creating a more timely measure of erie’s standard …...gilson, creating a more timely measure of...

FUNDED THROUGH THE UNDERGRADUATE STUDENT

SUMMER RESEARCH FELLOWSHIP PROGRAM

AND APPROVED BY SENIOR ASSOCIATE DEAN ROBERT LIGHT

CREATING A MORE TIMELY MEASURE OF ERIE’S

STANDARD OF LIVING

BENJAMIN C GILSON

SENIOR, BUSINESS ECONOMICS

PENN STATE ERIE, BEHREND COLLEGE,

(814) 873-0170, [email protected]

COOPERATING FACULTY MEMBER

JAMES A. KURRE, PH.D.

ASSOCIATE PROFESSOR OF ECONOMICS

DIRECTOR, ECONOMIC RESEARCH INSTITUTE OF ERIE (ERIE)

PENN STATE ERIE, BEHREND COLLEGE,

SAM & IRENE BLACK SCHOOL OF BUSINESS

(814) 898-6226, [email protected]

•December 2008•

Gilson, Creating a More Timely Measure of Erie’s Standard of Living P a g e | 1

Abstract

Unemployment rates help to show aspects of economic performance, but they do not

necessarily show the well-being of a population as a whole. The truth is some jobs pay

better than others and unemployment rates do not fully describe an area’s aggregate

earnings. Earnings data help to more fully describe an area’s economic performance, but

are lagged one and a half to two years. To address this issue, this project disaggregates

lagged earnings and current employment data industry by industry to estimate up to date

aggregate earnings for Erie County on a more timely basis. Is this method better than

focusing on aggregate earnings, income, and employment data? Comparisons in estimation

methods show that focusing on aggregate data is best when estimating aggregate earnings

and income, since industry specific data under NAICS are only available for 6 years, making

conclusive, accurate tests impossible.

Special Thanks To Todd Nesbit, Ph.D.

For his outstanding help in explaining the statistical and mathematical relationships and

methodologies that are used in this study.


Table of Contents

Introduction

Motivation……………………………………………………...

Original Research, Coomes & Olsen……………………….

Goals of this Project…………………………………………..

Methodology

Earnings Data & Correlation with Personal Income…….

Potential Advantages of Differing Forecasting Methods..

Limitations, SIC to NAICS Transition………………………

Creating a Monthly Index with Yearly Earnings Data…...

A Walk Through Each Forecasting Method…………….....

Results

Industrial Specific Data Forecast (2001-2006)…………...

Aggregate Data Forecast (2001-2006)…………………….

Aggregate Data Forecast (1969-2006)

Single Exponential Smoothing………………………...…

Naïve Forecast……………………………………………..

Simple Average Forecast…………………………………

Linear Trend Forecast……………………………………

Conclusions

Best Forecasting Method Tested…………………………….

Forecasts…....……………………………………...……………..

Extensions

Subsequent Steps to Predict Aggregate Earnings…………

References………………………………………………………...

Page 4

Page 5

Page 6

Page 8

Page 10

Page 11

Page 12

Page 17

Page 19

Page 19

Page 22

Page 23

Page 25

Page 29

Page 33

Page 37

Page 38


Introduction

Motivation

“November had seen Erie County's seasonally adjusted unemployment rate roll

back from 5.2 percent to 4.5 percent. In December, those numbers rolled right

back to where they started…Erie County wasn't the only place where November's

good news was replaced in December with a lump of statistical coal.” 1

The excerpt above shows public reaction to higher unemployment rates. It is commonplace to

see such articles in the daily newspaper discussing the implications of the area’s higher

unemployment, or lower employment, rates. Employment rates do help to reveal the area’s

standard of living in a timely manner, but should so much emphasis be placed on employment

data? Employment data are useful for indicating how many people have a job, but are also

limited in that they do not specify whether the job is a high paying, white collar job or if the job

is a low paying, floor sweeping job. For this reason, only using employment data to determine

the county’s economic performance will not yield precise results.

Income data, however, can accurately pinpoint the region’s total earnings and therefore is

superior at determining the region’s economic growth, but due to the difficulty of obtaining

income data, they are only available with a one and a half to two year lag. By that time the

informational value of the data is diminished, as it represents earnings that may not necessarily

be relevant to the present. For example, if a luxury goods merchant decides to set up a

dealership in Erie County based on high disposable income rates from 2 years ago, the dealer

could be surprised by an economic downturn since the most recent income data were released,

and could go bankrupt during the first year of operation.

When using just employment data to measure Erie’s economic performance instead of just

income data, a less accurate measure of the city’s performance becomes available during a more

relevant time. When income data are used instead of employment data, economic performance is

Martin, Jim. “Jobless Rate Rises, Good News From November Tempered by December’s Spike” Erie Times

News. 30 January 2008. http://www.goerie.com/apps/pbcs.dll/article?AID=2008801300395

http://www.goerie.com/apps/pbcs.dll/article?AID=2008801300395


measured with greater accuracy, but may not be available soon enough to be useful for current

decision making.

Original Research, Coomes & Olson

Coomes and Olson from the University of Louisville recognized that “a simple, but timely

measure of economic growth may be obtained by just counting metropolitan area jobs each

quarter.” Put into an index form, the employment data can easily be tracked over time to

measure growth. Recognizing that just employment data may be insufficient, Coomes and Olsen

also suggested that the job index could be improved by “multiplying the total number of jobs in

each industry in a city by the expected annual earnings per job in that industry.”2

By breaking employment data down industry by industry, the index can give appropriate weight

to each job based on the expected pay of that job. For example a new job that pays $50,000 will

add 2.5 times more value to an economic performance index than a new job that pays $20,000.

This is an especially useful method when tracking regional economic growth during times that

jobs shift from one sector to another, as the number of jobs may not change, but the average

income does.

Coomes’ and Olson’s technique for determining an economic performance index can be

represented by an equation in which the numerator is the estimated total income of all industries

added together using current compensation estimates, divided by the total income of all

industries added together during a base period.

2 Coomes, Paul A; Olson, Dennis O. “An Economic Performance Index for U.S. Cities”, Economic Development

Quarterly. November 1991: 335-341


The general equation (Equation One) to determine an income weighted economic performance

index, as proposed by Coomes and Olson, consists of the following components:

1. : The economic performance index at period

2. : The average earnings in industry i from the most recent 3 years of available

income data

3. : The average earnings in industry i during the index base year

4. : The number of jobs in industry i during the time at which the index value is being

calculated

5. : The number of jobs in industry i during the index base year

Equation One:

Goals of this Project

The overall goal of this project is to best predict current aggregate earnings. While current

earnings data are unknown, this project compares historic accuracy in various forecasting

methods and suggests using the top performing method. Accuracy is measured by mean

absolute percent error (MAPE) when calculating aggregate earnings. For example, if the

estimated total earnings for each industry are added together and equals 6 billion dollars during

2006 and the observed earnings is actually 5.7 billion dollars, then there is an error of 5.3%. The

lower the MAPE, the better the method performs. This project tests three different categories of

forecasting methods:

1) Coomes and Olsen’s method extended by projecting average earnings with a linear trend,

a quadratic trend, and by averaging earnings from the last 4 years.

2) Projecting total average earnings without industrial breakdown which will be multiplied

by employment.

3) Using a single exponential smoothing forecast, a naive forecast, a simple average forecast,

and a linear trend forecast to directly predict average earnings based on data from 1969-

2006, which will be multiplied by employment.


Methodology

Earnings Data & Correlation with Personal Income

Personal income is made up of components such as insurance payoffs, dividend payments,

unemployment benefits, and earnings by place of work. Because employment data are available

with only a one to two month lag, the methods used to determine the area’s aggregate income in

this project are heavily dependent on earnings by place of work data from the past to help

determine the current average earnings in each industry. Earnings data alone do not account for

100% of personal income and therefore the relationship between earnings and income must be

explored to help determine the validity of using earnings to estimate income.

Graph One: The graph below shows earnings by place of work as a percentage of total personal income.

Predicting total nonfarm earnings is the end result of this project and therefore earnings by place of work

have to be related to personal income. Data is from bea.gov.


Graph One shows the percentage of income that is accounted for by earnings. From the late 70s

to the mid 80s both “dividends, interest, and rent” and “personal transfer receipts” increased

substantially during a six year period while earnings by place of work decreased (Figure One),

causing a level shift in Graph One. For the last 20 years, however, the relationship between

earnings and income have remained fairly constant with only a small downward trend that can be

correlated with slightly greater growth in “dividends, interest, and rent” and “personal transfer

receipts” than in “earnings by place of work”.

Figure One: Three major components of personal income & their effect on the percentage of personal

income is made up by nonfarm earnings. Data are adjusted to 2007 dollars. Data is from bea.gov.


