The revealed cost of unemployment

Traditionally, the costs of unemployment have been thought of in terms of the output or national income directly foregone. The most notable of these approaches is Okun's Law, which states that a one-percentage point increase in the unemployment rate translates roughly into a threepercent shortfall

in output. Approaches such as this are incomplete for normative analysis because they do not provide a measure of the utility losses attributed to cyclical unemployment. Our proposed method for measuring these losses is based on the notion that the unemployment rate is a measure of general labor market risk. Because fluctuations in the unemployment rate reflect changes in risk, the cost of cyclical unemployment can be measured by the amount that people are willing to pay to avoid it.

Rosen (1979) and Roback (1982) view general labor market conditions, as represented by the unemployment rate, as a region-specific amenity that is taken into consideration when agents make migration decisions. The standard of living is the utility level that the average agent attains from the income and amenities of a region. If migration is frictionless: Utility-maximizing agents are optimally located at every point in time, the standard of living is uniform across regions, and interregional income differentials indicate the compensating differentials paid for differences in unemployment and other amenities (the "voting with your feet" criterion of Tiebout, 1956). Therefore, the compensating differential for a region's unemployment rate can be obtained by controlling for the differences in the other amenities.l

Following Tiebout, a large body of work has been produced in the regional economics and regional science literature dealing with compensating differentials, wages, and migration (see Porell, 1982, for a partial survey). At the same time, following Harris and Todaro (1970) and Hall (1970), macro-labor economists have produced many papers examining the relationships between migration, wages, and unemployment rates (see Ghatak, Levine, and Wheatley Price, 1996, for a survey). The most recent significant addition to this latter literature is Blanchflower and Oswald ( 1994), who have called into question a basic result of Harris-Todaro type models, which is that high unemployment rates are compensated for with higher wages.

The most glaring difference between the two approaches is that the macro-labor literature generally ignores the fact that potential migrants consider things other than wages and unemployment. Because of this, the literature searches for a link between those two variables as a means of proving or disproving that compensating differentials exist. It is recognized in the regional literature, however, that such a link, although interesting, proves little because wages and unemployment rates both can be compensated for with high levels of amenities. More importantly, given the ongoing debate among regional economists about the appropriateness of the assumption of standardof-living equivalence, which is common to both literatures, the empirical results of both should be viewed with some trepidation.2

Our approach follows Rosen (1979) and Roback (1982) in considering the unemployment rate as a region-specific amenity. It is a departure from their models in that we recognize the possibility that, in the short run, frictions may prevent the optimal allocation of agents across regions. Because of these frictions, differences in unemployment rates and other amenities are not likely to be completely compensated for, meaning that standard-of-living equivalence does not occur at each point in time. To account for this, we follow Greenwood, Hunt, Rickman, and Treyz (1991) in using migration rates to measure the extent to which the system deviates from standard-of-living equivalence.

In our model, the probability of a consumer migrating between his present region and any other region depends on moving costs and the standard-ofliving differential he perceives. When he does migrate, it is to the region that would give him the greatest standard-of-living improvement. Because of moving costs, the standard of living differs across regions in the short run, and high levels of unemployment will not be compensated for with higher levels of income. The net cross-migration rate between any two regions indicates the degree to which the standard of living differs between them, and can be used to estimate the income level that would make the standard of living the same across regions.

Using the above-described model, and data for interprovincial migration in Canada for 1971-90, we estimate the relationship between net crossmigration rates (representing differences in standard of living and differences in per-capita incomes, unemployment rates, and other amenities. See Ledent (1990), Day (1992), and Milne (1993) for discussions of migration in Canada. We then use this estimated relationship to calculate for each region the relative income that would have equated the actual standard of living and the standard of living without cyclical unemployment. This compensating differential is what we call the cost of cyclical unemployment.

In our model, preferences towards the tradeoff between unemployment and income are thus revealed by the actual utility-maximizing migration decisions of consumers.

In principle, any level of unemployment imposes a risk cost, regardless of whether the unemployment is cyclical or not. Because of this, our model need not be restricted to estimating the costs of cyclical unemployment, but also can be used to calculate the cost of having a level of unemployment above any benchmark rate. As we demonstrate, this can be done by comparing the actual standard of living with the standard of living that would have occurred had unemployment been at the benchmark rate.

