Unemployment in Canada and the United States

Unemployment in Canada and the United StatesAuthor(s): John McCallumSource: The Canadian Journal of Economics / Revue canadienne d'Economique, Vol. 20, No. 4(Nov., 1987), pp. 802-822Published by: Wiley on behalf of the Canadian Economics AssociationStable URL: http://www.jstor.org/stable/135417 .

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Unemployment in Canada and the United States JOHN McCALLUM McGill University

Abstract. Reduced form unemployment equations containing aggregate demand, structural, and frictional variables are estimated for Canada and the United States. Post-1981 increases in unemployment rates are explained almost entirely by aggregate demand variables, although structural / sectoral variables make important contributions to changes in the gap between the two countries' unemployment rates. For both countries, the results support the following 'monetarist' propositions: monetary variables are the prime determinants of the business cycle, exogenous investment shocks are typically of minor importance, and macro policy has tended to be destabilizing.

Les taux de chomage canadien et americain. On estime des equations de forme reduite pour les taux de chomage canadien et americain. Ces equations contiennent des variables frictionnelles, des variables structurelles / sectorielles, et des variables representant la demande agregee. I1 parait que les hausses des taux de chomage depuis 1981 ont e dues presqu'exclusivement a la demande agregee, quoique les variables structurelles / sectorielles ont joue un r6le important dans l'explication de l'evolution de l'ecart entre les taux de ch6mage des deux pays. Pour les deux pays, les resultats donnent d'appui aux propositions 'monetaristes' suivantes: les variables monetaires ont ete les determinants principaux du cycle economique, en general les chocs exogenes a l'investissement ont joue un r6le mineur, et la politique macro6conomique a e destabilisante.

In 1982 Canada's unemployment rate increased by 3.5 percentage points, and in 1984 the gap between the Canadian and us unemployment rates stood at 3.8 percentage points. Both of these numbers are without precedent: the first

I am grateful to the following for their useful comments on earlier drafts of this paper: Steve Ambler, Jean-Pierre Aubry, Benoit Carmichael, David Dodge, Pierre Fortin, Pat Grady, Sid Ingerman, Manfred Keil, Robert Lacroix, Mike McCracken, Louis Phaneuf, Steve Poloz, Yves Rabeau, Lucie Samson, and two referees. My thanks also to Philippe Laheurte for research assistance and to FCAR and SSHRC for financial assistance.

Canadian Journal of Economics Revue canadienne d'Economique, xx, No. 4 November novembre 1987. Printed in Canada Imprime au Canada

0008-4085 / 87 / 802-822 $1.50 O Canadian Economics Association



Unemployment in Canada 803

is the largest single-year increase in the unemployment rate of any OECD

country in postwar history, and the second is the largest Canada-us unemployment gap in the half century of recorded Canadian unemployment rates. A major objective of this paper is to explain these developments by providing decompositions of the sources of variation of both the Canadian unemployment rate and the Canada-us unemployment gap over the postwar period. Reduced form unemployment equations are estimated for each country, and these are then used to compute the decompositions.

The reduced form equations will be used to calculate four components of the unemployment rate: unemployment due to labour market variables, or frictional unemployment; unemployment due to sectoral shifts, or structural unemployment; unemployment due to aggregate demand variables; and the residual or unexplained component of the unemployment rate.

Beginning with the frictional component, the reduced form equations incorporate estimates of the natural unemployment rate (or NAIRU) by Gordon (1985) for the United States and Fortin (1988) for Canada. I begin with the hypothesis that these NAIRUS may be equated with the frictional component of the unemployment rate. This hypothesis is then tested.

The specification of the sectoral or structural component of the unemployment rate is influenced by the work of Lilien (1982, 1982a) and Samson (1985). However, while these authors use aggregate measures of the dispersion of employment demand as indicators of the importance of intersectoral shifts, the approach of this paper is to focus on specific sources of such shifts. The potential advantage of this approach is that it pinpoints specific events and shocks as sources of intersectoral shifts, rather than relying on 'black box' aggregate dispersion indexes which are subject to competing interpretations.1 Three sectoral variables are incorporated in the regressions: a variable designed to reflect fluctuations in the relative world prices facing Canada's resource sector; a variable reflecting changes in oil prices; and a variable reflecting shifts of employment in durable manufacturing or 'smokestack industries.' Also, the possibility that a Lilien-type dispersion index may influence unemployment even after taking account of these specific sectoral shocks will be tested in the course of the analysis.

The third component of the unemployment rate is the aggregate demand element. Standard aggregate demand variables that are included in the regressions include indicators of fiscal and monetary policy, the real exchange rate or competitiveness, and foreign aggregate demand. Two less standard indicators are also included: estimates of shocks to private fixed investment and changes in the personal saving rate. These are considered partly because differences between Canada and the United States in terms of both investment behaviour and the personal saving rate are sometimes mentioned as possible

I For example, Abraham and Katz (1986) argue that these indexes reflect mainly aggregate demand rather than sectoral shifts, and the approach has also been criticized by Beach and Kaliski (1986) and Landon (1985).



804 John McCallum

sources of diverging unemployment rates. Also, a us study by Gordon and Veitch (1985) reports a sizeable exogenous component of private fixed investment.

One important caveat should be mentioned at the outset. By its very nature, the reduced form approach does not identify the channel through which a particular variable affects the unemployment rate. This poses problems in defining the various components of the unemployment rate, because certain variables may play multiple roles. For example, in this paper higher unemployment due to lower world prices of Canada's resource products is classified as sectoral, although it might be argued that at least part of this higher unemployment should be put in the aggregate demand category. For this reason, the approach of this paper should perhaps be regarded as a preliminary exercise designed to highlight the variables that might warrant inclusion in a more structural analysis to be carried out at a later date. Also, information on the contributions of the individual variables is included, so that readers are free to make their own alternative classifications.

As already stated, a primary purpose of the paper is to identify the sources of Canada's exceptionally high unemployment since 1981. An additional and related purpose is to discriminate among three alternative views of the business cycle. These views may be labelled 'monetarist,' 'real,' and 'Keynesian.' The monetarist view, associated mainly with Milton Friedman, holds that monetary variables play a dominant role and that policy variables tend to be destabilizing. The real view, as represented in the present context by the Lilien / Samson studies, tends to de-emphasize money and stress the importance of sectoral or structural shifts. The Keynesian view might be associated with Keynes's focus on exogenous investment shocks or, more generally, with the view that 'is curve variables' play a major role. The results for both Canada and the United States will have implications for these three views.