Because this project predicts total earnings based on known employment data and projected

earnings data, the relationship between earnings and income is key to determining the county’s

total income. A straight trend line produced from 20 years of data predicts that in the year 2008

earnings will be about 74.75% of income. This relationship can also be put in terms of income

as a percentage of earnings. In this case personal income would equal 134% of earnings. This is

one ideal that can be used to relate aggregate nonfarm earnings to aggregate income.

Potential Advantages of Different Forecasting Methods

The first method for estimating current earnings, the Coomes and Olsen approach, has many

advantages as it accounts for shifts in employment from one industry to another. Though this is

a very powerful attribute, the Coomes and Olsen approach also faces the disadvantage of a

greatly diminished timeframe for which data are available (see: Limitations, SIC to NAICS

Transition). Due to the time this project was conducted, and due to the one and a half to two

year lag in earnings data, only six years of data are available to test. Once again, due to the one

and a half to two year lag, only the first four years of the six years of available data (2001-2004)

can be used in an objective test that predicts aggregate earnings for 2006 to be compared against

the holdout 2006 aggregate earnings data.

Coomes and Olsen suggest using the mean of average earnings for the last three years of known

data to serve as a forecast for expected average earnings in each industry. In the data set for Erie

County, finding the mean earnings average from the past four years performs better at predicting

2006’s aggregate earnings (See: Table Three).

This project also tests two different ways to project average earnings: projecting with a linear

trend and projecting with a quadratic trend. Because average earnings in any industry could be

growing with time, a simple average of the past four years may result in a consistently,

negatively biased prediction (see: Graph Two). If earnings remain fairly constant over time, the

trend would be horizontal, projecting close to the same value a mean would predict.


Graph Two: This graph illustrates extreme differences between projecting using a trend and projecting

using a simple average. In this case the difference is nearly $8,000 when predicting 2008’s average

earnings. This table uses earnings data from the BEA, while employment and CPI data were obtained

from the BLS.

The second method used will project average earnings, despite industrial specification. For

example if average earnings are projected to be $50,000 and there are 100,000 jobs, then total

earnings would be five billion dollars ($50,000*100,000). This method will only use data from

the from the six years of data available that is classified using NAICS, and will serve as a

measure of how well method one performs.

The third method will be to use aggregate data from 1969-2006 to predict average earnings for

2007 and 2008. This method has the advantages of a long data set, but does not take into

account that some jobs pay better than others. The forecasting method used on this data set is

single exponential smoothing, modified to predict two years ahead, as is needed for a 2008

prediction, but will predict one year ahead for 2007. Just as in the second method, method three

will multiply average earnings by total jobs to calculate a total earnings prediction.


Limitations, SIC to NAICS Transition

Coomes and Olson’s Economic Performance Index is a solid foundation for this research project,

as it offers a technique for estimating an area’s aggregate income without having current

earnings data. However, a problem presents itself in that the national standard for classifying

industries changed from the Standard Industrial Classification (SIC) to the North American

Industry Classification System (NAICS). This means that an index based on SIC data would be

prone to error, as many types of businesses are now classified differently under NAICS.

Both SIC and NAICS separate all employment and income data into smaller, more specific,

categories. For example, government is a category of total employment and can be split further

into federal, state, and local government employment. Because method one isolates data

industry by industry, two different systems of classifying industries makes the act of combining

the two time periods (SIC: 1969-2000, NAICS: 2001-present) impossible. Table One, shown

below, was created by the Bureau of Labor Statistics (BLS) to help illustrate the differences

between the two classification systems, by dividing NAICS supersector employment data into

columns based on how employees would be classified by the older SIC classification system.

It would be problematic to convert all data from one method to the other. For example, during

the first quarter 2001, as shown in Table One, NAICS supersector “Information” would have

been divided among several different SIC divisions. In this case three different SIC divisions

would have accounted for at least 20% of what NAICS defines as the Information supersector.

This is just one example of the immense complexity involved in converting from one

classification method to another.

The SIC to NAICS transition presents a problem when using one uniform method across time to

produce an estimate of total earnings by place of work for Erie County. It also becomes a

problem when comparing the predicted total nonfarm earnings against the actual total earnings as

data become available. The transition may be ignored, however, when looking at observed total

earnings, or in other words the amount of earnings observed from tax data which is then reported

by the Bureau of Economic Analysis (BEA). The idea here is that the aggregate nonfarm

earnings should not be affected by how data are divided into industries. This is especially useful

for method three.


Table One: “The following table shows, for the private sector, the distribution of employment between

SIC Divisions and NAICS Supersectors. For example, for NAICS the supersector Natural Resources and

Mining, 87.3 percent of employment comes from the SIC Mining Division and 12.7 percent from the

Manufacturing Division. The table was prepared using first quarter 2001 data from the Quarterly Census

of Employment and Wages Program and can be used to evaluate time series breaks in the CES data

series.” (http://stats.bls.gov/ces/cesdist.htm)

NAICS Supersectors

Mining Construction Manufacturing Transportation

& Utilities

Wholesale

Trade

Retail

Trade

Finance,

Insurance,

& Real

Estate

Services

Natural

Resources and

Mining

Employment 515895 -1 75136 -1 -1 -1 -1 -1

Percent 87.3 12.7

Construction Employment 16927 6288743 -1 -1 -1 -1 86317 78928

Percent 0.3 97.2 1.3 1.2

Manufacturing Employment -1 -1 16502531 -1 31444 147887 -1 128670

Percent 98.2 0.2 0.9 0.8

Trade,

Transportation,

and Utilities

Employment -1 1028 70766 4360015 6592520 14381315 -1 125292

Percent 0 0.3 17.1 25.8 56.3 0.5

Information Employment -1 -1 751927 1670345 -1 1224 9221 1262674

Percent 20.3 45.2 0 0.2 34.2

Financial

Activities

Employment -1 -1 -1 37900 -1 25055 6881809 671353

Percent 0.5 0.3 90.4 8.8

Professional

and Business

Services

Employment 15660 66252 613021 657832 155520 373538 431577 14172829

Percent 0.1 0.4 3.7 4 0.9 2.3 2.6 86

Education and

Health Services

Employment -1 -1 4421 101245 -1 -1 -1 14602041

Percent 0 0.7 99.3

Leisure and

Hospitality

Employment -1 -1 -1 24052 -1 8147235 8403 3402214

Percent 0.2 70.3 0.1 29.4

Other Services Employment -1 -1 12805 5145 -1 6207 103269 3614016

Percent 0.3 0.1 0.2 2.8 96.5

-1 = less than 1000 employees

Employment data are in thousands

Creating a Monthly Index with Yearly Earnings Data

It is crucial that the performance index this project creates is updatable on a monthly basis. The

timelier and more accurate the information this project yields the more useful it will be for

decision making. The problem is that earnings data are available in intervals of one year rather

than monthly. This means that this project must develop a method to estimate a monthly

updatable index value. To accomplish this task, employment for every month will be multiplied

by the average earnings observed or predicted for that year then will be divided by the aggregate

earnings observed in 1970 to convert the monthly data into an index. This will be highly

http://stats.bls.gov/ces/cesdist.htm


seasonal and therefore the index will be smoothed using E-Views’ Census X12 seasonal

adjustment method.

A Walk Through Each Forecasting Method

Method One, Industrial Specific Data Forecast (2001-2006):

To illustrate exactly how nonfarm earnings data are tested and used to predict aggregate nonfarm

earnings, this section will use data for the industrial supersector “Natural Resources, Mining &

Construction” from the years 2001-2004 to predict total earnings for 2006.

To start the process, average earnings for each year of available data, 2001-2004, must be

calculated as a means to predict average earnings for 2006. To find average earnings, total

earnings in an industry must be divided by the number of employees in that industry and CPI

adjusted to a base year dollar value. In this case 2007 will serve as the base year. Equation Two

shows the how employment, earnings, and CPI values are used to find average earnings for each

industry.

Equation Two:

Table Two:

Natural Resources, Mining & Construction, Erie Data

Year Earnings Employment CPI Avg. Earnings

Bea.gov Bls.gov Bls.gov

(Thousands) (Thousands)

2001 273,978 5.0 177.1 $64,153

2002 269,315 5.0 179.9 $62,079

2003 273,943 4.8 184.0 $64,311

2004 285,624 4.8 188.9 $65,314

Now that average earnings from 2001-2004 are calculated various forecasting methods can be

conducted. Linear trend, quadratic trend, and a simple four year mean will be used to predict

average earnings for 2006. Table Three shows the total earnings predicted from each method


and compares the three against the observed earnings in that industry (also in 2007 dollars) based

on the Mean Absolute Percent Error (MAPE). In this case, fitting a quadratic trend line and

projecting to 2006 worked best with a 0.56% error.

Table Three:

Natural Resources, Mining & Construction Earnings

Method

2006

Prediction

2006

Employment

Total Earnings

Prediction

Observed

Earnings MAPE

Average $63,964 4.6 $294,236 $305,220 3.60%

Linear Trend $65,966 4.6 $303,442 $305,220 0.58%

Quadratic Trend $65,981 4.6 $303,512 $305,220 0.56%

Graph Three: An illustration of 3 forecasting techniques, average, linear trend, and exponential trend.

