Full text of Working Paper (Federal Reserve Bank of Cleveland) : The Ohio Economy : Using Time Series Characteristics in Forecasting, Working Paper 85-08

The full text on this page is automatically extracted from the file linked above and may contain errors and inconsistencies.

http://clevelandfed.org/research/workpaper/index.cfm
Best available copy

Working Paper 8508

THE O H I O ECONOMY: USING TIME S E R I E S
CHARACTERISTICS I N FORECASTING

By James G. Hoehn and James J. Balazsy, J r .

Working papers of t h e Federal Reserve Bank o f Cleveland
are prelimiri.ary m a t e r i a l s , c i r c u l a t e d t o s t i m u l a t e
d i s c u s s i o n and c r i t i c a l comment. The views expressed
h e r e i n a r e those o f t h e authors and n o t n e c e s s a r i l y o f
t h e Federal Reserve Bank o f Cleveland o r the Board o f
Governors o f t h e Federal Reserve System. Diane Mogren
and Gordon Schlegel provided h e l p f u l programming
assistance. P a r t i c u l a r thanks are due t o W i l l i a m C.
Gruben o f t h e Federal Reserve Bank o f D a l l a s . The
authors acknowledge h e l p f u l discussions w i t h Michael
Bagshaw, John Erceg, P h i l i p I s r a i l e v i c h , and Robert
Schnorbus. Kathryn Begy and Linda Shy prepared t h i s
manuscript.

December 1985
Federal Reserve Bank o f Cleveland

http://clevelandfed.org/research/workpaper/index.cfm
Best available copy

Abstract

T.ne s e r i e s methods are used t o determine what i n f o r m a t i o n Ohio and
n a t i o r z i s t a t i s t i c s convey about the c u r r e n t and f u t u r e s t a t e o f the r e g i o n a l
econory.

P r o p e r t i e s o f a number of q u a r t e r l y s e r i e s measurin g aggregate

economic a c t i v i t y and p r i c e s i n Ohio are described, i n c l u d i n g t h e i r growth
r a t e s and v a r i a b i l i t y , c y c l i c i t y , c o r r e l a t i o n a t a moment i n time, tendency t o
foreshhdow each o t h e r ' s movements, and tendency t o be foreshadowed by n a t i o n a l
econom'c i n d i c a t o r s .

These p r o p e r t i e s are o f i n t e r e s t b o t h f o r f o r e c a s t i n g ,

e i t h e r Formal o r judgmental, and f o r understanding s t r u c t u r a l c h a r a c t e r i s t i c s
of the 3 h i o economy.

They a r e e x t e n s i v e l y t a b u l a t e d here.

I n s d d i t i o n , some methods of f o r e c a s t i n g , which e x p l o i t these time s e r i e s
p r o p e r t i e s , a r e assessed i n an out- of- sample f o r e c a s t p e r i o d .

The t r e a t m e n t

o f these methods and means f o r comparing them i s elementary and somewhat
pedogogiial f o r t h e b e n e f i t o f readers w i t h 1i t t l e p r i o r knowledge o f t i m e
s e r i e s f o r e c a s t i n g methods.
The nethod f o r b u i l d i n g a time s e r i e s model described i n Hoehn (1984) and
applied

Y -

Texas w i t h considerable f o r e c a s t i n g success i s a p p l i e d , w i t h some

m o d i f i c a t on, t o t h e economy o f Ohio.

-a p r i o r i ,

i s a l s o implemented.

A simple t r i c k l e - d o w n model, s p e c i f i e d

Forecasts combining these methods a r e assessed.
.. .

.

The f o r e c a s t s o f t h e m u l t i v a r i a t e models are f r e q u e n t l y found t o be b e t t e r
than those o f u n i v a r i a t e autoregressions.

I n some cases, they a r e

s i g n i f i c a n t l y s u p e r i o r , according t o an i n d i r e c t s t a t i s t i c a l t e s t adapted f r o m
Ashley, Granger, and Schmalensee (1980).

The r e s u l t s show t h a t i n f o r m a t i o n

can be i d e 2 t i f i e d as t o source and q u a n t i f i e d using v e r y simple r e g r e s s i o n
methods.

http://clevelandfed.org/research/workpaper/index.cfm
Best available copy

THE O H I O ECONOMY:

T I M E SERIES CHARACTERISTICS

The r e g i o n a l economist depends t o a l a r g e e x t e n t upon economic s t a t i s t i c s
i n assessing the c u r r e n t s t a t e and l i k e l y f u t u r e course o f h i s r e g i o n .
Consequently, an understanding of the p r o p e r t i e s o f the a v a i l a b l e s e r i e s can
enhance h i s understanding and forecasts of the region.
t h i s f e e l i s p u r e l y judgmental i n nature:

One way o f a c q u i r i n g

the a n a l y s t accumulates

understanding by i n f o r m a l thought and observation, g e n e r a l l y over a p e r i o d of
years.

More formal approaches i n v o l v e b u i l d i n g models.

S t r u c t u r a l models

impose d e t a i l e d and somewhat i n c r e d i b l e assumptions ( " i d e n t i f y i n g
r e s t r i c t i o n s " ) about economic r e l a t i o n s h i p s i n an attempt t o e x t r a c t knowledge
o t h e r w i s e hidden i n the data.

The time series approach a l l o w s d e s c r i p t i o n o f

the d a t a w i t h o u t the requirement o f imposing extensive assumptions o r p r i o r
knowledge.

I t l e t s the data s e t speak f o r i t s e l f .

The premise o f t h i s study i s t h a t the r e g i o n a l economist can b e t t e r
understand the Ohio economy by s t u d y i n g the p r o p e r t i e s o f i m p o r t a n t Ohio time
series.

The r e s u l t s show t h a t i n f o r m a t i o n i s a v a i l a b l e from sources t h a t can

be i d e n t i f i e d and q u a n t i f i e d through simple r e g r e s s i o n methods t h a t are widely
understood.

I. The Regional Forecastinq Problem
Regional economic time s e r i e s e x h i b i t v a r i a t i o n from secular, c y c l i c a l ,
and seasonal sources.

Regional f o r e c a s t e r s attempt t o assess c u r r e n t a c t i v i t y

and t o p r e d i c t the f u t u r e course o f t h e r e g i o n a l economy by e x p l o i t i n g t h e
i n f o r m a t i o n contained i n v a r i o u s time s e r i e s .

Usually, t h i s process o f

e x t r a c t i n g i n f o r m a t i o n i s q u i t e i n f o r m a l and judgmental.

I n o t h e r cases, the

process i n v o l v e s t h e use o f 'a formal s t a t i s t i c a l model o f some k i n d .
s t u d y seeks t o provide.forma1 t o o l s f o r the Ohio f o r e c a s t e r .

This

http://clevelandfed.org/research/workpaper/index.cfm
Best available copy

Figure

1

illustrates the single series that is perhaps o f greatest

interest to Ohio forecasters:
(seasonally adjusted).

payroll or establishment-survey employment

Although it has exhibited an upward trend, its growth
. .

has not proceeded smoothly.

The strong dependence o f Ohio on national

conditions is obvious from the National Bureau of Economic Research peaks and
troughs, denoted by " P s " and "T's," respectively.
i

If history tends to repeat

itself, then the regional forecaster can benefit from knowing the trend rate
o f growth, any predictable cyclical behavior, and any clues available from
national data, such as the leading indicator index.

Also, relations between

the regional series may potentially aid in forecasting.

This paper will

describe these characteristics and assess their value to regional forecasters.

Regional Forecasting Models

1 1

Regional forecasting models have attracted interest among government and
business planners and have proliferated with the availability o f regional
data.

Many o f these models are of the so-called structural variety, which

i nvol ve use o f detai 1 ed assumptions supposedly drawn from economic theory.

Their construction reflects a primary goal of estimating the behavorial
relationships (structure) corresponding t o the theory, although they are
employed for forecasting as well.

For some applications, involving analysis

o f the effects of structural change o r o f the response o f the regional economy
t o particular policies o r events, a structural model is necessary.

Despite

the recent proliferation o f structural models, little clear evidence exists on
their ability to forecast well.'
Time series models, the alternatives to structural models, are primarily
designed for forecasting.

Such models can be built even in contexts in which

the theory o r data set required t o build a structural model is unavailable.

Figure 1.

http://clevelandfed.org/research/workpaper/index.cfm
Best available copy

ESTABLISHMENT-SURVEY EMPLOYMENT
SEASONALLY ADJUSTED

http://clevelandfed.org/research/workpaper/index.cfm
Best available copy

Most regional forecasting problems occur in such a context.
The remainder of this paper is organized as follows.

A general survey of

some related work is presented and forecasting context and data series are
Subsequent sections characterize the uni vari ate properties,

described.

intraregional relationships, and national-regional o r so-called trickle-down
relationships.

These characteristics are then used to-suggest candidate

variables for inclusion in a multivariate autoregressive model (MAR) o f the
Ohio economy, using a stepwise regression procedure t o select among the
candidates.

An

priori trickle-down model is also implemented.

The latter

two models' forecasting ability is compared with that of univariate
autoregressions in the 1979-83 out-of-sample period.

111. A Brief Survey o f Previous Work
A number o f time series approaches have been implemented t o facilitate
regional forecasting.

The univariate model represents the simplest approach

and uses only the past history o f each regional variable t o predict its
future.

These models are the most straightforward t o implement, and their

forecasts are often as good as--and sometimes better than--more complex
models.

The forecasting accuracy o f univariate models serves as an

appropriate benchmark for evaluating the relative efficiency of other
methods.

The Box-Jenkins (1970) approach for identifying and estimating

autoregressive integrated moving average (ARIMA) models is perhaps the most
flexible and also the most popular framework for univariate time series
model ing.
Multivariate models use the history o f other variables to describe the
movement in the series t o be forecast--that is, they exploit delayed
interactions, o r lead-lag relations, between series.

The identification and

http://clevelandfed.org/research/workpaper/index.cfm
Best available copy

estimation of the appropriate multivariate model is problematic and is
currently subject to research along different paths.

The essential dilemma o f

the regional multivariate model is that o f using as much
information as
.
.

possible by including as many relevant series in the equations, yet minimizing
the inaccuracy due to multicollinearity and scarcity of degrees of freedom.
For example, the more variables that are included, the more sources of
information that are incorporated in the resulting model's forecasts, thus
tending to improve accuracy.

