Global Factors, Unemployment Adjustment and the Natural Rate

OECD unemployment rates show long swings which dominate shorter business cycle components and these long swings show a range of common patterns. Using a panel of 21 OECD countries 1960-2002, we estimate the common factor that drives unemployment by the first principal component. This factor has a natural interpretation as a measure of global expected returns, which is given added plausibility by the fact that it is almost identical to the common factor driving investment shares. We estimate a model of unemployment adjustment, which allows for the influence both of the global factor and of labour market institutions and we examine whether the global factor can act as a proxy for the natural rate in a Phillips Curve. In 15 out of the 21 countries one cannot reject that the same natural rate, as a function of the global factor, appears in both the unemployment and inflation equations. In explaining both unemployment and inflation, the global factor is highly significant, suggesting that models which ignore the global dimension are likely to be deficient. --


Introduction
OECD unemployment rates show long swings, which dominate shorter business cycle movements. Over periods like 1960-2003, unemployment rates in the 21 OECD countries we analyse appear to be very persistent series showing stochastic trends. They also show both a range of common patterns and a range of national differences. According to one view, broad movements in unemployment across the OECD can be explained by shifts in labour market institutions, e.g. Nickel et al. (2005), hereafter NNO. However, this view has been subject to a challenge, which attributes changes in unemployment to shocks in global capital or product markets rather than labour market institutions, e.g. Phelps (1994), Oswald (1997), Carruth et al. (1998), Pissarides (2001) or Baker et al. (2004). An intermediate position is that shocks drive unemployment, but the speed of adjustment of unemployment to the shocks, as well as the magnitude of the response, is determined by labour market institutions, e.g. Blanchard and Wolfers (2000), Layard et al. (1991) and chapter 17 of Phelps (1994). Evaluating these approaches empirically is problematic because both labour market institutions and global shocks are difficult to measure. We will use standard measures of labour market institutions and measure the global factor by the common component of OECD unemployment. We then investigate the role of domestic labour market institutions in transmitting this global factor into national unemployment rates and whether the global 1 factor can act as a proxy for the natural rate in a Phillips curve. Rather than trying to devise measures of global influences from the very large number of candidate measures, we look at the common component of OECD unemployment, measured by their first principal component 2 . This is not a cyclical measure because, like OECD unemployment rates, it is a very persistent series. The shocks can be represented by innovations to this series. Based on the empirical evidence, we also provide a possible interpretation of this factor. The demand for labour (and capital) will depend on the expected return on production, which will have a global and a national component. A large number of variables will influence global expected returns and the confidence with which these expectations are held. These include global competition which affects the elasticity of demand and labour costs; other input costs including oil, commodity prices and real interest rates which affect the cost of capital; technology which influences total factor productivity; and 'sunspot' variables which drive 'animal spirits'. A number of these variables have been suggested as possible explanations for persistently high unemployment.
One could of course try to measure expected returns or their determinants directly, but this is likely to be difficult for the same sort of reasons that measuring expected returns in finance is difficult (Pastor et al. (2006)). Therefore, it may be easier to measure them indirectly by their consequences, the common component in global labour (or capital) demand. The interpretation of the common factor in unemployment as reflecting expected returns is given added plausibility since the common factor in _________________________ unemployment is almost identical to the common factor in OECD shares of investment. In Section 2 we discuss the measurement of the global factor. In Section 3 we provide a model of the adjustment process by which national unemployment responds to the global factor and examine how labour market institutions may influence the parameters of that process. In Section 4 we provide estimates of the unemployment adjustment model. In Section 5 we provide estimates of a Phillips Curve augmented by global factors. Section 6 concludes.