In this example forecasting using a linear trend (black line) performs slightly better than an exponential

trend (red line), and both perform much better than a simple average (green line). Please note that both

the quadratic and linear trend lines virtually coincide, making it difficult to recognize that there are two

lines.

In this example, average earnings tend to rise over time. Anytime a trend is present when

forecasting, using a simple average of past values to predict future values will result in increasing

error with an increasingly long forecast period.


At this point the forecasting method to be used across all industries is still unknown. To

determine what method will ultimately be used, 2006’s average earnings will be predicted from

employment and earnings data from 2001-2004 for every industry. The method that yields the

lowest average error when predicting aggregate earnings will then be accepted as the best

performing method for determining average earnings in each industry.

Method two, Aggregate Data Forecast (2001-2006):

This method ignores the industrial classification of a job; it gives equal weight to each job based

on the county’s average earnings of all industries. Just like in method one, however, historic

average earnings will be projected using the same three methods, average, linear trend, and

exponential trend. Each projection will be tested for accuracy against 2006’s observed earnings.

The projection with the lowest MAPE is recognized as the top performing way to predict average

earnings within method two. The average earnings projection is then multiplied by total

employment to calculate a forecast of aggregate nonfarm earnings.

Method three, Aggregate Data Forecasts (1969-2006):

Single Exponential Smoothing

This method has the advantage of using nonfarm earnings data from 1969-2006 to forecast

average earnings, but lacks the ability to give weight to jobs based on how well they pay. The

equation to predict one period, or one year, forward is as follows:

Equation Three: Single Exponential Smoothing (SES)

Where:

The SES equation uses the forecast for the current period as a base and adjusts for error for the next

forecast period. Alpha is used to calculate what percentage of the difference between the current forecast

and observed value will be compensated for when predicting the next period’s forecast. To initiate this

forecasting method, the first observation in the data set will substitute for the forecast for the first


observation. Alpha is chosen to minimize fitting error in the observed data set. Figure Two uses real

nonfarm earnings and employment data in the form of average earnings to illustrate how SES works.

Figure Two: Illustrates how single exponential smoothing forecasts average earnings. Data is from Erie

County

Alpha = 1.32

Fitting Error 1981-1990 = 0.641%

Year Yt Ft MAPE

1969 $47,589 $47,589

1970 $47,444 $47,589 0.31%

1971 $47,444 $47,398 0.10%

1972 $49,781 $47,459 4.66%

1973 $50,607 $50,524 0.16%

1974 $49,424 $50,634 2.45%

1975 $48,576 $49,037 0.95%

1976 $49,368 $48,428 1.90%

1977 $50,371 $49,669 1.39%

1978 $50,150 $50,596 0.89%

1979 $48,825 $50,007 2.42%

1980 $47,125 $48,447 2.80%

1981 $46,596 $46,702 0.23%

1982 $46,429 $46,562 0.29%

1983 $46,834 $46,386 0.96%

1984 $47,370 $46,977 0.83%

1985 $47,376 $47,496 0.25%

1986 $47,826 $47,338 1.02%

1987 $47,800 $47,982 0.38%

1988 $48,005 $47,742 0.55%

1989 $47,720 $48,089 0.77%

1990 $47,067 $47,602 1.14%

1991 $46,896

When forecasting 2008’s average earnings, the most recent earnings data are from 2006 so the

forecast has to be for two periods ahead. To accomplish this, Equation Three is slightly adapted

to read as follows:

In this form alpha is still used to minimize fitting error, however it will likely be a different alpha

than is seen when the forecast is one period ahead. When initializing the equation in this form,

this project still uses Y0 to substitute for F0 and also uses Y1 to substitute for F1.


Naïve Forecast

This is one of the simplest forecasting methods used. A Naïve forecast uses the most recent

value in a time series data set as a forecast for the next period. For example: If in 2005 average

earnings were $45,883, the naïve forecast would predict that in 2006 average earnings will be the

same value, $45,883. This method can be useful when a time series displays random changes

period to period, but remains fairly stationary over larger periods of time (in this case decades).

Simple Average Forecast

This method averages earnings per employee over a number of years to use as a forecast for the

average earnings of the next period of interest. This is the same as method one, except instead of

using industry specific data over four years, this method uses county average earnings data, and

instead of using data from the past four years, this method will choose the number of years based

on the number of years that minimizes error from 1997-2006 when predicting two years forward

when looking at historical data.

Linear Trend Forecast

This method uses ordinary least squares on a number of past years of county average earnings

data to predict future average earnings. The number of years will be chose to minimize error in

historical data.


Results

Method One: Industry Specific Data Forecast (2001-2006)

Using an average of earnings over the past three years, as suggested by Coomes and Olsen,

performs quite well. This project also predicts 2006’s total nonfarm earnings by using an

average of the past four years to test how the two variations compare. Table Three shows the

results of this test. Note that using four years performed better than 3 years.

Table Three: this is a comparison between averaging 3 years of data and averaging 4 years of data to

use as a predictor in aggregate nonfarm earnings using method one. Data is from the BEA and BLS.

Averaging Earnings From 2002-2004 to use as a Prediction for 2006

Industry Avg Earn. Prediction Employment

Total Earnings Prediction Observed Total Earnings MAPE

Nat Resources, Mining &

Construction 68,754 4.6 316,270 305,220 3.62%

Manufacturing 69,062 24.7 1,705,823 1,585,472 7.59%

Trade, Transportation, & Utilities 38,799 22.7 880,734 868,753 1.38%

Information 71,914 2.3 165,403 133,816 23.61%

Financial Activities 69,268 6.6 457,170 473,060 3.36%

Professional & Business Services 40,184 12.0 482,207 498,672 3.30%

Educational & Health Services 44,139 25.7 1,134,368 1,078,652 5.17%

Leisure & Hospitality 14,941 12.2 182,281 184,788 1.36%

Other Services 33,042 6.1 201,553 208,968 3.55%

Government 58,875 16.3 959,668 915,834 4.79%

6,485,478 6,253,233 3.71%

Method One: Averaging Earnings From 2001-2004 to use as a Prediction for 2006

Industry

Avg Earn.

Prediction Employment

Total Earnings

Prediction

Observed Total

Earnings MAPE

Nat Resources, Mining & Construction 63,964 4.6 294,236 305,220 3.60%

Manufacturing 60,756 24.7 1,500,677 1,585,472 5.35%


Information 57,485 2.3 132,215 133,816 1.20%





Other Services 33,322 6.1 203,263 208,968 2.73%

Government 53,637 16.3 874,279 915,834 4.54%

6,071,271

6,253,233

2.91%


Table Three (cont.):

Projecting a Linear Trend Line From 2001-2004 to use to predict Average Earnings for 2006

Industry Avg Earn. Prediction Employment Total Earnings Prediction Observed Total Earnings MAPE


Manufacturing 68,311 24.7 1,687,270 1,585,472 6.42%


Information 68,544 2.3 157,650 133,816 17.81%





Other Services 33,824 6.1 206,328 208,968 1.26%

Government 57,883 16.3 943,499 915,834 3.02%

6,440,849 6,253,233 3.00%

Projecting a Quadratic Trend Line From 2001-2004 to use to predict Average Earnings for 2006

Industry Avg Earn. Prediction Employment Total Earnings Prediction Observed Total Earnings MAPE


Manufacturing 68,693 24.7 1,696,710 1,585,472 7.02%


Information 69,365 2.3 159,540 133,816 19.22%





Other Services 33,828 6.1 206,351 208,968 1.25%

Government 58,017 16.3 945,671 915,834 3.26%

6,456,675 6,253,233 3.25%

*** Data are for Erie Pennsylvania

*** Dollar values are CPI adjusted to 2007's average CPI

*** Compensation data are from the Bureau of Economic Analysis: http://www.bea.gov/bea/regional/reis/ using Table CA05 *** Employment data are from the Bureau of Labor Statistics: http://www.bls.gov/data/ using metro area Current Employment Statistics

The results suggest that using average earnings from the last four years as a forecast of average

earnings in each industry is the best approach to method one, displaying a MAPE of 2.91%


Method Two: Aggregate Data Forecast (2001-2006)

Method two predicts average earnings for all industries based on past aggregate earnings values divided

by past aggregate employment values. Shown in Table Four, each of the three projections (average,

linear trend, and quadratic trend), are the product of average earnings based on the last four years of

known data (2001-2004). The average earnings are then multiplied by aggregate employment to yield a

total earnings prediction. Despite not considering that some jobs pay better than others, this method

performed better than method one, with a MAPE of 1.60%.

