By now it is well established that the existence of unemployment

insurance (UI) affects decisions on both the supply and demand sides of

the labor market. Theoretical work on such effects has appeared within

the past decade, and empirical tests of the basic theoretical

propositions have appeared more recently. On the supply side, the

tendency of the availability of UI benefits to extend the duration of

nominally involuntary unemployment and perhaps to increase labor force

participation and improve the success of job search as evidenced by wage

gains of job changers has been examined and supported by recent

research.

A link between the existence of UI and labor demand has been

demonstrated by examination of the system of experience rating–or

incomplete experience rating–used to finance benefits in most States.

In the United States, States finance UI benefits through a payroll tax on covered employers. In the context of such a financing system,

experience rating is the use of payroll tax rates that change inversely with the stability of an employer’s labor demand, where that

stability is indicated by a measure such as a “reserve

ratio”–the employer’s accumulated contributions to the system

less his accumulated liability in the form of paid-out benefits, with

the difference expressed as percentage of his average taxable payroll

over some period. Incomplete experience rating limits the allowable tax

rates to a relatively narrow range; for example, no State tax rate

currently exceeds 10 percent of taxable payroll, and most States have a

nonzero minimum rate.

The intuitive argument about the effect of incomplete experience

rating on labor demand, or more particularly layoff rates, begins with

the realization that many employers assigned either the minimum or the

maximum UI payroll tax rate have a zero marginal tax cost of an extra

layoff. Those assigned the minimum rate will be contributing to the

system regardless of their benefit liability. To the extent that they

accumulate reserves beyond those required to maintain their minimum rate

assignment, they may have an incentive to draw down the excess through

extra layoffs, or “UI holidays.” Employers already at the

maximum rate cannot be further penalized for additional layoffs; thus,

they may also have an incentive to provide UI holidays as part of their

contract (implicit or explict) with their workers. Any resulting

benefit liability that exceeds their own contributions is paid from the

net contributions of other employers (cross-subsidization).

While this connection has been well established theoretically,

empirical support has been scarce because of a lack of data. However,

the three studies that have been published support the existence of such

a relationship. Indeed, the most recent of these finds that the

increase in temporary layoff unemployment resulting from the implicit

cross-subsidization that incomplete experience rating allows is not only

larger but also statistically more significant than the “supply

side” unemployment effect of the level of the benefits. The author

of that study concludes that, “without chaning benefit levels

available to unemployed workers, a significant reduction in layoff

unemployment could be achieved by changing the incentives offered by

current UI [financing] laws.” Moreover, he finds that “the

impact of the unemployment insurance subsidy on layoff unemployment is

powerful–the imputed subsidy accounts for more than a quarter of all

layoffs in the data. . . .” Unfortunately, none of the recent

studies considers the incentive that employers assigned the minimum rate

have to increase their layoffs, although there is some unpublished

evidence suggesting that this effect is small or nonexistent.

The growing body of evidence that incomplete experience rating does

increase the amount of layoff unemployment leads one to ask what

proportion of employers are subject to the layoff incentives of such

cross-subsidization, and, perhaps more importantly, how long particular

employers remain at tax rates that allow them to be implicitly

subsidized? These issues are important, for persistent subsidization of

some employers indicates that the employment stabilization incentives

built into the UI system are not working, and it may lead to distortions

in the industrial and occupational structure of a State’s economy.

To address these questions, I analyzed fiscal 1975-78 UI data for a

random sample of more than 17,000 New Jersey employers. The results,

presented below, show that, at any time, large proportions of employers

are assigned the minimum and maximum tax rates. More importantly, most

of these employers have a low probability of moving to any other rate

category over time. Indeed, most of them can be assumed to be assigned

a limiting rate permanently, thus precluding their effective experience

rating. Distribution of employers by rates

Table 1 shows the distribution of employers in the sample by tax

rate category for each of the study years. “Graded” employers

are firms for which the State had sufficient payroll and turnover

information to assign a UI tax rate. The group consists of employers at

the minimum rate (1.2 percent of taxable payroll); those at the maximum

rate (6.2 percent); and those taxed at one of a range of ra tes in

between the two limits. “Other” employers are those to which

a rate could not be assigned in the usual manner, either because of

inadequate data or their lack of experience in the system.

“Inactive accounts” are employers that were not in business

during a given year.

Mid-rate employers, the third category of graded units, are the

only ones that might be considered truly experience rated, in that their

tax rate assignments can respond in either direction to changes in their

turnover behavior; all other employers are at least temporarily immune

to changes in their payroll tax rate. Given this characterization of

the system, the imposition of employment stabilization incentives

through experience rating is remarkably incomplete. In each study year,

fewer than 41 percent of the active accounts fell into the mid-rate

category; moreover, table 1 indicates that only about half of the graded

employers could be considered effectively experience-rated.

