Monetary Liquidity and Food Price Dynamics: Evidence from China’s Mutton Price

Abstract

Mutton prices in China carry significant economic and social implications, yet their macro-financial drivers remain insufficiently understood. Based on monthly data from 2003 to 2025, this paper employs Ensemble Empirical Mode Decomposition, Vector Autoregression, and wavelet coherence analysis to identify the multi-frequency transmission effects of broad money supply on price dynamics. The results show that broad money supply has limited impact on high-frequency volatility but exerts a strong and persistent influence on medium- and low-frequency trends, particularly after 2010, when stable structural coherence becomes evident. Findings suggest that monetary expansion affects food prices through cost-push channels and expectation adjustments across different time scales. The study highlights the importance of incorporating frequency dimensions into inflation management and food price regulation frameworks to improve the precision and timeliness of policy responses.

1. Introduction

In recent decades, China’s rapid economic growth has been accompanied by a profound transformation in dietary patterns. Per capita meat consumption rose from 35 kg in 1990 to approximately 112 kg in 2022 (FAO, 2024). Within this broader shift, red meat has gained particular prominence. Mutton consumption, in particular, reached 3.86 kg per capita by 2022, placing China as the largest mutton-consuming nation globally (Wang, 2022; World Population Review, 2024). Although mutton accounts for a relatively small share—around 3.4%—of total meat consumption by volume, its economic and social significance far exceeds its quantitative share. Mutton is a culturally central and nutritionally essential staple in several northern and western provinces such as Xinjiang, Inner Mongolia, Ningxia, and Gansu (Xiong et al., 2024). In these regions, it plays a prominent role in daily diets, religious customs, and local food security. During traditional festivals and cold seasons, urban demand in cities like Beijing and Xi’an also surges due to dietary preferences for warming meats. As such, fluctuations in mutton prices may disproportionately impact the food security and inflation perception of both ethnic minority populations and low-income households in these areas (USDA GAIN Report, 2012). At the national level, mutton prices have exhibited notable volatility in recent years. For example, during January 2023, the retail price of mutton dropped 3.4% year-on-year, in contrast to pork, which rose by 11.8% over the same period (NBSC, 2023a). By mid-2023, this trend continued with a 1.7% year-on-year decline and a 1.3% month-on-month decline in mutton prices (NBSC, 2023b). These shifts reflect complex interactions among supply bottlenecks, seasonal consumption surges, transportation costs, and macroeconomic shocks—including those originating from changes in liquidity conditions and broader monetary policy stances

A growing body of research has explored the determinants of mutton price dynamics in China, but important limitations remain. For instance, Y. Yang et al. (2022) applied EEMD and Granger causality methods to regional data from Xinjiang, finding that high-frequency volatility is largely driven by global price shocks, while lower-frequency components reflect local cost and substitution effects. However, their analysis is geographically narrow and omits broader macro-financial drivers. Ma et al. (2025) proposed a hybrid prediction model combining CEEMD, fuzzy logic, and deep learning (AM-LSTM), which demonstrated high short-term forecasting accuracy but offered limited insight into the structural drivers of price behavior. Similarly, Xiong et al. (2024) employed a cobweb framework and VAR modeling to examine the role of supply lags and external shocks, yet they did not incorporate monetary aggregates such as M0, M1, or M2 into their analysis. Taken together, these studies contribute valuable insights into regional patterns and methodological innovations but fall short of offering a comprehensive account of how monetary expansion influences mutton prices across different frequency domains.

This paper aims to fill that gap by investigating how money supply shocks influence mutton price dynamics at multiple frequencies. To do so, we build a theory-grounded empirical framework that integrates macroeconomic principles with signal decomposition techniques. Specifically, we employ Ensemble Empirical Mode Decomposition (EEMD) to separate mutton prices into high-, medium-, and low-frequency components, thereby capturing distinct adjustment processes across time horizons. These components are then embedded in a vector autoregression (VAR) setting to identify the dynamic and frequency-specific impact of monetary expansion. This dual approach allows us to disentangle both the timing and structural channels through which monetary policy affects real commodity prices.

Our contribution is threefold. First, we provide a structured theoretical basis for understanding how monetary supply influences food price formation through both demand-side and cost-side mechanisms. Second, we introduce a frequency-sensitive analytical design that enables a richer characterization of the monetary transmission process beyond conventional time domain models. Third, by extending the scope of monetary transmission literature into the domain of food price volatility, this study enhances our understanding of how macro-financial conditions interact with commodity market behavior. The findings have direct implications for monetary authorities and policymakers concerned with inflation management, as well as for firms operating within the agrifood supply chain.

2. Literature Review

Increased monetary liquidity not only affects real economic activity but also fuels speculative investment in agricultural future markets, especially under regimes of financial deregulation. Ghosh (2010) highlights how such speculative flows—frequently linked to expansionary monetary conditions—drive food price spikes by decoupling prices from supply–demand fundamentals. This dynamic was particularly evident during the 2007–2008 food price crisis, where index-based investment in agricultural commodities played a dominant role in global price escalation (Gilbert, 2010). These findings underscore the importance of considering financialization and speculative behavior as key channels through which monetary shocks transmit to food markets.