Table Four: Results of Method Two

Type of Projection Average Earnings Prediction Employment

Total

Earnings

Observed Total

Earnings MAPE

Average Projection $46,020 133.2 $6,129,910 $6,253,233 1.97%

Linear Projection $47,695 133.2 $6,352,985 $6,253,233 1.60%

Quadratic Projection $47,715 133.2 $6,355,677 $6,253,233 1.64%

Method Three: Aggregate Data Forecast (1969-2006)

Single Exponential Smoothing (SES):

Because method two is not dependent on industrial breakdown, it is not noticeably affected by

the classification change from SIC to NAICS, allowing the use of data starting at 1969. This

opens the door for more complex forecasting techniques to be used. A slightly modified version

of the single exponential smoothing (SES) method, for example, can be used to forecast average

earnings. If average earnings are calculated for Erie County from 1969 to 2004 the SES equation

may be used to predict year 2006’s average nonfarm earnings. When this is done, as shown in

Figure Three, the MAPE’s between 1995 and 2004 are minimized when α = .75 which results in

an average earnings prediction for 2006 of $46,717, which is a 0.49% MAPE. This is also the

error when predicting aggregate nonfarm earnings.


Because the prediction is for two years ahead the equation reads as follows:

Equation Four: Modified Single Exponential Smoothing Method

Where:

Figure Three: Illustration of SES on average nonfarm earnings for Erie County where Ft+2

Alpha = .75

MAPE1995-2004 = 1.496%

MAPE1997-2006 = 1.444%

Year Yt Ft+1 APE 1969 $47,589 $47,589

1970 $47,444 $47,444

1971 $48,981 $47,589 2.84%

1972 $49,781 $47,444 4.69%

1973 $50,607 $48,633 3.90%

1974 $49,424 $49,197 0.46%

1975 $48,576 $50,114 3.17%

1976 $49,368 $49,367 0.00%

1977 $50,371 $48,960 2.80%

1978 $50,150 $49,368 1.56%

1979 $48,825 $50,018 2.44%

1980 $47,125 $49,955 6.00%

1981 $46,596 $49,124 5.43%

1982 $46,429 $47,832 3.02%

1983 $46,834 $47,228 0.84%

1984 $47,370 $46,780 1.25%

1985 $47,376 $46,933 0.94%

1986 $47,826 $47,223 1.26%

1987 $47,800 $47,265 1.12%

1988 $48,005 $47,675 0.69%

1989 $47,720 $47,666 0.11%

1990 $47,067 $47,923 1.82%

1991 $47,119 $47,706 1.25%

1992 $47,879 $47,281 1.25%

1993 $47,772 $47,266 1.06%

1994 $47,792 $47,729 0.13%

1995 $47,254 $47,645 0.83%

1996 $46,866 $47,776 1.94%

1997 $47,048 $47,352 0.64%

1998 $47,443 $47,094 0.74%

1999 $47,252 $47,124 0.27%

2000 $45,886 $47,356 3.20%

2001 $45,437 $47,220 3.92%

2002 $45,768 $46,254 1.06%

2003 $45,883 $45,883 0.00%

2004 $46,993 $45,889 2.35%

2005 $46,705 $45,883 1.76%

2006 $46,946 $46,717 0.49%


When forecasting one year ahead instead of two years ahead, the fitting error during the last ten

years of known observations is reduced from 1.496% to 1.010%, displaying even greater

accuracy, but is less timely. For example, predicting 2008’s average nonfarm earnings must be

done from data two years old because earnings data from 2007 are not yet available. 2007 on the

other hand, can be predicted because data from 2006 exists. The result for a SES where Ft+1 is

forecasted is shown in Figure Four.

Figure Four: Illustration of SES on average nonfarm earnings for Erie County where Ft+1

Alpha = .75

MAPE1996-2005 = 1.010%

MAPE1997-2006=0.951%

Year Yt Ft+1 MAPE 1969 $47,589 $47,589

1970 $47,444 $47,589 0.31%

1971 $48,981 $47,481 3.06%

1972 $49,781 $48,606 2.36%

1973 $50,607 $49,487 2.21%

1974 $49,424 $50,327 1.83%

1975 $48,576 $49,650 2.21%

1976 $49,368 $48,844 1.06%

1977 $50,371 $49,237 2.25%

1978 $50,150 $50,087 0.13%

1979 $48,825 $50,134 2.68%

1980 $47,125 $49,153 4.30%

1981 $46,596 $47,632 2.22%

1982 $46,429 $46,855 0.92%

1983 $46,834 $46,535 0.64%

1984 $47,370 $46,759 1.29%

1985 $47,376 $47,217 0.33%

1986 $47,826 $47,336 1.02%

1987 $47,800 $47,704 0.20%

1988 $48,005 $47,776 0.48%

1989 $47,720 $47,948 0.48%

1990 $47,067 $47,777 1.51%

1991 $47,119 $47,245 0.27%

1992 $47,879 $47,150 1.52%

1993 $47,772 $47,697 0.16%

1994 $47,792 $47,753 0.08%

1995 $47,254 $47,782 1.12%

1996 $46,866 $47,386 1.11%

1997 $47,048 $46,996 0.11%

1998 $47,443 $47,035 0.86%

1999 $47,252 $47,341 0.19%

2000 $45,886 $47,274 3.03%

2001 $45,437 $46,233 1.75%

2002 $45,768 $45,636 0.29%

2003 $45,883 $45,735 0.32%

2004 $46,993 $45,846 2.44%

2005 $46,705 $46,707 0.00%

2006 $46,946 $46,706 0.51%


Naïve Forecast:

Table Five: Shows the past performance of using naïve forecast to predict average non-farm earnings

when predicting both one year forward and two years forward. All dollar values are CPI adjusted to

2007 dollars. All data are for Erie County.

Year Observed Avg.

Earnings NFt+1 APENFt+1 NFt+2 APENFt+2

1969 $47,589

1970 $47,444 $47,589 0.31%

1971 $48,981 $47,444 3.14% $47,589 2.84%

1972 $49,781 $48,981 1.61% $47,444 4.69%

1973 $50,607 $49,781 1.63% $48,981 3.21%

1974 $49,424 $50,607 2.39% $49,781 0.72%

1975 $48,576 $49,424 1.75% $50,607 4.18%

1976 $49,368 $48,576 1.60% $49,424 0.11%

1977 $50,371 $49,368 1.99% $48,576 3.56%

1978 $50,150 $50,371 0.44% $49,368 1.56%

1979 $48,825 $50,150 2.71% $50,371 3.16%

1980 $47,125 $48,825 3.61% $50,150 6.42%

1981 $46,596 $47,125 1.14% $48,825 4.79%

1982 $46,429 $46,596 0.36% $47,125 1.50%

1983 $46,834 $46,429 0.87% $46,596 0.51%

1984 $47,370 $46,834 1.13% $46,429 1.99%

1985 $47,376 $47,370 0.01% $46,834 1.14%

1986 $47,826 $47,376 0.94% $47,370 0.95%

1987 $47,800 $47,826 0.06% $47,376 0.89%

1988 $48,005 $47,800 0.43% $47,826 0.37%

1989 $47,720 $48,005 0.60% $47,800 0.17%

1990 $47,067 $47,720 1.39% $48,005 1.99%

1991 $47,119 $47,067 0.11% $47,720 1.28%

1992 $47,879 $47,119 1.59% $47,067 1.70%

1993 $47,772 $47,879 0.22% $47,119 1.37%

1994 $47,792 $47,772 0.04% $47,879 0.18%

1995 $47,254 $47,792 1.14% $47,772 1.10%

1996 $46,866 $47,254 0.83% $47,792 1.97%

1997 $47,048 $46,866 0.39% $47,254 0.44%

1998 $47,443 $47,048 0.83% $46,866 1.22%

1999 $47,252 $47,443 0.40% $47,048 0.43%

2000 $45,886 $47,252 2.98% $47,443 3.39%

2001 $45,437 $45,886 0.99% $47,252 4.00%

2002 $45,768 $45,437 0.72% $45,886 0.26%

2003 $45,883 $45,768 0.25% $45,437 0.97%

2004 $46,993 $45,883 2.36% $45,768 2.61%

2005 $46,705 $46,993 0.62% $45,883 1.76%

2006 $46,946 $46,705 0.51% $46,993 0.10%

2007 $46,946 $46,705

2008 $46,946

MAPE1997-2006 1.006% 1.517%


Graph Four: Shows a time series of two naïve forecasts used to predict average earnings for Erie

County.

Simple Average Forecast:

This method averages nonfarm average earnings over a number of years to use as a forecast for

the year of interest. When forecasting one period ahead, using two periods worth of data

minimizes the prediction error between 1996 and 2005, the last ten years of testable data. Using

five periods of the most recent average nonfarm earnings data minimizes the prediction error

between 1995 and 2004, once again, the last ten years of testable data. Equation Five shows the

equation for this method, and Table Six and Graph Five show the results of this prediction

method.

Equation Five: A mathematic model for the simple average forecast

Where:


Table Six: Shows the results of using a simple average forecast to predict Erie County’s average

earnings where the forecast is conducted for both one and two years forward. N is selected as to

minimize error in the past ten years of testable data.

