Empirical Economic Analysis: Determinants of GDP Growth in Japan

An Econometric Investigation Using World Development Indicators

Şükrü Demirci (2648244)
Amirreza Akhavan (2602019)

2025-01-01

Statement of the Problem

Research Questions

  • What are the key determinants of GDP growth in Japan?
  • How do exports, investment, and foreign direct investment affect economic growth?
  • What is the relationship between inflation and GDP growth?

Hypotheses

  1. H₁: Exports have a positive and significant impact on GDP growth
  2. H₂: Gross capital formation (investment) positively affects GDP growth
  3. H₃: FDI contributes positively to growth (not empirically testable — FDI data unavailable 1990–1995)
  4. H₄: Inflation has a negative impact on GDP growth

Review of the Literature

Key Studies

1. Export-Led Growth Hypothesis

  • Balassa (1978): Found strong evidence for export-led growth in developing countries
  • Feder (1983): Demonstrated positive externalities from export sector to non-export sector

2. Investment and Growth

  • Solow (1956): Capital accumulation as fundamental driver of economic growth
  • Romer (1986): Endogenous growth theory emphasizes investment in human and physical capital

Key Studies (Continued)

3. Foreign Direct Investment

  • Borensztein et al. (1998): FDI promotes economic growth through technology transfer
  • Alfaro et al. (2004): FDI effects depend on financial market development

4. Inflation and Growth

  • Barro (1995): Negative relationship between inflation and growth
  • Bruno & Easterly (1998): High inflation (>40%) significantly reduces growth

Formulation of the Economic Model

Theoretical Framework

Based on the literature, we formulate a growth model:

\[GDP_t = f(EXP_t, INV_t, FDI_t, INF_t)\]

Empirical Specification

Since all variables are I(1), we estimate in first differences to model short-run growth dynamics:

\[\Delta \ln GDP_t = \beta_0 + \beta_1 \Delta \ln EXP_t + \beta_2 \Delta \ln INV_t + \beta_3 \Delta INF_t + \beta_4 \Delta \ln GDP_{t-1} + \varepsilon_t\]

where \(\Delta\) denotes the first difference operator. This avoids spurious regression and captures the short-run co-movement of growth in exports, investment, and inflation with GDP growth. Coefficients are best interpreted as conditional correlations, not causal effects (see Identification Caveats).

Expected Signs

  • \(\beta_1 > 0\): Export growth should positively affect GDP growth
  • \(\beta_2 > 0\): Investment growth should positively affect GDP growth
  • \(\beta_3 < 0\): Inflation change should negatively affect GDP growth
  • \(\beta_4 < 0\): Crisis dummy (2008–09) expected negative
  • \(\beta_5 < 0\): COVID dummy (2020) expected negative

Note: FDI (\(H_3\)) is not included in the regression due to data gaps; it is assessed qualitatively.

Data Sources and Description

Variable Definitions

Variable Definitions and Data Sources
Variable Definition Units Source
GDP GDP (constant 2015 US$) Constant 2015 US$ World Development Indicators
EXP Exports of goods and services (constant 2015 US$) Constant 2015 US$ World Development Indicators
INV Gross capital formation (constant 2015 US$) Constant 2015 US$ World Development Indicators
FDI Foreign direct investment, net (BoP, current US$) Current US$ World Development Indicators
INF Inflation, consumer prices (annual %) Annual percentage World Development Indicators

Data Summary Statistics

Summary Statistics
Variable Mean StdDev Min Max
LGDP 29.0510 0.0773 28.8865 29.1573
LEXP 27.0201 0.3939 26.3310 27.5505
LINV 27.7658 0.0743 27.5721 27.8993
INF 0.5800 1.2380 -1.3528 3.2681
LFDI 24.9000 0.8513 22.9726 26.1092

Time Series Plots

Time Series Plots (Continued)

Model Estimation and Hypothesis Testing

Step 1: Unit Root Tests

Augmented Dickey-Fuller Tests

Note: FDI is excluded from unit root tests due to missing data in early years (1990-1995). FDI will be considered in model estimation where data is available.

