Trajectories to High Income: Growth Dynamics in Japan, the People’s Republic of China, and the Republic of Korea

We analyze and compare the patterns of economic growth and development in the Japan, the People’s Republic of China, and the Republic of Korea in the postwar period. The geographical proximity and cultural affinity between the three countries, as well as the key role of the development state in the economies, suggest that an analytical comparison would be a meaningful and valuable exercise. Furthermore, Japan and the Republic of Korea are two of the few economies that have jumped from middle income to high income in a short period and thus offer potentially valuable lessons for the PRC. We use Cobb–Douglas production functions to assess the long-run equilibrium relationships between per capita gross domestic product, capital, and labor by means of cointegrated vector autoregressive models. We show that such equilibrium relationships cannot be rejected for all three countries, while the evidence is stronger for the PRC and the Republic of Korea than for Japan. Our hypothesis tests show that the estimated Cobb–Douglas production functions display coefficients of capital and employment that sum up to 1 and broken linear trends that can be attributed to structural breaks and (changes in) total factor productivity growth. We observe a striking similarity between the experience in the Republic of Korea and the PRC, which gives some optimism that the PRC may be capable of graduating to high income, like the Republic of Korea.


TABLES
I.

INTRODUCTION
Since the introduction of market reforms in 1978, decades of world-topping economic growth have transformed the People's Republic of China (PRC) into the world's second-biggest economy and an upper-middle-income economy. The PRC's remarkable economic transformation, triggered by a systemic shift from a centrally planned economy to a more market-oriented economy, may indeed be the most significant development in the global economic landscape since the Second World War. However, since the global financial crisis of 2008-2009, the PRC's growth has slowed down visibly, although it continues to grow at a healthy pace. While the slowdown is partly due to a less benign external environment, it is largely due to structural factors, such as rebalancing toward domestic demand and consumption, rapid income convergence toward high-income countries, population aging, and tertiarization. The PRC is already an upper-middle-income country with an income level at which growth typically slows down (see, for example, Eichengreen, Park, and Shin 2012;2014). Therefore, to some extent, the slowdown is a necessary transition to a more balanced and sustainable growth paradigm, not least against the many imbalances that built up during the high-growth decades. 1 At the same time, there is no guarantee that the PRC's transition from middle income to high income will be as smooth and fast as its transition from low income to middle income. In fact, economic theory suggests that sustaining rapid growth will be difficult because marginal returns to capital eventually decline as an economy grows richer and acquires a larger stock of capital. The gains from shifting workers from low-productivity agriculture to higher-productivity manufacturing also eventually decline. Furthermore, as countries approach the global technology frontier, they must begin to develop new technology on their own instead of relying exclusively on importing advanced technology from abroad. Generally, the essence of economic growth shifts from input accumulationthat is, deploying more capital, labor, and other inputs-to total factor productivity growth-that is, using all those inputs more efficiently.
Empirically, a large number of middle-income countries have failed to graduate to high-income status in a reasonable period. This well-known stylized fact has given rise to the concept of the middleincome trap. Of 101 middle-income countries in 1960, only 13 proceeded to high-income status by 2008. 2 Will the PRC be able to follow in their footsteps? Of the 13 economies mentioned, only a few appear to be comparable with the PRC. Albert, Jude, and Rebillard (2015) point out that only Japan; the Republic of Korea; Taipei,China; and Israel followed a growth strategy similar to that of the PRC: export-led growth paired with strong investment. Of special interest and relevance to the PRC is the experience of Japan and the Republic of Korea, which are relatively large countries. Although both economies are nowhere near as large as the PRC, they are much larger than Singapore and Hong Kong, China and substantially larger than Taipei,China.
The central objective of our paper is to assess empirically the PRC's prospects for transcending the middle-income range by looking in the rearview mirror and comparing the PRC's past experiences with those of Japan and the Republic of Korea. Accordingly, we analyze and compare the economic growth and structural transformation trajectory of the PRC, the Republic of Korea, and Japan on the macroeconomic level by estimating Cobb-Douglas production functions in a multivariate 1 See Wagner (2017) and Maliszewski and Zhang (2015). cointegration framework. To identify our models, we use ex ante knowledge about historical events as well as the results of Bai and Perron's (2003) structural break tests of the time series.
The rest of this paper is organized as follows. Section II reviews the relevant literature and describes the economic growth experiences of the PRC, the Republic of Korea, and Japan. The section divides the experiences of these countries into different stages of economic development and structural transformation. Section III derives our theoretical hypotheses for the equilibrium relationships and analyzes and compares the growth experiences of the PRC, the Republic of Korea, and Japan more rigorously based on econometric analysis performing structural break tests and cointegration analysis. Section IV concludes the paper.

