Demography and Exchange
MASTER THESIS IN: Economics
NUMBER OF CREDITS: 30 ECTS
PROGRAM OF STUDY: Urban, Regional and International Economics
AUTHOR: Robert Pölder
JÖNKÖPING June 2018
This thesis is a result of a master’s degree research project conducted at Jönköping University. I would first like to thank Scott Hacker and several people at Jönköping University for providing valuable assistance and advice throughout the research process. In addition, I would like to thank Aenne Ohainski for valuable feedback on my work. Lastly, I would like to acknowledge my family: while you may not know much about economics, you are always there to support me.
Master Thesis Economics
Title: Demography and Exchange Rate Movements – Evidence from Sweden Author: Robert Pölder
Supervisor: Scott Hacker
Key terms: real exchange rate, Sweden, demography, forecasts, life cycle hypothesis
This thesis analyzes how demographic changes influence the real effective exchange rate in Sweden. The study develops and tests recent models used to examine the link between the age structure of the population and the real effective exchange rate. One paper has explored this connection in Sweden; it found a relationship between changes in the Swedish demographic structure and the Swedish real effective exchange rate. The study at hand, however, instead argues that relative demographic change, in this case, the change in the Swedish age structure relative to that of its trading partners, is a superior explanatory factor when determining exchange rate movements during the sample period, the first quarter (Q1) of 1961 to 2016Q2. In order to investigate this, an ordinary least squares (OLS) model and a fully modified least squares (FMOLS) model are estimated and compared to a model using only the domestic age structure and to a random walk model (RW). The results show that the OLS and FMOLS models outperform the model using the domestic age structure for all forecast horizons, and the RW for all except at the shortest one. In addition, the conclusion in this thesis changes when relative demographic changes, instead of domestic changes, are used as explanatory factors in the model. This show that the prime aged population (i.e., people aged 25-49 years) has a depreciating effect on a real weighted index of the Swedish krona while the other age groups have the opposite effect. Lastly, forecasts were generated for the period 2016Q3 to 2032Q2 in order to explore how future demographic changes are expected to affect the Swedish real effective exchange rate. The results show that the Swedish krona is projected to undergo real depreciations until 2032Q2.
Table of Contents
Introduction ... 1
Literature review ... 3
2.1 Savings, demographics, and the current account ... 3
2.2 Demographics and the exchange rate ... 4
2.3 Forecasting the real exchange rate ... 5
The life cycle hypothesis and the real exchange rate ... 6
Methodological framework ... 7
4.1 Reference model ... 7
4.2 Ordinary least squares model ... 9
4.3 Fully modified least squares model ... 10
4.4 Control variables ... 13
4.5 Intercept correction... 14
4.6 Accuracy evaluation of the models: forecast performance ... 15
Description of the data and variables ... 17
Results and analysis ... 20
6.1 Estimation of the reference model ... 20
6.2 Estimation of the ordinary least squares model ... 23
6.3 Estimation of the fully modified least squares model ... 25
6.4 Robustness of the results ... 29
6.5 Analysis and comparison with previous studies ... 33
Forecasting and evaluation of the models ... 36
7.1 Forecast performance of the various models... 36
7.2 Projections ... 38
Conclusion ... 40
References ... 42
Figure 1. Age shares and relative age shares in the six age groups ... 19
Figure 2. Actual Swedish real effective exchange rate using the HP filter ... 32
Figure 2. Actual Swedish real effective exchange rate and projections ... 39
Figure 3. Relative demographic changes of the various age groups ... 49
TablesTable 1. Countries included in the TCW index and their weights ... 17
Table 2. Estimation results reference model ... 21
Table 3. Estimation results ordinary least squares model ... 24
Table 4. Engle-Granger cointegration test ... 26
Table 5. Fully modified least squares model ... 28
Table 6. Estimation results using the HP filter ... 30
Table 7. Evaluation measures out-of-sample forecasts ... 36
Table 8. Augmented Dickey-Fuller unit-root test ... 46
Table 9. Cointegration test – Engle-Granger excluding the dummies ... 46
Table 10. Estimation results error correction model ... 47
Table 11. Estimation results using the HP filter including dum72:3 ... 48 List of acronyms
ADF test Augmented Dickey-Fuller unit-root test
AIC Akaike information criterion
AÖ Andersson and Österholm (2005)
CPI Consumer price index
DGP Data-generation process
DW Durbin Watson
ECM Error correction model
FMOLS Fully modified least squares
IC Intercept correction
IMF International Monetary Fund
LCH Life cycle hypothesis
MAE Mean-absolute error
MAPE Mean-absolute-percentage error
OECD Organization for Economic Co-operation and development
OLG Overlapping generations model
OLS Ordinary least squares
RMSE Root-mean-square error
RW Random walk model
SIC Schwarz information criterion
TCW index Total competitiveness weights index VAR Vector autoregressive representation
Exchange rate movements can have a substantial impact on the performance of a small open economy. Exchange rate fluctuations, for example, affect the inflation rate and the demand for exports and imports. In Sweden, exports and imports comprise almost 90 percent of GDP; consequently, understanding the fundamentals behind exchange rate movements is essential for policymakers in Sweden. Nonetheless, to date, the best means of modelling exchange rate movements and their determinants are still a matter for debate. This thesis seeks to fill part of that gap.
Various models and theories attempt to explain exchange rate movements. One of the most famous theories used in empirical research and economic textbooks is that of Fleming (1962) and Mundell and Fleming (1963; 1964), which portrays the short-run relationship between an economy’s exchange rate, the interest rate, and economic output. In 1999, however, Cantor and Driskill introduced a new model, an overlapping-generations model (OLG)1 that relates demographic changes to national savings and, in turn, to the real
exchange rate. A disadvantage of Cantor and Driskill’s (1999) model is that the response of the real exchange rate to a demographic shock is ambiguous, evoking either depreciating or appreciating effects, depending on the country’s debt level and the time horizon. On the other hand, the life cycle hypothesis (LCH), which can also be used to explain the reaction of the real exchange rate to demographic changes, produces a well-defined prediction for this relationship.2 According to the hypothesis, households are net borrowers at certain stages
in life and at others, are net savers.3 Several studies have confirmed this life cycle pattern and
that, in turn, savings and spending affect the current account.4 If such an effect on the current
account occurs, then, likewise, savings, which induce capital flows, should also explain some of the variations in the real exchange rate.
Investigating the link between demography and the exchange rate is of particular interest because the population of the industrialized western world is aging. In Sweden, the pattern is similar: in 2017, the dependency ratio,5 which relates the number of non-workers
1 In an OLG model individuals’ life time overlaps at least one period of another agent’s life. 2 See Modigliani & Brumberg (1954) and Friedman (1957).
3 Numerous studies have found that a higher dependency ratio is associated with lower private savings. See, for
example, Higgins (1998), and Athukorala and Tsay (2003).
4 See, for example, Herbertsson and Zoega (1999), and Kim and Lee (2007; 2008).
5 The dependency ratio in this thesis is calculated as the number of people in the 0-19 age group plus the
number of people older than 64 divided by the number of people in the 20-64 age group. It thus shows the ratio between nonworkers and workers on an aggregated level.
to workers, was 0.75; by 2030, this ratio is expected to increase to 0.83 (Lundkvist, 2017), meaning that the economy will face a situation in which there is a ratio of 100 workers to 83 nonworkers. Consequently, fewer people will have to carry a greater burden, likely by paying higher taxes, in the future to be able to maintain the current standard of the public sector.
