Incomplete experience rating in state unemployment insurance Essay

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

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”

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.

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