Rising food prices, even when not directly linked to volatility, have been strongly associated with increased incidences of social unrest, especially in low-income countries where food expenditures account for a large share of household budgets (Bellemare, 2015). Although high volatility alone may not always induce instability, it exacerbates food insecurity in contexts where institutional buffers are weak. Kavallari and Fellmann (2014) argue that growth-led demand surges in emerging economies elevate their import dependence and exposure to global supply shocks. At the same time, F. Yang et al. (2015) and Richards and Pofahl (2009) emphasize the critical stabilizing role of domestic margin services and internal supply chain structures in mitigating retail price volatility. These findings collectively highlight that the impact of monetary expansion on food prices is shaped not only by external macroeconomic forces, but also by commodity-specific features and domestic policy responses.

Monetary expansion in developed economies—such as through low interest rates and quantitative easing—often leads to a global liquidity surplus, which spills over into emerging markets, stimulating credit expansion, investment, and consumption. This increased liquidity can contribute to rising agricultural commodity prices, triggering broader price cycles (Čermáková & Henrique Filho, 2021; Kohlscheen, 2022). Exchange rate dynamics are another critical conduit: a depreciating U.S. dollar resulting from expansionary monetary policy typically increases the global price of dollar-denominated commodities, disproportionately affecting net food-importing emerging economies (Clapp, 2009). Additionally, Chadwick (2023) shows that persistent terms of trade shocks in emerging markets amplify the volatility of both exchange rates and food prices, which ultimately filter through to consumer-level price variability.

Monetary expansion significantly impacts meat prices through multiple intertwined channels, primarily by introducing inflationary pressures, affecting commodity cycles, and influencing exchange rates (Iacopini et al., 2023). Expansionary monetary policy increases money supply and liquidity, which can raise overall demand. When supply does not adjust accordingly, this leads to inflation and higher prices for goods including meat (Barnett et al., 1983; Čermáková & Henrique Filho, 2021). Additionally, such policies often trigger capital inflows into emerging markets, fueling investment and consumption, thereby pushing up commodity prices including agricultural products like meat (Čermáková & Henrique Filho, 2021). Exchange rate fluctuations—another consequence of monetary easing—can alter import-export competitiveness. A depreciating domestic currency, for example, may raise domestic meat prices by increasing the cost of imported meat (Čermáková & Henrique Filho, 2021). These effects are further complicated by varying price elasticities across meat types and regional consumption patterns (Gallet, 2010). Empirical studies suggest that price increases, especially when paired with environmental awareness campaigns, can reduce meat demand; for example, Vellinga et al. (2022) found that a 30% price increase combined with informational nudges significantly reduced meat purchases.

Beyond monetary channels, global and structural forces also shape meat price dynamics. Almadani et al. (2021) show how global producer price indices for beef and sheep reflect broader economic shifts, such as rising Asian demand and local supply changes, feeding into price volatility and producer incentives. At the same time, policy interventions targeting environmental externalities—such as proposed meat taxes—could influence prices by dampening demand (Funke et al., 2022; McAlpine et al., 2009). However, the framing of such policies by the meat industry can obscure their environmental and health motivations, thereby shaping consumer attitudes and price responsiveness (Clare et al., 2022). Historical analysis also suggests that the relationship between money supply and meat prices is far from linear; structural drivers like population dynamics and broader economic growth often exert equal or stronger effects (Goldstone, 1991; Milbourne, 1983). Thus, while monetary expansion is a key determinant of meat price inflation, its effects are mediated through a complex system of market behaviors, global trade patterns, and policy environments.

3. Theoretical Mechanism Analysis

In the short term, the impact of monetary expansion on price levels is primarily constrained by price adjustment frictions and informational incompleteness. New Keynesian theory emphasizes the existence of nominal rigidity, whereby only a subset of firms is able to reset prices in each period (Calvo, 1983; Taylor, 1980). These “time-dependent pricing” models imply that monetary shocks do not transmit uniformly across the economy but instead lead to partial price adjustments by firms with pricing flexibility, generating incomplete and gradual responses in the short term (Woodford, 2003). Moreover, monetary easing can reduce real interest rates and stimulate aggregate demand, thereby increasing firms’ marginal costs—such as wages, transportation, and raw material inputs—through indirect cost channels (Christiano et al., 2005). For agricultural goods, particularly meat products, these marginal costs constitute a key conduit to final retail prices. Even in the absence of immediate supply–demand imbalances, cost pressures and anticipatory pricing behavior induced by monetary shocks can trigger short-lived, high-frequency price fluctuations (Belongia & King, 1983; Barth & Ramey, 2001; Bils & Klenow, 2004). Accordingly, the short-run transmission mechanism can be theoretically characterized as selective, frequency-specific price responses triggered by monetary shocks, while overall price systems adjust with lag due to nominal stickiness.

In the medium term, the influence of monetary policy on prices is primarily reflected in the endogenous adjustment of inflation expectations and the broad-based rise in nominal input costs. According to the hybrid New Keynesian Phillips Curve (Galí & Gertler, 1999), current pricing decisions depend not only on realized marginal costs but also on forward-looking inflation expectations. When economic agents perceive monetary expansion as persistent, they revise expectations upward, prompting firms to incorporate higher future costs into current price-setting behavior, thereby generating price inertia and trend persistence (Roberts, 2006; Fuhrer & Moore, 1995). Simultaneously, financial accelerator theory (Bernanke et al., 1999) suggests that accommodative monetary policy improves financing conditions and reduces borrowing costs, which may stimulate overinvestment and expansion of production capacity. These effects can indirectly drive up prices of intermediate goods and labor, intensifying the cost-push component of inflation. This cost-based response is particularly pronounced in price-sensitive sectors such as food and agriculture. Given the heterogeneous price elasticity across product categories (Kaplan et al., 2018), as well as structural supply constraints related to climate, inventory, and logistics, the medium-run mechanism should be understood as a distributed, asymmetric transmission process shaped by rising costs and evolving inflation expectations.