The organization of the remainder of the paper is as follows. The first part specifies the equations and defines the variables, the second part presents regression results, and the third part analyses and interprets the results. The final section presents conclusions.

ANALYTICAL FRAMEWORK

Following a quick presentation of the unemployment equation that will be estimated, the discussion turns to the derivation of the reduced form and a more detailed description of certain key variables. For both Canada and the United States, UGAP, which is the gap between the actual unemployment rate and the Fortin or Gordon NAIRU, is regressed on lagged UGAP and a series of aggregate demand and sectoral variables. One version of the equation is as follows:

UGAPt = al UGAPt-I + a2 ?A(m - P0t -) I + a3 A[ (B + S)/ YP)t-




+ a4 AFDt + a5 ARULCti X + a6 AIRESt

+ a7 ARPXt - + a8 LMANRESt + a9 ARPOIL -I + Et (1)

As will be seen in the empirical section, only a subset of these variables appears in the regression of each country. There is a maximum of five aggregate demand variables: the lagged growth rate of the actual-minus-equilibrium real money supply [ZA(m - p - ft)t -], the lagged change in the ratio of the sum of the cyclically adjusted budget surplus (B) and personal savings (S) to potential GNP (YP), a variable representing foreign aggregate demand shocks (AFDt), the lagged change in the real exchange rate as represented by relative unit labour costs in a common currency (A\RULCt_1), and a variable representing the exogenous component of changes in the ratio of private fixed investment to potential GiNP(AIRESt). UGAP also depends on three sectoral variables: the lagged change in the relative world price of exports (ARPXt i), a variable representing the exogenous component of changes in the ratio of employment in durable manufacturing to total employment (ZAMANRES1), and the lagged change in an oil price variable (A\RPOILtL1). Sources and more detailed definitions are given in appendix 1.

The equation has been written on the assumption that the Fortin / Gordon NAIRU can in fact be identified as the frictional unemployment rate. Providing that the coefficient on the lagged dependent variable is less than one, it can be seen that UGAP converges towards zero (i.e., the unemployment rate converges to NAIRU) when all of the first differences of the aggregate demand and sectoral variables are set equal to zero. This hypothesis is rejected if a constant term or a time trend or any labour market variable proves to be significantly different from zero when added to equation (1).

Derivation of the reducedform While the reduced-form equation is perhaps consistent with a variety of structural models, one possible derivation is provided by a standard Keynesian model that is set out in appendix 2. The model consists of an is curve, an LM curve, an Okun's Law equation, and an expectations-augmented price Phillips curve. Expected inflation is defined as a distributed lag on past inflation rates, and the model has standard neutrality properties in the long run. The lagged real exchange rate enters the is curve and the reduced form, but no attempt is made to model the exchange rate. Clearly the reduced form may display instability across exchange rate regimes, a possibility that will be tested.

The model is based on adaptive inflation expectations, which explains why the reduced form contains the lagged growth rate of the actual money supply rather than current and lagged values of unanticipated money growth. While this approach is certainly not fashionable, I would defend it on the basis of another paper (McCallum, 1 986a) which finds that rational expectations approaches to the business cycle are rejected, while the approach of the



806 John McCallum

appendix does not come close to being rejected. Alternatively, equation (1) could be regarded as following the branch of the rational expectations literature that relegates the surprise terms to the residual and captures adjustment cost effects through the lagged dependent variable rather than through lagged money surprises.2

The formulation of equation (1), while consistent with the model of appendix 2, is restrictive in the sense that all right-hand side variables have the same relationship between impact and long-run coefficients. It is certainly possible that dynamic effects not included in the model (due, for example, to adjustment costs of various kinds) might cause this condition to be violated. Consequently, more general formulations will also be estimated, and the restrictions imposed by equation (1) will be tested. One such restriction that will be tested is the neutrality proposition that in the long run UGAP iS

independent of the levels of all the right-hand side variables of equation (1).

The dependent variable I turn now to a more detailed discussion of certain key variables. The first of these is the Fortin estimate of NAIRU, and hence UGAP. The Fortin procedure involves two steps. First, a price Phillips curve is estimated over the period 1956-84. The labour market tightness variable is the adult male unemployment rate (UM), and a series of tests lead the author to conclude that the adult male NAIRU has been constant at 4.8 per cent throughout the period of estimation. Second, Fortin regresses the aggregate unemployment rate (U) on UM and a vector of labour market variables Z:

Ut = a UMt + Zt8 + qt (2)

The Z-variables include a constant term and variables relating to demography, unemployment insurance, minimum wages, unionization, and a cubic time polynomial.

Aggregate NAIRU is then defined as the predicted value of (2), with um set equal to 4.8 per cent (see below for a description of the numerical estimates of NAIRU for the two countries). Since a = 1.07 and since UGAPt - Ut - NAIRUt,

it follows that Fortin's UGAP is given by

2 Bennett McCallum (1979) makes the argument that the effects of adjustment costs should be represented by the lagged dependent variable rather than by lagged money surprises. This approach has been implemented by Gordon (1982), Demery (1984), and McGee and Stasiak (1985), among others. A generalization of this approach also forms the basis for my tests reported in McCallum (1986a), which may be summarized as follows. A reduced form containing several lagged values of output, employment, and energy prices is derived from a structural model that permits gradual adjustment of the capital stock and consumption as well as the demand for labour. In the context of this reduced form, 'rational' models do not permit real variables to be affected by actual money supply growth when money surprises with lags of up to three years are also included in the equation (three years is taken to be the length of the longest existing wage contract). On the other hand, 'non-rational' models do not allow money surprises to have real effects when current and lagged actual money growth are included in the equation. The 'rational' models were rejected, and the 'non-rational' models were not rejected.




UGAPt 1.07 (umt - 4.8) + -1t

- UMt - 4.8 (3)

The very simple definition of UGAP given by UM - 4.8 is highly correlated with Fortin's definition (r = 0.99). This is because the standard deviation of nt is less than 0.1 percentage point.

