Endogeneity in Structural Unemployment Equations
The Case of Canada

This paper examines the endogeneity of several structural variables which enter unemployment rate equations—the generosity of unemployment benefits, nonwage labor costs, the relative minimum wage, and the degree of unionization. It finds evidence of reverse causality for these structural variables based on causality tests. The structural unemployment rate equation is then estimated using instruments suggested by the empirical analysis of the structural variables. The paper confirms the earlier finding that the generosity of unemployment benefits, nonwage labor costs, and the relative minimum wage have a significant positive impact on the unemployment rate, but fails to find an effect for the degree of unionization.

Abstract

This paper examines the endogeneity of several structural variables which enter unemployment rate equations—the generosity of unemployment benefits, nonwage labor costs, the relative minimum wage, and the degree of unionization. It finds evidence of reverse causality for these structural variables based on causality tests. The structural unemployment rate equation is then estimated using instruments suggested by the empirical analysis of the structural variables. The paper confirms the earlier finding that the generosity of unemployment benefits, nonwage labor costs, and the relative minimum wage have a significant positive impact on the unemployment rate, but fails to find an effect for the degree of unionization.

I. Introduction

The objective of this paper is to examine the possibility of endogeneity of structural variables in unemployment rate equations in the case of Canada (1970-91). The paper also estimates a structural unemployment rate equation which is not subject to simultaneity bias. It also provides new estimates of the natural rate of unemployment in Canada and assesses how policy variables and other structural aspects of the Canadian economy have affected the natural rate in recent years.

A previous study by Coe (1990) 1/ estimated unemployment as a function of cyclical and structural variables—the generosity of the unemployment insurance system, nonwage labor costs, the minimum wage, and the unionization rate. For institutional reasons described in the paper, however, these structural variables are themselves a function of the unemployment rate. This paper demonstrates that reverse causality is present using Granger and Geweke tests, and estimates the unemployment rate equation with instruments suggested by the institutional structure governing unemployment benefit provision, social security contribution rates, and the minimum wage.

This paper contains two main findings. First, the re-estimation of the equation for the unemployment rate using an instrumental variables (IV) technique instead of OLS proved to have a small effect on the overall estimate of the natural rate. However, the re-estimation did have a larger effect on the decomposition of the natural rate into its causes. Using the IV estimation, the coefficients on the variables representing nonwage labor costs and the minimum wage were larger than those obtained with OLS, while the coefficient on the variable representing the generosity of the unemployment insurance system (UI) was unchanged and on the coefficient on unionization was smaller. Therefore, the study concludes that OLS produces a downward bias for nonwage labor costs and the minimum wage and an upward bias for the unionization rate.

The second main finding of this study is that it confirms that nonwage labor costs, the generosity of the UI system, and the real minimum wage have a significant positive effect on the unemployment rate. At the same time, however, the coefficient for the generosity of the UI system is relatively small, and unionization has no significant effect at all. These results have important implications for policy. First, because nonwage labor costs have a large coefficient in the equation for the unemployment rate, one is led to question the desirability of the recent large increases in UI premiums. 2/ Second, because the coefficients on the variables representing the generosity of the UI system are relatively small, UI reform might not have a large effect on the natural rate. The substantial tightening of eligibility requirements in January 1991 reduced the natural rate by only about ½ percent.

The remainder of the study is organized as follows. Section II describes the institutional context of the Canadian labor market, and tests hypotheses pertaining to the working of the labor market, discusses why the structural variables may be endogenous. Section III reports the results of causality tests. Section IV presents estimated equations for the unemployment rate based on OLS and IV and discusses the factors that have accounted for changes in the natural rate. Section V suggests possible areas for further research.

II. An Examination of the Structural Variables

Four structural variables have been (statistically) significant in previous study by David Coe which estimated the natural rate of unemployment: the generosity of the UI system (UIRR), nonwage labor costs as a percentage of the wage (TAXSIP), the log of the relative minimum wage (RELMW), and the unionization rate (%UNION). These variables are examined in turn below.