Observed

Avg. Errormin: Average last

2 known observations Errormin: Average last 5 known observations

Year Earnings Ft+1 APE Ft+2 APE

1969 $47,589

1970 $47,444

1971 $48,981 $47,517 2.99%

1972 $49,781 $48,213 3.15%

1973 $50,607 $49,381 2.42%

1974 $49,424 $50,194 1.56%

1975 $48,576 $50,016 2.96% $48,881 0.63%

1976 $49,368 $49,000 0.75% $49,248 0.24%

1977 $50,371 $48,972 2.78% $49,474 1.78%

1978 $50,150 $49,869 0.56% $49,551 1.19%

1979 $48,825 $50,260 2.94% $49,669 1.73%

1980 $47,125 $49,488 5.01% $49,578 5.20%

1981 $46,596 $47,975 2.96% $49,458 6.14%

1982 $46,429 $46,860 0.93% $49,168 5.90%

1983 $46,834 $46,512 0.69% $48,613 3.80%

1984 $47,370 $46,632 1.56% $47,825 0.96%

1985 $47,376 $47,102 0.58% $47,162 0.45%

1986 $47,826 $47,373 0.95% $46,871 2.00%

1987 $47,800 $47,601 0.42% $46,921 1.84%

1988 $48,005 $47,813 0.40% $47,167 1.75%

1989 $47,720 $47,903 0.38% $47,441 0.58%

1990 $47,067 $47,862 1.69% $47,676 1.29%

1991 $47,119 $47,394 0.58% $47,745 1.33%

1992 $47,879 $47,093 1.64% $47,684 0.41%

1993 $47,772 $47,499 0.57% $47,542 0.48%

1994 $47,792 $47,825 0.07% $47,558 0.49%

1995 $47,254 $47,782 1.12% $47,511 0.54%

1996 $46,866 $47,523 1.40% $47,526 1.41%

1997 $47,048 $47,060 0.02% $47,563 1.09%

1998 $47,443 $46,957 1.02% $47,513 0.15%

1999 $47,252 $47,246 0.01% $47,346 0.20%

2000 $45,886 $47,348 3.18% $47,281 3.04%

2001 $45,437 $46,569 2.49% $47,173 3.82%

2002 $45,768 $45,662 0.23% $46,899 2.47%

2003 $45,883 $45,602 0.61% $46,613 1.59%

2004 $46,993 $45,826 2.49% $46,357 1.35%

2005 $46,705 $46,438 0.57% $46,045 1.41%

2006 $46,946 $46,849 0.21% $45,994 2.03%

2007 $46,826 $46,157

2008 $46,459

MAPE1997-2006= 1.08% MAPE1997-2006= 1.72%


Graph Five: Shows the graphical results of using simple average forecasts when conducted for both one

and two years forward.

Linear Trend Forecast:

This method performs quite well, having a MAPE for a two year prediction from1997-2006 of

1.91%. Forecasting one period ahead using the nine previous years of average earnings data

minimizes observed error, while forecasting two periods ahead using the eight previous years of

average earnings data minimizes error, as shown at the bottom of Table Eight. Graph Six shows

the forecasts resulting from this method.


Table Seven: Shows the forecasted nonfarm earnings values based on “x” number of years as defined by

the top row header. For example: the number shown in bold in row 1986 is the result of projecting

earnings data from 1980 to 1985 one year using Ordinary-Least-Squares.

Four Years Five Years Six Years Seven Years Eight Years Nine Years Ten Years

Year Ft+1 Ft+2 Ft+1 Ft+2 Ft+1 Ft+2 Ft+1 Ft+2 Ft+1 Ft+2 Ft+1 Ft+2 Ft+1 Ft+2

1969

1970

1971

1972

1973 50,477

1974 51,776 51,288 51,392

1975 50,237 52,804 50,923 52,230 50,917

1976 48,397 50,453 49,124 51,482 49,917 51,474 50,135

1977 48,352 47,917 48,694 49,007 49,170 50,140 49,826 50,441 50,057

1978 50,343 47,896 49,510 48,408 49,526 49,088 49,774 49,991 50,263 50,298 50,438

1979 51,048 50,706 50,552 49,457 49,884 49,480 49,837 49,821 50,009 50,473 50,423 50,700 50,585

1980 49,217 51,620 49,843 50,877 49,726 49,922 49,318 49,857 49,352 50,087 49,561 50,625 49,986 50,831

1981 46,352 49,032 47,358 49,971 48,159 49,804 48,318 49,243 48,146 49,288 48,298 49,560 48,586 50,101

1982 45,083 45,246 45,441 46,755 46,247 47,899 47,006 48,117 47,256 47,889 47,200 48,086 47,405 48,452

1983 45,314 43,847 44,923 44,383 45,042 45,535 45,639 46,578 46,290 46,912 46,544 46,838 46,530 47,100

1984 46,486 44,542 45,758 43,956 45,230 44,126 45,150 44,946 45,544 45,814 46,056 46,145 46,261 46,127

1985 47,489 46,382 47,089 45,290 46,365 44,536 45,759 44,425 45,536 44,951 45,763 45,617 46,142 45,878

1986 47,847 47,762 47,672 47,162 47,353 46,127 46,705 45,294 46,102 44,996 45,814 45,291 45,937 45,775

1987 48,097 48,185 48,168 47,922 48,025 47,467 47,737 46,576 47,136 45,772 46,538 45,398 46,202 45,554

1988 48,028 48,395 48,158 48,502 48,256 48,297 48,169 47,902 47,933 47,101 47,395 46,323 46,828 45,896

1989 48,217 48,202 48,184 48,396 48,295 48,537 48,394 48,417 48,335 48,103 48,135 47,404 47,648 46,681

1990 47,809 48,403 48,005 48,353 48,044 48,512 48,183 48,648 48,311 48,570 48,296 48,309 48,143 47,689

1991 47,027 47,798 47,204 48,092 47,467 48,147 47,589 48,339 47,781 48,509 47,956 48,490 47,998 48,295

1992 46,650 46,779 46,852 47,044 46,987 47,419 47,220 47,587 47,352 47,843 47,549 48,071 47,736 48,125

1993 47,578 46,318 47,302 46,622 47,306 46,815 47,325 47,136 47,465 47,312 47,546 47,567 47,699 47,806

1994 48,178 47,631 47,786 47,216 47,530 47,223 47,489 47,248 47,472 47,435 47,572 47,540 47,631 47,735

1995 48,118 48,465 48,156 47,878 47,881 47,512 47,661 47,456 47,607 47,433 47,575 47,562 47,650 47,637

1996 47,211 48,310 47,618 48,367 47,765 47,974 47,615 47,671 47,468 47,599 47,442 47,557 47,429 47,653

1997 46,607 47,025 46,750 47,637 47,135 47,846 47,333 47,641 47,266 47,443 47,176 47,410 47,180 47,393

1998 46,586 46,282 46,635 46,495 46,695 47,046 46,997 47,318 47,176 47,229 47,132 47,112 47,061 47,117

1999 47,341 46,324 47,010 46,397 46,937 46,483 46,911 46,898 47,122 47,137 47,256 47,080 47,205 46,990

2000 47,541 47,416 47,345 46,920 47,081 46,815 46,995 46,779 46,950 47,061 47,119 47,235 47,234 47,170

2001 45,988 47,696 46,372 47,402 46,430 47,026 46,343 46,907 46,353 46,847 46,374 47,066 46,573 47,213

2002 44,658 45,620 45,179 46,197 45,573 46,279 45,711 46,159 45,706 46,172 45,765 46,200 45,826 46,454

2003 44,860 43,920 44,807 44,701 45,094 45,264 45,375 45,454 45,482 45,447 45,474 45,524 45,525 45,601

2004 45,824 44,370 45,188 44,291 45,008 44,700 45,151 45,087 45,341 45,230 45,408 45,219 45,383 45,284

2005 47,217 45,856 46,792 44,903 46,106 44,645 45,780 44,842 45,763 45,095 45,829 45,182 45,816 45,150

2006 47,318 47,695 47,286 47,058 47,000 46,078 46,421 45,629 46,092 45,607 46,026 45,693 46,044 45,677

2007 47,357 47,711 47,413 47,662 47,436 47,254 47,223 46,457 46,720 46,019 46,399 45,933 46,301 45,956

2008 47,647 47,731 47,763 47,471 46,800 46,383 46,258


Table Eight: shows the resulting error of the linear trend forecasts shown in Table Seven

Years of past observations

used to forecast Four Years Five Years Six Years Seven Years Eight Years Nine Years Ten Years

