ELSEVIER European Economic Review 41 (1997) 535-547

Assessing the Natural Rate Hypothesis

Challenges facing natural rate theory

Marco Bianchi a, Gylfi Zoega b,*

a Bank of England, Monetary Analysis, Threadneedle Street, London. UK ’ Department of Economics, Birkbeck College, 7-15 Gresse Street, London WIP 2LL., UK

Abstract

This paper attempts to test the natural rate hypothesis by looking at historical unemploy- ment data for France, the UK and the US. We find that the unemployment series can be described as stationary around an infrequently changing mean. Moreover, that the speed of convergence towards mean unemployment is slower when unemployment is high and differs across the three countries: the two European countries having more persistence. We do not find any evidence that the persistence of a change in unemployment is a function of the size of the change. We conclude that the data are consistent with multiple equilibria models where large shocks bring the economy from one equilibrium to another, and also with models with a moving natural rate. 0 1997 Elsevier Science B.V.

JEL classijication: C22; E24; E32

Keywords: Unemployment persistence; Shifting-mean-value model; Markov switching-regression model

1. Introduction

The European unemployment experience in the past twenty years has chal- lenged pervious orthodoxy and generated a renewed interest in the causes of

medium-run changes in unemployment. The result has been a spiralling literature culminating in a series of monographs by, amongst others, Lindbeck and Snower (1988), Pissarides (19901, Summers (19901, Layard et al. (1991) and Phelps (1994). At the centre of this debate lies the notion of a natural rate of unemploy-

ment.

* Corresponding author. Fax: (+44) 171 631 6416; e-mail: gzoega@economics.bbk.ac.uk.

0014-2921/97/$17.00 Copyright 0 1997 Elsevier Science B.V. All rights reserved.

PII SOO14-2921(97)00020-2

536 M. Bianchi, G. Zoega/ European Economic Review 41 (1997) 535-547

The objective of this paper is to attempt to assess the empirical validity of the

natural rate hypothesis proposed by Friedman (1968) and Phelps (1967, 1968). This hypothesis consists of two key propositions. First, in a hypothetical steady state, the equilibrium volume of unemployment, that is, the level consistent with correct expectations of wages etc., is unique and is independent of current and past

monetary variables. The natural rate hypothesis thus draws on the classical dichotomy that real variables are determined by tastes and technology while the supply of money only affects unemployment and real output in the short run; in the long run only prices are affected. Second, expectations tend to correct

themselves sooner or later so that actual unemployment tends sooner or later to converge toward the natural rate.

Any rejection of the natural rate hypothesis necessarily consists of refuting one or both of its basic tenets. In this paper we look directly at these two main tenets and, instead of estimating a given economic model of either the natural rate or persistent divergences away from it, we will look at unemployment series over long periods of time and attempt to test the two propositions directly.

2. The state of the debate

Following its conception, the natural rate of unemployment was taken to be a constant, and hence not suspectable to changes in macroeconomic policy. The presumption of a constant natural rate was maintained in some early empirical

work, such as Barro (1977, 1978). He does take into account demographic effects on the natural rate. However, no such thing was implied in the initial formulation by Friedman (1968) and Phelps (1967, 1968). But, importantly, the determinants of the natural rate were not given much attention. An exception is the discussion by Phelps (1968) of the influence of the rate of growth of the labour force. A higher rate of growth was supposed to raise the natural rate because of a rising marginal cost of training new workers. But in the absence of any theory describing the determination of the natural rate, hence reasons for its changes over time, the natural rate was in practice taken to be a constant.

The main line of attack against the natural rate hypothesis has consisted of a number of models which attempted to derive hysteresis in unemployment. Hys- teresis was initially taken to mean an effect of unemployment history on the natural rate itself (Phelps, 1972). By contrast, slow adjustment toward a unique natural rate was described as persistence of unemployment. But in practice, the models used in the 1980s did not make a clear distinction between these two terms. ’ Layard et al. (1991) use the term partial hysteresis if the sum of

’ Lindbeck and Snower (1989) are one exception, describing hysteresis as the existence of a unit root in unemployment while persistence referred to the case when the sum of significant coefficients in

an autoregressive process of the unemployment rate was high, but summed to less than one.

M. Bianchi, G. Zoega/ European Economic Review 41 (1997) 535-547 537

significant coefficients in an autoregressive process is high but less than one and pure hysteresis if it equals one. The terms hysteresis and persistence thus became practically indistinguishable.