Empirical research investigating the link between the real exchange rate and demography is, however, scant. In Sweden, one study was conducted by Andersson and Österholm (2005; henceforth, AÖ). They used an OLS model and concluded that demographic changes explain Swedish real exchange rate movements. Their results and model, however, indicate a spurious regression, a potentially false relationship induced by the series’ data generating process (DGP), a finding that this thesis further investigates. Accordingly, stationarity tests are required when estimating an age model and it is likely that AÖ's model has to be estimated differently.6
The objective of this study is threefold: (1) to investigate whether relative demographic changes can explain Swedish real exchange rate movements; (2) to examine whether relative demographic changes provide more information about the development of the krona than do domestic changes, and (3) to ascertain, whether it is possible to use relative age data to analyze past and predict future movements of the Swedish krona.
The remainder of this thesis is organized as follows: Section 2 comprises a literature review. The LCH is presented in Section 3. Section 4 explains the methodological approach, focusing on the differences between the model used by AÖ and the models used in this study. Section 5 presents the data and variables, while the results are presented and analyzed in Section 6. Section 7 conducts forecasts to evaluate models used and explore whether demographic changes can analyze past and predict future exchange rate movements. Finally, Section 8 summarizes and concludes the thesis.
2. Literature review
This section reviews the central empirical works and theories on the relation between demographic changes and real exchange rate movements. The existing empirical literature that has researched exchange rates is massive. Yet, research that considers the link between the age structure of the population and the exchange rate using nonstructural models, such as is the focus of this study, is limited. In contrast, a vast amount of research has considered the relationship between savings and the current account. Research in this area, however, provides a link to the relationship between demographics and the exchange rate. A positive current account, for example, indicates that the nation is a net lender to the rest of the world, which suggests high savings. According to the LCH, the savings behavior is related to age, thus indirectly linking savings, the current account, and the exchange rate by means of capital outflows and inflows. Section 2.1 provides a review of research examining the links between savings, demographics, and the current account, while Section 2.2 reviews studies that attempt to connect exchange rate movements and demography. The final subsection (2.3) reviews the existing empirical literature that focuses on forecasting exchange rate movements and, moreover, presents the Messe-Rogoff puzzle.
2.1 Savings, demographics, and the current account
The links between demographics and the current account are often suggested, based on the LCH, to work through savings; studies examining this relationship date back to the work of Leff (1969). Employing a cross-section approach, Leff found a link between the dependency ratio, savings, and the current account. The existence of this link is supported by both international and Swedish researchers: Lewis (1983), Higgins (1998), Lindh (1999), and Lindh and Malmberg (1999). Similarly, Cook (2005) found that the savings rate is connected to two key variables: the age structure of the population and, moreover, the rate of economic growth. The age structure and savings rate link is likewise stressed by Krueger and Ludwig (2007) in their theoretical model which predicts that a decline in the working age population decreases both savings and investments. Moreover, Gudmundsson and Zoega (2014) illustrate the relation between the age structure and the current account. They found that the share of people aged between 34 and 50 years is on average larger in countries with a current account surplus, while the share of the population over 50 is higher in countries with a deficit.
One anomaly though, frequently encountered in empirical research that examines savings, is the saving behavior of seniors. According to the LCH, savings decrease when an economic agent retires. However, rather than dissaving, it has been noted that several households continue to increase savings well beyond retirement age (Hassan, Salim, & Bloch, 2011). Carroll (1997) suggests that this anomaly can be linked to income uncertainty, an essential factor affecting saving decisions, something that the LCH does not consider. Consequently, this suggests that dissaving is expected to be higher among young households, or children, than among retired households.
2.2 Demographics and the exchange rate
The theoretical relationship between the real exchange rate and the age structure is derived from consumption and saving patterns in an economy. According to the LCH, people smooth their consumption by saving during their working years and by dissaving during the rest of their lifetimes (Modigliani & Brumberg, 1954). Thus, population dynamics are related to international capital flows and the current account, and, if this hypothesis holds, are likely to also indirectly influence other macroeconomic aspects such as the real exchange rate.
A theoretical attempt to link demography with the real exchange rate by means of national savings, was made by Cantor and Driskill (1999). Using an OLG, they found that demographic shifts induce changes in national savings, and that this sets in motion a dynamic adjustment of the current account and the real exchange rate. The reaction of the real exchange rate to a demographic shock, however, is complex and depends, for example, on the debt level of the country and the time horizon considered.7
On the empirical side, AÖ, using Swedish domestic age data, found that when a more significant proportion of the population are young adults (i.e., people aged 15-24 years) and people older than 64 years, who tend to borrow and hence reduce savings, there is an appreciating effect on the real exchange rate. In contrast, when a higher proportion of people are of working age (i.e., people aged 25-64 years), and are savers, generate capital outflows, there is a depreciating effect on the real exchange rate. Andersson and Österholm’s follow-up study on a panel of Organisation for Economic Co-operation (OECD) countries yielded similar results.8 Kim and Roubini (2008) confirm the link between increases in savings and
real exchange rate depreciations. Similar relations between demographics and exchange rates
7 Further explanation of Cantor and Driskill’s model is beyond the scope of this thesis. For additional details
readers are referred to Cantor and Driskill (1999).
were moreover found by Rose, Supaat, and Braude (2009), a study that used a data set covering 87 countries and showed that a decline in the fertility rate (thus, a relative decrease of people in the youngest age group) leads to exchange rate depreciations.
2.3 Forecasting the real exchange rate
A concern when forecasting the real exchange rate, using age structure, is that demographic changes occur slowly while fluctuations in the exchange rate occur more rapidly. Consequently, short-run variations in the exchange rate is something that are potentially difficult to capture using the demographic structure as an explanatory variable in a model. Demographic data likely works better as a device for forecasting medium- and long-run trends in the exchange rate than a short-run trend. However, whether this device does in fact work to predict a variable as volatile as the exchange rate has not thoroughly been investigated. Moreover, a concern when examining the possibility of forecasting exchange rate movements is that researchers have long struggled with the Messe-Rogoff puzzle. This puzzle states that it is difficult—almost impossible—to beat the random walk model (RW) in out-of-sample forecasts of the future exchange rate.9
As many macroeconomic variables are non-stationary, several papers have aimed to forecast future exchange rate movements by modelling a cointegrated system. Junttila and Korhonen (2011), for example, used an error correction model (ECM) and showed, empirically, that fundamentals10 can drive exchange rates; while, on the other hand, Burns
and Moosa (2015) demonstrate that the introduction of an error-correction term does not improve forecasting accuracy. It has been argued that the Messe-Rogoff puzzle arises as a result of the fact that it is difficult to link floating exchange rates to theoretical macroeconomic fundamentals such as the interest parity framework (Engel & West, 2005). The interest parity framework states that the expected return to domestic assets equals exchange-rate adjusted foreign assets. Consequently, the theoretical link suggests that a higher interest rate in a country leads to real appreciation. This, however, is a pattern that has been challenging to find in empirical research (see, e.g., Moosa and Vaz, 2016).
9This finding emanates from the findings of Meese and Rogoff (1983).
3. The life cycle hypothesis and the real exchange rate
In this section, the theoretical framework this thesis bases on is explained, linking demography to the exchange rate. This thesis suggests that exchange rate movements occur in relation to national savings and, in turn affect, the current account. According to the LCH, savings behavior is connected to the age of an economic agent (see Modigliani, 1975). In the hypothesis, households attempt to smooth consumption and maximize utility by borrowing and saving. Young individuals consume more than they save because of, for example, education expenditure, while a person of working age experience conditions more conductive to saving. The hypothesis anticipates that savings are high during this last-mentioned stage of life and decrease following retirement.
Accordingly, the underlying idea of utility maximization through consumption smoothing of the LCH is that: (1) people in their earning years (the working population) contribute positively to national savings, and that (2) agents who have retired or are too young to work (the non-working population) contribute negatively to national savings.