Because the tax rate reflects an employer’s recent history of

labor turnover, patterns of experience rating should lag the business

cycle by 1 to 2 years. Between 1973 and 1976, business conditions were

increasingly recessionary, and thus experience ratings should be rising

over the years covered in this study. This is, in fact, the story told

by table 1. The proportion of graded employers at the maximum tax rate

increased steadily from 8.5 percent in fiscal 1975 to 16.5 percent in

fiscal 1978, while the proportion at the minimum rate decreased steadily

from 38.0 percent to 32.4 percent. However, there is a surprising

regularity in these data for consecutive years, for, while there was a

clear shift of proportions from the minimum to the maximum rate as the

unemployment rate rose, the proportion of graded employers assigned the

middle rates remained at about half throughout the period, regardless of

business conditions.

In addition to this consideration of the likelihood of finding an

employer on the responsive portion of the tax schedule at a point in

time, it is necessary to examine the amount of time employers remain in

experience rating categories. An effective experience rating system

should induce employers to minimize their labor turnover, and employers

paying the maximum tax rate should have a special incentive to avoid

such a tax. However, the recent theoretical work on the effects of

incomplete experience rating suggests that this is a naive prediction.

In particular, theory suggests that employers have very little incentive

to avoid the maximum tax rate.

An approach to determining the effectiveness of an experience

rating system is to observe the movement of employers among the

assignable tax rates. One method of determining this involves the use

of Markov analysis.

We know that the movements of employers among tax rates can be

described by a transition matrix–in the current context, a 5-by-5

matrix composed of the three graded categories plus “other”

and “inactive accounts.” Any cell of the matrix indicates the

proportion of employers assigned the particular tax category given along

the vertical axis who move into a tax category given along the

horizontal axis in a particular year. The proportion in each cell is

thus a transition probability. Moreover, the transition probabilities

found along the diagonal of the matrix represent the proportion of

employers who remain in a particular category from one year to the next.

A “simple” Markov model would assume that the movement of

employers among the tax rates can be fully described by a single matrix

of transition probilities which applies to all employers–in this case,

that all employers in a rate assignment category have the same

probability of making a given transition to another category between

periods. A employers in a given category can be either movers, whose

rate assignments follow a regular transition matrix, or stayers, who

remain in their category permanently, that is, with a probability of 1.

In that case, there are two applicable transition matrixes: a

conventional one for movers; and another for stayers, having 1 in the

cells along its diagonal and zeros elsewhere.

The importance of determining which of these two processes better

describes the movement of employers should be clear. That is, is it

reasonable to assume that some employers are permanently either immune

to or subject to the employment stabilization incentives of the

experience rating system by staying in particular categories of ratings,

or is it more accurate to assume that all employers are movers?

Evidence that there are stayers in the nonresponsive minimum- and

maximum-rate categories and that they represent a large proportion of

employers would affect an assessment of the system’s degree of

experience rating: larger proportions of stayers in nonresponsive

categories are evidence of less effective experience rating.

To decide which of the two models is more appropriate for the New

Jersey data, I tested the statistical significance of the difference

between the proportion of employers who actually remained in a category

for the 4-year period and the proportion who would remain in that

category if only a simple Markov process of average transition

probabilities were operating.

Let d.sub.i represent the difference between the fraction of

employers in category i in the the initial period who remain in that

category through the terminal year of the data (f.sub.i.) and the

expected value of the fraction under the null hypothesis. Thus, d.sub.i

= f.sub.i -P.sup.-n.sub.ii where n = the number of transitions in the

data (in this case, n = 3); and

= the average probability of staying in a category for one period

under the assumption of a Markov process; with w.sub.ii.(t) = the number

of employers in category i in period t who are also in category i in

period t + 1; and w.sub.i.(t) = the number of employers in category i in

period t.

The square of d.sub.i divided by its variance (s.sup.2.sub.di.).sup.11 is distributed x.sup.2 with one degree of

freedom. The sum of the ratios for the five categories is distributed

X.sup.2 with five degrees of freedom. It is used to test the null

hypothesis that there is no significant difference between the number of

employers remaining in a category over the 4 years and the number that

would remain according to the simple Markov process. If the null

hypothesis is rejected, the mover-stayer model is more appropriate.

Following are the ratios of d.sup.2.sub.i to its variance for each

assignment category, as well as the summary test statistic for the null

hypothesis: Category Ratio value Minimum-rate 100.478 Mid-rate 40.968

Maximum-rate 75.524 “Other” 613.389 “Inactive

accounts” 3.824 Total 834.183

The value for “total” leads one to reject the null

hypothesis of a simple Markov process at the .005 level of significance.

Moreover, the relative values of the category ratios are interesting.

Given that a higher ratio implies a more significant deviation of a

category’s actual stayers from the expected proportion, one should

note that the ratios for minimum- and maximum-rated units are much

higher than that for mid-rated employers. This suggests that there is a

much stronger tendency for the former employers to stay in their

categories relative to the Markov process than is found among mid-rated

employers. This tendency in these categories which do not impose

employment stabilization incentives on employers weakens the effects of

experience rating, as does the stronger tendency for mid-rated employers

to move out of the responsive part of the tax schedule, as evidenced by

their relatively low ratio.

