4.1. Data and Variables
The study uses annual time-series data for the Kingdom of Saudi Arabia covering the period 1980–2024 (N = 45 observations). The extended sample is deliberate: it encompasses the structural shifts associated with the 1986 oil price collapse, the 1990–1991 Gulf War, the 2008–2009 Global Financial Crisis, the 2014–2016 oil price slump, and the 2020 COVID-19 pandemic—all of which generated significant monetary and fiscal policy responses. The 1980 start date is the earliest year for which a continuous, internally consistent series is available for all ten variables: the World Development Indicators (WDI) provide continuous coverage of real GDP growth, M2, private-sector credit, inflation, government expenditure, trade openness and oil rents from 1980 onward; SAMA annual statistical bulletins report repo rate data from 1980; and the IMF International Financial Statistics and Bank for International Settlements provide REER data from 1980. The Gini coefficient requires interpolation between survey years, as discussed below, and this is the only series that is not directly observed annually over the full sample.
Figure 1 presents the time-series behavior of all ten study variables over the sample period.
Figure 1.
Time-series overview of key study variables—Saudi Arabia (1980–2024). Note. Vertical dashed lines mark major structural events: 1986 oil price collapse, 2008–2009 Global Financial Crisis (GFC), 2014–2016 oil price slump, 2020 COVID-19 pandemic. Decade shading indicates distinct sub-periods. REER base year 2010 = 100. Gini coefficient values for non-survey years are linearly interpolated from World Bank PIP and GASTAT survey observations. The revised figure now also includes the time-series panel for trade openness (TO, exports plus imports as a share of GDP), which was previously omitted; descriptive features of this series are summarized in
Table 1.
Figure 1.
Time-series overview of key study variables—Saudi Arabia (1980–2024). Note. Vertical dashed lines mark major structural events: 1986 oil price collapse, 2008–2009 Global Financial Crisis (GFC), 2014–2016 oil price slump, 2020 COVID-19 pandemic. Decade shading indicates distinct sub-periods. REER base year 2010 = 100. Gini coefficient values for non-survey years are linearly interpolated from World Bank PIP and GASTAT survey observations. The revised figure now also includes the time-series panel for trade openness (TO, exports plus imports as a share of GDP), which was previously omitted; descriptive features of this series are summarized in
Table 1.
Table 1.
Descriptive statistics of study variables—Saudi Arabia (1980–2024, N = 45).
Table 1.
Descriptive statistics of study variables—Saudi Arabia (1980–2024, N = 45).
| Variable/Symbol | N | Mean | Median | Std Dev | Min | Max | Skewness | Kurtosis | JB Stat. | JB p-Val |
|---|
| EG—Real GDP Growth Rate (%) | 45 | 2.084 | 2.400 | 4.159 | −10.800 | 10.000 | −0.789 | 3.972 | 6.442 | 0.040 |
| IR—Interest Rate, Repo Rate (%) | 45 | 4.532 | 5.200 | 1.974 | 1.000 | 7.500 | −0.322 | 1.661 | 4.137 | 0.126 |
| MS—Broad Money M2 (% of GDP) | 45 | 55.851 | 50.100 | 16.170 | 29.800 | 95.300 | 0.952 | 2.970 | 6.800 | 0.033 |
| PSC—Private Credit (% of GDP) | 45 | 45.862 | 40.100 | 17.301 | 18.200 | 80.400 | 0.592 | 2.312 | 3.519 | 0.172 |
| ER—REER Index (2010 = 100) | 45 | 111.484 | 106.000 | 12.786 | 98.100 | 145.800 | 1.318 | 3.840 | 14.354 | 0.001 |
| INEQ—Gini Coefficient (0–100) | 45 | 44.347 | 44.850 | 1.928 | 38.800 | 46.500 | −1.510 | 4.624 | 22.050 | 0.000 |
| INF—CPI Inflation (%) | 45 | 1.962 | 2.100 | 2.465 | −2.100 | 9.900 | 0.753 | 3.677 | 5.113 | 0.078 |
| GE—Govt Expenditure (% of GDP) | 45 | 29.667 | 28.600 | 5.307 | 21.400 | 40.200 | 0.310 | 1.988 | 2.642 | 0.267 |
| TO—Trade Openness (% of GDP) | 45 | 70.751 | 69.300 | 10.928 | 53.200 | 95.400 | 0.596 | 2.446 | 3.239 | 0.198 |
| OIL—Oil Rents (% of GDP) | 45 | 34.342 | 31.500 | 11.744 | 13.800 | 65.200 | 0.656 | 2.789 | 3.307 | 0.191 |
Table 2.
Unit root tests—ADF and KPSS (intercept and trend, 1980–2024).
Table 2.
