Silviase/jgov_v1.4_full_ann huggingface dataset:
utility from his life-time consumption $ u(c) $ , along an optimal capital accumulation path in analogy of a representative firm that maximizes its net worth, under the condition that the country's debt cannot exceed the present value of the firm's life-time production. He used Solow's production function $ f(k) $ with per capita human capital h included.

Fukao’s model suggests that, with capital-labor ratio k of a country measured by labor competence hL, so that k = K/hL, a smaller k implies a larger current account deficit for the country. The reason why this is so is because if h is large and therefore k is small, then rapid capital accumulation of the country leads to a prospect of large net production, thereby inducing a larger consumption level than the current production level, which leads a current account deficit.

Recent discussion of social capital advocated by Putnam (1993) emphasizes that good social relationships, such as credibility, obedience to the rules, and networking, improve the efficiency of cooperative performance/activities of the society, and affect the growth of the economy. Knack and Keefer (1997) constructed a proxy of the social capital index for 29 countries, whereby they tested the correlation between the index and the growth rate of per capita GDP. They concluded that credibility improves labor productivity by affecting the quality of human capital. Their results, however, are not yet conclusive $ ^{10} $ .

### 2.2 Methods of Empirical Analysis

## (1) Cross-country Data Analyses

In the Harrod-Domar model, where production technology and the capital-labor ratio are fixed, capital accumulation is essential for growth. In the neoclassical Solow-Swan model, on the other hand, the capital-labor ratio changes to accommodate technology innovation, which is the source of growth. Barro (1990) and others, who advocate the endogenous growth theory, assert that the government policies, such as open trade and education, could stipulate the country's long-term growth rate. It has provoked many studies using cross-country empirical analysis $ ^{11} $ . King and Levine (1993), for example, specified a regression model with such explanatory variables as 1) financial depth, represented by the ratio of bank deposits to GDP as a proxy of progress in financial intermediation, and 2) the level of education, represented by the enrollment ratio at the secondary education level as a proxy of human capital.

Radelet, Sachs and Lee (1997) adopted the theory of conditional convergence in
identifying the factors responsible for differences in growth rates across countries, and conducted empirical analysis $ ^{12} $ using the cross country framework. The explanatory variables of their model were 1) output per worker in 1965 as an initial condition, 2) endowment of natural resources, 3) geographic characteristics, such as landlocked or tropics, 4) demographic characteristics, 5) education, and 6) government policies, such as openness and quality of institutions. Their results indicated that the rapid growth in East Asia could be mostly attributed to policy factors, and less to the initial conditions or the endowment of natural resources.

Since the 1960s, the World Bank has also conducted empirical analyses using the cross-country data for developing countries to estimate the effects of development assistance that the Bank and other multilateral institutions, as well as bilateral donors, had provided. The Bank presented the impact of ODA on the growth of developing economies in its report “Assessing Aid” (1998), based on the cross-country data analysis done by Burnside and Dollar (1997). The report concluded with the result that a sustained increase of ODA by one percent of the recipient’s GDP has an impact of accelerating its growth rate by 0.5 percent, if the recipient employs good policy management in terms of macroeconomic stability, openness of the market, and governance in institutions.

Kokumin Keizai Research Institute (KKRI), consigned by the former Economic Planning Agency of the Japanese government, repeated the above exercise done by Burnside and Dollar (1997) with more comprehensive data for 121 countries. KKRI (2000) concluded that good policy management had little effect on promoting the growth rate. In addition, it estimated the impacts of Japan's yen loans on economic growth, and concluded that sustained extension of yen loans equivalent to one percent of the recipient's GDP has an impact of accelerating its real per capita growth rate by 0.23 percent, while the total ODA extended by DAC countries other than yen loans has an impact of accelerating only by 0.03 percent.

## (2) General Equilibrium Model Analyses

The Computable General Equilibrium (CGE) model provides a powerful tool for assessing effects of policy changes on the worldwide economy. The CGE model has a static optimization mechanism in that it instantly restores imbalance occurring in the relative prices of goods and factors of production. The Walrasian mechanism built in to the model ensures that demand and supply in the goods, labor and capital markets would be equalized through the adjustment processes induced by the relative price.
changes. The Global Trade Analysis Project (GTAP) of the US designed, and has been revising a workable CGE model open to economists and research institutes in the world.

