Introduction

Increasingly, users of labor market information request more and more detailed data on Delaware's economy. One of the most frequent requests is for the state's short-term general economic outlook. In an attempt at satisfying those desires of business, the public, and other government agencies, we have developed a combined short-term state quarterly employment projection model and index of leading indicators.

Several private firms, as well as the Federal Reserve Bank of Philadelphia, already provide forecasts at varying levels of detail for Delaware's economy. Our model is not meant to supplant or compete with them, but to complement them. Short-term forecasting is a risky proposition (as is long-term forecasting, but here the analyst is further removed from his or her mistakes); users are probably best served by a variety of forecasts from different sources, generated by different methods. This model utilizes time series techniques, with the index of leading indicators appearing as an intervention variable. Details of both the model and the index are presented below.

Current Projections

Employment

After growing at a strong pace for three years, job growth in Delaware slowed in the second half of 2006. From mid-2003 until mid-2006, the state added a net 23,000 jobs, an average of nearly 8,000 per year. This annual rate of growth of slightly better than 1.8 percent was a little above Delaware's long-term average. During the last six months of 2006, fewer than 600 jobs were added to the state total, an annual rate of less than 0.3 percent. Although it is possible that job growth will bounce back to more typical levels in 2007, it is more likely that Delaware will face tepid job growth the rest of this year and into 2008. The possibility that there will be net job losses over this period cannot be discounted.

Two of Delaware's largest industries accounted for much of the turnabout in 2006. Retail Trade, which employs more workers in the state than any other industry, was adding jobs at a 1.8 percent annual rate at the beginning of 2006. By the end of the year, Retail Trade was losing jobs at a 0.3 percent annual rate. Financial Activities, Delaware's largest industry in terms of contribution to the state's gross product, was losing jobs at a 1.4 percent annual rate as 2006 began. By year's end, it was losing jobs at a 4.0 percent annual rate. The sub-industry Nondepository Credit Intermediation, commonly known as credit card banks, was where these job losses were concentrated, as a period of consolidation in the industry which began several years ago continued. A third industry, Construction, which has been a big contributor to Delaware's job growth in recent years, also slowed appreciably during 2006. It began the year with gangbuster growth of 8.0 percent, but ended with growth of 1.3 percent. With the housing market probably still not touching bottom, it is quite possible that Construction will also experience net job losses in 2007. Contracts for residential construction, which lead actual employment in the industry, peaked in mid-2005 and ended 2006 at their lowest level since the end of 2001

We currently expect that the number of jobs in the state will be about the same at the end of 2007 as it is now, at the beginning. There may be some slight job gain, but it is also possible that there will be a decline in the total number of jobs. At this point the forecast for 2008 is much the same.

After experiencing year-over-year gains of better than 8,000 jobs, job growth from the fourth quarter of 2005 to the fourth quarter of 2006 fell to below 2,800 jobs, with the bulk of that in the first two quarters. The chart below shows Delaware's total jobs annual change in thousands, measured as the quarterly total minus the total from same quarter in the previous year.

Annual Net Job Change, In Thousands

Leading Indicator

The Delaware index of leading economic indicators fell for the third consecutive quarter in the 4th quarter of 2006. In testing the index and employment forecast model historically, that has been the signal for potential future job losses. On average, the job losses have occurred three quarters later.

Three of the four components of the index were negative, with only the US index of leading economic indicators positive. Recently, the US index has been giving mixed signals; it has varied between rising and falling for the past two years.

The other components of the Delaware index have been negative since at least mid-year. The yield curve has been inverted for each of the last six months. This means that short-term interest rates are higher than long-term interest rates, and has long been widely viewed as a predictor of economic downturn. The four-quarter moving average of incorporations in Delaware has declined for three straight quarters. Most dramatically, the residential housing component has dropped by more than 20 percent in the last two quarters, albeit from a very high peak. Taken together, these indicators point to slowing job growth in 2007.

Details of the Model

Choosing a Coincident Indicator

When setting out to build a leading index and forecast model it is necessary to first determine just what is being forecast. Some broad measure which encompasses general economic activity would be ideal, but there is no consensus as to what constitutes economic activity. Economic activity can be described by such concepts as the value of real output (real GDP), employment levels, unemployment rates, and incomes, but quantifying it requires one of two approaches: a group of these measures can be combined mathematically into one measure known as a coincident index, or one particular economic variable may be singled out and used as a proxy for general economic activity. Under ideal conditions the index is the superior choice, but for reasons explained more fully below we use one variable, total nonagricultural employment, as the coincident measure of economic activity. In Delaware's case, we believe that incorporating other variables would introduce more noise than information.