Yet, at the same time, inclusion o f more

variables will increase the standard errors of the estimates o f the model's
parameters, especially if variables are highly correlated, thus tending to
reduce the accuracy bf forecasts.

Furthermore, as the results t o fol low will

illustrate, more complex models may become unstable and break down out o f the
sample used'-t o specify and estimate them.
for solving this dilemma is available.

Unfortunate.ly, no general procedure

Several recent efforts directed toward

regional forecasting are o f interest.
Anderson (1979) first implemented the "Bayesian approach u o f Litterman
(1979) for a regional model o f the Ninth Federal Reserve District.

The

dilemma referred t o above is dealt with in a clever and promising way:

many

of parameter estimates is
.
variables and lags are included, but the variance
.

limited by the imposition o f a random walk prior distribution.

The primary

disadvantage o f the procedure is the bias that it introduces into estimates of
parameters.

The greatest practical difficulty o f the approach is the choice

o f appropriate "tightness" restrictions o n the prior.'

Li tterman terms the

model a "vector autoregression" (VAR) because o f its (a) multivariate nature
and ( b ) the absence of moving average parameters (only autoregressive
parameters are present).

http://clevelandfed.org/research/workpaper/index.cfm
Best available copy

More recently, Amirizadeh and Todd (1984) have constructed five "Bayesian
VAR" models for each of five states of the Ninth Federal Reserve District.
They built an elaborate structure of linkages with forecasts of the national
economy.

They have undertaken real-time forecasting, and plan t o publish

their forecasts quarterly.
Kuprianov and Luppoletti (1984) adopt a VAR approach, but without imposing
priors, and implement models for the individual states o f the Fifth Federal
Reserve District.

The specification they employ uses six quarterly past

values o f state employment and deflated personal income, plus three national
variables t o forecast each of the two state variables.
Hoehn, Gruben, and Fomby (1 984a, 1984b) and Hoehn ( 1 984) explore a number
o f alternative methods for regional forecasting by applying them t o the state

of Texas and comparing their performance in an (admittedly short, 10-quarter)
out-of-sample forecast period.

The Bayesian VAR generally did not perform

well relative t o univariate ARIMAs, unless the VAR's prior distribution was
tinkered with extensively, in which case its forecasting accuracy in some
cases approached, but generally still fell short of, the univariate models.
Models with many variables and no priors, using alternatively (a) other
regional variables only (a closed-region model) o r (b) national variables only
(a trickle-down model), also performed poorly.

Using the latter two models

with univariate ARIMA models t o form an unweighted combination forecast
provided accuracy sometimes competitive with the ARIMAs alone.
Hoehn (19841, based o n this experience with alternative models, proposed a
method for-building a forecasting model and implements it for Texas.

( A more

formal variant of that identification procedure, using the stepwise regression
procedure, is described more fully below, where its a p p ~ r c a t i o nt o O h i o series
is presented.)

Essentially, "causality tests" are first used t o select a

http://clevelandfed.org/research/workpaper/index.cfm
Best available copy

small number o f variables that are candidates for inclusion in the equations
Then, combinations of variables and lag structures are used to find
well-fitting and parsimonious equations.

The resulting model for Texas
.

.

provided out-of-sample forecasts consistently superior to those o f univariate
ARIMAs, as measured by the criterion of the root mean square error (RMSE).
For some variables and forecast horizons, the difference in forecasting
accuracy between the multivariate and univariate model forecasts was
significant at the .05 level.

The model, while built according to strictly

statistical criteria, also appeared quite reasonable in light o f intuitions
about the regional economy.

IV.

The Forecasting Problem and the Approach
The objective o f the present study is the construction o f linear

forecasting equations that predict the growth rates o f Ohio variables by their
own lagged growth rates and by those of each other and national series.

For

example, let yt(k> be the forecast of the change in the logarithm o f a
regional variable Y, for period t+k, for k,O, formed at time t, when a1 1 t
realizations are observed.
period t growth.

For example, the k=l case involves forecasting

A linear forecasting equati0.n takes
the general form:
.
.

where a r and the b,, are parameters and S , t is the jth element of a
vector o f q information variables available at time t.

That vector, o r

information set, treats each relevant lag as a distinct variable in the above
equation.

The forecasting equations will be used t o forecast the level of y,

with particular emphasis o n the one-to-four quarter (Ockt4) horizons.

The

http://clevelandfed.org/research/workpaper/index.cfm
Best available copy

regional variables, Y, o f concern, are the following seasonally adjusted Ohio
variables:
(1)

Payroll Employment, total

(PAY ROLL)

(2)

Payroll Employment, Manufacturing

(MFG)

(3) Payroll Employment, Nonmanufacturing
(4)

Household-survey Employment

(NONMFG)
( EMPL)

(5) Civilian Labor Force

(LF)

(6) Personal Income

( INCOME

>

(7) Retail Sales

(RETAIL)

(8) Housing Starts

(STARTS

(9) Workweek in Manufacturing

(HOURS)

(10)

Consumer Prices

(PRICES)

Some of these series were seasonally adjusted by the reporting agency;
others were seasonally adjusted either by the data vendor o r by the authors.
Some data were transformed from monthly averages to quarterly averages.

The

Ohio consumer price series required an elaborate method of construction from
the Cleveland and Cincinnati Consumer Price Indexes.
data sources and adjustments is in Appendix A.

A fuller description of

The series themselves, after

these adjustments, but before transformation to logarithmic growth rates, are
listed in Appendix B.

The data series each began by at least the first

quarter o f 1965 (in the format we adopt, that quarter is denoted 65QI).

The

working data set for initial analysis included the growth rates for 65QIV
through 78QIV, o r 5 3 data points.

The period from 79QI t o 83QIV (20 data

points) was saved for out-of-sample analysis of models constructed during the
initial analysis.

http://clevelandfed.org/research/workpaper/index.cfm
Best available copy

V.

Information Gain:

A

Pedaqogy of the I-Statistic

The location of information available about the future course o f a given
Ohio series (the identity of the S vector) will be assessed by a systematic
.

battery o f nested hypothesis tests.

.

The tests involve successive

generalizations of the prediction equation to incorporate additional
variables.

The value of information will be measured by the improvement in

the fit o f an equation as the potentially informative variable is added.

The

techniques and their underlying statistical basis are presented in this
section.

A regressor (so-called "explanatory" variable) x is informative (or
contains information) about a regressand (so cal led "dependent" variable) y:to
the extent that knowledge o f x conditions knowledge o f y.

Formally, if

~[y-~(ylx)l~<E[y-E(y)l~then x is informative with respect t o y.

An

obviously useful quantitative measure o f the information value is the
reduction in the condi tional variance relative to the uncondi tional variance.
It is an exact measure if the loss attending an error, y-E(ylx),
proportional to its square.

is

When scaled, o r divided, by the unconditional

variance, this theoretical measure o f information value is identical to the
squared correlation coefficient, r' , where th.e
.relation
between y and x is
.
.
1 i near.

An a1 ternative measure, I-( 1-rL) "' , expresses the reduction of

the expectation of the square root o f the error (standard deviation o f the
disturbance term in the linear regression equation) relative t o the standard
deviation o f y.

This measure is referred to as the information gain from the

,
.
,
. It can be
use o f x to condition eipectations of y and is denoted I
estimated from the standard deviation of y, s,, and the standard ,error o f
the regression of y o n x, s,,,:

http://clevelandfed.org/research/workpaper/index.cfm
Best available copy

Where r e a l i z a t i o n s o f the s t a t i s t i c I a r e r e p o r t e d i n t h i s paper, they r e f l e c t
m u l t i p l i c a t i o n by 100, so t h a t i n f o r m a t i o n gains are expressed as a percentage
of t h e standard d e v i a t i o n .
.

A set o f variables,

XI,

xt,

. . . x,,

.

may be assessed f o r c o l l e c t i v e

i n f o r m a t i o n g a i n by c a l c u l a t i n g :

where

it2 is

the c o r r e c t e d c o e f f i c i e n t of determi q a t i o n .

More g e n e r a l l y , t h e i n f o r m a t i o n c o n t e n t of x above may be of i n t e r e s t i n
c o n t e x t s i n which another v a r i a b l e , say z , o r v a r i a b l e s a r e a l s o p o t e n t i a l l y
informative.

This c o n t e x t i n t r o d u c e s some ambiguity, i n t h a t whether

z

is

i n c l u d e d o r n o t w i l l a f f e c t t h e incremental r e d u c t i o n i n standard e r r o r .
Hence, the i n f o r m a t i o n g a i n of x w i t h r e s p e c t t o y i s dependent on which o t h e r
v a r i a b l e s a r e i n the i n f o r m a t i o n s e t .

Even more g e n e r a l l y , t h e i n f o r m a t i o n

g a i n o f a s e t o f v a r i a b l e s can be measured by t h e incremental r e d u c t i o n t h e i r
i n c l u s i o n i n a m u l t i v a r i a t e l i n e a r model b r i n g s t o i t s standard e r r o r , s u b j e c t
t o t h e i n c l u s i o n o f a s p e c i f i e d ( p o s s i b l y n u l l ) :st o f o t h e r i n f o r m a t i o n
variables.
Consider t h e f o r e c a s t i n g problem posed by t h e p r e s e n t study, i n which
c u r r e n t and f u t u r e values o f y a r e t o be c o n d i t i o n e d on p a s t r e a l i z a t i o n s o f
informatlon variables.

The i n f o r m a t i o n g a i n from own-lags i s f i r s t assessed

by p e r f o r m i n g r e g r e s s i o n ( 1 ) of y on i t s f i r s t two own-lags, i n o r d e r to
o b t a i n the r e d u c t i o n i n standard e r r o r o f t h e r e g r e s s i o n e q u a t i o n r e l a t i v e t o
t h e standard d e v i a t i o n .

http://clevelandfed.org/research/workpaper/index.cfm
Best available copy

Then the i n f o r m a t i o n gain from any s p e c i f i e d candidate v a r i a b l e x can be
assessed by performi ng the r e g r e s s i o n :

2

2
+ Z c,x,-, + u,.
. .
j=1
j =1
The Granqer c a u s a l i t y t e s t (see Granger and Newbold, L19771, pp. 224-6)

(2)

y t = a , + 1 b:yt-,

is

e q u i v a l e n t t o a t e s t of whether o r n o t x i s i n f o r m a t i v e w i t h respect t o y .
given past y .