Global Factors
We use OECD data for twenty-one countries 3 and forty-three years  on the unemployment rate it u in country i in year t , 1, 2,..., ; 1, 2,..., i N t T = = , which we can stack in the , T N × (43 21) × matrix U . Standard tests do not reject a unit root in all 21 series. We assume that it u has a factor structure Similarly we have data on the investment rate, Gross Domestic Fixed Capital Formation as a share of GDP, g it , stacked as G . We standardise the data and calculate the underlying global factors as the principal components (PCs) of the correlation matrices of U and G . These are the orthogonal linear combinations of the data that explain the maximal variances of the data 4 . If the idiosyncratic errors, it e above are I(0) the PC estimators for t f are consistently estimated (large N) independently of whether all the factors are I(0) or whether some or all of the factors are I(1) (Bai and Ng (2004)). We will assume that the errors are I(0) and that the long-memory in investment and unemployment comes from the persistent global factors. We test for the cointegration of unemployment and the global factor below.
The eigenvalues and proportion of variance explained by the first four PCs are given in Table 1. The first PC explains almost 70% of the variation in unemployment and almost 60% of the variation in investment; factors common to all countries clearly explain the bulk of the variation in both variables 5 . The first PC of unemployment is close to the mean with most countries having roughly equal weights, between 0.18 and 0.26, the main exception being the US, which has a low weight of 0.08, but a high weight in the second PC of unemployment. The eigenvectors (loadings) for the first four PCs are given in Appendix A1.

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3 Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Greece, Iceland, Ireland, Italy, Japan, the Netherlands, New Zealand, Norway, Portugal, Spain, Sweden, UK and US. 4 For forecasting, it may be more useful to estimate dynamic factors that take the principal components of the spectral density matrix. However, static factors are commonly used in the FAVAR literature. Stock and Watson (2005) discuss the relation between dynamic and static factor analysis. 5 The fact that a global factor is important for investment is also indicated by the Feldstein-Horioka literature, where there is substantial cross-section dependence in the residuals of panel regressions of investment shares on savings shares, e.g. Coakley et al. (2004).
www.economics-ejournal.org Notice that we have calculated the factors for unemployment and investment independently and not imposed a shared factor structure. However, by plotting the unemployment and investment PCs together we can judge whether they share a common factor or whether there are only variable specific factors. The first PCs for unemployment and investment are shown in Figure 1 below, in addition to average OECD unemployment. Note that we draw the negative of the PC for unemployment in order to create a more visible fit with the investment PCs.  1960 1965 1970 1975 1980 1985 1990 1995 2000  The first PCs for investment and unemployment are almost identical, 2 0.92 R = . This relationship is not spurious, they cointegrate 6 and the (1,-1) restriction on the cointegrating vector is accepted at the 5% level, t=1.53. The disequilibrium term feeds back significantly on investment but not on unemployment. Since employment can be adjusted faster than capital stock this is not surprising. The contemporaneous residual correlation is very high, 0.81, so they both seem to be responding to the same shocks, which we interpret as innovations to expected returns. As can be seen from the graph the fit is less good in the 1960s, which is consistent with growing globalisation over this period, particularly after the end of the fixed exchange rate Bretton Woods system.