Kawasaki (2002) compared the impact of yen loans extended by Japan to six Asian countries by using the GTAP simulation model, with the impact of trade liberalization facilitated by Japan’s unilateral abolition of tariff/non-tariff barriers against the imports from those countries. It concluded that the impact on growth of recipients’ economies is larger in case yen loans are provided, while the impact on recipients’ utility is larger in case trade liberalization is facilitated.

Yamashita (2003) tested the hypothesis of transfer paradox by using the GTAP model. The results of the simulation rejected transfer paradox, implying that the utility level of the capital recipients improves generally due to the quantity effects of the exports, in spite of the deterioration in the terms of trade. At the same time, the utility level of the donors improves, though to a lesser extent, due to the ameliorated terms of trade effects. It also tested the effects of technology transfers and unilateral tariff reductions to developing economies, and found the results favorable for the recipients.

## (3) Time-series Data Analyses $ ^{13} $

Empirical analysis using time-series data requires that each variable $ x_{t} $ is stationary, meaning that: 1) its mean $ \mathrm{E}(\mathrm{x}_{\mathrm{t}}) $ and variance $ \mathrm{V}(\mathrm{x}_{\mathrm{t}}) $ are constant over time t, and 2) the value of covariance $ \mathrm{Cov}(\mathrm{x}_{\mathrm{t}}, \mathrm{x}_{\mathrm{t}-\mathrm{k}}) $ between two time periods t and t-k depends only on the lag k and not on the actual time t at which the covariance is computed $ ^{14} $ . The problem of spurious regression is likely to arise, when two time-series exhibit both strong upward or downward trends. In this case the high $ R^{2} $ could be due to the presence of the trend, not due to any meaningful relationship between the two. It is known that if a time-series model includes one non-stationary variable, then the regression could be spurious, even though it exhibits a high $ R^{2} $ and significant t-values.

## a) Unit Root Tests

Let us denote the stochastic error term by $ u_{t} $ , which has zero mean, constant variance, and is not autocorrelated. Such an error term is called white noise. If $ \Delta x_{t} = x_{t} - x_{t-1} $ is stationary, where $ \Delta $ is the first-difference operator, the original series $ x_{t} $ is called integrated of order 1, and denoted by $ I(1) $ . In general, if a time series has to be differenced r times before it becomes stationary, it is integrated of order r, or $ I(r) $ .
Consider the autoregressive model $ x_{t} = \rho x_{t-1} + u_{t} $ , where $ u_{t} $ is white noise. If $ \rho = 1 $ , then $ x_{t} $ is a non-stationary time-series known as a random walk, and we say that $ x_{t} $ has a unit root. The model can be modified as $ \Delta x_{t} = (\rho - 1) x_{t-1} + u_{t} = \alpha x_{t-1} + u_{t} $ , where $ \alpha = \rho - 1 $ . The unit root is tested for $ x_{t} $ under the null hypothesis that $ \alpha = 0 $ .

More generally, the unit root is tested for $ x_{t} $ under the null hypothesis that $ \alpha = 0 $ in the time series model $ \Delta x_{t} = \alpha x_{t-1} + \beta t + \gamma + u_{t} $ , where t is a time trend, and $ \gamma $ is a drift parameter (intercept). If the error term $ u_{t} $ is autocorrelated, then the model is modified to include more lags:

$$ \Delta x_{_{t}}=\alpha\mathbf{x}_{t-1}+\delta_{_{i}}\sum_{i=1}^{m}\Delta x_{_{t-i}}+\beta\mathbf{t}+\gamma+\mathbf{u}_{t} $$

The number of lagged difference terms to include m is determined empirically by Akaike information criterion (AIC), or Schwarz criterion (SC). The unit root test for $ x_{t} $ under the null hypothesis $ \alpha = 0 $ applied to the model (1) is called augmented Dickey-Fuller (ADF) test. We can effectively apply the Phillips-Perron (PP) test to the same model, when $ u_{t} $ is autocorrelated.