An economy with a high proportion of people among the working population ought, ceteris paribus, to have a greater current account surplus than another country with proportionally more young and elderly in the overall population. Cantor and Driskill (1999) show that a there is a link between national savings and the current account. Consequently, if the age structure is linked to national savings and if savings cause capital outflows, thus, affecting the current account, then shifts in the real exchange rate are possibly linked to demographic movements.
Moreover, different stages of life are characterized by the demand of certain governmental services, which, likewise affect the current account. For example, young individuals and retired people consume more healthcare than the working-age-population. Increases in government spendings can cause capital inflows, affecting the budget deficit, as to fund the rise in consumption. Thus, according to the LCH, when the share of the non-working population grows, and government consumption and capital inflows increase, the current account surplus decreases and again reinforcing the appreciating effect the non-working population has on the currency. However, an aging population likely provides fewer investment opportunities since rising capital-labor ratios decrease the returns to investment; moreover, fewer investment opportunities cause capital outflows to countries where the returns to investment are higher. Whether, or to what extent, this offsets the above-mentioned effects is not evident.
4. Methodological framework
This section presents the statistical models used in this thesis to investigate whether demographic changes can explain movements of the Swedish krona, and whether relative demographic changes provide more information about the development of the krona than do domestic changes. Furthermore, spurious regression results are discussed as the results in AÖ, which applied an OLS regression with domestic age shares as regressors, showed an indication of being spurious. In the following step, this section describes how forecasts are generated and evaluated as a means of comparing the models to each other and to examine whether it is possible to beat the RW. A failure to beat the latter using the developed models would suggest that any forecast at all is superfluous.11
Section 4.1 presents the reference model, an OLS model using Swedish domestic age shares as regressors. Section 4.2 aims to improve the reference model by instead using relative demographic age shares (i.e., the Swedish age structure relative to its trading partners) as regressors. Thus, the model developed in Section 4.2 is used to attempt to answer the second research question: whether relative demographic changes provide more information about the development of the Swedish krona than domestic shifts. As a means of testing the robustness of the results found by the latter model, a third model, a fully modified OLS (FMOLS) model, is introduced in Section 4.3. It will test whether the exchange rate and the age regressors are non-stationary and cointegrated, to examine whether former results are spurious or superconsistent. Section 4.4 describes the relevant control variables included in the models.
Subsequently, Section 4.5 elucidates how intercept correction (IC) handles a non-time-invariant DGP and can potentially boost forecast performances. Lastly, Section 4.6 describes the different measures used to assess the various models’ forecasting performances.
4.1 Reference model
Using Swedish data for the period 1960 to 2002, AÖ aimed to investigate whether a relationship between the Swedish real exchange rate and the domestic demographic structure exists. This examination was conducted using an OLS model; however, demographic changes in the surrounding world were neglected. Moreover, their results were likely spurious
11 Generating forecasts would be superfluous as it is pointless to develop a sophisticated statistical model when
as age regressors and the exchange rate, the variables used in the model, are likely to be non-stationary (see, e.g., Lodha, 2017). Consequently, two disputes arise that require answers.
First, it is well-known in the literature that applying standard OLS techniques to non-stationary data may lead to spurious results12—and, indeed, the results in AÖ indicated a
spurious regression. This is a result that emerges when one random walk is regressed onto another independent random walk and is spurious because the regression may indicate a nonexistent relationship. A finding that is not a surprising as most economic time series are of non-stationary characteristics (Philips, 1995). However, an OLS estimator is not necessarily biased if the variables in the regression model are cointegrated. If the variables are cointegrated, the OLS estimator is superconsistent as the coefficients will rapidly converge to the true value. The current study therefore uses stationarity tests and a cointegration test and, moreover, estimates a FMOLS model (presented in Section 4.3) as it is designed to provide optimal estimates of non-stationary and cointegrated variables.
Second, considering domestic demographic changes while neglecting changes that occur in other economies is likely to be inappropriate. If other countries are facing a demographic shift comparable to Sweden’s, then exchange rate movements must emerge due to other reasons. As several western nations have experienced a demographic change (an aging population) similar to Sweden’s during the last decades, this study argues that a relative measure, considering demographic developments in the world, should be used.
Nevertheless, as a reference model, this study estimates the domestic age OLS model (i.e., a model similar to the one estimated in AÖ) to be able to test whether an improvement can be achieved when the relative demographic profile is considered instead.
Following the approach used in AÖ, the population is divided into six groups classified by age (displayed in parentheses): 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). In the reference model, however, one age group (i.e., the children group) has to be omitted in order to avoid perfect collinearity as the age shares add up to one. Moreover, this study extends AÖ’s model with the vector 𝑊, which contains control variables (presented in Section 4.4).13 The
following model, referred to as model (1), is therefore estimated:
12 The problem of spurious regressions was first described by Granger and Newbold (1974). If the regressors
are non-stationary, the OLS regression suffers from endogeneity and the errors are serially correlated (Hansen & Philips, 1990).
𝑞𝑡 = 𝑐 + 𝛽1𝑑15-24𝑡+ 𝛽2𝑑25-49𝑡+ 𝛽3𝑑50-64𝑡+ 𝛽4𝑑65-74𝑡+𝛽5𝑑75𝑡+
𝛾1𝑑𝑢𝑚82: 4 + 𝛾2𝑑𝑢𝑚92: 4 + Α𝑊𝑡+ 𝜀𝑡
where 𝑞 (also named 𝑟𝑒𝑎𝑙 𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑒𝑥𝑐ℎ𝑎𝑛𝑔𝑒 𝑟𝑎𝑡𝑒) is the log of the real effective exchange rate14 and 𝑑𝑋𝑋-𝑌𝑌 is the share of the population aged ≥ XX years and ≤ YY years.
The 𝑑 in 𝑑𝑋𝑋-𝑌𝑌 signifies the use of Swedish domestic age groups, in contrast to 𝑟 used in the next section, which refers to relative demographic constellations. 𝑑𝑢𝑚82: 4 and 𝑑𝑢𝑚92: 4 are dummies, the first included to account for the governmental devaluation of the krona in the fourth quarter of 1982 and the second added to account for the shift from a fixed to a floating exchange rate the fourth quarter of 1992. The dummy variables take a value of zero up to the structural shift and a value of one for all periods after the shift.15
4.2 Ordinary least squares model
The baseline model used in this thesis is an OLS model including measures of Swedish age shares relative to foreign age shares as regressors (the construction of the relative age group variables is explained in Section 5). This approach may improve the fit of the model compared to model (1) and, moreover, enables the inclusion of all age-group variables in the regression and makes the interpretation of the results easier.16
The baseline model, referred to as model (2), is estimated using the following equation: 𝑞𝑡 = 𝑐 + 𝛽1𝑟00-14𝑡+ 𝛽2𝑟15-24𝑡+ 𝛽3𝑟25-49𝑡+ 𝛽4𝑟50-64𝑡+ 𝛽5𝑟65-74𝑡+
𝛽6𝑟75𝑡+ 𝛾1𝑑𝑢𝑚82: 4 + 𝛾2𝑑𝑢𝑚92: 4 + A𝑊𝑡+ 𝜀𝑡
where all the regressors are the same as in model (1) except that the domestic age group variables, 𝑑𝑋𝑋-𝑌𝑌, have been switched to 𝑟𝑋𝑋-𝑌𝑌 variables. The 𝑟 indicates that relative age groups are used instead of domestic age groups. For its construction, a set of other countries whose economies Sweden is in a close trade relationship with is used as a proxy for world demographics. The relative age groups are constructed by relating the Swedish age structure to the age structure of the countries included in the total competitiveness weights
14 The construction of the real effective exchange rate, a currency index, is described in detail in Section 5. 15 In contrast to this thesis, the dummy variables in AÖ only take the value one at the quarter of the shift and
for eight more periods following the two events. This approach is not used as it is not straightforward for how many periods the events’ impact lasts, moreover, the approach used in this thesis is a more common approach used in empirical research (Gujarati & Porter, 2009).