All the Canadian regressions and tests of this paper were conducted on the basis of both the Fortin UGAP and the simpler specification UM -- 4.8. Since the results were virtually identical in all cases, only results based on the former measure are reported.

The monetary variable The monetary variable is defined as the actual-minus-equilibrium growth rate of the real money supply. For both countries money is defined as MI, and the price variable is the consumer price index. The equilibrium growth rate of the real money supply is that at which the impact of the real money supply on economic activity is neutral. In terms of an IS/LM diagram with the real interest rate on the vertical axis and detrended output on the horizontlal axis, the position of the LM curve is stable when the real money supply is growing at its equilibrium rate.

On the basis of the model of appendix 2, the empirical specification of this equilibrium growth rate is as follows:

t = b - yAApt+e + Aht,

where -y is the estimated interest elasticity of demand for money, /Apt+l e is the first difference of an estimate of the expected inflation rate between t and t + 1, ht is an estimate of shifts in the demand for MI as a result of financial innovations, and b is a constant term which satisfies the condition that the mean growth rate of (m - p) is equal to the mean growth rate of yt over the period of estimation. Only Canadian MI has been adjusted for demand shifts, and equations will be estimated on the basis of both adjusted and unadjusted MI. The method of adjustment is very similar to that of Boothe and Poloz (1986). Appendix 3 provides details on the construction of all of the components of the estimated equilibrium growth rate of the real money supply.3

The fiscal / savings variable If there is complete discounting of future taxes, fiscal policy should be represented by a government spending variable instead of a deficit variable. This will be tested, as will the implied equality of the coefficients on the lagged first differences of BIYP and SIYP. The reason for including the personal

3 In fact, the empirical specification for Ajt differs slightly from the above equation due to in- corporation of the effects of the lagged dependent variable in the money demand equation (see appendix 3).



808 John McCallum

savings rate is that there has been much discussion of the upward drift of the Canadian rate since the mid-1970s, with analysts often mentioning federal government savings incentives as a possible source of this increase (see, e.g., Jump and Wilson, 1986). Corporate saving has not been included in the regressions, if only because it would appear to be dominated by cyclical effects. Owing to data limitations, the saving and budget balance variables are not adjusted for inflation. This may not be a very important shortcoming in the case of Canada, since the Jump / Wilson estimates suggest that the inflation adjustments for S and B tend to cancel each other out.

Relative world prices of Canadian exports Canada, unlike the United States, is a net beneficiary of rising world commodity prices, and casual observation suggests that the Canadian economy has performed well relative to the us during periods of high real commodity prices and poorly during periods of low commodity prices. Indeed, according to the staple approach, Canadian economic history is best understood through an analysis of the characteristics and relative prices of a handful of basic commodities such as fish, fur, forest products, minerals, and wheat. Consequently, in trying to identify sources of sectoral shifts in Canada, a variable capturing conditions in the resource sector would seem to be a natural place to start.

Ideally, one would like to define such a variable on the basis of the relative world prices of a basket of goods that corresponds to Canadian exports or production. Because of practical problems in constructing such an index, I adopt a short-cut definition that is based largely on the work of Longworth (1980, 1980a). Changes in the relative price of Canadian exports are broken down into three sources: (i) changes in Canada's relative unit labour costs; (ii) changes in world prices of resource products relative to world products of manufactured goods; and (iii) all other factors. As described in detail in appendix 3, the export price variable ARPX is defined as the sum of points (ii) and (iii), the assumption being that these 'other factors' reflect mainly changes in relative world prices of Canadian products.

Shocks to investment and employment in manufacturing durables The investment shock variable AIRES is an estimate of the exogenous component of the change in the ratio of real business fixed investment to potential GNP[A(I/ YP) ]. It is defined as the residual of a regression of A(I/ YP) on all the other explanatory variables of equation (1) except ZMANRES, plus a constant. LMANRES is an estimate of the exogenous component of the change in the ratio of employment in durable manufacturing to total employment (AmAN). It is defined as the residual of a regression of AmAN on all the other variables of equation (1), plus a constant.

The key assumption in these procedures is that causation runs from AIRES

and AMANRES to the unemployment rate rather than the other way around. In




TABLE I

UGAP regressions, Canada and the United States (t-statistics in brackets)

Canada United States

Eq (i) Eq (ii) Eq (iii) Eq (iv) Eq (v) U(GAP- i 0.76 (11.6) 0.62 (12.2) 0.53 (12.4) 0.44 (8.1) 0.52 (8.6) A(mn-P-u),. -0.052 (2.5) -0.063 (3.8) -0.26 (9.5) -0.28 (10.6) -0.29 (1 1.1) A[(B +S~) r]t-- 0.14 (1.6) 0.27 (4.1) 0.30 (4.0) AG -0.23 (3.3) -0.21 (3.1) ARULCt, 0.062 (3.1) 0.061 (4.2) 0.038 (3.3) 0.019 (1.4) 0.00 (0.0) /IRESt -0.39 (4.0) -0.35 (4.7) -0.63 (6.5) --0.53 (5.5) -0.38 (3.4) AUSD)I, 0.60 (4.7) 0.65 (7.0) ARPX,. -0.060 (2.1) -0.066 (3.1)

RPOILt 0.057 (6.3) 0.059 (7.0) 0.050 (5.9) AMANRESt -1.38 (6.3) -1.21 (5.7) --1.07 (5.1) Constant -0.15 (0.6) Trend 0.016 (1.3) D845 1.54 (4.6) D825 0.66 (2.3) 0.90 (3.2) Period of 1954-85 1954-85 1954-85 1954-85 1957-85 estimation SE 0.45 0.35 0.34 0.32 0.31 SSR 4.56 2.86 2.97 2.39 2.09 Q (3) 0.6 0.8 2.5 3.3 4.1 RZ2 0.947 0.968 0.946 0.955 0.957 F-tests (i) Break 3.9 (2.9) 0.6 (3.1) 1.6 (2.8) 0.4 (3.1) 0.6 (3.2)

after 1981 (ii) Exchange 0.5 (2.7) 1.2 (2.5) 1.3 (2.6) 0.8 (2.6) 0.5 (2.7)

rate regime 3.1 (2.7) 0.9 (2.6) 0.7 (2.6) 1.0 (2.6) 0.7 (2.7) (iii) Chow (iv) Constant 3.7 (3.4) 0.6 (3.4) 1.0 (3.4) 0.1 (3.4) 0.6 (3.5)

and coefficient on trend both zero

NOTES: I Q(3) is Box-Pierce Q-statistic with three lags. Criticad value at 95 per cent confidence level is 7.8.