I t i s based on the F - s t a t i s t i c , c a l c u l a t e d from the sums o f

squared e r r o r s o f regressions ( 1 ) and ( 2 ) , denoted S e and S u , r e s p e c t i v e l y :

where q i s t h e number o f r e s t r i c t i o n s t e s t e d (e.g.,
number o f regressors i n the u n r e s t r i c t e d model.

= 1

-($)"'

c,=O> and k i s the

The I - s t a t i s t i c i s :

(n-k-l+q)"'
n-k- 1

N o t i c e t h a t , a s i d e f r o m t h e adjustment f a c t o r [In-k-l+q)/(n-k-l )1 '/'--which
depends u n i q u e l y upon n, k, and q--equal sums o f squared e r r o r s , which a r i s e
when the ciao, b r i n g about a z e r o value f o r I. The adjustment f a c t o r
e f f e c t i v e l y d e f l a t e s measured improvement i n f i t f o r t h e expenditure o f q
a d d i t i o n a l degrees o f freedom i n the u n r e s t r i c t e d r e g r e s s i o n ( 2 ) .
expressions r e v e a l t h e correspondence between F and I:

These

http://clevelandfed.org/research/workpaper/index.cfm
Best available copy

http://clevelandfed.org/research/workpaper/index.cfm
Best available copy

This relation is illustrated in Figure 2.

The lower bound for I, which occurs

i f F=O, is denoted L :

L approaches zero as the sample size n increases. (It would be -73 percent
for n=6!)

L is the proportional reduction in a regression's sum o f squared

errors that is expected t o occur from the inclusion of q noninformative
regressors.

It may also have some interpretation as a measure o f the

imprecision arising from finite degrees o f freedom.

Given a sample size of

53, as for the period up t o 78QIV, L=-2.04 percent.

For the sample through

83QIV, n-73 and L=-1.46 percent.

L is, roughly, inversely proportionate t o n;

L i s o f order n - '.

If F=l, the proportional reduction o f sum of squared errors of L is
achieved and I is zero.

As F approaches infinity (as the linear relation

becomes more precise), I approaches 100 percent.

These t w o properties are

desirable and illustrate the usefulness of I.
In the causality tests based o n the extended sample period (n=73), the
critical F-values are:
F.o,(2,68)
and F.01(2,68)

3.13
=

4.94

which correspond t o I-statistics of:
I.or(2,68)

=

1

-

70
(68+2(3.13)

'/'

=

2.91 percent

=

5.19 percent

The most common criterion for inclusion of a variable in a model if the ad

http://clevelandfed.org/research/workpaper/index.cfm
Best available copy

hoc rule that the t-statistic must exceed 2 in absolute value. This can be
shown to be equivalent t o the following inequality:

VI.

Univariate Properties
The mean and standard deviation o f each series' growth rate provide

measures o f the average growth rate and its variability.

Equivalently, they

provide the parameter estimates for the simplest univariate model worthy of
consideration, the random walk model. This model is of the form:
yt

=

a, + e t

where a, is the drift parameter and e t is a random variable with zero
autocorrelation at all lags (white noise) and a constant variance u:.
The random walk model serves merely to re-establish the appropriate level o f
the forecast function after acquisition of a new quarterly data point.

Future

growth rates are revised only to the extent that the expected long-term
average growth rate, a,,

is revised.

In particular, cyclical

behavior--persistence in high o r low growth rates--is ruled out in the random
walk model.
u,,

The mean and standard deviation, taken as estimates o f a, and

respectively, are shown in table 1 , in the first t w o columns, f o r the

longer sample ending 83QIV. for the 10 Ohio series.
Cyclicity of growth in time series is the tendency of persistence in
above- or below-average growth from one period t o the next.

This persistence

can be described by the correlation between.rates of change across different
intervals.

The series o f such correlations at various intervals is called the

autocorrelation function:

http://clevelandfed.org/research/workpaper/index.cfm
Best available copy

Table 1 Univariate Properties
Sample: 65QIV - 83QIV
Autocorrelation
at lag
2 3 4 yt
1
- -

.

.

Series

Mean

Standard
Deviation

PAY ROLL

.0028

.0099

.57 .32 .22

.12

.58

.OO

17.7**

- ,0027

.0204

.45 .22 .07 -.07

.45

.03

10.1**

NONMFG

.0054

.0070

.42 .32 .38 .37

.35

.19

9.6**

EMPL

.0028

.0130

.08 -.08 .02

.09 -.08

I NCOME

.0181

,0136

.40 -07 .06 -.05

RETAIL

.0164

.0258

-.26 .09 -.03 .06

-.24

.04

2.0

STARTS

-.0108

.I643

.06 .07 -.lo -.23

.05

.07

-1.0

HOURS

.0001

.0107

.ll -.07 .06 -.06

.ll

-.09

-0.5

PRICES

.0169

.0098

.56 .46 .34 .31

.42

.24

MFG

.06

Autoregressian Equation:
+ b l y t - , + bryt-, + e,

= a + bly,-,

.44 -

-0.8

1 7.6**

19.1**

**Significant at the .O1 level.

I

=

[(standard deviation

-

.

.

standard error of autoregression)/tstandard devSation)l x 100.

http://clevelandfed.org/research/workpaper/index.cfm
Best available copy

Given the sample size n, no autocorrelations are significantly different from
zero (at the .05 level, two-tailed) i f they all fall between approximately
With our samples of 73, the r , must exceed 0.23 in absolute
-+2n-"'.
value to provide strong evidence of persistence from quarter to quarter. The
autocorrelation function for lags one through four is presented in columns
three through six of table 1.
The table reveals substantial positive persistence in growth rates for
prices, payr0.11 employment and its two components, and personal income. The
presence of autocorrelation in both payroll sectors implies that cyclical
variation in Ohio employment is attributable to both the manufacturing and
nonmanufacturing sectors. The household survey based measure of employment,
EMPL,

exhibited no significant autocorrelation.

(1t.i~ interesting to note

that all of the foregoing results regarding autocorrelations of Ohio series
are consistent with those for Texas in Hoehn, Gruben, and Fomby C19841).
The significant autocorrelation in the f i v e s-eries mentioned above
suggests a persistence in growth rates that can be exploited by the regional
forecaster. An appropriate measure of the value of information contained in
the history of the series can be found by first estimating a second-order
autoregression (which we denote as A R 2 > ,

http://clevelandfed.org/research/workpaper/index.cfm
Best available copy

u s i n g t h e o r d i n a r y l e a s t squares method, and then comparing t h e standard e r r o r
of t h i s e q u a t i o n , s,,

t o t h e standard d e v i a t i o n o f y , s,.

can be expressed i n terms o f t h e i n f o r m a t i o n g a i n , [(s,-s,)/s,I
.

.

The comparison
x 100.

Table 1 , i n t h e l a s t t h r e e columns, r e p o r t s t h e e s t i m a t e d r e g r e s s i o n
c o e f f i c i e n t s and t h e a u t o r e g r e s s i v e i n f o r m a t i o n measure f o r each r e g i o n a l time
series.

R e s u l t s i n d i c a t e t h a t t h e one- quarter- ahead p r o j e c t i o n o f the

consumer p r i c e measure has a standard e r r o r about o n e - f i f t h l e s s , when account

i s made o f t h e l a s t two q u a r t e r l y growth r a t e s .

A g a i n of 18 p e r c e n t i s found

f o r p a y r o l l employment, g a i n s of about 10 p e r c e n t a r e achieved f o r the two
p a y r o l l c a t e g o r i e s and 8 p e r c e n t f o r personal income.

(These r e s u l t s o n l y

r e f l e c t t h e e s t i m a t e d i n f o r m a t i o n v a l u e of two lagged g r o w t h r a t e s , whereas
a u t o c o r r e l a t i o n f u n c t i o n s e v a l u a t e p e r s i s t e n c e a t l o n g e r l a g s as w e l l . )

VII.

Intrareqional Information
The v a l u e o f r e g i o n a l s e r i e s i n foreshadowing each o t h e r can be measured

i n t h e f o l l o w i n g way.

Regressions a r e performed t o e s t i m a t e t h e standard

e r r o r o f t h e e q u a t i o n s p e c i f i e d by:

where y and x , a r e two r e g i o n a l s e r i e s .

I f the series x k t r u l y aids i n

f o r e c a s t i n g y , t h e n t h e s t a n d a r d e r r o r o f t h i s b i v a r i a t e e q u a t i o n w i l l be
lower than f o r t h e a u t o r e g r e s s i o n ( i n which c , =

CL

=

0 i s imposed).

The

j o i n t significance t e s t o r F- test for the b , provides a " causality" t e s t i n
t h e sense o f Granger (Granger and Newbold, 1977, p. 225).
f i r s t 10 rows, r e p o r t s r e s u l t s o f these r e g r e s s i o n s .

Table 2, i n t h e

The r e d u c t i o n i n t h e

http://clevelandfed.org/research/workpaper/index.cfm
Best available copy

Table 2
Independent
Variables

...............................
PAYROLL

MFG

InformationGain'
Dependent Variables----------------------------

NONMFG

INCOME

Reqional
2.29

MFG

- . 42

NONMFG

-.53

4.51*

13.38**

PRICES

4.90*
2.65

1.48

.49

3.10

1 -9 5

-.98

9.33**

3.92

3.02*

1.20

4.07*

3.84,

- 1.45

9.35**

9.49**

1.33

- 1.40

1.93

-.46

.20

.01

4.26*

2.28

.30

6.25**

.87

-.73

-.43

- 1.26

-.a4

- 1.25

- 1.31

- 1.03

INCOM

-.I6

.01

1.61

RETAIL

-.55

- 1.03

3.08*

-1.06

.60

STARTS

8.16**

10.34*

2.39

2.51

- 1.29

9.45**

HOURS

-. 8 0

2.81

.58

- 1.43

-.72

PRICES

3.38*

.51
2.25

National
LEAD

19.25** 21 . 7 9 * *

COIN

14.51** 22.32**

PRODUCT

8.02**

14.55**

USPAYROLL

9.44**

10.62**

USMFG

6.61**

13.19**

USHOUSEHOLD

4.11*

7.91**

REALY P

4.53*

8.45**

USLF

HOURS

7.49**

.48

LF

STARTS

. .