(TCW) index. This index is a measure constructed by the International Monetary Fund (IMF), the countries, representing the world demographics, included in this index are henceforth referred to as TCW countries (see Section 5 for the listed countries).
The way the relative age shares are constructed, implies constancy for a 𝑟𝑋𝑋-𝑌𝑌 variable if a shift in the share of one Swedish age group is accompanied by the same change in that age group in the TCW countries. Similarly, it implies that an unequal shift in the share of one age group in the TCW countries and in the same Swedish age group induces the relative age-group variable to change over time.
4.3 Fully modified least squares model
The results in AÖ indicate a spurious regression and, therefore, this thesis estimates an error-correction model (ECM) to further examine the results found by model (2), The ECM is a two-step estimator that includes a long- and a short-run relationship. As suggested in Section 2, demographic changes likely have higher explanatory power on the real exchange rate in the long-run than in the short run, the focus is, therefore, on the long-run equation. The long-run equation is estimated using a FMOLS model. The short-run equation is estimated by including the residuals from the FMOLS model in an OLS model. However, the short-run equation is not explained further as it is only used in the analysis to determine whether the error correction term has the anticipated sign.
Understanding the error correction approach requires familiarity with the concept of cointegration. Cointegration offers a solution to the problem of spurious regressions evoked by non-stationary variables in a linear regression (Granger & Newbold, 1974). Cointegration can be explained by considering two time series that are integrated of order p and q respectively. A standard approach when encountering integrated variables is to use their
p and q first differences to achieve stationarity; however, then long-time horizon information
will be lost. However, if cointegration exists, differencing is not necessary. Instead, as Engle and Granger (1987) pointed out, if the series are integrated of the same order (i.e., p=q) and if a stationary linear combination of these variables exists, the variables are said to be cointegrated and can be used in level form. The linear combination is referred to as the cointegrating equation and is interpreted as the long-run equilibrium relationship between the variables.
The FMOLS technique was proposed by Hansen and Philips (1990) and employs a semi-parametric adjustment to remove the long-run correlation between the cointegrating
equation and stochastic regressor innovations.17 The basic idea behind the FMOLS estimator
is to correct for endogeneity bias and serial correlation and thereby allow for standard normal inference (Pedroni, 2001). It is a two-step estimator in which the first step estimates the covariance parameters. Hansen and Philips (1990) argue that this technique is efficient and robust in relation to the second-order bias problem and is asymptotically equivalent to the Johansen (1998) test18.
To illustrate how the model is estimated, consider an 𝑛 + 1 dimensional time series vector process (𝑦𝑡, 𝑋𝑡′). Let 𝑦𝑡 be the log of the exchange rate and let 𝑋𝑡 be an 𝑛-dimensional
vector of stochastic explanatory variables, the age share variables, for 𝑦𝑡. The cointegrating
equation takes the following form: 𝑦𝑡= 𝑋𝑡′𝛽 + 𝐷
1,𝑡′ 𝛾1 + 𝑢1,𝑡 (4.1)
where 𝐷𝑡 = (𝐷1,𝑡′ , 𝐷2,𝑡′ )′ consists of deterministic trend regressors, and 𝑢1,𝑡 is the error of
the cointegrating equation. The 𝑛 stochastic regressors are governed by the following system of equations:
𝑋𝑡= Γ21′ 𝐷1,𝑡+ Γ22′ 𝐷2,𝑡+ 𝜖2,𝑡, (4.2)
∆𝜖2,𝑡 = 𝑢2,𝑡 (4.3)
where 𝑢2,𝑡 are the residuals of the regressor equations. The vector of 𝐷1 enters the regression
equations and the cointegrating equation, while the vector 𝐷2 only enters the regression
equations. ∆𝜖2,𝑡 = 𝑢2,𝑡, the from equation 4.1 resulting residuals, can be obtained indirectly
from the levels regressions (i.e., equation 4.2).
Hansen (1992) assumed that the innovations, 𝑢̂𝑡 = (𝑢1,𝑡, 𝑢2,𝑡′ )′, are strictly stationary
and ergodic with zero means, contemporaneous covariance matrix Σ, a one-sided long-run covariance matrix Λ, and covariance matrix Ω, each of which is partitioned conformably with 𝑢𝑡:
17 A detailed description of this approach can be found in Hansen and Philips (1990). 18 See also Johansen (1991; 1995).
Σ = 𝐸(𝑢𝑡𝑢𝑡′) = [𝜎11 𝜎12 𝜎21 Σ22] , (4.4) Λ = ∑∞ 𝐸 𝑗=0 (𝑢𝑡𝑢𝑡−𝑗′ ) = [𝜆𝜆11 𝜆12 21 Λ22], (4.5) Ω = ∑∞ 𝐸 𝑗=−∞ (𝑢𝑡𝑢𝑡−𝑗′ ) = [ 𝜔11 𝜔12 𝜔21 Ω22]. (4.6)
It is further assumed that there exists a non-singular sub-matrix Ω22 for the rank 𝑛 long-run covariance matrix Ω. Consequently, the elements of 𝑦𝑡 and 𝑋𝑡 are integrated of
order one and are cointegrated, however, the assumptions exclude cointegration amongst the elements of the regressors. 19
Next, suppose that Ω̂ and Λ̂ are the long-run estimated covariance matrices, which are computed using the residuals, 𝑢̂𝑡= (𝑢̂1,𝑡, 𝑢̂2,𝑡′ )′, so that the modified data can be defined as:
𝑦𝑡+ = 𝑦
𝑡− 𝜔̂12Ω̂22−1û2, (4.7)
with the following projected bias correction term: 𝜆̂12+ = 𝜆̂
12− 𝜔̂12Ω̂22−1Λ̂22. (4.8)
Lastly, the FMOLS estimator is defined as:
𝜃̂ = [ 𝛽̂ 𝛾̂1] = (∑𝑇𝑡=1𝑍𝑡𝑍𝑡′)−1(∑ 𝑍𝑡𝑦𝑡+− 𝑇 [𝜆12 +′ 0 ] 𝑇 𝑡=2 ), (3) where 𝑍𝑡 = (𝑋𝑡′, 𝐷
𝑡′), and 𝜆̂12+ = 𝜆̂12− 𝜔̂12Ω̂22−1Λ̂22, which are referred to as bias-correction
terms. 𝑦𝑡+ is the correction term for endogeneity and 𝜆̂12+ is the correction term for serial
correlation in errors.
19 A central assumption when building a single-equation ECM is weak exogeneity, which is linked to whichever
variable adjusts to maintain the long-run relationship. The approach used in this study includes the implicit inference that the exchange rate is the only variable which equilibrium corrects.
4.4 Control variables
Except for the structural shift dummies, this thesis includes three control variables in the abovementioned models. The first control variable, 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑟𝑎𝑡𝑒 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑙, accounts for differences in interest rates between Sweden and the TCW countries. The hypothesis builds on the interest parity framework that claims that an increase in the domestic interest rate leads to an appreciation of the domestic currency, ceteris paribus (Gottfries, 2013). When investors can choose freely, they devote their capital to countries in which the interest rate is highest and, in turn, the exchange rate adjusts, so that the so-called no-arbitrage condition is satisfied. And indeed, several studies have found that there is a link between the interest rate and the real exchange rate, particularly in small open economies (see, e.g., Bjørnland, 2008; Andries, Bogda, Ihnatov, & Tiwari, 2017). The 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑟𝑎𝑡𝑒 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑙 is constructed by subtracting a real weighted interest rate of the TCW countries from the real Swedish interest rate:
𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑟𝑎𝑡𝑒 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑙 = 𝑖𝑇𝐶𝑊 𝑐𝑜𝑢𝑛𝑡𝑟𝑖𝑒𝑠− 𝑖𝑆𝑤𝑒𝑑𝑒𝑛,
where 𝑖 is the real interest rate.