2 Figures in brackets after F-statistics are critical values at 95 per cent confidence level. 3 Personal savings (S) are excluded from the fiscal variable in the case of the United

States.

the case of employment shocks, it has been conventional to attribute the residual variation of industry employment growth rates to sector-specific shocks and to assume that causation runs from these shocks to unemployment rather than vice versa. In the case of investment, the results were not sensitive to a more conservative approach which defined the investment shock variable net of the effect of contemporaneous non-investment GNP on AIRESt.

It should also be noted that because AIRES, and AMANRESt are orthogonal to the other explanatory variables by construction, the estimated coefficients on these other variables are not affected by the inclusion of AIRESt and AMANRESt.

Furthermore, as demonstrated by Pagan (1984, 232-3), OLs estimates of



810 John McCallum

equation (1) are correct, since the equation contains generated residuals but no generated predicted values and no lagged residuals or predicted values.

REGRESSION RESULTS

The preliminary regressions used to generate AIRES and AMANRES were much as expected and are reported in appendix table Al. Most of the explanatory variables played significant roles, and R2 ranged between 0.58 and 0.74. Table 1 reports two unemployment equations for Canada and three for the United States. All are estimated with annual data, and all except the last equation are estimated over the period 1954-85. (Because of data limitations, the us equations are estimated either for 1957-85 with the adjusted budget balance or for 1954-85 with a government spending variable.) The Canadian equations reported in the table are based on unadjusted MI, and AUSDt is a weighted average of changes in the us fiscal, monetary, investment, and real exchange rate variables. The weights are the estimated coefficients in the us equation reported in column (iii).

The equations reported in table 1 impose long-run neutrality with respect to all aggregate demand and sectoral variables (the regressors are entered as first differences). As noted above, the equations also impose the condition that all right-hand-side variables have the same relation between impact and long-run coefficients. These restrictions were tested by estimating equations in which the two components of all differenced variables were entered separately in level form. A further set of regressions added two additional lags on UGAP and / or an additional lag on all explanatory variables (e.g., the variable lARPXti - was replaced with RPXt -1, RPXt-2, and RPXt-3). In all of these cases and for both countries, the restrictions implied by the regressions of table 1 did not come close to being rejected.

Before commenting on individual coefficients, I examine the extent to which the equations can predict the events of the 1980s, as well as the hypothesis that frictional unemployment can be equated with the Gordon / Fortin NAIRU. The table reports four F-statistics at the bottom of each equation. Three of these test for structural breaks across exchange rate regimes, between the two halves of the sample period, and between the periods 1954-81 and 1982-5. The fourth statistic tests the proposition that both the constant term and the coefficient on a time trend are zero. Rejection of this hypothesis is taken to mean that frictional unemployment as estimated by the reduced forms cannot be equated with the Gordon / Fortin NAIRU estimates.4

The first equation indicates that the constant and time trend are jointly significant for Canada over the period 1954-85. However, the F-statistics indicate instability both between the two halves of the sample period and between 1954-81 and 1982-5. When the equation was estimated over the period 1954--81 and used to predict UGAP for 1982-5, the predictions for




the 1981-3 rise in the unemployment rate were very accurate, but the predicted 1983-5 fall in unemployment was much larger than the actual fall. Consequently, the equation reported in the second column adds a dummy variable (D845) that is set equal to one in 1984 and 1985 and otherwise zero. It can be seen that the coefficient on D845 is large and highly significant, that the stability of the equation increases dramatically, and that the time trend and constant are no longer significantly different from zero. In particular, the F-statistic of only 0.6 relating to the 1981-2 break suggests that no parameters other than the constant term have shifted in the -post-1982 period.

In short, up to 1983, Canada's unemployment experience is well explained, and Fortin's estimated NAIRU stands. On the other hand, the unexplained increase in the constant term in 1984-5 may or may not signify a rise in the natural unemployment rate. One possible explanation may lie in the concept of 'hysteresis' as discussed by Hargreaves Heap (1980), Blanchard and Summers (1985), and others. Also, my own research in progress indicates that virtually all the unexplained increase in unemployment has occurred in western Canada, suggesting that developments in the resource sector that are not captured by the export price variable ARPX may have played an important role.

The two us equations reported in columns (iii) and (iv) display a similar but less extreme pattern. The first of these equations indicates that zero values for the constant and time trend cannot be rejected, but there is a modest indication of structural shift after 1981. Sample predictions starting after 1981 indicate that the us unemployment rate in 1982-5 was consistently about one percentage point higher than predicted. This result is confirmed by the statistically significant coefficient on a dummy variable D825 as shown in equation (iv). Stability and explanatory power increase with the addition of this variable, but by less than for Canada. Equation (v), estimated using the alternative fiscal variable over the shorter sample period, provides further confirmation of this result.

The estimated coefficients are consistent with the expectation that coefficients on domestic (external) variables should be smaller (larger) for the more open economy (Canada). Another point that tends to increase confidence in the coefficients is that most of them are similar to those that I estimated in another study (McCallum, 1986) which used similar explanatory variables but an entirely different methodology.5 The coefficients on AMANRES imply that 100 permanent job losses in durable manufacturing result in some 120 people becoming unemployed in that year, with this amount of unemployment subsequently declining at a rate of some 40 to 50 per cent per year.

4 An alternative test of the Fortin NAIRU would be to include not only a constant and a time trend as additional regressors, but also the other labour market variables that Fortin includes in his regression (the Z-variables of equation (2) of this paper). If only because these Z-variables are so numerous, the Fortin results fared better under this alternative test than under the simpler tests reported in table 1.



