Page 1

Regional Aggregation in Forecasting:

An Application to the Federal Reserve’s

Eighth District

Kristie M. Engemann, Rubén Hernández-Murillo, and Michael T. Owyang

of cross-regional correlations yet still restrict the

number of parameters estimated.2They argue that,

under certain conditions, the sum of the forecasts

from an order-p,q space-time autoregression

[ST-AR?p,q?] can outperform both aggregate mod-

els and models that do not account for the spatial

nature of the data. The ST-AR?p,q? model includes

p temporal lags and q spatially distributed lags—

that is, lags of the other regional series weighted

by proximity. Thus, the ST-AR?p,q? model exploits

both the spatial correlations and the information

content in the disaggregated series.

Hernández-Murillo and Owyang (2006) take

this approach to national employment data, show-

F

regional forecasts may improve forecasts of national

indicators. For example, Hendry and Hubrich

(2006) use disaggregate models to form forecasts

for aggregate variables. Similarly, Giacomini and

Granger (2004) show that using a disaggregate

model that accounts for spatial correlations can

reduce the root mean squared error of the fore-

casts. Their disaggregate forecasts take advantage

orecasting, especially as it pertains to

policymaking, is typically conducted at

the national level.1However, a few recent

papers have indicated that aggregating

Hernández-Murillo and Owyang (2006) showed that accounting for spatial correlations in regional

data can improve forecasts of national employment. This paper considers whether the predictive

advantage of disaggregate models remains when forecasting subnational data. The authors conduct

horse races among several forecasting models in which the objective is to forecast regional- or

state-level employment. For some models, the objective is to forecast using the sum of further

disaggregated employment (i.e., forecasts of metropolitan statistical area (MSA)-level data are

summed to yield state-level forecasts). The authors find that the spatial relationships between

states have sufficient predictive content to overcome small increases in the number of estimated

parameters when forecasting regional-level data; this is not always true when forecasting state-

and regional-level data using the sum of MSA-level forecasts. (JEL C31, C53)

Federal Reserve Bank of St. Louis Regional Economic Development, 2008 4(1), pp. 15-29.

1

There are, however, some notable exceptions of forecasting economic

indicators at the subnational level (dates and regions noted in paren-

theses): Glickman (1971, Philadelphia MSA); Ballard and Glickman

(1977, Delaware Valley); Crow (1973, Northeast Corridor); Baird

(1983, Ohio); Liu and Stocks (1983, Youngstown-Warren MSA);

Duobinis (1981, Chicago MSA); LeSage and Magura (1986, 1990,

Ohio); and Rapach and Strauss (2005, Missouri; 2007, Eighth Federal

Reserve District).

2

Compared with a standard vector autogression (VAR), the space-time

autoregression (AR) model posited in Giacomini and Granger (2004)

requires the estimation of ?n2– n – 1?p fewer parameters for the same

lag order p.

Kristie M. Engemann is a senior research associate, Rubén Hernández-Murillo is a senior economist, and Michael T. Owyang is a research officer

at the Federal Reserve Bank of St. Louis. This paper was prepared for the 4th Annual Business and Economics Research Group conference spon-

sored by the Federal Reserve Bank of St. Louis and the Center for Regional Economics—8th District. The authors thank Dave Rapach for comments.

©2008, The Federal Reserve Bank of St. Louis. The views expressed in this article are those of the author(s) and do not necessarily reflect the

views of the Federal Reserve System, the Board of Governors, or the regional Federal Reserve Banks. Articles may be reprinted, reproduced,

published, distributed, displayed, and transmitted in their entirety if copyright notice, author name(s), and full citation are included. Abstracts,

synopses, and other derivative works may be made only with prior written permission of the Federal Reserve Bank of St. Louis.