The second control variable, 𝐺𝐷𝑃 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑙, is included to account for growth differentials. The concept is similar to that of the interest rate: higher growth rate is expected to be linked to a domestic exchange rate appreciation. Several studies have investigated whether growth differentials can help in forecasting future currency movements, however, the results are mixed (see, e.g., Ball, Lopez, & Reyes, 2013; Amir, 2013). However, this study orientates towards the one of Cook (2005), that claimed that the savings rate is connected to the rate of economic growth (see also Section 2) and accordingly includes a 𝐺𝐷𝑃 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑙 as a control. The variable is constructed by subtracting a real weighted growth rate of the TCW countries from the real Swedish growth rate:
𝐺𝐷𝑃 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑙 = 𝑔𝑇𝐶𝑊 𝑐𝑜𝑢𝑛𝑡𝑟𝑖𝑒𝑠− 𝑔𝑆𝑤𝑒𝑑𝑒𝑛,
where 𝑔 is the real growth rate.
Thelast control variable, 𝑠𝑡𝑜𝑐𝑘 𝑚𝑎𝑟𝑘𝑒𝑡 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑙, assesses for differences in the Swedish and TCW countries’ stock markets. The hypothesis is, that faster rising domestic stock market prices than foreign stock market prices causes domestic capital inflows, and
thus lead to an appreciation of the domestic currency. Empirical research examining the link between stock market prices and exchange rates has provided mixed results (see, e.g., Sheng-Ping, 2017; Moses, Mela, & Godfrey, 2018). To control for a potential link a 𝑠𝑡𝑜𝑐𝑘 𝑚𝑎𝑟𝑘𝑒𝑡 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑙 is constructed by subtracting a weighted growth in stock prices of the TCW countries from the Swedish stock prices growth:
𝑠𝑡𝑜𝑐𝑘 𝑚𝑎𝑟𝑘𝑒𝑡 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑙 = 𝑝𝑇𝐶𝑊 𝑐𝑜𝑢𝑛𝑡𝑟𝑖𝑒𝑠− 𝑝𝑆𝑤𝑒𝑑𝑒𝑛, where 𝑝 is the growth rate of the stock market index.
4.5 Intercept correction
When performing forecasts, AÖ used the IC technique and found that it improves the forecasting performance of their model. Likewise, this thesis evaluates whether IC enhances the forecasting performances of the models. Yet, I argue that the IC technique should be used with caution as it has credibility costs: if one believes in a model, there should be no purpose of overruling the forecasts as it is done with the IC technique.20
The IC technique was suggested by Clements and Hendry (1994; 1996) and its use may be beneficial if past systematic forecast errors occur, or if a recent deterministic shift has emerged. In this thesis, a simple form of the technique is applied. To exemplify how the method is used, let us consider the one-step-ahead forecast of an estimated 𝐴𝑅(1) model, which is 𝑞𝑡+1= 𝜇̂ + ∅̂𝑞𝑡. For this model, the IC for the one-step-ahead forecast is:
𝑞𝑡+1 = 𝜇̂ + ∅̂(𝑞𝑡+ 𝜀𝑡),
where 𝜇̂ + ∅̂𝜀𝑡 is the new intercept used for the forecast for the next period, and 𝜀𝑡 is the value of the previous forecast error. Consequently, the correction represented by 𝜀𝑡, emerges
due to the original model’s misspecification which is assumed to continue into the next forecast period.
4.6 Accuracy evaluation of the models: forecast performance
The sharpness and the performances of the models are evaluated by comparing their forecasts. I choose to start eleven years back in time, which is 2005Q2 and estimate all models with the data up to this point so that their forecast evaluation is not overly dependent on their performance in the latter part of the sample. Additionally, using a long-time horizon when performing forecasts helps to reveal whether significant structural shifts occurred in the latter part of the sample, which can be assessed by comparing the forecasts with and without IC.
First, the models will be estimated using data from the first quarter (Q1) of 1961 up to 2005Q2. Next, forecasts are generated for one, two, three, and four years ahead. In the subsequent step, the models are re-estimated to also include 2005Q3. Forecasts are again generated for one to four years ahead. This procedure is repeated for the whole sample (1961Q1 to 2016Q2), thus resulting in 40 one-year-ahead forecasts, 36 two-year-ahead forecasts, and so on.
The present thesis uses several evaluation measures to determine the three models’ capability to forecast future exchange rate movements. The reason for using diverse evaluation methods is that different methods often yield divergent results and offer unequal information.
The evaluation measures used, are the root-square error (RMSE), the mean-absolute error (MAE), and the mean-mean-absolute-percentage error (MAPE). The first two measures are based on the distance between the actual value and the forecast value and no distinction between positive and negative forecast errors is made. The latter measure, MAPE, provides the forecast error in the form of a percentage.21 The evaluation criterion is the same
for all measures: the smaller the value, the better the forecasting ability. The test values are estimated as follows: 𝑅𝑀𝑆𝐸 = √∑𝑁𝑡=1(𝑞̂𝑡−𝑞𝑡)2 𝑁 , 𝑀𝐴𝐸 =∑𝑁𝑡=1|𝑞̂𝑡−𝑞𝑡| 𝑁 , 𝑀𝐴𝑃𝐸 =𝑁1 ∑ |𝑞̂𝑡−𝑞𝑡| 𝑞𝑡 𝑁 𝑡=1 ∗ 100
where 𝑁 represents the number of forecasted periods (i.e., the number of observations), 𝑞̂𝑡
symbolizes the predicted value of the real effective exchange rate, and 𝑞𝑡 signifies the
true value. To simplify the comparison, each model’s performances are compared to the simple RW.
Although the RW is rather simple, it has been shown that it is difficult to develop a model that can beat its forecast (see, e.g., Rossi, 2013). However, Burns and Moosa (2014) argued that in exchange rate models the inclusion of a lag of the dependent variable, which is a random walk component, enables those models to perform better than the RW. Thus, outperforming the RW occurs by using another random walk. Nevertheless, the base line model in this study does not include any lags of the dependent variable, although information on the lag of the dependent variable is added by using the previous forecast error (i.e., when using the IC technique).22
22 A further discussion of the RW, however, is out of scope of this paper and the reader is referred to, for
5. Description of the data and variables
This section presents the data and the choice of variables, definitions, and how the relative demographic age share variables are constructed. The estimation sample in this thesis covers the period 1961Q1 to 2016Q2.
The dependent variable is defined as the real effective exchange rate (the terms real effective exchange and real exchange rate are used interchangeably in this study). The two most common nominal weighted exchange rate values reported by the Swedish Riksbank are the TCW index and the kronindex (KIX) index. The weightings in the KIX index change frequently, which causes problems with the construction of the relative age group regressors and thus creates issues affecting comparisons. Therefore, this thesis uses the TCW index that uses fixed weights, and which is widely used (see, e.g., Erlandsson & Markowski, 2006). The weight each country is assigned, based on the TCW index, is presented in Table 1.
Table 1. Countries included in the TCW index and their weights
Country TC W-weight Australia 0.27 Austria 1.71 Belgium 3.55 Denmark 5.6 Finland 6.69 France 7.15 Germany 2 2.28 Greece 0.27 Ireland 0.77 Italy 6.05 Japan 5.2 Canada 1.16 Netherlands 4.24 Norway 5.58 New Zealand 0.14 Portugal 0.93 Switzerland 2.74 Spain 2.48 United Kingdom 1 1.56 United States 1 1.63 Sum 10 0 Source: Riksbank.