812 John McCallum

TABLE 2

Decompositions of variance of UGAP, 1954-85 (percentages)

Proportion explained by: Canada United States

A. Monetary variables 45% 39% Non-monetary variables 25% 38%

B. Domestic policy variables 19% 44% Non-policy variables 51% 35%

C. Aggregate demand variables 100% 64% Sectoral variables 4% 25%

D. Domestic variables 36% NA

External variables 36% NA

NOTES: I The calculations are based on equations (ii) and (iv) of table 1. 2 The total variation to be explained excludes the effects of the error term and the dummy

variables D845 and D825. Each pair sums to 100 per cent if the interaction term is zero.

3 For Canada, 'monetary variables' include both us and Canadian monetary variables; 'domestic policy variables' include domestic fiscal and monetary variables; 'sectoral variables' include only the export price variable; and 'external variables' include the export price and us aggregate demand variables. us variables are classified according to the same principles.

Sensitivity tests Several additional specifications of these equations were tested. The budget surplus variable consistently outperformed the government spending variable, the latter not playing a statistically significant role when the former was also included in the regression. When the components of the monetary variable, the composite us aggregate demand variable AUSDt, or the Canadian fiscal / savings variable were entered separately, the constraints imposed in the reported regressions did not come close to being rejected. There were no substantive changes when the us monetary variable alone was used instead of AUSD, although the other components of us aggregate demand did contribute significantly to explanatory power. Also, the coefficients on the Canadian monetary variable adjusted for demand shifts were much the same as the reported coefficients on the unadjusted variable (see below for how this adjustment influences the estimated effects of Canadian monetary policy on unemployment). Neither was there any significant change when the Canadian monetary variable was redefined to include only the component that could not be explained by the us monetary variable.6 Neither the oil price variable nor the Canadian version of lAMANRES played significant roles when added to the Canadian equations. Finally, the Lilien / Samson dispersion indexes had no significant effect when they were added to the equations, which suggests that the effects of sectoral shifts seem to be represented adequately by the specific

5 This study estimates a single equation in which the dependent variable is the change in the unemployment rate in each of eighteen OECD countries in each of the five years 1980-4 (i.e., ninety observations). The regression incorporates country-specific structural parameters allowing for differences in Okun's Law coefficients and the degree of openness.




sectoral variables Z\RPXt, LARPOILt11, and AMANRESP.

ANALYSIS OF THE RESULTS

This section begins with an analysis applying to the period 1954-85 as a whole and then examines the events of the 1980s in more detail. Table 2 begins by defining four different pairings of the variables: monetary versus non-monetary variables, policy versus non-policy, aggregate demand versus sectoral, and domestic versus external. For each of these pairings separately the table indicates the proportion of the total variance of UGAP over the period 1954-85 that is explained directly by each of the two sets of variables.7 For example, us monetary and non-monetary variables accounted directly for, respectively, 39 per cent and 38 per cent of the variance of UGAP, with the remaining 23 per cent due to the interaction term.

The results for both countries have a strong 'monetarist' flavour, not only because the monetary variables have been the principal source of the business cycle,8 but also because macro-economic policy has been strongly pro-cyclical. The results cannot be said to support a 'Keynesian' emphasis on the role of exogenous investment shocks.9 The pro-cyclical nature of policy is quite striking: all other things equal (i.e., ignoring the Lucas critique), zero variance for domestic policy variables would have reduced the variance of UGAP by 49 per cent for Canada and 65 per cent for the United States. It might be noted, however, that in the case of Canada this result is sensitive to the period under review, with policy variables very strongly pro-cyclical in the 1 980s and moderately counter-cyclical in the 1970s. The table also indicates that sectoral variables have accounted directly for about one quarter of the variance of UcGAP for the United States but only 4 per cent for Canada. The us result is about

6 This test was conducted in response to a comment from Steve Poloz, who suggested that lagged changes in the Canadian real money supply may overstate the effects of Canadian policy to the extent that Canadian policy merely follows us policy. Although this point poses less of a problem when both countries' monetary variables are included in the Canadi- an equation, nevertheless the point was addressed by redefining Canadian money supply growth as the residual of a regression of Canadian money supply growth on us money supply growth. While the estimated coefficient was close to one, R2 was only about 0.2, and this procedure had negligible effects on the simulated effects of the Canadian monetary variable. (The reason is that us money growth has been much less volatile than Canadian money growth, with the result that the relatively low Canadian coefficient multiplied by the us money growth rate gives a series that shows very little variation.)

7 All of the decompositions are based on simulations of UGAP over the period 1954-85, beginning with the case in which all explanatory variables are set equal to zero and then adding the effects of each variable in subsequent simulations. There is a small unattributed effect owing to the fact that UGAP was not zero in 1953, but it becomes very close to zero from 1956 onwards.

8 The role of the us monetary variable is even stronger if one compares the relative importance of is shifts and LM shifts in accounting for variations in UcGAP due to all aggregate demand variables. The results for the United States indicate that LM shifts accounted directly for 60 per cent of the total variance, compared with 19 per cent for is shifts and 21 per cent for the interaction term.



814 John McCallum

4

3 -Total gap

-Gap adjusted 2 , for different

NAIRUS

-2 -

-3 -, Th?e components of adjustedgawp:

| < \ _ r -Scc~~~~~~~~~~~~~~~~etoral \ \ | ~~~~~~~variables

0 |- _- -Aggregate /<demad

,l , ~~variables

: > , X \< . 0 ,| ~~~~~~~~~~~~~~variables

/ I V / |-Unexplained

l1955 1 960 1 965 1 970 1 975 1 980 1985 i

FIGURE I Canada-us unemployment rate gap, 1954i85 (in percentage points)

halfway between the Lilien (1982) conclusion that sectoral shifts have been the single most important factor and the Abrahiam I Katz (1984) conclusion that such shifts have had no significant effects on unemployment.

Another perspective is provided by figure 1, which plots the components of the Canada-us unemployment gap over the period 1954o85. The chart includes

9 For both countries, the investment shock term accounted for only 5 per cent of the total variance of UGAP over the full period 1954-85, although the Canadian figure is considerably higher at 14 per cent for the first half of the period. This does not imply that fluctuations in investment have been unimportant, but only that the component of invrestment fluctuations that cannot be explained by macro-economc policy, oil prices, etc, appe-ars to have played a minor role.




series for the actual gap, the gap adjusted for differences in NAIRU, and the components of the gap attributable to sectoral variables and aggregate demand variables. The subcomponent of the aggregate demand series that is due to fiscal and monetary policy is also set out in the chart. It should be noted that the effect of, say, monetary policy on the unemployment gap is defined as the effect of Canadian and us monetary policy on Canadian unemployment minus the effect of us monetary policy on us unemployment.