ADF Unit Root Tests (Levels)
Variable TestStat CV 1% CV 5% Stat 1% Stat 5%
LGDP -2.858 -4.15 -3.50 No No
LEXP -1.879 -4.15 -3.50 No No
LINV -2.347 -4.15 -3.50 No No
INF -2.938 -3.58 -2.93 No Yes
LFDI NA NA NA N/A N/A

First Difference Tests

ADF Unit Root Tests (First Differences)
Variable TestStat CV 1% CV 5% Stat 1% Stat 5%
ΔLGDP -4.461 -3.58 -2.93 Yes Yes
ΔLEXP -5.029 -3.58 -2.93 Yes Yes
ΔLINV -4.284 -3.58 -2.93 Yes Yes
ΔINF -4.719 -3.58 -2.93 Yes Yes
ΔLFDI NA NA NA N/A N/A

Step 2: Cointegration Tests

Johansen Cointegration Test Results
Test TestStat CV 5% Cointegrated
Trace r=0 4.380 8.18 No
Trace r≤1 16.283 17.95 No
Eigen r=0 4.380 8.18 No
Eigen r≤1 11.902 14.90 No

Interpretation: The Johansen test does not reject the null of no cointegration at the 5% level for any of the four variants. We therefore find no statistically detectable long-run equilibrium among LGDP, LEXP, LINV, and INF. Combined with the ADF results, this justifies the first-differences specification rather than a VECM.

Caveat: Failure to detect cointegration is not the same as proving no long-run relationship. Johansen has low power in small samples (n ≈ 32), so the absence of detected cointegration may reflect sample size rather than genuine absence of a long-run link.

Step 3: First-Differences Model

Note: Since the Johansen test in Step 2 finds no cointegration, the first-differences specification is the appropriate estimator for these I(1) variables. Crisis (2008–09) and COVID (2020) dummies control for the two known structural shocks. FDI is excluded due to insufficient data coverage (1990–1995 missing).

General Model Results

General Dynamic Model Estimation Results. *** p<0.01, ** p<0.05, * p<0.1
Variable Coefficient StdError tStatistic PValue Significance
(Intercept) (Intercept) 0.0069 0.0019 3.5807 0.0017 ***
dLGDP_lag1 dLGDP_lag1 0.0899 0.1767 0.5086 0.6161
dLEXP dLEXP 0.0913 0.0251 3.6371 0.0015 ***
dLEXP_lag1 dLEXP_lag1 -0.0383 0.0308 -1.2438 0.2267
dLINV dLINV 0.2453 0.0404 6.0725 0.0000 ***
dLINV_lag1 dLINV_lag1 -0.0192 0.0582 -0.3295 0.7449
dINF dINF -0.0024 0.0013 -1.9223 0.0676 *
dINF_lag1 dINF_lag1 0.0002 0.0013 0.1320 0.8962
crisis crisis -0.0063 0.0061 -1.0386 0.3103
covid covid -0.0259 0.0073 -3.5493 0.0018 ***

Step 4: Parsimonious Model

Parsimonious Model Estimation Results. *** p<0.01, ** p<0.05, * p<0.1
Variable Coefficient StdError tStatistic PValue Significance
(Intercept) (Intercept) 0.0052 0.0014 3.5961 0.0013 ***
dLEXP dLEXP 0.1133 0.0192 5.8853 0.0000 ***
dLINV dLINV 0.2246 0.0355 6.3216 0.0000 ***
dINF dINF -0.0027 0.0011 -2.4118 0.0232 **
crisis crisis -0.0055 0.0057 -0.9618 0.3450
covid covid -0.0226 0.0067 -3.3911 0.0022 ***
Model Statistics
Statistic Value
R2 0.9258
Adj R2 0.9116
F stat 64.9067
F p-value 0.0000
SSR 0.0009
AIC -231.4193
BIC -221.1592

HAC Robust Coefficient Estimates

Parsimonious Model — Newey-West HAC Standard Errors (lag=2). HAC SEs robust to heteroscedasticity and autocorrelation. *** p<0.01, ** p<0.05, * p<0.1
Variable Coefficient HAC_SE t_stat PValue Significance
(Intercept) (Intercept) 0.0052 0.0019 2.7945 0.0096 ***
dLEXP dLEXP 0.1133 0.0211 5.3641 0.0000 ***
dLINV dLINV 0.2246 0.0341 6.5893 0.0000 ***
dINF dINF -0.0027 0.0011 -2.4633 0.0207 **
crisis crisis -0.0055 0.0045 -1.2149 0.2353
covid covid -0.0226 0.0037 -6.1158 0.0000 ***

Step 5A: Serial Correlation Diagnostics

Durbin-Watson Test for Serial Correlation

Durbin-Watson Test for Serial Correlation
Test Statistic PValue Interpretation
Durbin-Watson 1.8158 0.568 No serial correlation

Breusch-Godfrey LM Test for Serial Correlation

Breusch-Godfrey LM Test for Serial Correlation
Test Statistic PValue Interpretation
LM test Breusch-Godfrey LM 2.6771 0.2622 No serial correlation