A good index of current economic activity would contain measures of different aspects of economic activity, representing employment, incomes and output. The national coincident index maintained by the Conference Board consists of four variables: employees on nonagricultural payrolls, personal income (less transfer payments), a measure of manufacturing and trade sales, and an index of industrial production. Of these, only total nonagricultural employment is available at the state level for Delaware on a timely basis. It is essential that data are reasonably accurate and available promptly, and desirable that the data undergo minimal revision for a variable to be usefully included in an index. We are unable to find anything other than total nonagricultural employment that meets these criteria for Delaware. There are two other coincident measures of Delaware's economic activity of which we are aware: an index built and maintained by the Federal Reserve Bank of Philadelphia¹ and an index built by the Bureau of Economic Research (BER) at the University of Delaware which is no longer maintained.²

The BER coincident index combined Delaware's total nonagricultural employment with industrial electric sales in Delaware and the U.S. index of coincident indicators. While industrial electric sales may be a good proxy for industrial output, technological change may make the relationship less than tight. More troubling is the inclusion of the national coincident index, which we feel muddies more than it illuminates. Economic conditions tend to change in different ways and at different times across the nation. In trying to determine what is currently happening in Delaware and its immediate region, a measure of what is happening elsewhere in the nation is not likely to be helpful. Indeed, if conditions are substantially different in California, a state which would have a large impact on the U.S. coincident index, inclusion of this index would paint a false picture of Delaware's economic condition.

The Federal Reserve's coincident index for Delaware consists of the state's total nonagricultural employment, average hours worked in manufacturing, and lagged values of the state's unemployment rate. While theoretically sound, in Delaware (and most likely other small states as well), the inclusion of average hours worked poses a practical problem - the data contain a large amount of noise which cannot be filtered out. As employment in manufacturing steadily becomes a smaller proportion of the state's overall employment, the proportion of manufacturing firms included in the Current Employment Statistics (CES) survey declines. Smaller sample size increases sampling error. In addition, because it is more difficult for firms to calculate average hours worked than the number of people working, hours worked tends to have a larger error component. This is really nonsampling error, making it impossible to determine when significant changes in manufacturing hours worked have occurred. At the national level, these errors can be expected to largely cancel each other; this becomes less likely as the sample size is reduced.

The inclusion of lagged unemployment rates is problematic both from a practical and a theoretical standpoint. Theory indicates that the unemployment rate is itself a lagging indicator. That is, the current unemployment rate is more indicative of economic conditions in the recent past than it is of current conditions. Lagged values of the unemployment rate (the unemployment rate from the last few months) would be representative of economic conditions even further in the past. We believe that any statistical relation between past unemployment and current economic conditions is most likely due to the tendency of both series to be autocorrelated. None of the lagged values of the unemployment rate in the Federal Reserve's coincident index for Delaware had a coefficient significantly different from zero at usual levels of confidence. Only the contemporaneous unemployment rate is statistically significant. We do not include it as a measure of current economic activity for two reasons: it is more properly considered a lagging indicator, and the national Bureau of Labor Statistics has changed the methodology for computing state unemployment rates, making them even less suitable for use in a coincident index.

The current method of producing monthly unemployment rates is tied more closely to changes in payroll employment than to changes in the more volatile Current Population Survey(CPS), as was previously the case. This is done to reduce monthly movement in the unemployment rate. Early in the following year the data are benchmarked, based on the CPS. Monthly rates may change substantially. Being largely based on movements in payroll employment, changes in contemporaneous unemployment rates (unbenchmarked) provide little additional information. Because they may be revised up to a year after they are produced, they have the potential to mislead.

Using total nonagricultural employment as the sole coincident indicator has one other advantage, at least in Delaware. It produces a smoother series than the composite indexes, but still hits all of the turning points. This smoothness matters because noise introduced by other variables will make it more difficult to develop a leading index.