Three main points from this chart may be highlighted. First, it can be seen that a significant gap between the two countries' NAIRUS starts to open up in the late 1960s, but the gap has been closed by the end of the period in 1985. This is because of a relatively stable us NAIRU in combination with a Canadian NAIRU that rises from 6 per cent in 1970 to a peak of 7.8 per cent in 1977-8 and then falls to a low of 6.2 per cent in 1985. This bell-shaped profile is due to a similar profile for the structural variables on which Fortin's estimated NAIRU iS based, notably a minimum wage variable, the weight of young people in the total labour force, and a variable measuring the generosity of the unemployment insurance program. The second point to note is that the sectoral variables have played a central role in explaining fluctuations in the difference between unemployment rates in the two countries, despite the modest role of these variables for each country in isolation. Because the two periods of rising oil prices were also the two periods of rising world prices for Canadian exports, the sectoral variables contribute an estimated -2 percentage points to the Canada-us unemployment gap in 1975 and --2.5 percentage points in 1981. Finally, the table indicates that Canada managed to avoid the us recession of the mid-1970s because of a combination of favourable sectoral variables and much more expansionary fiscal and monetary policy in Canada than in the United States.

Sources of rising unemployment in the 1980s Table 3 sets out four components of each country's unemployment rate over the period 1981-5: frictional, structural, aggregate demand, and unexplained. (Recall, however, the caveat regarding such classifications that was noted in the introduction.) The table indicates that most of the very large increase in Canadian unemployment between 1981 and 1983 was due to aggregate demand variables, although unfavourable export prices also played a part. Within the aggregate demand category, it can be seen that the us recession, tight monetary policy, and an appreciating real exchange rate were the main factors at work. However, conclusions with respect to the role of monetary policy are uncertain because of the important effects of the adjustment for money demand shifts, and also because an unknown fraction of the real exchange rate effects might be attributed to monetary policy. Fiscal policy made a small contribution to rising unemployment in 1981-2, but this was more than offset in 1982-5.

The gap between the two countries' unemployment rates peaked at 3.8 percentage points in 1984, with estimated components as follows: different



816 John McCallum

TABLE 3

Decompositions of Canadian and US unemployment rates, 1981-5'

1981 1982 1983 1984 1985

United States Frictional 5.9 6.0 6.0 6.0 6.0 Structural 2.0 1.2 0.0 0.4 0.3 Keynesian -0.3 1.9 2.5 0.3 -0.3 Unexplained 0.0 0.6 1.0 0.8 1.2

Total 7.6 9.7 9.6 7.5 7.2

Canada Frictional 7.3 7.4 7.1 6.7 6.2 Structural -0.6 -0.3 0.1 0.4 0.3 Keynesian 0.2 3.3 4.2 2.1 0.9 Unexplained 0.6 0.6 0.5 2.1 3.1

Total 7.5 11.0 11.9 11.3 10.5

Keynesian Components -0.3 1.3 2.0 (.8 0.4

US Demand 0.4 0.8 1.5 1.( 1.0 Monetary policyb (0.2) (0.2) (0.8) (0.5) (0.6) Fiscal policy 0.0 0.2 0.1 -0.2 -0.5 Real exchange rate -0.3 0.2 0.5 0.5 0.3

Investment 0.1 0.2 -0.4 0.1 -0.1 Personal saving 0.3 0.6 0.5 -0. 1 -0.2

Total 0.2 3.3 4.2 2.1 0.9

a The decompositions are based on equations (ii) and (iv) in table 1. The frictional components are equal to the Gordon/Fortin NAIRUS; the Keynesian components are as indicated for Canada; the structural components include the effects of oil prices and durables employment shocks for the United States and export price variable for Canada; and the unexplained components include the effects of the residuals and the dummy variables.

b The figures in parentheses are estimates based on Ml adjusted for demand shifts (see appendix 3).

NAIRUS, 0.7; sectoral variables, 0.0; macro policy, 1.1; other aggregate demand variables, 0.6; and error term, 1.4. However, the residual component increases to a substantial 1.9 percentage points in 1985, and it has been seen that the reasons for the relatively slow decline in Canadian unemployment after 1983 remain unidentified.

CONCLUSIONS

If one ends the story in 1983, the results are straightforward. The Fortin NAIRU

estimates (7.1 per cent in 1983) can be equated with the frictional unemployment rate as estimated by the reduced form. The sectoral component due to changing world prices of Canadian exports is statistically significant but generally of modest importance. Ninety per cent of the 4.4 percentage point increase in the Canadian unemployment rate between 1981 and 1983 can be attributed to specific aggregate demand variables, with the remainder due to falling commodity prices. These results strengthen the Fortin NAIRU estimates




by allowing one to pinpoint the sources of the unemployment gap. They also strengthen the intersectoral shift hypothesis in the sense that specific sources of such shifts have been identified for both countries. However, while the sectoral variables play a key role in explaining changes in the gap between Canadian and us unemployment rates, their role in explaining each country's own unemployment rate is distinctly secondary in relation to aggregate demand variables. On a less positive note, the analysis provides no explanation for the relatively slow decline in Canadian unemployment since 1983: the regressions indicate a large jump in the constant term for 1984-5, with all other coefficients remaining unchanged.

Finally, while this last point does not come easily to one who spent his formative undergraduate years under the influence of Joan Robinson and Nicholas Kaldor, it is clear that a byproduct of this paper is support for three characteristically 'monetarist' positions: that macro policy has tended to be destabilizing, that monetary variables are the prime determinants of the business cycle, and that exogenous investment shocks have usually been of minor importance. Providing the monetary variable is defined on a continental basis, all three of these propositions receive strong support from the results for both Canada and the United States.