The TCW index, computed by the IMF, employs weights that depend on the trade intensity Sweden has with the corresponding country. The data of the TCW index was obtained from the Riksbank. Note that during the sample period several of the countries listed in Table 1 introduced the euro (from here onwards called euro countries). However, as this study uses the exchange rate, adjusted for country specific inflation, thus the real exchange rate, variations between euro countries exist.
To construct the real exchange rate, the consumer price index (CPI), collected from the OECD, for each country was used to deflate the TCW index.23 Accordingly, the real
effective exchange rate is calculated as follows:
𝑟𝑒𝑎𝑙 𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑒𝑥𝑐ℎ𝑎𝑛𝑔𝑒 𝑟𝑎𝑡𝑒 = 𝑛𝑜𝑚𝑖𝑛𝑎𝑙 𝑇𝐶𝑊 𝑖𝑛𝑑𝑒𝑥𝐶𝑃𝐼 𝑖𝑛 𝑡ℎ𝑒 𝑇𝐶𝑊 𝑐𝑜𝑢𝑛𝑡𝑟𝑖𝑒𝑠𝐶𝑃𝐼 𝑖𝑛 𝑆𝑤𝑒𝑑𝑒𝑛
Age data for the TCW countries and Sweden was sourced from the World Bank. Since this data set consists of annual observations, it has been interpolated to convert it to quarterly data. To construct the relative demographic share variables each TCW country’s demographic age group was first assigned the weight, w𝑖, listed in Table 1. Second, the sum
of the n TCW countries’ weighted age group, 𝑑𝑋𝑋-𝑌𝑌𝑇𝐶𝑊𝑖, was related to the corresponding Swedish age group by dividing the latter by the first. The logarithm of this ratio yields the relative demographic share variables:
ln (∑ 𝑤𝑑𝑋𝑋−𝑌𝑌 𝑖∙𝑑𝑋𝑋−𝑌𝑌𝑇𝐶𝑊𝑖 𝑛
𝑖=1 ) = 𝑟𝑋𝑋-𝑌𝑌,
where 𝑑𝑋𝑋-𝑌𝑌 is the share of the Swedish population aged ≥ XX years and ≤ YY years, and 𝑑𝑋𝑋-𝑌𝑌𝑇𝐶𝑊𝑖 is the share of population aged ≥ XX years and ≤ YY years in the i-th TCW country. Figure 1 plots 𝑑𝑋𝑋-𝑌𝑌 and 𝑟𝑋𝑋-𝑌𝑌 during the sample period. The figure reveals that a positive change in one of the series does not necessarily imply the same change for the other, and vice versa, thus indicating that the two variables cannot be used interchangeably.
23 Note that due to data constraints, values for data on the TCW index for the period 1961Q1 to 1981Q4 were
Figure 1. Age shares and relative age shares in the six age groups
Note: The quarterly values of 𝑑𝑋𝑋-𝑌𝑌 and 𝑟𝑋𝑋-𝑌𝑌 correspond to the left and right y-axis respectively. Time period 1961Q1 to 2016Q2.
Moreover, to conduct forecasts of the real exchange rate for the period 2016Q3 to 2032Q2, projections of the future age structure is needed. The World Bank provides projections of the TCW countries’ and Sweden’s future age groups. I argue that these forecasts are reliable predictions of the future population structure as the current age distribution is known, future births and deaths can be extrapolated with high precision.
Data for the control variables (except the time-period dummies) were collected from the OECD. As a proxy for the interest rate in Sweden and the interest rates in the TCW countries (i.e., the foreign interest rate), the short-term interest rate is used. The real GDP growth rates (seasonally adjusted), applying the expenditure approach, is used to construct the 𝐺𝐷𝑃 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑙 variables. To create the 𝑠𝑡𝑜𝑐𝑘 𝑚𝑎𝑟𝑘𝑒𝑡 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑙 variable, the share price indices is used. It should be noted that for some TCW countries, data is missing for the early years of the sample. In the case of a missing value, the concerning country was excluded for that quarter, while the other countries in the TCW index received a higher weight as to convert the weights in Table 1, so that they again sum to 100.
-0.25 -0.15 -0.05 0.05 0.15 0.25 0.14 0.16 0.18 0.2 0.22 0.24 61 Q 1 65 Q 1 69 Q 1 73 Q 1 77 Q 1 81 Q 1 85 Q 1 89 Q 1 93 Q 1 97 Q 1 01 Q 1 05 Q 1 09 Q 1 13 Q 1 d0-14 r0-14 -0.25 -0.15 -0.05 0.05 0.15 0.25 0.1 0.12 0.14 0.16 0.18 0.2 61 Q 1 65 Q 1 69 Q 1 73 Q 1 77 Q 1 81 Q 1 85 Q 1 89 Q 1 93 Q 1 97 Q 1 01 Q 1 05 Q 1 09 Q 1 13 Q 1 d15-24 r15-24 -0.1 -0.05 0 0.05 0.1 0.3 0.32 0.34 0.36 0.38 61 Q 1 65 Q 1 69 Q 1 73 Q 1 77 Q 1 81 Q 1 85 Q 1 89 Q 1 93 Q 1 97 Q 1 01 Q 1 05 Q 1 09 Q 1 13 Q 1 d25-49 r25-49 -0.15 -0.05 0.05 0.15 0.25 0.15 0.16 0.17 0.18 0.19 0.2 6 1Q 1 6 5Q 1 6 9Q 1 7 3Q 1 7 7Q 1 8 1Q 1 8 5Q 1 8 9Q 1 9 3Q 1 9 7Q 1 0 1Q 1 0 5Q 1 0 9Q 1 1 3Q 1 d50-64 r50-64 -0.2 -0.1 0 0.1 0.2 0.3 0 0.03 0.06 0.09 0.12 0.15 61 Q 1 65 Q 1 69 Q 1 73 Q 1 77 Q 1 81 Q 1 85 Q 1 89 Q 1 93 Q 1 97 Q 1 01 Q 1 05 Q 1 09 Q 1 13 Q 1 d65-74 r65-74 -0.2 -0.1 0 0.1 0.2 0.3 0 0.02 0.04 0.06 0.08 0.1 61 Q 1 65 Q 1 69 Q 1 73 Q 1 77 Q 1 81 Q 1 85 Q 1 89 Q 1 93 Q 1 97 Q 1 01 Q 1 05 Q 1 09 Q 1 13 Q 1 d75 r75
6. Results and analysis
This and the subsequent section apply the models presented in Section 4 in order to answer the research questions and thus to determine whether the LCH can be used to link exchange rate movements to the demography. The first research question, whether relative demographic changes can explain Swedish real effective exchange rate movements, is evaluated by estimating the three models and by conducting forecasts throughout Section 6 and 7. The second research question, whether relative demographic changes (variables used in model ) provide more information about the development of the krona than do domestic changes (variables used in model ) is answered in Sections 6.2. Note that stationarity tests are not performed until Section 6.3 as sections 6.1 and 6.2 are concerned with the question of whether including the relative demographic profile improves model (1). Section 6.3, however, performs stationarity and cointegration tests to examine whether the results found in Section 6.2 are spurious or not and performs FMOLS estimates as a potential improvement over the OLS estimates. Section 6.4 offers a robustness check using the Hodrick-Prescott (HP) filter, while Section 6.5 concludes the findings in Section 6 by comparing the results of this study with those of previous studies. The third research question, whether it is possible to use relative age data to predict past and future exchange rate movements, is investigated in Section 7.
6.1 Estimation of the reference model
To be able to determine whether the relative demographic profile has a higher explanatory power than the domestic profile, this study estimates model (1), i.e., the reference model explained in Section 4.1. The reference model (also referred to as OLS ref.) is an extended version of the model in AÖ since it includes control variables. The reference model uses Swedish domestic age groups as regressors and, therefore, one age group has to be dropped from the model so to avoid perfect collinearity since the age shares sum to one.
