By now it is well established that the existence of unemploymentinsurance (UI) affects decisions on both the supply and demand sides ofthe labor market.

Theoretical work on such effects has appeared withinthe past decade, and empirical tests of the basic theoreticalpropositions have appeared more recently. On the supply side, thetendency of the availability of UI benefits to extend the duration ofnominally involuntary unemployment and perhaps to increase labor forceparticipation and improve the success of job search as evidenced by wagegains of job changers has been examined and supported by recentresearch. A link between the existence of UI and labor demand has beendemonstrated by examination of the system of experience rating–orincomplete 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 thatstability is indicated by a measure such as a “reserveratio”–the employer’s accumulated contributions to the systemless his accumulated liability in the form of paid-out benefits, withthe difference expressed as percentage of his average taxable payrollover some period. Incomplete experience rating limits the allowable taxrates to a relatively narrow range; for example, no State tax ratecurrently exceeds 10 percent of taxable payroll, and most States have anonzero minimum rate. The intuitive argument about the effect of incomplete experiencerating on labor demand, or more particularly layoff rates, begins withthe realization that many employers assigned either the minimum or themaximum UI payroll tax rate have a zero marginal tax cost of an extralayoff. Those assigned the minimum rate will be contributing to thesystem regardless of their benefit liability.

To the extent that theyaccumulate reserves beyond those required to maintain their minimum rateassignment, they may have an incentive to draw down the excess throughextra layoffs, or “UI holidays.” Employers already at themaximum rate cannot be further penalized for additional layoffs; thus,they may also have an incentive to provide UI holidays as part of theircontract (implicit or explict) with their workers. Any resultingbenefit liability that exceeds their own contributions is paid from thenet 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 sucha relationship. Indeed, the most recent of these finds that theincrease in temporary layoff unemployment resulting from the implicitcross-subsidization that incomplete experience rating allows is not onlylarger but also statistically more significant than the “supplyside” unemployment effect of the level of the benefits. The authorof that study concludes that, “without chaning benefit levelsavailable to unemployed workers, a significant reduction in layoffunemployment could be achieved by changing the incentives offered bycurrent UI [financing] laws.” Moreover, he finds that “theimpact of the unemployment insurance subsidy on layoff unemployment ispowerful–the imputed subsidy accounts for more than a quarter of alllayoffs in the data. .

. .” Unfortunately, none of the recentstudies considers the incentive that employers assigned the minimum ratehave to increase their layoffs, although there is some unpublishedevidence suggesting that this effect is small or nonexistent. The growing body of evidence that incomplete experience rating doesincrease the amount of layoff unemployment leads one to ask whatproportion of employers are subject to the layoff incentives of suchcross-subsidization, and, perhaps more importantly, how long particularemployers remain at tax rates that allow them to be implicitlysubsidized? These issues are important, for persistent subsidization ofsome employers indicates that the employment stabilization incentivesbuilt into the UI system are not working, and it may lead to distortionsin the industrial and occupational structure of a State’s economy. To address these questions, I analyzed fiscal 1975-78 UI data for arandom sample of more than 17,000 New Jersey employers.

The results,presented below, show that, at any time, large proportions of employersare assigned the minimum and maximum tax rates. More importantly, mostof these employers have a low probability of moving to any other ratecategory over time. Indeed, most of them can be assumed to be assigneda limiting rate permanently, thus precluding their effective experiencerating. Distribution of employers by rates Table 1 shows the distribution of employers in the sample by taxrate category for each of the study years. “Graded” employersare firms for which the State had sufficient payroll and turnoverinformation to assign a UI tax rate. The group consists of employers atthe minimum rate (1.2 percent of taxable payroll); those at the maximumrate (6.

2 percent); and those taxed at one of a range of ra tes inbetween the two limits. “Other” employers are those to whicha rate could not be assigned in the usual manner, either because ofinadequate data or their lack of experience in the system.”Inactive accounts” are employers that were not in businessduring a given year. Mid-rate employers, the third category of graded units, are theonly ones that might be considered truly experience rated, in that theirtax rate assignments can respond in either direction to changes in theirturnover behavior; all other employers are at least temporarily immuneto changes in their payroll tax rate. Given this characterization ofthe system, the imposition of employment stabilization incentivesthrough experience rating is remarkably incomplete. In each study year,fewer than 41 percent of the active accounts fell into the mid-ratecategory; moreover, table 1 indicates that only about half of the gradedemployers could be considered effectively experience-rated. Because the tax rate reflects an employer’s recent history oflabor turnover, patterns of experience rating should lag the businesscycle by 1 to 2 years.