Reverse causality is conceivable for several structural variables. The generosity of the UI system may depend on the state of the labor market if extended benefits are available when unemployment is high. Also, UI premiums (a major component of nonwage labor costs) will increase directly with the unemployment rate if there is a requirement that the UI account be in balance. Third, the minimum wage is a policy instrument which can be manipulated—typically by not adjusting the minimum wage to inflation—to accommodate businesses in times of recession. Finally, the degree of unionization may be a function of the unemployment rate because of correlation between cyclicality and the degree of unionization across industries, among other reasons.

1. Generosity of unemployment insurance system (UIRR and UIRRadj)

In Coe (1990), two proxies are used for the generosity of the unemployment insurance system: the UI replacement rate adjusted for coverage (UIRR), and UIRR adjusted for changes in the duration of benefits and in the length of employment required to qualify for benefits (UIRRadj). 3/

UIRRadj is defined as UIRR times an “index of eligibility”. The index is defined as:

Σisi*(52-MINQi)/(52-MAXBi),

This is a weighted sum of the eligibility index across regions (denoted by i). si are the shares of each region in unemployment, MINQi is the minimum qualifying period for benefits (the length of time one must have worked in order to be eligible for benefits) in region i, and MAXBi is the maximum duration of benefits for a person who has worked just long enough to qualify for benefits.

While UIRR can reasonably be assumed to be exogenous since its constituent components (coverage and the replacement rate) are set independently of unemployment, the same is not true for UIRRadj. In Canada, benefit rules specifically provide for qualifying periods and duration of benefits that depend on the unemployment rate in the region of residence of the unemployed.

Benefit rules have been changed three times since 1970. 4/ Chart 1 shows the relationship between MINQ, MAXB and regional unemployment under 1978-90 and 1991 rules, and also displays the index of eligibility as a function of unemployment.

To avoid simultaneity bias, UIRR is used as an instrument in the unemployment-rate equation. This is an appropriate instrument since it is both independent of the error term (it is not a function of the unemployment rate) and is correlated with UIRRadj (by definition). Sufficient variation remains in UIRR, reflecting both variation in the replacement rate and in coverage (both benefit levels and coverage were reduced in 1978 and again in 1991). 5/

2. Nonwage labor costs (TAXSIP)

TAXSIP consists of all nonwage labor costs paid by employers, including social security taxes, unemployment insurance premiums, contributions to private pensions, casualty insurance, life insurance, and similar schemes. 6/ UI premiums, a major component of TAXSIP, potentially depend on unemployment, owing to the objective of fiscal integrity of the UI accounts in Canada. In particular, the authorities take expected unemployment into account when setting rates.

UI premiums are normally set by the Canada Employment and Immigration Commission, though Parliament has the right to overrule the Commission and has done so on occasion. 7/ The rate-setting process comprises two stages. First, a statutory rate is computed. This is the premium rate which would exactly pay for total program costs, averaged over the last three years. Second, a cumulative deficit is projected, based on the statutory rate and on projections of the number of contributors and beneficiaries. The Department of Finance’s forecast of the unemployment rate is a critical input in these calculations. 8/ If a cumulative deficit is projected at the statutory rate, the Commission is required by law to set a rate exceeding the statutory rate. The law does not require that the rate be such that the cumulative deficit be exactly zero, however. In practice the commission has been willing to increase rates when this was necessary to maintain fiscal integrity. A recent example consists of the introduction of two bills raising the premium rate, in 1990 and July 1991, to offset the effects of the withdrawal of government participation in the financing of the scheme and because of increasing costs associated with higher unemployment.

The objective of fiscal integrity is verified by the data. The current surplus in the UI account is well described by the lagged cumulative surplus (with coefficient 0.4, implying 40 percent of a cumulative deficit will be eliminated the following year), the unemployment rate, a trend variable, and a dummy for the period 1990-91 when the Government stopped subsidizing the unemployment insurance account 9/ (see Table 1, panel 1, using annual data). Further, the results in panel 2 indicate that the cumulative surplus has a significant negative impact on future premium rates, proving that premium rates are set to maintain fiscal integrity. The case for simultaneity bias would be strengthened if it were shown that Finance Canada predicts unemployment rates accurately. It should be emphasized that TAXSIP will depend on contemporaneous unemployment only when unemployment is well predicted. To test this hypothesis, one could proceed to evaluate the Department of Finance’s forecast record on the unemployment rate, as those estimates form the input into the Committee’s projection of the expected cumulative surplus. The records exist beginning at least since 1970, but a time-series has not yet been compiled.