FEDERAL RESERVE BANK OF ST. LOUIS REGIONAL ECONOMIC DEVELOPMENTVOLUME 4, NUMBER 1 2008

15

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VOLUME 4, NUMBER 12008

FEDERAL RESERVE BANK OF ST. LOUIS REGIONAL ECONOMIC DEVELOPMENT

ing that out-of-sample forecasts can be improved by

modeling the spatial interactions between Bureau

of Economic Analysis regions. They compare a

ST-AR?p,q? model with vector autoregressions

(VARs) with various levels of disaggregation. They

concluded that, as predicted by Giacomini and

Granger (2004), information in regional employment

data is useful for forecasting national employment.

In this paper, we are interested in whether the

information content of regional data can be observed

at a more disaggregated level. In particular, we ask

whether information for states helps forecast

regional data and whether information from cities

helps forecast state data. To this end, we construct

horse races among four competing models with

different levels of disaggregation. We then conduct

out-of-sample tests to determine which model pro-

duces the best short- and long-horizon forecasts.

The data used in these experiments are state- and

metropolitan statistical area (MSA)-level payroll

employment. In each experiment, the disaggregate

data are summed to yield either state- or regional-

level aggregates. In each case, we ask whether

models using the disaggregate data provide lower

mean squared prediction errors (MSPEs) than the

aggregate alternatives. We find that the spatial

relationships among states have sufficient predic-

tive content to overcome small increases in the

number of estimated parameters. The same is not

always true when forecasting state- and regional-

level variables using the sum of MSA-level forecasts.

The next section reviews the four models used

in the horse races, followed by a section that dis-

cusses the subnational data and the construction

of the “aggregate” data. The results of the out-of-

sample experiments are then presented, followed

by the conclusion.

MODELS

The goal of this experiment is to produce an

h-period-ahead forecast of an aggregate time

series—for example, employment. In this context,

“aggregate” does not necessarily mean “national,”

although it is an obvious interpretation. Instead,

here aggregate time series are data that are the sum

or weighted sum of a number of (forecastable) dis-

aggregate series. These series can be disaggregated

in any manner (e.g., by regions or industries). The

aggregate forecast then can be constructed directly

from aggregate data or from the sum (or weighted

sum) of its components. We examine four

alternatives.

Suppose that period-t aggregate employment

is denoted Ytand can be written as the sum of its

N disaggregate counterparts (henceforth referred

to as “regions,” which depending on the applica-

tion may refer to either states or metro areas), ynt,

without error.3Let Ŷt+hbe the h-period-ahead

forecast of Y. A forecast from the simplest model,

a univariate aggregate order-p autoregression

(AR?p?, Model 1), has the form

(1)

where p is the number of lags and Φjare scalar

coefficients.4

A similar univariate model can be constructed

to forecast each of the individual components—

in particular, region n’s h-period-ahead level of

employment, ŷn,t+h.5The aggregate forecast is the

sum of the N regional forecasts (Model 2):

(2)

where ŷuni

from the univariate AR?p? model and φnjare scalar

coefficients.

An alternative to Model (2) that accounts for

the comovement between the regions is a VAR

forecast (Model 3). The aggregate forecast obtained

from such a model can be written as

n,t+his region n’s employment forecast

ˆY

Y

j t h

+

t h j

+ −

j

p

=

=∑Φ

1

,

ˆ

Y

ˆ

yy

t h

+

n t h

+

,

uni

n

N

∑

njn t h j

+ −

,

j

p

n

N

∑

===

==

∑

111

φ

, ,

Engemann, Hernández-Murillo, Owyang

3

The implicit assumption made here is that the aggregate is exactly

the sum of its component parts. That is,

holds identically. Of course, the validity of this assumption depends

greatly on the choice of data.

4

Potential constants and time trends are suppressed in this section

for notational convenience.

5

Henceforth, we refer to the disaggregate components as “regions,”

although they can, in principle, be of any type (e.g., industry, state,

MSA).

Yy

t nt

n

N

=

=

∑

1

Page 3

(3)

where ŷvar

Γnkjis the (scalar) lag-j effect of region k on region

n’s employment taken from the VAR coefficient

matrices.

