Research Article 
Corresponding author: Nikita D. Fokin ( fokinikita@gmail.com ) © 2024 Nonprofit partnership “Voprosy Ekonomiki”.
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Citation:
Fokin ND, Malikova EV, Polbin AV (2024) Timevarying parameters error correction model for real ruble exchange rate and oil prices: What has changed due to capital control and sanctions? Russian Journal of Economics 10(1): 2033. https://doi.org/10.32609/j.ruje.10.111503

This paper aims to analyze changes in the longterm and shortterm oil price elasticities of the real ruble exchange rate, as well as the speed of convergence of the exchange rate to a longterm equilibrium. The analysis is conducted using an error correction model with timevarying parameters. The results indicate that the shortterm oil price elasticity of the exchange rate has consistently increased after the 2008–2009 crisis, reaching its peak in 2015. This peak coincided with the implementation of an inflation targeting regime by the Bank of Russia, as well as economic crises caused by sanctions and a decline in oil prices. During this period, the shortterm elasticity exceeded the longterm elasticity, leading to a significant “overshooting” effect in response to oil shocks. Subsequently, the shortterm elasticity gradually decreased as the economic situation stabilized, and by 2022–2023, it became insignificant. This was influenced by such factors as the inaction of financial markets and the implementation of capital controls. On the other hand, the longterm oil price elasticity remained relatively stable throughout most of the observation period, although it decreased during crisis periods.
real ruble exchange rate, oil prices, error correction model, timevarying parameters model, capital control, sanctions, Russian economy.
The real effective exchange rate (REER) assesses a national currency’s value against a weighted average of major trading partners’ currencies, serving as a primary indicator of a country’s international competitiveness. It is essential to model the REER for formulating effective monetary policies and analyzing their consequences.
The terms of trade are a major determinant of the real ruble exchange rate. Given that oil, oil products, and natural gas constitute vital components of Russian exports, oil prices are often used as a proxy for the terms of trade.
This study examines the relationship between the ruble real effective exchange rate and oil prices, utilizing an error correction model with timevarying parameters. The analysis covers data spanning from 1994 to 2023 encompassing shifts in Russia’s monetary policy regimes, such as the ruble devaluation during the 2008–2009 crisis and the transition to a floating exchange rate regime with inflation targeting in 2014. This approach allows an estimation of the error correction model while accommodating changes in the studied relationship.
A substantial body of literature underscores the influence of oil prices on the real ruble exchange rate. Utilizing an error correction model is a prominent approach in studying this dependence. Cointegration, in particular, provides an effective foundation for modeling longterm relationships. Many studies aim to capture temporal shifts in this relationship, accounting for structural breaks, crises, and economic reforms.
Various research groups modeled the relationship between the exchange rate and oil prices (
Sosunov and Shumilov (2005) estimated an error correction model, factoring in terms of trade, productivity in the nontradable goods sector, and capital flows as fundamental variables for REER analysis. The estimated longterm oil price (terms of trade) elasticity of the real effective exchange rate stood at 0.64 (data up to 2003), with an adjustment rate of –0.3, indicating relatively swift convergence to equilibrium. Other studies endeavor to incorporate regime changes when modeling the relationship between the real effective ruble exchange rate and oil prices (
This paper attempts to estimate a timevarying parameter error correction model (TVPECM) for the real ruble exchange rate, capturing fluctuations in all parameters over time through a random walk process. This class of models is widely used in macroeconomic research. Pioneering works (
In recent years, the relationship between the real exchange rate and oil prices has been studied in the context of the COVID19 pandemic and the uncertainty associated with oil prices.
Future research could focus on identifying causes of oil shocks (
To examine the cointegration relationship between the ruble’s real effective exchange rate and oil prices, a timevarying parameters error correction model (TVPECM) is employed. This model enables the evaluation of changes in both longterm and shortterm relationships between the two variables and utilizes data from the maximum available time period. Additionally, this approach is capable of capturing nonlinear relationships within the data. The estimation of this model was conducted using the Bayesian approach. The analysis is based on monthly data spanning from January 1994 to June 2022. The equation to be estimated is given below:
Δy_{t} = θ_{t} (y_{t}_{–1} – α_{t}_{–1} – β_{t}_{–1} x_{t}_{–1}) + ϕ_{t} Δy_{t}_{–1} + ψ_{t} Δx_{t} + ε_{t} , (1)
where y_{t} — natural logarithm of the ruble’s real effective exchange rate; x_{t} — natural logarithm of the real price of Brent crude oil; ε_{t} — random error that follows a normal distribution, N(0, σ_{ε}^{2}).