II. LITERATURE REVIEW
Will the PRC be able to close the gap to the high-income economies? Some convergence theories predict that this will be the case. Lee (2016) argues that the PRC's growth experience overall resembles the experience of Japan and the Republic of Korea. Figure 1 compares the status quo of the PRC, the Republic of Korea, and Japan in terms of catching up with the United States (US). 3 Every value expresses gross domestic product (GDP) per capita in relation to the US. 4 Hence, the difference between the countries' graphs and the y-axis can be interpreted as the remaining catching-up potential.
We can observe that all three countries are converging toward the US's GDP per capita level, yet the remaining catching-up potential is different for the three economies. Japan caught up quickly with the US and graduated to high-income status by the late 1960s. 5 After the nation-building phase in the Republic of Korea had ended in the early 1960s, it grew dynamically until the early 1980s and then entered several stabilization processes, which are continuing until today. High-income status was reached around the turn of the millennium. By about 2014, the Republic of Korea had caught up with Japan. Due to its specific circumstances, the fast-growth phase in the PRC only started in the late 1970s. The remaining catching-up potential for the PRC is still high. Based on Figure 1, we can argue that the developments in each country lead those of the 'following' countries by about 27-30 years. The arrows in Figure 1 show that the PRC's recent state of catching-up with the US was achieved by the Republic of Korea in the early 1980s and by Japan in the early 1950s.The clear interpretation of this figure is that the three countries started from different initial conditions and thus have also undergone different phases of growth. Roughly, we can characterize these phases as follows.
Looking at the drivers of the convergence observed in Figure 1, the related literature points toward growth theories and structural change. Lewis (1954) argues that structural change in the sense of reallocation of labor between sectors is an important driver of economic growth. In Japan, the service sector share in employment surpassed the agricultural share in 1956 (the industry sector surpassed the agriculture sector in 1962); the corresponding intersections happened in 1980 (1984) in the Republic of Korea andin 2011 (2014) in the PRC. Thus, structural change in Japan leads that in the Republic of Korea by 24 years and the Republic of Korea's structural change leads the PRC's by 31 years (Murach and Wagner 2017). Thus, the difference in the catching-up process seems to be mimicked by the respective process of structural change.  1952 1955 1958 1961 1964 1967 1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012 Republic of Korea PRC Japan Dalgaard and Strulik (2013) merge unified growth theory and neoclassical growth theory to explain income differences between countries. They argue that the beginning of the fertility decline is an important indicator for the takeoff of an economy. This takeoff can be defined as the transition from a phase of economic stagnation to a phase in which these countries grow persistently in terms of income per capita. To time the takeoff, two measures are proposed, the first of which is the year of fertility decline. The point of fertility decline can be defined as the point at which the population growth decreases. The second measure proposed by Dalgaard and Strulik (2013) is the year of industrialization, which measures the first year when the industry share in the total employment is greater than that of agriculture. For Japan, the Republic of Korea, and the PRC, the initial years of fertility decline were 1950, 1960, and 1970(as reported by Reher 2004. The year of industrialization corresponds to the years in brackets in the previous paragraph. Table 1 summarizes our findings. Year of fertility decline (see Reher 2004Reher ) 1950Reher 1960Reher 1970 Structural change (see Murach and Wagner 2017) 1956(1962) 1980(1984 2011 (2014) Year of industrialization (see Dalgaard andStrulik 2013) 1962 1984 2014 Dalgaard and Strulik (2013) argue that neoclassical growth theory is valid especially in the post-takeoff phase. Neoclassical growth theory considers, in particular, the effects of input factors on economic growth. In this modeling framework, the Solow (1956) model explains growth as a function of capital, labor, and technological progress. The seminal work by Mankiw, Romer, and Weil (1992) empirically proves the general explanatory power of such models. They show in a first step that the standard Solow model indicates a share of 0.60 of physical capital in income, which, explicitly including a measure of human capital, decreases to 0.31. 6 Applying a different methodology, Barossi-Filho, Silva, and Diniz (2005) find support for a capital share of one-third. By contrast, Hamilton and Monteagudo (1998) argue that physical capital may indeed have a greater impact on growth than in the original analysis by Mankiw, Romer, and Weil (1992). They assert that capital may also be able to include technological improvements. Besides the impact of physical capital, they find that population growth and the initial level of output are important in the analysis. Other works continue to extend this fundamental framework in different directions, promoting a differentiated view on the sources of economic growth, for example, an open-economy model or the effects of health capital (see, for example, Barro, Mankiw, and Sala-i-Martin 1995;Knowles and Owen 1995). This augmented model type is also applied to the PRC in recent research to evaluate the growth prospects of the economy (see Barro 2016, Lee 2016. Besides cross-country comparisons like that undertaken by Mankiw, Romer, and Weil (1992), some authors focus solely on the growth dynamics in one or two countries. Durlauf, Kourtellos, and Minkin (2001) recommend considering local Solow models, as country-specific heterogeneity is likely 6 See Mankiw, Romer, and Weil (1992 , Tables I and II). to exist. This shows that examining the dynamics of individual countries can be a helpful exercise in analyzing the common drivers of economic growth. Chow (1993Chow ( , 2015 analyzes the growth dynamics for the PRC. Chow and Lin (2002) compare the developments in the PRC with those in Taipei,China, arguing that the initial conditions were different and hence the analysis of the growth dynamics is an interesting exercise. Obviously, the initial conditions in which one economy is nested are important and have implications for its future growth prospects. Chow (1993) estimates production functions for the economy of the PRC and its sectors. For this purpose, he constructs a measure of capital formation. He analyzes the effects of important political campaigns, like the Great Leap Forward (1958-1962) and the Cultural Revolution (1966-1976. Based on a figure that plots log (national income/labor) against log (capital/labor) for the period 1952-1985, he argues in favor of the exclusion of the years 1958-1969 because they are 'abnormal because of the great leap upheavals of the Great Leap Forward movement and the Cultural Revolution'. 7 For the aggregate economy, capital coefficients of about 0.60 are estimated. A further finding of his paper is the absence of technological progress between 1952 and 1980. Chow explains this finding by pointing out that the PRC concentrated on central planning and investments in heavy industries. Thus, incentives for private enterprises were scarce during this period. He argues further that technological progress is an important feature of market economies but is unlikely to be visible in an economy in which private initiatives and the adoption of new technologies from abroad are not present. Cheremukhin et al. (2015) support this view, as they find in their review of the related literature that total factor productivity (TFP) growth accelerated moderately between 1978 and 1985. Of the industrial TFP growth in the 1980s, 87% can be explained by improved incentives, intensified product market competition, and improved factor allocation (see also Li 1997). Chow and Lin (2002) perform a comparative analysis of the PRC and Taipei,China. For the PRC, the sample is now 1952-1998. They estimate a Cobb-Douglas production function with a trend beginning with t = 1 in 1979. The coefficient of ln (K/L) and the time trend t are estimated with 0.64 and 0.0262 remaining unchanged over the sample period. In comparison with Taipei,China, Chow and Lin comment on the relatively small exponent of labor in the PRC. This is explained by the relative abundance of labor in the PRC. Chow and Lin argue that, over time, labor will be less abundant as the economy grows and the ratio of capital to labor increases. They add that, in their sample, the abundance of labor has persisted, which is explained by still-poor regions in Western PRC with lower wages. 8 In a third approach, Chow (2015) investigates the Cobb-Douglas production function for the PRC between 1952 and 2012. For this sample, the coefficient of ln (K/L) is estimated as 0.59 and the trend is estimated as 0.298. Chow basically reproduces the arguments of Chow and Lin (2002) to support his results. He additionally argues that Mankiw, Romer, and Weil (1992) estimate a coefficient of 0.6 with data for many developing countries. The analyses by Chow will be our roadmap for our estimations in section III. 7 Figure 2 in Section III.B, which plots log (income/population) against log (capital/labor) displays the same pattern of nonlinearity of the years 1958-1969 (see also Chow 1993, Figure I, p. 821). 8 It is noteworthy that the comparison between Taipei,China and the PRC is based on different estimations. For Taipei,China, human capital is considered, which reduces the coefficient of various capital stock measures in relation to labor to about one-third. This is consistent with the results obtained by Mankiw, Romer, and Weil (1992).
Finally, we would like to comment briefly on some similar inner dynamics and characteristics of the three countries that we investigate to support the similarity of the growth dynamics. Morck and Yeung (2017) review the financial and economic developments in East Asia, focusing on Japan, the Republic of Korea, and the PRC. As common characteristics of the three countries, they identify, among others, the following. i) A weakening in traditional institutions is observed before the phases of rapid economic development. 9 Thus, a serious obstacle to growth-generating reforms was reduced.
ii) Literacy in the three countries was high early on, which was helpful for building up human capital later. iii) Moreover, relative openness due to the export-and investment-led growth model brought about early international competition and supported the state-directed process of foreign technology adaption. iv) Product diversification was reached via business groups, like the zaibatsu in Japan, chaebols in the Republic of Korea, and state control over huge sectors of the economy in the PRC. v) Lastly, Japan's zaibatsu, the Republic of Korea's chaebols, and the PRC's state machinery were able to create a 'Big Push'.
These similar inner characteristics of the three countries make it an interesting exercise to compare whether these similarities have manifested themselves in similar results of our estimations of their respective production functions.