Finally, we consider a ST-AR?p,q? model

(Model 4), which accounts explicitly for the spatial

correlations between regions by imposing a relation-

ship that depends on the proximity to a region’s

neighbors. The spatial weights wnkare chosen a

priori and are intended to reflect proximity between

pairs of regions, for example, in terms of geographic

characteristics such as contiguity or distance. Inter -

action between regions is governed by a weighting

matrix W = {wnk} satisfying

n,t+his region n’s employment forecast and

(4)

where φjand ψlare scalar autoregressive and scalar

spatial lag coefficients, respectively. The weighting

matrices used in the empirical applications are

discussed below.

The primary differences among the four models

involve a tension between modeling the (in-sample)

cross-spatial correlations and parameter prolifera-

tion. Clearly, Models (1) and (2) are the most parsi-

monious models. However, these models neglect

potentially predictive information in the comove-

ment between the variables. On the other hand,

the VAR depicted in Model (3) may overfit the in-

sample data. Under parameter certainty, the VAR

forecast in Model (3) weakly dominates the three

alternative Models (1), (2), and (4). However,

Giacomini and Granger (2004) show that forecasting

from an estimated VAR (Model 3) is less efficient

than forecasting from the ST-AR model (Model 4).6

ˆ

Y

ˆ

yy

t h

+

n t h

+

,

n

N

∑

nkj k t h j

+ −

,

j

p

k

N

==

=

==

∑

var

1

11

Γ

∑ ∑

1

∑

=

n

N

,

www

nknn nk

k n

≠

≥==

∑

001, , and?? ???

ˆ

Y

ˆ

y

y

j

w

l

y

t h

+

n t h

+

,

n

N

∑

n t h j

+ −

, nk k t,

=

=

=+

star

1

φ

1

ψ

1

+ + −

h l

====

∑

l

∑

k

∑

j

∑

n

q

N

p

N

11

,

Because the ST-AR model is a restricted form of

the VAR, the error associated with parameter uncer-

tainty decreases. Giancomini and Granger, however,

are unable to determine whether the ST-AR model

or the univariate model is more theoretically effi-

cient (i.e., whether interaction between regions

yields significant information for forecasting). In

the following section, we investigate whether

accounting for spatial interaction in regional

employment data is sufficiently elucidative to

warrant the use of disaggregate data in forecasting.

EMPIRICAL DETAILS

Hernández-Murillo and Owyang (2006) tested

the forecasting efficacy of the spatially disaggre-

gated model for national employment. Here, we

consider further disaggregation by examining the

model’s ability to forecast state- and Federal Reserve

District–level employment. We conduct three

experiments. First, we forecast Eighth District

employment using the sum of state-level employ-

ment.7Second, we forecast District employment

using the sum of Eighth District MSA–level employ-

ment.8Finally, we forecast state-level employment

for each of the seven District states using MSA-

level employment.

Data

Although a number of aggregate business cycle

indicators exist, relatively few series are available

at the disaggregate level. Two series available at a

state level with both a reasonable frequency and

sufficiently large sample are personal income

(quarterly) and employment (monthly).9At an

MSA-level, only employment is readily available.

6

Under certain conditions, the univariate aggregate model yields a

lower mean squared error. For a discussion of these conditions, see

Giacomini and Granger (2004).

Engemann, Hernández-Murillo, Owyang

FEDERAL RESERVE BANK OF ST. LOUIS REGIONAL ECONOMIC DEVELOPMENT VOLUME 4, NUMBER 12008

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7

The Federal Reserve’s Eighth District contains portions of seven

states: Missouri, Illinois, Tennessee, Arkansas, Kentucky, Indiana,

and Mississippi. Only Arkansas lies entirely in the Eighth District.

However, for purposes of this experiment, we make the simplifying

assumption that the District consists of the entirety of all seven states.

8

In constructing District-level employment for this experiment and

state-level employment for the next experiment, we use the sum of

MSA-level employment. For the former, we include only MSAs

located in the Eighth District, and for the latter, we include all MSAs

in the states. Rural employment is omitted in each case.