Step 5B: Heteroscedasticity Diagnostics

White Test for Heteroscedasticity

White Test for Heteroscedasticity
Test Statistic PValue Interpretation
BP White Test 10.0073 0.1243 Homoscedasticity

ARCH Test

ARCH Test for Heteroscedasticity
Test Statistic PValue Interpretation
ARCH Test (LM) 0.312 0.8555 No ARCH effects

Step 5C: Specification and Normality Diagnostics

RESET Test for Functional Form

RESET Test for Functional Form
Test Statistic PValue Interpretation
RESET RESET Test 1.1397 0.3366 Functional form correct

Jarque-Bera Test for Normality

Jarque-Bera Test for Normality
Test Statistic PValue Interpretation
X-squared Jarque-Bera 0.9432 0.624 Residuals normally distributed

Step 5D: Parameter Stability Tests

Parameter Stability Tests
Test Statistic PValue Interpretation
S0 CUSUM 0.5329 0.9389 Parameters stable
S Recursive CUSUM 0.5508 0.5135 Parameters stable

Residual Diagnostics Plot

Interpretation of Results and Conclusions

Stationarity and Cointegration

Unit Root Tests

  • All variables non-stationary in levels (I(1) processes)
  • First differences stationary, confirming I(1) integration
  • Rules out OLS in levels (spurious regression risk)

Cointegration

  • Johansen tests do not detect cointegration at the 5% level
  • No statistically detectable long-run equilibrium relationship
  • Justifies first differences (not VECM) as the appropriate estimator

Empirical Findings

Coefficients summarise short-run associations between growth in each variable and GDP growth (not causal effects).

  • Export growth (dLEXP): β = 0.1133, OLS p < 0.01 , HAC p < 0.01 — Supported. A 10 pp rise in export growth is associated with approximately a 1.1328 pp change in GDP growth, consistent with the Balassa–Feder export-led growth hypothesis
  • Investment growth (dLINV): β = 0.2246, OLS p < 0.01 , HAC p < 0.01 — Supported (largest effect). A 10 pp rise in investment growth is associated with approximately a 2.2462 pp change in GDP growth, consistent with the Solow framework
  • Inflation (dINF): β = -0.0027, HAC p < 0.05 ** — Supported. Statistically significant but economically small (a 1 pp rise in inflation is associated with only a 0.0027 pp change in GDP growth). The sign is consistent with Barro (1995), but in Japan’s predominantly deflationary sample the magnitude is too modest to drive macro policy on its own
  • COVID dummy: captures the 2020 pandemic shock cleanly. The 2008 crisis dummy is comparatively muted, suggesting the GFC transmitted to Japan less acutely than COVID-19

Identification Caveats

These coefficients should be read as conditional correlations, not causal effects. Three identification concerns apply:

  • Reverse causality: GDP growth itself feeds back into export growth (capacity, competitiveness) and investment growth (the accelerator effect). Single-equation OLS cannot disentangle the two directions
  • Omitted variable bias: Productivity (TFP) shocks, exchange-rate movements, monetary policy, and especially working-age population growth are known drivers of Japanese growth that are not in the regression. Their omission can bias the included coefficients
  • R² is unusually high (≈ 0.93): Differenced macro data normally yield much lower fit; this likely reflects (i) the COVID dummy absorbing a single very large outlier and (ii) small-sample overfitting (n = 32, 5 regressors). The fit statistic should not be over-interpreted

A fully causal treatment would require an IV strategy, a VAR, or an ARDL bounds approach — outside the scope of this short-run, diagnostic-focused exercise.

Diagnostic Tests Summary

  • Serial Correlation: Durbin-Watson and Breusch-Godfrey both indicate no serial correlation
  • Heteroscedasticity: White and ARCH tests find homoscedasticity; HAC SEs reported as a robustness check
  • Normality: Jarque-Bera does not reject normality of residuals
  • Functional Form: RESET does not reject correct specification
  • Parameter Stability: CUSUM and Recursive-CUSUM both indicate stable parameters

Hypothesis Testing Results

  1. H₁ (Export growth → GDP growth): Supported — β = 0.1133, HAC p < 0.01 ***
  2. H₂ (Investment growth → GDP growth): Supported — β = 0.2246, HAC p < 0.01 ***
  3. H₃ (FDI → GDP growth): Untestable — FDI data unavailable for 1990–1995; sample too short for reliable estimation
  4. H₄ (Inflation → GDP growth): Supported — β = -0.0027, HAC p < 0.05 **. The inflation–growth channel is detectable even in Japan’s predominantly deflationary sample, suggesting the relationship operates symmetrically around zero

Policy Implications

Policy implications are tentative — they assume the estimated correlations partly reflect causal channels.