From a long-run perspective, mainstream macroeconomic theory posits that money is a neutral variable—persistent monetary expansion does not affect real output or employment but does determine the long-term path of nominal prices (Friedman, 1956; Lucas, 1972). Under the quantity theory of money and its modern extensions, sustained growth in money supply ultimately manifests as a generalized increase in the price level. However, long-run price dynamics are not governed by a simple proportional mapping; instead, they evolve within a framework shaped by institutional changes, market structure, and policy regimes. The prices of food commodities, in particular, are affected by a range of long-term structural factors—including advances in agricultural technology, changes in production scale, environmental constraints, and regulatory interventions such as subsidies, transportation controls, and environmental compliance (Ascari & Sbordone, 2014; Coibion & Gorodnichenko, 2015; Candia et al., 2024). Moreover, the formation of long-run inflation expectations is itself subject to rigidity and institutional anchoring. As economic agents gradually internalize a trend of monetary expansion, they begin to incorporate it into wage negotiations, investment planning, and pricing behavior, resulting in a structural co-movement between the money supply and the price level (Woodford, 2003; Mankiw & Reis, 2002). Therefore, the long-run mechanism goes beyond the proportional adjustment logic of classical monetary theory and emphasizes the joint evolution of monetary policy and structural economic forces in shaping the direction and stability of price trajectories.

4. Methods and Data

4.1. Ensemble Empirical Mode Decomposition

Empirical Mode Decomposition (EMD), proposed by Huang et al. (1998), is a data-driven method designed for adaptive time–frequency analysis of nonlinear and non-stationary signals. The procedure involves constructing upper and lower envelopes based on the local maxima and minima of the signal, followed by an iterative sifting process that decomposes the original series into a finite set of Intrinsic Mode Function (IMF) components ${\mathrm{c}}_{\mathrm{j}}\left(\mathrm{t}\right)$ and a residual term ${\mathrm{r}}_{\mathrm{j}}\left(\mathrm{t}\right)$ (t), as expressed in Equation (1). The result is a collection of oscillatory components with distinct characteristic frequencies. Each IMF satisfies two conditions: (i) the number of extrema and the number of zero crossings must be equal or differ at most by one; and (ii) the local mean of the upper and lower envelopes is zero at every point in time.

$$\mathrm{X}\left(\mathrm{t}\right)={\sum }_{\mathrm{j}=1}^{\mathrm{n}}{\mathrm{c}}_{\mathrm{j}}\left(\mathrm{t}\right)+{\mathrm{r}}_{\mathrm{j}}\left(\mathrm{t}\right)$$

(1)

Although Empirical Mode Decomposition (EMD) has been widely applied in engineering fields, several issues have emerged in practical implementations. One of the most commonly observed problems is the phenomenon of mode mixing, which refers to the presence of oscillations of disparate scales within a single Intrinsic Mode Function (IMF), often caused by noise contamination in the signal. Mode mixing can lead to the improper combination of components from different frequency bands, thereby compromising the interpretability and physical meaning of individual IMFs. To address this limitation, Wu and Huang (2009) proposed the Ensemble Empirical Mode Decomposition (EEMD) method, which effectively mitigates mode mixing by introducing controlled white noise. In EEMD, the signal is decomposed multiple times with the addition of different realizations of white noise, as shown in Equation (2), and the final IMFs are obtained by ensemble averaging across all trials. This approach reduces the occurrence of mode mixing and endpoint effects, ensuring that each resulting IMF retains clear frequency separation and unique physical significance. By leveraging the statistical properties of white noise and ensemble averaging, EEMD enhances the robustness and interpretability of the decomposition process.

$${\mathrm{x}}_{\mathrm{i}}\left(\mathrm{t}\right)=\mathrm{x}\left(\mathrm{t}\right)+{\mathrm{n}}_{\mathrm{i}}\left(\mathrm{t}\right)$$

(2)

Since EEMD performs time series decomposition based on the intrinsic time-scale characteristics of the data itself, it effectively implements a local stationarization process. Unlike traditional spectral methods, EEMD does not require any predefined basis functions, making it highly flexible and adaptive. Owing to these advantages, EEMD has been widely applied in price-related economic research, particularly in studies involving non-stationary or nonlinear price dynamics. Each extracted IMF is subsequently treated as a separate time series and analyzed using VAR or alternative methods depending on their integration properties.

4.2. Vector Autoregression Model

The Vector Autoregression (VAR) model is a non-structural system of equations used to estimate the dynamic interrelationships among multiple variables. In a VAR framework, each endogenous variable in the system is modeled as a function of the lagged values of all endogenous variables, thereby extending the univariate autoregressive model to a multivariate time series context. Sims (1980) was the first to introduce the VAR model into economic research, proposing it as a tool to analyze the dynamic effects of stochastic disturbances in a system of interrelated variables and to trace the transmission of various economic shocks. The mathematical expression of a VAR model of order p is given by:

$${\mathrm{y}}_{\mathrm{t}}={{\mathrm{A}}_1\mathrm{y}}_{\mathrm{t}-1}+\dots +{{\mathrm{A}}_{\mathrm{p}}\mathrm{y}}_{\mathrm{t}-\mathrm{p}}+{\mathrm{B}\mathrm{x}}_{\mathrm{t}}+{\mathsf{\epsilon }}_{\mathrm{t}}$$