9

Gross state product, which is the state-level equivalent to national

gross domestic product, is annual and only available at a one-year lag.

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VOLUME 4, NUMBER 12008

FEDERAL RESERVE BANK OF ST. LOUIS REGIONAL ECONOMIC DEVELOPMENT

Engemann, Hernández-Murillo, Owyang

modeling the comovements between rural and

urban employment. In particular, for the spatial

model (4), modeling the distance between the

rural and MSA centroids is problematic.

Forecasting Scheme

We could use one of two forecasting schemes—

recursive or rolling window. A recursive forecasting

scheme fixes the initial period for the in-sample

data. Each additional period is added to the sample

and the model is reestimated. Thus, the estimation

window expands as the sample expands. Con -

versely, the rolling window scheme fixes the size

of the dataset used to make the forecast. With each

new period, recent data are added and data at the

beginning of the sample are dropped. The rolling

window scheme is particularly useful for cases in

which the data-generating process experiences

structural breaks. This has been shown to be the

case for both state- and MSA-level employment

(see Owyang, Piger, and Wall, 2005, forthcoming,

and Owyang, et al., forthcoming). Therefore, we

choose to use a rolling window forecasting scheme

with a 13-year sampling period. The number of

We, therefore, concentrate our efforts on the appro-

priate employment forecasts.

For our forecasting experiments, we use state-

and MSA-level employment data from the Bureau

of Labor Statistics’ payroll employment survey.

For the first experiment, state-level employment

is summed to yield an approximation of the Eighth

District employment level. In the same manner,

the appropriate aggregates are constructed from

MSA-level data in the following two experiments

for forecasting District- and state-level data. For

each exercise, the full sample is January 1990 to

December 2007. For convenience, the state- and

MSA-level data are plotted in Figures 1 and 2,

respectively. Summary statistics for the data are

provided in Tables 1 and 2.

For each of the last two experiments, we con-

struct the District- and state-level aggregates by

omitting rural employment. Table 3 shows that

the rural component of employment for each state

in the Federal Reserve’s Eighth District is significant.

The difficulty, however, of adding rural employ-

ment to the forecasting regressions (at least those

that account for cross-regional correlations) lies in

1,000

500

1,500

2,000

2,500

3,000

3,500

4,000

4,500

5,000

5,500

6,000

6,500

$ Thousands

0

Jan. 1990 Jan. 1992

Jan. 1996

Jan. 1998 Jan. 2000 Jan. 2002Jan. 2004 Jan. 2006

Jan. 1994

Arkansas

Illinois

Indiana

Kentucky

Mississippi

Missouri

Tennessee

Figure 1

Eighth District States’ Payroll Employment

NOTE: The employment series for each state is seasonally adjusted.

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FEDERAL RESERVE BANK OF ST. LOUIS REGIONAL ECONOMIC DEVELOPMENTVOLUME 4, NUMBER 12008

19

Engemann, Hernández-Murillo, Owyang

400

200

600

800

1,000

1,200

1,400

1,600

1,800

2,000

$ Thousands

0

Jan. 1990 Jan. 1992

Jan. 1996

Jan. 1998 Jan. 2000 Jan. 2002Jan. 2004 Jan. 2006

Jan. 1994

Arkansas

Illinois

Indiana

Kentucky

Mississippi

Missouri

Tennessee

Figure 2A

Eighth District MSAs’ Payroll Employment, by State

NOTE: The employment series for each state is seasonally adjusted and consists of the sum of all MSAs in that state.

1,000

500

1,500

2,000

2,500

3,000

3,500

4,000

4,500

5,000

$ Thousands

5,500

0

Jan. 1990 Jan. 1992

Jan. 1996

Jan. 1998 Jan. 2000Jan. 2002Jan. 2004 Jan. 2006

Jan. 1994

Arkansas

Illinois

Indiana

Kentucky

Mississippi

Missouri

Tennessee

Figure 2B

Total State MSAs’ Payroll Employment, by State

NOTE: The employment series for each state is seasonally adjusted and consists of the sum of all MSAs in that state.