There are three components to this project:

- The Worcester Economic Index. An index of the recent performance of the greater Worcester economy based on local employment data.
- A growth forecast for the Worcester Economic Index over the coming 3-6 months which is estimated using a set of national leading indicators.
- A diffusion index of local leading indicators.

The methodology used for each component is described below.

## Worcester Economic Index

The Worcester Economic Index utilizes the methodology introduced by Stock & Watson (1989) and applied by Clayton-Matthews & Stock (1998/99), Crone & Clayton-Matthews (2005) and Tebaldi and Kelly (2012) to estimate an index of an underlying economy. Unlike the national economy where a broad measure of economic activity (GDP) is reported on a timely basis, state and local economic performance data such as personal income or local GDP are reported with substantial lag times. In order to fill in the gaps, the above authors have demonstrated how an index of the underlying state of the economy can be estimated for a dynamic single-factor model using the Kalman filter. Stock & Watson (1989) applied the methodology to the national economy, while Clayton-Matthews & Stock (1998/99), Crone & Clayton-Matthews (2005), and Tebaldi and Kelly (2012) estimated state indexes. The use of this methodology to estimate an index of the Worcester economy is one of the first at the sub-state level. By relying on local employment and unemployment data that is released monthly by the Bureau of Labor Statistics^{i}, an index of local economic performance is found that is more current than local personal income or local contribution to GDP estimated reported by the Bureau of Economic Analysis.

The Worcester Economic Index is based on the movements of three employment variables for the Worcester area: total nonfarm payroll employment, total household employment, and the unemployment rate. Total nonfarm payroll employment is available from the Bureau of Labor Statistics (BLS) on a monthly basis and is based on the Current Employment Statistics Survey of business establishments. Total household employment and the unemployment rate are both products of the Local Area Unemployment Statistics program of the BLS, which is based on the Current Population Survey of households. All three variables are for the Worcester NECTA which includes 37 cities and towns in south central Massachusetts, as well as 3 northeastern Connecticut towns. The BLS provides seasonally adjusted data for total payroll employment, while total household employment and the unemployment rate are only available on a not seasonally adjusted basis. Therefore these variables are seasonally adjusted each month using the X-12 ARIMA program available from the U.S. Census Bureau.

The three variables used to estimate the Worcester Economic Index are transformed prior to estimation. Payroll employment and household employment are each logged and first-differenced to assure they are stationary, while the unemployment rate is first-differenced only. In addition, all three variables are normalized so that each has a mean of 0 and a standard deviation of 1.

Following the notation of Crone & Clayton-Matthews (2005), the dynamic single-factor model can be represented as:

where Δx_{t} is a G x 1 vector of observable stationary variables, Δc_{t }is the unobserved common factor that explains the changes in the observable variables, μ_{t} is a vector of uncorrelated mean-zero autoregressive processes, εt and ηt are mutually uncorrelated processes, L is a lag operator and the subscript t represents time period. D(L) is assumed to be a diagonal matrix and all of the polynomials except for γ(L) are one-sided.

Payroll employment, household employment, and the unemployment rate are the variables that make up the 3 x 1 vector Δx_{t}. The parameters of equations (1)-(3) are found using maximum-likelihood, and estimates of the common factor are obtained by using the Kalman filter. The estimates of the common factor, Δct are linear functions of the observable variables Δx_{t}. The linear function can be expressed as

Estimates of Δc_{t} must be integrated (reverse-differenced and exponentiated) to obtain an estimate of the underlying economy. In order for the index to better track the economy, it is appropriate to recalibrate the estimates so they follow the same trend and variation around trend as another series of interest. Crone & Clayton-Matthews (2005) retrend the estimates so they track the gross state product for each state. For this project, the index is recalibrated so it follows the trend in local contribution to GDP using

where a and b are the average growth rate and the standard deviation of the growth rate of GDP for the Worcester area, respectively. The Worcester Economic Index (WEI) is then estimated using this retrended common factor as follows:

The resulting Worcester Economic Index is scaled so it follows the long-run trend of local contribution to GDP and can be interpreted as the path of the underlying local economy. The index is set to equal 100 in January 2001.

## Forecasting the Growth of the Worcester Economic Index

Clayton-Matthews and Stock (1998/99) describe how to forecast the 6-month growth rate of an economic index using a set of leading economic indicators. The model used for this forecast can be expressed as:

where f_{t}(6) = c_{t}+6 – c_{t}, and y_{t} is a vector of leading indicators. Equation (7) expresses the six-month change in the underlying common factor c, as a function of recent monthly growth rates of the common factor Δc, as well as the growth rates of leading indicators Δy.

