Time-varying saving–investment relationship and the Feldstein–Horioka puzzle

Economic Modelling 53 (2016) 166–178

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Time-varying saving–investment relationship and the Feldstein–Horioka puzzle✩ Wei Ma, Haiqi Li∗ College of Finance and Statistics, Hunan University, Changsha, 410006, China

A R T I C L E

I N F O

Article history: Accepted 23 November 2015 Available online xxxx Keywords: Feldstein–Horioka puzzle Saving-retention coefficient Long-run solvency constraint Time-varying cointegration

A B S T R A C T Numerous studies have been devoted to the Feldstein–Horioka puzzle. However, no consensus has been reached in the literature. This paper examines the dynamic saving–investment relationship by using a time varying cointegration model. The saving-retention coefficients are found to be high for developed economies, but low for less developed economies, which could be explained by the difference of the longrun solvency constraint between developed and less developed economies. While more evidence is found for time-varying cointegration using quarterly data, the magnitudes of saving retention coefficients have no substantial difference from those of annual data. © 2015 Elsevier B.V. All rights reserved.

1. Introduction In a highly influential paper, Feldstein and Horioka (1980) examined the relationship between saving and investment, and they found a large value for the saving–investment (saving-retention) coefficient. They documented that the saving–investment correlation measured the degree of international capital mobility. Therefore, if the capital markets are integrated, domestic investment could be financed by foreign savings, and domestic saving could also seek out higher foreign return, thereby implying a low correlation between saving and investment. Given the prevailing integration of current financial markets, this finding reveals a contradiction, which is currently known as the Feldstein–Horioka puzzle. Obstfeld and Rogoff (2000) regarded the Feldstein–Horioka puzzle as “the mother of all puzzles” in international monetary economics. For the past three decades, many theoretical and empirical studies have attempted to resolve this puzzle. The vast literature regarding the Feldstein–Horioka puzzle can be classified into

✩ We would like to thank the co-editor, Paresh, K. Narayan, and one anonymous referee for their useful comments and suggestions. This project was supported by the National Natural Science Foundation of China (NSFC) (No.71301048), the Ministry of Education of Humanities and Social Sciences Project of China (No.12YJC790093), the Natural Science Foundation of Hunan Province in China (No.14JJ3053), and the training program for young scholars in Hunan University. Corresponding author. E-mail addresses: [email protected] (W. Ma), [email protected] (H. Li).

*

http://dx.doi.org/10.1016/j.econmod.2015.11.013 0264-9993/© 2015 Elsevier B.V. All rights reserved.

three categories.1 The first category attempted to reconcile the high saving–investment correlation with high capital mobility by constructing new theoretical models and/or providing new explanations. For example, Coakley et al. (1996) showed that the long-run solvency constraint implied the stationarity of the current account balance and thus the cointegration between saving and investment. Therefore, the high saving–investment correlation might be driven by the long-run solvency constraint, rather than low capital mobility. Bai and Zhang (2010) found that when two types of financial frictions—limited enforcement and limited spanning are combined, they interact to generate a high saving–investment correlation and endogenously restrict capital flows, thereby solving the Feldstein–Horioka puzzle. Chang and Smith (2014) showed that the introduction of the long-run risk component in the shock process helped solve the Feldstein–Horioka puzzle. Murphy (1984), Harberger (1980), Baxter and Crucini (1993), and Ho and Huang (2006) attributed the high saving–investment correlation to the large country effect. They documented that a large country tended to finance investment projects from domestic saving rather than the foreign saving. In this sense, Feldstein and Horioka (1980) claimed that, if a country was large, it would behave like a closed economy.

1 Given that the literature related to the Feldstein–Horioka puzzle is enormous, we are not intending to give an exhaustive review. We would like to offer our sincere apologies to those who made contributions in this field for our omission. For an excellent survey, see Apergis and Tsoumas (2009) and Coakley et al. (1998).

W. Ma, H. Li / Economic Modelling 53 (2016) 166–178

The second category casts doubt on the findings of Feldstein and Horioka (1980) on the high saving–investment correlation. For example, Chu (2012) showed that a common deflator—final domestic demand might cause the spurious saving–investment correlation. Krol (1996) argued that the Feldstein–Horioka puzzle was related to the estimation technique and found a lower saving–investment correlation using a fixed-effect panel data model. While the findings of Krol (1996) were criticized by Coiteux and Olivier (2000) and Jansen (2000) because of the inclusion of Luxembourg, Ho (2002) found that the inclusion or exclusion of Luxembourg did not affect the results when using the nonstationary panel data approach. The third category employed more advanced econometric techniques. Most of the studies, however, tended to support the Feldstein–Horioka puzzle. Tobin (1983) first criticized the OLS methodology employed by Feldstein and Horioka (1980) because both saving and investment are possibly endogenous. In addition, given that both saving and investment ratio are likely to be unit root nonstationary, the cointegration approach attracted much attention to the study of the Feldstein–Horioka puzzle. These recent works include those by Alexakis and Apergis (1994), Miller (1988), De Vita and Abbott (2002), and Narayan (2005a,b). Another group of studies adopted the panel data approaches, such as those by Fouquau et al. (2008), Herwartz and Xu (2010), Krol (1996), Narayan and Narayan (2010), and Oh et al. (1999). It follows that there is no consensus in the existing literature regarding the Feldstein–Horioka puzzle. In the literature, Narayan and Narayan (2010) did not find any cointegration relationship between saving and investment. Thus, they showed that the capital in G7 countries was highly mobile. However, Narayan and Narayan (2010) focused only on the G7 countries. As Coakley et al. (1999) pointed out, the relationship between saving and investment for less developed countries was different from that of developed countries. For this reason, this paper studies the relationship between saving and investment for both developed and less developed economies by using the time-varying cointegration approach developed by Park and Hahn (1999). This paper contributes to the literature in two ways. First, to the best of our knowledge, this paper is the first to apply the time-varying cointegration approach to examine the relationship between saving and investment. Even though Chen and Shen (2015), Ho (2000), Ho and Huang (2006), Özmen and Parmaksiz (2003), andTelatar et al. (2007) employed the regime-switching or timevarying coefficient approach, none of them used the time-varying coefficient or regime-switching cointegration. Second, this paper analyzes both annual and quarterly data. As far as we know, we are the first to investigate the robustness of the Feldstein–Horioka puzzle to the data frequency. As Narayan and Sharma (2015) showed, a hypothesis test might be dependent on data frequency, given that relatively high-frequency data provided additional information. By virtue of the additional information, the statistical and economic relationship between variables might be changed. Phan et al. (2015b), Narayan et al. (2013), and Narayan et al. (2015) have shown that the profitability of the commodity market was dependent on data frequency. Narayan and Sharma (2015) also found that data frequency did matter relative to the impact of forward premium on spot exchange rate. Phan et al. (2015a) showed that the effect of oil price change on stock returns was robust to the data frequency. Apart from the prevalent annual data, the quarterly data was used to study the Feldstein–Horioka puzzle. Such studies include those by Chang and Smith (2014) and Ketenci (2012). Therefore, one may wonder whether the relationship between saving and investment is robust to data frequency. The correlation between domestic saving and investment might not be invariant to the policy regime change. Thus, international capital mobility is essentially a time-varying phenomenon that cannot be represented by a fixed coefficient model. The well-known

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Locas critique pointed out, “given that the structure of an econometric model consists of optimal decision rules of economic agents and that optimal decision rules vary systematically with changes in the structure of series relevant to the decision maker, it follows that any change in policy will systematically alter the structure of econometric models.” The possible structural change for the saving-retention coefficient was also noted in the literature, such as in the studies of Sinha (2002), Özmen and Parmaksiz (2003), Narayan and Narayan (2010), and Ketenci (2012), who all employed the cointegration model with structural breaks; Chen and Shen (2015), Ho (2000), Ho and Huang (2006), and Telatar et al. (2007), who adopted the regime-switching model; Fouquau et al. (2008), who used the panel smooth transition regression model; and Herwartz and Xu (2010), who applied the function coefficient model. This paper employs the smooth timevarying coefficient cointegration model, in which model parameters change smoothly rather than abruptly in the model with structural breaks. Conventional wisdom suggests that the model parameters in the cointegration model might have some structural breaks. However, as Hansen (2001) pointed out, “it may seem unlikely that a structural break could be immediate, and it might seem more reasonable to allow a structural change to take a period of time to take effect.” Indeed, given the menu cost, the effect of technological progress and policy switch might have time lags. This paper examines the time-varying relationship between saving and investment for both developed and less developed economies, namely Australia, Bolivia, Canada, Chile, Denmark, France, Germany, Hong Kong, Iceland, India, Israel, Japan, Malaysia, Norway, Paraguay, Peru, the Philippines, South Korea, Thailand, Iran, the United Kingdom, and the United States, given that we can obtain sufficient annual and quarterly data for these economies. We show that the saving-ratio and investmentratio are unit root nonstationary. Given that debt cannot explode, the long-run solvency constraint requires the current account balance to be stationary, thus implying that saving and investment are cointegrated with a unit coefficient. In the literature, Chen (2011, 2014), Chen and Xie (2015), and Christopoulo and Leon-Ledesma (2010) found that the current account balance was stationary. By the conventional Johansen cointegration and the autoregressive distributed lag (ARDL) bounds testing approach of Pesaran et al. (2001), we do not find any cointegration relationship between saving and investment for most of the cases. The time-varying cointegration relationship between saving and investment is found for Australia, Canada, Chile, Israel, South Korea, and the United States. However, using the quarterly data, saving and investment are time-varying cointegrated for more economies. The less evidence for time-varying cointegration given by annual data might be attributed to the serious size distortion of the time-varying cointegration test in the small sample case. Indeed, the magnitudes of saving-retention coefficients for quarterly data have no substantial difference from those of annual data. The remainder of this paper is organized as follows: Section 2 presents a brief discussion of the time-varying coefficient cointegration. Section 3 summarizes the data and results for unit root tests. Section 4 provides the empirical results and analysis. Section 5 discusses the results of the cointegration with structural breaks, as well as the robustness of the time-varying cointegration results to data frequency. Section 6 concludes.