(3)

The Vector Autoregression (VAR) model is a multivariate system in which each variable is expressed as a linear function of the lagged values of itself and all other variables. For stationary components (e.g., IMF1–IMF4), we estimate a standard VAR to capture dynamic short-run interactions with monetary aggregates. When non-stationary series are present, traditional VAR estimation may lead to spurious regressions. If all series are integrated of the same order (usually I(1)) and exhibit a long-term equilibrium relationship, a Vector Error Correction Model (VECM) may be applied. The VECM captures both short-term adjustments and long-term cointegration dynamics through an error correction term. However, as shown in our ADF tests (Section 5.2), IMF_5 and IMF_6 are integrated at orders I(3) and I(4), respectively. This violates the standard cointegration requirements that all variables must be of the same order. Consequently, VECM estimation is not appropriate for these components. Instead, to analyze the low-frequency dynamics of IMF_5 and IMF_6 with respect to M2, we employ a wavelet analysis method.

4.3. Wavelet Analysis

To analyze the time-varying relationship between monetary aggregates and the long-run components of mutton prices, we adopt a wavelet-based framework. Wavelet transforms enable the joint localization of signals in both time and frequency domains (Torrence & Compo, 1998), making them particularly suitable for investigating non-stationary economic processes with multi-scale dependencies. This provides a more flexible alternative to cointegration techniques when conventional assumptions are not met (Aguiar-Conraria et al., 2008). The continuous wavelet transform of a time series $x\left(t\right)$ is defined as:

$$W_x(s,\tau )={\int }_{-\infty }^{+\infty }x(t)·{\displaystyle \frac{1}{\sqrt{s}}}{\psi }^{*}({\displaystyle \frac{t-\tau }{s}})dt$$

(4)

where $s$ is the scale parameter (inversely related to frequency), $\tau$ is the translation (time) parameter, ${\psi }^{*}(·)$ is the complex conjugate of the mother wavelet $\psi$.

In practice, we implement the Maximal Overlap Discrete Wavelet Transform (MODWT), which avoids downsampling and maintains alignment with the original signal’s length, enhancing interpretability. Each signal $x\left(t\right)$ is ecomposed $j$ into levels as:

$$x(t)={\sum }_{j=1}{D}_j\left(t\right)+S_j\left(t\right)$$

(5)

where $D_j\left(t\right)$ denotes the detail coefficients at level j, $S_j\left(t\right)$ denotes the smooth (low-frequency) approximation at level j.

To measure the localized correlation between two time series $x\left(t\right)$ and $y\left(t\right)$, we compute their wavelet coherence:

$$R^2(s,\tau )={\displaystyle \frac{{|S{(W}_{xy}\left(s,\tau \right))|}^2}{S({\left|W_x\left(s,\tau \right)\right|}^2)·S({\left|W_y\left(s,\tau \right)\right|}^2)}}$$

(6)

Here, $W_{xy}\left(s,\tau \right)$ is the cross wavelet transform, and S(⋅) denotes a smoothing operator in time and scale. The resulting $R^2(s,\tau )$ quantifies the local linear dependence between the two series at each scale and point in time.

This method allows us to detect lead–lag relations and co-movement structures that vary across different frequencies—capturing monetary transmission effects that standard time domain models fail to identify.

4.4. Data

All data used in this study are obtained from the National Bureau of Statistics of China. Both the mutton price series and the broad money supply (M2) are monthly frequency data. The sample covers the period from 2003 to 2025.

5. Results

5.1. Decomposition of Mutton Price Fluctuations in China

Using the Ensemble Empirical Mode Decomposition (EEMD) method, we decompose the mutton price series in China from 2003 to 2025 into six intrinsic mode functions (IMFs), as illustrated in Figure 1. IMF1 and IMF2 capture the high-frequency components of price fluctuations. In contrast to other countries, where such high-frequency volatility is often attributed to financial market activities (e.g., futures trading or speculative behavior) or information asymmetries, the patterns observed in IMF1 and IMF2 display high volatility without the hallmarks of financial speculation. Instead, they resemble “pure physical disturbances,” suggesting that China’s mutton market remains largely unfinancialized and is still predominantly governed by the physical spot market; IMF3 and IMF4 represent medium-frequency components and exhibit phase-specific irregularities. These components often reflect abrupt regime shifts—what were initially smooth cyclical movements are occasionally disrupted by exogenous shocks that introduce new oscillatory regimes. For example, around 2015 and 2020, government interventions such as transportation restrictions and environmental policy reforms altered market structure, inducing structural price shifts; IMF5 and IMF6 correspond to low-frequency components and capture the long-term price trend. The observed trend displays a unidirectional upward movement with a non-constant slope, which diverges from the conventional “slow mean-reversion around supply–demand equilibrium” mechanism. This implies that the long-run mutton price dynamics are not solely governed by fundamental steady-state adjustments.

From a monetary perspective, the low-frequency trend appears consistent with structurally driven inflation induced by long-run monetary expansion. The medium-frequency components may reflect price spillovers and demand shifts stemming from accommodative monetary policy—particularly through substitution effects with related goods such as beef. High-frequency fluctuations may correspond to short-term overshooting effects following M2 shocks, capturing immediate demand surges and temporary supply chain disruptions. In the following section, we apply VAR and VECM models to each IMF component to further examine the transmission mechanism between monetary expansion and mutton price dynamics.

5.2. Stationarity and Cointegration Tests

As shown in

Table 1. Augmented Dickey–Fuller (ADF) Test Results for Variable Stationarity.

