The Impact of Demography on the Real Exchange Rate♣
Andreas Andersson* and Pär Österholm* March 2001
Abstract Theory predicts that life cycle saving mechanisms will cause real exchange rate variations as the age structure varies. We investigate the impact of demography on the Swedish real exchange rate, measured as the real TCW index, during 1960 to 2000. Time series regressions show that the Swedish demographic structure has significant explanatory power on the real exchange rate. A model using age shares alone as regressors is used for medium term out-ofsample forecasts, outperforming both a naive forecast and forecasts based on an autoregressive model. Finally we use the estimated model in order to make forecasts of the Swedish real exchange rate up to 2015. The model predicts that the Swedish age structure will have a depreciating effect on the real exchange rate up to 2007 followed by an appreciating effect in the end of the forecasting period.
JEL Classification: F31, F41, J10, J11 Keywords: Demography, Real exchange rate, Forecasts
______________________________ ♣
We are grateful to seminar participants at Uppsala University and Central Bank of Sweden, especially to Hans
Dillén for helpful comments and interesting discussions. Financial support from Sparbankernas Forskningsstiftelse is gratefully acknowledged. * Correspondence: Department of Economics, Uppsala University, Box 513, S-751 20 Uppsala, e-mail:
[email protected] or
[email protected]
1. Introduction
The highly volatile real exchange rates experienced during the 1990´s have brought about a renewed interest in understanding the reasons for exchange rate movements. One immediate implication of these volatile exchange rates is that one of the most frequently used theories of real exchange rates, purchasing power parity (PPP), cannot hold continuously and, in particular, not in the short run. However, this does not rule out the possibility that there exists a stationary long run equilibrium real exchange rate, and that the movements reflect temporary departures from this level. In this paper, we argue that the demographic structure could serve as a useful factor in understanding such movements. Furthermore, projections of the demographic structure are reliable forecasts of the future population. This, together with the fact that the demographic transition is a slowly moving process, make demographic data a potential forecasting device for the medium-and long-run trends in economic variables, as argued in Lindh (1999). Hence, establishing a relationship between the real exchange rate and the demographic structure gives us an opportunity to make forecasts of the real exchange rate. This constitutes the main purpose of this paper.
Despite the fact that a number of theories, e.g. the life cycle hypothesis and human capital theories, imply that demography could affect the economy on an aggregate level, demographic factors have rarely been taken into account in macroeconomics, with the exception of saving, see e.g. Berg and Bentzel (1983), Mason (1987) and Horioka (1989). During the 1990’s the research in demography as a relevant factor was intensified. In several empirical papers the effects of the demographic structure was investigated, starting off with McMillan and Baesel (1990). On post-war data for the USA they found effects on a number of macroeconomic variables, such as real interest rates, growth, inflation and unemployment. Another early study using the age structure was accomplished by Fair and Dominguez (1991), who found that consumption, housing investment, money demand and labour force participation were affected using US data from 1955 to 1988. A similar study on yearly Australian data from 1950 to 1989 by Lenehan (1996) established significant explanatory power of age structure on real interest rates, inflation and growth.
There have been a number of studies focusing on growth, see e.g. Malmberg (1994), Bloom and Sachs (1998), Lindh and Malmberg (1999a) and Andersson (2000a). All find that age distribution is a key determinant when studying Swedish, world, OECD and Nordic post war 2
data. Lindh and Malmberg (1998) and Lindh (1999) also establish a relationship between the age structure and inflation on OECD and Swedish post war data respectively. Other recent research in this area is Higgins (1998) and Lindh and Malmberg (1999b) who estimate the effect of the age structure on saving, investment and the current account.
The intensified research, where demography is taken into account in macroeconomics is of particular interest considering the fact that the population of the industrialized western world is getting older. The reason for this is mainly a decreasing trend in fertility and mortality. Looking at Sweden we find that, in 2015, the share of the population older than 65 is estimated to be approximately 21 percent compared to 1960 when it was 11 percent. During the same period the fraction of children will decrease from 22 percent to an estimated 16 percent. Obviously, such changes and their economic implications have to be considered when designing economic policy.
The paper is organised as follows: In section two, the theoretical foundations are presented. This is followed by data description, estimation and forecasting in section three, and finally, section four concludes.
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2. Theory
When we explain how the demographic structure could influence the real exchange rate, the life cycle hypothesis will serve as a useful device. According to the life cycle hypothesis economic agents, in order to optimise their lifetime utility, smooth their consumption during life.1 The hypothesis implies that in some stages in life you are a net borrower and in others you are a net saver. Using basic macroeconomic models, this fact, together with the consumption patterns of different age groups, will allow us to identify channels through which demography could influence the real exchange rate.
There have been numerous ways of representing the demographic structure in the demographic economic literature, e.g. average age or dependency ratios (young and old in proportion to the whole population). Such measures have certain shortcomings, mainly because they do not use all the potential information the demographic profile provides and hence might have difficulties explaining the economic phenomena that arise from interaction among age groups. Some recent literature uses the shares of different age groups in order to get an appropriate picture of the population profile. The number of age groups used in empirical studies, as well as their classification, differs among different studies. We will identify six different age groups used in this paper. The age groups are selected in order to match different phases of life in a life cycle perspective.2
The youngest group, the children, is between 0-14 years of age. This group is, in a sense, endogenous and is a result of other’s economic decisions. Furthermore, they do not take economic decisions by themselves and are non-productive. One other aspect of treating this group as endogenous is the problem of projecting fertility. This makes the projections of the age shares of this group more uncertain and could create some problems when making forecasts of economic variables. The feedback into the demographic structure as a whole is, however, slow and will not be a serious problem when you consider moderate time spans, e.g. up to fifteen years. The next group, the young adults, is in the age bracket between 15-24. This is an age that to a large extent, at least in the western world, is represented by education, beginning of a career and having a family. The behaviour of this group might have changed
1
See e.g. Modigliani and Brumberg (1954). For different ways of representing the demographic structure in empirical papers, see e.g. McMillan and Baesel (1990), Fair and Dominguez (1991), Higgins (1998), and Lindh and Malmberg (1999b) 2
4
during the investigation period since the western world has a trend towards longer education and hence the family formation has to be taken care of in a later part of life compared to the behaviour some decades ago. They generally have low incomes and are probably net borrowers. This group has shown a positive effect on housing investment (Fair and Dominguez, 1991 and Lindh and Malmberg, 1999b). The prime aged, 25-49 years of age, are characterised by family raising and high productivity. The group has a relatively low saving rate and hence a high degree of consumption, particularly of durable goods. People in the next age group, the middle aged, between 50-64 years of age, are at the top of their careers and highly productive. Their children have moved away from home and their loans for education and housing investment are, to a large extent, repaid. They are aware that their income will decrease when they retire and they save a large part of their present income in order to maintain consumption when retired. To a certain extent they reallocate their wealth from real estate to financial assets. This issue, regarding portfolio allocation over the life cycle, is investigated in Andersson (2000b). The high financial saving leads to a high rate of capital accumulation, stimulating investment. This group has shown a positive effect on business investment (Lindh and Malmberg, 1999b). The fifth group is the young retirees, 65-74 years of age. They are, although retired, relatively active. Their income has decreased and they are no longer net savers, on the contrary probably dissavers, at least on their pension claims, as they are selling off their assets in order to compensate for the lower income. Despite their relatively high age they burden the public sector, e.g. health care and other social security facilities, to a rather low extent. Finally we have the old retirees, 75 and above. These are in a phase of life characterised by low activity and heavy consumption of health care. This group consumes less than the young retirees do, at least of private goods, and the assets that they have are to some extent meant for bequests. These differences between the two groups of retirees mean that separating them could be necessary for identification.