It is important to note that it is only in the case of genuine hysteresis that the natural rate hypothesis is violated. In the case of persistence it is implied that actual unemployment converges slowly towards a given equilibrium path and/or that it converges slowly along an equilibrium path towards the natural rate. Neither creates any difficulty for the natural rate hypothesis although, we must admit, very slow convergence makes it less relevant.

The main hysteresis models evolved around physical capital (Modigliani, 1987), insider-outsider relations (Lindbeck and Snower, 1986; Blanchard and Summers, 1986) and human capital. Recessions are assumed to affect the human capital of those unemployed (Okun, 1973; Layard and Bean, 1989; Pissarides, 1992), the search effectiveness of the unemployed (Layard and Nickell, 1987) or at least the perception of employees of the unemployed (Blanchard and Diamond, 1994): the effective labour force is reduced.

The defence of the natural rate hypothesis has consisted of attempts at finding (nonmonetary) variables which could have caused the natural rate to change over time. Examples include energy prices (Bruno and Sachs, 1985), payroll taxes, the level and the rate of growth of productivity (Pissarides, 1990; Manning, 1991), real interest rates (Hoon and Phelps, 1992), international trade (Sachs and Shatz, 1994; Wood, 19941, and union activity. As it is clear that in the long run unemployment is stationary - it never hits either one or zero - while over shorter periods it has often been taken to be nonstationary, possible causal variables should have this property. ’

In this paper we do not estimate a particular model of hysteresis (as, for example, Blanchard and Summers, 1986) or changes in the natural rate (as, for example, Phelps, 1994). Instead, we want to look at the time-series properties of unemployment in three countries - France, the UK and the US - over a period of more than one hundred years. This is done in order to prevent the appearance of small sample results but a unit root in unemployment frequently arises for sufficiently short time series. We fit a statistical model to each series and on that basis attempt to judge the empirical plausibility of the natural rate hypothesis.

3. Hypotheses

Our starting point is the expectations-augmented Phillips curve of Friedman and Phelps,

w=f(u-u’) +we, f’(.) CO, (1)

2 Darby and Wren-Lewis (1993) attempt to find a cointegrating relationship between u and a set of

‘structural’ characteristics for the UK economy, 1954-1989.

538 M. Bianchi, G. Zoega / European Economic Reuiew 41 (1997) 535-547

where w denotes the log of the nominal wage, u is the rate of unemployment and

U* is the natural rate of unemployment. Wages are equal to expected wages plus an effect of the unemployment rate. If unemployment is below (above) the natural rate, wages are higher (lower) than expected. Assuming a linear form for the function f( . ) and subtracting lagged wages from both sides gives

u=u* -(‘rr-,rP). (2)

Assuming adaptive expectations, we get the standard result that unemployment can only be brought below the natural rate if there is accelerating (nominal wage)

inflation. Hysteresis affects the natural rate by definition. We write

u, * =u* *

f +g(+ (3)

where u is a vector of past unemployment rates. The part of the natural rate which is independent of unemployment history, u * * , has here been separated out from

the one which is path-dependent. The natural rate is determined by the intersection of a labour demand curve and

a wage curve, 3 the latter reflecting real wage rigidity. Adopting the human capital

models, the depreciation of human capital would affect the position of the wage curve: u* * would then denote the rate of unemployment which would arise if the wage curve had not been affected by past unemployment history - all workers maintained their potential ability level - while g(u) is the additional unemploy- ment which is created by human capital depreciation among the unemployed; the wage curve is shifted towards the origin. 4 Importantly, we put a subscript t on U * * to indicate that it can change over time for reasons unrelated to past unemployment history.

While there is nothing to prevent us from imagining nonlinear path-depen- dence, in practice only linear functional forms have been used. As an example of nonlinear path-dependence, this could arise in the insider-outsider model if membership rules were made endogenous such that the recently unemployed were more likely to lose their membership status, the more numerous they were.

Keeping to linear path-dependence, we get

g(U) = kPi’,-i. (4)

i= I

Hysteresis implies that the /3’s sum to one. However, if they sum to a high number which is nevertheless significantly lower than one, u * can be looked at as a short-run equilibrium which gradually converges towards its steady state.

3 The curve can be derived in both efficiency wage models and models with labour unions.

4 In a shirking model (such as Shapiro and Stiglitz, 1984). this would be caused by employed workers fearing dismissal less because they knew that those unemployed did not match their abilities -

a new job would not be very difficult to find.