Ft+1 Ft+2 Ft+1 Ft+2 Ft+1 Ft+2 Ft+1 Ft+2 Ft+1 Ft+2 Ft+1 Ft+2 Ft+1 Ft+2

Year

1969

1970

1971

1972

1973 0.26%

1974 4.76% 3.77% 3.98%

1975 3.42% 8.71% 4.83% 7.52% 4.82%

1976 1.97% 2.20% 0.50% 4.28% 1.11% 4.26% 1.55%

1977 4.01% 4.87% 3.33% 2.71% 2.38% 0.46% 1.08% 0.14% 0.62%

1978 0.38% 4.50% 1.28% 3.47% 1.24% 2.12% 0.75% 0.32% 0.22% 0.29% 0.57%

1979 4.55% 3.85% 3.54% 1.29% 2.17% 1.34% 2.07% 2.04% 2.42% 3.37% 3.27% 3.84% 3.60%

1980 4.44% 9.54% 5.77% 7.96% 5.52% 5.94% 4.65% 5.80% 4.73% 6.29% 5.17% 7.43% 6.07% 7.86%

1981 0.52% 5.23% 1.64% 7.24% 3.35% 6.88% 3.70% 5.68% 3.33% 5.78% 3.65% 6.36% 4.27% 7.52%

1982 2.90% 2.55% 2.13% 0.70% 0.39% 3.17% 1.24% 3.64% 1.78% 3.14% 1.66% 3.57% 2.10% 4.36%

1983 3.25% 6.38% 4.08% 5.23% 3.83% 2.77% 2.55% 0.55% 1.16% 0.17% 0.62% 0.01% 0.65% 0.57%

1984 1.87% 5.97% 3.40% 7.21% 4.52% 6.85% 4.69% 5.12% 3.86% 3.28% 2.77% 2.59% 2.34% 2.62%

1985 0.24% 2.10% 0.61% 4.40% 2.13% 6.00% 3.41% 6.23% 3.88% 5.12% 3.41% 3.71% 2.60% 3.16%

1986 0.04% 0.13% 0.32% 1.39% 0.99% 3.55% 2.34% 5.30% 3.60% 5.92% 4.21% 5.30% 3.95% 4.29%

1987 0.62% 0.80% 0.77% 0.25% 0.47% 0.70% 0.13% 2.56% 1.39% 4.24% 2.64% 5.03% 3.34% 4.70%

1988 0.05% 0.81% 0.32% 1.03% 0.52% 0.61% 0.34% 0.21% 0.15% 1.88% 1.27% 3.50% 2.45% 4.39%

1989 1.04% 1.01% 0.97% 1.42% 1.20% 1.71% 1.41% 1.46% 1.29% 0.80% 0.87% 0.66% 0.15% 2.18%

1990 1.58% 2.84% 1.99% 2.73% 2.08% 3.07% 2.37% 3.36% 2.64% 3.19% 2.61% 2.64% 2.29% 1.32%

1991 0.19% 1.44% 0.18% 2.07% 0.74% 2.18% 1.00% 2.59% 1.40% 2.95% 1.78% 2.91% 1.87% 2.50%

1992 2.57% 2.30% 2.14% 1.74% 1.86% 0.96% 1.38% 0.61% 1.10% 0.07% 0.69% 0.40% 0.30% 0.51%

1993 0.41% 3.04% 0.98% 2.41% 0.97% 2.00% 0.94% 1.33% 0.64% 0.96% 0.47% 0.43% 0.15% 0.07%

1994 0.81% 0.34% 0.01% 1.20% 0.55% 1.19% 0.63% 1.14% 0.67% 0.75% 0.46% 0.53% 0.34% 0.12%

1995 1.83% 2.56% 1.91% 1.32% 1.33% 0.55% 0.86% 0.43% 0.75% 0.38% 0.68% 0.65% 0.84% 0.81%

1996 0.73% 3.08% 1.60% 3.20% 1.92% 2.36% 1.60% 1.72% 1.28% 1.56% 1.23% 1.47% 1.20% 1.68%

1997 0.94% 0.05% 0.63% 1.25% 0.18% 1.70% 0.60% 1.26% 0.46% 0.84% 0.27% 0.77% 0.28% 0.73%

1998 1.81% 2.45% 1.70% 2.00% 1.58% 0.84% 0.94% 0.26% 0.56% 0.45% 0.66% 0.70% 0.81% 0.69%

1999 0.19% 1.96% 0.51% 1.81% 0.67% 1.63% 0.72% 0.75% 0.28% 0.24% 0.01% 0.36% 0.10% 0.56%

2000 3.61% 3.33% 3.18% 2.25% 2.60% 2.02% 2.42% 1.95% 2.32% 2.56% 2.69% 2.94% 2.94% 2.80%

2001 1.21% 4.97% 2.06% 4.33% 2.19% 3.50% 1.99% 3.24% 2.02% 3.10% 2.06% 3.59% 2.50% 3.91%

2002 2.42% 0.32% 1.29% 0.94% 0.43% 1.12% 0.12% 0.85% 0.13% 0.88% 0.01% 0.95% 0.13% 1.50%

2003 2.23% 4.28% 2.34% 2.58% 1.72% 1.35% 1.11% 0.94% 0.87% 0.95% 0.89% 0.78% 0.78% 0.62%

2004 2.49% 5.58% 3.84% 5.75% 4.23% 4.88% 3.92% 4.06% 3.52% 3.75% 3.37% 3.78% 3.43% 3.64%

2005 1.09% 1.82% 0.18% 3.86% 1.28% 4.41% 1.98% 3.99% 2.02% 3.45% 1.88% 3.26% 1.90% 3.33%

2006 0.79% 1.60% 0.72% 0.24% 0.12% 1.85% 1.12% 2.81% 1.82% 2.85% 1.96% 2.67% 1.92% 2.70%

MAPE1995-2004 1.75% 2.86% 1.91% 2.54% 1.68% 1.99% 1.43% 1.54% 1.22% 1.47% 1.19% 1.60% 1.30% 1.69%

MAPE1997-2006 1.68% 2.64% 1.65% 2.50% 1.50% 2.33% 1.49% 2.01% 1.40% 1.91% 1.38% 1.98% 1.48% 2.05%


Graph Six: Shows observed earnings vs. a linear trend forecast


Conclusions

The overall goal of this project is to provide a reliable, timely method to estimate the economic

performance of a county. The Bureau of Labor Statistics (BLS) posts county specific estimates

of employment with only a one to two month lag, which are useful for showing employment as

an economic indicator, but do not account for the fact that some jobs pay better than others.

Income and earnings data are available from the Bureau of Economic Analysis (BEA), but come

with a one and a half to two year lag, resulting in decayed usefulness.

One method this project tests that combines the timeliness of employment data with the added

economic performance detail of earnings and income data is the Coomes and Olsen method. The

general idea is that we use past industrial specific earnings data to forecast current earnings for

each supersector as defined by North American Industry Classification System (NAICS). Total

earnings for each supersector in a county can be estimated by multiplying the number employed

in that supersector by the forecasted earnings. Adding total earnings from each supersector

together results in an aggregate earnings estimate. By doing this we can numerically account for

the fact that some jobs pay better than others.

This method was tested on Erie County using industrial specific earnings data from 2001-2004 in

conjunction with industrial specific employment data from 2001-2006. When this project used

Coomes and Olsen’s method to predict earnings for 2006, a 2.91% error was observed. This is a

fairly good estimate, but lacks performance history due to only six years of data available under

the current NAICS.

Performing the Coomes and Olsen method, using industrial specific data, takes significantly

longer than just using aggregate data. Method two uses aggregate earnings and employment data

to calculate observed earnings per job for Erie County and then projects the average two years

forward. Using a linear projection of average earnings resulted in an error of 1.60% (see: Table

Four) when predicting aggregate earnings for 2006. Just like Coomes and Olsen’s method, this

method lacks the benefit of a performance history, raising doubt that either method is as accurate

as each sample suggests.


Method three ignores industrial specific data all together, just like method two, and forecasts

average earnings for Erie County using average earnings data from 1969-2006. The longer set of

average earnings data allows for many different forecasting methods to be tested over time.

With a MAPE of 0.95%, single exponential smoothing (SES) performed best at predicting

average earnings for Erie County over the past ten years of testable data (see: Table 10 and 11).

SES is the best-performing predictor of average earnings tested in this project. That’s not to say

that SES is necessarily the best of all possible methods, as there are many methods that are not

tested in this project. But with a MAPE around one percent, it does perform quite well at

predicting earnings which can then be used to forecast income.

Table Nine: Shows the best performing variation of Coomes’ and Olsen’s Method

Method One: Averaging Earnings From 2001-2004 to use as a Prediction for 2006 (Thousands of Dollars)

Industry

Avg Earn.