PAY ROLL

EMPL

RETAIL

- 1.22

-.88

CPI

6.93**

6.48**

PPI

2.32

2.17

DEFLATOR

5.20**

3.32*

3.40*
1.87
5.08*

3.12*

-.99
-.52

3.93*
-1 .OO

.55
-.38

1.45

2.71

3.09*

- 1.20

- 1.07

-.64

11.36** - 1.22
.75

-1 - 3 1

http://clevelandfed.org/research/workpaper/index.cfm
Best available copy

Table 2 c o n t i n u e d ,
Independent
Variables

...............................

Dependent Variables----------------------------

INCOME :RETAIL
-

P AY R O LL

MFG

NONMFG

USREALSALE

6.04**

7.96**

2.69

4.49*

USSTARTS

3.43*

.69

4.64*

-.75

REALGNP

4.78*

9.74**

3.27*

10.80**

GNP

-.76

.50

-.lo

2.73

USY P

4.31*

6.69**

-.67

.71*

1.42

-.94

6.89**

4.11*

FUNDS

.98

MOODY

7.67"

Information Gain'

.18

S TA RT S

HOURS

PRICES

6.41**

.84

-.68

7 . 9 2 * * - 1 .15

.73

.70

-.80

-.28

.67

9.21**

.62

1.21

7.18**

-.83

.28

1.65

-.35

5.78**

3.14*

-.75

-.04

3.11*

-.86

5.24**

7.39**

1.69

.63

3.76,

-.92

.79

9.64**

2.85

--.I0

.25

4.13*

1.25

-.76

11.55** 10.72**

- 1.16

.69
2.31

* S t a t i s t i c a l l y s i g n i f i c a n t a t t h e .05 l e v e l ; g a i n exceeds 2.91 c r i t i c a l v a l u e .
* * S t a t i s t i c a l l y s i g n i f i c a n t a t t h e .O1 l e v e l ; g a i n exceeds 5.19 c r i t i c a l v a l u e .

' For each c o m b i n a t i o n o f dependent and i n d e p e n d e n t v a r i a b l e s , t h e f i g u r e s i n t h e
t a b l e show:

1

I = ( s t a n d a r d e r r o r o f t h e AR2 e q u a t i o n ) - ( s t a n d a r d e r r o r , o f t h e b i v a r i a t e e q u a t i o n ) x 100
s t a n d a r d e r r o r of t h e AR(2) e q u a t i o n

http://clevelandfed.org/research/workpaper/index.cfm
Best available copy

standard error is expressed as a percent of the univariate autoregression
equation's standard error.
Significant evidence, at the

-05

level, is found for 25 different
. .

causalities, or leading relations, involving regional variables. Housing
starts is the only series that provided significant leading information about
the total payroll employment. Housing starts and personal income appear to be
the two most useful regional series: they account for 5, 4, and 4 of the
significant results, respectively. These series may. however, merely reflect
the same underlying forces as are more clearly revealed in national
indicators. Of the two components of payroll employment, the manufacturing
sector measure contains 1 eadi ng information about the nonmanufacturing sector
but not vice versa. Surprisingly, the manufacturing workweek, HOURS, tended
to lag behind manufacturing employment. Hours had been included in this study
in the expectation that they would provide leading information on employment.
The consumer price and retail sales series were the only ones for which other
regional variables provided no leading information.

VIII.

National-Reqional Information
regional series can be
The value of national series in foreshadowing
. .
.

.

measured in a way analogous to the regional interactions of the previous
section. Regressions are performed to estimate the standard error of the
equation specified by the bivariate equation in section VII, where x, is the
quarterly logarithmic growth rate of one of the 18 national variables listed
in the Appendix A glossary.

Rows 11-28 of table 2 report the national

variable information gains. Of 180 possible relations, 89 are significant at
the .05 level. Most notable is the dependence of the employment series on
national economic conditions. Of the two payroll sectors, the manufacturing

http://clevelandfed.org/research/workpaper/index.cfm
Best available copy

sector i s most dependent on the n a t i o n .

This dependence conforms t o a v a i l a b l e

p r i o r n o t i o n s , which tends t o c o n f i r m both the notions and the p r e s e n t
methodology.

Ohio payroll. employment tends t o r e f l e c t ,
.

t o a substantial

.

degree, previous movements i n the n a t i o n a l leading and c o i n c i d e n t indexes, the
n a t i o n a l p a y r o l l s e r i e s , and several o t h e r indicators - - even when lagged values
( a u t o r e g r e s s i o n s > o f the Ohio p a y r o l l s e r i e s i t s e l f a r e taken i n t o account.
The manufacturing workweek and household- survey employment d i s p l a y a s i m i l a r
dependence on p a s t n a t i o n a l c o n d i t i o n s t h a t i s s i m i l a r t o t h a t o f p a y r o l l
employment.

Movements i n Ohio personal income and housing s t a r t s appear t o

r e f l e c t p a s t n a t i o n a l c o n d i t i o n s more than t h e i r own p a s t movements.

Least

dependent on p a s t n a t i o n a l conditions., s u r p r i s i n g l y , a r e Ohio r e t a i l s a l e s and
consumer p r i c e s .

( I n the Texas study, r e t a i l sales and consumer p r i c e s were

more s t r o n g l y r e l a t e d t o n a t i o n a l i n d i c a t o r s . )

We cannot r e j e c t t h e n o t i o n

t h a t r e t a i l sales and consumer p r i c e s a r e exogenous w i t h r e s p e c t t o the o t h e r
series.
One o f the most u s e f u l n a t i o n a l i n d i c a t o r s i s the n a t i o n a l p a y r o l l s e r i e s ,
which i s s i g n i f i c a n t l y causal w i t h r e g a r d t o a l l of t h e Ohio s e r i e s except
r e t a i l sales and p r i c e s .

Others o f p a r t i c u l a r value a r e t h e composite i n d i c e s

o f l e a d i n g and c o i n c i d e n t s e r i e s , i n d u s t r i a l p r o d u c t i o n , and manufacturing
payrolls.

The U.S.

consumer p r i c e index and the long- run i n t e r e s t r a t e

appeared t o c o n t a i n l i t t l e l e a d i n g i n f o r m a t i o n f o r t h e r e g i o n a l f o r e c a s t e r
when we used d a t a through 78QIV. b u t became more i n f o r m a t i v e when t h e sample
was extended.

Generally, though, t h e p r i c e and i n t e r e s t r a t e s e r i e s were

r e l a t i v e l y uninformative.

http://clevelandfed.org/research/workpaper/index.cfm
Best available copy

IX. A Trickle-Down Model
A

simple trickle-down model was built that attempted to summarize the

information from sources that actual regional forecasters are likely to be
.

currently placing greatest emphasis on.

.

In each equation for regional

variables, right-hand-side variables included a constant, two own-lags, Ohio
payroll employment, and one lag each o f the national leading and coincident
indexes.

The t w o national series' equations include two own-lags and one lag

o f the other national series.

The resulting model, which will be referred to

as the trickle-down (TD) model, may be both too unparsimonious and not fully
reflective of the information avai lable from the causality tests.

O n the

other hand, it embodies a rough prior notion about which series ought to b e most valuable t o the regional forecaster.

Hence, it represents an interesting

alternative and benchmark for a regional forecaster.

It may be especially

useful in combined forecasts, t o be considered later.
The trickle-down model is presented in Table 3.

As an illustration and

an aid t o interpreting that table, the equation for payroll employment i s
presented below.
respect:

It should be noted that this aquation is unique in one

because the lagged growth o f payroll employment is the first own-lag

of the equation, there is one less parameter than in the equations for the
other nine regional equations.

http://clevelandfed.org/research/workpaper/index.cfm
Best available copy

Table 3

Trickle- Down E q u a t i o n s :

A l n y t = a + b , A l n y t - , + b , A l n y t - c + C , A ~ ~ L E A D +, - ~C , A ~ ~ C O I N+~ -c,AlnPAYROLL,-,
~

+ e,

Using Data f r o m 65QIV-83QIV
Dependent
Variable

Parameter E s t i m a t e s (and Standard E r r o r s )

Goodness- of- Fit Measures

.0004
(.0008)

-.06
(.20)

.36
(.I21

.18
.06)

.16
(.13)

--

.56

.006524

19.5

(

MFG

-.0104
( .0028)

-.44
( .24)

.26
(-12)

.31
(.I21

.70
(.29)

.17
(.51)

.55

.01369

25.3

NONMFG

.0030
(.0012)

.02

.20
(.I21

.03
(.I21

7.5

(

.20
.25)

-005882

(

.07
.05)

-31

( . 19)

.0014
(.0014>

-.34
(.I31

-.31
(.12)

-.I3
( .08)

.68
(.21)

-. 13

.29

-010960

16.1

INCOME

.0148
(.0034)

-.08
(.18)

.07
(.I11

.18
( .08)

.39
(.20>

-.I6
(.35)

-43

.O 1030

18.4

RETAIL

.0197
(.0043>

-.32
(.I31

.05
(.I21

.39
(.19)

-. 62

.90
(.76)

-06

.02498

1.2

-.0120
(.0195>

-. 18

-.01
(.12>

4.16
(1.33)

- 4.23
(2.93)

-. 84

.16

.I510

9.0

HOURS

-.0022
(.0011)

-.35
(.I31

-. 08

.21
(.06)

.44
-. 78
( . I S . ) - - . (.24>

-44

.007976

25.5

PRICES

.0068
(.0023)

.42
(.I11

.19
(.I21

-. 12

.25
(.I51

-.35
(.24)

.35

.007898

0.7

.0057
(.0024)

.84
(.12)

.22
(.13>

---

-. 89

.43

.01919

12 .O

(.I91

---

.0015
(.0016)

.02
(.16)

.22
(.12)

.51
( .09)

--

--

.54

.01276

15.7

PAY ROLL

EMPL

STARTS

LEAD
COIN

(.I31

-

(.lo)

( .06)

(.49)

--

--

(

.34)

(4.47)

--

* I is the percent reduction o f the standard error of the trickle-down equation relative
to the AR(2) regression equation..

http://clevelandfed.org/research/workpaper/index.cfm
Best available copy

X.