APPENDIX 1: DEFINITIONS AND) SOURCES OF VARIABLES

Most of the data are from Economic Report of the President, 1985 for the United States and Department of Finance, Economic Review, April 1985. These sources are designated respectively ERP and ER

U: Aggregate unemployment rate: Canada, ER, 103 (pre-1966 data from CANSIM); us, ERP, 266 (civilian workers)

UGAP: U minus estimated NAIRU, from Fortin (1988) for Canada and Gordon (1985) for United States. The Fortin series begins in 1961, and Canada's NAIRU

for 195340 was set equal to its 1961 value

Am: Annual percentage growth rate of MI. For Canada, from Bank of Canada. For United States: pre-1955 from Barro (1981, 155); post-1954 from International Monetary Fund, International Financial Statistics Yearbook 1984 (series 34x)

Ap: Annual percentage growth rate of consumer price index, from ERP, 291 and ER, 120

Az: See appendix 2

B! YP: Cyclically adjusted budget balance as per cent of cyclically adjusted GNP. For Canada, from ER, 129 (all governments) and for United States, from Survey of Current Business, December 1983, 32-3, col. 2 (federal government only)



818 John McCallum

SI YP: Defined as PS/(PGNP X YP), where Ps is nominal value of personal savings and PGNP iS GNP deflator. For both countries the potential output series used for the savings and investment variables is obtained from a regression of the log of real GNP on time and the square of time over the period 1952-85. PS

and PGNP are from ER, 86, 118

G: Real government purchases of goods and services from ERP, 235

I: Real gross private fixed investment from ERP, 234 and ER, 68

ARULC: Percentage change in unit labour costs in manufacturing relative to a weighted average of six trading partners, expressed in a common currency. For both countries 1960-83: us Department of Labor, Bureau of Labor Statistics, 'International Comparisons of manufacturing productivity and labor cost trends,' mimeo, 1984. Updated to 1984 from IMF, International Financial Statistics Yearbook 1985. Pre-1960 Canada: based on comparison with us unit labour costs only. Pre-1960 United States: set equal to zero

ARPX: For details of construction, see appendix 2. The relative world price of resource goods is defined as the price index for 'Crude materials for further processing' divided by the index for 'Finished consumer goods excluding food.' Both series from us producer price index, ERP, 297-8

ARPEN: First difference of 100 (PE/PC) where PE iS the energy price component of the us consumer price index and Pc is the consumer price index. From ERP, 294 (pre-1958: based on fuel price component of producer price index)

AMAN: First difference of employment in durable manufacturing as per cent of total employment, from ERP, 275

APPENDIX 2: STRUCTURAL MODEL

One possible derivation of equation (1) is given by the following five-equation model:

AYGAP -aAr + Au (is curve) (i)

A(M - p) 8/A(YGAP + yP)

- y A(r + Ap?+e) + Ah (LM curve) (ii)

AP =A/jpe - SUGAP + AZ (Phillips curve) (iii)

Ape 2 Ap1i + ... (Inflation expectations) (iv)

UGAP = - 4/YGAP (Okun's Law equation) (v)

New variables include the real interest rate (r), the logarithm of potential output (yP), the difference between the logarithms of actual and potential output




TABLE Al

Investment and durables employment regressions (t-statistics in brackets)

Canada

A(I/YP)t = -0.045 - 0.01 1UGAP, - 0.001 A(Mi - p - II)t_I - 0.33 A[ (B + S)/YP]t _1 (0.3) (0. 1) (0.0) (2.0)

- 0.046 ARULC_I - 0.85 AUSDt + 0.18 ARPXt-1 (1.3) (3.8) (3.3)

1954-85 RT = 0.58 SE 0. 89 Dw 1.65

United States

(i) A(I/YP)t = 0.012 + 0.44 UGAP,_I + 0.17 A(m - p )t- I 0.21 A(G/Y)t (0. ) (5.0) (3.0) (1.3)

- 0.008 ARULCt__I - 0.055 ARPOIL,_1

(0.4) (2.9)

1954-85 R = 0.62 SE = 0. 70 I)W = 2.05

(ii) AMANt -0.17 + 0.18 UGAPt-I + 0.1 1 A(m - p - /.L)t + 0.16 A(G/ YP)t (2.7) (4.6) (4.5) (2.2)

-- 0.027 ARULCt_I - 0.017 ARPOILt-1 + 0.27 AIRESt

(2.6) (2.1) (3.1) 2

1954-85 R = 0.74 SE = DW = 1.95

(YGAP), the expected inflation rate (Ape), and the shock terms u, h, and z. Equations (i) and (ii) are first differences of standard is and L.M curves

(notice that YGAP + Y is the logarithm of actual output and r + Ap + Ie is the nominal interest rate), equation (iii) is an expectations-augmented price Phillips curve, equation (iv) states that expected inflation is given by a distributed lag on past inflation rates and perhaps other variables, and equation (v) is an Okun's Law equation. In his Phillips curve work based on annual data, Fortin (1988) finds support for the simple specification Ape = lp-1. Under this assumption, the model can be solved to give the following expression for UGAP:

UJGAP XOUGAP- - XI A(m - p - -- I AA(m -

- X2AU + XIAZ, (vi)

where Ali = 83AyP - yAAp?+ e + Ah, X0 = &2[y + a8), X =-- 2a4l, X2 =WY and Q = (y + a,8 + a438)-- . This is consistent with equation (1) of the text, except that the variable involving current money supply growth has been excluded. The various aggregate demand variables are incorporated in Au. A few price shock variables corresponding to Az were tried, but with the exception of the oil price variable in the us regressions, they did not appear to play a significant role, perhaps because of multicollinearity with the monetary variable.



820 John McCallum

APPENDIX 3: SPECIFICATION OF MONETARY AND EXPORT PRICE

VARIABLES

Monetary variable Following Boothe and Poloz (1986), the impact of financial innovations on the demand for MI was approximated by three dummy variables set equal to one beginning in 1976, 1979, and 1981. The following money demand equation was estimated using annual data over the period 1953-84 (with t-statistics in parentheses):

log (M/P)t = 1.47 + 0.56 log (M/P)t_- - 0.071 log it + 0.40 log Yt (3.5) (6.6) (5.7) (6.8)

-0.033 D76 -0.027 D79 - 0.082 D81

(2.4) (1.5) (3.7)

R2 = 0.99 Standard error = 0.0229 p = -0.42 (2.1)

M is MI, P is the consumer price index, i is the ninety-day treasury bill rate, and Y is real GNP. The adjustment to MI was the difference between simulated MIP with and without the dummy variables.

