the best(Again, the difference between models III and information. Making the same model compari-IV being the inclusion of the federal funds rate sons as indicated above with sample B, wein model IV, in addition to M2). With regard to conclude that for the later data sample that thethe information content of money, the results information content of MI, the monetary base,with the later sample are consistent with those and the federal funds rate degraded substantiallyobtained with the earlier sample. However, when forecasting the CPI during the 1980–1997comparing the MAPEs from models I, II, IV, period. However, the information content of M2and V to those from the AR model show a dramatically improved for this sample.distinct erosion in the information content ofboth measures of interest during this later 4.2. Forecasts of nominal personal income

5period.Table 7 reports the MAPEs of forecasts of

nominal personal income. Using the Sample A4.1.1. Sensitivity of CPI forecasts to monetarydata set, we find that model II produces theaggregatelowest MAPEs in 9 out of 12 step-aheadWe repeated the forecasting experiments firstforecasts and beats the AR forecasts in 11 out ofusing MI and then the monetary base as the

6 12 steps. Thus, similar to the results of forecast-monetary aggregate in place of M2. The resultsing industrial production over this samplefrom these forecasting experiments are summa-period, the paper-bill spread provides informa-rized in Table 6. By comparing the MAPEstion content when forecasting nominal personalfrom models III through V, we can examine theincome. As pointed out by Emery (1996) andrelative advantage of including a monetaryThoma and Gray (1998), this result may be dueaggregate only, only federal funds rate (FF), orto the 1974 outlier in the spread data.both a monetary aggregate and FF when fore-

Using the Sample B data set, model IVcasting prices. Similarly, a comparison of theproduces the lowest MAPEs in 5 out of 12 stepsMAPEs from the AR model to those fromand beats the AR model in 11 out of 12 steps.models I, III, and IV examines the relativeAlso, model V produces the lowest MAPEs in 5contribution of a monetary aggregate. Fromout of 12 steps and beats the AR model in 11these comparisons there is strong evidence thatout of 12 steps. These two results provide strong

5 evidence that both M2 and the Federal FundsUsing a 1981:1–1997:3 sample, we found that model IVrate provides information content for nominal(with industrial production as the measure of output)

produced the lowest MAPEs in ten of the 12 steps. This personal income over the later sub-period.too lends support for Emery’s (1996) claim of an outlier inthe 1980 data. 4.2.1. Sensitivity of forecasts of nominal6The monetary base used was that from the St. Louis

personal income to monetary aggregateFederal Reserve Bank. Using the base from the FederalAs above, we conducted the forecastingReserve Board of Governors produces essentially the same

results. experiments first using M1 and then the monet-


Table 7Comparison of the means of the absolute percentage error (MAPEs) of forecasting nominal personal income with two sampleperiods


I II III IV VPY,CPI,M2,SP PY,CPI,SP PY,CPI,M2 PY,CPI,M2,FF PY,CPI,FF

Sample A: 1959:1 –1979:10. Forecast Horizon: 1973:12 –1979:10a1 0.319 0.360 0.361 0.330 0.316 0.312

a2 0.529 0.484 0.481 0.529 0.442 0.444a3 0.712 0.598 0.579 0.681 0.560 0.610

a4 0.932 0.710 0.673 0.835 0.714 0.804a5 1.125 0.821 0.757 0.976 0.866 0.988a6 1.316 0.932 0.817 1.083 1.009 1.182a7 1.497 1.049 0.896 1.191 1.133 1.355a8 1.649 1.110 0.949 1.294 1.210 1.506a9 1.830 1.267 1.122 1.455 1.395 1.704a10 2.002 1.428 1.261 1.594 1.538 1.900a11 2.186 1.550 1.426 1.721 1.670 2.097a12 2.417 1.673 1.640 1.878 1.817 2.294

Sample B: 1980:1 –1979:3. Forecast Horizon: 1991:5 –1979:3a1 0.575 0.593 0.581 0.588 0.586 0.598

a2 0.647 0.654 0.651 0.636 0.623 0.636a3 0.806 0.819 0.792 0.765 0.737 0.748a4 0.890 0.882 0.858 0.833 0.805 0.807

a5 0.924 0.895 0.882 0.842 0.821 0.814a6 0.954 0.935 0.921 0.902 0.901 0.861a7 1.039 1.003 0.983 0.962 0.946 0.908a8 1.095 1.019 0.995 0.979 0.974 0.919a9 1.205 1.069 1.089 1.018 0.985 0.955

a10 1.326 1.072 1.190 0.999 0.997 1.021a11 1.477 1.056 1.311 0.974 0.979 1.120

a12 1.515 1.008 1.341 0.911 0.894 1.130a Indicates the model with the lowest MAPE for that particular step-a-head forecast.

ary base as the monetary aggregate in place of 4.3. Forecasts of the producer price indexM2. The results from these forecasting experi-

We forecasted the producer price index firstments are summarized in Table 8. Making theusing industrial production and then real person-same model comparisons as were described in

Section 4.1.1, the results reported in Table 8 al income as the output / income variables. Inprovide very strong evidence that all monetary addition, we alternated the monetary aggregateaggregates and the federal funds rate are strong by first using M2, and then M1 and finally thecandidates as information variables when fore- monetary base. We do not include the tablescasting nominal personal income during both detailing the results as we did in Tables 4 and 5the early (sample A) and later (sample B) for forecasts of the CPI. Instead, the resultsperiods. from the forecasting experiments of the PPI are


Table 8 Table 9aA summary of the forecasts of nominal personal income A summary of the forecasts of the producer price index

reported in Table 7 and those not previously reported usingMAPE Summary of forecasts of the PPIaM1 and then the monetary base as the monetary aggregatecomparison with three monetary aggregates