Prediction Employment

Total Earnings

Prediction

Observed Total

Earnings MAPE


Manufacturing 60,756 24.7 1,500,677 1,585,472 5.35%


Information 57,485 2.3 132,215 133,816 1.20%





Other Services 33,322 6.1 203,263 208,968 2.73%

Government 53,637 16.3 874,279 915,834 4.54%

6,071,271

6,253,233

2.91%


Table 10: Side by side comparison of various forecasting methods when forecasting one year ahead

Forecast Ft+1 Observed Avg. SES Naïve Simple Average Linear Trend

Year Earnings Ft+1 APE Ft+1 APE Ft+1 APE Ft+1 APE

1969 $47,589

1970 $47,444 $47,589 0.31%

1971 $48,981 $47,481 3.06% $47,444 3.14% $47,517 2.99%

1972 $49,781 $48,606 2.36% $48,981 1.61% $48,213 3.15%

1973 $50,607 $49,487 2.21% $49,781 1.63% $49,381 2.42%

1974 $49,424 $50,327 1.83% $50,607 2.39% $50,194 1.56%

1975 $48,576 $49,650 2.21% $49,424 1.75% $50,016 2.96%

1976 $49,368 $48,844 1.06% $48,576 1.60% $49,000 0.75%

1977 $50,371 $49,237 2.25% $49,368 1.99% $48,972 2.78%

1978 $50,150 $50,087 0.13% $50,371 0.44% $49,869 0.56% $50,438 0.57%

1979 $48,825 $50,134 2.68% $50,150 2.71% $50,260 2.94% $50,423 3.27%

1980 $47,125 $49,153 4.30% $48,825 3.61% $49,488 5.01% $49,561 5.17%

1981 $46,596 $47,632 2.22% $47,125 1.14% $47,975 2.96% $48,298 3.65%

1982 $46,429 $46,855 0.92% $46,596 0.36% $46,860 0.93% $47,200 1.66%

1983 $46,834 $46,535 0.64% $46,429 0.87% $46,512 0.69% $46,544 0.62%

1984 $47,370 $46,759 1.29% $46,834 1.13% $46,632 1.56% $46,056 2.77%

1985 $47,376 $47,217 0.33% $47,370 0.01% $47,102 0.58% $45,763 3.41%

1986 $47,826 $47,336 1.02% $47,376 0.94% $47,373 0.95% $45,814 4.21%

1987 $47,800 $47,704 0.20% $47,826 0.06% $47,601 0.42% $46,538 2.64%

1988 $48,005 $47,776 0.48% $47,800 0.43% $47,813 0.40% $47,395 1.27%

1989 $47,720 $47,948 0.48% $48,005 0.60% $47,903 0.38% $48,135 0.87%

1990 $47,067 $47,777 1.51% $47,720 1.39% $47,862 1.69% $48,296 2.61%

1991 $47,119 $47,245 0.27% $47,067 0.11% $47,394 0.58% $47,956 1.78%

1992 $47,879 $47,150 1.52% $47,119 1.59% $47,093 1.64% $47,549 0.69%

1993 $47,772 $47,697 0.16% $47,879 0.22% $47,499 0.57% $47,546 0.47%

1994 $47,792 $47,753 0.08% $47,772 0.04% $47,825 0.07% $47,572 0.46%

1995 $47,254 $47,782 1.12% $47,792 1.14% $47,782 1.12% $47,575 0.68%

1996 $46,866 $47,386 1.11% $47,254 0.83% $47,523 1.40% $47,442 1.23%

1997 $47,048 $46,996 0.11% $46,866 0.39% $47,060 0.02% $47,176 0.27%

1998 $47,443 $47,035 0.86% $47,048 0.83% $46,957 1.02% $47,132 0.66%

1999 $47,252 $47,341 0.19% $47,443 0.40% $47,246 0.01% $47,256 0.01%

2000 $45,886 $47,274 3.03% $47,252 2.98% $47,348 3.18% $47,119 2.69%

2001 $45,437 $46,233 1.75% $45,886 0.99% $46,569 2.49% $46,374 2.06%

2002 $45,768 $45,636 0.29% $45,437 0.72% $45,662 0.23% $45,765 0.01%

2003 $45,883 $45,735 0.32% $45,768 0.25% $45,602 0.61% $45,474 0.89%

2004 $46,993 $45,846 2.44% $45,883 2.36% $45,826 2.49% $45,408 3.37%

2005 $46,705 $46,707 0.00% $46,993 0.62% $46,438 0.57% $45,829 1.88%

2006 $46,946 $46,706 0.51% $46,705 0.51% $46,849 0.21% $46,026 1.96%

2007 $46,886 $46,946 $46,826 $46,399

MAPE1997-2006 0.95% 1.01% 1.08% 1.38%


Table 11: Side by side comparison of various forecasting methods when forecasting two years ahead

Forecast Ft+2 Observed Avg. SES Naïve Simple Average Linear Trend

Year Earnings Ft+2 APE Ft+2 APE Ft+2 APE Ft+2 APE

1969 $47,589

1970 $47,444

1971 $48,981 $47,589 2.84% $47,589 2.84%

1972 $49,781 $47,444 4.69% $47,444 4.69%

1973 $50,607 $48,633 3.90% $48,981 3.21%

1974 $49,424 $49,197 0.46% $49,781 0.72%

1975 $48,576 $50,114 3.17% $50,607 4.18% $48,881 0.63%

1976 $49,368 $49,367 0.00% $49,424 0.11% $49,248 0.24%

1977 $50,371 $48,960 2.80% $48,576 3.56% $49,474 1.78%

1978 $50,150 $49,368 1.56% $49,368 1.56% $49,551 1.19% $50,298 0.29%

1979 $48,825 $50,018 2.44% $50,371 3.16% $49,669 1.73% $50,473 3.37%

1980 $47,125 $49,955 6.00% $50,150 6.42% $49,578 5.20% $50,087 6.29%

1981 $46,596 $49,124 5.43% $48,825 4.79% $49,458 6.14% $49,288 5.78%

1982 $46,429 $47,832 3.02% $47,125 1.50% $49,168 5.90% $47,889 3.14%

1983 $46,834 $47,228 0.84% $46,596 0.51% $48,613 3.80% $46,912 0.17%

1984 $47,370 $46,780 1.25% $46,429 1.99% $47,825 0.96% $45,814 3.28%

1985 $47,376 $46,933 0.94% $46,834 1.14% $47,162 0.45% $44,951 5.12%

1986 $47,826 $47,223 1.26% $47,370 0.95% $46,871 2.00% $44,996 5.92%

1987 $47,800 $47,265 1.12% $47,376 0.89% $46,921 1.84% $45,772 4.24%

1988 $48,005 $47,675 0.69% $47,826 0.37% $47,167 1.75% $47,101 1.88%

1989 $47,720 $47,666 0.11% $47,800 0.17% $47,441 0.58% $48,103 0.80%

1990 $47,067 $47,923 1.82% $48,005 1.99% $47,676 1.29% $48,570 3.19%

1991 $47,119 $47,706 1.25% $47,720 1.28% $47,745 1.33% $48,509 2.95%

1992 $47,879 $47,281 1.25% $47,067 1.70% $47,684 0.41% $47,843 0.07%

1993 $47,772 $47,266 1.06% $47,119 1.37% $47,542 0.48% $47,312 0.96%

1994 $47,792 $47,729 0.13% $47,879 0.18% $47,558 0.49% $47,435 0.75%

1995 $47,254 $47,645 0.83% $47,772 1.10% $47,511 0.54% $47,433 0.38%

1996 $46,866 $47,776 1.94% $47,792 1.97% $47,526 1.41% $47,599 1.56%

1997 $47,048 $47,352 0.64% $47,254 0.44% $47,563 1.09% $47,443 0.84%

1998 $47,443 $47,094 0.74% $46,866 1.22% $47,513 0.15% $47,229 0.45%

1999 $47,252 $47,124 0.27% $47,048 0.43% $47,346 0.20% $47,137 0.24%

2000 $45,886 $47,356 3.20% $47,443 3.39% $47,281 3.04% $47,061 2.56%

2001 $45,437 $47,220 3.92% $47,252 4.00% $47,173 3.82% $46,847 3.10%

2002 $45,768 $46,254 1.06% $45,886 0.26% $46,899 2.47% $46,172 0.88%

2003 $45,883 $45,883 0.00% $45,437 0.97% $46,613 1.59% $45,447 0.95%

2004 $46,993 $45,889 2.35% $45,768 2.61% $46,357 1.35% $45,230 3.75%

2005 $46,705 $45,883 1.76% $45,883 1.76% $46,045 1.41% $45,095 3.45%

2006 $46,946 $46,717 0.49% $46,993 0.10% $45,994 2.03% $45,607 2.85%

2007 $46,500 $46,705 $46,157 $46,019

2008 $46,889 $46,946 $46,459 $46,800

MAPE1997-2006 1.44% 1.52% 1.72% 1.91%


Forecasts

Predicting Yearly Earnings and Income

This project’s goal is to find how to best determine Erie County’s economic performance on a

more timely basis. Now that the results of this project are known, it will actually predict average

earnings for 2007-2008 and aggregate earnings for 2007.