The Srzpwise Regression Model
Causa:'ty t e s t s performed u s i n g the sample ending 7 8 Q I V ( n o t r e p o r t e d )

served as :he p o i n t of departure f o r b u i l d i n g a m u l t i v a r i a t e autoregression
model f o r :hie.

The o b j e c t was t o f i n d a w e l l - f i t t i n g , y e t reasonably

parsimonious, equation f o r each of the r e g i o n a l s e r i e s .
each serie;,

I n the equation f o r

every v a r i a b l e t h a t was s i g n i f i c a n t a t t h e 0.10 l e v e l i n the

c a u s a l i t y r e s t s was a candidate f o r i n c l u s i o n .

The search f o r a p p r o p r i a t e

equations $as made problematic by the l a r g e number of s i g n i f i c a n t causal
r e l a t i o n s ~ i s c o v e r e d 3.
The mccel was c o n s t r u c t e d u s i n g a single- equation method; t h a t i s , each
e q u a t i o n was chosen ( i d e n t i f i e d ) and estimated i n i s o l a t i o n .

More complex

i d e n t i f i c a r i o n and e s t i m a t i o n procedures might be s l i g h t l y more e f f i c i e n t ,
though less t r a n s p a r e n t .

A l e s s formal and more judgmental, b u t s i m i l a r

methodology i s described i n Hoehn (1984).
" automatic" and formal procedure.

The p r e s e n t method employs a more

The process of s e l e c t i n g t h e f i r s t equation

o f the mode-'s, f o r p a y r o l l employment, i l l u s t r a t e s the p r e s e n t procedure,
which i s b; red on t h e stepwise r e g r e s s i o n technique.

A s u b r o u t i n e f r o m PEC

(Program f o r Econometric Computation, Kim Pec, Yale U n i v e r s i t y ) was employed.
T h i s program proceeds by " forward stepping," o r adding v a r i a b l e s t o t h e
e q u a t i o n t h a t o b t a i n e d t - s t a t i s t i c s of 1.96 o r more i n a b s o l u t e value, and
"backward stepping," o r removing v a r i a b l e s whose t - s t a t i s t i c s f e l l below one
i n absolute value a f t e r o t h e r v a r i a b l e s a r e included.

The backward- stepping

f e a t u r e appears t o reduce the importance o f the o r d e r i n which v a r i a b l e s a r e
i n c l u d e d i n the f o r w a r d steps.

(As a p r i m i t i v e check, t h e o r d e r o f v a r i a b l e s

was e x a c t l y reversed f o r the PAYROLL equation, b u t t h e e q u a t i o n t h e stepwise
procedure s e l e c t e d was u n a f f e c t e d by t h a t reordering.)

The stepwise procedure

a r r i v e d a t an e q u a t i o n f o r Ohio p a y r o l l employment t h a t had ( a forced c o n s t a n t

http://clevelandfed.org/research/workpaper/index.cfm
Best available copy

plus) the second lag of Ohio housing starts, plus one lag of the national
coincident index. This equation had a standard error of .006308. In a third
step, the same stepwise routine was repeated except that two own-lags were
forced (that is, included regardless of their significance).

This resulted in

inclusion of the first lag of the national leading index and payroll
employment, the second lag of national real personal income, and two lags of
national housing starts. This equation, with eight parameters in all, had a
standard error of .005316. Finally, the significant lags of each of the
causal variables was tried to see if its inclusion would substantially reduce
the standard error. In only three cases did this occur:

the first lag of

Ohio housing starts reduced the standard error to .005194; the first lag of
national real retail sales, to .005188; and the second lag of national payroll
employment, to .005288. An

ad hot choice was made to tentatively include

U.S.

retail sales, but to exclude the other two. Last, some tinkering was done
with the equation on an ad hoc basis. For the equation for payroll
employment, elimination of the (insignificant) second own lag was tried, but
that increased the standard error too much. The equation thus settled upon is
that shown below.

The stepwi se model's other equations were determined in a similar manner
based on the sample ending 78QIV. Their specifications are available f-rom the
authors upon request.

http://clevelandfed.org/research/workpaper/index.cfm
Best available copy

XI. Contemporaneous Correlations

The information gains described in the last three sections involve
lead-lag relationships and ignore contemporaneous relationships. The latter
cannot be used for forecasting the future. They are valuable, however, in
estimating as-yet unreported realizations o f variables conditional on reported
figures for other variables.

These conditional estimates are important to

real-time forecasting and monitoring of the regional economy.

For example,

the analyst may desire to estimate personal income for a period for which
employment data are available, but a direct measure of income is not.

The

contemporaneous correlations between growth rates of the 10 O h i o variables and
the U.S. leading and coincident indices are shown in the upper half o f table'
4.

The bottom half shows correlations between residuals of the

autoregressions.

These residuals are nearly uncorrelated with their own past

values, so that their correlations with each other, unlike those of raw growth
rates, are uncontaminated by autocorrelation that can lead to spuriously
significant relationships.

Sample correlations have an approximate variance

of n-' , so they are significant at the .OS level if they exceed
approximately 2n-"'

-- 0.23.

Correlations among variables appear not t o be due merely t o
autocorrelation.

The national series, especially the coincident index, have

substantial correlation with the employment and income series.

The payroll

employment hours, and income series generally display the highest correlations
with other series.

Payroll figures contain more information about current

personal income than d o household-survey figures.

The low correlation between

manufacturing and nonmanufacturing payrolls, despite their high correlation
with the U.S. coincident index, suggests that shifts between
them--intersectoral technology o r preference shifts at the regional level--are

http://clevelandfed.org/research/workpaper/index.cfm
Best available copy

important. (Lillian [19821, interprets national employment and unemployment
fluctuations as arising from intersectoral shifts.)
Ohio consumer prices and the labor force show li-ttle dependence on the
national business cycle or o n other regional series.

Housing starts and

retail sales are weakly related to other series.

XII.

Out-of-Sample Forecasting:

Univariate Models

The ultimate proving-ground of any forecasting procedure is its
performance outside o f the sample over which it was identified and estimated.
The partition o f data available for the present study into a model-building
period and an out-of-sample forecasting period was motivated by a desire t o
provide evidence of the efficiency o f the forecasting model immediately.
rather than after the passage o f time t o allow evidence t o accumulate.

The

10-quarter period o f the Texas study appeared t o o short, because the
systematic improvements o f the MAR relative t o the univariate benchmarks were
generally not found t o be statistically significant.

A period of 20 quarters

was therefore reserved for out-of-sample forecasting in the O h i o study.
period began in 7991 and ended in 8 3 Q I V .

This

A longer reserved period would have

had the cost of unreasonably reducing the a m o u n t of data that could be used t o
identify the appropriate forecasting model.
The k-step-ahead forecast error for a period t forecast is
et,r

= yt

-

yt-,(k)

where y is the logarithm o f the series (the level, Jon

the growth rate) and

y,-,(k) is the k-step-ahead forecast y, formed at time t-k (conditioned o n
real i zations dated t-k and earl i er) . The criterion employed for forecast
performance evaluation is the root mean square error (RMSE);4

http://clevelandfed.org/research/workpaper/index.cfm
Best available copy

Table 4

Contemporaneous C o r r e l a t i o n s
65QIV-83QIV
C o r r e l a t i o n C o e f f i c i e n t s of G r o w t h R a t e s
PAYROLL
MFG

.92

NONMFG

.82

MFG
- NONMFG

EMPL
-

INCOME

RETAIL

STARTS

.

HOURS PRICES LEAD
-

.

.54

EMPL
LF

I NCOME
RETAIL
STARTS
HOURS
PRICES
LEAD
COIN
C o r r e l a t i o n C o e f f i c i e n t s of Residuals i n Second Order Autoregressions
65QIV-83QIV
PAYROLL
MFG
NONMFG
EMP L
LF
INCOME
RETAIL
STARTS
HOURS
PRICES
L EAO
COIN

.87

MFG
- NONMFG

EMPL

INCOME

RETAIL

STARTS

HOURS

PRICES

LEAD

http://clevelandfed.org/research/workpaper/index.cfm
Best available copy

where n i s the out- of- sample size and RMSE(k) denotes the r o o t mean square
e r r o r of the k-step-ahead f o r e c a s t s .
The mean e r r o r

provides i n s i g h t i n t o the e x t e n t t o which the RMSE i s due t o b i a s i n o r t o
variance o f the f o r e c a s t r e l a t i v e t o r e a l i z e d values.
I n e v a l u a t i n g each f o r e c a s t i n g method, the model was re- estimated each
q u a r t e r t o r e f l e c t a-new q u a r t e r of data.

The models were n o t r e - i d e n t i f i e d

each q u a r t e r , however, so t h a t the procedure does n o t f u l l y r e f l e c t the
e f f i c i e n t use o f new i n f o r m a t i o n t h a t a r e a l - t i m e f o r e c a s t would make.

This

c o n s i d e r a t i o n i s o n l y r e l e v a n t f o r the stepwise model, because i t was the o n l y
one n o t s p e c i f i e d 5 p r i o r i .
An examination o f the random walk model i s p a r t i c u l a r l y i n s t r u c t i v e
because o f i t s s i m p l i c i t y .

Only one parameter, a,

c o n s t r u c t the random walk f o r e c a s t .

Since a,

needs t o be estimated t o

i s merely t h e average growth

.
between t h e l o g of the
.
r a t e , i t can be c a l c u l a t e d by d i v i d i n g the difference

l a s t value o f t h e v a r i a b l e from t h e l o g o f i t s i n i t i a l value ( a t time p e r i o d
zero) by the l e n g t h of the s e r i e s , t:
a,,,,
where a,,,,

= t-'(yt

-

yo)

i s t h e estimated value o f a,

conditioned on d a t a a v a i l a b l e a t

time t, and y i s the n a t u r a l l o g o f the v a r i a b l e .

The f o r e c a s t f u n c t i o n ,

which associates a forecasted value o f y w i t h each k steps ahead, i s

A t t+k, the e r r o r yt+,-y,(k)

i s calculated.