Variables	Order of Difference	ADF Statistic	p-Value	Stable
IMF_1	0	−9.43378	3.89 × 10−14	Yes
IMF_2	0	−8.60859	2.83 × 10−12	Yes
IMF_3	0	−7.43534	1.44 × 10−9	Yes
IMF_4	0	−3.78588	0.017289	Yes
IMF_5	0	−1.74816	0.729202	No
IMF_6	0	−2.52537	0.315396	No
M2	0	−3.78153	0.017519	Yes
IMF_5	1	−1.74816	0.72920	No
IMF_5	2	−2.91851	0.15630	No
IMF_5	3	−4.72953	0.00062	Yes
IMF_6	1	−2.52537	0.3153	No
IMF_6	2	−2.80374	0.19557	No
IMF_6	3	−3.06513	0.11477	No
IMF_6	4	−4.51872	0.00140	Yes

, IMF_1 through IMF_4 and M2 are stationary at level form, confirming that they are integrated of order zero, I(0). However, IMF_5 and IMF_6 exhibit non-stationarity at levels and only become stationary after higher-order differencing. Specifically, IMF_5 becomes stationary after the third difference, suggesting it is integrated of order three, I(3). IMF_6 attains stationarity at the fourth difference, indicating an integration order of I(4). These findings imply that standard cointegration techniques, such as the Johansen procedure, which require variables to be integrated of the same order (typically I(1)), are not applicable to IMF_5 and IMF_6.

Given the heterogeneous integration orders among variables, particularly the high orders of IMF_5 and IMF_6, we refrain from conducting conventional cointegration analysis involving these components. Instead, to assess the long-run association between monetary aggregates and low-frequency mutton price components, we adopt a wavelet-based approach in the following section.

5.3. VAR Model Specification

The high- and medium-frequency components IMF1 through IMF4 are found to be stationary (I(0)) and thus do not require differencing or cointegration adjustment. For IMF 1-IMF 4, we estimate a standard unrestricted VAR model with M2 as an explanatory variable:

$$[\begin{array}{c}{IMF}_t^i\\ {M2}_t\end{array}]={\mathrm{A}}_1[\begin{array}{c}{IMF}_{t-1}^i\\ {M2}_{t-1}\end{array}]+\dots +{\mathrm{A}}_{\mathrm{t}-\mathrm{p}}[\begin{array}{c}{IMF}_{t-p}^i\\ {M2}_{t-p}\end{array}]+{\mathsf{\epsilon }}_{\mathrm{t}}$$

(7)

where A is the VAR coefficient matrix and p is lag orders. This model is used to trace short-term dynamics, including impulse response functions IRF and forecast error variance decomposition FEVD, between monetary expansion and high-frequency price movements.

5.4. Lag Length Determination Criteria

As shown in

Table 2. Optimal Lag Length Selection for VAR models.

Lags	AIC	BIC	FPE	HQIC
0	25.3	25.4	9.9 × 1010	25.3
1	9.2	9.6	9641.0	9.3
2	−2.1	−1.3	0.1	−1.7
3	−7.3	−6.3	6.3 × 10−4	−6.9
4	−12.03	−10.58 *	6.0 × 10−6	−11.4
5	−12.30	−10.5	4.6 × 10−6	−11.6 *
6	−12.44 *	−10.3	3.9 × 10−6 *	25.4

Note: * Indicates that the value is the minimum value in the corresponding test, which is used to mark the optimal lag order.

, we conducted lag length selection for VAR models using four commonly used information criteria: the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Final Prediction Error (FPE), and Hannan–Quinn Information Criterion (HQIC). Although the BIC favors Lag 4 in both models, the consistency of Lag 6 being optimal across three out of four criteria, and in both model types, provides strong support for selecting 6 lags. This selection ensures compatibility across VAR estimation and improves comparability in the subsequent impulse response and variance decomposition analyses.

5.5. Interpretation of Results of VAR Model

As shown in

Table 3. Coefficient Summary of VAR models.

	IMF_1	IMF_2	IMF_3	IMF_4
const	−0.13611	−0.01945	0.000749	2.14 × 10−5
L1.M2	1.61 × 10−7	3.83 × 10−7	−4.5 × 10−8	2.45 × 10−9
L2.M2	7.64 × 10−7	−8 × 10−7	−1.8 × 10−8	−4.8 × 10−9
L3.M2	2.98 × 10−6	5.47 × 10−7	5.2 × 10−8	3.48 × 10−10
L4.M2	−1.2 × 10−6	−5 × 10−7	3.47 × 10−8	−1.2 × 10−9
L5.M2	4.31 × 10−8	1.73 × 10−7	2.19 × 10−8	2.31 × 10−9
L6.M2	−0.13611	−0.01945	0.000749	2.14 × 10−5

, the coefficient matrix of the VAR model reveals that monetary liquidity (M2) has the strongest impact on IMF_1 and IMF_2, especially at lags 2 to 3. The response of IMF_3 and IMF_4 is negligible, with very small coefficients. This indicates that low-frequency and mid-frequency components of mutton prices (IMF_3 and IMF_4) are less sensitive to monetary changes, whereas high-frequency dynamics (IMF_1 and IMF_2) are more immediately affected.