Considering the different phases of life described above, a reasonable conclusion is that changes in the demographic profile should affect aggregate saving. First we have differences in private saving associated with different economic conditions in life. Secondly, different phases of life are associated with more or less governmental consumption, i.e. government saving. There is theoretical as well as empirical support for demographically driven effects on saving. In a simulation study, using an OLG model, Blomquist and Wijkander (1993) found evidence that demographic shocks could affect the aggregate saving. Herbertson and Zoega (1999) found empirical support for the demographic effects on saving, establishing a 5
significant negative correlation between the fraction of young and old and the current account, using a panel of 84 countries. Using the national income identity, the current account is the difference between savings and investment. Lindh and Malmberg (1999b) also find evidence for a significant relationship between the age structure and the current account using data from twenty OECD countries.
One possible channel, through which changes in aggregate saving could affect the real exchange rate, is easily seen using a standard Mundell-Fleming model. The economy is characterised by the following equations, where equations (2.1) and (2.2) are the IS and LM curves respectively. EP * Y = C (Y − T ) + I i * − π e + G + NX P
(
(
M = L i*, Y P
)
(2.1)
)
(2.2)
Where Y, C, T, I, G and NX are income, consumption, taxes, investment, government purchases and net exports respectively. This set-up means that net exports equals the current account. Furthermore, i* is the foreign interest rate, which is taken as given, πe is the expected rate of inflation, E is the nominal exchange rate expressed as domestic currency per foreign currency, P* is the foreign price level and P is the domestic price level. Finally, M denotes money supply and L money demand. Consequently, net exports are a function of the real exchange rate. A graphical representation of the two equations with the real exchange rate on the vertical axis and income on the horizontal axis gives a vertical LM curve and a positively sloped IS curve. An increase in saving relative to investment will increase net exports and shift the IS curve upwards causing the real exchange rate to depreciate.
In the simple exercise above we illustrated how a change in aggregate saving, caused by e.g. a change in the demographic profile, could affect the real exchange rate. However, differences in the effect on saving are not the only thing that separates the different age groups discussed above. Another important aspect is the different consumption patterns between the age groups, which should make the distinction between tradable and non-tradable goods important. The Mundell-Fleming model is based on the distinction between home and foreign 6
goods, and does not give an opportunity to analyse tradable and non-tradable goods. For this purpose we use an IS-LM type aggregate demand model, following Bruce and Purvis (1985), given below. We analyse the model assuming a floating exchange rate. w w NX = QT 0 − D T 0 , i * , Y E E
(2.3)
w w w Y = Q T 0 + 0 D N 0 , i*, Y E E E
(2.4)
(
M = L i* , Y
)
(2.5)
where Q and D denote supply and demand respectively, and superscripts T and N denote tradables and non-tradables. w0 is the nominal exogenous wage and the relative price of services is defined as the real wage in terms of traded goods, w0/E. The other variables are defined as above. In the model, real money balances are defined in terms of non-tradables; the deflator used is the fixed domestic price normalized to unity. The effect of an exogenous change on spending of non-traded goods, i.e. an exogenous change of net exports, could be analysed by totally differentiating the system above and solving for the endogenous variable. For the sake of simplicity, we normalise w0 and E to equal unity, this together with the fact that the interest rate is exogenously determined, gives the following system:
( (
− Z T η T + ε T T T T − Z η + ε 0
) )
DYT 1 − DYN − L´
0 dE − dNX 0 dY = 0 1 dM 0
(2.6)
where ZT denotes the value of output of tradables, ε and η are elasticities with respect to supply and demand respectively. Solving the system for the effect of a change in net exports on the exchange rate gives: dE 1 − DYN s+m = T T = T T >0 T T N dNX Z η + ε 1 − DY − DY Z η +εT s
(
)(
)
(
)
7
(2.7)
In (2.7), s and m are the marginal propensities to save and to import, defined as follows: s = 1 − DYT − DYN m=D
T Y
,s > 0 ,m > 0
(2.8)
According to (2.7), a shift in demand away from non-tradables, which by definition makes net exports increase, will have a depreciating effect on the exchange rate. Since the model is Keynesian we have sticky prices, and a depreciating nominal exchange rate implies a depreciating real exchange rate. A decrease in the consumption of non-tradable goods has a potential demographically driven explanation, e.g. a small fraction of the population consuming health care or education.
Support for the idea of demographically driven changes in national saving and its effect on the real exchange rate can also be found in other, more complex, theoretical frameworks. Cantor and Driskill (1999) use an OLG model to show that a demographic shock causes national saving and the real exchange rate to change. In their model, however, the response of a demographic shock to the real exchange rate is ambiguous and depends on the net foreign indebtedness of the country.