Between 1973 and 1976, business conditions wereincreasingly recessionary, and thus experience ratings should be risingover the years covered in this study. This is, in fact, the story toldby table 1. The proportion of graded employers at the maximum tax rateincreased steadily from 8.5 percent in fiscal 1975 to 16.5 percent infiscal 1978, while the proportion at the minimum rate decreased steadilyfrom 38.0 percent to 32.

4 percent. However, there is a surprisingregularity in these data for consecutive years, for, while there was aclear shift of proportions from the minimum to the maximum rate as theunemployment rate rose, the proportion of graded employers assigned themiddle rates remained at about half throughout the period, regardless ofbusiness conditions. In addition to this consideration of the likelihood of finding anemployer on the responsive portion of the tax schedule at a point intime, it is necessary to examine the amount of time employers remain inexperience rating categories. An effective experience rating systemshould induce employers to minimize their labor turnover, and employerspaying the maximum tax rate should have a special incentive to avoidsuch a tax. However, the recent theoretical work on the effects ofincomplete experience rating suggests that this is a naive prediction.

In particular, theory suggests that employers have very little incentiveto avoid the maximum tax rate. An approach to determining the effectiveness of an experiencerating system is to observe the movement of employers among theassignable tax rates. One method of determining this involves the useof Markov analysis. We know that the movements of employers among tax rates can bedescribed by a transition matrix–in the current context, a 5-by-5matrix composed of the three graded categories plus “other”and “inactive accounts.” Any cell of the matrix indicates theproportion of employers assigned the particular tax category given alongthe vertical axis who move into a tax category given along thehorizontal axis in a particular year.

The proportion in each cell isthus a transition probability. Moreover, the transition probabilitiesfound along the diagonal of the matrix represent the proportion ofemployers who remain in a particular category from one year to the next. A “simple” Markov model would assume that the movement ofemployers among the tax rates can be fully described by a single matrixof transition probilities which applies to all employers–in this case,that all employers in a rate assignment category have the sameprobability of making a given transition to another category betweenperiods. A employers in a given category can be either movers, whoserate assignments follow a regular transition matrix, or stayers, whoremain in their category permanently, that is, with a probability of 1.In that case, there are two applicable transition matrixes: aconventional one for movers; and another for stayers, having 1 in thecells along its diagonal and zeros elsewhere. The importance of determining which of these two processes betterdescribes the movement of employers should be clear.

That is, is itreasonable to assume that some employers are permanently either immuneto or subject to the employment stabilization incentives of theexperience 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- andmaximum-rate categories and that they represent a large proportion ofemployers would affect an assessment of the system’s degree ofexperience rating: larger proportions of stayers in nonresponsivecategories are evidence of less effective experience rating. To decide which of the two models is more appropriate for the NewJersey data, I tested the statistical significance of the differencebetween the proportion of employers who actually remained in a categoryfor the 4-year period and the proportion who would remain in thatcategory if only a simple Markov process of average transitionprobabilities were operating. Let d.sub.

i represent the difference between the fraction ofemployers in category i in the the initial period who remain in thatcategory through the terminal year of the data (f.sub.i.) and theexpected 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 thedata (in this case, n = 3); and = the average probability of staying in a category for one periodunder the assumption of a Markov process; with w.sub.ii.(t) = the numberof employers in category i in period t who are also in category i inperiod t + 1; and w.

sub.i.(t) = the number of employers in category i inperiod 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 offreedom.

The sum of the ratios for the five categories is distributedX.sup.2 with five degrees of freedom. It is used to test the nullhypothesis that there is no significant difference between the number ofemployers remaining in a category over the 4 years and the number thatwould remain according to the simple Markov process. If the nullhypothesis is rejected, the mover-stayer model is more appropriate. Following are the ratios of d.sup.

2.sub.i to its variance for eachassignment category, as well as the summary test statistic for the nullhypothesis: Category Ratio value Minimum-rate 100.478 Mid-rate 40.968Maximum-rate 75.524 “Other” 613.389 “Inactiveaccounts” 3.