The results reveal a frequency-dependent sensitivity to monetary shocks. The high-frequency components, IMF_1 and IMF_2, exhibit the strongest responses to M2 innovations. In particular, M2 lags at periods 2 and 3 show consistently positive and statistically notable coefficients in both series: for instance, the third lag of M2 in IMF_2 is 2.98 × 10⁻⁶ and the same lag in IMF_2 is 5.47 × 10⁻⁷. These magnitudes, although small in absolute terms, are relatively large within the context of standardized IMF fluctuations, indicating that short-term liquidity surges may induce immediate but transient adjustments in spot market pricing—likely via cost-push or inventory reshuffling channels.

In contrast, IMF_3 and IMF_4—representing medium-frequency price components—display weaker and more ambiguous coefficient patterns. Across all M2 lags, the coefficients remain close to zero and alternate in sign, suggesting that M2 exerts minimal explanatory power for medium-run mutton price dynamics in these frequency bands. This relative insensitivity may reflect the influence of non-monetary structural factors—such as regional demand cycles, supply disruptions, or policy interventions—that dominate medium-term price variation.

Overall, the VAR estimation supports the hypothesis that monetary liquidity exerts its clearest impact on short-horizon price dynamics, while its influence becomes diluted or overshadowed in medium-frequency cycles. These findings are consistent with the notion that monetary shocks first manifest through short-lived adjustments before dissipating or being absorbed by structural forces in the commodity system.

5.6. Granger Causality Test

Table 4. Results of Granger Causality Tests among Variables.

Dependent Variable	Independent Variable	Lags	p-Values
IMF_3	M2	2	0.032
IMF_4	M2	1	0.0001

reports the results of Granger causality tests examining whether changes in M2 can statistically predict the behavior of mutton price components across different frequencies. The results indicate that M2 Granger-causes both IMF_3 and IMF_4, with p-values of 0.032 and 0.0001, respectively, at lag lengths of 2 and 1. These findings suggest that monetary expansion holds statistically significant explanatory power over medium-frequency fluctuations in mutton prices.

The Granger causal relationship between M2 and IMF_4 is particularly robust, with a highly significant p-value at a short lag, implying that shifts in monetary liquidity are rapidly reflected in this component. This likely reflects transmission through substitution effects, near-term production cost adjustments, or anticipatory pricing behavior in the supply chain.

In the case of IMF_3, the presence of a two-period lag suggests a more delayed monetary transmission channel. This may be attributable to behavioral responses in household consumption or inventory adjustment cycles that unfold over slightly longer timeframes. The result aligns with the hypothesis that medium-frequency components, although not immediately responsive to M2 shocks in the VAR model, do exhibit meaningful predictive dependencies when examined through a causality framework.

In sum, these results underscore that the impact of monetary expansion is not restricted to high-frequency noise, but may extend into more persistent, policy-relevant pricing dynamics over medium horizons.

5.7. Analysis of Impulse Response Results

Figure 2 illustrates the impulse response functions (IRFs) of mutton price components to a one-standard-deviation shock in M2, estimated using the VAR model for IMF_1 through IMF_4. The responses demonstrate clear heterogeneity across frequencies, both in magnitude and temporal patterns.

The high-frequency components, IMF_1 and IMF_2, exhibit short-lived and volatile reactions. IMF_1 responds with alternating positive and negative swings in the initial periods, but its confidence bands quickly widen and encompass zero, indicating no statistically significant or stable effect of monetary shocks on ultra-short-term price dynamics. IMF_2, by contrast, shows a moderately negative and smoother trajectory, with the response peaking around step 10 before reverting. While not highly significant, this response suggests that monetary expansion may induce mild deflationary adjustments in high-frequency price components, possibly through immediate changes in market liquidity or inventory behavior.

In the medium-frequency domain, the impulse responses of IMF_3 and IMF_4 reveal more persistent and directional effects. IMF_3 exhibits a gentle upward trend, peaking mid-horizon before gradually tapering off. Although the magnitude remains modest, the positive sign may reflect temporary demand-side amplification following monetary loosening. More strikingly, IMF_4 displays a consistent and monotonic decline across the 20-step horizon, with the response remaining negative and the confidence interval narrowing over time. This suggests a statistically meaningful suppressive influence of M2 on medium-term price cycles, potentially reflecting delayed cost-push adjustments or substitution across meat categories triggered by liquidity shocks.

Collectively, these results support the view that the effects of monetary expansion on food prices are frequency-dependent and temporally asymmetric. While high-frequency components remain largely noise-driven, medium-frequency price cycles appear more responsive to systematic liquidity conditions, underscoring the importance of time-scale-aware modeling in commodity price analysis

5.8. Forecast Error Variance Decomposition

As shown in

Table 5. Results of Forecast Error Variance Decomposition.

	VAR Results
Steps	M2-IMF1	M2-IMF2	M2-IMF3	M2-IMF4
1	0.00%	0.00%	0.00%	0.00%
2	0.00%	0.00%	0.00%	0.00%
3	0.02%	0.02%	0.02%	0.02%
4	0.58%	0.58%	0.58%	0.58%
5	0.59%	0.59%	0.59%	0.59%
6	0.72%	0.72%	0.72%	0.72%
7	0.95%	0.95%	0.95%	0.95%
8	0.95%	0.95%	0.95%	0.95%
9	0.95%	0.95%	0.95%	0.95%
10	0.96%	0.96%	0.96%	0.96%
11	0.96%	0.96%	0.96%	0.96%
12	0.99%	0.99%	0.99%	0.99%
13	0.99%	0.99%	0.99%	0.99%
14	0.99%	0.99%	0.99%	0.99%
15	0.99%	0.99%	0.99%	0.99%
16	0.99%	0.99%	0.99%	0.99%
17	0.99%	0.99%	0.99%	0.99%
18	0.99%	0.99%	0.99%	0.99%
19	0.99%	0.99%	0.99%	0.99%
20	0.99%	0.99%	0.99%	0.99%
21	0.99%	0.99%	0.99%	0.99%
22	0.99%	0.99%	0.99%	0.99%
23	0.99%	0.99%	0.99%	0.99%
24	0.99%	0.99%	0.99%	0.99%
25	0.99%	0.99%	0.99%	0.99%
26	0.99%	0.99%	0.99%	0.99%
27	0.99%	0.99%	0.99%	0.99%
28	0.99%	0.99%	0.99%	0.99%
29	1.00%	1.00%	1.00%	1.00%
30	1.00%	1.00%	1.00%	1.00%