The results are expected to be similar to the results in AÖ; however, AÖ used data for the period 1960Q2 to 2002Q1 while the estimation sample in this study reaches from period 1961Q1 to 2016Q2. The results from OLS ref., with a stepwise inclusion of the control variables (described in Section 4.4), are presented in Table 2.
Table 2. Estimation results reference model
Dependent variable: 𝑟𝑒𝑎𝑙 𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑒𝑥𝑐ℎ𝑎𝑛𝑔𝑒 𝑟𝑎𝑡𝑒
Variable O LS ref. I O LS ref. II O LS ref. III
𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 - ( 1.75* 1.05) - ( 2.14** 1.04) - ( 1.92* 1.05) 𝑑15-24 ( 4.19*** 0.83) ( 4.29*** 0.82) ( 4.20*** 0.82) 𝑑25-49 1 ( 1.61*** 1.99) 1 ( 2.60*** 1.99) 1 ( 2.12*** 2.01) 𝑑50-64 1 ( 2.55*** 1.43) 1 ( 2.99*** 1.41) 1 ( 2.71*** 1.42) 𝑑65-74 ( 6.49*** 1.12) ( 6.91*** 1.11) ( 6.65*** 1.12) 𝑑75 -1 ( 2.04*** 1.01) -1 ( 3.15*** 1.05) -1 ( 2.79*** 1.08) 𝑑𝑢𝑚82: 4 ( 0.15*** 0.02) ( 0.18*** 0.02) ( 0.17*** 0.02) 𝑑𝑢𝑚92: 4 ( 0.20*** 0.02) ( 0.20*** 0.02) ( 0.19*** 0.02) 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑟𝑎𝑡𝑒 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑙 ( 0.06*** 0.02) ( 0.05*** 0.02) 𝑠𝑡𝑜𝑐𝑘 𝑚𝑎𝑟𝑘𝑒𝑡 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑙 - ( 0.06 0.05) 𝐺𝐷𝑃 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑙 - ( 0.00 0.00) Durbin-Watson statistics 0.32 0.38 0.42 F-test 14 8.71*** 13 6.13*** 10 9.55*** Adjusted R-square 0.82 0.83 0.83 R-square 0.83 0.84 0.84
Note: The abbreviation “ref,” indicates that the reference model is used. Standard errors are in parentheses. If the real effective exchange rate rises, the Swedish krona depreciates. A positive value of the differential variables implies a higher rate in the TCW countries. ***indicates significance at the 1% level, ** indicates significance at the 5% level, and * indicates significance at the 10% level. Estimation sample 1961Q1 to 2016Q2.
The first specification (OLS ref. I) includes the two dummy variables, the second specification (OLS ref. II) extends the model by including the interest rate differential, and the third specification (OLS ref. III) adds the GDP differential and the stock index differential to the model. A rise in the real effective exchange rate signifies a weaker Swedish krona, hence, a negative coefficient denotes that an increase in the corresponding variable implies an appreciation of the Swedish krona.
Using more recent data reveals that the relationship found in AÖ has changed slightly. Four coefficients of the five age-group variables are in line with the findings in that study, which found all coefficients to be positive. Note that as all age-group variables in AÖ had a depreciating effect that study examined the relative magnitude instead of the sign of the coefficients.
However, Table 2 shows that the coefficient for 𝑑75 is negative across all specifications.24 For reasons of simplicity and interpretation, the next paragraph of the
analysis of Table 2 disregards the variable 𝑑75, which shows a negative coefficient across all specifications, and uses the argument of AÖ: examining the relative effect between the age groups and putting no weight on evaluating the sign of the coefficients.
Applying this argument enables to argue that the coefficients are in line with the LCH, with young adults (𝑑15-24) and young retirees (𝑑65-74) appearing to have a relatively weaker depreciating effect on the real exchange rate than the prime aged (𝑑25-49) and middle aged (𝑑50-64) groups.
However, as has been stressed, the sign for 𝑑75 (old retirees) is negative and, the coefficient moreover, largely deviates from the coefficients found for the other age groups. This finding contradicts the LCH, which suggests a lower possibility of saving during the non-working lifetime period; accordingly, the coefficient for old retirees (𝑑75) is anticipated to be close to the coefficients for the age groups 𝑑15-24 and 𝑑65-74 as these groups are expected to have similar spending and saving patterns. There is no clear theoretical explanation for these findings as, for instance, one might expect that spending for retirees also decreases with age due to health reasons. Lower spending, ceteris paribus, implies less borrowing and thus a smaller effect on the current account. Consequently, the results in Table 2 are difficult to interpret and, moreover, the model fails to explain how the children age group (0-14) affects the krona.25
Turning to the other variables in Table 2: the two time-dummies, statistically significant at the 1% level across all specifications, are positive as anticipated and accordingly have a weakening effect on the krona.26 The second specification adds the
𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑟𝑎𝑡𝑒 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑙 variable, which exhibits a coefficient significant at the 1% level and yields the expected sign: a higher foreign interest rate relative to the domestic one triggers the krona to depreciate. The third specification includes the variables 𝐺𝐷𝑃 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑙 and 𝑠𝑡𝑜𝑐𝑘 𝑚𝑎𝑟𝑘𝑒𝑡 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑙, however, both are insignificant.
24 Andersson and Österholm (2005) found the coefficients for 𝑑15-24, 𝑑25-49, 𝑑50-64, 𝑑65-74, and 𝑑75
to be 4.69, 12.83, 14.41, 3.83, and 6.93, respectively.
25 Although it can be argued that the effect of the children age group (0-14) is partly captured by the intercept. 26 The coefficients are in line with expectations as the Swedish currency was devaluated in 1982, and in 1992
Sweden changed from a fixed to a floating exchange rate. When the Swedish currency began to float it depreciated rapidly.
The fit of the model appears to be good: the R-squares and adjusted R-squares range from 0.82 to 0.84. However, the Durbin-Watson (DW) statistics are low (between 0.32 and 0.42), indicating spurious regressions.27 Granger and Newbold (1974) argue that if the
adjusted R-square exceeds the DW statistics, this is a sign of a spurious regression. Moreover, low DW statistics cause concerns as the first-order autocorrelation can profoundly affect the computed coefficients. The indication of autocorrelation is reinforced when examining the correlogram of the residuals. Moreover, a simple correlation analysis is conducted and the results signpost that the regressors in the model are highly correlated, thus suggesting that a multicollinearity problem exists.28 High variance inflation factors reinforce this latter result.29
Thus, the approach used above to analyze how demographic changes affect the Swedish krona suffers from several shortcomings. Consequently, the results listed in Table 2 are not certainly stable and, moreover, they partly deviate from the ones found in AÖ, which used a similar approach. Notably, the results appear to be affected by the chosen sample period, indicating unstable results or that the spending and saving patterns of the Swedish population have changed.
6.2 Estimation of the ordinary least squares model
Section 6.1 showed that the relationship found by AÖ partly changes when using more recent data and including control variables. One possible explanation for this may be a spurious regression. Section 6.3 returns to this problem and evaluates whether the age variables are integrated. This step is omitted from this subsection as it aims only at examining whether relative demographic variables improve model (1). One advantage of model (2) compared to model (1), is that it allows the inclusion of all age groups in the model and it enables to determine the direction of the impact each age group has on the krona thus does not distort the results. The results from estimating model (2), using three specifications with a stepwise inclusion of the control variables, are presented in Table 3.
27 The DW statistics is a test for first-order serial correlation. If there is no serial correlation, the DW is
approximately two (Gujarati & Porter, 2009).
28 When two or more independent variables are modestly or highly correlated, multicollinearity exists. If
multicollinearity is less than perfect, the regression coefficients possess large standard errors and thus they cannot be computed with high precision (see Gujarati & Porter, 2009).