The Model and Index Components

The new model is a time series based short-term projection of total nonagricultural employment with a new Delaware index of leading indicators as an intervention variable. It is hoped that incorporating a leading index into the projections will help the model to avoid a major weakness of time series techniques - difficulty in forecasting major changes in direction.

Vector autoregression techniques were used in preliminary investigations and were considered for the model, but degrees of freedom problems precluded their use. Data on initial claims for unemployment insurance benefits, a variable we consider essential, are only available from 1986. The model is quarterly, with only 144 data points in total available, making parsimony a serious concern. The current model (we expect to periodically review and if necessary revise the model) forecasts the log difference of establishment employment (seasonally adjusted) based on three variables, all lagged three quarters: the percentage change in the U.S. index of leading indicators³, the log difference of permits issued for Delaware residential housing construction in real dollars, seasonally adjusted, and the level of initial claims in Delaware for unemployment insurance, seasonally adjusted and modified to reflect activity in the automobile assembly industry.

The index of leading indicators consists of the percentage change in the U.S. index of leading economic indicators, a four quarter moving average of the real value of new Delaware residential housing construction (log difference), a four quarter moving average of new incorporations in Delaware (log difference), and the change in the spread between the 10 year U.S. Treasury bond rate and the federal funds rate. Near expected turning points in economic activity, this index acts on the employment forecast model through the log difference in modified initial claims variable, as explained more fully below.

The rationale for including the U.S. index of leading indicators in a model of Delaware employment is obvious: a small state such as Delaware is clearly influenced by changes in national economic activity. Timing and magnitude may differ, but the general direction tends to be the same. Cross correlation of Delaware employment changes and the national leading index indicates the strongest relation at lags of one and three quarters. Using only the three quarter lag in the forecast model enables the projections of employment up to three quarters ahead based on actual data. This holds true for the other variables in the model as well.

Variables relating to residential construction have a long history in economic forecast models; the theory underlying their use is quite sound. Not only does increased construction generate increased current economic activity, it generates subsequent activity through purchases of furniture, landscaping, decorating, and other goods and services. These secondary activities, along with the data taking the form of permits for housing starts to begin within 60 days, justifies this variable entering the model with a three quarter lag.

The housing data are provided by the F.W. Dodge division of The McGraw-Hill Companies as building permits issued for residential construction in Delaware beginning within 60 days, in terms of dollar value of the construction. These data are adjusted for inflation using the national producer price index for capital equipment and then seasonally adjusted. Similar data are available for commercial construction, but no relationship with total employment was found.

The initial claims variable proved most troublesome. Reliable data on claims are only available in Delaware back to 1986. This covers only one complete business cycle, normally not enough to be included in a model such as this. Theory strongly indicates that it should be included, however. There is a sound basis for expecting a negative relationship between initial claims and employment levels, as was found. As one of the few available Delaware-specific variables, its value in the model exceeds its potential statistical problems. The best relationship with total employment was found to be the level of claims lagged three quarters.

An initial claims variable usually enters a forecast model in percent change or log difference form, as do most other variables. Often this is to avoid having an integrated process in the model, a potential problem here as well.⁴ For a small state like Delaware, however, the change in initial claims may not be as important as the level. This is because layoffs are discrete events. If a large employer has large layoffs, initial claims rise. This "raises the bar," making it more likely that initial claims will fall next period, not rise. In a large state there may be enough large employers to approximate a continuous process, making initial claims rise more or less uniformly in a recession. A small state with few large employers is likely to see initial claims increase discretely, with decreases in claims occurring in between large layoffs, even in recession. A small state would then see an increase in the variance of initial claims during recession and a decrease in the variance during expansion, with the log difference having a nearly equal probability of being positive or negative in any economic phase. We do observe this cyclically changing variance in Delaware's initial claims, but the time series is too brief to statistically estimate its effect with much confidence. This presents possible avenues for future research.

Another problem with initial claims in Delaware, and potentially in other small states, is the presence of several large employers who periodically layoff workers for reasons unrelated to the state of the economy. Delaware's two automobile assembly plants shut down periodically for retooling. Large layoffs at even one plant can cause the level of initial claims to increase dramatically. Although the workers idled are considered unemployed while the plant is shut down, these retoolings do not portend a general economic slowdown. We therefore modify the initial claims counts by excluding claims from the automotive assembly plants unless they are due to slow sales. The modified claims variable is also seasonally adjusted. (Unlike school year-related layoffs which can be accounted for by seasonal adjustment, the automotive assembly plant retoolings occur at varied times and for varied durations.)