## b) Vector Autoregressive (VAR) Models

A reduced form of the autoregressive model with multi-variable time series is denoted as follows, where $ y_{t} $ is a j vector of endogenous variables, $ x_{t} $ is a k vector of exogenous variables, $ \lambda_{i} $ and $ \mu_{i} $ are matrixes of coefficients to be estimated, and $ u_{t} $ is a j vector of error terms or impulses in the language of VAR:

$$ \mathbf{y}_{\mathrm{t}}=\sum_{i\mathrm{ 臼 }}^{m}\lambda_{i}\mathbf{y}_{\mathrm{t}-\mathrm{i}}+\sum_{i\mathrm{ 臼 }}^{m}\boldsymbol{\mu}_{i}\mathbf{x}_{\mathrm{t}-\mathrm{i}}+\boldsymbol{\gamma}+\mathbf{u}_{\mathrm{t}} $$

Since VAR models do not distinguish the dependent variables from the independent variables, the notation of $ y_{t} $ and $ x_{t} $ is conventional. Under the assumption that $ u_{t} $ is neither autocorrelated nor correlated with any of the right-hand side variables, we can appropriately estimate the coefficients by OLS. The number of lags m is again determined by Akaike information criterion (AIC), or Schwarz criterion (SC).

## c) Granger Causality Tests

Consider the two-variable VAR model with m lags for simplicity:

$$ \mathbf{y}_{\mathrm{t}}=\sum_{i=1}^{m}\lambda_{_{i}}\mathbf{y}_{\mathrm{t-i}}+\sum_{i=1}^{m}\boldsymbol{\mu}_{_{i}}\mathbf{x}_{\mathrm{t-i}}+\boldsymbol{\gamma}+\mathbf{u}_{\mathrm{t}}. $$

We say that a time series $ x_{t} $ Granger causes a time series $ y_{t} $ , if lagged $ y_{t} $ and lagged $ x_{t} $ explain current $ y_{t} $ . More specifically, if the null hypothesis $ \mu_{i}=0 $ (for all i) is
rejected, then $ x_{t} $ Granger causes $ y_{t} $ . Conversely, if we cannot reject the null hypothesis, then $ x_{t} $ does not Granger cause $ y_{t} $ .

The null hypothesis is tested by the F-value:

$$ F(m;n-2m-1)=\frac{(RSSR-USSR)/m}{USSR/(n-2m-1)}\ldots\ldots\ldots\ldots\ldots(4) $$

Here n is the number of observations, and n-2m-1 is the degree of freedom in estimating (3) by OLS. USSR is the sum of squared residuals unrestricted of the estimation, and RSSR represents the sum of squared residuals restricted by $ \mu_{i}=0 $ (for all i) of the same estimation. This F-test is called Granger causality test.

## d) Impulse Response Analyses

An impulse response function is created by converting the VAR model (2) to the vector moving average model of infinite order $ \mathrm{VMA}(\infty) $ . It traces the effects of one standard deviation shock to one of the impulses $ u_{t} $ on current and future values of the endogenous variables $ y_{t} $ in the converted form. The impulses are usually correlated, so that they have a common component which cannot be associated with a specific variable.

A common method of dealing with this issue is to attribute all of the effects of any common component to one variable that comes first in the VMA $ (\infty) $ model. More technically, the error terms are orthogonalized by Cholesky decomposition, so that the covariance matrix of the resulting impulses is diagonal. While this method is widely used, it is rather arbitrary, and changing the Cholesky ordering of the variables could dramatically change the impulse responses.

## e) Variance Decompositions

Variance decomposition provides a different method of depicting the system dynamics. It decomposes variation in a targeted endogenous variable $ y_{t} $ into the component shocks to all endogenous variables in the $ \mathrm{VMA}(\infty) $ model, and provides information about the relative importance of each random impulse $ u_{t} $ to the targeted variable.
Figure 2-1 Static Trade Model
Figure2-2 Two-gap Model

$$ S_{d} $$
In conducting empirical tests using the VAR model, we have selected nine developing countries (given in Table 3-2) out of 14 countries listed in Table 3-1 as samples to be tested. These samples were chosen on the condition that the country has annual data of the real and current GDP, per capita real GDP (denoted as GDPP), total ODA received (net of repayment), real domestic investment (INVS), foreign direct investment (FDI), and real exports (E) and imports (M) from 1970 through 1999.