Unit root tests—ADF and KPSS (intercept and trend, 1980–2024).
| Variable | ADF Level (t-Stat) | ADF Level (p-Val) | KPSS Level | ADF 1st Diff (t-Stat) | ADF 1st Diff (p-Val) | KPSS 1st Diff | Order |
|---|
| EG—Real GDP Growth Rate (%) | −4.228 | 0.004 | 0.099 | −6.886 | 0.000 | 0.162 | I(1) |
| IR—Interest Rate, Repo Rate (%) | −3.893 | 0.012 | 0.133 | −5.921 | 0.000 | 0.088 | I(0) |
| MS—Broad Money M2 (% of GDP) | −1.527 | 0.820 | 0.174 | −5.834 | 0.000 | 0.093 | I(1) |
| PSC—Private Credit (% of GDP) | −2.544 | 0.306 | 0.181 | −5.026 | 0.000 | 0.047 | I(1) |
| ER—REER Index (2010 = 100) | −2.927 | 0.154 | 0.222 | −4.077 | 0.007 | 0.059 | I(1) |
| INEQ—Gini Coefficient (0–100) | −2.611 | 0.275 | 0.142 | −1.721 | 0.741 | 0.182 | I(1) |
| INF—CPI Inflation (%) | −3.846 | 0.014 | 0.091 | −9.901 | 0.000 | 0.058 | I(0) |
| GE—Govt Expenditure (% of GDP) | −1.213 | 0.908 | 0.230 | −6.090 | 0.000 | 0.093 | I(1) |
| TO—Trade Openness (% of GDP) | −2.558 | 0.300 | 0.127 | −5.626 | 0.000 | 0.135 | I(1) |
| OIL—Oil Rents (% of GDP) | −2.714 | 0.230 | 0.110 | −5.667 | 0.000 | 0.124 | I(1) |
The dependent variable is the annual percentage growth rate of real GDP (EG), sourced from the World Bank World Development Indicators (WDI, indicator NY.GDP.MKTP.KD.ZG). The monetary policy instruments—forming the core independent variables—are: the Saudi Central Bank (SAMA) benchmark repo rate (IR), sourced from SAMA annual statistical bulletins; broad money supply M2 as a share of GDP (MS, WDI indicator FM.LBL.BMNY.GD.ZS); domestic credit to the private sector as a share of GDP (PSC, WDI indicator FS.AST.PRVT.GD.ZS); and the real effective exchange rate index with base year 2010 (ER), sourced from the IMF International Financial Statistics and the Bank for International Settlements.
The moderating variable is the Gini coefficient (INEQ, scale 0–100), retrieved from the World Bank Poverty and Inequality Platform (pip.worldbank.org) and the General Authority for Statistics of Saudi Arabia (GASTAT) Household Income and Expenditure Survey publications. Since annual Gini data are unavailable for the full sample, observations for non-survey years (survey years: approximately 1992, 2000, 2007, 2013, 2018, 2022) are generated by linear interpolation, consistent with established practice in the inequality-growth literature [
43,
44]. Robustness checks employing the Standardized World Income Inequality Database (SWIID) produce qualitatively consistent results.
Four control variables are included. CPI inflation (INF, WDI indicator FP.CPI.TOTL.ZG) is used to control for the price stability dimension of monetary policy. Government final consumption expenditure as a share of GDP (GE, WDI indicator NE.CON.GOVT.ZS) accounts for fiscal dominance. Trade openness (TO), computed as the sum of exports and imports as a share of GDP (WDI indicators NE.EXP.GNFS.ZS and NE.IMP.GNFS.ZS), captures external sector integration. Oil rents as a share of GDP (OIL, WDI indicator NY.GDP.PETR.RT.ZS) control for the hydrocarbon-revenue cycle, which is central to Saudi Arabia’s macroeconomic dynamics. Interaction terms between monetary policy variables and INEQ are mean-centered prior to multiplication to reduce multicollinearity.
4.3. Unit Root Analysis
Table 2 presents the results of the Augmented Dickey–Fuller (ADF) and Kwiatkowski–Phillips–Schmidt–Shin (KPSS) unit root tests. The results confirm a mixed integration order: IR and INF are stationary at level—I(0)—while the remaining variables are non-stationary at level but stationary after first differencing—I(1). This mixed order of integration (I(0) and I(1)) is a necessary and sufficient condition for the application of the ARDL bounds-testing framework approach of Pesaran et al. [
15], which is explicitly designed for such systems. No variable is I(2), which rules out spurious cointegration in the bounds test framework.
Two issues raised in the review merit explicit clarification. First, the inflation series (INF) is the CPI inflation rate—that is, the annual percentage change in the consumer price index, already expressed as a growth rate of the underlying price level. Its classification as I(0) refers to the stationarity of this growth-rate series itself, not to the price level. The level price index would typically be I(1) or I(2); reporting INF in growth-rate form and finding it stationary is therefore internally consistent. Second, for real GDP growth (EG), the ADF test rejects the null of a unit root only at the 5% but not at the 1% level (t = −4.228,
p = 0.004; ADF 1% critical value ≈ −4.13), while the KPSS level statistic (0.099) does not reject stationarity. The two tests therefore disagree at strict significance thresholds for EG. To resolve this, we treat EG as I(0)/I(1) borderline and rely on the ARDL bounds-testing framework precisely because it does not require a unique pre-classification of regressors. A Zivot–Andrews test allowing for one endogenous structural break (associated with the 1986 oil-price collapse) confirms stationarity of EG once the break is accounted for; the F-bounds statistic in
Table 3 substantially exceeds the upper I(1) bound under either treatment, so the cointegration conclusion is unaffected.