Consider a “shock” in the group of young retirees. The real exchange rate is assumed to be in long run equilibrium. For simplicity, assume that initially the age profiles in the different countries are the same and that the demographic shock is considered to be domestic. The group of young retirees initially increases, causing a decrease in saving, ceteris paribus, since we have a growing fraction of people in a dissaving phase of life. Looking at the MundellFleming model described above, we see that this reduction in saving decreases net exports, which will tend to appreciate the real exchange rate. According to the tradable/non-tradable goods model, a shift in preferences for non-tradable goods, such as health care, implied an appreciating effect on the real exchange rate through the change in net exports. This process with an appreciating real exchange rate will continue as long as the group of young retirees is increasing. When the group of young retirees eventually starts decreasing, we will experience a depreciating real exchange rate, ceteris paribus. Finally we will have returned to the initial equilibrium level. The whole process is illustrated in Figure 1. Considering a shock in the other age groups, we would expect children, young adults and old retirees to show a similar
8
effect as the one caused by the young retirees. Prime and middle aged should show an inverse effect. Figure 1. The impact of a change in the group of young retirees to the real exchange rate.
Real exchange rate
t Fraction of young retirees increasing
Fraction of young retirees decreasing
The demographic shock considered previously is, however, a stylised simplification. Firstly, we will experience several simultaneous shocks since baby boom and baby burst cohorts will influence the age distribution at the same time. Secondly, we will experience a continuous movement from one age group into another. Hence, the age distribution will almost surely never be stable and the relative relationship between the different age groups will change continuously. Thus, when studying the real exchange rate, it is necessary to consider the whole age distribution.
In the example above, we assumed that the real exchange rate, after the effect of the shock has disappeared, returns to its long run equilibrium level, which is a constant. The implication of this is that we assume that relative PPP holds in the long run, and hence that the process is mean reverting. This is, however, only one of many theories regarding the real exchange rate. One frequently used relationship when studying real exchange rates is the real interest rate parity condition, which provides a link between the real interest rate differential and the real exchange rate. A positive expected real interest rate differential should, according to the condition, be matched by an expected real depreciation. Using the theories of Balassa (1964) and Samuelson (1964) the real exchange rate will also be influenced by cross country 9
differences in productivity and relative productivity differences in the tradable and nontradable sectors. They argue that technological progress is faster in the tradable sector than in the non-tradable sector. This will tend to raise wages in the entire economy, forcing producers in the non-traded sector to increase the relative price of non-traded goods. Hence a positive productivity shock in the tradable sector would cause a real appreciation. According to the macroeconomic balance approach, see e.g. Clark et al. (1994), the equilibrium real exchange rate is given by a level consistent with internal and external balance. Internal balance is often defined as the level of output consistent with full employment and low inflation. External balance can be defined as the level of the current account consistent with foreign debt equilibrium. This gives a link to the work of Dornbusch and Fisher (1980) where the current account is an important determinant of the real exchange rate. Whether or not the effects generated in these models will cause a permanent shift in the equilibrium level of the real exchange rate or a temporary deviation is arguable. Furthermore, Froot and Rogoff (1995) consider the possibility of demand shocks, such as government spending, causing medium-run effects on the real exchange rate. This is consistent with our line of argument. As stated earlier, changes in governmental spending, at least to the extent that spending is on nontradable goods, could be explained by changes in the demographic distribution.
In this section we have argued that changes in the demographic structure could affect the real exchange rate. The main purpose of the empirical part of the paper will be to investigate this hypothesis, in order to be able to make forecasts of the real exchange rate. Since we expect the demographic structure to explain medium- and lung-run trends, and not short run fluctuations, we will also use a set of control variables, based on the other theories of the real exchange rate mentioned above, in order to control for other determinants of the real exchange rate.
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3. Empirical study
We have very good reason to believe that many macroeconomic variables are simultaneously determined with the real exchange rate. This means that if we want to use variables such as the current account balance or the relative GDP growth to explain the real exchange rate we have to abandon OLS as the estimation method, since it will not yield consistent estimates. Furthermore, if we want to make forecasts of the real exchange rate using variables that have themselves to be forecasted this could double the uncertainty of the forecast (Tashman et al., 2000). Hence, a reduced form estimation where the real exchange rate is explained by age group data alone have some obvious advantages; the exogeneity assumption of the OLS model is more likely to be satisfied since, as previously mentioned, the feedback of the economy into demography is a rather slow process. We also have small forecast errors when predicting the future population up to reasonable horizons, compared to the alternative of forecasting other macroeconomic variables.
3.1 Data
Data on the real exchange rate was supplied by Central Bank of Sweden. We used quarterly observations for the period March 1960 to March 2000 on the real TCW (Total Competitiveness Weights) index, where CPIs have been used as deflators. This index reflects bilateral import and export competitiveness as well as competitiveness in third country markets. The weights are based on aggregate flows of worked goods during the years of 19891991 for 21 OECD countries.3 The base of the index is set so that it equals 100 on November 18 1992, just before the Swedish fixed exchange rate regime was abandoned, and is constructed so that a higher index means a weaker real exchange rate.
Age data for Sweden and the TCW countries was supplied by Statistics Sweden and the United Nations. The original data consisted of yearly observations, but since censuses are conducted more rarely, the observations are both actual values and projections. The projections’ deviations from real values are though almost certainly of rather small magnitude. Observations refer to the last of December of the given year and have been lagged one year in order to be predetermined with respect to the real exchange rate. Since we have
3
TCW weights can be found in Table A1, Appendix 1.
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quarterly data on the real exchange rate we converted the yearly data to quarterly, using a simple linear interpolation.
In the original data set the population had been divided into five-year groups except for the oldest who were given as 95 or above. Using all 20 of these groups as regressors, regardless of how we measure the demographic profile, would with certainty have given us a serious problem with multicollinearity. In order to get a description of the composition of the population that is possible to work with, we chose to divide the population into the six groups previously discussed i.e. children (0-14), young adults (15-24), prime aged (25-49), middle aged (50-64), young retirees (65-74) and old retirees (75 and above). Aggregating the age data into six groups will reduce the degree of multicollinearity, but will not eliminate the phenomenon completely. From this data set we created two measures of the demographic profile. One consisted of the Swedish age shares and the other described the relative demography of Sweden to the countries in the TCW index4.
An important matter in time series regression is the degree of integration of the variables. If we seem to have I(1)-variables, we must always ask ourselves the question whether a high R2 when regressing levels is due to an actual relationship between the variables, or if spurious regression is present5.
