Dynamic Relationship Analysis Between Gas Used and Gas Price in Ethereum Using VAR and Granger Causality Tests

his study investigates the dynamic relationship between network activity and transaction fees in the Ethereum blockchain by analysing the interaction between Gas Used and Gas Price through a multivariate time series model. The objective is to determine whether variations in network demand influence short-term gas price fluctuations. Daily data of Gas Used and Gas Price were transformed into different logarithmic forms to ensure stationarity. The Augmented Dickey–Fuller test confirmed that both variables are stationary at the five percent significance level, with ADF statistics of −6.21 for Δlog (Gas Used) and −7.12 for Δlog (Gas Price), and p-values below 0.001. The Vector Autoregression model was estimated with an optimal lag length of fourteen days, selected using the Akaike Information Criterion, reflecting the persistence of network and fee dynamics. The results of the Granger causality test indicate a unidirectional causal relationship from Gas Used to Gas Price, with an F-statistic of 3.72 and a p-value of 0.018, suggesting that fluctuations in network demand significantly precede changes in gas pricing. The reverse direction is not significant, with an F-statistic of 1.26 and a p-value of 0.28, indicating that transaction fees do not predict network activity. The impulse response analysis shows that a one standard deviation shock in Gas Used increases Gas Price for two to three days before returning to equilibrium, while shocks in Gas Price have minimal effects on Gas Used. These findings confirm that Ethereum’s fee market operates primarily as a demand-driven mechanism were congestion and transaction volume shape short-term gas price movements.