The question we are addressing is similar to that of Lucas (1987), Imrohoroglu (1989), Clark, Leslie, and Symons (1994), and Dolmas (1998), who wish to measure the costs of the business cycle in terms of what people are willing to pay to avoid businesscycle fluctuations. They use calibrated models of a risk-averse representative agent to calculate the costs of macroeconomic fluctuations around trend growth paths. Welfare costs arise in these models because the agent gets disutility from fluctuations in his consumption. While our question is similar to this, it is not compatible with theirs because their notion of the business cycle, as fluctuations around a trend, is different from our more traditional notion based on cyclical unemployment. Additionally, in our model, individual uncertainty about employment prospects exists even in the absence of aggregate uncertainty.

In this paper, Section I presents the model and Section II describes the data, estimation methods, and regression results. We calculate the revealed costs of cyclical unemployment and the levels of unemployment in Section III, and in Section IV we present our conclusions.

THE MODEL IMAGE FORMULA 8IMAGE FORMULA 9IMAGE FORMULA 10

EMPIRICAL RESULTS

Data and Estimation

The best country to apply our model to is Canada. Not only are the migration and other data of very high quality, but, more importantly for our present purposes, reliable estimates of provincial noncyclical rates of unemployment are readily available. Crossmigration data are from the Total Migration Series from Statistics Canada 1971-90, as calculated from census figures and Family Allowance accounts. The migration data go back to 1950, but as reported by Statistics Canada, they are much more reliable after 1970. Real per-capita provincial income is calculated using provincial price indices.

In implementing equation 5, we allow amenity values to change every five years. It is possible to allow amenities to vary more frequently, but doing so would increase the variability of the estimates. Let Z denote the number of periods over which the amenities are fixed, and P the number of provinces. There is one observation per-year per unique pair of provinces, for a total of ZP(P-1)12 = 900 observations, each containing the log of real relative income ln(YjlYi), the log of relative unemployment ln(UilUj), and a set of discrete variables that identify the provinces. The discrete variables are necessary to estimate relative amenities, and consist of one discrete variable for each province for each five-year period. Within its corresponding five-year period, each discrete variable has the value of I if the province is province i, - I if the province is provincej, and zero otherwise. We avoid singularity by imposing the restriction that the ;Ls sum to zero for each five-year period, meaning that the amenity estimates are relative to zero.

The regression results are summarized by Table 1. The coefficients on real income and unemployment are positive and statistically different from zero. Note that Y> (i.e., the standard of living is more responsive to a change in relative income than to a change in relative unemployment.

Although our primary focus here is to calculate the relative values of other amenities the costs of unemployment, our model can be used to calculate the relative values of other amenities across provinces. Refer to fable 1 and note that , > 0 indicates that the utility value of amenities (exclusive of the unemployment rate) was higher than the

IMAGE TABLE 13

Table 1

national average, and vice versa. The provinces are listed in order of the value of their amenities. See Douglas and Wall (2000) for the use of these results to rank the provinces by total standard of living.

THE REVEALED COST

OF UNEMPLOYMENT

Cyclical Unemployment

In this section, we calculate the amount of income that people would be willing to give up in return for having no cyclical unemployment. Define the noncyclical standard-of-living in provincej as the standard of living that would prevail if the unemployment rate is at the noncyclical rate Uj" and if per-capita income were Yj. The noncyclical standard of living is then IMAGE FORMULA 16

If a province's actual unemployment rate is greater than the noncyclical rate, then RY` is less than one. The rate at which Y' is less than actual income is the amount of income that people would be willing to give up to have no cyclical unemployment, which is what we call the cost of cyclical unemployment. Thus, the cost of cyclical unemployment is Lit ---1-RY t for province j in year t. Aggregation of these costs across provinces and over time is straightforward, and is described in the appendix. The next step is to find appropriate measures of U'. to substitute into equation 7. We use two possible measures to give us the lower and upper bounds of the costs of cyclical unemployment.