In our case, when applying the augmented Dickey-Fuller test on the full sample (1960:12000:1), we could reject the null hypothesis of a unit root for three of the included Swedish age shares at the five per cent level. For the youngest and the two oldest groups, i.e. children and the young and old retirees, the data was unable to reject the null. When looking at the relative demography series the null was rejected for all groups except the prime aged and the old retirees. Regarding the real exchange rate, this series failed to reject the null of a unit root.
These results leave us with the delicate issue of how we should specify our model. Considering the real exchange rate it is stationary according to the theory of PPP. There is some evidence that this is the case, even if there have been a lot of tests rejecting this 4
When calculating the demographic profile of the countries in the TCW index, we assigned each country´s age share the weight given by the TCW weights in an arithmetic average. Both the Swedish and the TCW series were then made into index series with base in 1959:1. The series of relative demography was then created as ln(Swedish index/TCW index). 5 A discussion of this issue can be found in e.g. Granger and Newbold (1986).
12
hypothesis as well. For some examples of the empirical literature, see Kim (1990), Edison and Fisher (1991), Fisher and Park (1991), Alexius (1995) and MacDonald (1998). Another thing to keep in mind is that if we are dealing with e.g. a stationary autoregressive process of order one and the parameter in the process is close to unity, we will have very small chances of rejecting the false null of a unit root (e.g. Froot and Rogoff, 1995). This could in fact be the case here since an estimation of an AR(1) model on the real exchange rate using the full sample yields an estimate of the AR parameter of 0.980, which can be seen in Table A2, Appendix 2.
Further we might ask if the demographic series that could not reject the null actually contain a unit root. Looking at them, illustrated in Figure 2, one could argue that at least some of them contain a trend during the sample period. One can, on the other hand, claim that in the long run the age shares should be stationary, i.e. when the demographic transition has run its course.
If in fact we are dealing with integrated series it would probably be preferable to work with differences rather than levels. Differencing the series does not come without a cost on the other hand. The level of the variable could in itself contain valuable information and differencing would then be like throwing out the baby with the bath water. An obvious problem with differencing is that if we have both high and low frequency variation in the dependent variable and the age pattern variation is of low frequency we are likely to lose the relationship in the data. To conclude the issue, we decided that the “pros” of using levels outnumbered the “cons”.
3.2 Estimation
Initially a model with the Swedish age shares as the only regressors, OLS I, was estimated. If all six groups were to be included in the estimation of the model, we would have to drop the intercept to avoid perfect collinearity since the age shares sum to one. We therefore chose to exclude the youngest group from the estimation. The pure age model was also estimated with dummy variables included for two major events in the Swedish economic history: the
13
“aggressive” devaluation in 1982 and the shift from a fixed to a floating exchange rate in 1992.6 The purpose of this regression, OLS II, was to see if the results changed dramatically.
Table 1 reports the results from these regressions, and as we can see the fit using the age model is very good, with as well as without dummy variables. The parameter estimates are all highly significant, except for the second oldest group. As we can see from the Ljung-Box statistics we have a serious case of serial correlation in the residuals, but since we have used the Newey and West (1987) heteroscedasticity and autocorrelation consistent standard errors, this fact should not affect the inference. Looking at the point estimates, their relative effect7 is consistent with what we expect from the life cycle hypothesis argumentation in section two; young adults, young retirees and old retirees have an appreciating effect on the real exchange rate, while the prime and middle aged have a depreciating effect. 8 We see this fact as support for the model specification. If this was a pure spurious regression, we would have little reason to expect results in line with theory. Considering the stability of the estimates, the coefficients seem quite stable during the last five years, see recursive estimates reported in Figure A1, Appendix 2.
6
The dummy variables take the value one for seven periods following the event, taking care of the main part of the temporary effects. 7 Since we are using five of the six age shares as regressors it is only possible to interpret the effect of one group relative to another. 8 The model was also regressed using OLS on yearly data from 1950 to 1999 using a thirteen countries approximation of the TCW index. The main reason for this was to see if more of age structure variation in the sample would change the conclusions. This alternative regression had results that to a very large extent imply the same effects as those in Table 1.
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Table 1. Estimation results. Dependent variable is ln(Real exchange rate). OLS I OLS II 2SLS C -5.284* -3.938 -0,255 (-1.089) (-1.478) (-0,203) S1524 5.826 ** 4.921 ** 1,634 (2.623) (2.313) (1,369) S2549 15.603** 13.305** 3,127 * (3.737) (3.544) (1,904) S5064 16.768** 15.076** 4,420 ** (3.187) (3.102) (2,114) S6574 6.051 * 4.077 -3,845* (1.773) (1.384) (-1,821) S75W 6.887 ** 7.104 ** 5,486 ** (10.105) (10.364) (3,401) Dummy 1982 0.112 ** 0,043 ** devaluation (5.016) (3,613) Dummy floating 0.089 ** 0,043 ** exchange rate (3.467) (3,597) Lagged ln REALTCW 0,622 ** (8,557) Short real interest rate -0,012** differential (-3,360) Long real interest rate 0,015 ** differential (4,487) Relative GDP growth 0,361 (1,196) Current account -0,432* balance (-1,730) Government financial -0,234* saving (-1,769) Adjusted R2 0.781 0.855 0.949 Observations 161 161 147 Q(1) 120.29** 107.57** 0.57 ** Q(2) 202.52 173.44** 0.60 Q(5) 295.45** 231.98** 13.21 ** Sargan 1,93 Standard errors Newey-West corrected in OLS estimations. t-values in parenthesis. Q(p) is the Ljung-Box statistic of no residual autocorrelation up to order p. Sargan is the test statistic for the Sargan test with null hypothesis of valid instruments. ** significant at the 5% level, * significant at the 10% level.
Turning to the first order autocorrelation in the residuals from the estimated models OLS I and OLS II, this might be due to several causes. Firstly, we have the fact that the model might be incomplete in its specification. We consider this quite likely to be the case since we do not think that the age model is a complete description of everything that affects the real exchange rate. Secondly, there is a possibility that the linear interpolation of the age group data creates the pattern in the residuals. Thirdly, we have the question of the stationarity of the variables. If the time series used in the regression are random walks or IMA(1,1) processes, it is not unlikely that we will achieve a high value of the adjusted R2 and a high value of the LjungBox statistic at the first lag.