The l e v e l o f the f o r e c a s t

http://clevelandfed.org/research/workpaper/index.cfm
Best available copy

Table 5

Out-of-Sample I n f o r m a t i o n Gains: Reduction i n 1-Period-Ahead RMSE
( f i g u r e s i n parentheses show g a i n due t o r e d u c t i o n i n ME)

RMSE(ME> of
Random Walk
Mode 1
PAYROLL
MFG

NONMFG
EMP L
LF
INCOME
RETAIL
STARTS
HOURS
PRICES
AVERAGE

Reduction i n Four-Period-Ahead RMSE
( f i g u r e s i n parentheses show g a i n due t o r e d u c t i o n i n ME)
RMSE(ME> o f
Random Hal k
Mode 1
PAYROLL
MFG
NONMFG
EMPL
LF
INCOME
RETAIL
STARTS
HOURS
PRICES
AVERAGE

1

I

.0440
.0799
.0346
.0357
.0165
.0460
.0413
.5346
.0258
.0430

AR2IRH

TDlAR2

SWlAR2

UC2lAR2

(-.0384)
(-.0584)
(-.0328)
(-.0287)
(-.0148)
(-.0358)
(-.0280)
(-.I2561
(-.0002)
( .0265)
3.3

(

9.1)

8.2

(

-2.5)

8.0

(

10.3)

9.8

(

4.0)

* S i g n i f i c a n t a t t h e .05 l e v e l , according t o a t e s t adapted f r o m Ashley, Granger, and
Schmalensee (see t e x t ) .

http://clevelandfed.org/research/workpaper/index.cfm
Best available copy

function is revised upward by that error. In addition, the growth rate, or
slope o f forecast function, is also revised at t+l by ( t + l > - ' times the
error.
The M E and RMSE for the first 10 steps ahead for the random walk model
were calculated and are reported in table 5 for steps 1 and 4. Three
characteristics of the results are particularly worthy o f note.

First, the

mean errors indicated that forecasts were typically for too-high growth,
except for consumer prices (whose errors were on average positive) and the
Ohio manufacturing workweek (whose forecasts were nearly unbiased).

Second,

the increase in RMSEs as the forecast horizon lengthens revealed that
uncertainty about the series is unbounded as the horizon is extended for aF1
series, except for the workweek. In other words, only the workweek appears to
have a stationary trend. (In fact, it appears to be stationary in its
level.)

Consequently, none of the series, except hours, should be treated in

any empirical analysis as having deterministic trends; their trends are
stochastic.

Third, the mean absolute error accounted for most of the

magnitude o f the RMSEs for all series, except the workweek, for forecasts of
more than a quarter o r two ahead.

What this implies is that the main source

of forecast errors was the overall weakness o f the Ohio economy during most o f
the 7991-83QIV period, rather than great variability in forecast accuracy from
quarter to quarter.
The random walk model serves as the appropriate benchmark for the
autoregressive model.

The out-of-sample comparison can reveal whether the

autoregression found in the within-sample period not only continued to occur
in the out-of-sample period, but also was sufficiently stable in its character
t o be a dependable source of forecasting information.

The out-of-sampl e

performance of the second-order autoregressive equations generally compares

http://clevelandfed.org/research/workpaper/index.cfm
Best available copy

f a v o r a b l y w i t h t h e random walk model.

The RMSE of the AR2 was lower than f o r

the random walk f o r seven of the ten r e g i o n a l v a r i a b l e s i n one-step-ahead
f o r e c a s t s and f o r s i x o f the 10 i n four- step- ahead f o r e c a s t s .

These

comparisons, and those between the AR2 and the o t h e r f o r e c a s t i n g methods, are
shown i n t a b l e 5 .

I n the cases f o r which the random walk model outperforms

the AR2, the d i f f e r e n c e i s modest.

But some of the improvements o f the

forecasts o f t h e a u t o r e g r e s s i v e equations over those o f t h e random walk a r e
substantial.

For example, t h e one- quarter- ahead forecasts o f PAYROLL had an

RMSE o f .0089 i n the AR2 model, 26 p e r c e n t below the RMSE o f .0121 f o r the RW

model.

The mean e r r o r was -.0033 i n t h e AR2, compared w i t h -.0077 i n the RW

model.

The r e d u c t i o n i n t h e RMSE i n t h e AR2 model r e l a t i v e t o the RW model-

can be a t t r i b u t e d t o r e d u c t i o n i n the a b s o l u t e value o f t h e mean e r r o r ; t h e
l a t t e r r e d u c t i o n , .0044, represents 36 p e r c e n t o f the RMSE o f the RW model.
The f i g u r e s i n parentheses i n t a b l e 5 i n d i c a t e t h a t t h e general improvement i n
f o r e c a s t accuracy o f t h e AR2 model r e l a t i v e t o t h e RW model i s due t o
r e d u c t i o n i n the absolute value of the mean e r r o r .

The a u t o r e g r e s s i v e terms

tended t o presage o r adapt t o c y c l i c a l movements, which tended t o e x e r t a
downward i n f l u e n c e on t h e s e r i e s i n the 1979-83 p e r i o d .
. . of t h e AR2 r e l a t i v e t o t h e RW
The improvement i n f o r e c a s t i n g performance
.

.

model was g r e a t e s t f o r p a y r o l l employment, i t s nonmanufacturing component,
consumer p r i c e s , and personal income.

The comparison was most unfavorable t o

t h e AR2 model f o r the l a b o r f o r c e , household- survey employment, and housing
starts.

There was l i t t l e difference

i n f o r e c a s t accuracy f o r r e t a i l sales.

The out-of-sample r e s u l t s tend t o c o n f i r m the presence o f u s e f u l
a u t o r e g r e s s i o n i n PAYROLL, MFG, and PRICES.

INCOME had b o r d e r l i n e

a u t o r e g r e s s i v e p r o p e r t i e s w i t h i n sample, b u t t h e out- of- sample r e s u l t s suggest
moderately s t r o n g autoregression.

NONMFG d i s p l a y e d no a u t o r e g r e s s i o n w i t h i n

http://clevelandfed.org/research/workpaper/index.cfm
Best available copy

sample, but substantial autoregression out of sample. Results for the 1979-83
period confirmed the lack of autoregression in EMPL, STARTS, HOURS, and
RETAIL. LF was borderline within sample, but was ultimately seen to lack
useful autoregression. All these conclusions are verified by the estimation,
using the sample through 1983, of the

AR2

equations and their associated

I-statistics, shown in the bottom half of table 2.

XIII. Out-of-Sample Forecastinq: Multivariate Models
The univariate autoregression results serve as the appropriate
benchmark for the muitivariate models, which add terms to the autoregressiv-e
equations in an attempt to capture information from other national and
regional data. The out-of-sample evidence generally suggests that such
information can be extracted.
Table 5 displays the relative forecast performance of the trickle-down and
stepwise models; their RMSEs are generally lower than those of the
autoregressive model. Figure 3 depicts the performance of both the
multivariate and univariate models, in their forecasts of payroll employment
for forecast horizons of one to 10 quarters. The relative efficiency of
.

.

multivariate as compared with the univariate autore7ressions do not derive
particularly from reduction in the magnitude of bias, but rather more to a
closer "fine-tuning" of the forecast each quarter in light of national and
regional data. The payroll variable had little importance in the trickle-down
model. Hence, the trickle-down model's forecasting efficiency relative to the
autoregressive model can be taken as an indication of the usefulness of the
lagged trickle-down relationships.

In other words, those relations are

sufficiently strong and stable to be useful.

Figure 3.

http://clevelandfed.org/research/workpaper/index.cfm
Best available copy

ROOT MEANS OF SQUARE ERROR
OF THE PAYROLL FORECASTS

-

Random Walk

Trickle-Do wn

ommommmmmm

STEPS AHEAD

http://clevelandfed.org/research/workpaper/index.cfm
Best available copy

The t r i c k l e - d o w n model, as estimated w i t h the 1965-78 sample, suggested
strong i n f o r m a t i o n gain r e l a t i v e t o the autoregressive model f o r PAYROLL, MFG,
EMPL, INCOME, HOURS, and NONMFG.

This strong gain c a r r i e d over t o comparisons
.

.

o f RMSEs i n the 1979-83 p e r i o d , f o r a l l these v a r i a b l e s except NONMFG.

Weaker

gains i n LF and STARTS found i n 1965-78 were confirmed i n the f o r e c a s t i n g
period.

The absence o f gain f o r PRICES was a l s o confirmed.

Finally,

i n f o r m a t i o n g a i n f o r RETAIL was n o t found i n e i t h e r the 1965-78 o r the 1965-83
sample, b u t arose i n the f o r e c a s t performance comparisons.

Aside from the

r e s u l t s f o r RETAIL, the s h o r t and long samples and the out- of- sample f o r e c a s t
simulation provide consistent r e s u l t s :
i n one-period-ahead

RMSES,

i n f o r m a t i o n gains, I, and r e d u c t i o n s

were remarkably simi l a r f o r each v a r i a b l e .

The s t a t i s t i c a l s i g n i f i c a n c e of the improvement i n f o r e c a s t accuracy o f
t h e TD model r e l a t i v e t o the AR2 model can be measured by t h e method proposed
i n Hoehn (1984, pp. 27-81.

The method i n v o l v e s an a d a p t a t i o n o f a " c a u s a l i t y "

t e s t suggested by Ashley, Granger, and Schmalensee (1980).

A t t h e .05 l e v e l ,

one-period-ahead f o r e c a s t RMSEs are s i g n i f i c a n t l y lower f o r PAYROLL, MFG, LF,
and INCOME.

For four- period- ahead f o r e c a s t s , the TO model i s s i g n i f i c a n t l y

b e t t e r o n l y f o r MFG and LF.
s i g n i f i c a n t l y worse.

I n no case does the t e s t f i n d t h e TD forecasts

The t e s t has some problematic i n t e r p r e t a t i o n s i n some

cases, and r e s u l t s do n o t o f t e n conform t o i n t u i t i o n s , suggesting a l i m i t e d
usefulness o f t h e t e s t .

These ambiguities a r i s e f r o m t h e need t o make an

e s s e n t i a l l y f o u r - t a i l e d t e s t u s i n g a s i n g l e F - s t a t i s t i c , u s u a l l y used f o r
one- tailed tests.