2. Time-varying coefficient model The relationship between saving and investment was first examined by the traditional linear regression model. Let IR and SR denote

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the investment (-GDP) ratio and saving (-GDP) ratio, respectively. A linear regression model can be represented as

IRt = a + b • SRt + et .

(2.1)

The parameter b is known as the saving-retention coefficient. Given that investment ratio IR and saving ratio SR are found nonstationary, the cointegration methodology, pioneered by the Nobel prize winner Clive W.J., Granger, has been widely used to investigate the relationship between saving and investment. The presence of a cointegrating relationship indicates a close correlation between saving and investment, which further implies the Feldstein–Horioka puzzle. The conventional cointegration approach assumes that there is a fixed-coefficient long-run equilibrium relationship between saving and investment. The economic structure, however, evolves over time, and the volatile economic and financial situation also has an influence. The degree of capital mobility might also vary over time because of some historical episodes, such as the prevalence of floating exchange regimes beginning from the 1970s, the creation of the European Union, the Asian financial crisis in 1997, and the global financial crisis in 2008. For these reasons, Özmen and Parmaksiz (2003) and Ketenci (2012) used the cointegration approach with structural breaks proposed by Gregory and Hansen (1996) and Kejriwal and Perron (2008, 2010). This approach assumed abrupt structural breaks. As Hansen (2001) himself pointed out, however, “it may seem unlikely that a structural break could be immediate, and it might seem more reasonable to allow a structural change to take a period of time to take effect”. Indeed, given the menu cost, the effect of the technological progress and policy switch might have time lags. Therefore, we assume that the saving retention coefficient evolves smoothly or gradually over time. That is,

IRt = a + b(t/T) • SRt + et ,

t = 1, 2, · · · , T.

(2.2)

Model (2.2) is a time-varying coefficient version of Model (2.1). Note that the coefficients are assumed to be functions of ratio t/T rather than time t. This “intensity” specification guarantees that the nonparametric estimators for b( • ) are consistent. The intuition is that, if we regard b( • ) as the ordinates of smooth functions on an equally spaced grid over [0, 1], the grid becomes finer as T → ∞. Therefore, the local information around a time point of interest increases. Given that both investment ratio IR and saving ratio SR are usually nonstationary, we use the time-varying cointegration approach developed by Park and Hahn (1999) to estimate the time-varying coefficient b( • ). In brief, Park and Hahn (1999) approximated the time-varying coefficient by using the Fouries flexible form (FFF) functions which include the trigonometric functions, apart from the polynomial functions of t/T, particularly,

bK (r) = kK,1 + kK, 2 r +

K 

(k2j+1 , k2j+2 )vj (r),

(2.3)

j=1

where vj (r) = (sin(2pjr), cos(2pjr) (i = 1, 2,· · · ,K) make up the trigonometric function base. If kK,2 = · · · = kK,2K+2 = 0, b(r) is fixed, then Model (2.2) is reduced to Model (2.1). The coefficient bK (r) can be rewritten as bK = fK kK ,

(2.4)

where fK = (1, r, v1 (r), · · · , vK (r)) with r ∈ [0, 1], and kK = (kK,1 , · · · , kK, 2K+2 ) . Therefore, Model (2.2) can be represented as IRt = a + b(t/T)K • SRK, t + et ,

t = 1, 2, · · · , T,

(2.5)

where SRK, t = fK (t/T) ⊗ SRt , and ⊗ is the Kronecker product. Once K is chosen,2 it is natural to consider OLS estimators kˆ j , j = 1, 2, · · · , 2K + 2. Although the OLS estimator is super-consistent, its asymptotic distribution depends on nuisance parameters arising from the endogeneity of the regressors and serial correlation of the errors. Indeed, both saving and investment could be possibly endogenous and could be affected by alternative macroeconomic factors, such as technological shocks, population growth, and the like. Fortunately, the canonical cointegration regression (CCR) approach developed by Park (1992) enables efficient estimation and valid inference under endogeneity. Generally, the CCR procedure can be divided into two steps. First, to eliminate the endogeneity and serial correlation, the variable must be transformed by using the variance and the (one-sided) long-run variance of the errors. Second, regress the transformed dependent variable on the independent variables. For more details, see Park and Hahn (1999). To test whether Model (2.1) or Model (2.2) is correctly specified, Park and Hahn (1999) put forward two specification tests by extending the variable addition approach of Park (1990). In particular, the tests can be formulated as Q1∗ = Q∗ =

∗p

∗ − RS SFC RS SFC ˆ 2∗ y

∗p

∗ − RS STVC RS STVC

y2∗

,

∗ ∗ where RS SFC and RS STVC are the sum of residuals from the CCR regression for Model (2.1) and Model (2.2), respectively. Moreover, ∗p ∗p RSSFC and RS STVC are the sum of residuals from the CCR regression, separately, for Model (2.1) and Model (2.2), augmented with p ˆ 2∗ is the estimation additional superfluous regressors 1, t, t2 , · · · , tp . y for the long-run variance of the errors from Model (2.2). The test statistic Q1∗ is used to test Model (2.1) against our time-varying coefficient model (Model (2.2)) and the test statistic Q1∗ is used to test Model (2.2) against the spurious time-varying coefficient regression. Under the corresponding null hypothesis, both Q1∗ and Q * converge to a chi-square distribution with p degrees of freedom. Under the alternatives, they diverge.

3. Data and unit root test The data are downloaded from the International Financial Statistics of the International Monetary Fund, the OECD statistics, and the CEIC database. Given the data availability, the annual data for these economies are used: Australia (1960–2014), Bolivia (1960– 2013), Canada (1981–2014), Chile (1960–2013), Denmark (1960– 2013), France (1960–2014), Germany (1970–2014), Hong Kong (1961–2013), Iceland (1960–2013), India (1960–2013), Israel (1960– 2013), Iran (1960–2010), Japan (1955–2013), Malaysia (1955–2013), Norway (1960–2013), Paraguay (1962–2013), Peru (1960–2013), the Philippines (1948–2013), South Korea (1952–2013), Thailand (1950– 2013), the United Kingdom (1960–2014), and the United States (1960–2014). The selection of countries (or regions) is dictated by the availability of data for a reasonable length of time. Saving is defined as GDP minus total consumption (private and government consumption), whereas investment is measured based on the gross fixed

2 There is no guide on the choice of the optimal K. The results, however, are not sensitive to the choice of K. In this paper, we use the Akaike information criterion (AIC).

W. Ma, H. Li / Economic Modelling 53 (2016) 166–178

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Table 1 Descriptive Statistics.

Australia SR IR Bolivia SR IR Canada SR IR Chile SR IR Denmark SR IR France SR IR Germany SR IR Hong Kong SR IR Iceland SR IR India SR IR Israel SR IR Iran SR IR Japan SR IR Malaysia SR IR Norway SR IR Paraguay SR IR Peru SR IR Philippines SR IR South Korea SR IR Thailand SR IR U.K. SR IR U.S. SR IR

Mean

Variance

Skewness

Kurtosis

JB(p-value)

SW(p-value)

BDS(3, s) (p-value)

0.2714 0.2756

0.0296 0.0241

0.4075 0.1509

1.8910 2.2405

4.08(0.1301) 1.27(0.5307)

0.9302*** (0.0033) 0.9736(0.2653)

45.6655*** (0.0000) 31.189*** (0.0000)

0.1501 0.1538

0.0633 0.0279

0.3696 0.4929

1.9893 2.7645

3.27( 0.1952) 2.35(0.3086)

0.9527** (0.0326) 0.9652(0.1183)

57.0227*** (0.0000) 9.6326*** (0.0000)

0.2342 0.2154

0.0225 0.0174

−0.6850 0.1216

2.9621 1.8785

2.94(0.2302) 1.53(0.4664)

0.9365** (0.0485) 0.9633(0.3027)

9.0945*** (0.0000) 28.8826*** (0.0000)

0.2073 0.1873

0.0732 0.0433

−0.1077 0.2441

1.7928 1.7817

3.03(0.2199) 3.55(0.1699)

0.9518** (0.0297) 0.9405*** (0.0098)

219.118*** (0.0000) 90.4212*** (0.0000)

0.2399 0.2116

0.0305 0.0248

0.1174 0.1546

2.20447 2.07

1.27(0.5298) 1.86(0.3947)

0.9747(0.3065) 0.9682(0.1607)

33.12*** (0.0000) 23.22*** (0.0000)