The first PC reflects some of the more important macroeconomic events of the past forty years: the oil shocks, the recessions of the mid-seventies, early eighties and early nineties and the gradual but only partial recovery in the second half of the eighties. This component describes the shocks causing the persistent slump that occurred in many countries in the seventies, eighties and nineties. 7 As noted above, the expected return to production may depend on a large number of factors, many of which are difficult to measure. But in a globalised world the broad movements of the expected rate of return are likely to be quite similar across the advanced industrial countries, and reflected in their investment and employment decisions. Whereas investment and unemployment in any one country will be noisy measures of this, the common component across countries may be a better measure. While we do not observe expected returns, we do observe a variable related to it. Figure  2 plots a discount factor calculated from the world real rate of interest: d = 1/(1+r), where r is the average (long) real rate of interest for the G7 countries. 8 A clear relationship is present between the two PCs, on the one hand, and the discount factor, on the other hand. This suggests that the long swings of employment may trace their roots to factors affecting expected returns and the same factors drive investment. This pattern is consistent with a variety of theoretical models. For instance, Xiao (2004) derives an International Real Business Cycle (IRBC) model with increasing returns in the production technology that generate sunspots. These sunspots are interpreted as self-fulfilling demand shocks, like animal spirits, and generate positive international correlations of output, employment and investment, unlike most IRBC models. Similarly Harrison and Weder (2006) find that a sunspot model driven by a measure of expectations can explain the entire Great Depression era in the US. Increasing returns are not necessary, Hashimzade and Ortigueira (2005) find that a neoclassical model with labour market frictions displays expectations driven business cycles where the indeterminacy of equilibrium stems from job search externalities. In _________________________ 6 The AIC chooses no intercept, no trend in the relationship and with this the trace test for the rejection of no cointegrating vectors has a p value of 0.0173, while the less reliable max eigenvalue test has a p value of 0.0519. 7 There is a growing literature that seeks to explore the similarities and linkages between macroeconomic cycles across countries. For instance, Kose et al (2003) also find a common world cycle. But again they are examining the stationary component, rather than the persistent component that we focus on. 8 The world real rate of interest is calculated as the weighted average of the real rate of interest in the G7 countries; the real rates being the difference between the long nominal rates and annual inflation and the weights being the Heston-Summers relative GDP for each country.
www.economics-ejournal.org the unemployment literature, we have models where equilibrium unemployment depends on the real rate of interest. In Pissarides (2001) firms respond to higher real interest rates by opening up fewer vacancies, resulting in an elevation of equilibrium unemployment. In Phelps (1994) higher interest rates make firms train fewer recruits, charge higher markups of price over marginal cost and reduce the production of labourintensive capital goods. This causes the natural rate of unemployment to increase. Changes in labour supply may provide an alternative explanation. However, the composition of the labour force is slow moving, both in terms of the share of the working-age population as well as in terms of the educational composition. Francesconi et al. (2000) demonstrate that changes in the educational composition of the labour force affect both the level and the behaviour over time of the aggregate national unemployment series. Interestingly, they find that that the US unemployment series have the "European" shape -experience upward mean shifts in the mid 1970s and the early 1980s -once changes in the educational composition are accounted for because the within-education group series all have that appearance. Hence, taking labour supply into account will make the first unemployment PC explain more and render the second PC less important. Shimer (1998) finds that changes in the age composition of the US labour force explain the rise in unemployment during the fifties and the sixties and the decline in the eighties and the nineties. He finds that the entry of the baby boom led to an increase in unemployment while the aging of this generation has the effect of lowering the aggregate US unemployment rate. However, these changes are too gradual to fit the pattern of the first unemployment PC.

The Adjustment Process
Firms will determine their profit-maximising levels of employment and investment conditional on their expectations of the rate of return on production. Corresponding to the profit maximising level of employment will be an optimal or equilibrium rate of unemployment, * it u . This profit maximising level will be shifted by factors shifting the expected returns; the more profitable expected production, the lower optimal unemployment. Suppose that we take the interpretation of the first PC of OECD unemployment, f t , as a measure of global expected returns then the optimal level of unemployment is given by * . it t u a bf = + (2) Below we will allow the parameters to vary with countries and time, but we abstract from that for the moment. There will be a similar equation for the share of investment.
Following the approach in Nickell (1985) let us assume that firms have an infinite horizon and minimise the present value of future loss where δ is the discount factor and θ measures costs of adjustment. The loss stems from employment differing from the profit-maximising level and the cost of adjusting employment, measured by the parameter θ. The Euler equation takes the form Solving the Euler equation requires finding the two roots 1 Calling the stable root μ , the optimal policy is then given by (1 ) , the present discounted value of all expected future targets. To make this operational requires a model for optimal unemployment, * it u , which will be driven by .