Lower limit of the costs of cyclical unemployment. In this subsection we calculate the costs of cyclical unemployment using estimates of provincial noncyclical unemployment rates for each year from 1971-86, taken from Burns ( 1991 ) and reported in Table 2. As described by Burns> his estimates of the noncyclical rates are based on what would be expected in the steady state. The Canadian unemployment experience over this period is summarized by Figure 1. The estimated national steady-state unemployment

IMAGE TABLE 19

Table 2

in Canada ranged between 6 and 7 percent during the 1970s, and rose to around 8 percent during the early 1980s. For all years but 1973 and 1974, cyclical unemployment was positive at the national level. The provincial noncyclical rates, reproduced in Table 3, varied greatly across Canada during this period.

Table 3 presents the cost of cyclical unemployment as a percentage of provincial income for each province for each year (LJr). The bottom row is each province's cost as a percent of income over the entire time period (Lj)> and the last column is

the aggregate cost for Canada for each year (Lt). The bottom right-hand corner is the total cost of cyclical unemployment for Canada for the period 1971-86 (L).

Cyclical unemployment was most costly for Ontario, 4.7 percent of provincial income over the period. The provinces with the lowest costs of cyclical unemployment were New Brunswick, Newfoundland> Nova Scotia, and Saskatchewan; 0.7 to 1.1 percent of provincial income. This was achieved in Saskatchewan with low steady-state unemployment and low actual unemployment, whereas the other three had high levels of both, but with little difference between them. For the remaining five provinces the cost of cyclical unemployment was between 2.2 and 3.2 percent of provincial income.

IMAGE GRAPH 23

Figure 1

For Canada as a whole, yearly costs of cyclical unemployment were low during the early 1970s, rose to a peak of 7.9 percent of national income in 1983, and fell to 4.2 percent by 1986. For the entire period of 1971-86, the costs of cyclical unemployment were 3.3 percent of national income.

IMAGE TABLE 27

Table 3

Upper limit of the costs of cyclical unemployment. There is a potential problem with using estimates of the noncyclical unemployment that are based on what should occur in the steady state, as we have done above. When there is unemployment hysteresis, an increase in cyclical unemployment can cause the steady-state level of unemployment to rise.3 if current cyclical unemployment increases future steady-state rates, then the use of steady-state unemployment rates suppresses the effect that past unemployment has on current risk. Because of this, we must eliminate the possible effects that the actual unemployment rates may have had on steadystate rates.

In order to obtain an upper limit on the costs of unemployment over the period, we assume that all changes in the steady-state rates estimated by Burns (1991) are attributed to hysteresis. Thus, to eliminate the effect that the unemployment history may have had on the steady-state unemployment rates, we use the estimates of the steady-state rates for 1971 as the noncyclical unemployment rate for the entire period. These estimates of the costs of cyclical unemployment are presented in Table 4.

Note that the sums of the upper limits of costs of cyclical unemployment are for 1971-86 only, so that they are comparable to the lower limits calculated above. The difference between the upper and lower limits are greatest for the Maritime Provinces, where the increases in the steady-state unemployment rates were quite large. Only for Alberta, Manitoba, and Ontario are the upper limits not more than twice the lower limits. For Canada as a whole, when all changes in the steady-state unemployment rates are attributed to the unemployment history the costs of cyclical unemployment between 1971 and 1986 was 7.4 percent of national income.

Summary. Another way of interpreting the costs of cyclical unemployment is to call them the benefits that would accrue from policies that eliminated cyclical unemployment. If these policies also have the effect of slowing down growth, it is useful to know the growth-unemployment tradeoff to see if the policies would have been worthwhile. For Canada between 1971 and 1986, in which real growth averaged 3.6 percent a year, a growth rate that was 0.40.8 percent higher in each year would have generated enough income to compensate for the 3.3-7.4 percent costs of cyclical unemployment. In other words, the social benefit of eliminating cyclical fluctuations of unemployment during this period would have been the same as the social benefit of having a growth rate that was 0.4-0.8 percent higher in each year. Real growth in Canada averaged 4.6 percent a year from 1950 to 1970. If growth from 1971 to 1986 had kept up with this rate, even the upper limit of the costs of cyclical unemployment would have been compensated for.