We opted for this simple and concise specification as the experiments conducted indicated that the other lags did not have a significant impact.
To confine the adjustment parameter within the range of (–1; 0), we employ the following transformation:
${\theta}_{t}=f\left({\kappa}_{t}\right)=\frac{{e}^{{\kappa}_{i}}}{1+{e}^{{K}_{i}}}$(2)
where κ_{t} and other parameters represent the random walk process:
κ_{t} = κ_{t}_{–1} + ν_{t} , (3)
α_{t} = α_{t}_{–1} + η_{t} , (4)
β_{t} = β_{t}_{–1} + γ_{t} , (5)
ϕ_{t} = ϕ_{t}_{–1} + ζ_{t} , (6)
ψ_{t} = ψ_{t}_{–1} + ξ_{t} . (7)
Following
${\alpha}_{0}~\mathrm{N}(\hat{{\alpha}^{OLS}},4{\sigma}_{\hat{{\alpha}^{OLS}}}^{2}),$ (8)
${\beta}_{0}~\mathrm{N}(\hat{{\beta}^{OLS}},4{\sigma}_{\hat{{\beta}^{OLS}}}^{2}),$ (9)
${\varphi}_{0}~\mathrm{N}(\hat{{\varphi}^{OLS}},4{\sigma}_{\hat{{\varphi}^{OLS}}}^{2}),$ (10)
${\psi}_{0}~\mathrm{N}(\hat{{\psi}^{OLS}},4{\sigma}_{\hat{{\psi}^{OLS}}}^{2}),$ (11)
The mean and variance of prior distribution for κ_{0} were calculated using the delta method:
${k}_{0}~\mathrm{N}({f}^{(1)}\left(\hat{{\theta}^{OLS}}\right),4{\sigma}_{\hat{{\theta}^{\text{OLS}}}}^{2}{\left[{f}^{(1{)}^{\text{'}}}\left(\hat{{\theta}^{\text{OLS}}}\right)\right]}^{2}),$ (12)
where f (·) corresponds to the function from equation (2).
For the standard deviation of the error ε_{t}, the lognormal prior distribution is used:
$\mathrm{ln}\sigma {}_{e}~N(\mathrm{ln}\sigma \hat{{}^{OLS}},1)$, 1) . (13)
Precision of error distributions in equations (2)–(7), τ = 1/σ^{2}, are treated as hyperparameters. The following values are used: τ^{(α)} = τ^{(β)} = 2000, τ^{(κ)} = 500, τ^{(ϕ)} = τ^{(ψ)} = 250.
After calibrating the prior distributions, the TVPECM model was estimated on the subsample from January 2000 to June 2023 using WinBUGS, where the posterior distribution of parameters is estimated using MCMC methods.
In this section the results of the DFGLS test for unit roots and the Engle–Granger test (
Variable  Observed Value  Number of Lags 
y_{t}  –0.52  3 
∆y_{t}  –12.09^{***}  0 
x_{t}  –1.23  2 
∆x_{t}  –9.01^{***}  0 
Test for cointegration was conducted using the twostep Engle–Granger procedure. In the first step, a cointegration relation is estimated using OLS on the sample data from 2000 to 2023. In the second step, the residuals of the estimated relation were tested for a unit root using MacKinnon critical values (
The ADF test with MacKinnon critical values results for residuals of the estimated with OLS cointegration relation.
Variable  Observed value  Critical values 
${y}_{t}\hat{{a}^{OLS}}\hat{{\xdf}^{OLS}}{x}_{t}$  –5.68^{***}  1% critical value = –3.94 
5% critical value = –3.36  
10% critical value = –3.06 
The results of the model estimation indicate that the parameter of adjustment to the longterm equilibrium, θ_{t}, is significant for the entire period. The estimate ranges from –0.15 to –0.11 (Fig.
Correction parameter (θ_{t}) estimate and 68% confidence interval. Source: Authors’ calculations.
The coefficient of the current difference of the logarithm of oil prices (shortterm elasticity)^{1} is depicted in Fig.