Table 1.

Determinants of Non-wage Labor Costs

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t-statistics in parentheses.

The lagged cumulative surplus and lagged NWLC are insignificant in equations which include the unemployment rate, with the t-statistic on the unemployment rate equal to 1.7.

Employer premium rate.

Significance level, in percent.

Since TAXSIP includes employer contributions for UI, it follows that TAXSIP is closely related to premium rates, and hence potentially to unemployment. This is confirmed in panel 3, which reports on a regression of TAXSIP on its own lag, the premium rate, and two trends (a linear and a quadratic trend).

Based on the results of Table 1, the lagged cumulative surplus, the set of trends, and a dummy will be used as instrument for TAXSIP. 10/ The use of a short lag of TAXSIP as an instrument for contemporaneous values is tempting. However, this would not necessarily resolve the problem of simultaneity bias in practice. TAXSIP, being set for a year, will be related to unemployment in each quarter of the year in question. The independent variable, in this case TAXSIP, needs to be lagged by one year. 11/

3. The relative minimum wage (RELMW)

In Canada, the minimum wage is periodically adjusted for inflation, but there is no provision of full indexation. This leaves policymakers the room to allow the real minimum wage to fall when this is considered warranted in light of high unemployment and/or low profitability. Indeed, it is broadly acknowledged that the relative minimum wage was allowed to decline during the 1980s in order to improve employment prospects. Policymakers set the minimum wage for the coming year. If policymakers have rational expectations about the unemployment rate, unemployment will have an effect on minimum wages, and bias will be introduced when unemployment is regressed on the contemporaneous relative minimum wage. Furthermore, as policymakers do not adjust the minimum wage more than once a year, short lags of RELMW will also be correlated with the contemporaneous unemployment rate (because of the correlation between the quarterly unemployment rate and the year-ahead forecast made at the beginning of the period). 12/

Regression analysis confirms the role of the unemployment rate in the formation of the minimum wage. Express commercial wages (waget) and the minimum wage at time t (mint) as the wage in some initial period multiplied by its compounded annual growth rate (d for commercial wages and g for the minimum wage). The growth rate of the minimum wage in period t (gt) is assumed to be a fraction (a) of the growth rate of commercial wages (d), where a is a function of the unemployment rate (UR).

wageT=wage0.πt(1+dt)minT=min0.πt(1+gt)wheregt=at*dtat=c+b*URt;dt=((waget/waget-1)-1)

By substituting the expression for the commercial wage (wage) the following expression for the log of the relative minimum wage (RELMW) is obtained:

log(minT/wageT)=log(min0/wage0)+Σtlog(1+at*dt)-Σtlog(1+dt)

Using the approximation log(1+x) = x, one obtains

RELMWT=k+bΣtURt*dt+(c-1)Σtdtwherek=log(min0/wage0)

The sum (beginning in 1970) of URt·dt and of dt is calculated and the above expression estimated. Because Σ URt*dt is mostly determined by past unemployment, it is considered predetermined with respect to RELMW. To ensure that the residuals are not serially correlated, lagged RELMW and a trend are included. The results are reported in Table 2. Both Σtdt*URt and Σtdt are significant. This regression confirms that unemployment plays a role in the determination of the minimum wage. In the re-estimation of the unemployment rate equation, RELMW lagged one year will be substituted for RELMW.

Table 2.

Determinants of Relative Minimum Wage 1/

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t-statistics in parentheses.

In percent.

4. Degree of unionization (%UNION)

There are several channels through which the unemployment rate affects the degree of unionization, and the sign of the correlation is not clear a priori. One reason for procyclical behavior of unionization is that union bargaining power is low in recessions, when, owing to unemployment among members, the financial resources from union dues are small. At the same time, however, union density, may behave counter-cyclically owing to the establishment size effect. Larger firms tend to be both more highly unionized and to provide greater employment stability. Finally, employment shares by industry move cyclically, with corresponding effects on unionization. Thus the tendency for the employment share of public administration (which is highly unionized in Canada) to rise in recessions, provides an upward push to unionization during recessions. The opposite force exists as well, and, as shown below, outweighs the former: the procyclical behavior of the employment share in manufacturing and construction (which are highly unionized) leads to a procyclical behavior of the percent unionized. 13/

Only the effect of different degrees of unionization by industry is explored here. Corrections for the establishment size density effect cannot be made because data on unionization by firm size do not exist, although research could proceed based on U.S. parameters.