The data for t f , which determines * it u do not reject a unit root; the estimate of 0.58 ρ = and the constant is not significantly different from zero. This can then be used to forecast the future targets and, with this specification the unemployment adjustment equation becomes This is a standard error correction equation, in which changes in unemployment are driven by shocks, changes in the global factor, t f , and by the adjustment of it u to its steady state value determined by the same variable. 9 The parameters of the expectations process for t f Δ seem structurally stable by Cusum and CusumSquared tests, but one would not expect the economic parameters (the discount rate, δ , and the cost of adjustment, , θ which determine μ ) to be constant across countries and time. In particular, it is possible that institutions would influence both the discount rate and the cost of adjusting employment. Suppose that we have a 1 k × vector of variables it x , which measure labour market institutions with the first element being unity, then we can make the economic parameters functions of it x : where , , , a b c d are now 1 k × parameter vectors 10 . There are four routes that the institutional variables can influence unemployment: (a) through the domestic component of the equilibrium level of unemployment; (b) through the long-run effect of the global factor on the equilibrium level of unemployment; (c) through the impact of shocks to the global factor on the change in unemployment and (d) the speed of adjustment to equilibrium.
To allow for higher order adjustment processes we add the lagged change of the global factor and the lagged change in unemployment. To allow for national shocks and perhaps monetary policy, we add lagged inflation. 11 We treat the coefficients of these last three variables as independent of institutions to save degrees of freedom. Adding the additional variables and an error term gives: There are a large number of possible institutional variables that could be included as elements of it x . We use five that have appeared regularly in the literature, taken from the Labour Market Institutions database of Nickel and Nunziata, extrapolating the final values to the rest of our sample. They are generally measured over multi year periods and available for 19 of our 21 countries, not Greece and Iceland. These are; the coordination of bargaining (coord) with a range {1,3} increasing in the degree of coordination on employers as well as unions side; benefit replacement rates (rr); the duration of benefits (dur); employment protection (emp) with range {0,2} increasing with the strictness of employment protection; and, finally union density (den).
There is the obvious problem that institutions are likely to be endogenous, responding both to global factors and national unemployment. To investigate this we _________________________ 9 Higher order autoregressive processes for * it u Δ add further lags of it in the equation. In the case of t f Δ the second lag is just significant. We allow for this in estimation. Pesaran (1991) suggests an alternative interpretation of higher order in terms of further adjustment costs. 10 Strictly the coefficient on it it c x b x , but we use this simpler formulation.

11
The first difference of the inflation rate turned out to have a statistically insignificant coefficient throughout.
www.economics-ejournal.org ran a random effects 12 panel estimator for each institutional measure on its lagged value, the lagged global factor and lagged unemployment. The global factor was just significant for emp (t=-2.071) and significant for den (t=-3.008). Thus there may be some effect of the global factor on those two variables, but since national unemployment is never significant, endogeneity is unlikely to be a problem.

Empirical Results
To assess the explanatory power of our global factor, we first estimated a model in which the parameters are constant over time but differ for each country: The estimates for the individual countries are given in Appendix A2. For large N and T, Pesaran (2006) shows that, under relatively weak assumptions, such regressions using weighted averages, like t f , as additional regressors give consistent estimates of the coefficients and reduce cross-section dependence in the residuals 13 .
Using standard critical values t f Δ is significant in 17 countries; 1 t f − is significant in 14; and 1 t f − Δ in 6. Only in Japan is no measure of the global factor significant. Lagged unemployment is significant in 16, the lagged change in 11 and lagged inflation in 6. The 2 R for changes in unemployment is below 0.5 in Iceland and Japan; and above 0.7 in 10 countries. Under the null of no long-run relationship the test statistics are nonstandard. Pesaran Shin and Smith (2001) provide a bounds test for a long-run relationship, which is appropriate whether the variables are I(0) or I(1). Assuming the variables are I(1) we can reject the null hypothesis of no long-run relationship between unemployment and the global factor in 12 of the 21 countries at the 5% level 14 . Another four are uncertain, lying between the 10% I(0) bound and the 5% I(1) band. The tests would not reject no long-run relation in Denmark, Germany, Ireland, New Zealand and Sweden. On balance this suggests that the national idiosyncratic factors are I(0) in most countries and the stochastic trend in unemployment comes from the global factor. Panel cointegration tests would not be informative here, since the null hypothesis of such tests, no cointegration in any country, is not very interesting because there is clearly cointegration in most countries.