0.2390 0.2299

0.0283 0.0201

0.4269 0.2274

1.6874 1.9458

5.34* (0.0691) 2.71(0.2581)

0.8950*** (0.0002) 0.9584*(0.0549)

73.9204*** (0.0000) 61.8665*** (0.0000)

0.2357 0.2299

0.0222 0.0273

−0.2900 0.6082

2.3078 3.1205

1.32(0.5172) 3.09(0.2124)

0.9660(0.2054) 0.9247*** (0.0061)

23.3677*** (0.0000) 19.3004*** (0.0000)

0.3036 0.2506

0.0413 0.0452

−0.9775 0.3691

4.6310 2.6679

14.31*** (0.0008) 1.44(0.4850)

0.9430** (0.0136) 0.9673 (0.1540)

8.41*** (0.0000) 16.39*** (0.0000)

0.2364 0.231

0.0412 0.0486

0.2148 0.1212

1.595 2.446

4.51(0.1051) 0.62(0.7341)

0.9248*** (0.0023) 0.9801(0.5045)

932.95*** (0.0000) 17.95*** (0.0000)

0.2099 0.2127

0.0639 0.0568

0.2906 0.5377

2.1852 2.2916

2.25(0.3241) 3.73(0.1548)

0.9522** (0.0309) 0.9197*** (0.0015)

28.52*** (0.0000) 28.74*** (0.0000)

0.2671 0.2268

0.0490 0.0412

0.6907 0.6379

3.695 2.388

5.818*(0.0545) 4.484(0.1062)

0.9469** (0.0235) 0.9339*** (0.0053)

10.372*** (0.0000) 22.84*** (0.0000)

0.3105 0.2671

0.1007 0.04896

−0.0834 0.6907

1.7320 3.695

3.11(0.2109) 5.82*(0.0545)

0.9551*(0.0515) 0.9469** (0.0235)

122.05*** (0.0000) 10.372*** (0.0000)

0.3012 0.2807

0.0536 0.0446

−0.4013 −0.2335

2.5391 2.0030

2.11(0.3490) 2.98(0.2254)

0.9658*(0.0955) 0.9578** (0.0392)

30.53*** (0.0000) 44.82*** (0.0000)

0.3269 0.2422

0.0873 0.0867

−0.0621 0.4567

1.7700 2.6643

3.75(0.1528) 2.32(0.3122)

0.9431*** (0.0081) 0.9541** (0.0261)

169.66*** (0.0000) 27.83*** (0.0000)

0.3170 0.2552

0.0402 0.0575

0.6019 0.4264

2.3410 2.0520

4.18(0.1238) 3.43(0.1797)

0.9342*** (0.0054) 0.9286*** (0.0032)

18.92*** (0.0000) 51.09*** (0.0000)

0.1857 0.1878

0.0702 0.0505

0.3660 0.5677

1.6900 2.2410

4.58(0.1013) 3.93(0.1400)

0.9142*** (0.0011) 0.9267*** (0.0033)

105.10*** (0.0000) 39.29*** (0.0000)

0.2052 0.1916

0.0559 0.0429

0.5362 0.4022

2.3960 2.5000

3.33(0.1894) 1.91(0.3852)

0.9411** (0.0103) 0.9656(0.1231)

13.36*** (0.0000) 15*** (0.0000)

0.1748 0.1914

0.0443 0.0433

0.5019 0.2419

2.7414 2.4023

2.95(0.2281) 1.62(0.4435)

0.9432*** (0.0045) 0.9771 (0.2610)

19.25*** (0.0000) 52.05*** (0.0000)

0.2486 0.2644

0.1344 0.0886

−0.6498 −0.8097

1.9439 2.4524

7.13** (0.0283) 7.43** (0.0244)

0.8687*** (0.0000) 0.8675*** (0.0000)

61.43*** (0.0000) 25.78*** (0.0000)

0.2522 0.2450

0.0768 0.0781

−0.0719 0.4313

1.7095 2.8945

4.49(0.1056) 2.01(0.3653)

0.9267*** (0.0009) 0.9400*** (0.0038)

275.96*** (0.0000) 29.28*** (0.0000)

0.1960 0.2010

0.0305 0.0239

−0.4234 0.3229

2.0201 2.7659

3.61(0.1644) 1.05(0.5918)

0.9487** (0.0201) 0.9783(0.4188)

35.0784*** (0.0000) 19.1278*** (0.0000)

0.2062 0.2169

0.0276 0.0143

−0.5141 −0.7623

2.2358 3.1293

3.62(0.1635) 5.77*(0.0559)

0.944** (0.0127) 0.9435** (0.0120)

29.2322*** (0.0000) 9.4376*** (0.0000)

Notes: JB and SW denote the normality tests proposed by Jarque and Bera (1982) and Shapiro and Wilk (1965), separately. BDS(m, l) denotes the test statistic for the linearity proposed by Brock et al. (1996), where m is the embedding dimension and l is the distance parameter. Here, s denotes the standard error of the series. The numbers in parentheses are p values for the corresponding test statistics, respectively. ∗∗∗ Denotes significance at the 1% level. ∗∗ Denotes significance at the 5% level. ∗ Denotes significance at the 10% level.

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capital formation. Moreover, the saving and investment ratios are defined as percentages of GDP and denoted by SR and IR, respectively. Table 1 summarizes the results for some descriptive statistics, the normality test, and the nonlinearity test. The mean values for all the series are below 0.4. Furthermore, the variances are small for all series except for the SR of Iran and South Korea. The normality tests proposed by Jarque and Bera (1982) reject the null hypothesis of normality for SR and IR of South Korea; SR of France, Hong Kong, and Israel; and IR of Iran and the United States. However, according to the normality test of Shapiro and Wilk (1965), we reject the normality for series except for SR and IR of Denmark; SR of Germany; and IR of Australia, Bolivia, Canada, Hong Kong, Iceland, Peru, the Philippines, and the United Kingdom. In addition, the BDS test put forward by Brock et al. (1996) rejects the linearity for all series at 1% significance level. This indicates that all series are highly nonlinear, which necessitates the introduction of nonlinear analytical instrument. To check whether the series are stationary, we first perform four unit root tests: the modified ADF test (DF-GLS) proposed by Elliot et al. (1996); the PP test proposed by Phillips and Perron (1988); the NP test proposed by Narayan and Popp (2010); and the KPSS test proposed by Kwiatkowski et al. (1992). The null hypothesis of the DF-GLS, PP, and NP tests is a unit root, whereas that of the KPSS test is that the series are stationary. Perron (1989) showed that the structural breaks would be falsely regarded as an evidence for the unit roots if they are ignored. Therefore, it is of great importance to consider the unit root tests with structural breaks. The NP test allows two unknown structural breaks in level (denoted as Model M1), or in level as well as slope (denoted as Mode M2). Narayan and Popp (2013) showed that the NP test had better size properties and identified the unknown breaks more accurately than tests by Lumsdaine and Papell (1997) and Lee and Strazicich  (2003). Specifically, letting TB,i (i=1,2) denote the true break dates, Narayan and Popp (2010) formulated two test equations for M1 and M2 as follows: yM1 t

     = qyt−1 + a1 + b t + h1 D TB 1,t + h2 D TB 2,t + d1 DU1,t−1 ∗

 +d2 DU2,t−1 +

p 

bj Dyt−j + et ,

(3.1)

j=1

 yM2 = qyt−1 + a1 + j1 D(TB )1,t + j2 D(TB )2,t + d∗1 DU1,t−1 t    +d∗2 DU2,t−1 + c∗1 DT1,t−1 + c∗2 DT2,t−1 +

p 

bj Dyt−j + et , (3.2)

j=1

        where DUi,t = 1 t > TB,i = 1 t > TB,i and DTi,t (t − TB,i ). The unit root null hypothesis is H0 : q = 1. Note that the dummy variables   DUi,t and DTi,t in Eqs. (1) and (2) are lagged. This specification enables us to identify the unknown breaks more accurately than the wellknown Perron-type tests. Since the true break dates are unknown,  TB,i (i = 1, 2) has to be estimated in advance. Narayan and Popp (2010) developed a sequential procedure to obtain the estimates for  TB,i (i = 1, 2). Moreover, they provided the critical values for the M1and M2- type tests for various sample sizes; see Narayan and Popp (2010) for details. For the DF-GLS and NP tests, the Akaike information criterion (AIC) with a maximum lag length of [4 • (T/100)1/4 ] is used to choose the optimal lag orders. For the PP and KPSS tests, [4 • (T/100)1/4 ] gives the value of the automatic bandwidth to compute the long-run variance, where [ • ] denotes the integer part of a real number. Table 2 reports the results for unit root tests. As shown in Table 2, the SR and IR of Chile, France, Japan, Thailand, and the United Kingdom; the SR of Australia, Bolivia, Denmark, Germany, Iceland, Israel, Malaysia, Norway, and South Korea; and the IR of India and Peru can be deemed

Table 2 Unit root tests.