Table 3-1 shows that the ratios of FDI and ODA to current GDP are very small, compared to the ratio of real domestic investment to real GDP. They could thus hardly work as the driving force of growth of per capita GDP. The growth rate of Latin American countries fell in the 1980s and 1990s, while in most Asian countries it accelerated during the same decades. The ratio of FDI to current GDP increased in all countries, while that of ODA decreased in most countries.

Another important consideration for the sample country was that the first difference of the logarithm of per capita GDP, denoted as D( $ \log $ GDPP) and implying the annual growth rate of per capita GDP, should be stationary. The data were collected by the Kokumin Keizai Research Institute (KKRI) commissioned by the Economic and Social Research Institute (ESRI) of the Cabinet Office in 2002.

### 3.1 VAR Model Specification

We conduct the VAR estimates based on the theoretical framework of the two-gap model discussed in Section 2.1(2). We concentrate on the performance of the variable $ \log $ GDP. All other variables in the estimates are the ratios to real GDP (INVSR, ER and MR), or the ratios to current GDP (ODAR and FDIR). The two-gap model argues that the economic growth is limited by two restraining factors: the current account (foreign exchange) restraint and the domestic savings restraint (see Figure 2-2).

The foreign exchange restraint curbs the imports of capital goods and input materials, which are essential for the country's investment and production. The domestic savings restraint curbs investment and imports. Exports are the main source of foreign exchange earnings. FDI is a long-term capital transfer to finance investment, while ODA is a concessionary capital transfer to finance imports, investment, or government consumption. Here, we introduce a variable GAIKA=ER+ODAR+FDIR to represent the foreign exchange restraint. Explanatory variables representing the savings restraint are the GDP ratios to investment INVSR and imports MR.
### 3.2 Unit Root Tests

Table 3-2 presents the results of the unit root tests to check that the variables used in the VAR models are stationary. The unit roots were tested for the levels and the first differences of all variables by the Phillip-Perron test and the augmented Dicky-Fuller test with one-year lags. Most variables rejected the null hypotheses of being the unit roots for their first differences with 5 percent significance, while only a few variables rejected the hypothesis for their levels. Some variables passed the augmented Dicky-Fuller tests with lags longer than one year.

### 3.3 Granger Causality Tests

Table 3-3 gives the results of the Granger causality tests using the above VAR models with varying lags from one to three. Only the cases that rejected the null hypothesis of causality with 10 percent significance are reported in the table. The variables that promote or curb economic growth differ from country to country. In Bangladesh, China, Indonesia, Malaysia, and Pakistan, INVSR is the factor that promotes (restrains) growth. The same factor is GAIKA in Thailand, and MR in Malaysia.

GAIKA affects investment in Bangladesh, Peru, and Thailand, while it affects imports in China, Indonesia, and Thailand. Conversely, economic growth affects investment or imports in Bangladesh, Brazil, Indonesia, Malaysia, Pakistan, and Thailand. Since production is the source of domestic savings, growth could be an indirect factor of the savings restraint. Therefore, once a country takes off and attains high economic growth, it could resolve the savings restraint by itself, and ride on a sustainable development path, as Imaoka (1998) advocated.

### 3.4 Impulse Response Analyses

Figure 3-4 presents the responses of D(logGDPP) to the impulses given by one standard deviations of the lagged explanatory variables D(logGDPP)_{-1}, D(INVSR)_{-1}, D(MR)_{-1}, and D(GAIKA)_{-1}. We placed D(logGDPP)_{-1} first in Cholesky ordering as the most influential explanatory variable, following the suggestion given by Sims (1980). However, the figures show that the impulses do not necessarily have positive or consistent impacts on economic growth across the countries.