The cyclicality of employment shares is studied by regressing employment shares by sector on unemployment and the change in unemployment. Table 3 shows that job stability is high in the relatively more unionized sectors such as government employment (public administration and transportation). However, job stability is also relatively high in financial and trade services, which have lower degrees of unionization than manufacturing or construction.

Table 3.

Canada: Cyclical Sensitivity of Employment Shares 1/

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Defined as share of sector in total employment in Canada. Regressions are based on annual data from 1971 to 1989.

A cyclically neutral degree of unionization was calculated by substituting the sample average for unemployment and the change in unemployment in the regression equations by sector. These cyclically adjusted shares are then applied to sectoral union membership rates obtained from CALURA to calculate a cyclically adjusted aggregate union membership rate. 14/ In net, the industry effect leads to a procyclical bias in unionization. 15/ The adjustment to the unionization rate is minor, on the order of ½ a percentage point.

It should be noted that the CALURA data used in this study are different from the source in Coe (1990) where the data come from DLO (Directory of Labor Organization). CALURA was used here, because DLO does not provide data on union membership by industry. Originally, the intention was to use the cyclically adjusted degree of unionization (obtained from CALURA data) as an instrument for the unionization rate. However, the data for the aggregate membership density in both sources turned out to be substantially different from each other, with a correlation coefficient close to zero. For this reason the one-year lag of the unionization variable will be used as an instrument instead. 16/ %UNION1 will refer to DLO data and %UNION2 to CALURA data.

III. Tests of Causality

Granger and Geweke tests are conducted to test whether there is reverse causality from unemployment to the structural variables. 17/ Under the null hypothesis there is no reverse causality. Table 4 gives the results of the tests for UIRR, UIRRadj, %UNION, RELMW, and TAXSIP. The equations are based on quarterly data.

Table 4.

Results of Causality Tests: Significance Level under Null

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Note: Regressions are based on 1971-91 data; see text for description of equations. Tests causality from unemployment to structural variables. Table presents significance level under which hypothesis of no causality from unemployment rate to structural variables can be rejected.

In the application of the Granger test, each structural variable is regressed on four lags of itself, four lags of the unemployment rate, and other variables of importance in the determination of the structural variable at hand. 18/ The test is based on an F test for the significance of the lags of the unemployment rate. If the lags are significant, the hypothesis that there is no reverse causality can be rejected. The short lag length chosen reflects the interest in testing the claim of simultaneity bias.

The Geweke test, which is similar but preferable to the better-known Sims test, 19/ is applied by running a regression of the unemployment rate on four lags of the unemployment rate and four lags and leads of the structural variables. 20/ If the leads are found to be significant, the hypothesis of reverse causality can be rejected.

The Granger test indicates that there is reverse causality, from the unemployment rate to UIRRadj, RELMW, %UNION and TAXSIP, 21/ while the Geweke tests indicate the presence of reverse causality from the unemployment rate to UIRRadj, and %UNION. 22/ While not confirmed by the Geweke test, the finding under the Granger test that lagged unemployment has an impact on RELMW and TAXSIP is considered important, as those equations, which include relevant structural variables on the right-hand side, appear to be properly specified (see Durbin-Watson and Liung-Pierce statistics). Reverse causality did not appear to be present for UIRR or %UNION2.

The lack of causality from unemployment to %UNION2 points to the desirability of using that variable in the regressions. 23/ The findings on TAXSIP, UIRRadj, RELMW and %UNION indicate that the instrumental variables estimation of the unemployment rate equation is appropriate.