Table 3. Estimation results ordinary least squares model Dependent variable: 𝑟𝑒𝑎𝑙 𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑒𝑥𝑐ℎ𝑎𝑛𝑔𝑒 𝑟𝑎𝑡𝑒 Variable O LS I O LS II O LS III 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 ( 4.86*** 0.03) ( 4.85*** 0.03) ( 4.86*** 0.03) 𝑟0-14 - ( 3.42*** 0.61) - ( 3.40*** 0.60) - ( 3.32*** 0.60) 𝑟15-24 - ( 1.27*** 0.35) - ( 1.22*** 0.34) - ( 1.18*** 0.34) 𝑟25-49 ( 2.67*** 0.63) ( 2.98*** 0.62) ( 2.95*** 0.62) 𝑟50-64 - ( 1.53*** 0.44) - ( 1.52*** 0.43) - ( 1.48*** 0.43) 𝑟65-74 - ( 1.99*** 0.25) - ( 1.99*** 0.24) - ( 1.97*** 0.24) 𝑟75 - ( 0.50*** 0.17) - ( 0.41** 0.18) - ( 0.41** 1.08) 𝑑𝑢𝑚82: 4 ( 0.17*** 0.02) ( 0.19*** 0.02) ( 0.19*** 0.02) 𝑑𝑢𝑚92: 4 ( 0.24*** 0.03) ( 0.24*** 0.02) ( 0.24*** 0.03) 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑟𝑎𝑡𝑒 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑙 ( 0.06*** 0.02) ( 0.05*** 0.02) 𝑠𝑡𝑜𝑐𝑘 𝑚𝑎𝑟𝑘𝑒𝑡 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑙 - ( 0.06 0.05) 𝐺𝐷𝑃 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑙 - ( 0.00 0.00) Durbin-Watson statistics 0.48 0.57 0.62 F-test 17 5.09*** 16 4.59*** 13 5.91*** Adjusted R-square 0.86 0.87 0.87 R-square 0.87 0.87 0.88
Note: If the real effective exchange rate rises, the Swedish currency depreciates. Standard errors are in parentheses. A positive value of the differential variables implies a higher rate in the TCW countries. ***indicates significance at the 1% level, ** indicates significance at the 5% level, and * indicates significance at the 10% level. Estimation sample 1961Q1 to 2016Q2.
The interpretation of the relative age-group model is more straightforward than that of model (1). Table 3 reveals that all relative age group variables are highly significant and that the conclusions found in the previous section alter. It appears that only the prime aged group (25-49) has a weakening effect on the krona, which contrasts with the results found in Table 2 that indicates that both prime aged (25-49) and middle aged (50-64) have a similar depreciating impact on the krona. Thus, a finding that indicates that spending and saving patterns differ between these two groups.
The outcomes of model (2) suggest that children (0-14) have the most substantial appreciating effect on the krona and that this effect decreases slightly for young adults (15-24). Likewise, young retirees (65-74) and old retirees (75+) have an appreciating effect, however the latter group have a smaller impact (in absolute terms) on the krona. This finding could suggest that people tend to spend more as young (65-74) than old retirees (75+).
Turning to the effects of the remaining explanatory variables, they are in line with the findings in the previous section: the two dummies and the variables 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑟𝑎𝑡𝑒 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑙 are significant, whereas the variables 𝐺𝐷𝑃 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑙 and 𝑠𝑡𝑜𝑐𝑘 𝑚𝑎𝑟𝑘𝑒𝑡 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑙 are insignificant in each of the respective specifications. As OLS II excludes the latter two insignificant variables this is the preferred model, which will be used in the subsequent sections for further examinations. Moreover, note that including the control variables changes the coefficients in the three specifications for the age variables to a negligible extent.
Compared to model (1), the fit of model (2) appears to be slightly better, the R-squares and adjusted R-squares range between 0.86 and 0.88 and also the DW statistics increased, it shows the values 0.48 up to 0.62. Thus, a sign that relative demographic changes provide more information about the development of the krona than do domestic changes.
However, there is still an indication of spurious results. It is likely that autocorrelation and the sign of a spurious regression are due to an incomplete specification: the model is not a perfect description of all factors affecting the exchange rate as it is difficult to determine all these factors. However, the aim of this study is not to determine all factors that influence the exchange rate in Sweden, but rather to examine whether demographic changes affect the Swedish krona. Nevertheless, that an incomplete specification causes the indication of a spurious regression is speculative and the results found in this section have to be tested and examined in greater detail. This is undertaken in the next subsection by investigating whether the relative age group variables and the exchange rate are cointegrated and whether an error correction model fits the data.
6.3 Estimation of the fully modified least squares model
The approach so far relies on the assumption that the variables are stationary. It is well known in the literature that when integrated variables are used in a regression, the estimated relationships may be spurious. However, when the variables follow a random walk, it is possible either to use the differences of the variables, losing long-run information, or to estimate a long-run relationship if the variables are cointegrated. This section investigates whether the variables are integrated and whether the age variables and the real effective exchange rate are cointegrated.
First, the order of integration of each variable has to be detected. This is undertaken using the augmented Dickey and Fuller (1979) unit-root (ADF) test. The real effective
exchange rate and all age group series, both the relative age groups and the domestic age share groups in Sweden,30 appear to have a unit root (see Table 8 in the appendix for the
results).31 Furthermore, when the variables are tested in first-differences, it is confirmed that
they become stationary, implying that they are I(1). In contrast, the tests suggest that the control variables 𝐺𝐷𝑃 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑙, 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑟𝑎𝑡𝑒 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑙, and 𝑠𝑡𝑜𝑐𝑘 𝑚𝑎𝑟𝑘𝑒𝑡 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑙, are stationary in levels.
The next step is to test for a cointegrating relationship between the variables 𝑟𝑋𝑋-𝑌𝑌 and 𝑟𝑒𝑎𝑙 𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑒𝑥𝑐ℎ𝑎𝑛𝑔𝑒 𝑟𝑎𝑡𝑒. Several tests for cointegration have been proposed in the literature (see, e.g., Johansen 1991; 1995). The test for cointegration used here is that proposed in Engle and Granger (1987), which is residuals-based—it tests the null hypothesis of no cointegration against the alternative of cointegration.32 The lag length of the variables
is set to zero based on the Akaike information criterion (AIC) (using the Schwarz information criterion [SIC] yields the same lag length). The results are presented in Table 4. Table 4. Engle-Granger cointegration test
Cointegrated series: 𝑟𝑒𝑎𝑙 𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑒𝑥𝑐ℎ𝑎𝑛𝑔𝑒 𝑟𝑎𝑡𝑒, 𝑟0-14, 𝑟15-24, 𝑟25-49, 𝑟50-64, 𝑟65-74, 𝑟75 Cointegrating equation deterministic: 𝑑𝑢𝑚82: 4, 𝑑𝑢𝑚92: 4
Lag length: 0
V alue Prob.
Engle-Granger tau-statistic - 5.52 0.01
Engle-Granger z-statistic -5 3.65 0.01
Note: The lag length is selected using the AIC.
The Engle-Granger test indicates cointegration at the 5% level; however, the critical values assume no exogenous series. To control for this, a robustness check excluding the dummies is conducted (results from the robustness check are presented in Table 9 in the appendix). When the dummies are excluded, the cointegration relationship appears not to be as strong as it was when including the dummies. The Engle-Granger tau-statistic in Table 9 indicates cointegration at the 15% level, while the z-statistic indicates rejection of the null hypothesis of no cointegration at the 1% level. Thus, there is a strong indication of a cointegration relationship as the two structural breaks are expected to have a significant impact on the results of the cointegration test.
30 That are, the 𝑟𝑋𝑋-𝑌𝑌 variables and the 𝑑𝑋𝑋-𝑌𝑌 variables, respectively. 31 The Philips and Perron (1998) test yields similar results.