A. Developing Theoretical Hypotheses
As our analysis is motivated by the works of Chow (1993Chow ( , 2015, we orientate ourselves toward his procedure. Chow (2015) suggests a Solow (1956)-type model of economic growth. In this framework, one equation explains the aggregate output through capital and labor inputs in the form of a Cobb-Douglas production function: The exponents (1 − ) and measure the rate of change of output vis-à-vis changes in capital (stock) and labor (employed persons). measures the change in output per unit over time even if the inputs of capital and labor are not changed. This may be the consequence of institutional or technological change due to economic reform policies. For = 0, this change is not present. If = 0.01, this can be interpreted as TFP growth of 1% per year. can be interpreted as the initial level of technology in the economy (see Chow 2015).
As we are especially interested in the evolution of the per capita GDP, we have to include the following changes. We would like to have on the left-hand side of equation (1), where is the economy's total population. Thus, we divide (1) by on both sides. However, on the right-hand side, we would rather like to express by different variables to avoid a direct source of collinearity. 9 This is not necessarily identical to the definition of the fast-growth phases earlier in this section. Hence, we express by : = • . With ≥ 1. This is the inverse of the employment rate.

This gives
Taking natural logarithms, we obtain Rearranging terms leaves us with a linear equation with testable hypothesis for the coefficients, where we add as the error term. Specifically, we will estimate and test