The largest statistical effects on employment occur with the level of initial claims lagged three quarters and with the contemporaneous log difference in claims. The three quarter lag before maximum effect is curious; many of the claimants would normally return to work in that long a period. This is probably picking up some employment autocorrelation. Changes in employment in Delaware are positively autocorrelated at two and three quarter lags. A negative contemporaneous relation with initial claims would then show up as a negative effect for claims after a lag. Model specifications explicitly including this employment autocorrelation did not perform as well as the current model.

The contemporaneous log difference in initial claims is useful in explaining past changes in employment, but would not normally be useful for forecasting. The best guess of future changes in claims, without additional information, is that they will be zero. This really forms the basis of our model, which is actually two models: one estimated assuming the current log difference in initial claims for unemployment insurance benefits is zero (normally its expected value), and another estimated from past relations of realized claims and employment changes. Forecasts are made by substituting the expected values of the explanatory variables into the model (past the three quarter forecast window where actual data for the lagged variables are available). When the local index of leading indicators signals a possible recession, the best forecast of the change in initial claims is no longer zero. Initial claims are on average 22 percent higher when our index of leading indicators has declined two consecutive quarters and 34 percent higher after three consecutive declines. These values then replace the zero expected value of the log difference of initial claims until the index of leading indicators reverses course. This intervention yields a time series based projection model capable of reacting to changing economic conditions in a timely fashion, so long as the leading index provides adequate warning of future turning points.

Index Performance

The new Delaware index of leading indicators consists of the percent change in the U.S. index of leading indicators, a four quarter moving average of the real value of new Delaware residential housing construction (log difference), a four-quarter moving average of new incorporations in Delaware (log difference), and the change in the yield curve, as measured by the spread between the 10-year Treasury bond rate and the federal funds rate. The change in each variable is standardized by dividing the current quarter's change by its absolute average historical change. These standardized changes are then averaged to arrive at the index.

Using a decision rule that three consecutive quarterly declines in the leading index signals an economic downturn, the index predicts three of the last four recessions in Delaware with lead times of two quarters, three quarters, and five quarters. The index produced one false alarm, with three consecutive declines from the fourth quarter of 1995 through the second quarter of 1996, but this signal was quickly reversed. (Delaware's economic growth did falter a little in 1996, with payroll employment even declining in the third quarter, but the state did not experience a recession.) The one recession that the index missed, the very brief downturn in the second half of 1981, is particularly instructive.

Both the Philadelphia Federal Reserve (Fed) and the Bureau of Economic Research at the University of Delaware (BER) record that Delaware went through two recessions in rapid succession in the early 1980's. The Fed shows Delaware's economy in recession from February 1980 through April 1980, then again from July 1981 through January 1982. BER has Delaware's economy in recession from the third quarter of 1979 into the second quarter of 1980, then from the third quarter of 1981 into the first quarter of 1982. Our new leading index turns on, signaling a possible recession, in the fourth quarter of 1978, and does not turn off until the fourth quarter of 1982.⁵ The expansion between these two recessions was so short and so weak that the entire period could be looked at as one of recession. Delaware's employment in the quarters between the recessions (as measured by BER) grew at an annual rate of just 0.5 percent; including the non-recessionary quarters immediately before and after the two recessions when our index was on employment averaged just 1.17 percent annual growth. By contrast, average annual employment growth during non-recessionary quarters from 1970 through 1997 was 2.8 percent. With the major purpose of the new leading index being its use as an additional predictor of employment growth, its failure to turn off between the two recessions in the early 1980's is probably a strength. Figure 1 shows movements in the leading index and Delaware employment since the early 1970's.

Figure 1

Delaware Leading Index (right scale) and Total Non-Farm Employment (left scale). Shaded areas are Delaware Recessions as defined by the Bureau of Economic Research.

Model Diagnostics

We have conducted a number of tests of the model, both in-sample and out-of-sample. The coefficients appear to be robust across a variety of specifications.