824 Total 834.183 The value for “total” leads one to reject the nullhypothesis 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 acategory’s actual stayers from the expected proportion, one shouldnote that the ratios for minimum- and maximum-rated units are muchhigher than that for mid-rated employers. This suggests that there is amuch stronger tendency for the former employers to stay in theircategories relative to the Markov process than is found among mid-ratedemployers. This tendency in these categories which do not imposeemployment stabilization incentives on employers weakens the effects ofexperience rating, as does the stronger tendency for mid-rated employersto move out of the responsive part of the tax schedule, as evidenced bytheir 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) thetransition probabilities (m.sub.ij.) of a Markov matrix for movers only.Leo Goodman suggests using the following approximations to maximumlikelihood estimators of these parameters when the sample size is largeand there are a number of periods of data: s.sub.

i = the proportion ofemployers in experience rating class i in the initial period who remainin 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 oneperiod who are in category i in the following period divided by theaverage number of employers in category i over all periods but the last,for all i and j (both averages calculated after deleting the estimatednumber of stayer employers from category i).

Estimates of s.sub.i shown below indicate that large proportions ofemployers stay in their category over time: Assignment category Percentstayers Graded employers at: Minimum rate 55.9 Mid rates 57.1 Maximumrate 66.1 “Other” employers 30.0 “Inactive accounts”0.0 Among the graded employers, the proportion of stayers is alwaysmore than one-half.

The important result here is that the proportionsof stayers in the minimum- and maximum-rate categories are so high: inparticular, almost two-thirds of the maximum-rated employers remain intheir category throughout the period. While the virtually permanentassignment of the maximum rate to such a large proportion of employerscould be at least partly attributable to factors such as the naturallyhigher turnover rates of some industries (for example, construction)relative to others (such as banking), it is also consistent with theconclusion that incomplete experience rating actually induces higherlayoff 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 thanto move between periods. (See table 2.) Moreover, among the gradedemployers, the highest such “retention” rate is for themaximum-rate category, where almost two-thirds of the movers remained inthe category from period to period. Thus, even for employers designatedas movers, transition between categories seems slow, especially amongthe nonresponsive maximum-rate group.

Interpreting the results The significance of these results is probably best understood inlight of some related findings regarding the extent ofcross-subsidization in the New Jersey UI system. Available data allowone to estimate the average surplus or deficit per employee-yearexperienced by each covered employer since its UI account was opened. Asurplus position indicates that, on average over the life of thebusiness, an employer has contributed more to the system than hislaid-off employees have drawn in benefits; a deficit position indicatesthat the employer, through laid-off employees, has been receiving a netsubsidy from the system.

The calculations for the sample of employersstudied here show that, as of the end of 1975 and 1976, those assignedthe maximum tax rate had net deficit positions per employee-year of $844and $728, respectively, or about 9 percent of the State’s 1975annual gross wage for a production worker in manufacturing. Taken withthe finding that about two-thirds of the employers at this tax rate canbe assumed to be “stayers,” this suggests that the majority ofemployers at the maximum rate have been receiving an annual payrollsubsidy of about 9 percent of their gross wages. While thesecalculations are admittedly crude, they do hint at the magnitude of thecross-sudsidization that incomplete experience rating can allow. These results also help one understand the explanatory power of theminimum and maximum tax rates in layoff equations. Studies by JosephBecker and Frank Brechling indicate that narrower bounds on assignabletax rates result in a larger proportion of employers being assigned thelimiting tax rates. The preceding discussion indicates that, for agiven rate schedule, most employers assigned to a limiting tax rate tendto stay there even as business conditions change, and those that moveaway from such categories do so only very slowly. Thus, a State’smaximum and minimum rates represent not only the potential range ofresponsiveness of its experience rating system but also the potentialfor actual avoidance of the employment stabilization incentives by alarge proportion of employers. Evidence such as Robert Topel’ssuggests that employers at these limiting rates–especially at themaximum rate–do indeed generate extraordinary turnover rates throughtheir layoffs.

However, the New Jersey results must also be considered in light ofthe number of employees affected. Because employers at the maximum orminimum rates account for about 20 percent of employment in the sample,the proportion of workers affected by incomplete experience rating issmaller than the proportion of employers–a situation that somewhatmitigates the unemployment effects of the lack of experience rating atthe limiting rates. Also, one must keep in mind that differentmacroeconomic conditions (such as falling unemployment rates) couldyield different parameter estimates.

For example, conditions of fullemployment could result in a smaller estimate of the proportion ofstayers in the maximum-rate category, although the number ofminimum-rate stayers would probably rise. EVEN SO, THE IMPRESSION left by this discussion of tax rateassignments 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 sortthemselves into tax categories Thus, most employers are either always ornever facing the employment stabilization incentives of the UIexperience rating system.

For employers at the maximum rate, thisresults in large negative reserves that require subsidization by otheremployers in the given State’s system.