### 3.5 Variance Decompositions

Table 3-5 presents the variance decomposition of the estimated error terms of D(logGDPP) responding to the impulses of the above explanatory variables. The decomposition shows the relative magnitude of impacts on growth of each impulse.
We verified that the changes in Cholesky ordering of explanatory variables other than $ D(\log\mathrm{GDPP})_{-1} $ do not affect the results much.

The results indicate that the dominant factors affecting the growth in per capita GDP vary from country to country. Aside from the growth in the previous year, investment is the primary factor in Bangladesh, China, Pakistan and Thailand. Similarly, imports are a prominent factor in Malaysia. Investment and imports are both influential in India, while investment, imports and foreign exchange are all influential factors in Peru. In Brazil, however, none of those seems to be a dominant factor.

### 3.6 Conclusions

We conducted various tests using the VAR model analysis to identify the factors that promote or restrain economic growth based on the two-gap model. The results of the Granger causality tests in Section 3.3 do not give clear evidence that domestic savings and foreign exchange are two restraining factors on growth across the countries. It shows, however, that once a country attains high economic growth, the country could resolve the savings restraint by itself, and lead to a sustainable growth path.

The relaxation of the foreign exchange restraint, on the other hand, could promote investment and imports of the country, but it would not directly lead to higher growth. In China, for example, the prominent driving force is investment. However, an increase in foreign exchange promotes imports rather than investment. The results of the variance decomposition of growth in Section 3.5 reveal that the growth-promoting (restraining) factors vary across the countries, implying that each country requires its own development strategies.
Table 3-1 Development Path of Major Countries