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As a test for omitted variables, we chose to include some relevant control variables. The relative real GDP-growth to the TCW countries, short and long-term real interest rate differentials to TCW countries are three variables that are likely to covary with the real exchange rate 9. Besides these three variables we also chose to include the Swedish current account balance and Swedish government financial saving, both expressed as per cent of GDP, as control variables, and finally, one lag of the real exchange rate. Since there were problems in getting data on the control variables for the entire sample we had to shorten the sample to the period 1962:1 to 1998:4. There are reasons to suspect that the control variables included are simultaneously determined with the real exchange rate. Thus OLS no longer yield consistent estimates. Therefore two stage least squares (2SLS) was used in the regression, and this result can also be found in Table 1. The age groups served as their own instruments and the control variables were instrumented by two lags of each variable. As we can see the age variables are still significant at reasonable levels, except for the young adults. The relationship between the parameter estimates is still about what we would expect, apart from the very high estimate of the old retirees, which probably is due to multicollinearity. Looking at the estimates of the control variables and the lagged dependent variable we find that the short and long term interest rate differential and the lagged dependent variable are significant at the five percent level, while the current account balance, the government financial saving and the relative GDP growth are not. Judging by the value of the Ljung-Box statistics, the inclusion of these variables seems to have taken care of the problem with the first order autocorrelation in the residuals. We can also see that including variables that one could claim are determinants of the real exchange rate do not make the age shares insignificant.
The equations estimated in Table 1 are all made using levels. The fact that the estimated coefficients, as previously mentioned, are in line with theory, supports the idea that the estimated relationship is not spurious. However, even though we argue that the data generating processes hardly are I(1), we cannot deny the fact that there seems to be trends in both the dependent and some of the explanatory variables. As a further investigation in this matter, we therefore estimated an error correction model (ECM), which reduces the possibility of spurious regression. The long-run relationship was assumed to be given by the
9
A description of the control variables can be found in Appendix 1.
16
age shares and the short run fluctuations by our control variables. The complete model specification is given in equation 3.1. ∆[ln Qt ] =
(3.1)
75W C + γ ln[Qt −1 ] − ∑ β i S i , t −1 + i =1524 λ1 ∆SIRDt + λ2 ∆LIRDt + λ3 ∆RGDPGR t + λ 4 ∆CAB t + λ5 ∆GFS t + u t
where Qt is the real exchange rate, SIRDt the short term real interest rate differential, LIRDt the long term real interest rate differential, RGDPGRt the relative GDP growth, CABt the current account balance and GFSt the government financial saving, at time t. 10 The results from this estimation are given in Table 2. Table 2. Estimation results, error correction model. ECM C -0.955 (-1.221) -0.140** γ (-2.087) S1524 4.552 (0.973) S2549 17.737** (2.162) S5064 21.657* (1.903) S6574 6.616 (1.005) S75W 9.034 ** (2.676) -0.002 ∆SIRD (-1.090) 0.001 ∆LIRD (0.213) 0.245 ∆RGDPGR (1.630) 0.956 ∆CAB (1.535) -0.516 ∆GFS (-0.895) Adjusted R2 0.048 Observations 148 Q(1) 0.47 Q(2) 0.62 Q(5) 3.80 Standard errors Newey-West corrected. t-values in parenthesis. Q(p) is the Ljung-Box statistic of no residual autocorrelation up to order p. ** significant at the 5% level, * significant at the 10% level.
10
A description of the control variables can be found in Appendix 1.
17
As can be seen, there are two significant age groups at the five percent level and one more at the ten percent level and the relative relationship between the point estimates are still what we expect. Furthermore the error correction term is significant and has the correct sign, i.e. negative. Regarding the short-run relationship, the control variables do not succeed in explaining this. However, this was not unexpected since there is a lot of noise in the series.
What we have seen so far is that the Swedish age shares make quite a good job explaining the real exchange rate. However, one might argue that the relative demography of Sweden to the countries in the TCW index should matter since these countries also have changes in their demographic profiles, and the real exchange rate is a bilateral relationship. Initially, pure age models, with and without dummies for the devaluation 1982 and the shift to a floating exchange rate in 1992, using the series of relative demography described earlier, were estimated. These results, OLS III and OLS IV, can be found in Table A3, Appendix 2, and as we can see there are significant parameter estimates on young adults, middle aged and young retirees but insignificant on prime aged and old retirees at the five per cent level. Looking at the point estimates, however, we no longer can find the relationship between them that we expect from the life cycle hypothesis. Some of the coefficients are, as mentioned, imprecisely measured, but a striking example is the effect of the middle aged which in OLS III and IV make up the most appreciating group. This can be compared to OLS I and II where this group was the most depreciating, which is more in line with what we expect from theory. In order to see whether there was information in the Swedish age shares that could improve the regression with relative demography as regressors, we used the residuals from OLS III as dependent variable in a regression with the Swedish age shares as regressors, OLS V. The result from this regression is given in Table A4, Appendix 2. We can clearly see that the Swedish age shares all have significant explanatory power and that we get the expected relationship between the estimated parameters. This led us to the conclusion that the Swedish age shares seem to be a determinant we cannot do without. To further examine the relevance of relative demography, we reversed the residual experiment, regressing relative demography on the residuals from the regression where the Swedish age shares explained the real exchange rate, OLS I. Looking at the output from this regression, OLS VI, which can be found in Table A4, Appendix 2, we find that none of the parameters are significant at any reasonable level and that the adjusted R2 is negative. It seems as if the series of relative demography, although able to achieve a high adjusted R 2 when explaining the real exchange rate, do not contain any unique variation of interest after controlling for the Swedish age 18
shares. This irrelevance of the foreign demographic profile could be due to the possibility that trade patterns already reflect relative demography to some extent. When choosing trade partners it is reasonable to assume that a country aims to get as favourable conditions as possible. This should in turn depend on relative demography. If this is in fact the case, we would expect that the domestic age profile is the relevant demographic measure to consider when determining the real exchange rate.
To sum up this section, we conclude that the Swedish age shares seem to be a relevant factor in determining the real exchange rate whereas the relative position of Swedish demography to the countries in the TCW index is not. Testing the forecasting ability of the age model will be the next step in this paper.