As suggested in the section “Earnings Data & Correlation with Personal Income”, personal

income will be predicted based on the strong relationship between nonfarm earnings and

personal income. Note however that this project’s focus is estimating earnings, and a

comprehensive personal income forecast should look at other components in addition to the

nonfarm earnings which make up approximately 75% of personal income in Erie County.

Table 12: Forecasted aggregate earnings based on best performing method for predicting average

earnings and also based on actual employment data for 2007. Personal income is predicted based on the

relationship found between nonfarm earnings and personal income in the section “Earnings Data &

Correlation with Personal Income”. Data and forecasts are for Erie, Pennsylvania.

2007 2008

Average Earnings (see: SES Tables 10 and 11) $46,866 $46,889

Known Average Employment (see: bls.gov) 133800

Aggregate Earnings $6,270,670,800

Expected Earnings to Income Ratio 74.90% 74.81%

Personal Income (Earnings/.749) $8,372,318,312

Table 12 presents the output of this project after considering many different approaches. This

section also opens up the project for future criticism as all predictions will be proven to be wrong

by a certain amount. The hope is that by risking the project’s credibility, by testing it, that it will

perform well and will be considered a legitimate resource for predicting current earnings.


Hindsight on 2007’s Forecast

Due to the time this project was conducted, personal income and earnings by place of work for

2007 became available while the project was ongoing. None of the 2007 data were viewed while

working on the prediction for 2007. As shown in Table 12, personal income for Erie County was

predicted to equal 8.372 billion dollars. The observed income for Erie County in 2007 was

actually 8.505 billion dollars, resulting in a prediction absolute error of 1.56%, which implies

that this technique gives a reasonable result.

Monthly Index

Finally, this project creates a monthly performance index for Erie County using the techniques

explained in Methodology: Creating a Monthly Index with Yearly Earnings Data, page 11. The

output of this method is shown below in Graphs Seven and Graph Eight, and in Table 13. For

years 1969-2006 each month’s index value is determined by multiplying that year’s average

earnings by the employment that month and then is divided by the average earnings observed in

1970. The resulted index value is then seasonally adjusted using Census x12. From January

2007 to July 2008, the index is calculated the same way with the exception that forecasted

average earnings (using single exponential smoothing) replace observed earnings. This index is

significant in that it uses real earnings data and real employment data from 1969 to 2006 to

calculate the observed aggregate earnings index values and estimates index values from 2006 to

July, 2008 using forecasted average earnings data and observed employment data obtained from

the BLS. Using this method accounts for both changing employment and changing average

income.


Graph Seven: This graph is the output of a monthly index as defined in Methodology: Creating a Monthly

Index with Yearly Earnings Data from 1969-2008

0

20

40

60

80

100

120

140

1970 1975 1980 1985 1990 1995 2000 2005

Seasonally Adjusted Aggregate Earnings Index

for Erie County (1970 Base)

Ind

ex

Valu

es

Year

Graph Eight: This graph is a numerically exact copy of Graph Seven, zoomed in on the years 2000-2008.

122

124

126

128

130

132

134

2000 2001 2002 2003 2004 2005 2006 2007 2008

Seasonally Adjusted Aggregate Earnings Index

for Erie County (1970 Base)

Ind

ex

Valu

e

Year


Table 13: shows Index values that represent aggregate earnings for each month. 2000-2006 are

calculated using observed earnings and employment data, while 2007 and 2008 are calculated using

predicted average earnings (using SES) and real employment data.

Year Month

Smoothed

Index

Value

2000 Jan 130.7

2000 Feb 130.4

2000 Mar 131.4

2000 Apr 132.5

2000 May 132.4

2000 Jun 132.7

2000 Jul 132.3

2000 Aug 132.5

2000 Sep 132.3

2000 Oct 131.5

2000 Nov 131.4

2000 Dec 131.1

2001 Jan 130.5

2001 Feb 130.4

2001 Mar 129.9

2001 Apr 129.0

2001 May 128.4

2001 Jun 127.6

2001 Jul 126.9

2001 Aug 126.8

2001 Sep 126.4

2001 Oct 126.3

2001 Nov 126.0

2001 Dec 125.9

2002 Jan 127.4

2002 Feb 126.5

2002 Mar 126.8

2002 Apr 126.4

2002 May 126.7

2002 Jun 126.8

2002 Jul 127.2

2002 Aug 127.7

2002 Sep 127.6

2002 Oct 127.0

2002 Nov 126.8

2002 Dec 126.5

Year Month

Smoothed

Index

Value

2003 Jan 126.4

2003 Feb 125.8

2003 Mar 125.8

2003 Apr 125.8

2003 May 126.1

2003 Jun 125.5

2003 Jul 124.0

2003 Aug 124.7

2003 Sep 124.4

2003 Oct 126.0

2003 Nov 126.2

2003 Dec 125.7

2004 Jan 128.9

2004 Feb 128.8

2004 Mar 128.7

2004 Apr 129.0

2004 May 129.6

2004 Jun 129.6

2004 Jul 130.8

2004 Aug 130.5

2004 Sep 131.2

2004 Oct 131.2

2004 Nov 131.4

2004 Dec 131.5

2005 Jan 130.7

2005 Feb 130.4

2005 Mar 130.2

2005 Apr 131.5

2005 May 131.4

2005 Jun 132.2

2005 Jul 131.8

2005 Aug 131.9

2005 Sep 131.8

2005 Oct 131.2

2005 Nov 131.2

2005 Dec 131.3

Year Month

Smoothed

Index

Value

2006 Jan 131.7

2006 Feb 131.6

2006 Mar 131.9

2006 Apr 131.8

2006 May 131.3

2006 Jun 131.1

2006 Jul 132.6

2006 Aug 131.9

2006 Sep 131.8

2006 Oct 132.2

2006 Nov 132.0

2006 Dec 131.8

2007 Jan 131.8

2007 Feb 131.9

2007 Mar 132.3

2007 Apr 131.8

2007 May 132.6

2007 Jun 132.2

2007 Jul 132.0

2007 Aug 131.9

2007 Sep 131.8

2007 Oct 132.0

2007 Nov 132.4

2007 Dec 132.8

2008 Jan 133.2

2008 Feb 133.4

2008 Mar 132.6

2008 Apr 132.8

2008 May 132.9

2008 Jun 132.7

2008 Jul 132.6

2008 Aug

2008 Sep

2008 Oct

2008 Nov

2008 Dec


Extensions

What Comes Next?

The biggest roadblock this project faced was lack of data when testing the Coomes and Olsen

method. With six years of data and a one and a half to two year lag in earnings data, only four

years of data could be used for a testable forecast. It would be better to try the Coomes and

Olsen method in 2012. When predicting average earnings per job does not account for some

jobs paying better than others, but until more data are collected under NAICS, using earnings per

job predictions in conjunction with employment data may be the best method to predict

aggregate income.

Another method that could be looked into is direct forecasting of aggregate income based on past

aggregate income. Due to time constraints this method is not included in this project, receiving a

lower priority since is somewhat different than the projects focus of using both employment and

earnings forecasts to estimate income.

In order to predict income, this project used ordinary least squares (OLS) to estimate the

relationship between earnings and income (see: Graph One on page six). Expanding on that

model could help to explain more variation in the regression model to more accurately define a

relationship between earnings and personal income. For example, one explanatory variable

might be overall change in stock market indexes during each year.

To test relative usefulness of the SES estimation index this project creates, it may be

advantageous to compare percent changes produced by the SES estimation index with percent

changes in an employment and unemployment indexes already used. If pure employment or

unemployment rates match percent changes in income more closely than percent changes in the

SES estimation index, they would be more ideal for explaining a county’s aggregate personal

income.


References

Martin, Jim. “Jobless Rate Rises, Good News From November Tempered by December’s Spike”

Erie Times News. 30 January 2008.

Coomes, Paul A; Olson, Dennis O. “An Economic Performance Index for U.S. Cities”

Economic Development Quarterly. November 1991: 335-341

U.S. Department of Commerce, Bureau of Economic Analysis. Regional Economic Information

System. Available online at: http://www.bea.gov/bea/regional/reis/

U.S. Department of Labor, Bureau of Labor Statistics. Databases, Tables & Calculators by

Subject: All Urban Consumers (Current Series) Consumer Price Index. Available online

at: http://www.bls.gov/data/

U.S. Department of Labor, Bureau of Labor Statistics. Databases, Tables & Calculators by

Subject: Employment, Hours and Earnings – State and Metro Area. Available online

at: http://www.bls.gov/data/

U.S. Department of Labor, Bureau of Labor Statistics. “Distribution of Employment from SIC

Divisions to NAICS Supersectors” Current Employment Statistics - CES (National). 6

January 2004. Available online at: http://stats.bls.gov/ces/cesdist.htm

http://www.bea.gov/bea/regional/reis/

http://www.bls.gov/data/

http://www.bls.gov/data/

http://stats.bls.gov/ces/cesdist.htm

creating a more timely measure of erie’s standard …...gilson, creating a more timely measure of...

Documents