M. Bianchi, G. Zoega / European Economic Review 41(1997) 535-547 539

Combining Eqs. (2)-(4) and assuming rational expectations; w = +ve + 7,

where 7 is an i.i.d. expectations error, gives what we call the sh$r&-mean-o&e model:

ut=tt:*(Sj)+ ~&u,_~+TJ, q-i.i.d.(O,qZ), i= 1 (5)

r(i)+lItl7~(i+l), i=O,l,..., n, j=l,..., m, mln+l,

where: m is the number of states in unemployment (for example the state of low and the state of high unemployment); u * * (Sj> is the mean rate of unemployment in state Sj, in the subsample m(i) + 1 to GT(~ + l), with ~(0) = 0 and rr(n + 1) = T; n is the number of mean shifts in the series as the result of large shocks occurring infrequently at time ~(11,. . . ,dn).

The specification of Eq. (5) is consistent with models of unemployment hysteresis. Thus Layard et al. (1991) end up with a reduced form equation very similar to Eq. (5) with 77 approximated by the first difference of the inflation rate

and only one lag of the unemployment rate included. A basic finding is that by limiting the duration of unemployment benefits and hence preventing the creation of long-term unemployment, the skill erosion of unemployed workers is limited and hence the persistence of unemployment; the lags become less important.

Eq. (5) is also consistent with the alternative approach of explaining changes in U * * . In Phelps (1994), the variable u * * is replaced by a function of real variables taken from his recent natural rate models. His results suggest that taxes on labour income, both direct income taxes and payroll taxes, the world real rate of interest (which affects the shadow price of workers in his model) and the real price of oil (see also Bruno and Sachs, 1985) explain most of the decade to decade changes in unemployment. The lags receive less attention. Bean (1994) estimates an almost identical equation, 5 but puts the emphasis on explaining the determinants of the lagged effects, following in tbe footsteps of Layard et al. (1991). He finds that the

duration of unemployment benefits and the fraction of manufacturing employees of short tenure have the greatest explanatory power. He concludes that hiring and

firing costs, on the demand side, and human capital effects, on the supply side, are the most important reasons for unemployment persistence.

4. Historical data

Our econometric approach consists of, first, estimating the shifting-mean-value

model, Eq. (5), using the Markov switching-regression model, and, second, testing

’ The main difference lies in his use of changes in the rate of growth of world nominal GDP as a

measure of demand shocks while Phelps uses the first difference of the inflation rate.

540 M. Bianchi, G. &ega/European Economic Review 41(1997) 535-547

for nonlinear path-dependence. By estimating the shifting-mean-value model we

can test if it is more likely that infrequent changes in mean unemployment, u * * , or the effect of lagged unemployment - hysteresis - can account for the medium-

to long-run changes in unemployment. But as we have mentioned, monetary factors could also affect the natural rate in a nonlinear fashion. So we test separately for nonlinearities in the relationship between the coefficient of lagged unemployment and the size of the shocks, measured by the estimated residuals, holding u * * constant.

4.1. Estimation of the shifting-mean-value model

Fig. 1 has the historical unemployment plots for our three countries. The

French data are from 1894 to 1994, the UK data from 1855 to 1994 and the US data from 1890 to 1994.

Looking first at the US data, there were three major contractions over this period. The first one occurred in the 189Os, then there was a brief but sharp depression in 1920- 1921 and finally the Great Depression, lasting from 1929 until the beginning of the second world war. Another distinguishing feature of the data is the fall in the variance of unemployment after the second world war. Lastly, there does not appear to be any trend in unemployment over long periods of time.

In the UK, two serious contractions occurred in the 1930s and the 1980s. Also,

the three decades following the second world war appear to be unique, in the sense that both the level and the variance of unemployment reached a historical low. Thus, instead of the 1980’s experience being unique, it is more accurate to say that it is merely a return to an earlier pattern.

In France, the dramatic increase in unemployment since the mid-1970s dwarfs the Great Depression and signifies the most important development in the past century. Compared to the UK and the US, we also note that unemployment prior to this recent increase is much more stable in France: the variance appears to be smaller and, moreover, has not changed significantly over time.

We now estimate the timing of shifts in mean unemployment, u * * , using the Markov switching-regression model. 6 Preliminary inspection of the data implies the existence of two modes in the density for the UK and the US and three modes for France. Taking the number of states to be equal to the number of modes in the density, we calculate the following parameters using the Markov switching-regres- sion model (Table 1). We estimate the mean 7 and the variance for each state and the coefficient of lagged unemployment, in addition to the transition probabilities. ’ Notice that the variance is higher in the high-unemployment states.

6ami1ton (1989, 1993).

7 The unemployment rates are written in percentages.

’ We could not let the programme converge for France when lagged unemployment was included.

M. Bianchi, G. Zoega / European Economic Review 41(1997) 535-547 541

Fig. 1. The rate of unemplyment: top panel - France, 1894-1994, middle panel - UK, 1855-1994;

bottom panel - US, 1890-1994.