After the specification of equation (7) is determined, the parameter estimates can be used to predict the six-month growth of the common factor. For this project, model specification followed the steps laid out by Clayton-Matthews & Stock (1998/99) who based model selection on six criteria: predictive least squares, Bayesian information criterion, contribution of leading indicators, equality of contribution by leading indicators, number of leading indicators, and the number of correct signs on estimated coefficients. Many specifications of (7) were evaluated using these criteria. Eight national leading indicators were considered for inclusion in the model: average weekly hours in manufacturing, new orders of consumer goods, Institute of Supply Management New Orders Index, new orders of nondefense capital goods, S&P 500 stock index, Leading Credit Index (LCI^{TM}), interest rate spread, and the University of Michigan Index Of Consumer Expectations^{ii}. The model was estimated for all possible combinations of these indicators. The specification that was deemed “best” included only four of the eight leading indicators tested: S&P index, LCI, interest rate spread, and consumer expectations.

Each month the model is re-estimated to obtain a prediction of the six-month growth of the WEI. Following Clayton-Matthews & Stock, the predicted growth rate can be broken down to show how changes in WEI, changes in the leading indicators, and a trend component all contribute to the estimated growth rate. (See Clayton-Matthews & Stock (1998/99) for a more detailed explanation of the procedure)

## A Diffusion Index of Local Leading Indicators

In order to provide additional information about the Worcester economy several other leading indicators are considered. Unlike the nationally based indicators used to forecast growth in the WEI, these indicators are all based on local information. The four data series that are available at the local level are: initial unemployment claims, new business incorporations, online help-wanted advertising (HWOL^{TM}), and new building permits issued (value). Each of these variables may provide leading information on the direction of the local economy. In order to summarize the changes in these leading indicators a diffusion index is calculated.

Following the procedure used by The Conference Board^{iii}, a diffusion index is found by first calculating the percentage change for each component in the index over the relevant time frame in this case six months. Next, components which increase more that 0.05% are given a value of 1, components that decreases more than 0.05% are given a value of zero, and components that basically unchanged (between -0.05% and +0.05%) are given a value of 0.5. The values are then summed and the total is divided by the number of components. If all of the indicators are unchanged the resulting diffusion index will be 50, therefore an index above 50 says that a majority of the indicators have been increasing and is a positive signal for future economic conditions. Conversely, and index below 50 shows the leading indicators are on balance declining and signal an economic downturn.

The four indicators used to estimate the diffusion index are the best available leading indicators for the local area. The first local leading indicator is initial unemployment claims^{iv} for the Worcester region, an increase in which signals a drop off in economic activity. The second indicator is the amount of online help-wanted advertising for the Worcester area^{v}. An increase in help-wanted ads should be a precursor to increased hiring and employment. The third leading indicator is the number of new business incorporations in the local area^{vi}. An increase in incorporations may lead new hiring by those firms. Finally, since building permits^{vii} are required before new residential construction can take place, an increase in building permits would foreshadow increases in future employment. In comparison with national level data, local data can be quite volatile and therefore short-term changes in any variable or the diffusion index as a whole should considered with caution. Only when the diffusion index is above or below 50 for at least three months should it be considered a signal of future economic activity.

Prepared by:

Thomas White, Ph.D.

Department of Economics & Global Studies

Assumption College

508-767-7556

twhite@assumption.edu

February 5, 2014

^{i} Establishment employment data are available from the Current Employment Statistics program. www.bls.gov/sae/

Unemployment statistics are available from the Local Area Unemployment Statistics program. www.bls.gov/lau/

^{ii} Data for all of these indicators were obtained from The Conference Board Business Cycle Indicators Database.

^{iii} The Conference Board, http://www.conference-board.org/data/bci/index.cfm?id=2180

^{iv} Massachusetts Department of Employment and Training

^{v} The Conference Board, Help Wanted Online® (HWOL)

^{vi} Secretary of the Commonwealth of Massachusetts

^{vii} U.S. Census Bureau, Building Permits Survey

References:

Clayton-Matthews, A., & Stock, J. H. (1998/99). An Application of the Stock-Watson Index Methodology to the Massachusetts Economy. *Journal of Economic and Social Measurement, 25*, 183-233.

Crone, T. M., & Clayton-Matthews, A. (2005). Consistent Economic Indexes for the 50 States. *The Review of Economics and Statistics, 87*(4), 593-603.

Stock, J. H., & Watson, M. W. (1989). New Indexes of Coincident and Leading Economic Indicators. *NBER Macroeconomics Annual*, 351-394.

Tebaldi, E., & Kelly, L. (2012). Measuring economic conditions: an extenstion of the Stock/Watson methodology. *Applied Economic Letters, 19*, 1865-1869.

The Conference Board. (n.d.). *How to Compute Diffusion Indexes*. Retrieved January 2014, from The Conference Board: http://www.conference-board.org/data/bci/index.cfm?id=2180