Australia SR IR Bolivia SR IR Canada SR IR Chile SR IR Denmark SR IR France SR IR Germany SR IR Hong Kong SR IR Iceland SR IR India SR IR Israel SR IR Japan SR IR Malaysia SR IR Norway SR IR Paraguay SR IR Peru SR IR Philippines SR IR South Korea SR IR Thailand SR IR Iran SR IR UK SR IR US SR IR

DF-GLS

PP

KPSS

NP-M1

NP-M2

−1.8790 −1.3210

−2.2000 −1.9670

0.8395*** 0.2162***

−3.6353 −4.1774*

−4.2527 −4.6754

−1.581 −2.671***

−2.378 −2.819*

0.1702* * 0.1435

−2.1238 −3.5624

−2.1909 −3.1839

−1.779* −1.1850

−2.4420 −3.0680

0.1347 0.2107**

−3.1424 −4.2372*

−3.1839 −2.8665

−1.124 −2.032

−1.983 −2.657

1.104* * * 0.1275*

−2.7492 −2.7020

−2.9299 −3.8178

−1.453 −2.201**

−1.665 −2.176

0.7678* * * 0.4032*

−2.9467 −2.7274

−2.1219 −2.6051

−0.3333 −1.4440

−1.2010 −1.4280

1.12* * * 0.898***

−3.0165 −2.6306

−3.2527 −2.4594

−1.1400 −0.4241

−2.2890 −2.1610

0.4168** 0.9871***

−2.9292 −4.4869*

−4.3146 −3.0789

−0.77 −3.63***

−3.81*** −2.86*

0.48** 0.09

−4.2979* −5.0534**

−4.3779 −4.8475*

−1.0099 −1.453

−1.6065 −2.4898

0.9847* * * 0.5016**

−3.3196 −3.0180

−4.0264 −5.9027**

−3.15* * −2.95*

−4.01* * −2.56

1.34* * * 1.33***

−2.7010 −1.6402

−3.0971 −1.0366

−1.1364 3.5148**

−1.2551 −3.0998

0.8167* * * 0.7527***

−2.8798 −4.1209

−4.6392 −5.0688*

−1.39 −1.12

−2.68 −1.81

0.94*** 0.76***

−3.4735 −4.4455*

−2.6484 −4.6546

−1.39 −2.01

−2.68 −2.05

1.35*** 0.67**

−2.4971 −2.8192

−3.3792 −5.8109**

−1.27 −2.843*

−2.445 −3.188*

0.5259** 0.0869

−2.5061 −3.5981

−2.6411 −2.8911

−1.114 −1.209

−1.791 −1.816

0.883*** 0.2987

−4.2942* −4.8762**

−3.2519 −3.6278

−2.675* * * −1.877*

−2.345 −1.992

0.2998 0.4857**

−2.5791 −3.5773

−1.4598 −3.3286

−1.67* −2.40**

−1.78 −2.14

0.33 0.80***

−2.2969 −3.2193

−3.7285 −3.5835

−0.47 −0.48

−1.28 −2.23

1.35* * * 1.18***

−1.6297 −4.1811*

−3.8685 −4.4960

−1.66 −1.91

−2.22 −1.93

1.49* * * 0.96***

−2.7265 −3.1411

−2.6580 −3.4929

−2.5837 −2.7654***

2.2593 −3.1619**

0.6841** 0.1222

−1.9080 −3.7787

−2.2141 −4.4791

−0.9222 −1.6610

−1.1770 −2.4610

0.7981* * * 0.2616***

−2.4699 −3.9277

−3.9794 −3.4964

−0.5666 −2.2050

−0.8840 −2.4610

1.282* * * 0.12*

−3.5452 −4.7992**

−2.7610 −4.9607*

Notes: DF-GLS and PP are, respectively, the modified augmented Dickey–Fuller test proposed by Elliot et al. (1996), and Phillips and Perron’s (1988) test for the null hypothesis of a unit root. KPSS is a test for stationarity developed by Kwiatkowski et al. (1992). NP-M1 and NP-M2, which are proposed by Narayan and Popp (2010), are the unit root tests with two structural breaks in level and in both level and slope, respectively. ∗∗∗ Denotes significance at the 1% level. ∗∗ Denotes significance at the 5% level. ∗ Denotes significance at the 10% level.

W. Ma, H. Li / Economic Modelling 53 (2016) 166–178

171

Table 3 OLS regression results. Australia

Bolivia

Canada

Chile

Denmark

France

Germany

Hong Kong

Iceland

India

Israel

a (p-value) b (p-value) R2

0.0878 (0.0000) 0.6922 (0.0000) 0.7237

0.1428 (0.0000) 0.0729 (0.2320) 0.0274

0.1556 (0.0000) 0.2552 (0.0567) 0.1088

0.0917 (0.0000) 0.4609 (0.0000) 0.6064

0.1734 (0.0000) 0.1594 (0.1550) 0.0384

0.0929 (0.0000) 0.5732 (0.0000) 0.6519

0.2404 (0.0000) −0.0447 (0.8130) 0.0013

0.1943 (0.0001) 0.1854 (0.2252) 0.0287

0.1317 (0.0007) 0.4203 (0.0083) 0.1266

0.0342 (0.0000) 0.8503 (0.0000) 0.9130

0.2477 (0.0000) −0.1813 (0.0192) 0.1010

a (p-value) b (p-value) R2

Japan 0.0412 (0.0001) 0.7952 (0.0001) 0.9120

Malaysia 0.0751 (0.0540) 0.5112 (0.0000) 0.2650

Norway 0.3640 (0.0000) −0.3432 (0.0807) 0.0575

Paraguay 0.2065 (0.0000) −0.1007 (0.3230) 0.0196

Peru 0.0803 (0.0000) 0.5424 (0.0000) 0.5009

Philippines 0.0910 (0.0001) 0.5746 (0.0001) 0.3460

South Korea 0.1108 (0.0001) 0.6179 (0.0001) 0.8790

Thailand 0.0407 (0.0520) 0.8097 (0.0520) 0.6350

Iran 0.2253 (0.0000) 0.1347 (0.0490) 0.0768

U.K. 0.0694 (0.0000) 0.6713 (0.0000) 0.7368

U.S. 0.1683 (0.0000) 0.2483 (0.0000) 0.4399

as stationary by four unit root tests. However, for other series, we obtain conflicting results. In particular, with respect to the IR series of Australia, Canada, Germany, Iceland, Japan, South Korea, and the United States, the DF-GLS and PP tests cannot reject the unit root null hypothesis, and the KPSS test rejects the null hypothesis of stationarity. However, the NP-M1 or NP-M2 tests reject the unit root, which implies that it is of great importance to take structural breaks into accounts. 4. Empirical analysis Table 3 provides conventional OLS regression results. It clearly shows that the saving-retention coefficients (b) for all economies except for Bolivia, Denmark, Germany, Hong Kong, and Paraguay are significant. All economies but Germany, Israel, Norway, and Paraguay have positive saving-retention coefficients. This indicates that saving and investment are highly correlated for most of the economies. Table 4 Johansen’s cointegration tests. kmax

Australia Bolivia Canada Chile Denmark France Germany Hong Kong Iceland India Israel Japan Malaysia Norway Paraguay Peru Philippines South Korea Thailand Iran U.K. U.S. Critical values 10% 5% 1%

ktrace

Lags

r≤1

r=0

r≤1

r=0

4 2 2 3 4 2 2 6 2 2 6 2 3 2 2 2 4 4 3 5 2 2

3.21 2.72 4.00 2.29 1.08 1.57 0.47 0.22 1.15 0.68 0.20 0.11 2.41 4.11 2.71 4.73 3.20 6.32 1.82 0.69 1.8 1.09

9.05 8.86 8.90 9.33 10.75 6.52 19.09** 12.82 16.21 13.65 7.49 16.90* * 14.81* 7.82 9.79 10.30 7.98 10.93 8.38 8.66 11.65 16.23**

3.21 2.72 4.00 2.29 1.08 1.57 0.47 0.22 1.15 0.68 0.20 0.11 2.41 4.11 2.71 4.73 3.20 6.32 1.82 0.69 1.80 1.09

12.26 11.58 12.90 11.62 11.83 8.09 19.56 13.04 17.36 14.33 7.69 17.01* 17.23* 11.93 12.50 15.03 11.18 17.25* 10.20 9.35 13.45 17.32

6.50 8.18 11.65

12.91 14.90 19.19

6.50 8.18 11.65

15.66 17.95 23.52

Notes: r = 0 denotes the null hypothesis of no cointegration and r ≤ 1 denotes the null hypothesis of at least one cointegrating vector. kmax and ktrace denote the Johansen’s maximum eigenvalue test statistic and trace test statistic, respectively. “Lags” denotes the optimal lag order. ∗∗ Denotes significance at the 5% level. ∗ Denotes significance at the 10% level.