IV. Estimation

The unemployment rate equation is estimated using instrumental variables. UIRR is introduced as an instrument for UIRRadj, and the cumulative surplus of the unemployment insurance system (lagged one year) as an instrument for TAXSIP. 24/ One-year lags are used as instruments for %UNION and RELMW. As there may be reverse causality from the unemployment rate to %UNION (as indicated by the causality tests), and as quarterly data for %UNION were obtained through extrapolation, %UNION lagged less than one year would not be an appropriate instrument. Similarly, the one-quarter lag of the minimum wage, could depend on the current unemployment rate, through the correlation of annual and quarterly unemployment rates, as explained above. Other variables include the relative price of energy (RELPREN) and the terms of trade (RELPREX), two lags of the unemployment rate (UR), the change in capacity utilization (CU), and the output gap (GDPGAP) 25/ (see data appendix for definitions and sources). The following equation is estimated:

UR = UR(-1) + UR(-2) + [CU-CU(-1)] + GDPGAP(-1) + RELPREN + RELPREX(-1) + UIRRadj + RELMW(-1) + %UNION + TAXSIP(-1) 26/

The results are tabulated in Table 5. Results are presented for the period 71:1-91:4, for OLS and IV estimation. For comparison, the results of the OLS estimation for the period 71:1-88:2 (the period of Coe’s study) are presented as well. 27/

Table 5.

Unemployment Rate Equations: OLs and Instrumental Variables 1/2/

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The instrument list consists of the cyclical and supply-shock variables, as well as UIRR, CUMSURP(-5), RELMW(-4) AND %UNION1(-4). See appendix for variable definitions.

t-statistics in parentheses.

In percent.

Note first, that extending the sample period makes little difference to the results. The only exception is the variable %UNION, which loses some of its significance. The coefficients on the other structural variables are almost unchanged.

Second, estimation with instrumental variables also has little impact on the estimates, except in the case of %UNION. The coefficient on RELMW and TAXSIP do increase somewhat and the coefficient on UIRRadj remains unchanged. The variable %UNION loses all significance.

The finding that TAXSIP has a significant coefficient with IV estimation strengthens the case made by David Coe that TAXSIP has an adverse impact on the unemployment rate. In the case of UIRRadj and RELMW the coefficients are significantly different from zero, and one can conclude that these variables also affect the unemployment rate. %UNION loses its significance with IV estimation indicating that further examination of its relationship to the unemployment rate is warranted.

In light of the uncertain quality of DLO data used to calculate %UNION, the unemployment equation was re-estimated using CALURA data. The last available observation for these data is the first quarter of 1989, bringing the estimation period to 1971:1-1989:1. Using the CALURA data (see Table 6, bottom panel) %UNION loses significance and the size of its coefficient is drastically reduced. This finding raises further doubts about the effect of unionization on the unemployment rate. Note also that the coefficient on UIRR is insignificant in the equation with %UNION from CALURA data, raising doubts about the significance of UIRR.

Table 6.

Comparison of Different Measures of Union Density 1/2/

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Regressions based on UIRR instead of UIRRadj to avoid complications arising from known source of simultaneity bias.

t-statistics in parentheses.

In percent.

The natural rate estimate

The natural rate can be derived by setting unemployment equal to lagged unemployment and by using cyclically neutral values for the output gap 28/ and period averages for all other variables except UIRR, RELMW, %UNION and TAXSIP which are set equal to their historical values.

Chart 2 provides a graph of the natural rate based on IV estimates, as well as of the natural rate obtained by extending the OLS regression to the end of 1991. The series are not substantially different, although the new IV-based estimates of the natural rate are slightly smaller in the period 1981-86.

Chart 2
Chart 2

CANADA: Actual and Natural Unemployment Rate 1/

Citation: IMF Working Papers 1993, 094; 10.5089/9781451950694.001.A001

1/ Based on instrumental variables estimates.

The natural rate reached a local minimum in mid-1989, with a rate just below 8 percent. The impact of the structural variables on the natural rate since that time has been mixed. Major increases in the unemployment insurance (UI) premiums on several occasions have put upward pressure on the natural rate, while the tightening of eligibility requirements for UI benefits in 1991 has had the opposite effect. The net effect has been an increase in the natural rate to about 8 ¾ percent at the end of 1991.