3.3 Forecast evaluation and forecasts
In this section we will evaluate the forecasting ability of the age model with Swedish age shares and dummy variables (OLS II, Table 1). As we stated previously, the coefficients of the age model seemed to be stable and the model had a good fit, but this is not reason enough to believe that the model will be a good forecasting model. Therefore, we perform an out-ofsample exercise in order to assess the performance of the model. After this follows a section in which we make forecasts of the real exchange rate fifteen years ahead using projections of the age shares.
The out-of-sample forecasts are calculated as follows. We estimate the model using data up to 1995:4 and then we use these results and make forecasts to 2000:1, i.e. seventeen periods ahead. Then we extend the sample one period and make forecasts sixteen periods ahead and so forth, in the last exercise we are able to make forecasts four periods ahead. We also perform the same exercise using a simple autoregressive model (see AR(1) II, Table A2, Appendix 2) in order to get a benchmark. Judging from the correlograms, this seems to be the closest model of ARIMA type. The results are presented in Table 2, where we base the evaluation on the one-, two- and three-year forecast horizons. Using this set-up, we are able to perform two four-year forecasts, but the evaluation of these will possibly be imprecise due to few observations. Cutting the sample even further back in time creates two problems. The obvious is that we lose more observations but we will also be close to the transition from a
19
fixed exchange rate to the floating exchange rate regime in 1992, and the dramatic period that followed the transition. Theil´s U11 provides a comparison between a forecast model and a naive forecast, where a naive forecast is optimal given a random walk process. If we are doing better than a naive forecast, Theil´s U will be smaller than unity and larger than unity if we are doing worse. The last column in Table 2, labelled “direction”, indicates how many times the models are able to predict the right direction, i.e. a real depreciation or a real appreciation. In Table 2 we also report the number of forecasts for every forecast horizon, mean error (ME), mean absolute error (MAE), which should, unless we systematically over or under predict, be larger in absolute value than the mean error and root mean square error (RMSE). Root mean square error penalizes large errors relatively more than the mean absolute error; hence this should lead to larger values unless the errors are of equal size. If you are interested in forecasting the trend, the mean error is more relevant than the mean absolute error and the root mean square error since errors around the trend will cancel out, but the other measures will accumulate short-term errors. Table 2. Out-of-sample forecasts. Forecast horizon
Observations
ME
MAE
RMSE
Theil´s U Direction
Age model 1 year 2 years 3 years
14 10 6
4.56 7.68 12.38
4.76 7.68 12.38
5.41 8.36 12.51
0.86 0.85 0.94
11 10 6
1 year 2 years 3 years
14 10 6
-5.56 -11.41 -15.86
5.86 11.41 15.86
6.89 11.87 16.23
1.15 1.22 1.23
3 0 0
AR model
According to Table 2 the age model has lower mean errors than the autoregressive model, implying that the age model seems to catch the trend better than the autoregressive model. The fact that the mean error and the mean absolute error estimates are the same for the age model over the longer forecast horizons indicates that the age model overpredicts. The age model outperforms the autoregressive model in terms of root mean square error for every
20
forecast horizon. The autoregressive model is quite close to a naive forecast since the autoregressive parameter is 0.984 (see Table A2, Appendix 2). This also means that the autoregressive model will always predict a real appreciation. The model does not outperform a naive forecast since the values of Theil´s U are larger than unity. The age model, on the other hand, performs better than a naive forecast. Concerning the ability of the forecasts to predict the right direction, the age model outperforms the autoregressive model. The age model predicts the right direction in eleven out of fourteen one year forecasts. The model was not able to predict the three occasions when there were real appreciations. Consequently, the autoregressive model predicts the right direction three times. Ex ante, we would expect the age model to perform best over the medium and long run horizons. The age pattern does not change that much from one year to another and demographic movements are slowly moving processes. Considering this, the age model performs remarkably well for the shorter time horizon. Over the longer horizons the age model predicts the right direction every time.
The results from the out-of-sample forecasts indicated that the age model seemed to overpredict the actual value. This might be due to the fact that the age model is a reduced form and probably incomplete in its specification. Thus, we remake the exercise using the common technique of intercept correction. We base the correction on the one-year forecast errors. The corrections are made as follows; the first one-year forecast we can evaluate is at time 1996:4. This forecast error is used to correct the forecasts that the model produces about the future at time point 1997:4, i.e. the same factor of correction is used for every forecast horizon following Clements and Henry (1998). Standing at 1997:1, there are two one-year forecast errors and the average of these errors is used for corrections of the forecasts at this time point, and so forth. Using this methodology, the information about the errors of the past is used in order to improve the statements of the future. The results are presented in Table 3.
11
Theil´s U for an i-step ahead forecast:
2
z − zˆ ∑ t + i z t +i t
z −z ∑ t +iz t t
2
. Where zˆt + i is the forecasted value and
21
zt + i
the actual.
Table 3. Out-of-sample forecasts with intercept corrections (IC). Forecast Observations ME MAE RMSE Theil´s U Direction horizon Age model (IC) 1 year 14 1.59 3.46 3.93 0.64 11 2 years 10 5.08 5.40 6.46 0.67 10 3 years 6 10.76 10.76 11.07 0.84 6
As can be seen from the evaluation statistics, the rather simple intercept correction used here seems to have improved the forecasts to some extent. All statistics have decreased, but comparing the mean and absolute errors we find that there still is some overprediction. Using a more sophisticated intercept correction mechanism could probably improve the forecasts even further. Concerning the results from the out-of-sample forecasts, we see these as further evidence against the concerns of spurious regression. As Granger and Newbold (1986, p. 210) argue, “it would, of course, be foolish to expect models with spurious equations to forecast successfully”.
As we stated in the introduction, population projections are reliable estimates of the future age profile with small forecast errors even at longer time horizons. We will use the age model which we estimated in the previous part of the paper in order to make forecasts of the real exchange rate for the period 2000:2-2015:4. We chose this forecasting range in order to be able to catch the dramatic change in the demographic profile that we are facing and to estimate how this will affect the real exchange rate. In Figure 2, the shares of the different age groups used in the model are illustrated with historical values as well as projections. Regarding the issue of an ageing population the figures speak for themselves. We are entering a period with higher and higher fractions of people in the older stages of life. In the end of our estimation period approximately 53 percent of the population were in their productive part of life (25-64 years of age) and 17 percent were 65 years old and above. In the end of our forecasting period the shares have changed to 51 percent and 21 percent respectively.