More importantly, some less developed economies such as India, Malaysia, Peru, the Philippines, and Thailand have large savingretention coefficients. Some developed economies such as Canada, Hong Kong, and the United States have small saving-retention coefficients. The results are inconsistent with the literature that found low saving–investment correlation for less developed countries—for example, Coakley et al. (1999). Both saving and investment, however, are possibly endogenous since they could be affected by alternative macroeconomic factors, such as technological shocks and population growth. Moreover, both IR and SR are highly persistent as we have shown in Section 3. Therefore, it might not be appropriate to apply the OLS methodology directly. Since both IR and SR are unit root nonstationary, we examine their relationship by deploying the cointegrating approach. First, the Johansen’s cointegration test results are presented in Table 4, in which r = 0 denotes the null hypothesis of no cointegration and r ≤ 1 denotes the null hypothesis of at least one cointegrating vector. For all cases, the null hypothesis r ≤ 1 for both maximum eigenvalue test kmax and the trace test ktrace cannot reject the null hypothesis, implying the possibility of the cointegrating relationship. However, the weak evidence against the null hypothesis r = 0 is found only for Germany, Japan, South Korea, Malaysia, and the United States. Specifically, in the case of Japan and Malaysia, both kmax and ktrace tests reject the null hypothesis at 10% significance level. With regard to Germany and the United States, only the kmax test rejects the null hypothesis at 5% significance level. In the case of South Korea, only the ktrace tests reject the null hypothesis at 10% significance level. Therefore, going by Johansen’s cointegration test, no strong evidence to support the cointegration is found for all cases. This means that there is no long-run equilibrium between saving and investment for these economies, which indicates the absence of the Feldstein–Horioka puzzle. From Table 2, we can see that SR and IR have different integration order. However, the Johansen cointegration testing approach requires that all the variables in the system are integrated of the same order. Therefore, we employ the autoregressive distributed lag (ARDL) bounds testing approach by Pesaran et al. (2001), which enables us to test the cointegration relationship irrespective of whether the related variables are integrated of the same order or not. In brief, the ARDL bounds test is based on the following ARDL regression

DIRt = b0 +b1 IRt−1 +b2 SRt−1 +

p  i=1

ki DIRt−i +

q 

dj DSRt−j +et . (4.1)

j=1

The null hypothesis of no coinintegration can be checked by an F-test for H0 : b1 = b2 = 0, or a t-test for H0 : b1 = 0. Under the alternative hypothesis, there is an equilibrium relationship between SR and IR. The t test and F test have a non-standard distribution that depends on the number of regressors in the ARDL regression,

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Table 5 ARDL tests.

Australia Bolivia Canada Chile Denmark France Germany Hong Kong Iceland India Israel Japan Malaysia Norway Paraguay Peru Philippines South Korea Thailand Iran U.K. U.S.

Lags

F-statistic

t-Statistic

Outcome

0 0 0 2 3 3 0 0 1 3 2 0 3 0 3 3 0 0 0 3 0 0

5.1103a 11.8479a 1.5874c 0.4018c 1.1716c 0.2168c 5.5778a 1.5221c 0.3568c 0.5200c 0.6072c 6.1564a 0.5175c 1.1578c 0.5480c 0.2052c 1.9232c 3.5927c 1.3869c 0.0670c 2.7753c 1.9098c

−3.8624a −5.7660a −1.5084c −1.6635c −1.6500c −0.3155c −3.8397a −1.9172c −1.2019c −2.1469c −1.4055c −4.2814a −1.7500c −1.4527c −2.1529c −1.1123c −2.3531c −2.9961a −1.7384c −0.7338c −0.9592c −2.3812c

Cointegration Cointegration No cointegration No cointegration No cointegration No cointegration Cointegration No cointegration No cointegration No cointegration No cointegration Cointegration No cointegration No cointegration No cointegration No cointegration No cointegration Mixed evidence No cointegration No cointegration No cointegration No cointegration

Notes: The lag order is selected based on the AIC. a Indicates that the statistic lies above the 0.10 upper bound. c Indicates that the statistic lies below the 0.10 lower bound.

the sample size, whether the ARDL regression includes an intercept and/or trend, and whether variables in the ARDL regression are I(0) or I(1). Table CI(iii) and CII(iii) in the approach by Pesaran et al. (2001) provide the critical values for the F-test and t-test, respectively. If the test statistics are below the lower critical values, the null hypothesis cannot be rejected. Likewise, if the test statistics exceed the upper critical values, the null hypothesis is rejected. Finally, if the test statistics fall between the lower and upper critical values, results are inconclusive. For the choice of lag order, we let the maximum lag order be [4 • (T/100)1/4 ], and obtain the optimal lag order by AIC. For simplicity, we let p = q. Table 5 reports the results of the ARDL bounds tests. As shown in Table 5, we find a cointegration relationship only between SR and IR for Australia, Bolivia, Germany, and Japan. With respect to South Korea, it is inconclusive. Therefore, there is no substantial difference between the Johansen cointegration test and the ARDL bounds test since both of them assume that the cointegration coefficient is fixed. The long-run equilibrium relationship, however, might be timevarying, as we have documented in Section 2. Given that our data

sample is long time spanned, one may wonder whether there is a time-varying cointegrating relationship between saving and investment. Indeed, many profound historical events happened during the period of our data sample, including the introduction of floating exchange regimes beginning from the 1970s, the creation of the European Union, the Asian financial crisis in 1997, and the global financial crisis in 2008. For these reasons, we investigate the timevarying cointegration relationship between saving and investment as follows. Table 6 gives the test results for the time-varying cointegration. To perform both fixed-coefficient cointegration test Q FC and time-varying coefficient cointegration test Q TVC , four polynomial terms t, t 2 , t 3 and t 4 are considered as superfluous regressors. Therefore, both Q FC and Q TVC converge to the w 2 (4) distribution asymptotically. It is shown in Table 6 that, for all cases except for Peru, Q FC rejects the null hypothesis of fixed coefficient cointegration at 1% level. Q TVC rejects the null hypothesis of time-varying coefficient cointegration for France, Hong Kong, Iceland, India, Malaysia, Norway, Paraguay, Peru, the Philippines, and the United Kingdom at 1% level; for Bolivia, Denmark, Japan, Thailand, and Iran at 5% level; and for Germany at 10% level. In addition, with respect to Australia, Canada, Chile, Israel, South Korea, and the United States, Q TVC cannot reject the time-varying cointegration at 10% level. Therefore, there exists time-varying cointegration relationship between saving and investment for these countries, and weak time-varying cointegration for Bolivia, Denmark, Japan, Thailand and Iran. In terms of GDP, Australia, Canada, Israel, South Korea, and the United States could be regarded as big countries, and thus they are more like closed economies. This is because big countries tend to finance domestic investment by domestic saving. Therefore, there might exist more close relationship between domestic saving and domestic investment. Our results are consistent with Narayan (2005a) but different from the findings of Sinha (2002) according to which saving and investment were found not cointegrated for Japan and South Korea by using the cointegration approach with structural breaks. The estimates for the time-varying saving-retention coefficients are depicted in Figs. 1 and 2. First, for Australia, Bolivia, Canada, Chile, France, Iceland, Israel, Peru, and United Kingdom, the savingretention coefficients exhibit snake-like varying patterns. The variations of the saving-retention coefficients for the developed countries, i.e., Australia, Canada, France, Israel, and the United Kingdom are small in magnitude. In contrast, the developing countries, i.e., Bolivia, Chile and Peru have large coefficient variations, indicating their instable economic structure. Second, with regard to Denmark, Germany, Iceland, and Norway, the saving-retention coefficients decrease slowly over time, reflecting the gradually opening economic situation.

Table 6 Model specification tests.

Q TVC Q FC

Q TVC Q FC

Australia

Bolivia

Canada

Chile

Denmark

France

Germany

Hong Kong

Iceland

India

Israel

0.87 8.10*

11.09** 15.14***

7.11 176.02***

3.65 58.30***

11.05** 332.99***

21.42*** 218.97***

8.79* 525.95***

180.08*** 294.49***

32.09*** 103.98***

16.67*** 54.72***

4.08 51.28***

Japan

Malaysia

Norway

Paraguay

Peru

Philippines

South Korea

Thailand

Iran

U.K.

U.S.

12.33** 33.42***

21.41*** 221.39***

32.75*** 425.02***

27.79*** 379.76***

58.03*** 6.03

20.42*** 131.42***

7.21 49.96***

11.16** 100.79***

9.57** 26.00***

21.47*** 28.11***

4.69 126.13***

Critical values 10% 5% 7.78 9.49

1% 13.28

Notes: Q FC and QTVC are the test statistic for the null hypothesis that IR and SR are fixed-coefficient cointegrated and time-varying coefficient cointegrated, respectively. The additional superfluous regressors are time polynomial terms, t, t 2 , t3 , t 4 . Under the null hypothesis, both Q FC and Q TVC converge to a w2 (4) distribution asymptotically. ∗∗∗ Denotes significance at the 1% level. ∗∗ Denotes significance at the 5% level. ∗ Denotes significance at the 10% level.

W. Ma, H. Li / Economic Modelling 53 (2016) 166–178

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Bolivia

0.35

−0.2

0.50

0.4

Austrlia

1960

1965

1970

1975

1980

1985

1990

1995

2000

2005

2010

2014

1960

1965

1970

1975

1980

1990

1995

2000

2005

2010

1990

1995

2000

2005

2010

Chile

0.0

0.3

0.6

0.35 0.50 0.65

Canada

1985

1981

1985

1990

1995

2000

2005

2010

1960

1965

1970

1975

1980

France

0.6

0.45

0.8

0.60

1.0

Denmark

1985

1960

1965

1970

1975

1980

1985

1990

1995

2000

2005

2010

1960

1965

1970

1975

1980

Germany

1985

1990

1995

2000

2005

2010

2014

0.0 0.2 0.4

0.2 0.4 0.6

Hong Kong

1970

1975

1980

1985

1990

1995

2000

2005

2010

2014

1961

1965

1970

1975

1980

1990

1995

2000

2005

2010

1990

1995

2000

2005

2010

1990

1995

2000

2005

2010

India

0.0

−1.2

0.3

−0.6

0.6

Iceland

1985

1960

1965

1970

1975

1980

1985

1990

1995

2000

2005

2010

1960

1965

1970

1975

1980

Israel

0.1

0.4

−1.0 0.0

0.7

Islamic Republic of Iran

1985

1960

1965

1970

1975

1980

1985

1990

1995

2000

2005

2010

1960

1965

1970

1975

1980

1985

Fig. 1. Time-varying saving retention coefficients.