Country Year	Population (millions)	Real GDP (US$ billion)	Real GDP	Ratio to Real GDP (%)	Ratio to Current GDP (%)
(US$)	Growth (%)	Import	Export	Invest	FDI	Cur Acct	ODA net	Debt
Argentina
1960-69	22	129	5,813	2.56	4.7	4.0	21.3	--	--	0.1	--
1970-79	26	186	7,202	1.30	3.8	4.4	23.6	0.11	--	0.06	18.8
1980-89	31	205	6,826	-2.19	4.6	6.1	18.3	0.65	-3.09	0.08	55.6
1990-99	35	258	7,449	3.19	9.9	9.1	18.0	2.51	-2.52	0.07	39.7
Bangladesh
1960-69	58	14	234	1.24	7.6	3.8	18.8	--	--	0.00	--
1970-79	76	16	213	-0.47	8.0	3.9	15.6	0.00	--	4.70	13.5
1980-89	97	24	251	1.73	10.2	4.8	19.0	0.00	-2.63	6.59	33.4
1990-99	119	38	315	3.15	14.7	10.1	19.4	0.13	-0.51	4.28	40.5
Brazil
1960-69	83	161	1,932	2.98	5.3	3.2	25.4	--	--	0.92	--
1970-79	107	359	3,317	5.92	7.6	3.4	33.2	1.13	-4.19	0.17	21.3
1980-89	134	549	4,095	0.93	5.0	5.4	25.0	0.67	-2.02	0.07	40.0
1990-99	158	681	4,299	0.36	8.2	7.8	21.5	1.49	-1.68	0.03	29.0
China
1960-69	715	70	98	0.41	--	--	21.6	--	--	0.00	--
1970-79	902	122	135	4.10	14.4	14.2	34.2	0.00	--	0.00	--
1980-89	1,047	263	249	7.89	20.7	20.0	36.6	0.51	-0.38	0.36	7.7
1990-99	1,195	669	555	8.55	20.5	23.3	38.2	4.09	1.77	0.47	17.0
India
1960-69	483	95	195	1.61	--	--	19.8	--	--	2.02	--
1970-79	608	131	215	0.40	9.3	6.5	22.2	0.04	0.73	1.13	13.6
1980-89	759	201	264	3.72	12.4	6.9	22.9	0.04	-1.59	0.80	17.5
1990-99	922	347	374	3.73	13.3	9.9	23.6	0.39	-1.27	0.56	28.2
Indonesia
1960-69	104	27	256	1.46	10.8	32.0	7.0	--	--	--	--
1970-79	131	50	379	5.31	21.8	41.5	14.2	0.77	--	2.86	40.2
1980-89	162	98	601	4.41	27.8	26.6	22.9	0.37	-3.15	1.17	45.6
1990-99	193	186	961	3.05	27.1	26.8	26.9	1.06	-1.12	1.11	77.8
Korea
1960-69	28	43	1,522	5.61	5.9	2.6	14.7	--	--	6.36	--
1970-79	35	103	2,939	6.80	14.5	12.3	23.5	--	--	1.63	35.9
1980-89	40	216	5,299	6.56	19.4	21.6	28.2	0.26	-0.05	0.07	40.8
1990-99	45	461	10,250	5.20	28.5	30.7	33.5	0.67	0.53	-0.01	21.9
Country Year	Population (millions)	Real GDP (US$ billion)	Real GDP	Ratio to Real GDP (%)	Ratio to Current GDP (%)
(US$)	Growth (%)	Import	Export	Invest	FDI	Cur Acct	ODA net	Debt
Malaysia
1960-69	9	11	1,148	3.49	41.4	45.8	17.2	--	--	0.71	--
1970-79	12	21	1,746	5.18	36.8	44.6	22.0	2.97	0.51	0.70	19.4
1980-89	16	40	2,585	3.02	48.8	52.5	27.2	3.18	-2.87	0.64	56.2
1990-99	20	83	4,043	4.55	82.3	87.1	35.2	5.53	-1.57	0.22	45.2
Mexico
1960-69	43	83	1,928	3.48	17.2	6.9	33.1	--	--	0.16	--
1970-79	58	154	2,618	3.33	16.0	7.1	33.7	0.80	--	0.09	25.3
1980-89	75	238	3,200	0.12	14.8	14.7	25.8	0.98	-0.82	0.08	54.4
1990-99	90	302	3,338	1.54	31.1	27.5	26.1	2.19	-3.72	0.07	40.2
Pakistan
1960-69	52	11	216	3.87	54.4	14.0	26.0	--	--	7.21	--
1970-79	70	20	277	1.62	36.8	11.5	20.1	0.13	--	4.54	47.5
1980-89	94	36	378	4.02	26.4	12.2	20.0	0.33	-2.78	3.07	39.9
1990-99	121	59	488	1.47	21.2	15.4	18.1	0.89	-4.03	1.94	49.7
Peru
1960-69	11	24	2,149	2.30	16.4	13.1	29.3	--	--	0.42	--
1970-79	15	38	2,499	1.12	13.2	9.8	16.8	0.37	--	0.77	50.8
1980-89	19	47	2,426	-1.90	10.9	9.9	18.5	0.13	-4.81	1.29	76.5
1990-99	23	50	2,141	1.50	15.7	13.1	21.6	2.92	-5.22	0.97	64.9
Philippines
1960-69	32	25	780	1.85	18.8	17.0	18.8	--	--	0.84	--
1970-79	43	42	978	3.06	18.8	15.5	22.5	0.30	--	1.24	35.3
1980-89	54	58	1,081	-0.55	22.9	22.4	21.2	0.57	-3.56	1.63	75.5
1990-99	70	74	1,061	0.41	40.4	33.6	22.1	1.71	-2.03	1.77	61.1
Thailand
1960-69	30	17	570	4.59	24.4	14.4	25.2	--	--	1.07	--
1970-79	41	37	888	4.58	26.1	16.8	30.6	0.57	-4.93	0.84	15.6
1980-89	51	70	1,372	5.40	26.4	23.0	29.3	0.97	-3.90	1.07	36.2
1990-99	59	150	2,539	3.94	41.9	40.0	35.3	2.58	-2.80	0.60	57.3
Venezuela
1960-69	9	36	4,000	1.22	--	--	22.7	--	--	0.15	--
1970-79	13	54	4,291	0.44	21.7	27.2	30.8	-0.37	1.08	0.04	18.5
1980-89	17	60	3,569	-2.69	20.4	20.1	21.9	0.16	1.39	0.04	55.6
1990-99	22	76	3,514	0.02	21.2	26.8	17.6	2.60	3.44	0.06	54.4