Because the mover-stayer model is more appropriate, I estimated (1)

the proportions of stayers (s.sub.1.) in each category and (2) the

transition probabilities (m.sub.ij.) of a Markov matrix for movers only.

Leo Goodman suggests using the following approximations to maximum

likelihood estimators of these parameters when the sample size is large

and there are a number of periods of data: s.sub.i = the proportion of

employers in experience rating class i in the initial period who remain

in that class for the next n periods (n = 3 here); and m.sup.-.sub.ij =

the average number of employers in experience rating category i in one

period who are in category i in the following period divided by the

average number of employers in category i over all periods but the last,

for all i and j (both averages calculated after deleting the estimated

number of stayer employers from category i).

Estimates of s.sub.i shown below indicate that large proportions of

employers stay in their category over time: Assignment category Percent

stayers Graded employers at: Minimum rate 55.9 Mid rates 57.1 Maximum

rate 66.1 “Other” employers 30.0 “Inactive accounts”

0.0

Among the graded employers, the proportion of stayers is always

more than one-half. The important result here is that the proportions

of stayers in the minimum- and maximum-rate categories are so high: in

particular, almost two-thirds of the maximum-rated employers remain in

their category throughout the period. While the virtually permanent

assignment of the maximum rate to such a large proportion of employers

could be at least partly attributable to factors such as the naturally

higher turnover rates of some industries (for example, construction)

relative to others (such as banking), it is also consistent with the

conclusion that incomplete experience rating actually induces higher

layoff rates.

Estimation of the transition matrix for movers (m.sup.-.sub.ij.)

indicates that, with the exception of the “inactive accounts”

category, movers are more likely to stay in their current category than

to move between periods. (See table 2.) Moreover, among the graded

employers, the highest such “retention” rate is for the

maximum-rate category, where almost two-thirds of the movers remained in

the category from period to period. Thus, even for employers designated

as movers, transition between categories seems slow, especially among

the nonresponsive maximum-rate group. Interpreting the results

The significance of these results is probably best understood in

light of some related findings regarding the extent of

cross-subsidization in the New Jersey UI system. Available data allow

one to estimate the average surplus or deficit per employee-year

experienced by each covered employer since its UI account was opened. A

surplus position indicates that, on average over the life of the

business, an employer has contributed more to the system than his

laid-off employees have drawn in benefits; a deficit position indicates

that the employer, through laid-off employees, has been receiving a net

subsidy from the system. The calculations for the sample of employers

studied here show that, as of the end of 1975 and 1976, those assigned

the maximum tax rate had net deficit positions per employee-year of $844

and $728, respectively, or about 9 percent of the State’s 1975

annual gross wage for a production worker in manufacturing. Taken with

the finding that about two-thirds of the employers at this tax rate can

be assumed to be “stayers,” this suggests that the majority of

employers at the maximum rate have been receiving an annual payroll

subsidy of about 9 percent of their gross wages. While these

calculations are admittedly crude, they do hint at the magnitude of the

cross-sudsidization that incomplete experience rating can allow.

These results also help one understand the explanatory power of the

minimum and maximum tax rates in layoff equations. Studies by Joseph

Becker and Frank Brechling indicate that narrower bounds on assignable

tax rates result in a larger proportion of employers being assigned the

limiting tax rates. The preceding discussion indicates that, for a

given rate schedule, most employers assigned to a limiting tax rate tend

to stay there even as business conditions change, and those that move

away from such categories do so only very slowly. Thus, a State’s

maximum and minimum rates represent not only the potential range of

responsiveness of its experience rating system but also the potential

for actual avoidance of the employment stabilization incentives by a

large proportion of employers. Evidence such as Robert Topel’s

suggests that employers at these limiting rates–especially at the

maximum rate–do indeed generate extraordinary turnover rates through

their layoffs.

However, the New Jersey results must also be considered in light of

the number of employees affected. Because employers at the maximum or

minimum rates account for about 20 percent of employment in the sample,

the proportion of workers affected by incomplete experience rating is

smaller than the proportion of employers–a situation that somewhat

mitigates the unemployment effects of the lack of experience rating at

the limiting rates. Also, one must keep in mind that different

macroeconomic conditions (such as falling unemployment rates) could

yield different parameter estimates. For example, conditions of full

employment could result in a smaller estimate of the proportion of

stayers in the maximum-rate category, although the number of

minimum-rate stayers would probably rise.

EVEN SO, THE IMPRESSION left by this discussion of tax rate

assignments is that the system analyzed here, which is not atypical,

seems to lack strong incentives for employment stabilization,

particularly for employers at the maximum rate. Employers tend to sort

themselves into tax categories Thus, most employers are either always or

never facing the employment stabilization incentives of the UI

experience rating system. For employers at the maximum rate, this

results in large negative reserves that require subsidization by other

employers in the given State’s system.