In the case of Hong Kong, the saving-retention coefficient decreased rapidly from 1961 to the early 1970s. After rising a little from the early 1970s to the early 1980s, it stayed relatively stable from the early 1980s to the late 1990s. It then dropped lose to zero. The two turning points for Hong Kong’s saving-retention coefficient coincide with the occurring time of three historical events. In 1973, a large number of countries adopted the floating exchange rate regime. As a response to the Black Saturday crisis in 1983, Hong Kong adopted the linked exchange rate regime for which the exchange rate of the Hong Kong dollar to US dollar is fixed to 7.80 (direct quotation). The adoption of the linked exchange rate regime helped Hong Kong stabilize its international trade and capital mobility. In 1997, the Asian financial crisis took place, and moreover, the United Kingdom transferred the sovereignty over Hong Kong to China. Since then, the economic and business links between Hong Kong and mainland China have intensified greatly, accompanied by a large capital mobility. The saving-retention coefficient for India appears monotone and increases from 0.1 to 0.6. Moreover, it looks not being affected by the historical events. The low saving-retention coefficient for India in the 1960s can be attributed to the large foreign aid it received during that period. According to Sinha (2002), one-sixth of the investment for India in the 1960s was from foreign aid. With regard to Japan, the saving-retention coefficient is large in magnitude and varies between 0.6 and 0.7, while Narayan (2005a) found that the saving retention coefficient for Japan was 0.68 as per a fixed-coefficient model. For South Korea, the saving-retention coefficient increased rapidly from 1953 to 1970, and then stayed around 0.8 from the early 1970s.

The recent high saving-investment correlation for Japan and South Korea could be ascribed to their large economy. In the late 1960s, Japan became the second largest economy. Although surpassed by China in 2010, it is still the third largest economy by nominal GDP. South Korea had one of the world’s fastest growing economies from the early 1960s to the late 1990s, and remains one of the fastest growing developed countries in the 2000s. The results for Japan and South Korea are consistent with the argument of Harberger (1980) and Murphy (1984), which put down the high saving–investment correlation to large country bias rather than low capital mobility. With respect to Malaysia, the saving-retention coefficient was positive from the mid-1970s to the mid-2010s, negative before the mid 1970s, and close to zero after the mid 2010s. For the Philippines and Thailand, the patterns of saving-retention coefficients are similar. Specifically, they increase to 0.5, and then fluctuate around 0.4 after a slight decrease. Finally, the saving-retention coefficient for the United States is increasing and larger than 0.8 during the whole sample period. Therefore, the saving-retention coefficients of the developed economies are significantly higher than those of less developed economies. These findings are consistent with those of Coakley et al. (1999). Coakley et al. (1999) showed that the saving-retention coefficients for less developed countries were significantly lower than those for OECD countries. However, this does not imply that capital is more mobile among less developed countries. On the contrary, we interpret this according to the long-run solvency constraint theory of Coakley et al. (1996). The long-run solvency constraint entails that the current account balances be stationary since debt

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W. Ma, H. Li / Economic Modelling 53 (2016) 166–178 Malaysia

0.55

−0.8

0.65

−0.2 0.2

0.75

Japan

1955

1960

1965

1970

1975

1980

1985

1990

1995

2000

2005

2010

1955

1960

1965

1970

1975

1980

1990

1995

2000

2005

2010

Paraguay

−0.4

−0.2 0.2

−0.1

0.6

0.2

Norway

1985

1960

1965

1970

1975

1980

1985

1990

1995

2000

2005

2010

1960

1970

1975

1980

1985

1995

2000

2005

2010

Philippines

−0.1

−0.2

0.2

0.2 0.4 0.6

0.6

Peru

1990

1960

1965

1970

1975

1980

1985

1990

1995

2000

2005

2010

1948

1955

1960

1965

1970

1975

1985

1990

1995

2000

2005

2010

2000

2005

2010

Thailand

−0.4

−0.2

0.2

0.6

0.2 0.6 1.0

South Korea

1980

1953

1960

1965

1970

1975

1980

1985

1990

1995

2000

2005

2010

1950

1955

1960

1965

1970

1980

1985

1990

1995

0.8

0.2

1.0

United States of America

0.4

United Kingdom

1975

1960

1965

1970

1975

1980

1985

1990

1995

2000

2005

2010

2014

1960

1965

1970

1975

1980

1985

1990

1995

2000

2005

2010

2014

Fig. 2. Time-varying saving retention coefficients.

cannot explode. Since the current account balance is equal to the difference between saving and investment, it implies that these two factors are cointegration with a unit coefficient, irrespective of the degree of capital mobility. Moreover, as Coakley et al. (1999) pointed out, the solvency-maintaining feedback mechanism might be weaker in less developed countries since the risk-premium market mechanism may be less effective in eliminating their current account deficits due to the distorted interest rate.

5. Robustness test The time-varying cointegration approach assumes a gradual and smooth structural change in the cointegration coefficient. However, the cointegration with structural breaks developed by Gregory and Hansen (1996) was also widely used in the literature, for example, Narayan (2005a), Narayan and Narayan (2010), and Sinha (2002).3 Gregory and Hansen (1996) developed three models to consider three forms of structural breaks. The first model is a level shift model denoted by C:

IRt = l1 + l2 0tt + aSR + et , t = 1, 2, · · · , n,

(5.1)

where the dummy variable  0tt =

0,

if t ≤ [nt],

1,

if t > [nt].

The unknown parameter t ∈ (0, 1) denotes the timing of the change point and [ • ] denotes the integer part. In the level shift model, l1 is the intercept before the shift and l2 is the change in the intercept at the time of the shift. The second model is a level shift model with trend denoted by C/T: IRt = l1 + l2 0tt + bt + aSR + et , t = 1, 2, · · · , n. The third model is a regime shift model denoted by C/S: IRt = l1 + l2 0tt + kSR + aSR0tt + et , t = 1, 2, · · · , n.

Zt∗ = Zt (t), We thank the referee for suggesting this robustness test.

(5.3)

It is a conventional practice to let t ∈ (0.15, 0.85) in order to obtain the reasonable estimates for the structural breaks. If the residual et is stationary, then IR and SR are cointegrated with structural breaks. To test the null hypothesis of no cointegration, Gregory and Hansen (1996) proposed three test statistics as follows: Za∗ = Za (t),

3

(5.2)

ADF∗ = ADF(t).

W. Ma, H. Li / Economic Modelling 53 (2016) 166–178

175

Table 7 Cointegration tests with a structural break.

Australia

Bolivia

Canada

Chile

Denmark

France

Germany

Hong Kong

Iceland

India

Israel

Japan

Malaysia

Norway

Paraguay

Peru

Philippines

South Korea

Thailand

Iran

U.K.

U.S.

Model

ADF*

C C/T C/S C C/T C/S C C/T C/S C C/T C/S C C/T C/S C C/T C/S C C/T C/S C C/T C/S C C/T C/S C C/T C/S C C/T C/S C C/T C/S C C/T C/S C C/T C/S C C/T C/S C C/T C/S C C/T C/S C C/T C/S C C/T C/S C C/T C/S C C/T C/S C C/T C/S

−3.9494 −4.3847 −4.0172 −3.0785 −3.9955 −3.1870 −3.6178 −5.2059** −3.5465 −4.5817* −4.6103 −4.5996 −4.6953** −4.4618 −5.2085** −3.6376 −4.0437 −3.8082 −3.9856 −5.6717*** −4.0194 −5.0616** −5.5886*** −4.8569* −4.1945 −4.4951 −4.7573 * −5.2080*** −4.2411 −5.3589** −4.7495** −4.5265 −4.4679 −3.5718 −3.7771 −3.8011 −4.3893* −4.9596* −4.7284* −5.6369*** −4.9756* −5.4056** −2.9545 −4.1936 −3.3899 −4.2518 −4.1965 −4.2098 −4.9313** −4.5948 −4.7367* −4.8131** −4.9360* −4.6600 −6.1364*** −6.2290*** −6.1119*** −2.5782 −5.1705** −2.5538 −4.3675* −4.3075 −4.4448 −4.1321 −3.7876 −3.7229