IMAGE TABLE 33

Table 4

Any complete discussion of our results must keep in mind that the results are very sensitive to the time period examined. We selected our time period because the migration data are much more reliable after 1970, and because the most recent estimates we have of the natural rate for all the provinces are from 1986. Adding years to the beginning or the end of our period would lower the estimated total costs, and also lower the additional growth that would have compensated for the costs. For instance, simply by including 1987-90 in calculating the upper limit of the costs of cyclical unemployment, the compensatory growth per year falls to 0.6 percent. In addition, because the years 1971-86 have been the most economically turbulent years in post-war Canada, our estimates of the costs of cyclical unemployment over the period are higher than for other periods. We should also keep in mind that policymakers may have already learned lessons from the period, and that the likelihood of a repetition of the reflation/ deflation cycle of the late 1970s and early 1980s may be low However, with policymaking being what it is, we should not count on this being true. Unemployment Levels

Another way of looking at the costs of unemployment is that there is some benchmark level of unemployment that is viewed subjectively as desirable or optimal. An unemployment rate above this benchmark level is socially suboptimal and therefore imposes costs on society. Thus, the cost of unemployment can be viewed as the cost of it being above some acceptable benchmark level. The method described above can be adapted easily to include these other costs of unemployment. Note that our calculations are not net of the costs of achieving the benchmark rates.

IMAGE TABLE 38

Table 5

Substitute any benchmark unemployment rate for U'. in equation 7, and the interpretation of Li, becomes the percent of provincial income that people would be willing to pay to have the benchmark unemployment rate. In other words, it is the cost of having unemployment above the benchmark rate. Compared to the calculation of the costs of cyclical unemployment, the only difference here is that if a province's actual unemployment is lower than the benchmark rate, then the cost of unemployment is zero.

The selection of a benchmark unemployment rate is completely subjective. There are many different views about what the "desirable," "optimal," or "minimally acceptable" level of unemployment is.

Without apologies, the arbitrary unemployment benchmark that we chose for each province for each year is 6 percent. The costs of unemployment above this benchmark are presented in Table 5. Although it is perfectly reasonable to believe that the desirable unemployment rate is different for provinces and across time, we leave this calculation to the reader. Note that in Table 5, the total costs over time are calculated for the years 1971-86, so that they are comparable to the total costs calculated in Tables 3 and 4.

As indicated by Table 5, the costs of having unemployment above 6 percent during 1971-86 varied widely across provinces. For British Columbia, New Brunswick, Newfoundland, Nova Scotia, Prince Edward Island, and Quebec, the costs were above 10 percent of provincial income. Saskatchewan and Manitoba, on the other hand, had costs of only 1.8 and 3.0 percent, respectively For Canada as a whole, the cost of having unemployment above 6 percent was lowest during 1973-74, peaked at 14 percent during 1983, and was 7.5 percent of national income over the period. Additional growth of 0.6 percent a year would have compensated for these costs.

CONCLUSIONS

The problem with existing methods of measuring the costs of unemployment is that they are not particularly useful for normative policy analysis. Their focus is on the output that is foregone when there is unemployment, instead of on the utility losses that result from unemployment. In contrast, we propose an approach that yields estimates of the utility costs of unemployment as measured by the amount that people would be willing to pay to avoid the risk of unemployment. Under the assumptions of our model, the difference in the standard of living between two regions is equal to the difference in the rates of cross migration. We then estimate the extent to which income, unemployment, and other amenities contribute to differences in the standard of living. Using these estimates, we calculate the amount of income that people would be willing to pay in order to avoid the possibility of unemployment. We estimate the cost of cyclical unemployment in Canada from 1971 to 1986 to have been between 3.3 and 7.4 percent of national income over the period. Additional growth of 0.4 to 0.8 percent per year would have generated enough income to have compensated for these costs.

IMAGE TABLE 46

Appendix

FOOTNOTE

1 Rosen and Roback do not use their models to estimate the costs of unemployment. They include unemployment rates to control for standard-of-living differences not accounted for by differences in other amenities.

2

See Evans (1990) and Hunt (1993) for discussions.

FOOTNOTE

3 See Lindbeck and Snower (1986) and Layard, Nickell, and Jackman (1991).

REFERENCE

REFERENCES

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REFERENCE

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AUTHOR_AFFILIATION

Stratford Douglas is an associate professor of economics at West Virginia University. Howard J. Wall is a senior economist at the Federal Reserve Bank of St. Louis. The authors are grateful for the helpful suggestions of Gylfi Zoega, participants in the Labour Market Imperfections Group of the CEPR, and seminar participants at the Federal Reserve Bank of Cleveland.