B. Data Description and Historical Events
We use Penn World Tables (PWT) of the version 9.0 for our estimations. For the PRC, the Republic of Korea, and Japan we collect data for GDP, capital, employment, and population. Data are available from 1952 to 2014 for the PRC, from 1953 to 2014 for the Republic of Korea, and from 1950 to 2014 for Japan. Chow (2015) constructs capital data for the PRC from publications of the China Statistical Yearbook. However, Holz (2006) discusses an earlier version of Chow's dataset and lists a number of shortcomings of Chow's measures. In a recent publication, he proposes some newly constructed capital measures for the PRC (see Holz and Yue 2017). We do not try to construct capital measures for the PRC, the Republic of Korea, and Japan ourselves but instead rely on the time series provided by the PWT (see Feenstra, Inklaar, and Timmer 2015). This naturally causes difficulties, as research shows that conclusions drawn under one version of the PWT may not hold under another version (see Ponomareva and Katayama 2010).
Figure 2 displays prima facie evidence of the relationships between capital intensity (on the x-axis) and per capita GDP (on the y-axis) both in logarithms in the PRC, the Republic of Korea, and Japan. The circles refer to data from the PRC, the diamonds refer to the Republic of Korea, and the squares in light grey represent data for Japan.
The relationships for the PRC and the Republic of Korea especially appear to be fairly linear and very similar. Japan seems to present about the same slope as the Republic of Korea and the PRC until about 1973. From a relative perspective, the PRC seems, for an extended period, to follow a path that is very close to the previous experience of the Republic of Korea. Japan seems to be a different case, presenting much less linearity and a different average slope. At the beginning of the PRC's development path (around the years 1958-1969), we observe the same irregularities as Chow (1993). That is why Chow (2015) excludes these data from his estimations. A more detailed view of the individual country time series is presented in Figures 3-5. The variables Y_P_CHN, K_EMP_CHN, and G_CHN are the logarithms of the PRC's per capita GDP, the logarithms of the capital-employment ratio, and the logarithms of the inverse of the employment rate in the PRC. For each variable, we present the level values (continuous lines; left axis) and the first differences (dashed lines; right axis). In the following, we refer to the respective country with the variable endings CHN for the PRC, KOR for the Republic of Korea, and JP for Japan. Figure 3 shows that the PRC's per capita growth was comparably volatile before 1979. The same is true for the growth in the capital-employment ratio, which became increasingly strong over the sample period, with the exception of a strong slump around the end of the 1980s. 11 The inverse of the employment rate decreased over the whole sample period, indicating that the overall employment in the population increased.

11
This is also in line with the assessment by Chow and Lin (2002) in section II.  1954 1956 1958 1960 1962 1964 1966 1968 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998  1954 1956 1958 1960 1962 1964 1966 1968 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 Figure 4 displays the developments in the Republic of Korea. The per capita GDP growth rates peaked around 1980 and then decreased. Important recessions happened in 1980 and during the Asian Crisis. Altogether, the per capita GDP growth rates display a humped-shaped pattern. The capitalemployment ratio rose strongly in the 1960s (the fast-growth phase), and the growth rates were very high until the 1980s, when they experienced a strong cutback and decreased further throughout the Asian Crisis. 12 The inverse of the employment rate shows the same behavior as in the PRC. 12 For separate time series of capital and employment for Japan, the PRC, and the Republic of Korea, we refer the interested reader to Figure A1 in the Appendix.  1953 1956 1959 1962 1965 1968 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 1953 1955 1957 1959 1961 1963 1965 1967 1969 1971 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 4 1953195619591962196519681971197419771980198319861989199219951998200120072010G_KOR d_G_KOR 2013 In Japan (see Figure 5), we observe a more or less stable decrease in the per capita growth rates over the whole sample period. Higher per capita growth rates corresponded to fast increases in capital intensity until the oil crisis in 1973. Afterwards, the capital-employment ratio decreased, although we observe a short-lived boom during the second half of the 1980s. The inverse of the employment rate rose until the oil crisis and then seems to have followed the Japanese business cycle. Figure A1 in the Appendix shows the separate time series for capital and employment for the three countries.  1950 1953 1956 1959 1962 1965 1968 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 1950 1953 1956 1959 1962 1965 1968 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 9 1950 1953 1956 1959 1962 1965 1968 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 2004 2007 2010 2013 G_JP d_G_JP

C. Univariate Properties of the Data
For the unit root tests, we analyze the period from 1956 to 2014. In the previous section, we saw that the growth rates decreased or increased over time. We thus assume that the time series under consideration present deterministic trends and hence test especially for unit roots of the most general form, allowing for a constant and a deterministic trend. According to the unit root tests, the per capita GDP can be assumed to be integrated of order one (I(1)) for all three countries. The same is valid for the employment time series. The tests lead to less convincing results for the capital and capitalemployment ratio series. We conclude that the levels of the time series are at least integrated of order one (I(1)). The capital and capital-employment ratio time series may even be I(2). 13 The I(2) properties of the capital-employment ratio time series could require an I(2) analysis. However, Juselius (2006) points out that the behavior of an I(2) trend can be mimicked with an I(1) stochastic trend around a broken linear deterministic trend. Thus, it is possible to avoid an I(2) analysis by including an appropriate number of deterministic (linear, broken linear, or quadratic) trends in the data. Our estimations will rely on the variables in levels. This is the procedure that we choose for this section. To obtain a better understanding of where deterministic components could be fitted into our models, we analyze the time series for potential structural breaks in the next section.

D. Structural Break Tests
From a visual inspection of the time series growth rates, we can assume the occurrence of some structural breaks in the time series. These could also contribute to the results of the unit root tests. To obtain further information about the occurrence of structural breaks in the data, we apply the Bai and Perron (2003) structural break tests, which allow us to obtain a number of interesting details about whether, when, and in which way structural breaks are present in the data. We assume that the time series values evolve in the following way: If is equal to 1, this process characterizes a random walk plus drift, which can be assumed to be the data-generating process of many macroeconomic time series. The test identifies two breaks. The results for the three countries are displayed in Table A1.
In the PRC, structural breaks are first present around the high tide of the Cultural Revolution (1966)(1967)(1968). The second period during which breaks are found is the end of the Cultural Revolution in 1976 and the beginning of the first reform period (1979). Finally, the breaks in the early 1990s could be associated with Deng Xiaoping's Southern Tour (in 1992).
For the Republic of Korea, we observe structural breaks during the high-growth phase from the mid-1960s to the mid-1970s. The beginning of the stabilization phase in 1980 appears to have had permanent effects on employment and output. The final period of structural breaks is related to the Asian Crisis.
For Japan, a relatively clear point to take away from the tests is that we observe structural breaks in the early 1970s. These are most likely related to the end of the fast-growth phase in 1972 and the beginning of the oil shock phase in 1973. The second break seems to occur toward the end of the 13 The unit root tests are not displayed but are available from the authors on request. bubble economy phase and at the beginning of the lost decade in the late 1980s. The employed persons' time series indicates instability during the Asian Crisis in 1997 but could also point toward the lost decade. The tests provide some evidence that the Japanese economy began to stagnate from about the late 1990s onward, as the coefficient of is well below 1.