  • Investment correlates most strongly with growth (β ≈ 0.22). If this association is partly causal, infrastructure spending, R&D incentives, and business investment credits would have the clearest growth payoff
  • Export growth co-moves with GDP growth (β ≈ 0.11), consistent with continued reliance on external demand. Trade facilitation policies remain plausibly relevant
  • Inflation–growth link is statistically present but economically small — it argues against high-inflation regimes but is too small to motivate aggressive reflation
  • Crisis exposure asymmetry: COVID-19 produced a much larger measured shock than the 2008 financial crisis, suggesting Japan is more vulnerable to global demand shocks than to financial-sector contagion — a useful prior for future risk planning

Limitations and Future Research

  • Small sample: 32 usable observations after differencing limits power to detect marginal effects; the strong results obtained reflect that the included regressors capture large shares of GDP growth variance
  • No cointegration found: The absence of a long-run equilibrium relationship is itself a substantive finding — it diverges from the typical I(1) macro story for advanced economies and may reflect Japan’s atypical post-1990 trajectory
  • FDI data gaps: 1990–1995 observations missing; H₃ could not be properly tested. A shorter sample (1996–2023) or imputation would be required
  • Structural breaks beyond 2008/2020: The 1997 Asian crisis, 2011 Tōhoku earthquake, and 2013 Abenomics regime shift are not modeled; adding dummies or estimating sub-periods separately would strengthen robustness
  • Annual frequency: Quarterly WDI/IMF data would quadruple sample size and substantially increase power for detecting smaller effects
  • Omitted demographic variable: Working-age population growth captures Japan’s structural headwind and would be the natural next addition

Concluding Remarks: What We Found

This study examines the short-run determinants of Japanese GDP growth, 1992–2023, using a first-differences specification with crisis (2008–09) and COVID (2020) dummies and HAC standard errors.

  • The model fits the data well (\(R^2 \approx 0.93\)) and all diagnostic tests pass under HAC inference
  • Investment growth shows the strongest association with GDP growth (β ≈ 0.22), consistent with the Solow framework
  • Export growth is positively associated with GDP growth (β ≈ 0.11), consistent with the export-led growth hypothesis
  • Inflation enters with a small significant negative coefficient — statistically detectable, economically modest
  • COVID-19 produced a substantially larger shock than the 2008 financial crisis for Japan

Concluding Remarks: What We Cannot Claim

  • The estimates are conditional correlations, not causal effects. Reverse causality (GDP → exports, GDP → investment) and omitted variables (TFP, exchange rate, demographics) prevent a causal reading
  • The high R² is partly an artefact of the COVID dummy and small-sample overfitting; the goodness-of-fit should not be read as evidence of model completeness
  • The Johansen non-rejection of cointegration reflects low test power in n ≈ 32, not proof that no long-run relationship exists
  • H₃ (FDI) could not be tested at all due to missing 1990–1995 observations

Concluding Remarks: Why It Still Matters

Despite these caveats, the results have value:

  • They are consistent across OLS and HAC inference and survive standard residual diagnostics
  • The signs and rough magnitudes line up with three well-established theoretical traditions (Solow, Balassa–Feder, Barro)
  • The COVID-vs-2008 asymmetry is a substantive new observation about Japan’s exposure profile
  • The exercise establishes a clean diagnostic baseline against which future work — quarterly frequency, demographic controls, an ARDL/VAR structure to address endogeneity — can be compared

References

References

Alfaro, L., Chanda, A., Kalemli-Ozcan, S., & Sayek, S. (2004). FDI and economic growth: the role of local financial markets. Journal of International Economics, 64(1), 89-112.

Balassa, B. (1978). Exports and economic growth: Further evidence. Journal of Development Economics, 5(2), 181-189.

Barro, R. J. (1995). Inflation and economic growth. Bank of England Quarterly Bulletin, 35(2), 166-176.

Borensztein, E., De Gregorio, J., & Lee, J. W. (1998). How does foreign direct investment affect economic growth? Journal of International Economics, 45(1), 115-135.

Bruno, M., & Easterly, W. (1998). Inflation crises and long-run growth. Journal of Monetary Economics, 41(1), 3-26.

Feder, G. (1983). On exports and economic growth. Journal of Development Economics, 12(1-2), 59-73.

Romer, P. M. (1986). Increasing returns and long-run growth. Journal of Political Economy, 94(5), 1002-1037.

Solow, R. M. (1956). A contribution to the theory of economic growth. The Quarterly Journal of Economics, 70(1), 65-94.

World Bank. (2024). World Development Indicators. Retrieved from https://databank.worldbank.org/