Due to the short time period for which unemployment insurance claims data are available, opportunities for out of sample testing are limited. The model was estimated using data available through the fourth quarter of 1995, then this model was used to predict employment levels for the next eight quarters. The model appears to perform well, but in honesty this was not a period of economic turmoil in Delaware. The model did capture most of the large jump in employment in the second quarter of 1996 and its growth slowed considerably the following quarter, but it could not predict that one-quarter decline in employment. The initial employment level in the fourth quarter of 1995 was 369,458. The results of this out-of-sample test are shown in Table 1.

Table 1.

Date	Predicted Employment Level	Actual Employment Level	Percent Difference
1996:1	370,085	370,111	-0.01
1996:2	377,275	378,681	0.37
1996:3	378,997	377,142	0.49
1996:4	382,047	379,504	0.67
1997:1	384,476	383,223	0.33
1997:2	386,920	385,532	0.36
1997:3	389,380	388,993	0.10
1997:4	391,855	393,212	-0.35

In-sample testing uses coefficients estimated from the full data set, then produces forecasts as though the input values were unknown. We have simulated eight quarter forecasts for each quarter from 1989 through 1996. Each subsequent forecast updates the previous forecast and extends it by one quarter. As might be expected, the accuracy of the forecasts declines as the forecast period is extended. Through 33 simulated forecasts, the average absolute percentage error for employment level was 0.32 percent one quarter out and rose to 1.78 percent eight quarters out. It should be noted that this period includes the 1990 recession and subsequent slow and halting recovery, a period few economic models handled very well. The forecast using data available in the fourth quarter of 1989 was the first to predict declining employment levels; employment began to decline in the third quarter of 1990, the same quarter as the model predicted. Average absolute percentage errors for the in-sample test are found in Table 2, the complete test is in the Appendix.

 

Table 2

Forecast Period	Average Absolute Percentage Error
1 quarter out	0.32
2 quarters out	0.39
3 quarters out	0.46
4 quarters out	0.59
5 quarters out	0.83
6 quarters out	1.09
7 quarters out	1.43
8 quarters out	1.78

Model Specification

When the leading index trigger is turned off, the model is specified as

where:

= the log difference of establishment employment, seasonally adjusted

= the level of modified initial claims for unemployment insurance

benefits, seasonally adjusted and lagged three quarters

= the log difference of new residential housing construction

and

= the percent change in the U.S. index of leading indicators.

When the leading index trigger is turned on, the model specification becomes

where

= the log difference of modified initial claims for unemployment insurance

benefits, seasonally adjusted, and all other variables remain the same.

 

For forecasting purposes, the two models are identical when the leading index trigger is off, because the expected value of is zero for all t in the future. In estimating the model we look back, so the value of is known for all time periods. This produces different coefficient estimates for each model specification. The estimated coefficients are in Table 3 and other selected statistics are presented in Table 4 below.

Table 3.

Trigger Off Model	Estimate	0.0138	n.a.	-2.17E-6	0.022502	0.02003
	t-Statistic	5.46	n.a.	-3.75	4.25	4.63
Trigger On Model	Estimate	0.015055	-0.009731	-2.46E-6	0.019523	0.018634
	t-Statistic	6.39	-2.96	-4.55	>3.94	4.66

Table 4.

		Adj.	F-statistic	DW	S.E.E.
Trigger Off Model	0.57	0.54	18.43	2.22	0.004855
Trigger On Model	0.65	0.62	18.64	2.17	0.004452

 

We plan to reestimate the model coefficients at the end of each year, and to continually evaluate and, hopefully, improve the model as new information becomes available.

Footnotes

¹ Theodore M. Crone, "New Indexes Track the State of the States," Business Review, Federal Reserve Bank of Philadelphia, January/February 1994, pp. 19-31.

² "Delaware Economic Report 1993-94," Bureau of Economic Research, University of Delaware.

³ While a national indicator may not be suitable as a component of the state's coincident index, it is valid as a predictor of future economic activity.

⁴ The hypothesis of a unit root cannot be rejected at even the 10 percent level of significance using Augmented Dickey-Fuller or Phillips-Perron tests. However, the best representation of the level of claims is an AR(2) model, where the sum of the two autoregressive coefficients is 0.77, with the error term exhibiting no serial autocorrelation through eight lags. We feel the inability to rule out nonstationarity is probably due to the brevity of the series, and cautiously include it as an independent variable.

⁵ The index turning off is taken to mean two consecutive quarters of increases in the index. The index increased for one quarter three different times during this period.

Last Updated: Thursday July 05 2007