E. Econometric Framework
To determine whether the respective countries were following comparable growth paths toward high income, we use the concept of cointegration. Cointegration appears to be especially appropriate for our research question, as the notion of cointegration states that, between two or more nonstationary time series, a linear combination exists that generates residuals that are stationary (see Engle and Granger 1987). The error correction representation of the cointegrated vector autoregressive (CVAR) model in the multivariate case is is a vector that contains the variables included in the model. is a vector of the deterministic components of the model. The Γ matrices contain the short-run information of the model, while Π contains the information about long-run relationships (which we are especially interested in) and can be rewritten as a vector product of α•β'. Here β' comprises the long-run information, while α contains the information on how and how quickly deviations from the long-run relations are corrected. Cointegration emerges when two or several nonstationary time series are driven by the same persistent shocks (Juselius 2006). In our case, we assume that the shocks driving our cointegrating relationships derive from economic policy measures implemented in the corresponding reform periods. Long-run relations can then be interpreted as economic steady-state relations. Extraordinary events can lead to outliers violating the normality assumption, as they lead to excess skewness and kurtosis (see Juselius 2018). Some of these problems can be resolved by including intervention dummies to account for significant political or institutional events. Less feasible seems to be the possibility to split the sample into more homogeneous periods, as only yearly data for our variables are available. A subsample analysis would hence suffer from problems associated with small samples.
Even if the residuals of the VAR pass the misspecification tests sufficiently well, this does not rule out the possibility that the model suffers from parameter nonconstancy. For this reason, Juselius (2006) provides a description of several tests to assess the parameter constancy of the CVAR model. In the next section, we will discuss three selected tests for each model that we estimate to identify any remaining signs of parameter instability.
First, we are especially interested in the stability of the long-run relationships, that is, the stability of . can be seen as the average of the related coefficients over the sample period. It could be assumed that structural breaks induced by reforms affected not only the TFP growth but also the output elasticity of inputs. The optimal capital intensity could hence have changed (see Stijepic and Wagner 2011). Theoretically this is also proved by the work of Acemoglu (2003). To test this, we perform a test of the 'known beta'. This test checks for the consistency of , that is, the stability of the long-run relations. The basic idea is that the model is estimated for a subsample period 1 to , with < , and then the recursive sample is extended until is reached (see Juselius 2006).
Second, we apply recursive calculated prediction tests for the long-run relation. If the test value is above 1, the model is not able to predict the observation for this period within the 95% confidence bands. This can be a helpful test to diagnose systematic predictive failure of the model (Juselius 2006).
Third, we can test the stability of the estimated coefficients over a sample period. This can give us additional insights into the stability of the long-run relations (Juselius 2006).

F. Estimation
The variable set that we use is relatively small. It is difficult to obtain data in sufficient quality that reach back far enough. Multivariate cointegration analysis allows for multiple equilibrium relationships. Hence, with n variables in the system, up to n-1 cointegrating relations are possible. (Over-) identification of these relationships requires a sufficient amount of theoretical assumptions on what the concrete cointegrating relationships are. With a rising number of variables, it becomes more and more difficult to identify the 'true' structure of the data. In any case, cointegrating relationships that have already been identified should remain stable when additional variables are added. Hence, what we detect in the following should remain present in a richer information environment.
As mentioned in the previous section, we assume a simple Cobb-Douglas production function as the starting point of our analysis. Our vectors for the PRC, the Republic of Korea, and Japan are for each country j. As mentioned earlier _ _ stands for the respective countries per capita GDP, _ _ is the capital-employment ratio, _ refers to the inverse of the employment rate. All variables are in logarithms. _ captures deterministic components like dummy variables and (broken) linear trends.
We start by specifying the model for the PRC. To test for cointegration, we first have to obtain a well-specified VAR model of the data. As TFP is usually captured by the residuals of the equation, we take into consideration the need to capture technological progress and other variables that are not accounted for by the introduction of deterministic trends. Juselius (2006) generally proposes two approaches to identifying cointegrating relationships: the general-to-specific and the specific-togeneral approaches. As we face a relative lack of restrictions and theories, we find it appropriate to start with a narrow model like that motivated by Chow (2015). Imposing restrictions on the model is crucial to decide how well the data fit our theoretical assumptions. We hence rearrange our baseline theoretical model to obtain a representation that allows us to impose overidentifying restrictions. Chow (2015) estimates several specifications of his production function. The most specific is one with a fixed capital-labor ratio ( / ), which corresponds to capital intensity.