The equation was estimated by the Swamy RCM method (see Appendix A3), which takes precision weighted averages of the individual country coefficients, with nonparametric standard errors, and by fixed effects, which imposes homogeneity of slopes across countries. The results are given in Table 2.

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12 Because some institutions in some countries do not change a fixed effect estimator cannot be used.
13 There is an issue as to whether it is better to use a priori weights (e.g. the mean) or estimated weights (e.g. the PC). Here it does not make much difference since the PC is very close to the mean and they both give very similar results. There is also an issue as to how one would endogenise the global factor. Both issues are discussed in Pesaran and Smith (2006 For the fixed effect, 2 0.48, The maximised log-likelihood for the fixed effect estimator 818 − compared to a total MLL of -484 for the heterogeneous estimator given in A2. Homogeneity of the parameters is massively rejected, but if we are primarily interested in average effects, which is what most of the theory is concerned with, this may not matter. The Fixed Effect Estimates are very similar to the Swamy estimates, except that the speed of adjustment is lower, which is what one should expect from the heterogeneity bias discussed in Pesaran and Smith (1995). The long-run effect of the global factor is almost identical, 0.68 versus 0.7. Imposing homogeneity does not seem to influence the estimates of the average effect.
We examined various alternative measures of the global factor. If one uses a two way fixed effect estimator, which allows for an unrestricted factor influence by introducing 39 completely free time dummies the MLL is -815 as compared to -818 using the t f variables in Table 2. This is a tiny improvement for a lot of extra estimated parameters. Using mean unemployment instead of the global factor gets the same fit as the two way fixed effect as one would expect. Because the first principal components of unemployment and investment and mean OECD unemployment are so highly correlated, it makes very little difference to the estimates which is used. The first principal component of unemployment seems to fit slightly better than the first principal component of investment using the fixed effect estimator so this is our preferred measure. We also added the second principal component of unemployment to the first and this is not significant. The full results are given in Appendix A4.
We examined the structural stability of the relationship by estimating the model over the period 1963-1982 and 1983-2002. The RCM estimates are given in Table 3. The estimates for the two periods are very similar, the biggest difference being that the coefficient on lagged unemployment is larger in the first period. The long run effect of the global factor is 0.61 in the first period and 0.87 in the second, perhaps reflecting increased globalisation. It is probably safer not to put too much weight on this, since a trend interacted with the global factor was not significant. It is also noticeable that the coefficient of lagged unemployment is lower in both sub-periods than in the whole period. This may reflect the downward small T bias that results from reducing T from 40 to 20. The fixed effect estimates for the two periods showed similar features. With _________________________ www.economics-ejournal.org the fixed effect estimates one can test for coefficient equality in the two periods. Since the variances were very similar in the two periods, Chow's first test is appropriate. Each fixed effect regression estimates 6 slope parameters and 21 intercepts, so the distribution is F (27,786). The test statistic is 2.6 which would certainly reject the null of parameter constancy, given the large sample. But while significant the differences are not large. We now allow the variation in parameters between countries and over time to be determined by the institutional variables. To allow for country specific intercepts, we used deviations from the means, it it i u u u = − % and estimated by non-linear least squares the full model for the 19 countries for which we had institutional data, dropping Greece and Iceland. The fixed effects estimates for the 19-country sample were almost identical to those from the 21-country sample with a MLL of -746.9. The full model has 26 slope parameters: This had a MLL of -714.3 and the results are given in Appendix A5. Dropping the least significant coefficient (except constants) and re-estimating sequentially led to the specification shown in Table 4, where the t ratios are calculated using robust standard errors. The 2 R in levels is 0.96, close to that obtained by NNO of 0.98, with country specific trends and time effects and many more variables. The fit for the individual countries was generally good, with the 2 R for the level of unemployment over 0.95 in 13 of the 19 countries. It was below 0.9 only for the US, 0.3, and Portugal 0.88. The US appears to be different, this 2 R is a lot lower than obtained with the country specific equation shown in A2: allowing for institutions but otherwise imposing common parameters leads to a severe deterioration in the explanation for the US. Over all countries, the institutional variables have no effect on the domestic component of equilibrium unemployment. Increased coordination reduces the speed of adjustment from 0.19, when coordination takes its lowest value 1, to 0.07 when it takes its highest value 3. NNO get a speed of adjustment of 0.15. Increased employment protection reduces the short run effect of changes in the global factor on changes in unemployment www.economics-ejournal.org but increases the long run effect of the global factor on equilibrium unemployment. A higher replacement ratio increases the short run effect of changes in the global factor. A higher duration of benefits increases the long-run effect on equilibrium unemployment. Higher lagged inflation raises equilibrium unemployment. Specification searches can be sensitive to the order restrictions are imposed, so the levels of the institutional variables were added to the final model and were not significant individually or jointly. The product of dur and rr, the change in den and the product of coord and den used by NN0, were also not significant. The current and lagged change and lagged level of either the second unemployment PC or the first investment PC were also not significant.