Chart 3 gives a decomposition of the change in the natural rate since 1971 into the contributions by each of the structural variables. 29/ The figure shows that the decline and then the increase of the natural rate during 1989-90 can be explained by changes in TAXSIP. There is also a positive contribution of UIRR in late 1990 reflecting extended benefits due to higher unemployment. During the second quarter of 1991, the natural rate declines reflecting both the reform of the UI system under which eligibility rules were tightened and the decline in RELMW (minimum wages remained constant at first quarter levels while wages in the rest of the economy grew). In the last quarter of 1991, the natural rate increases again slightly, reflecting the delayed impact (built into the regressions) of the increase in social security tax rates by 24 percent in July 1991. The natural rate increases further in the first quarter of 1992, because of an increase in unemployment insurance premiums and the annual adjustment of the minimum wage. Chart 4 show the evolution of the structural variables.

Chart 3
Chart 3

CANADA: Decomposition of Change in Natural Rate Since 1971

Citation: IMF Working Papers 1993, 094; 10.5089/9781451950694.001.A001

1/ Based on DLO data.
Chart 4
Chart 4

CANADA: Structural Variables

Citation: IMF Working Papers 1993, 094; 10.5089/9781451950694.001.A001

1/ Adjusted for eligibility.2/ Cyclically adjusted based on industry employment shares.

The natural rate has increased by about 3 ½ percentage points since 1971, with increases in TAXSIP accounting for 5 percent points, declines in RELMW accounting for -2 ¼ percentage points, and increases in UIRR contributing ½ percent point. %UNION does not contribute to the increase in the natural rate. David Coe found a smaller contribution from TAXSIP, a larger contribution from %UNION and UIRR, and a smaller negative contribution from the decline in the relative minimum wage. 30/

V. Further Research

Further research could proceed along three lines. First, to strengthen the case for reverse causality from unemployment to UI premium rates and the minimum wage, it would be useful to estimate the relationship between the policymakers’ forecast of the unemployment rate and the outturn. This research could be based on year-ahead forecasts (made once a year at the time of the budget exercise) for the unemployment rate.

Second, the estimates of the natural rate could be used to compare different unemployment insurance systems. A system where the premium rates are determined to ensure fiscal integrity over an entire cycle, as opposed to over just a few years as in the present case, can be expected to exhibit less amplitude in the unemployment rate. This could be shown on the basis of simulations, by modeling the output gap as a sine wave, for example. Different models of expectation formation by policymakers (rational or backward looking) could be built into the simulations.

Third, the estimates of the natural rate could be used to simulate the effect on the natural rate (through a decline in unemployment-insurance premiums, less generous extension of UI benefits and more generous increases in the minimum wage) of the expected drop in the actual unemployment rate as the Canadian economy recovers. This involves simulating a system consisting of equations for the natural rate, nonwage labor costs, unemployment benefits and minimum wages. Such an exercise would show that the natural rate falls with the actual rate, if the procyclical declines in unemployment insurance premiums and in the generosity of unemployment benefits dominate the effect of increases in minimum wages. In this case wage pressures would be less than if structural variables did not depend on the unemployment rate.

Appendix I: Data Sources

1. Taxsip

Employer contributions to social security as percentage of the wage

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Source: OECD, National Accounts, detailed tables, volume 2;

2. %Union

2.a. %Union1

Number of union members of all union federations and of independent local unions with 50 members or more, as a percent of nonagricultural dependent employment.

Source: Labor Canada, Directory of Labor Organizations (DLO); also available from Bureau of Labor Information, Union Membership in Canada 1991.

Available: 1920-91

2.b. %Union2

Number of union members of unions with 100 members or more, as a percentage of dependent employment.

Source: Statistics Canada, Corporations and Labor Unions Returns Act (CALURA).

Available: 65-89+

3. Relmw

log(minimum wage/commercial wage)

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Source: Finance Canada.

RELMW(-1) available: 69:2-92:1

4. Uirr

4a. Uirr
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Source: Research Department, Bank of Canada.
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4b. UIRRadj
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minimum work requirement

MINQ and MAXB are a function of the unemployment rate which is available from January 1966 to July 1992.

Source: Formulas in Coe (1990) and tables provided in the text; Statcan for unemployment rate.