Lag Length Selection and Diagnostic Testing of the Unrestricted Vector Autoregressive
As we have yearly data, a lag length of order 1 appears to be appropriate, as it not very likely that information further back than 1 year is included in the investment and employment decisions. Lag reduction tests support this assumption. A lag length of 1 is superior to lag lengths of 2 or more. As the test statistics for the CVAR rely on the assumption of Gaussian residuals, deviation from the normality assumptions may distort the results. We hence must establish the necessary residual properties before we test for possible long-run relationships. From sections III.B to III.D, we already have a certain idea about possible outliers, trends, or (structural) breakpoints in the data. For the PRC, we choose the sample period of 1969-2014. This excludes the 'abnormal' years of the Cultural Revolution (see Figure  2 in section II). The Cultural Revolution was officially announced to be complete in 1969. We thus only miss out four values included by Chow (2015), whose sample is 1952-2012, omitting (1958-1969). 14 From our theoretical hypotheses in (7), we assume that we will have to include a deterministic trend in the model that allows for economic growth even if the input factors remain constant. We will, however, test the validity of this assumption. Chow (2015) argues that such a trend would catch increases in TFP. Including a deterministic trend in the CVAR model is also the most general specification that one can choose. Hence, we include a deterministic trend over the whole sample period, additionally allowing for a break in this trend that mirrors a structural break induced by reforms or political events. Chow (1993) finds no evidence of TFP prior to 1980 and thus includes a broken linear trend beginning with t = 1 in 1979 (Chow 2015). With our data, a break in the deterministic trend appears in 1976 (often seen as the de facto end of the Cultural Revolution) such that t = 1 in 1977 seems to be more in line with the data. We additionally include intervention dummies for 1976, 1989, 1990, and 1991. We also include a shift dummy for 1990. With this specification, we obtain a relatively well-specified VAR model, as can be seen from the residual diagnostic tests in Table 2 as there are no signs of autocorrelation, and heteroscedasticity. Skewness and kurtosis are also in line with the assumption of normally distributed residuals

Rank Determination and Testing Restrictions on the Cointegrated Vector Autoregression
A likelihood-ratio (LR) test of long-run exclusion indicates that is not part of the equilibrium relationship and hence we exclude it from the information set. Any external influences that are not accounted for by the variables in the system are caught by either the deterministic components or the residuals. The trace tests propose one cointegrating relationship, which we would also expect from the theory. We thus restrict the rank to be equal to 1. This gives the following just-identified model (see Table 3). At this stage of our identification of the long-run relations, we test whether the data is in line with our theoretical hypothesis, that is, the long-run relation between per capita GDP and the capital-employment ratio should be positive, and deterministic trends which account for technological change should also have a positive relation with per capita GDP growth. Table 3 displays the stationary relationship. The first line gives the stationary long-run relationship. Hence, to see how the capitalemployment ratio and the deterministic trends are connected with per capita GDP in the PRC, we have to invert the signs of the former. All variables then would have the expected (positive) signs. Besides the long-run relation in the first line, Table 3 (as well as the following tables) also presents the short-run adjustment coefficients in the second row. We refrain from interpreting these in the following, but nonetheless present them for the sake of completeness. All the variables have the expected sign, and the GDP per capita and the capital-employment ratio commove in a positive long-run relationship. TFP growth, proxied by the broken linear trend, has a positive effect on output and a significant coefficient of 0.033. In the next step, we relax the implicitly imposed restriction that the coefficients of capital and employment sum up to 1 by including capital and employment separately. By including the same dummy variables, we obtain a rather well-specified model without autocorrelation and mild skewness. The trace test indicates one cointegrating relationship. We continue to assume that the rank of Π is equal to 1, which means that there is one single equilibrium relationship among the variables. Again, the trend is insignificant, as displayed in Table 3. We thus exclude the deterministic trend by imposing a 0 on the corresponding coefficient. Additionally, we explicitly test the coefficients of capital and labor to be of the same size. In this way, we impose more restrictions on the data and may be able to obtain overidentified cointegrating relationships. This overidentified cointegrating relation is displayed in Table 4. The overidentifying restrictions are accepted with a p-value of 0.135 and a (2) of 4.010. 15 This shows that the restrictions we have imposed on the data are not rejected hence the PRC's growth path in our sample can be represented by a long-run equilibrium relationship of the form: Our empirical results show that the coefficient of capital intensity, given by the difference between capital stock and employed persons in the PRC has a coefficient of 0.42. Additionally, the data are in line with a positive deterministic trend which could be interpreted as 2.2% annual TFP growth. Figure 6 displays the corresponding cointegrating relationships. The residuals of the concentrated model ( Figure 6) show that the relationship is stable.

Tests of Constancy
The test of beta constancy is displayed in Figure 7. As we can see from Table A1, this is a very challenging test, as 1992 (the beginning of the subsample for the test in Figure 7) is actually an important breakpoint in the PRC data. The forward recursive calculated test shows that the model performs fairly well. After the assumed breakpoint in 1992 (Deng Xiaoping's Southern Tour of 1992), there is some instability, but the test statistic approaches its critical value of 1 relatively quickly. The Asian Crisis of 1997 and the Global Financial Crisis of 2007-2009 seem to have introduced some instability, but altogether we can assume that the coefficients remain stable after the Asian Crisis. 15 Juselius (2006) suggests applying the small-sample Bartlett correction in moderately sized samples of 50-70 observations, which applies in our case (45 observations). The noncorrected values are p = 0.063 and a chi-square (2) of 5.537 (correction factor: 1.381).