Institutions seem to influence adjustment to the global factor but have no influence on the natural rate, which is determined just by the global factor. But even after allowing for institutions there is substantial heterogeneity between countries. The institutional model in Table 4, has 28 parameters and an MLL of -727. The heterogeneous model of Table A2 has, for the 19 countries, 133 parameters and an MLL of -441. These models are not nested. The institutional model allows time-variation in the parameters but restricts between-country variation to that associated with institutional variables; the heterogeneous model allows parameters to differ freely over countries, which can pick up the effect of country specific institutions, but does not allow variation over time. They can however be compared using model selection criteria. The AIC would select the heterogeneous model; the BIC, which penalises overparameterization more heavily, would select the institutional model. Given possible concerns about the quality of the institutional data it seems preferable to use the heterogeneous model which we do below. www.economics-ejournal.org

The Phillips Curve
Section 4 showed that the global factor shifts the equilibrium level to which unemployment adjusts, thus it can be interpreted as a determinant of the natural rate. This prompts the question, how does it perform as a measure of the natural rate in a Phillips Curve? We return to the sample of 21 countries, since we are not using the institutional variables. (We investigated including the institutional variables in the Phillips Curve in the 19 country sample, but they were not significant, see Appendix A6) We assume that the natural rate is a function of the global factor as in (2) We can parameterize (15) If 1 i θ = , lagged inflation drops out of the equation.
Equation (16) was estimated separately for each country and the results are given in Appendix A7. The RCM and fixed effect estimates are shown in Table 5. Although homogeneity is strongly rejected, both, the RCM and fixed effect estimates have the right sign for every variable. Unemployment has a negative effect and the natural rate a positive effect. The change in world inflation has a coefficient close to one. There is rapid adjustment of inflation to average inflation, over half the deviation made up in a year. This is consistent with the literature on inflation convergence, e.g.