Zt * (0.8182) (0.8182) (0.2727) (0.6296) (0.3889) (0.8148) (0.7353) (0.2941) ( 0.7353) (0.5185) (0.5185) (0.7222) (0.4630) (0.5000) (0.4444) ( 0.4000) ( 0.8364) (0.5636) (0.6444) (0.7111) (0.6444) (0.8302) (0.3019) (0.3019) (0.4074) (0.7593) (0.7222) (0.1667) (0.8519) (0.2407) (0.3704) (0.3704) (0.3704) (0.1525) (0.4915) (0.8305) (0.6949) (0.7627) (0.7458) (0.5000) (0.5370) (0.4630) (0.5962) (0.2115) (0.3654) (0.3148) (0.3889) (0.3148) (0.5152) (0.3939) (0.4848) (0.4590) (0.2295) (0.1967) (0.7188) (0.7188) (0.7188) (0.5294) (0.1961) (0.3922) (0.3818) (0.2000) (0.3818) ( 0.8545) (0.2909) (0.2545)

−3.9630 −4.1149 −3.9640 −3.2165 −4.0375 −3.2431 −3.6762 −5.2081** −3.6200 −4.6923** −4.7201* −4.6754* −3.8931 −3.9724 −3.9526 −3.4597 −4.1170 −4.0320 −3.0296 −3.6909 −3.0529 −2.9058 −2.9439 −2.8785 −3.4125 −3.4541 −5.0867** −5.2579*** −4.1747 −5.3956** −3.4856 −4.1341 −3.4668 −3.6823 −3.9908 −3.9645 −4.3195 −4.2211 −4.8054* −3.6005 −3.8419 −3.5494 −2.5246 −4.2409 −3.4190 −3.5120 −3.9670 −3.6861 −4.3212 −4.4033 −4.9540* −4.8602** −4.7589* −4.7609* −5.1444*** −5.4555*** −5.1840 ** −4.1598 −4.7729* −4.6506 −3.4975 −3.5337 −3.4974 −2.6579 −2.5294 −2.6598

Za * (0.3636) (0.3636) (0.3636) (0.6296) (0.4074) (0.6296) (0.7353) (0.2941) (0.7353) (0.5185) (0.5185) (0.5000) (0.5370) (0.5370) (0.4815) (0.8545) (0.8364) (0.5818) (0.6444) (0.1778) (0.6444) (0.1509) (0.3208) (0.8491) (0.3889) (0.4074) (0.8333) (0.1667) (0.1667) (0.2407) (0.3519) (0.1852) (0.3889) (0.1525) (0.4746) (0.8305) (0.7119) (0.7627) (0.7458) (0.5000) (0.2222) (0.4815) (0.1923) (0.2500) (0.4038) (0.3333) (0.7963) (0.2407) (0.4242) (0.8333) (0.6515) (0.4918) (0.4918) (0.4918) (0.7188) (0.7344) (0.7188) (0.6078) (0.3137) (0.3922) (0.7273) (0.3273) ( 0.7273) (0.2727) (0.8545) (0.2364)

−25.7988 −27.5628 −25.7950 −18.3954 −26.3900 −18.7064 −15.7532 −22.6153 −15.5283 −32.7456 −33.0392 −33.6589 −22.5525 −22.1278 −25.4427 −16.4233 −21.1547 −21.9181 −14.9646 −22.7306 −15.4217 −16.4381 −17.1501 −15.7730 −21.4213 −21.7647 −35.9295 −37.3220* −28.2075 −38.0529 −21.6533 −27.2337 −21.5100 −25.0440 −28.7055 −23.8531 −27.8748 −29.281 0 −31.0130 −23.4686 −26.5990 −22.7785 −12.4308 −25.5870 −18.4780 −23.0417 −26.8518 −23.9383 −28.9899 −29.1867 −35.9943 −33.4912 −33.0018 −32.5130 −39.9749* −42.4420 −40.1646 −26.6781 −32.0620 −31.3650 −21.4530 −22.6858 −21.5315 −14.1752 −12.7619 −14.1943

Notes: The symbols C, C/T, and C/S refer to Model (5.1), (5.2) and (5.3), respectively. The numbers in the parentheses are the estimated breakpoints. ∗∗∗ Denotes significance at the 1% level. ∗∗ Denotes significance at the 5% level. ∗ Denotes significance at the 10% level.

(0.3636) (0.3636) (0.3636) (0.6296) (0.4074) (0.6296) (0.7647) (0.2941) (0.7647) (0.5185) (0.5185) (0.5000) (0.5370) (0.5370) (0.4815) (0.3636) (0.5636) (0.5636) (0.6444) (0.1778) (0.6444) (0.1509) (0.5660) (0.8491) (0.3704) (0.3889) (0.7222) (0.1667) (0.1667) (0.2407) (0.3519) (0.1852) (0.3889) (0.1525) (0.4746) (0.2712) (0.7119) (0.7627) (0.7458) (0.5000) (0.2407) (0.4815) (0.1923) (0.2500) (0.3654) (0.3333) (0.7963) (0.5926) (0.4242) (0.6515) (0.6515) (0.4918) (0.4918) (0.4918) (0.7188) (0.7344) (0.7188) (0.6078) (0.1569) (0.3922) (0.7091) (0.3273) (0.7091) (0.2364) (0.8545) (0.2364)

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Table 8 Model specification tests (quarterly data).

Q TVC Q FC

Q TVC Q FC

Australia

Bolivia

Canada

Chile

Denmark

France

Germany

Hong Kong

Iceland

India

Israel

9.09* 19.90***

8.36* 91.31***

45.27*** 374.09***

13.63*** 105.67***

10.79** 39.84***

37.54*** 194.39***

4.99 429.89***

6.11 33.18***

11.16** 244.78***

5.84 103.64***

3.35 38.68***

Japan

Malaysia

Norway

Paraguay

Peru

Philippines

South Korea

Thailand

Iran

U.K.

U.S.

3.14 60.32***

4.53 275.08***

6.16 82.70***

Critical values 10% 5% 7.78 9.49

1.52 100.49***

4.55 23.49***

4.27 132.09***

**

12.70 37.18***

5.96 168.68***

**

5.92 45.48***

11.91 14.21***

6.74 96.43***

1% 13.28

Notes: Q FC and QTVC are the test statistic for the null hypothesis that IR and SR are fixed-coefficient cointegrated and time-varying coefficient cointegrated, respectively. The additional superfluous regressors are time polynomial terms, t, t2 , t3 , t 4 . Under the null hypothesis, both Q FC and QTVC converge to a w2 (4) distribution asymptotically. ∗∗∗ Denotes significance at the 1% level. ∗∗ Denotes significance at the 5% level. ∗ Denotes significance at the 10% level.

The asymptotic distributions of Za∗ , Zt∗ , and ADF * are functions of the Brownian motions, and therefore their critical values have to be obtained by simulation. The critical values depend on the number of regressors and the assumed models. Table 1 of Gregory and Hansen (1996) tabulated the critical values. Table 7 reports the test results. First, among the three tests, the Za∗ test has the lowest rejection rate, and it rejects the null hypothesis of no cointegration only for India and South Korea. Second, with respect to the Zt∗ test, it rejects the null hypothesis for Canada, Chile, Iceland, India, Malaysia, the Philippines, South Korea, Thailand, and Iran. Finally, the ADF * test rejects the

null hypothesis of no cointegration for Canada, Chile, Denmark, Germany, Hong Kong, Iceland, India, Israel, Malaysia, Norway, the Philippines, South Korea, Thailand, Iran, and United Kingdom. The results imply that the cointegrating relationship might have a structural change, which is consistent with the findings of the time-varying cointegration test. However, in the time-varying cointegration, we assume that the structural change in the cointegration relationship is smooth and gradual rather than abrupt. More importantly, Narayan and Sharma (2015) documented that the hypothesis test might be dependent on the data frequency, given that relatively high-frequency data provided additional information.

Bolivia

−1.0

−0.4

0.20 0.35 0.50

Austrlia

1960:Q1

1970:Q1

1980:Q1

1990:Q1

2000:Q1

1990:Q1

2010:Q1

1995:Q1

2000:Q1

2010:Q1

2014:Q1

Chile

−0.4

−0.1

0.20 0.35 0.50

Canada

2005:Q1

1981:Q1

1988:Q1

1995:Q1

2002:Q1

2009:Q1

2014:Q1

0.5 0.7 0.9 1977:Q1

1983:Q1

1990:Q1

1996:Q1

2000:Q1

2004:Q1

2002:Q1

2008:Q1

2014:Q1

2008:Q1

2012:Q1

France

0.30 0.45 0.60

Denmark

1996:Q1

1960:Q1

1970:Q1

1980:Q1

2000:Q1

2010:Q1

Hong Kong

0.2

−0.3

0.4

0.6

0.0 0.2

Germany

1990:Q1

1970:Q1

1979:Q1

1988:Q1

1997:Q1

2006:Q1

2015:Q1

0.4 −0.2 1997:Q1

2001:Q1

2005:Q1

1983:Q1

2009:Q1

2005:Q1

2013:Q1

1993:Q1

2003:Q1

2013:Q1

India

0.00 0.10 0.20

Iceland

1973:Q1

2007:Q1

2009:Q1

2013:Q1

Israel

−0.4

−0.6 −0.2

0.0

0.2

Islamic Republic of Iran

2011:Q1

1988:Q1

1993:Q1

1998:Q1

2003:Q1

2008:Q1

1980:Q1

1986:Q1

1991:Q1

Fig. 3. Time-varying saving retention coefficients (Quarterly data).