Shortterm oil prices elasticity of the real ruble exchange rate parameter (ψ_{t}) estimate and 68% confidence interval. Source: Authors’ calculations.
This could be attributed to the fact that in 2022, there were significant restrictions on operations in the financial market, which affected the dynamics of the exchange rate. The oil market has a characteristic feature of price rigidity in contracts, meaning that substantial supplies of Russian oil, gas, and oil products are determined by fixed contract prices. In a period of flexible exchange rate formation, an increase in prices on the global oil market leads to expectations of future changes in contract prices. This, in turn, results in an inflow of petrodollars into the country and strengthens the exchange rate. This process involves an information channel, where economic agents anticipate a future strengthening of the ruble and engage in operations that strengthen it at present.
However, due to the restrictions in the financial market, this channel does not operate effectively. The dependence of the ruble exchange rate on the current increase in oil prices diminishes, and adjustments towards longterm equilibrium occur slowly. In 2023, there was some relaxation of financial restrictions. Nevertheless, sanctions were imposed, including price ceilings for oil purchases and limitations on insurance for oil transportation by sea. As a result, actual sales prices of oil became largely undisclosed, and world oil prices became a noisy indicator of actual oil sales. Moreover, aggregate statistics on actual export earnings from oil sales were published with a significant delay. Consequently, the dynamics of the ruble exchange rate became largely influenced by shocks in economic agents’ expectations.
Our findings indicate that longterm elasticity^{2} of the real exchange rate remains relatively stable throughout the analyzed period (Fig.
Longterm oil prices elasticity of the real ruble exchange rate parameter (β_{t}) estimate and 68% confidence interval. Source: Authors’ calculations.
The overshooting effect refers to a situation where the real exchange rate responds more in the short run to a shock, such as changes in oil prices, than it does in the long run. In this case, the value of the longrun change in the real exchange rate is significantly lower than the initial change observed after the shock. From 2010 to 2021, there was a prolonged period where this overshooting effect was observed in the response of the Russian ruble’s real exchange rate to oil shocks. This means that when there was a shock in oil prices, the ruble’s real exchange rate would initially experience a larger change compared to the longterm equilibrium level. However, over time, the real exchange rate would gradually adjust and move closer to its longrun value.
Fig.
The real ruble exchange rate timevarying impulse response function to a 10% permanent oil prices shock. Source: Compiled by the authors.
This figure illustrates our previous findings regarding the adaptation trajectory of the real exchange rate to equilibrium in response to oil price shocks. The response trajectory evolves over time. In the initial period under consideration (2000–2009), the dynamics of the responses were conventional, characterized by a slow adjustment towards equilibrium within the framework of a managed nominal exchange rate regime. Following the 2008–2009 crisis and the implementation of a more flexible exchange rate, the trajectory underwent changes. The shortterm response of the real exchange rate became more pronounced than the longterm response (the overshooting effect), which was particularly evident in 2014–2015, caused by the transition of the Bank of Russia to the inflation targeting regime and the abandonment of interventions in the nominal exchange rate, despite sporadic interventions in certain periods. The introduction of a fiscal rule in 2017 began to steer the response trajectory back towards the patterns observed in the 2000s. However, the subsequent pandemic led to a return to the 2014–2015 dynamics. Of particular interest is the current period of 2022–2023, during which the response of the real exchange rate has once again exhibited a smooth adjustment in response to shocks. At present, the impulse response trajectory is reverting to the dynamics observed during the managed nominal exchange rate regime, which carries the risk of higher inflation compared to a more flexible exchange rate regime.
Additionally, we explore the use of the ARX model as an alternative to the ECM model to test the robustness of our results. The ARX model does not assume cointegration between the variables being analyzed. It is possible that we may have overlooked other important longterm determinants of the ruble’s real exchange rate, such as the productivity differential between the tradable and nontradable sectors compared to trading partners. The omission of this variable from our econometric model is due to the difficulty of its measurement.
The absence of these important longterm exchange rate determinants may introduce problems in evaluating the ECM model due to the incorrect specification of the cointegration relationship. However, this is not a problem for evaluating the vector autoregressive (VAR) model in first differences for a subset of noncointegrated variables. According to
Furthermore, if the initial process is described by a vector error correction model (VECM), it can be easily represented as a VAR model by introducing a new variable representing the deviation from the cointegration relationship. In practice, when the moving average (MA) component of the VARMA model is invertible, it can be approximated by a finiteorder VAR model.