www.economics-ejournal.org Hyvonen (2004). Lagged inflation is insignificant, which is required for consistency: averaging the equations over country must give average inflation. While we do not reject 1 i θ = , on average, it is rejected in a number of countries. The RCM Phillips curve estimate of the average natural rate as a function of the global factor (which has mean zero over the sample) in percent is * 4.3 0.48 t t u f = + . The RCM unemployment adjustment estimate of the average natural rate from Table 2  , appears in both. The two equation system was estimated for each country and the cross-equation restriction tested. The system is given by equations (13) and (16), which simplifying the notation is Notice that the system is recursive, current unemployment influences inflation, but current inflation does not influence unemployment. The cross-equation restriction is that the , The two equations were estimated as a system for all 21 countries allowing for the covariance between 1 2 ( , ) where 1 it x − is a set of variables observed at time t-1. This allows us to test both 1 i φ = and the cross-equation restrictions implied by rational expectations: 1 it x − only enters the Phillips curve through inflation expectations: The is very persistent and thus predictable and its predictable component is captured by 1 ( ) leaving the realization of the deviation of unemployment from its natural rate insignificant. In fact rejection of 1 i φ = seemed to be more common when i β was significant. When the system was estimated imposing all four restrictions, the two implied by a common natural rate, 1 i φ = and the restriction implied by rational expectations, the joint restrictions were rejected in 11 of the 21 countries. 16 Therefore it seems more useful to work with the estimates in Appendix A7, where rational expectations are not imposed and the deviation of unemployment from its natural rate is significant in many countries. A simple Phillips curve, assuming a common form of equation in each country, works quite well, once one takes account of global factors, both in determining the natural rate and in influencing national inflation. When the Phillips curve was estimated together with the unemployment adjustment equation as a system, the hypothesis that the same natural rate, * , appeared in both equations could not be rejected in 15 out of the 21 countries. The data are also consistent for many countries with a vertical Phillips Curve and rational expectations, though when these restrictions are imposed, the deviation of unemployment from its natural rate tends to become insignificant.

Conclusions
There is a large common component in OECD unemployment, which accounts for about 70% of the total variance. This common component is a very persistent series; is almost identical to the common component in investment shares and explains a substantial amount of national unemployment variation. It has a natural interpretation in terms of the global expected return on production and is consistent with a variety of sunspot or animal spirit models. We propose a simple model of unemployment adjustment and allow five measures of labour market institutions to influence unemployment; (a) through the equilibrium level of unemployment; (b) through the long-run effect of the global factor on the equilibrium level of unemployment; (c) through the impact of shocks to the global factor on the change in unemployment and (d) the speed of adjustment to equilibrium. We find that the institutional variables have no effect on the equilibrium level of unemployment; that increased coordination reduces the speed of adjustment; that increased employment protection reduces the short run effect of changes in the global factor but increases the long run effect; and that a higher replacement ratio increases the short run effect of changes in the global factor. However a model without institutions but which allowed for more cross-country heterogeneity was selected by the AIC, though not the BIC. Conditional on our measure of global factors, it appears that labour market institutions influence the transmission of global influences rather than determining the equilibrium level of unemployment which is determined by the global factor. Given this we examined a Phillips Curve in which the natural rate is determined by the global factor and where equilibrium inflation adjusts to the global average inflation rate. This worked well and on average we found a vertical Phillips Curve once one allowed for global influences on the natural rate. When the Phillips curve and unemployment adjustment equations were estimated as a system, the hypothesis that the same natural rate appeared in both could not be rejected in 15 out of the 21 countries. Idiosyncratic factors are important. Although the equations have a common form, the parameters differ significantly across countries. In explaining both unemployment and inflation, global factors are very significant suggesting that models which ignore them are likely to be deficient. where i y is a T×1 vector, and i W is a T×(k+1) vector. The fixed effect estimator constrains the k slopes to be the same. The parameters are assumed to be random, If this estimator is not positive definite (which it rarely is), the last term is set to zero and Ω used. The Swamy estimator of the mean is Notice that the Swamy estimator of the standard errors is non-parametric it depends on the distribution of the ˆi δ and therefore is likely to be robust to serial correlation and heteroskedasticity.
is a feasible GLS fixed effect estimator. The desirable properties of this test depend on T being large relative to N, which is the case in our application.
Appendix A4: Alternative Measures of the Global Factor The correlation of the first PC of unemployment with mean unemployment is 0.998 and with the first PC of investment factor -0.961. The correlation between the investment PC and mean unemployment is -0.952. The second PC of unemployment is uncorrelated with the first and has correlations of -0.07 with both the first PC of investment and mean unemployment. Below in sequence are given (a) the two way fixed effect estimates which allow for an implicit unobserved factor by adding 39 free time dummies, then the Swamy RCM and Fixed Effects estimates using as factors (b) the first PC of unemployment (given in the text), (c) the first PC of investment, (d) average unemployment across the OECD sample (e) the first and second PCs of unemployment.