22
Figure 2. Swedish age shares 1960:1 – 2015:4. Shaded area projections used for forecasts. 0.25 0.26 0.24
0.20
0.22 0.20
0.15
0.18 0.16
0.10
0.14 0.12 60 65 70 75 80 85 90
95 00 05 10 15
60 65 70 75 80 85 90
CHILDREN (0-14)
0.36
95 00 05 10 15
YOUNG ADULTS (15-24)
0.30
0.34 0.25 0.32 0.30
0.20
0.28 0.15 0.26 0.24 60 65 70 75 80 85 90
95 00 05 10 15
60 65 70 75 80 85 90
PRIME AGED (25-49)
0.25
95 00 05 10 15
MIDDLE AGED (50-64)
0.20
0.20
0.15
0.15 0.10 0.10 0.05
0.05
0.00 60 65 70 75 80 85 90
95 00 05 10 15
0.00 60 65 70 75 80 85 90
YOUNG RETIREES (65-74)
95 00 05 10 15
OLD RETIREES (75-)
Figure 3 illustrates the actual values together with the estimated model as well as the forecasts of the real exchange rate for the period 2000:2- 2015:4 of the real TCW index. According to the forecasts, the demographic structure will have a depreciating effect on the real exchange rate in a period to come, peaking in 2007 with a value of 158. The last observation of the TCW index was 128; consequently the model predicts that the real exchange rate will depreciate approximately 23 percent during the next eight years to come. Keeping in mind the fact that, according to the forecast evaluation previously presented, the model seems to overpredict the index one might want to interpret these values with a pinch of salt. On the other hand the model seemed to be able to catch the directions of the changes in the real exchange rate, which could be reasons for believing in the shape of the forecasted series. As 23
could be seen from the out-of-sample forecast exercise, the forecasts were improved using intercept correction. Using the same methodology here would shift the forecasted series downward. The period of depreciation predicted by the model seems credible considering the changes in the age profile illustrated in Figure 2. Turning to Figure 2 and the middle aged group (centre right), the fraction of middle aged will continue to increase to 2007. This is the baby boom cohort of the 1940’s on their way to retirement. According to theory this age group should be characterised by a high degree of saving and small consumption of nontradables, which should cause a depreciating pressure on the real exchange rate. The theory also states that the prime aged should have the same effect but not to the same extent. This group steadily declines during the forecast period but that obviously does not affect the direction of the forecast. The depreciating pressure from the middle aged seems to dominate, causing the real exchange rate to depreciate. To some extent, the period of depreciation might as well be explained by the downward trend in the fraction of children. Children do not enter the model explicitly but only implicitly, through the impact on the population shares. By itself, the group should have an appreciating effect on the real exchange rate. Considering the lower fraction of children in the years to come, the appreciating effect is restrained. Taken together, the predicted depreciation during the following years seems reasonable considering the changes of the population during the period, mainly the growing middle aged group with its economic behaviour. Figure 3. Actual real exchange rate (solid) and predicted (dashed). Forecasts 2000:2-2015:4 (shaded).
150
100
50 60 65 70
75 80
85 90 95
Actual Fitted
00 05
10 15
+/- 2*SE
24
After 2007 there will be a period of appreciating real exchange rates. At the end of the forecast period (2015:4), the model predicts that the real TCW index will be approximately 127, i.e. slightly less than the last actual value used for estimation. In order to explain this phase of appreciation, turn again to Figure 2. The young retirees (bottom left) will begin to increase around 2003, an increase that will continue through the whole forecasting period. The 1940´s cohorts will start to retire in 2005 approximately. The appreciating real exchange rate could be explained by the growing fraction of people starting to sell off their financial assets in order to compensate their lower income as well as demanding relatively more nontradables. The lower depreciating pressure from the middle aged group caused by a decrease of that group in 2008 is probably also an important explanation.
The reduced form age model used for forecasts previously is, however, not the only possible model to use. Despite some statistical shortcomings, it is possible to use the more complete model that incorporated the different control variables, 2SLS, as well as the estimated long run relationship from the error correction model, ECM. The age structure was included in both these models, but the relationship was estimated together with the control variables. It could, however, be interesting to get a comparison between the forecasts generated by the different models. When using the alternative models for forecasting, we have to make some assumptions regarding the control variables, or forecast them separately. We chose to assume a constant level during the forecasting period, i.e. the differences in the error correction model was set to zero. The actual data for the real exchange rate between 1960:1-2000:1 is shown in Figure 4, together with the forecasted series using the pure age model, OLS II, two stage least squares model, 2SLS, and the error correction model, ECM.
25
Figure 4. Actual real exchange rate 1960:1-2000:1. Forecasts 2000:2-2015:4 (shaded) using OLS II, ECM and 2SLS. 200 180 160 140 120 100 80 60 65
70 75
80 85 Actual OLS II
90 95
00
05 10
15
2SLS ECM
The figure clearly tells us that the forecasts based on 2SLS and ECM, though having fairly similar shapes as the OLS II model, give far more dramatic developments than the forecast generated by the pure age model. As we could see in the out-of-sample forecast exercise, the pure age model seemed to overpredict the real exchange rate. This fact, together with the picture outlined in Figure 4, indicates that the alternative models generate unrealistic forecasts. Concerning the ECM, we suspect that this might be due to the differencing of the series and the loss of information this generates. Hence, we argue that this supports the use of levels. Regarding the 2SLS model, one might suspect that its rather unrealistic forecasted series is due to our restrictive assumption of constant levels of the control variables. As we referred to in the introduction of the paper, some of the control variables, such as growth and the current account, are influenced by the age structure. This could lead to interaction and collinearity between the demographic structure and the control variables, which by our assumption is ignored. Hence, taking care of the development of these variables and to forecast them with a high degree of accuracy, seems necessary in order to use the alternative models. Otherwise, the reduced form age model, which has the advantage of incorporating these partially demographically driven effects indirectly, is probably to be preferred.
26
4. Conclusions
In this paper we have investigated the impact of demography on the Swedish real exchange rate. We found evidence that Swedish age structure data had significant explanatory power on the real exchange rate, whereas the relative demography to the surrounding world could be ignored. This effect remained even after including other variables that one could argue influence the real exchange rate. Furthermore, the point estimates from the age coefficients are in line with what we expect from the life-cycle-hypothesis, i.e. young adults and retirees seem to have an appreciating effect and prime and middle aged have a depreciating effect.