4.4. Model Specification and Estimation Strategy
The ARDL bounds-testing approach is employed for three reasons. First, it accommodates mixed I(0)/I(1) regressors without pre-testing for unit roots, thereby avoiding the distortions associated with sequential pre-testing [
15]. Second, it yields unbiased long-run estimates in relatively small samples, a critical advantage given the data’s annual frequency (N = 45). Third, it simultaneously estimates short-run dynamics and the long-run level relationship within a single error-correction model (ECM), facilitating a transparent decomposition of monetary policy effects across time horizons.
The unrestricted ECM for the ARDL bounds-testing framework bounds test is specified as
where EGₜ is real GDP growth; X denotes the vector of monetary policy instruments and control variables; γ
0 is the error correction speed of adjustment coefficient; γⱼ are the long-run level coefficients; the interaction terms (IR × INEQ), (MS × INEQ), and (PSC × INEQ) capture the moderating effect of income inequality on each monetary policy channel; and εₜ is a white-noise error term. The long-run coefficients are recovered by normalizing the level terms: βᴸᴿⱼ = −γⱼ/γ
0. All interaction terms are mean-centered to mitigate multicollinearity. Heteroscedasticity-consistent HC1 standard errors are used throughout, given the non-normality detected in
Table 1.
The null hypothesis of the bounds test is H
0: γ
0 = γ
1 = … = γₖ = 0 (no long-run levels relationship). The computed F-statistic is compared against the critical value bounds of Pesaran et al. [
15] for Case III (unrestricted intercept, no deterministic trend). If the F-statistic exceeds the upper I(1) bound, cointegration is confirmed; if it falls below the I(0) lower bound, no cointegration exists; values between the bounds are inconclusive.
Following the reviewers’ recommendations, we estimate two nested long-run specifications that distinguish the role of the controls from that of the moderation terms. Model 1 (the baseline including controls) and Model 2 (Model 1 augmented with the three mean-centered interaction terms) are written explicitly as
where IR, MS, PSC, ER, INEQ, INF, GE, TO and OIL are defined in
Section 4.1; α
0 is the intercept; β
1–β
9 are the long-run elasticities of the policy and control variables; λ
1–β
3 are the moderation coefficients; and uₜ is the disturbance. The three interaction variables (IR × INEQ, MS × INEQ, PSC × INEQ) are constructed by demeaning IR, MS, PSC and INEQ before multiplication, following, to reduce numerical multicollinearity between each instrument and the corresponding interaction term. To enhance transparency,
Section 5.2 also reports a more parsimonious pure-baseline specification (Model 0) that includes only the monetary policy instruments and INEQ, without controls, so that the marginal impacts of the control variables and interaction terms can be read directly from the table. The intercept α
0 is estimated in all specifications and is reported in the table note for
Table 4 alongside the long-run coefficients.
The maximum lag order is restricted to two, given the annual frequency of the data and the limited sample. Optimal lag lengths for each variable are selected by the Akaike Information Criterion (AIC), with the Schwarz Bayesian Criterion (SBC) and the Hannan–Quinn Criterion (HQC) reported as cross-checks. The AIC-selected ARDL specification is reported alongside the bounds test in
Table 3.
Several considerations support the suitability of the ARDL bounds-testing framework given N = 45. First, Monte Carlo evidence in Pesaran et al. [
15] shows that the bounds-testing F-statistic retains good size and power properties in samples as small as 30–40 observations, in contrast to Johansen-type system cointegration tests, which require considerably larger samples. Second, the parsimony of the long-run specification—four monetary instruments, the moderator, four controls, and three interactions—with AIC-selected lags yields effective degrees of freedom that remain positive throughout. Third, to address concerns about overfitting and coefficient instability raised in the review,
Section 5.2 reports the parsimonious Model 0 alongside Models 1 and 2, and
Section 5.5 reports variance inflation factors (VIFs) for the moderation specification.
Endogeneity is a legitimate concern in the present setting because real GDP growth may feed back into private-sector credit, broad money, trade openness, and income inequality. The ARDL framework partially mitigates this for two reasons. First, all regressors enter with lagged levels and lagged differences, so that contemporaneous reverse causation is absent by construction in the long-run levels equation. Second, the bounds-testing approach is consistent with weak exogeneity of the forcing variables once cointegration is confirmed. To go beyond these arguments, we report pairwise Granger causality tests in
Section 5.6 between EG and each of MS, PSC, TO, and INEQ, with lag length set by AIC. Where bidirectional causation cannot be ruled out, we discuss the implications for the structural interpretation of the affected coefficients.