1996:Q1

2001:Q1

2006:Q1

2011:Q1

2015:Q1

W. Ma, H. Li / Economic Modelling 53 (2016) 166–178

177 Malaysia

0.40

−0.7

−0.4

0.50

−0.1

0.60

Japan

1955:Q1

1965:Q1

1973:Q1

1983:Q1

1993:Q1

2003:Q1

1991:Q1

1996:Q1

2001:Q1

2011:Q1

−0.2 −0.4

−0.6

−0.3

0.0

Paraguay

0.0

Norway

2006:Q1

1961:Q1

1969:Q1

1977:Q1

1985:Q1

1993:Q1

2001:Q1

2009:Q1

1994:Q1

1999:Q1

2004:Q1

2014:Q1

Philippines

0.0

0.0

0.2

0.2

0.4

0.4

0.6

Peru

2009:Q1

1979:Q1

1986:Q1

1993:Q1

2000:Q1

2007:Q1

1980:Q1

2014:Q1

1986:Q1

1991:Q1

2001:Q1

2006:Q1

2011:Q1

−0.6

−0.2

0.2

−0.2

0.2

Thailand

0.6

South Korea

1996:Q1

1960:Q1

1973:Q1

1983:Q1

1993:Q1

2003:Q1

2013:Q1

1993:Q1

1998:Q1

United Kingdom

2003:Q1

2008:Q1

2013:Q1

1.1 0.9 0.7

0.0

0.2

0.4

United States of America

1960:Q1

1970:Q1

1980:Q1

1990:Q1

2000:Q1

2010:Q1

1960:Q1

1970:Q1

1980:Q1

1990:Q1

2000:Q1

2010:Q1

Fig. 4. Time-varying saving retention coefficients (Quarterly data).

By virtue of the additional information, the statistical and economic relationship between variables might be changed. Phan et al. (2015b), Narayan et al. (2013) and Narayan et al. (2015) have shown that the profitability of commodity markets was dependent on the data frequency. Narayan and Sharma (2015) found that data frequency did matter relative to the impact of forward premium on the spot exchange rate. Phan et al. (2015a) showed that the effect of oil price change on stock returns was robust to the data frequency. Apart from the prevalent annual data, the quarterly data was used to investigate the relationship between saving and investment. Such studies include those by Chang and Smith (2014), Ketenci (2012). It follows that, one would like to see whether the saving–investment relationship is dependent on the data frequency. Given the data availability, different data samples for different economies are used: Australia (1960:Q1–2015:Q2), Bolivia (1990:Q1–2014:Q3), Canada (1981:Q1–2015:Q2), Chile (1996:Q1–2015:Q1), Denmark (1977:Q1– 2015:Q1), France (1960:Q1–2015:Q2), Germany (1970:Q1–2015:Q2), Hong Kong (1973:Q1–2014:Q3), Iceland (1977:Q1–2015:Q1), Iran (1988:Q1–2007:Q4), Israel (1980:Q1–2015:Q1), India (2005:Q1– 2014:Q3), Japan (1955:Q2–2014:Q3), Malaysia (1991:Q1–2014:Q3), Norway (1961:Q1–2015:Q1), Paraguay (1994:Q1–2014:Q4), Peru (1979:Q1–2015:Q1), the Philippines (1980:Q4–2014:Q3), South Korea (1960:Q1–2014:Q3), Thailand (1993:Q1–2014:Q3), the United Kingdom (1960:Q1–2015:Q2), and the United States (1960:Q1– 2015:Q2). Table 8 gives the results of cointegration tests for quarterly data. First, the fixed-coefficient test Q FC rejects the null hypothesis of cointegration for all cases at 1% level. Second, the time-varying coefficient test Q TVC rejects the null hypothesis for Canada, Chile, and

France at 1% level; for Denmark, Iceland, South Korea, and the United Kingdom at 5% level; and for Australia and Bolivia at 10% level. Therefore, we find more evidence for time-varying cointegration by using the quarterly data. One possible explanation for this contradiction is that the time-varying cointegration test might have serious size distortion in the small sample. Indeed, the longest data sample for annual data is from 1948 to 2013 for the Philippines. Figs. 3 and 4 display the time-varying saving-retention coefficients for the quarterly data. It should be noted that the saving-retention coefficients for developed economies: Australia, Canada, Denmark, Germany, France, Japan, South Korea, the United Kingdom, and the United States are relatively large in magnitude, while they are small for less developed economies: Bolivia, Chile, India, Iran, Malaysia, Paraguay, Peru, and Thailand. However, two exceptions are Hong Kong and the Philippines. The saving-retention coefficient for Hong Kong is small, whereas it is large for the Philippines. Therefore, while the results for time-varying cointegration tests change a lot, the magnitudes for the saving-retention coefficients do not have large variations. As was argued in Section 4, the low saving-retention coefficient could be explained by the theory of the long-run solvency constraint—the solvency-maintaining feedback mechanism might be weaker in less developed countries due to the distorted financial markets.

6. Concluding remarks This paper investigated the Feldstein–Horioka puzzle, which found high saving-investment correlation, accompanied by high degree of capital mobility. By using a time-varying cointegration

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approach, we found that the saving retention coefficients varied over time. In general, the saving retention coefficients were higher for more developed economies and lower for less developed economies, which was likewise consistent with the findings of Coakley et al. (1999). One caveat, however, should be borne in mind: this does not imply that capital is more mobile among less developed countries. While Feldstein and Horioka (1980) related the high saving-retention coefficient with low capital mobility, we interpreted it according to the long-run solvency constraint theory of Coakley et al. (1996). The long-run solvency constraint entails that the current account balances be stationary since debt cannot explode, thereby implying that saving and investment are cointegration with a unit coefficient irrespective of the degree of capital mobility. Moreover, as Coakley et al. (1999) pointed out, the solvency-maintaining feedback mechanism might be weaker in less developed countries since the risk-premium market mechanism might be less effective in eliminating their current account deficits due to the distorted interest rate. Therefore, care should be taken by policymakers since the weak saving–investment association for less developed countries might not be the signal for high capital mobility. References Alexakis, P., Apergis, N., 1994. The Feldstein–Horioka puzzle and exchange rate regimes: evidene from co-integration tests. J. Policy Model 16, 459–472. Apergis, N., Tsoumas, C., 2009. A survey of the Feldstein–Horioka puzzle: what has been done and where we stand. Res. Econ. 63, 64–76. Bai, Y., Zhang, J., 2010. Solving the Feldstein–Horioka puzzle with financial frictions. Econometrica 78, 603–632. Baxter, M., Crucini, M., 1993. Explaining saving–investment correlations. Am. Econ. Rev. 83, 416–436. Brock, W.A., Dechert, W.D., Scheinkman, J.A., LeBaron, B., 1996. A test for independence based on the correlation dimension. Econ. Rev. 15, 197–235. Chang, Y., Smith, R., 2014. Feldstein–Horioka puzzles. Eur. Econ. Rev. 72, 98–112. Chen, S., 2011. Current account deficits and sustainability: evidence from the OECD countries. Econ. Model. 28, 1455–1464. Chen, S., 2014. Smooth transition, non-linearity and current account sustainability: evidence from the European countries. Econ. Model. 38, 541–554. Chen, S., Shen, C., 2015. Revisiting the Feldstein–Horioka puzzle with regime switching: new evidence from European countries. Econ. Model. 49, 260–269. Chen, S., Xie, Z., 2015. Testing for current account sustainability under assumption of smooth break and nonlinearity. Int. Rev. Econ. Financ. 38, 142–156. Christopoulo, D., Leon-Ledesma, M., 2010. Current account sustainability in the U.S.: what did we really know about it?. J. Int. Money Financ. 29, 442–459. Chu, K., 2012. The Feldstein–Horioka puzzle and spurious ratio correlation. J. Int. Money Financ. 31, 292–309. Coakley, J., Hasan, F., Smith, R., 1999. Saving, investment, and capital mobility in LDCs. Rev. Int. Econ. 7, 632–640. Coakley, J., Kulasi, F., Smith, R., 1996. Current account solvency and the Feldstein–Horioka puzzle. Econ. J. 106, 620–627. Coakley, J., Kulasi, F., Smith, R., 1998. The Feldstein–Horioka puzzle and capital mobility: a review. Int. J. Financ. Econ. 3, 169–188. Coiteux, M., Olivier, S., 2000. The saving retention coefficient in the long run and in the short run: evidence from panel data. J. Int. Money Financ. 19, 535–548. De Vita, G., Abbott, A., 2002. Are saving and investment cointegrated? An ARDL bounds testing approach. Econ. Lett. 77, 293–299. Elliot, G., Rothenberg, T., Stock, J., 1996. Efficient tests for an autoregressive unit root. Econometrica 64, 813–836. Feldstein, M., Horioka, C., 1980. Domestic saving and international capital flows. Econ. J. 90, 314–329. Fouquau, J., Hurlin, C., Rabaud, I., 2008. The Feldstein–Horioka puzzle: a panel smooth transition regression approach. Econ. Model. 25, 284–299. Gregory, A., Hansen, B., 1996. Residual-based tests for cointegration in models with regime shifts. J. Econ. 70, 99–126. Hansen, B., 2001. The new econometrics of structural change: dating breaks in U.S. labor productivity. J. Econ. Perspect. 15, 117–128. Harberger, A., 1980. Vignettes on the world capital market. Am. Econ. Rev. 70, 331–337.

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