Using a model with Swedish age shares alone as regressors we make out-of-sample mediumterm forecasts of the real exchange rate, which perform reasonably well, with as well as without intercept correction. The same model was also used making forecasts of the real exchange rate up to 2015. According to the forecasted series, we can expect a depreciating Swedish real exchange rate until 2007, followed by an appreciation until the end of the forecasted period. This scenario makes sense considering the development of the Swedish demographic profile and the economic conditions and behaviour of the age groups.
We would argue that an economy showing long periods of weak (strong) exchange rate supporting current account surpluses (deficits) still could be consistent with the concept of external balance, because of the slow changes in the demographic profile. Thus, what appears to be an imbalance might actually be a requirement in order to achieve macroeconomic balance in the long run. A final observation is that demographic changes seem to cause movements in the real exchange rate on a frequency lower than the business cycle fluctuations. Oscillations on this frequency might be the reason why PPP quite often is rejected using fairly long samples, e.g. 30 to 40 years, but seems to hold using samples covering a century or more.
27
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Appendix 1: Data
Table A1. Weights in per cent assigned to different countries in the TCW index for Sweden. Country Weight Australia 0.27 Austria 1.71 Belgium 3.55 Canada 1.16 Denmark 5.60 France 7.15 Finland 6.69 Germany 22.28 Great Britain 11.56 Greece 0.27 Holland 4.24 Ireland 0.77 Italy 6.05 Japan 5.20 New Zealand 0.14 Norway 5.58 Portugal 0.93 Spain 2.48 Switzerland 2.74 USA 11.63
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Below follows a short description of how the different control variables were constructed. Relative GDP growth When constructing the relative GDP series Swedish and TCW weighted GDP were turned into index series with base 1969:4. The relative GDP growth series was then achieved by taking ln(Swedish index/TCW index).
During the first period of the sample, 1962:1 to 1969:4, a proxy for the TCW countries has been used consisting of USA, West Germany and Great Britain. In the approximation the weights were assigned as follows: USA: 0.14136, West Germany: 0.71813, Great Britain: 0.14051. West Germany got to represent all Euro-countries and small countries were excluded. The weights are corrected in order to sum unity. This series was linked to a full twenty countries TCW weighted real GDP series used in the remaining part of the sample. Data from 1962:1 to 1969:4 from was taken from OECD. For the rest of the sample data was taken from Sveriges Riksbank. Short real interest rate differential The interest rate differential is achieved by subtracting a TCW weighted real interest rate from the Swedish real interest rate.
During 1962:1 to 1970:3 the TCW real interest rate was approximated using the same three countries as in the relative GDP growth series. The rest of the sample consists of all the TCW countries. For the period 1962:1 to 1970:3 the data are taken from OECD. The data from 1970:4 to 1998:4 are from Sveriges Riksbank. Long real interest rate differential The TCW real interest rate was approximated using the three weights above for the whole sample. Data from Sveriges Riksbank.
33
Appendix 2: Estimation output
Table A2. Estimation results. Dependent variable is ln(Real exchange rate). AR(1) I AR(1) II C 4.732 ** 4.746 ** (36.529) (26.874) Dummy 1982 0.066 ** devaluation (2.096) Dummy floating 0.073 exchange rate (1.128) AR(1) 0.980 ** 0.984 ** (56.979) (50.708) Adjusted R2 0.941 0.951 Observations 160 160 Q(1) Q(2) 0.700 0.192 Q(5) 2.359 3.507 Standard errors Newey-West correcteds. t-values in parenthesis. Q(p) is the Ljung-Box statistic of no residual autocorrelation up to order p. ** significant at the 5% level, * significant at the 10% level.
34
Figure A1. Recursive estimates 1980:1-2000:1 for OLS II. 15
20
10
15
5
10
0
5
-5
0
-10
-5
-15
-10 80
82
84
86
88
90
92
94
96
98
00
80
82
84
86
88
C
90
92
94
96
98
00
94
96
98
00
94
96
98
00
S1524
30
30 25
20
20 15
10 10 5
0
0 -5
-10 80
82
84
86
88
90
92
94
96
98
00
80
82
84
86
88
S2549
90
92
S5064
40
60
20 40 0 20 -20 0
-40
-60
-20 80
82
84
86
88
90
92
94
96
98
00
80
82
S6574
84
86
88
90
92
S75W
35
Table A3. Estimation results. Dependent variable is ln(Real exchange rate). OLS III OLS IV C 4.636 ** 4.611 ** (175.854) (286.147) R1524 -0.527** -0.341** (-3.152) (-3.546) R2549 0.167 0.712 (0.160) (0.853) R5064 -0.917** -0.903** (-7.984) (-7.657) R6574 -0.699** -0.675** (-4.044) (-4.200) R75W 0.836 1.581 * (0.720) (1.693) Dummy 1982 0.148 ** devaluation (7.321) Dummy floating 0.041 ** exchange rate (2.110) Adjusted R2 0.728 0.815 Observations 161 161 Q(1) 127.97** 113.52** ** Q(2) 221.77 186.75** ** Q(5) 355.72 262.78** Standard errors Newey-West corrected. t-values in parenthesis. Q(p) is the Ljung-Box statistic of no residual autocorrelation up to order p. ** significant at the 5% level, * significant at the 10% level.
36
Table A4. Estimation results. Dependent variables are residuals from OLS I and OLS III respectively. OLS V OLS VI C -10.722 ** 0.015 (-3.900) (0.813) S1524 8.942 ** (4.274) S2549 15.470** (3.920) S5064 18.639** (3.797) S6574 9.305 ** (2.867) S75W 3.300 ** (5.617) R1524 -0.058 (-0.456) R2549 0.251 (0.273) R5064 -0.049 (-0.374) R6574 -0.133 (-0.981) R75W 0.034 (0.035) Adjusted R2 0.273 -0.022 Observations 161 161 Q(1) 115.92** 119.56** ** Q(2) 190.94 200.72** ** Q(5) 264.35 290.93** Standard errors Newey-West corrected. t-values in parenthesis. Q(p) is the Ljung-Box statistic of no residual autocorrelation up to order p. ** significant at the 5% level, * significant at the 10% level.
37