Figure 7: Test of Beta Equal to the 'Known Beta', People's Republic of China
Source: Authors' representation.
The one-step prediction tests in Figure 8 show that major prediction errors can again be related to Deng Xiaoping's Southern Tour of 1992, a major reform in 1994 (see Cheremukhin et al. 2015), and the Asian and the Global Financial Crisis.  As can be seen in Figure 9, the coefficients of capital and labor remain relatively stable. We cannot deny that there seems to be a visible shift in all the coefficients roughly after the end of the Asian Crisis in 1998, as the coefficient of capital intensity is somewhat higher for the later part of the sample. There are two explanations for this fact. Following the arguments of Chow (2015), a higher coefficient for capital could be explained by the still relative abundance of labor in the PRC. Another explanation could be that capital was actually invested more efficiently over time and hence received a larger share of production. TFP growth also seems to have profited from the PRC's World Trade Organization (WTO) entry in 2001. However, this is somewhat speculative, as all three coefficients only show minor fluctuations. We find that the long-run evolution of per capita GDP, capital stock, and employment in the PRC can be reconciled with Cobb-Douglas production functions, which is the first notable result. Coefficients of capital stock and labor that sum up to 1 are not rejected. We find evidence of a (broken) linear trend in the cointegrating relations that can point to changes in TFP growth. The structure of the data is reconcilable with the hypothesis that TFP growth in the PRC started around 1977.
For the PRC, our model in (11) is able to reproduce the main features of Chow (2015). We estimate a coefficient of 0.41 for the capital share. This coefficient is smaller than Chow's estimates but relatively close. Chow (1993) also estimates production functions for nonagriculture sectors. The coefficients are highest for the industry sector but much smaller for service-related sectors, like commerce and transportation. 16 Given that our sample includes 2 more years in which the service sector share in employment in the PRC has increased strongly, this result seems to be acceptable. 17 However, the choice of sample has a strong impact on the coefficient size, as the inclusion of some of the abnormal years leads directly to a lower coefficient for the capital share. Our coefficient for TFP growth of 0.022 is similar in size to the estimates in Chow (2015), which range between 0.025 and 0.030. 18 In addition, our use of Y/N instead of Y or Y/L in our estimations may lead to lower estimates. As pointed out by Chow (2015), a higher coefficient for capital points toward relative abundance of labor relative to capital. We could hence also argue that, although still considerable in an international comparison, the reservoir of labor is slowly dropping relative to earlier periods.
To obtain (11), we make extensive use of the ex ante information of section III.B and section III.D. We exclude most of the abnormal years of the 1950s and 1960s, and our sample thus starts in 1969. This year appears to signal a structural break (see Table A1) that could be an indication of the economic takeoff, as the point of fertility decline in the PRC is reported as 1970. TFP growth from 1977 onward could also be justified with the results from Table A1, which indicates a structural break between the years 1976 and 1979. The one-step prediction test in Figure 8 shows that the breakpoint in 1991/1992 (possibly related to the Southern Tour) is (only) of a transitory nature. We hence feel that we have convincingly modeled the major features of the PRC economy. The fact that the cointegration relation for the concentrated model in Figure 6 increases between 2001 and 2007 could be interpreted as the positive effect of the PRC's WTO entry in 2001. However, this does not become a break in TFP, because the financial crisis halted it. We are a little disappointed with the estimated alpha coefficients of the long-run relationships. Table 4 indicates that capital and employment show errorcorrecting behavior to deviations from the long-run relationship, but the per capita GDP appears to be weakly exogenous.

Lag Length Selection and Diagnostic Testing on the Unrestricted Vector Autoregression
For the Republic of Korea model, the lag reduction tests point to a lag length of 1. There is some controversy about the sources of growth in the Republic of Korea. For instance, Young (1995) argues that most of the dynamic growth in the so-called Four Asian Tigers can be explained by factor accumulation and labor reallocation between sectors. Accounting for these explanatory variables would lead to much lower estimates of the TFP growth. In a more recent analysis by Jeong (2017), the results are similar, as it is explained that human capital was the main driver of growth during the 1960s and capital deepening in the 1970s. Productivity growth was then the main driver of growth in the 1980s, 1990s, and 2000s. This would justify two possible specifications of deterministic components. Either we could include a deterministic trend over the whole sample period, or we could include such a trend only from 1980 onward with the initiation of the stabilizing stage in the Republic of Korea.
We start with the most general setting concerning deterministic components in our model. We allow the data to be trend stationary and to have nonzero intercepts to see whether trends persist or disappear in the cointegrating relations. We first analyze the specific relation between the GDP per capita and the capital-employment ratio. In this model, we decide to use four dummy variables for the years 1968, 1969, 1980, and 1998. The diagnostic tests are presented in Table 5. The model can be regarded as being well specified.

Rank Determination and Testing Restrictions on the Cointegration Vector Autoregression
The trace test indicates one cointegrating relationship, as displayed in Table 6. Normalizing on the per capita GDP, we obtain the following just-identified model (see Table 7). Assuming that TFP growth set in around 1980 supports the assumption that the forces that drove the Republic of Korea's growth actually changed during this period. Introducing a broken linear trend in 1980 actually renders the TFP growth over the whole period (close) to 0 and more importantly insignificant (while still having the correct sign).
In the next step, we loosen our restrictions by allowing capital and employment to move independently. We assume that TFP growth only set in significantly around 1980. With the same dummy variables as in the previous modeling cycle, we obtain a fairly well-specified model of the data. Table 8 displays the diagnostic test of the residuals of the VAR(1) with three variables. The overidentifying restrictions are accepted with a p-value of 0.324 and a (2) of 0.324.

19
The long-run equilibrium relationship for the Republic of Korea is thus: Figure 10 displays the corresponding cointegration graph. The residuals of the concentrated model appear to be fairly stationary. A visual inspection cannot rule out the possibility that some TFP growth was also present prior to the early 1980s.