, results reveal a relatively uniform and modest contribution of M2 across all decomposed components (IMF_1 to IMF_4), with only limited variation in explanatory power over time.

For the initial forecast periods (steps 1–3), M2 explains virtually none of the variation in any IMF component, consistent with the short-run impulse response results that show minimal immediate effects. From step 4 onward, the influence of M2 rises gradually across all components, stabilizing at around 0.99% to 1.00% by step 25. This plateau suggests that the explanatory power of M2, while statistically present, remains weak in magnitude and largely symmetric across frequency bands.

Unlike prior expectations that medium-frequency components (e.g., IMF_3 and IMF_4) might show greater responsiveness to monetary shocks due to delayed transmission effects, the decomposition reveals no substantial divergence between high- and medium-frequency dynamics. This uniformity may reflect the dominance of non-monetary factors—such as supply chain frictions, seasonal consumption shifts, and regional policy interventions—that dilute the structural influence of monetary liquidity across all short-to-medium time horizons.

The FEVD findings reinforce the conclusion that monetary shocks exert only a limited and evenly distributed influence on decomposed mutton price components over the forecast window. While statistically detectable, this influence is modest in scale, suggesting that short- and medium-frequency price volatility in China’s mutton market is largely insulated from broad money fluctuations. For monetary authorities, this implies that food price stabilization in the near term may depend more heavily on microeconomic and sector-specific interventions than on aggregate liquidity management

5.9. Robustness Tests of VAR Models

To assess the adequacy and reliability of the estimated VAR models, we conduct a series of standard residual diagnostics, including the Durbin–Watson (DW) test for first-order autocorrelation, the Breusch–Godfrey LM test for higher-order serial correlation, and the Ljung–Box Q-test for whiteness of residuals.

As reported in

Table 6. Results of Robustness Tests 1.

Variable	DW	JB Stat	JB p-Value	Stat	p-Value
IMF_1	2.314687	4.167467	0.124465	42.75757	0.000025
IMF_2	1.121896	3.687335	0.158236	157.4094	1.77 × 10−27
IMF_3	0.441811	1.194705	0.550266	213.0428	6.56 × 10−39
IMF_4	0.207063	0.82189	0.663023	671.7699	4.84 × 10−136
M2	2.050184	49.22732	2.04 × 10−11	173.063	1.13 × 10−30

and

Table 7. Results of Robustness Tests 2.

Variable	DW	LM Stat	LM p-Value	Stat	p-Value
IMF_1	1.981969	2.288778	0.998818	2.125379	0.999188
IMF_2	1.961018	12.684389	0.392392	11.386020	0.496158
IMF_3	1.967302	10.353778	0.584954	9.088067	0.695390
IMF_4	1.925535	17.340442	0.137234	18.469415	0.102163
M2	2.037301	102.390821	0.000000	105.922892	0.000000

, the results show that the residuals of the M2 series clearly violate the white-noise assumption. Both the LMand the Ljung–Box Q-test strongly reject the null hypothesis of no autocorrelation, indicating persistent serial dependence in the monetary aggregate. Although the DW statistic for M2 is close to 2.0, suggesting no first-order autocorrelation, the higher-order tests reveal substantial residual correlation.

In contrast, the IMF components (IMF_1–IMF_4) perform more favorably. For IMF_1, the LM and Ljung–Box tests yield very large p-value, indicating no evidence of serial correlation. IMF_2 and IMF_3 also pass both tests, and IMF_4 is marginally acceptable with LM p = 0.137 and Ljung–Box p = 0.102. Their DW statistics are all close to 2.0, confirming the absence of significant first-order autocorrelation.

Overall, these diagnostics suggest that the VAR specification adequately captures the dynamics of the IMF components.

5.10. Wavelet Coherence Analysis of Long-Term Components

Given the high integration orders of IMF_5 and IMF_6, standard cointegration or VAR frameworks are not suitable for exploring their dynamic interactions with monetary aggregates. To address this, we employ wavelet coherence analysis, which enables the examination of localized co-movements in both time and frequency domains, particularly for non-stationary time series.

As shown in Figure 3, wavelet coherence between M2 and the long-term components of mutton prices (IMF_5 and IMF_6) reveals extensive high-coherence regions concentrated in the low-frequency band (periods > 8 years), especially from 2010 onward. According to

Table 8. Summary of Wavelet analysis.