We estimate the ARX model with the same number of lags as in the ECM model (other lags were insignificant):
Δy_{t} = ϕ_{t} Δy_{t}_{–1} + ψ_{t} Δx_{t} + ε_{t} , (14)
where ε_{t} — normal distributed random variable, N(0, σ_{ε}^{2}). The parameters ϕ_{t} and ψ_{t} are random walks (see equations 6–7), and their values defined as in ECM model (see equations 10–11). For the standard deviation of the error ε_{t}, the lognormal prior distribution is used (see equation 13).
Here we are taking the OLS estimates from ARX model estimated on the 19941999 sample.
Figs
Shortterm oil prices elasticity of the real ruble exchange rate parameter (ψ_{t}) estimate in the ECM and the ARX models and 68% confidence interval. Source: Authors’ calculations.
Real ruble exchange rate first lag parameter (ϕ_{t}) estimate in the ECM and the ARX models and 68% confidence interval.
Source: Authors’ calculations.
Based on these figures, it can be observed that the point estimates of the parameters exhibit similar dynamics. While there are some differences in the shortterm elasticity between the ARX and ECM models, the overall trends remain consistent. In both models, the shortterm elasticity experiences growth throughout most of the period until the 2022 crisis.
Based on the results, despite a sharp decline in the shortterm elasticity of the exchange rate concerning oil prices, the longterm elasticity remains high. Analyzing only the shortterm correlations between the exchange rate and oil prices may create the illusion that the dependence of the exchange rate on oil prices has weakened, when in fact it has only weakened in the short term. This consideration is crucial when formulating economic policy measures, as the ruble exchange rate impacts inflation through the exchange rate passthrough effect on prices (
Currently, significant risks exist regarding potential future decreases in oil revenues due to sanctions and reduced global business activity. Additional risks arise from the international community’s intention to curb hydrocarbon consumption as part of the fight against global warming. Consequently, substantial risks are present for a weakening of the ruble exchange rate, which could lead to negative socioeconomic consequences. Therefore, economic authorities must develop a comprehensive set of measures to support the population and citizens in the event that such negative scenarios materialize.
In both the media and academic circles, an alternative perspective has often been presented, suggesting that the overall relationship between the exchange rate and oil prices has diminished. Such a viewpoint could lead to distortions in the perceptions of economic agents and decisionmakers.
The analysis of the real ruble exchange rate in this study was conducted using an error correction model with timevarying parameters. This approach allowed for an assessment of the relationship between the real effective exchange rate and oil prices over a wide time interval, including periods of crises and changes in monetary policy regimes. The estimates obtained in this study are consistent with previous research findings and also reveal a change in the relationship based on new data for 2023.
As demonstrated in this paper, the process of adjusting the real ruble exchange rate has undergone significant changes during the observation period. Initially, the adjustment process was slow due to low shortrun elasticity. The speed of adjustment, as indicated by the correction parameter, increased slightly compared to shortrun elasticity. This suggests that the adjustment of the real exchange rate to oil shocks was driven more by inflation than by sizable changes in the nominal exchange rate, even during periods of high oil price growth.
Following the recession in 2009, the situation changed, and the real exchange rate became more flexible. This flexibility continued for five years after the Bank of Russia switched to an inflation targeting regime instead of managing the nominal exchange rate. The fast adjustment of the real exchange rate to a new equilibrium caused by oil shocks, and even the occurrence of “overshooting” effects, where the real exchange rate changes more in the shortterm than in the longterm, were observed during this period.
Currently, the mechanism has returned to its pre2009 version, which can be attributed to the impact of sanctions and capital controls, resulting in less flexibility of the real exchange rate. However, the longterm elasticity remains stable. Therefore, analyzing only the shortterm correlation between the exchange rate and oil prices may create an illusory impression that the overall relationship between the exchange rate and prices has diminished.
We would like to thank Andrei Shumilov and an anonymous reviewer for useful comments and suggestions. Andrey Polbin prepared the paper in the framework of a research grant funded by the Ministry of Science and Higher Education of the Russian Federation (grant ID: 075152022326).