Tests of Constancy
The test of beta constancy in Figure 11 shows that there was some instability in the long-run relations at the beginning of the stabilization stage in the 1980s. However, the test statistics remain under the critical value of 1 and hence the beta coefficients were stable over this subsample period.
The one-step prediction test (see Figure12) for the concentrated model performs quite well. At the beginning of the stabilizing stage in the early 1980s, it shows a few noticeable prediction errors. The Asian Crisis in 1997 generated a single and very high prediction error. For the remaining years, the model is able to predict the developments very well.   0 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 The coefficients displayed in Figure 13 of the long-run relations in the case of the Republic of Korea remained relatively stable over the subsample period. There was some instability from around 1987 until 1990. For Japan, the lag reduction tests point towards a lag order of 1. Additionally to the deterministic trend, we include one breakpoint (t = 1 in 1973) to account for changes in the light of the oil crisis. Additionally, we include dummies for 1973 and 1997 (shift dummies) as well as an intervention dummy for 2009. We thus obtain a fairly well-specified model, as displayed in Table 9.

Rank Determination and Testing Restrictions on the Cointegration Vector Autoregression
The rank test indicates one or two cointegrating relationships (see Table 10). Additionally, this time, the test of long-run exclusion does not suggest that is not part of the cointegrating relationships. We assume a rank of 1. This model gives the long-run relationship displayed in Table 11. The capital-employment coefficient is comparably small. The trend points to overall TFP growth over the whole sample. The break in 1973 sets off most of it. Afterward, TFP growth would only be as high as 0.08 on average. We also note that is significant and very close to the theoretical value of 1 that we derived in section III.A.
In the model including capital and employment separately, the inclusion of is not rejected as well. Here, the trace test indicates two cointegrating relationships, and we try to impose the theoretical relation developed in (7) on the second relation. This gives the following overidentified model (see Table 12). These restrictions are accepted with a p-value of 0.493 and a CHISQR (1) of 0.493. The second cointegrating relationship is our estimate for the production function. 20 For the sake of completeness, the first cointegration graph is displayed in Figure A2 in the Appendix.
ADB Economics Working Paper Series No. 622

Figure 14: Second Cointegrating Relation for Japan
Source: Authors' calculations.

Tests of Constancy
The test of beta constancy indicates extended periods of instability of the beta coefficients from the mid-1980s onward. Toward the Asian Crisis, instability decreased considerably but remained significant. The revitalization phase fits with the overall stable beta coefficients (see Figure 15). The one-step prediction tests in Figure 16 give the impression that the model fails to make trustworthy predictions for the sample period. While the two largest prediction errors are related to the Asian Crisis and the Global Financial Crisis, the model also has increasing difficulties in predicting the developments during the bubble economy phase of [1985][1986][1987][1988][1989][1990] and the beginning of the lost decade.
The coefficients displayed in Figure 17 of the long-run relations in the case of Japan remained very unstable over the phase of the bubble economy in the 1980s. They give a clear indication that the Japanese economy was not on its equilibrium path during this period. 21

IV. CONCLUSION
Sustained rapid growth has transformed the PRC from a low-income economy into a middle-income economy in a remarkably short period of time. The next challenge for the PRC is to graduate from middle income to high income. How well and smoothly the PRC tackles this difficult challenge has sizable ramifications not only for the PRC but, given the PRC's large and growing footprint on the global economy, for the rest of the world.
In this paper, we sought to obtain some clues about the future dynamics of the PRC's economic growth by looking at Japan's, the Republic of Korea's, and the PRC's past patterns of growth. Accordingly, we analyzed and compared the growth experiences of the three countries, which share many similarities. Section II pointed out these similarities. Perhaps the most significant common denominator was capable bureaucracy and a developmental state that prioritized economic growth (favoring export-and investment-led growth) and played the role of a catalyst in the rapid growth and structural transformation of the three countries. As such, structural policies and reform played a major role.
Our analysis and comparison of the patterns of economic growth and structural breaks in Japan, the Republic of Korea, and the PRC yielded a number of interesting findings. The descriptive analysis of section II and the more in-depth econometric analysis of section III both support the view that many features of the PRC's economic development mirror the earlier experiences of Japan and the Republic of Korea. The GDP growth and capital-labor ratio moved together in a positive long-run relationship in all countries, which can be brought into line with the hypotheses derived from section III.A. An interesting finding is hence that the export-and investment-led growth models that all three countries followed for an extensive period are reconcilable with Cobb-Douglas production functions with broken linear trends.
However, there is one interesting and significant difference between the three countries in their economic growth trajectory. Specifically, our analysis indicates that the PRC experienced growth based on TFP gains at a much earlier stage in its development path than the Republic of Korea. If the PRC shifted toward TFP growth at a similar stage to the Republic of Korea, the shift would have occurred around 2011. In fact, the shift in the PRC began as early as the late 1970s. In comparison with Japan, there are no visible signs that TFP growth in the PRC slowed down significantly in our sample period.
The broader question that we sought to address through our comparative analysis of the growth experiences of the PRC, Japan, and the Republic of Korea is whether the PRC can replicate especially the Republic of Korea's success in graduating smoothly from middle income to high income in a relatively short period of time. At a broader level, the balance of evidence from our analysis provides cautious grounds for optimism about the PRC's prospects for a smooth and quick transition to high income. Above all, the fact that the PRC's growth has been led by TFP growth in addition to factor accumulation suggests that it may be sustainable.
However, to continue its enviable track record of rapid TFP growth, the PRC must forcefully implement structural reforms, such as state-owned enterprise reform and reducing the role of the state in the financial system. Structural challenges, such as population aging, and new risks, such as rising global protectionism, further strengthen the case for such TFP-promoting reforms.   1955 1958 1961 1964 1967 1970 1973 1976 1979 1982 1985 1988 1991 1994 1997