5. UR

Average unemployment rate for the quarter, seasonally adjusted, arithmetic average of monthly data.

Source: Statcan, D767611.

6. Relpren

Price of energy relative to CPI

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Source: Statcan; PEN is available starting 49:1 based on D130447 (Research Department, Bank of Canada); for P484549 prior to 74:1, see B820200 (calculated by the Bank of Canada). Monthly data are averaged.

7. Relprex

Price of exports relative to price of imports

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Source: Statcan.

8. GDP

Real GDP (constant 1986 prices)

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Note: There were revisions to 88 and 89 data.Source: Statcan.

9. CU

Capacity utilization in total non-farm goods producing industries.

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Source: Statcan.Note: Series was extensively revised in 1990.

10. Surplus, Cumsurp, Rate, Erate, Trate

Surplus, cumulative surplus, and premium rates (employee (rate), employer (erate) and total premium rate (trate)).

Source: Appendix II: A New Chapter: the UI program becomes self financing (1972-1991), supplemented by information provided by Canada Employment and Immigration Commission (1970-1991).

References

  • Coe, David,Structural Determinants of the Natural Rate of Unemployment in Canada”, IMF Staff Papers (March 1990).

  • Employment and Immigration Commission, Appendix II: A New Chapter: the UI Program Becomes Self-financing (1972-1991)

  • Geweke, J., R. Meese, and W. Dent,Comparing Alternative Tests of Causality in Temporal Systems,” Journal of Econometrics. V. 21 (1983).

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  • Granger, C. W. J.,Investigating Causal Relations by Econometric Models and Cross-Spectral Models,” Econometrica, V. 37 (1969)

  • Sims, C.A.,Money, Income, and Causality,” American Economic Review, V. 62 (1972).

*

Ms. Van Rijckeghem was an economist in the Western Hemisphere Department when this paper was prepared. She is now in the Fiscal Affairs Department. She wishes to thank David Wong for assistance in running causality tests, Renee Ruivivar for research assistance, David Coe, Tarhan Feyzioglu, Jorge Márquez-Ruarte, Eswar Prasad, and Murat Ucer for helpful comments and suggestions, Robert Billings (Finance Canada), Craig Chamberlin (Labor Canada), Stuart McLeod (Statistics Canada), Ron Parker (Bank of Canada), and Cathy Wright (IMF) for kindly providing data.

1/

Coe, David, “Structural Determinants of the Natural Rate of Unemployment in Canada,” Staff Papers, International Monetary Fund (Washington), (March 1990).

2/

Premiums were raised by 24 percent in July 1991 and by 7 percent in January 1992. Since 1989 premium rates were increased by more than 50 percent.

3/

The replacement rate is defined as maximum weekly benefits divided by average hourly earnings. Maximum weekly benefits are 60 percent of maximum insurable earnings (Canadian policy defines maximum insurable earnings as the two-year lag of a moving average of the growth in average earnings). Coverage is defined as the number of workers covered by unemployment insurance divided by the labor force.

4/

Coe’s study contains equations which express MINQi and MAXBi as functions of regional unemployment rates for the period up to 1990.

5/

The generosity in terms of qualification period and duration of benefits also changed in 1978. The duration of benefits was decreased at unemployment rates below 8 percent, and increased for rates above 8 percent.

6/

System of National Accounts definition.

7/

For example, in 1986 the Government felt that increases in premiums proposed by the Commission would put the emerging recovery at risk. Also, in 1987, the Government wanted to ensure that the difficulties experienced as the result of the stock market crash were not compounded by increases in premiums.

8/

As a rule of thumb, the Canadian authorities estimate that each 1 percentage point increase in the unemployment rate leads to an increase of almost 0.3 percentage points in the employee premium rate.

9/

It is understood that the unemployment rate is endogenous and that its coefficient will be biased.

10/

A composite regression of nonwage labor costs directly on its own lag, the cumulative surplus, trend variables, and a dummy produces a t-statistic of only 1.4 for the cumulative surplus (see Table 2, bottom of panel 3). This is still satisfactory in light of the theoretical framework and the regressions reported above so that the cumulative surplus is maintained as an instrument.