As a r e s u l t , t h e t e s t i s o f t e n of low power.

I n f o r e c a s t i n g w i t h the stepwi se model , the exogenous n a t i o n a l v a r i a b l e s
used (14 d i f f e r e n t v a r i a b l e s , n o t d i s t i n g u i s h i n g d i f f e r e n t l a g s ) were
f o r e c a s t e d u s i n g second-order autoregressive equations.

This may have

handicapped t h e SW model somewhat i n f o r e c a s t s o f more than one q u a r t e r

http://clevelandfed.org/research/workpaper/index.cfm
Best available copy

ahead.

=orecasts o f two national variables, the leading index (LEAD) and the

coincidert index (COIN), were both 14 percent lower for one-steps-ahead, and
19 and 9 sercent lower, respectively, for 4-periods-ahead, in the trickle-down

model.

Also a handicap is the maintenance of the specification of the

equations throughout the period.

Although the other models were not revised

with regard to regressors either, their a priori specifications preclude the
use of new data to revise the specifications. (Of course, the stepwise
model's ccefficient values were updated each quarter.)
The out-of-sample forecasting performance of the stepwise model relative
to the autoregressive model confirmed a strong dependency of four regional
variables t o lagged national and.regiona1 information variables:
STARTS, PAYROLL, and MFG.
RETAIL.

EMPL,

Weaker confirmation was implied for LF, HOURS, and

Fina-lly, the information gain vanished for NONMFG, INCOME, and PRICES.

The stepwise model significantly outperformed the AR2 model a t the .05
level, according t o the test adapted from Ashley, Granger, and Schmalensee, in
the following cases.

For one-period-ahead forecasts, the improvement was

significant for EMPL and LF; for four-period-ahead forecasts, the improvement
was significant for PAYROLL, LF, and STARTS.
The properties of the errors in the T D and .SW. models were often somewhat
different with regard t o bias and variance around means.
consider the four-step-ahead forecasts of PAYROLL.

For example,

The TD and SW models had

similar RMSEs, of .0358 and .0360, respectively, representing improvements of.
6.8 and 6.3 ~ e r c e n trelative t o the RMSE o f .0384 in the AR2 model.

Yet the

source o f erTor differed somewhat among the models, with mean errors of -.0291
in the T D mcdel and -.0205 in t h e S W model.

The SW model forecasts benefited

f r o m lower !.:.osolute> bias, but suffered from a larger variation in accuracy
f r o m o n e quarter t o the next.

A forecast that combines the forecasts of the

http://clevelandfed.org/research/workpaper/index.cfm
Best available copy

two models is particularly promising in such a case. Giving weight to the
model might seem unpromising because of its higher

RMSE.

SW

Yet giving the SW

model weight in a combined forecast will definitely reduce the magnitude of
bias. This benefit must be balanced against the cost, in terms of

RMSE,

that

results from higher variance. But unless the errors of the two forecasting
models are perfectly correlated, the variance of combined forecasts will be
less than the sum of the variances of the components. As it turns out, the
combined, unweighted forecast (UC2 for "unweighted combination of two"
forecasts) has an RMSE of -0348, lower than the TD or SW models. The contrast
with the AR2 model's performance is summarized in the last two columns of
table 5 , for one- and four-quarter forecasts. The UC2 forecasts do generally
as well as the TD model, and better than the

SW

model for one-step-ahead

forecasts. -,They generally do as well or better than the TD model for
four-step-ahead forecasts, and better than the SW model at that forecast
horizon for 8 of the 10 Ohio variables. According to the test adapted from
Ashley, Granger, and Schmalensee, the improvement of the UC2 relative to the
AR2 is significant at the .05 level for PAYROLL, MFG, LF, and RETAIL for
forecasts one quarter ahead, but significant only for LF for the four-quarter
forecasts. The improvements of the UC2 relative to the TD model do not appear
substantial and are unlikely to be significant, according to casual
inspection. Only small gains appear available from combining the models, as
compared with giving the TD model all the weight. In the terminology of
Granger and Newbold (1977, p. 2831, the TD model is conditionally efficient
with respect to the alternatives considered.
The importance of updating coefficients during the out-of-sample period
was relatively easy to determine.

Forecast performance for the TD model

without updating was generally inferior to performance of the model with

http://clevelandfed.org/research/workpaper/index.cfm
Best available copy

updating.

Only f o r forecasts of HOURS, short- horizon forecasts f o r INCOME,

and long- range f o r e c a s t s o f RETAIL were RMSEs lower w i t h o u t updating; i n a l l
o t h e r cases u p d a t i n g was h e l p f u l .

Mean e r r o r s were always lower i n absolute

magnitude; u p d a t i n g had the e f f e c t of reducing p r o j e c t e d growth d u r i n g the
weak c o n d i t i o n s of t h e out-of-sample p e r i o d .

Generally, t h i s r e d u c t i o n

accounted f o r a l l of the improvement--indeed, the means.of absolute e r r o r
(MAEs) o f t e n r e f l e c t e d l e s s improvement than MEs.

For example, i n

one- period- ahead f o r e c a s t s of PAYROLL, updating changed the ME f r o m -.0051 t o
-.0040.
t o .0071.

But the MAE was o n l y reduced from .0061 t o .0056; the RMSE from . k 7 8
On average, updating reduced t h e RMSEs by 4.1 percent, 5.6 p e r c e n t ,

and 4.4 percent, f o r one- quarter, four- quarter- , and 10- quarter- ahead
f o r e c a s t s , r e s p e c t i v e l y , f o r t h e 10 r e g i o n a l v a r i a b l e s .
I n t h e stepwise model, updating brought s i m i l a r b u t l e s s c o n s i s t e n t gains;
the r e d u c t i o n i n b i a s was l e s s c o n s i s t e n t , b u t g e n e r a l l y s m a l l e r .
f o r e c a s t s were q u i t e adversely a f f e c t e d .

PRICE

A more i m p o r t a n t , y e t unanswered,

q u e s t i o n i s what l o s s of f o r e c a s t i n g accuracy r e s u l t e d from n o t r e s p e c i f y i n g
the stepwise model each q u a r t e r i n l i g h t of new data.

Some p a r t i a l evidence

on t h i s q u e s t i o n c o u l d be provided by r e s p e c i f y i n g t h e equations a f t e r t h e end
o f t h e out- of- sample p e r i o d .

For t h e PAYROLL equation, such r e s p e c i f i c a t i o n

r e s u l t e d o n l y i n t h e e x c l u s i o n o f t h e second l a g on U.S. housing s t a r t s .
m i g h t be regarded as n e a r l y t h e s l i g h t e s t p o s s i b l e change.

This

However, we have

n o t undertaken a systematic and f u l l y s a t i s f a c t o r y a n a l y s i s o f t h e b e n e f i t s o f
period- by- period r e - s p e c i f i c a t i o n .

Such b e n e f i t s could c o n c e i v a b l y a l t e r

comparisons between t h e TD and SW models.

However, we do n o t p l a c e much

emphasis on such a comparison; such a comparison i s d i f f i c u l t t o i n t e r p r e t i n
any case.

http://clevelandfed.org/research/workpaper/index.cfm
Best available copy

The use of the ordinary least squares estimation procedure can be t o some
degree inefficient in cases in which errors of equations estimated are
correlated. Correlations in the errors o f both multivariate models were
.

.

frequently larger than 2n-"' . Again, we have not undertaken a full and
systematic study o f this issue, but have examined its implications for the
PAYROLL equation.

In the TD model, PAYROLL, LEAD, and COIN f o r m a system o f

three variables in the equations that determine forecasts o f PAYROLL: the
other regional variables' forecasts fol low recursively.

Applying general ized

least squares (seemingly unrelated regression) to allow for a non-diagonal
disturbance variance-covariance matrix offered a potential improvement,
suggested by the high correlations between residuals of ordinary least squares
equations for PAYROLL and COIN (0.69) and LEAD and COIN (0.61). When compared
with the 0rd.inary 1 east squares estimates, the general ized least squares
method reduced the magnitude of all the coefficients of the PAYROLL equation
except the one o n COIN,-,. The effects o f the equations for national
variables were rather small.

Forecasts of PAYROLL with the generalized least

squares estimates o f the T D model were somewhat worse than for the ordinary
least squares version, where the comparison is of models whose coefficients
were not re-estimated each quarter.

The RMSEs of the generalized least
.

.

squares version (of the ordinary least squares version) were .0085 (.0078),
.0421(.0389), and .1103(.1083),
respectively.

for one, four, and 10 steps ahead,

This comparison may have been affected by the special

characteristics of the 1979-83 period, particularly since trickle-down effects
o f the national economic weakness were given less range by the generalized
least squares coefficients' smaller value^.^

http://clevelandfed.org/research/workpaper/index.cfm
Best available copy

IX. Conclusion
The location of information about each o f 10 Ohio variables representing
aggregate economic activity has been identified, measured, and subjected to
confirming tests.

Generally, the results verify two prior beliefs:

(1)

univariate forecasting models can be outperformed by simple multivariate
models, although not consistently by a large margin, and ( 2 ) most (lagged)
information other than from a variable's own past comes from national
variables, and may be summarized reasonably well by the coincident and leading
indices. Ohio housing starts, however, seems to contain independent leading
information for other regional series such as employment.
Our study is also of interest as a practical application o f statistical
principles and forecasting methods in a context in which a number o f sources

of information are likely t o be valuable. Conclusions in this regard may be
quite sensitive t o the particular data samples employed. The two models
specified

priori, the univariate autoregressions and the trickle-down model,

provided gains relative t o their appropriate benchmark models that were,
overall, approximately equal in the 1965-78 sample and the 1979-85
out-of-sample period.

In the case o f the trickle-down model, the relation

between within-sample gain and out-of-sample gains in o n e period-ahead
forecasts was remarkably close:

the gain delivered out-of-sample approximated

that o f within the sample, o n a variable-by-variable basis.

The stepwise

model, as might have been expected in light o f the "overfitting" problem,
could not deliver out-of-sample results t o match those within the sample, nor
was there much relation between them on a variable-by-variable basis.
However, the stepwi se model operated under several handicaps.