An expected inflation series was generated by regressing the annual inflation rate on two lagged values of the Canadian inflation rate and the MI growth rate, as well as two lagged values of the us treasury bill rate (other variables were initially tried and then discarded because of low significance levels). The expected inflation component of l\i incorporates the effect of the lagged dependent variable in the money demand equation and is defined as the first difference of 0.56 Apte - Apt+?e. The unit coefficient on Apte is consistent with the estimated interest elasticity when the interest rate is 7.1 per cent. The same procedures were also carried out for the United States, except that no demand shift dummy variables were included in the us money demand equation.

Export price variable Assume first that the logarithm of the price level of Canadian exports (Px) is given by a weighted average of the logarithms of: (i) world prices of resource products adjusted for the exchange rate (PWR + e); (ii) world prices of manufactured goods adjusted for the exchange rate (PWM + e); and (iii) domestic unit labour costs (ULC). The logarithm of the Canadian GNP deflator (py) is given by a weighted average of the same three variables but with different weights.

Hence the logarithm of the price of exports relative to the GNP deflator may be written:

PX - PY = ao(PWR + e) + a, ULC - (ao + al)(PwM + e),

where a0 is the weight of resource goods subject to world prices in the export




price index minus the weight of such goods in the GNP deflator (a0 > 0) and al is defined in the same way for unit labour costs (a1 < 0). Since the three weights of each price index sum to one, the three coefficients in the relative price equation must sum to zero.

Now, assuming that PWM may be approximated by world unit labour costs (WULC) and adding an error term to the equation, one obtains the following expression:

Px - py = ao(PWR - PWM) + a 1 (ULC - WULC - e) + 1.

This equation was estimated in first-difference form over the period 1953-84 with A(PWR - PwM) lagged one year and A(ULC - WULC - e) unlagged. The estimated coefficients and standard errors were a0 = 0.41 (0057) and

a, = -0.32 (0.077), with R2 = 0.70. Consequently, the export price variable ARPX was defined as 0.41 A(PWR - PWM)-I + A .

In practice, the two components of ARPXt - were of about equal importance in the unemployment equations, and when they were entered as separate variables, the two coefficients were of very similar size. If, as in an earlier version of this paper, the export price variable is defined simply as the lagged value of A(Px - PY), then the role of this variable in the unemployment equations becomes much more important. However, as can be seen from the above derivation, this is an inappropriate procedure, since the effects of /A(Px - PY) incorporate both the relative world price effect and the competitiveness effect.

REFERENCES

Abraham, Katherine G. and Lawrence F. Katz (1986) 'Cyclical unemployment: sectoral shifts or aggregate disturbances?' Journal of Political Economy 94, Pt 1, 507-22

Barro, Robert J. (1981) 'Unanticipated money growth and economic activity in the United States.' In Money, expectations and business cycles (New York: Academic Press)

Beach, C.M. and S.F. Kaliski (1986) 'Structural unemployment: demographic change or industrial structure?' Canadian Public Policy 12, 356-67

Blanchard, 0. and L. Summers (1986) 'Hysteresis and the European unemployment problem.' NBER Working Paper No. 1950

Boothe, Paul and Stephen S. Poloz (1986) 'Unstable money demand and dynamic exchange rate models.' Paper presented at Meetings of Canadian Economics Asso- ciation, Winnipeg, May

Demery, David (1984) 'Aggregate demand, rational expectations and real output: some new evidence for the U.K. 1963.2-1983.2.' Economic Journal 94, 847-62

Fortin, Pierre (1988) 'How "natural" is Canada's high unemployment rate?T European Economic Review, forthcoming

Gordon, Robert J. (1982) 'Price inertia and policy ineffectiveness in the United States, 1890-1980.' Journal of Political Economy 90, 1087-117 (1985) 'Understanding inflation in the 1980s.' Brookings Papers on Economic Activ- ity 1, 263-99



822 John McCallum

Gordon, Robert J. and John M. Veitch (1984) 'Fixed investment in the American business cycle, 1919-83.' NBER Working Paper No. 1426

Hargreaves Heap, S.P. (1980) 'Choosing the wrong "natural" rate: accelerating inflation or decelerating employment and growth?' Economic Journal 90, 611-20

Jump, Gregory V. and Thomas A. Wilson (1986) 'L'epargne au Canada: retrospective et prospective.' In John Sargent, ed., La croissance economique: Sesfacteurs determinants et ses perspectives (McDonald Commission)

Landon, Stuart (1985) 'Sectoral shifts and aggregate unemployment in Canada: a re- examination of the evidence.' Mimeo, University of Alberta

Lilien, David M. (1982) 'Sectoral shifts and cyclical unemployment.' Journal of Politi- cal Economy 90, 777-93 (1982a) 'A sectoral model of the business cycle.' University of Southern California, Modelling Research Group Working Paper No. 8231

Longworth, David (1980) 'The determinants of the Canadian terms of trade.' Mimeo, Bank of Canada (1980a) 'The terms of trade: the Canadian experience in the 1970s.' Bank of Cana- da Review, January

McCallum, Bennett (1979) 'On the observational inequivalence of classical and Keynesian models.' Journal of Political Economy 82, 395-402

McCallum, John (1986) 'Unemployment in OECD countries in the 1980s.' Economic Journal 96, December

- (1986a) 'A test of four competing theories of the business cycle.' Departement des sciences economiques, Universite du Quebec a Montreal, Cahier No. 8610D

McGee, Robert T. and Richard T. Stasiak (1985) 'Does anticipated money matter? Another look.' Journal of Money, Credit, and Banking 17, 16-27

Pagan, Adrian (1984) 'Econometric issues in the analysis of regressions with general- ized regressors.' International Economic Review 25, 221-47

Samson, Lucie (1985) 'A study of the impact of sectoral shifts on aggregate unemployment in Canada.' This JOURNAL 18, 518-30



Documents

Unemployment in Canada and the United States