[Paper Review] Kalman Filter in the Problem of the Exchange and the Inflation Rates Adequacy To Determining Factors

N. S. Gonchar, Wolodymyr Hlib Kozyrski+2 more|ArXiv.org|Mar 13, 2025

Economic Issues in Ukraine4 citations

TL;DR

The paper formulates an unobservable state-space model for the hryvnia/dollar exchange rate and inflation, applies Kalman filtering to estimate their adequacy to economic determinants, and presents policy implications for Ukraine.

ABSTRACT

Using introduced concept of the exchange and inflation rates adequacy, the relevance of them to the determining factors is found. We established close positive relation between hryvnia / dollar exchange and inflation rates, fiscal deficit, price level of energy sources, and money supply. On this basis, we give proposals for state macroeconomic policy to stabilize Ukrainian economy.

Motivation & Objective

• Introduce the concept of adequacy of the hryvnia/dollar exchange rate and inflation to their determining factors in a non-competitive economy.
• Formulate an unobservable stochastic state-space model for the exchange rate and inflation rate.
• Apply Kalman filtering to estimate the unobservable state and assess factor adequacy.
• Identify correlations between exchange rate, inflation, and macroeconomic variables (deficit, energy prices, money supply).
• Provide macroeconomic policy recommendations to stabilize Ukraine's economy based on empirical findings.

Proposed method

• Formulate a two-dimensional unobservable state x_k representing adequate exchange rate and inflation rate evolving as x_{k+1}=F_{k,k+1} x_k + w_k with F as identity and w_k as Gaussian noise.
• Model observed factors Y_k as Y_k = H_k x_k + ν_k with Gaussian observation noise ν_k.
• Determine H_k by minimizing a quadratic functional of observation residuals to obtain the Kalman gain G_k and update the state estimate.
• Use Kalman recursion: x_k^- = F_{k,k-1} x_{k-1}^-, P_k^- = F_{k,k-1} P_{k-1} F_{k,k-1}^T + Q_{k-1}, G_k = P_k^- H_k^T (H_k P_k^- H_k^T + R_k)^{-1}, x_k = x_k^- + G_k (Y_{k+1} - H_k x_k^-), P_k = (I - G_k H_k) P_k^-.
• Apply regression-based growth and regression diagnostics to connect observed monetary variables (money supply, deficits, energy prices) to exchange rate and inflation dynamics across 2012-2014.
• Derive money-circulation equations and PPP-informed relations to interpret the 2012-2014 dynamics and to support policy recommendations.

Experimental results

Research questions

• RQ1 To what extent are the hryvnia/dollar exchange rate and the inflation rate adequately determined by selected macroeconomic factors?
• RQ2 Can a Kalman-filter-based state-space model recover the unobservable adequate exchange rate and inflation rate from observable indicators?
• RQ3 What are the quantified relationships between exchange rate, inflation, budget deficits, energy prices, and money supply in Ukraine during 2012-2014?
• RQ4 What macroeconomic policy prescriptions arise from the estimated relationships to stabilize the Ukrainian economy?

Key findings

• A close positive correlation was found between the hryvnia/dollar exchange rate and inflation, budget deficit, energy prices, and money supply.
• The exchange rate during 2012-2013 was artificially restrained, preceding a sharp depreciation in 2014.
• The estimated model yields high determination coefficients in several specifications (e.g., R^2 values around 0.77 to 0.99 for various regressions), indicating strong fit between factors and the exchange rate or inflation.
• Money circulation rate trends indicate inflation unwinding and deteriorating living standards during 2012-2014.
• Policy implications include stabilizing the exchange rate to stabilize inflation, and a balanced macro policy targeting deficits and energy prices to achieve stability.