11/

Lagging TAXSIP a few quarters will not in general remove its dependence on the contemporaneous unemployment rate. Concretely, during each quarter of a given year, say 1985, TAXSIP will depend on the forecast for unemployment for that year E(UR1985). Lagging TAXSIP one quarter will not eliminate the dependence from the unemployment forecast for the year (except in the case of the first quarter). For example, in the second quarter of 1985, lagged TAXSIP (first quarter 1985) will still be related to the unemployment projection for 1985 and therefore to the second quarter’s unemployment rate (quarterly and annual unemployment rates are highly correlated).

12/

Recall the result that the quarterly unemployment rate is well explained by the annual unemployment rate.

13/

While the degree of unionization is very high in public administration (80 percent) its employment share is only 7 percent.

14/

The Canada Labor Union Reporting Act. CALURA data are not available after 1989. Membership for 1990 and 1991 was held constant at the 1989 level.

15/

The difference between the adjusted %UNION and %UNION is explained in a regression on a constant (-.9; t=-19.9) and the unemployment rate (.11; t-20.5).

16/

CALURA is probably a preferable source because data-reporting is compulsory under the financial reporting legislation of the CALURA act (applicable to unions with membership above 100). DLO is simply a directory providing names, addresses, and membership of all union federations and of independent local unions with 50 members or more; unions voluntarily update forms sent to them. Two other concerns with the DLO data are: the lack of updating, and double counting (e.g., when unions change affiliation both the old and the new federation report the union as a member). A Canadian official noted that the increase in the unionization rate reported by DLO for 1991 reflects the addition of previously existing unions to the records, and that the unionization rate probably has not changed since 1989.

17/

The tests are based on untransformed variables (no moving averages or lags are taken).

18/

In the case of UIRR, %UNION, %UNION2, the other variables consist only of trends (linear and quadratic) for lack of further information on their structural determinants. In the case UIRRadj, UIRR was included in addition to trends, while in the case of TAXSIP the cumulative surplus in the unemployment insurance account (lagged one year) was included. RELMW was expressed only in terms of trends, as its known determinants, Σtdt*URt and Σtdt, are correlated with the unemployment rate.

19/

The Sims test does not include the lags of the dependent variable, in this case the 4 lags of the unemployment rate.

20/

In addition all explanatory variables from Coe’s equation are included, though all structural variables are lagged once to reduce the probability of simultaneity bias.

21/

The lagged unemployment rate does not have a significant effect on %TAXSIP when trend and quadratic trend are included. However, when the quadratic trend is dropped from the equation, the lagged unemployment rate does have a significant impact on %TAXSIP.

22/

The significance level under the Geweke test is 18 percent for UIRRadj. This is considered acceptable however, given a significance level of 7 percent under the Granger test.

23/

One is led to ask why DLO data would be more cyclical than CALURA data. This could be related to the fact that DLO data include smaller firms, so that membership will fall more steeply in a recession than in the case of CALURA data (both sources have similar denominators, see data appendix).

24/

UIRR and TAXSIP are introduced as two-period moving averages.

25/

The output gap is defined as the difference between log(GDP) and the fit of log(GDP) from an equation which regresses log(GDP) against a quadratic trend for the period 1961:1-1991:4.

26/

TAXSIP and UIRRadj are entered as two-period moving averages, following Coe (1990).

27/

These results are broadly equal to those first obtained by Coe (1990). Small differences are attributable to data revisions.

28/

The cyclically neutral value for the output gap is defined as the average of two estimates: (1) the sample average of the output gap, and (2) its mean value between 87:2 and 88:2, a period of full employment. This procedure follows Coe (1991).

29/

Defined as the change in each structural variable since 1971, multiplied by the value of the long-run multiplier.

30/

In Coe’s study the observed increase in TAXSIP contributes 2 ½ percentage points to the 3 ½ percentage-point increase in the natural rate over the period 1970-88. Unemployment insurance generosity and unionization each contribute 1 percent to the increase in the natural rate, while the decline in the relative minimum wage over the period contributes one point to the decline in the natural rate.

Endogeneity in Structural Unemployment Equations: The Case of Canada
Author: International Monetary Fund