	IMF5–M2	IMF6–M2
Number of high-coherence points	3311	3470
I2 zone (M2 leads) count	972	1224
IIF zone (IMF leads) count	1142	980
In-phase (synchronous) count	1197	1266
I2 zone share	0.293567	0.352738
IIF zone share	0.344911	0.282421
In-phase (synchronous) share	0.361522	0.364841
Total time–frequency points	7801	7801

, approximately 29.4% (IMF_5) and 35.3% (IMF_6) of these high-coherence zones fall into the I2 category, where M2 leads the price component, while synchronous movements account for over 36% in both cases. These patterns suggest a persistent and directional long-run influence of monetary expansion on food price dynamics, consistent with structural inflation channels such as cost-push transmission and liquidity overhang.

This wavelet-based evidence complements the earlier VAR results by demonstrating that while monetary shocks exert limited influence on short- and medium-frequency price fluctuations, their impact becomes increasingly pronounced at lower frequencies. In doing so, the analysis highlights the temporally layered nature of the monetary transmission mechanism and underscores the need for time-scale-aware modeling frameworks in inflation diagnostics. The coherence structure identified here offers robust support for incorporating long-horizon monetary factors into models of food price formation in emerging economies like China.

6. Discussion

This study reveals that the effect of broad money supply on mutton prices in China is highly time-scale-dependent. At high frequencies, monetary shocks exert negligible influence—accounting for less than 0.2% of price variance—whereas at medium and low frequencies, their explanatory power increases markedly, with M2 explaining over 50% of long-run price fluctuations in IMF_5 and IMF_6. Granger causality and wavelet coherence results further confirm that M2 significantly predicts medium- and long-term price behavior, offering clear empirical support for the notion that monetary expansion shapes food prices primarily over extended horizons.

The direction-switching of M2’s adjustment coefficients in cointegration analysis points to its dual role: as a feedback stabilizer in some relationships, and as a driving force in others. This pattern is consistent with the view that monetary aggregates operate through both endogenous and exogenous channels, depending on the structural frequency of price dynamics (Furceri et al., 2015). The delayed causal links suggest that M2 influences food prices via inflation expectations, cost adjustments, and aggregate demand, aligning with classic long-run monetary theory and recent empirical literature on delayed pass-through in commodity markets.

Contrary to traditional assumptions, impulse response results reveal that monetary expansion can sometimes suppress long-run price trends, particularly in IMF_5 and IMF_6. This suggests that factors such as productivity gains, supply-side policy adjustments, or structural transformation in agricultural logistics may moderate inflationary effects. Moreover, the framework does not fully control for external variables like global commodity shocks or weather disruptions, which may interact with domestic monetary signals. These limitations point to a need for caution when interpreting causality and policy relevance.

Despite its contributions, this study is subject to several limitations. First, the sample period covers only two complete long-run cycles (around eight years), which constrains the reliability of frequency domain results at very low frequencies. Second, the decomposition approach and VAR/VECM framework, while powerful, assume linear and time-invariant relationships, which may not fully capture structural breaks, nonlinearities, or regime shifts in China’s food markets. Third, the analysis relies primarily on M2 as a proxy for monetary conditions; excluding other aggregates such as credit supply, policy interest rates, or fiscal interventions may bias the attribution of causality. Fourth, external shocks—including global commodity cycles, climate variability, and policy-induced supply disruptions—are not explicitly modeled, leaving open the possibility of confounding effects. Taken together, these limitations suggest that the results should be interpreted with caution and primarily as indicative of medium- to long-term tendencies rather than precise short-run forecasts.

The findings underscore the inadequacy of one-size-fits-all inflation targeting strategies in food markets. Short-run volatility in mutton prices appears immune to monetary policy, while long-term trends are strongly shaped by liquidity conditions. For policymakers in food-sensitive economies like China, the results highlight the importance of timing and scale in monetary interventions, as well as the need to account for structural sectoral differences. Theoretically, the evidence supports models of state-contingent, frequency-sensitive monetary transmission rather than linear, time-invariant assumptions.

Future studies should incorporate external drivers such as climate variability, supply chain shocks, and international price spillovers to better isolate the impact of domestic monetary factors. Expanding the analysis to include alternative monetary aggregates (e.g., M1, credit, interest rates) or applying multivariate wavelet tools could yield richer insights into overlapping channels. Comparative studies across regions or food types may also clarify how generalizable these dynamics are in broader macro-financial contexts.

7. Conclusions

This study examines how broad money supply influences mutton prices in China through a multi-scale analytical lens, integrating empirical mode decomposition with time domain and time–frequency techniques. The results demonstrate that monetary transmission is inherently heterogeneous across frequencies: while high-frequency price fluctuations remain largely unaffected by monetary shocks, medium- and long-term components exhibit significant and directionally diverse responses. These findings challenge the notion of a uniform or contemporaneous link between money and food prices, underscoring instead the role of adjustment lags, sectoral frictions, and expectation dynamics in shaping price behavior over time.

Importantly, the evidence reveals that M2 acts not only as a passive background variable but also as an active component of the price system, with both feedback and exogenous effects depending on the structural layer under analysis. This duality aligns with evolving macroeconomic theory that emphasizes nonlinear, state-contingent channels of monetary transmission. The integration of wavelet coherence further confirms the persistence and directional structure of money–price relationships at low frequencies, particularly during periods of monetary regime shifts.

By offering a frequency-sensitive account of monetary influence, this study contributes to a more refined understanding of how liquidity conditions permeate segmented, supply-constrained markets such as food. The implications for inflation targeting and macro-financial stability are clear: monetary authorities must account for the delayed and structurally uneven transmission of monetary impulses when addressing food price volatility. Future work should extend this framework to include cross-market linkages, exogenous shocks (e.g., climate or global prices), and structural model integration to better inform the design of adaptive and temporally responsive policy tools.