Its

specification was not revised, as would be done by a real-time forecaster
using the stepwise procedure of model construction.

Second,

http://clevelandfed.org/research/workpaper/index.cfm
Best available copy

f o r e c a s t s o f more than one-step- ahead p r o b a b l y were handicapped by t h e use o f
u n i v a r i a t e a u t o r e g r e s s i o n s t o p r o v i d e paths f o r t h e exogenous n a t i o n a l
variables.
The p r e s e n t study adds t o t h e growing knowledge of how t o deal p r a c t i c a l l y
w i t h t h e t r a d e o f f between t h e c o s t s o f i g n o r i n g i n f o r m a t i o n and t h e problems
o f "overfitting."

Gains o v e r u n i v a r i a t e equations have been a c h i e v e d i n t h e

p r e s e n t study o f Ohio, as had been achieved f o r Texas (Hoehn, 1 9 8 4 ) .

However,

t h e p a r t i c u l a r methods employed a r e u n l i k e l y t o be " o p t i m a l " i n any sense."
The r e s t r i c t i o n t o l i n e a r and nonseasonal models (of s e a s o n a l l y a d j u s t e d d a t a )
and t h e equal weights i n combined f o r e c a s t i n g schemes a r e a source o f
inefficiency.

~ e v e r ~ h e l e s swe
, contend t h a t t h e u n d e r s t a n d i n g and f o r e c a s t i rrg

of an economic system, whose t r u e s t r u c t u r e i s unknown. can be enhanced by t h e
s i m p l e and tr:ansparent t i m e - s e r i e s methods employed.

S t r u c t u r a l models i n

such a c o n t e x t m i g h t b e s t be c o n s t r u c t e d a f t e r t h e s t y l i z e d f a c t s o f t h e t i m e
s e r i e s a r e uncovered.

http://clevelandfed.org/research/workpaper/index.cfm
Best available copy

Footnotes
1 . Strictly speaking, a structural model cannot forecast in the same fashion
as a time series model. The former is always "incomplete" in the sense that
it forecasts the endogenous variables conditional on arbitrarily specified
'values of the exogenous variables, which the forecaster~must provide. While
thi s condi tional nature of structural forecasting al'lows for interesting
simulations of "what if" questions, it complicates forecast construction and
performance evaluation in the more realistic case for which no future values
o f any variables are known when forecasts are made. This difference between
structural and time series models makes this relative forecast performance
difficult to assess. (See, for example, Granger and Newbold (1977, pp.
289-302).

2. These issues are more fully addressed in Hoehn, Gruben, and Fomby
(1984a>, pp. 34-49.
3 . Ohio series displayed more frequently significant dependence on lagged
national series than did Texas series, in conformance with prior beliefs.
Also, this study of Ohio examined 19 national variables whereas only 14 wereexamined in the Texas study. In the latter, only 21 out of 92, or 24 percent,
o f the possible trickle-down causal relations were significant at the .05
level (see pp. 26-27, Hoehn, Gruben, and Fomby, 1984b). The proportion for
this Ohio study was 47 percent. However, the comparison may be affected b y .
the longer sample for Ohio.

4. The RMSE is an exact criterion for comparison of alternative forecast
generating mechanisms if the loss function is proportional to the square of
forecasting errors (see Granger and Newbold, 1977, pp. 279-280).
5. However, other studies have also suggested that the gains from accounting
for contemporaneous correlations in errors in the estimation of linear
forecasting models may be slight. Unpublished results by Hoehn for "VARsU of
the Texas economy showed generally inferior forecasts for seven regional
series, with updating.
6. Granger and Newbold (1977, pp. 268-9) offer . some reasons why optimal
.
forecasts are practically never available.
.

.

http://clevelandfed.org/research/workpaper/index.cfm
Best available copy

References
Amirizadeh, Hossain, and Richard M. Todd. "More Growth Ahead f o r
Ninth D i s t r i c t S t a t e s , " Q u a r t e r l y Review, Federal Reserve Bank o f
Minneapolis, F a l l 1984, pp. 8-17.
. .

Anderson, Paul A . "Help f o r the Regional Forecaster: Vector
Autoregression," Q u a r t e r l y Review, Federal Reserve Bank o f Minneapolis.
v o l . 3 , no. 2 (Summer 1979). pp. 2-7.
Ashley, Richard A . , C.W.J. Granger, and R. Schmalensee. " A d v e r t i s i n g
and Aggregate Consumption: An Analysis of C a u s a l i t y , "
~conometiica,
v o l . 48, no. 5, ( J u l y 1980), pp. 1149-67.
Box, G.E.P., and G.M. Jenkins. Time Series Analysis:
C o n t r o l . San Francisco: Holden-Day, 1976.
Granger, C.W.J., and Paul Newbold.
York: Academic Press, 1977

Forecastinq and

Forecastinq Economic Time Series.

New

Hoehn, James G., and '~ames J . Balazsy, J r . "The Ohio Economy: A Time Series
Analysis," Economic Review,. Quarter 111, 1985, Federal Reserve Bank o f
Cleveland.
Hoehn, James'.G. " A Regional Forecasting Procedure A p p l i e d t o Texas,"
Working Paper No. 8402, Federal Reserve Bank o f Cleveland, September 1984.
Hoehn, James G., Wi-lliam C. Gruben, and Thomas B. Fomby. "Time Series
Models o f the Texas Economy: A Comparison," Economic Review, Federal
Reserve Bank o f D a l l a s (May 1984a1, pp,. 11-23.

. "Some Time Series Methods o f Forecasting the Texas
Economy,"~orkinq
Paper No. 8402, Federal Reserve Bank o f D a l l a s , A p r i l
1984b.
Kuprianov, A n a t o l i , and W i l l i a m L u p o l e t t i . "The Economic Outlook f o r F i f t h
D i s t r i c t States i n 1984: Forecasts from Vector Autoregression Models,"
Economic Review, Federal Reserve Bank o f Richmond, v o l . 7011
(JanuaryIFebruary 19841, pp. 12-23.
L i 1ien, David M. " Sectoral S h i f t s and Cycl i c a l Unemployment, "
Journal o f P o l i t i c a l Economy, v o l . 90, no. 4 (August 19821, pp. 777-93.
Litterman, Robert 8. "Techniques o f Forecasting Using Vector
Autoregressions," Working Paper No. 115, Federal Reserve Bank o f
Minneapolis, 1979.
Nelson.
Charles R. " A Benchmark f o r t h e Accuracv o f Econometric
- f o i e c a s t s o f GNP," Business Economics, v o l . i 9 , no. 3 ( A p r i l 19841,
pp. 52-58.

, and Charles I. Plosser. "Trends and Random Walks i n
Macroeconomic Time Series: Some Evidence and I m p l i c a t i o n s , " Journal o f
Monetary Economics, v o l . 10, no. 2 (September 19821, pp. 139-62.

- 35 Appendix A:

http://clevelandfed.org/research/workpaper/index.cfm
Best available copy

Glossary of Variables

Regional variables*
Mnemon i c

Description

EMPL
-

Total civilian employment (household survey), in thousands,
Bureau o f Labor Statistics (BLS). Seasonally adjusted by
Chase Econometrics (Chase). Transformed from monthly values
t o quarterly averages by Hoehn and Balazsy (HB).

HOURS

Average weekly hours in manufacturing. BLS. Seasonally
adjusted by Chase. Transformed from monthly t o quarterly by
HB.

I NCOME

Personal income at annual rates, in billions o f current
dollars. Commerce Department. From Data Resources, Inc.
(DRI).

LF
-

Labor force, in thousands. BLS. Seasonally adjusted by
Chase. Transformed from monthly t o quarterly by HB.

MFG
-

Employment in manufacturing, in thousands. BLS. Seasonally
adjusted by Chase. Transformed from monthly t o quarterly by
HB.

PAY ROLL

Total nonagricultural employment: total private and.
government, in thousands. Seasonally adjusted by Chase.
Transformed from monthly t o quarterly by HB.

PRICES

Constructed average for consumer prices for Ohio. Constructed
f r o m bi-monthly series for Cleveland CPI and Cincinnati CPI,
BLS. S e e special description of construction method, below.

RETAIL

Total retail sales, in millions of current dollars. Bureau o f
Census. Seasonal ly adjusted by Chase. Transformed from
monthly t o quarterly by HB.

STARTS

Total private housing starts, in thousands o f units, at annual
rates, Bureau of Census.

Special note o f PRICES
The consumer price index for O h i o (PRICES) was constructed in the following
manner. First, t h e seasonal adjustment factors f o r each month for the U.S.
CPI was determined by dividing the U.S. CPI, not seasonally adjusted, by the
U.S. CPI, seasonally adjusted. This factor was used t o seasonally adjust
values for the (bimonthly) Cleveland and Cincinnati CPIs. From these
seasonally adjusted bimonthly figures, quarterly averages were constructed for
each city. The average used the available months within each quarter (one o r
two) rather than interpolated values. Then the quarterly city values were
averaged.

http://clevelandfed.org/research/workpaper/index.cfm
Best available copy

National Variables*
Mnemon ic

Description

COIN

Coincidental Indicators Composite Index with Trend Adjustment.

CP I

Consumer Price Index (Revised) - A11 Items.

DEFLATOR

Gross National Product Implicit Price Deflator.

FUNDS

Effective Rate on Federal Funds.

GNP

Gross National Product

LEAD

Leading Indicators Composite Index with Trend Adjustment.

MOODY

Yield on Moody's Industrial Corporate Bonds.

PPI

~ r o d i c e rPrice Index

PRODUCT

Total Industri a1 Production Index.

REALGNP

Gross National Product in 1972 Dollars.

REALYP

Personal Income in 1972 Dollars.

USHOUSEHOLD

Nonagricultural Employment (Household Survey).

USLF

Civilian Labor Force.

USMFG

Manufacturing Employment.

USPAYROLL

Nonagricultural Establishments Employment.

USREALSALE

Total Retail Sales in 1972 Dollars.

USSTARTS

Total Private Housing Starts Including Farm.

USYP

Personal Income.

-

Finished Goods.

EHHEA

*The source of a1 1 the national variables is Data Resources Inc. All
variables, except the two interest rates, are seasonally adjusted.

http://clevelandfed.org/research/workpaper/index.cfm
Best available copy