MAPE Summary of forecasts of nominal personalPercentage of cases wherecomparison income with three monetary aggregatesMAPE comparison at left is true

Percentage of cases whereExperi- Experi- Experi-MAPE comparison at left is truements ments ments

Experi- Experi- Experi- using M2 using M1 using Basements ments ments

A B A B A Busing M2 using M1 using BaseAR,I 100 92 96 100 83 100A B A B A BAR,II 100 67 100 67 100 67

AR,I 8 25 8 25 8 8 AR,III 100 96 42 100 42 100AR,II 8 17 8 17 8 17 AR,IV 100 83 79 83 62 96AR,III 8 8 8 17 8 8 AR,V 96 62 96 62 96 62AR,IV 0 8 0 17 0 8 I,IV 0 29 4 25 0 25AR,V 0 8 0 8 0 8 II,V 0 42 0 42 0 42I,IV 75 0 75 8 83 8 III,IV 100 8 100 12 96 17II,V 83 8 83 8 83 8 III,V 46 0 96 0 96 0III,IV 0 8 0 83 0 92 IV,V 0 4 79 0 92 4III,V 67 33 75 8 58 17 a The values in columns headed sample ‘A’ and sampleIV,V 92 58 92 0 100 8

‘B’ indicate the percentage of cases for their respectivea The values in each columns headed sample ‘A’ and sample that the MAPE comparison on the left is true

sample ‘B’ indicate the number of cases for their respec- summed over the forecasts of the PPI using industrialtive sample that the MAPE comparison is true. production and then real personal income, and substituting

the various monetary aggregates indicated in this table.

summarized in Table 9. Making the modelcomparisons described earlier, the results in rates provide information content for output ifTable 9 deliver strong evidence that no monet- the inclusion of these variables improved uponary aggregate can serve as a reasonable candi- an autoregressive forecast. Our procedure pro-date of an information variable when forecast- duced 12-month-ahead forecasts, continuallying the PPI with either sample A or sample B. updating the model estimates after each month.While there is weak support for the federal We then compute the mean of the 12-forecast-funds rate as an information variable with both ing errors for each month. This provides asamples, there is no such support for the interest time-varying measure of forecasting ability ofrate spread for the 1959–1979 period. money, the interest rate and spread for each

month in time and for each variable of interest.With this procedure, we considered two sam-ples: 1959–1979 and 1980–1997.5. Conclusions

Consistent with previous in-sample estimates,The forecasting experiments here provide an our out-of-sample forecasts show that with the

alternative to looking at F-statistics when ex- later sample the paper /bill spread but notamining whether money, interest rates or the monetary aggregates aid in forecasts of indus-paper-bill spread provide information content trial production and real personal income. Asfor subsequent movements in output, income, or this was obtained with the later sample, thisprices. Here monetary aggregates and interest result is in contrast to recent claims that the


Black, D. C., & Dowd, M. R. (1994b). The moneyinformation content of the spread was due to anmultiplier, the money market, and the LM curve.outlier in the 1974 data. Our results differ fromEastern Economic Journal 30, 301–310.other arguments in that we find that money

Dotsey, M., & Otrok, C. (1994). M2 and monetary policy:improves the forecasts of the CPI and nominal a critical review of the recent debate. Federal Reservepersonal income. These results show, in contrast Bank of Richmond Economic Quarterly 80, 41–59.to recent claims, that financial market variables Emery, K. M. (1996). The information content of the

paper-bill spread. Journal of Economics and Businessstill serve as important information variables.48, 1–10.The forecasting experiments of the PPI pro-

Friedman, B. M., & Kuttner, K. N. (1992). Money,duced substantially different results: no monet-income, prices and interest rates. American Economic

ary aggregate provides information content Review 82, 472–492.when forecasting the PPI. Friedman, B. M., & Kuttner, K. N. (1993). Another look at

the evidence on money-income causality. Journal ofEconometrics 57, 189–203.

Garfinkel, M. R., & Thornton, D. L. (1991). The multiplierAcknowledgementsapproach to the money supply process: a precautionarynote. The Federal Reserve Bank of St. Louis Review 73,We thank James P. LeSage, Rebecca47–64.Neumann, David Tufte, Mark Wheeler, Cal

Gauger, J., & Black, H. A. (1991). Asset substitution andWinegarden, the participants in session 26B at monetary volatility. Journal of Money, Credit, andthe 1998 Southern Economic Association’s An- Banking 23, 677–691.nual Conference, and the anonymous referees Granger, C. W. J. (1988). Some recent developments in a

concept of causality. Journal of Econometrics 39, 199–for helpful comments and suggestions. Any211.remaining errors are our responsibility. For

Hafer, R. W., & Kutan, A. M. (1997). More evidence oncorrespondence contact Michael Dowd at thethe money–output relationship. Economic Inquiry. 35,

above address. 48–58.Jacobs, R. L., Leamer, E. E., & Ward, M. P. (1979).

Difficulties with testing for causation. Economic InquiryReferences 17, 401–413.

Ohanian, L. E. (1988). The spurious effects of unit rootson vector autoregressions. Journal of Econometrics 39,Akhtar, M. A. (1997). Understanding open market opera-251–266.tions, Public Information Department, Federal Reserve

Thoma, M. A., & Gray, J. A. (1998). Financial marketBank of New York.variables do not predict real activity. Economic InquiryBlack, D. C., & Dowd, M. R. (1994a). Asset substitution: a36, 522–539.note on the factors that influence both money supply

and demand. Journal of Economic Education 25, 167– Walsh, C. E. (1998). Monetary theory and policy, MIT171. Press, Cambridge, MA.

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New dogs and old tricks: do money and interest rates still provide information content for forecasts of output and prices?