Table 1

Parameter estimates in the switching-regression model. a

Country u* ‘Csj) OCs,) PI

France 1.31 3.90 9.11 0.20 1.30 2.01

(0.06) (0.26) (0.45) (0.04) (0.43) (1.05)

UK 2.16 4.45 0.19 4.88 0.87 (0.62) (0.71) (0.06) (0.75) (0.05)

us 5.31 9.12 1.16 28.9 0.7 1

(0.47) (1.04) (0.26) (7.57) (0.07)

a Standard errors in parentheses.

542 M. Bianchi, G. Zoega / European Economic Reuiew 41 (1997) 535-547

Table 2

Dating of the mean shifts inferred from the filter probabilities and p-values of Chow F-tests for the

parameters of an autoregressive model

Country Dates F-test

* I u PI France 18944, 1930+, 1942-, 1967+, 1980+ 10.2 13.9

UK 1870-, 1875+, 1895-, 1900+, 1914-, 1918+, 1940-, 1974+ 3.83 3.47

us 1898-, 1907+, 19088, 1913+, 1925-, 1929+, 1942- 4.23 4.91

Table 2 has the dating of the shifts in mean unemployment. A plus sign indicates a rise in unemployment and a minus sign indicates a fall. In addition, we include the results of Chow tests which test, separately, for the equality of mean

unemployment and the coefficient of the first lagged term across the different periods.

We note that most of the dates correspond to major shocks to the three economies. These include the first and the second world war, the Great Depression

and the supply shocks of the 1970s. The Chow tests indicate that with more than 99% probability, both the mean

and the coefficient of lagged unemployment differ across the periods. In addition, we find that for France and the UK, the lags are more important in states of high unemployment. 9

We now move on to test if the sum of significant coefficients of the lagged terms is smaller when the mean-shifts are taken into account. We use a bootstrap test for this purpose. lo The results are in Table 3. The upper half of the table has results when we only allow the mean values calculated by the Markov switching- regression model. The bottom part has the comparable results when we allow each period to have its own local mean. In the latter case, we use the dating of the shifts

in the mean given by the Markov switching model but we allow for more than two values of the mean for the UK and the US, and more than three for France. The second column has the number of states and the third the number of shifts between the two states. pi denotes the coefficient of lagged unemployment from the original series, and /3; the coefficient from the residual series when the shifting means have been taken out. The fourth and the fifth column show the 95% confidence interval for pi.

The confidence intervals for the raw series are (0.85, 0.98) for France, (0.76, 0.91) for the UK and (0.62, 0.83) for the US. For the UK and the US, we would

9 When both the mean and the coeffkient of lagged unemployment are allowed to differ between

states, we get the following point estimates for the latter: France (0.43, 0.80, 0.841, UK (0.53, 0.791,

US (0.65, 0.60). lo The bootstrap test is described in Bianchi and Zoega (1994).

M. Biunchi, G. Zoega / European Economic Review 4lfl997) 535-547 543

Table 3

Test for equality of the two measures of persistence, pi and /3,. a

Country m* n Lower Upper P; P1

Number of mean values equal lo the number of states France 3 5 0.36 0.64 0.52 0.93

UK 2 I 0.80 0.94 0.89 0.87

us 2 7 0.53 0.11 0.66 0.16

Mean values differ beiween all periods France 3 5 0.43 0.70 0.57 0.93

UK 2 7 0.48 0.70 0.61 0.87

US 2 7 0.21 0.56 0.42 0.76

a The tests are based on 95% (c = 0.95) confidence intervals, obtained by bootstrapping the errors of

an AR(l) model fitted to the residual (i.e. actual minus local means) unemployment series. Number of

bootstrap replications, B = 10000.

conclude that there is mean-reversion in unemployment but not in the case of France. ”

The results imply that we can reject at the 5% level, the hypothesis that the lags are as important when the shifting means have been removed from the series, and

each period is allowed to have its own mean unemployment rate. However, this cannot be done for the UK if only two means are allowed, while in the case of France and the US we also have a rejection with three and two means respectively.

Comparing the three countries when each period is allowed to have its own mean unemployment rate, we find that p; for France and the UK lies above the upper bound for the US, and /3; for the US lies below the lower bound for France and the UK. Thus we can say with 95% probability that unemployment converges slower to each mean value in the European countries than in the US.

We conclude that unemployment appears to converge towards an infrequently changing mean. This, however, does not cast any light on what causes mean unemployment to change: monetary shocks could be responsible. But for this to be the case, nonlinearities are necessary: big downturns have a persistent effect while

the smaller ones do not. We now move to test for such nonlinearities.

4.2. Testing for nonlinear path-dependence

In order to test for nonlinear path-dependence, we estimate Eq. (5) when the constant term is not allowed to change over time, in a moving window of 30 observations. We then estimate a relationship between the estimated coefficient of lagged unemployment, &, and the absolute value of the estimated residual in the

I1 Unit-root tests reject the existence of a unit root for the US and marginally for the UK, but not for

France.

544 M. Bianchi, G. Zoega / European Economic Review 41 (1997) 535-547

last observation. This way we can test if large values of the residual make the coefficient take a higher value. The results are the following: ”

France: & ,,,+ 30 = 0.876 + 0. 026(Z1+30), t = 1894,. . . ,1994, (0.59)

UK: &1+30=O.779-O. 018 lZ,+3,,/, t= 1855 ,..., 1994, (-3.65)

us: 6 ,,,, +30 = 0.715 - 0. 021 lir+301, t= 1890,.. .,1994. (-2.82)

These results are not sensitive to the exact size of the window. Note that the coefficient of the estimated error term is significant and negative for the UK and the US. Thus, contrary to our expectations, large values of the residual appear to have a less persistent effect than the smaller ones. Although our results are hopefully not the last word on this issue, they do not suggest that large shocks are more persistent than the smaller ones.

5. Conclusions

We have concluded that the historical unemployment series for France, the UK and the US are stationary around an (infrequently) changing mean. The infrequent changes in mean unemployment coincide with large shocks to the economy: in all three countries there was a period of low unemployment following the second world war which was followed by a period of high unemployment in the European countries after the two oil shocks of the 1970s.

We conclude that models of unemployment hysteresis - such as the insider- outsider model - are most likely to explain slow adjustment towards a (changing) equilibrium and do not pose a threat to the natural rate hypothesis. This hypothesis

and models of hysteresis appear to be complementary. However, the most important question appears to be what makes equilibrium -

or average - unemployment be low in one period - such as the three decades following the second world war - and high in others. We propose two possible answers. First, as suggested by Manning (1990), there may be multiple equilibria - fragile equilibria in the terminology of Blanchard and Summers (1988) - caused by either an upward-sloping labour demand curve or a downward-sloping wage curve. The latter can be derived from the insider-outsider modeE (Lindbeck and Snower, 1986) - a smaller group of employees asks for a higher wage - and the former from a model with search externalities yielding a high- and a low-activity equilibrium (Diamond, 1982).

A second possible explanation involves changes in a (unique) natural rate over time, as proposed by Phelps (1994). The rise in oil prices could have reduced the

12 r-statistics in parentheses

M. Bianchi, G. Zoega/European Economic Review 41fl997) 535-547 545

demand price of labour and the expansion of the welfare state raised the supply price, to take just two examples. The challenge faced by this approach is to find nonmonetary variables which could explain the shift from one unemployment plateau to another.

The message of this paper is that in order to account for medium-term changes in unemployment, one needs models which explain differences across epochs of high- and low unemployment. The interesting question is what makes an economy go from one regime to another and, also, why unemployment persists in the new

regime. We suspect that the most fruitful way of approaching the issue is through studies at the micro-level - which could, for example, detect reasons for nonlinear

hysteresis - rather than the study of relatively short macroeconomic time series.

Acknowledgements

We would like to thank Pierre Villa, EPII, Paris, for providing historical data on French unemployment. This paper was written while the second author was visiting the University of Iceland. Many thanks go to Thorvaldur Gylfason and Tryggvi Herbertsson for their hhospitality.

Appendix A

Sources of data

A. 1. France

Unemployment rate (in percentage of the active civilian population)

All years, excluding 1914-1918 and 1940-1945: Villa, Pierre, 1996, Se’ries macroe’conomiques historiques (INSEE, Paris).

1914-1918 and 1940-1945: Villa, Pierre, 1988, Macroeconomic series for a long period of time (CEPREMAP, Paris).

A.2. UK

Unemployment rate (in percentage of the civilian labour force)

1855-1965: Feinstein, C.H., Statistical Tables of National Income, Expenditure

and Output of the U.K. 1855-196.5 (Cambridge University Press, Cambridge).

1966-1994: Economic Trends, various issues.

546 M. Bianchi, G. Zoega / European Economic Review 41 (1997) 535-547

A.3. US

Unemployment rate (in percentage of the civilian labour force)

1890-1970: Bureau of the Census, Historical Statistics of the United States:

Colonial Times to 1970, Bicentennial edition, 1970.

197 1- 1994: Economic Report of the President, February, 1996.

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