Chilean Money Demand: A Cointegration Analysis

The study begins by outlining the macroeconomic context of Chile from the mid-1980s to 2000, highlighting key trends. Inflation significantly decreased from over 30% to under 4% annually by mid-2000. This deflation occurred alongside steady real output growth averaging 7.3% annually until mid-1998, making Chile a fast-growing economy globally. However, a sharp recession from late 1998 to mid-1999, the first under the new independent Central Bank (established in 1989), marked a notable economic shift. The research aims to examine the transactions demand for money in Chile within this context, particularly focusing on how the private sector's money demand responds to the Central Bank's inflation-targeting policy and the 1998-99 recession. The study justifies its contribution to the already extensive literature on Chilean money demand by emphasizing the importance of regular review for effective Central Bank policymaking, given the reliance on money demand assumptions in policy design. The study also acknowledges the significance of analyzing the impact of the inflation-targeting policy and the 1998-99 recession on the accuracy of money demand models.

The paper adopts a standard portfolio approach to model money demand in an open economy, starting with a representative private agent holding four assets: money, real capital, and claims on the rest of the world. Money is directly included in the agent's utility function, capturing transaction costs and cash-in-advance constraints. The study discusses the common form of conditional demand function (Equation 4) and mentions various estimation approaches found in existing literature, including non-linear least squares and artificial neural networks. The authors highlight two key specification issues: the role of real financial wealth and the treatment of asset prices. Regarding financial wealth, the analysis acknowledges the ambiguous impact of increased wealth on money demand due to offsetting income and portfolio diversification effects. The study reviews prior research on wealth's role in money demand models in the UK and mentions studies on Argentina and VAR-based work conducted within the Central Bank of Chile. The paper’s empirical analysis will focus on key asset market information used by the private sector for determining its money demand, rather than a comprehensive examination of the Chilean asset market's term structure. The study also explains the use of the Tasa Efectiva Politica (TEP) as a key interest rate under the inflation-targeting regime. The TEP is converted to an ex-post nominal interest rate in the empirical work for analysis.

The empirical analysis begins with an examination of the time-series characteristics of the data using a battery of unit root tests (Augmented Dickey-Fuller, Phillips-Perron, and KPSS tests), which are conducted to assess the stationarity of various time series. The results show that the macroeconomic time series exhibit trend-stationary behavior, yet this trend is best characterized as stochastic rather than deterministic. Based on these findings, the study employs Johansen's (1995) cointegration method to analyze long-run relationships within a vector error correction model (VECM). The authors then present the results, discussing the income elasticity of money demand and the interest rate elasticity. The analysis also considers alternative specifications, incorporating various measures of economic activity (LIMAE and LIMAEX), different functional forms for the interest rate (logarithmic and semi-log), and additional asset returns. The effects of deposit interest rates, inflation, real interest rates, and the exchange rate on money demand are investigated. The study also assesses the statistical significance and economic plausibility of the estimated parameters within the model.

The paper then evaluates the model's out-of-sample forecasting performance. The initial out-of-sample forecasts, using the model estimated up to 1998, show poor performance, particularly in predicting the 1998-99 recessionary period. The model systematically overpredicts money demand during the recovery phase. This leads to a discussion of potential reasons for this poor forecast accuracy, such as model misspecification or a structural break in the money demand function related to the regional stabilization crisis of 1998. The analysis then focuses on addressing the issue of the forecast error by incorporating a correction for a shift in the long-run equilibrium. The authors re-estimate the model, incorporating an intercept correction to account for the change in velocity of circulation, improving out-of-sample forecast accuracy. They highlight the importance of this adjustment and discuss its implications for understanding long-run money demand behavior in Chile.

The initial step involves a thorough examination of the time-series characteristics of the key macroeconomic variables used in the money demand model. These variables include money aggregates, income measures, and wealth proxies. Recognizing the low power of standard unit root tests, the study employs a battery of tests to assess stationarity. These include the Augmented Dickey-Fuller (ADF) and Phillips-Perron (PP) tests, which test the null hypothesis of a unit root (non-stationarity). Conversely, the Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test assesses the null hypothesis of stationarity. Further tests examine joint hypotheses about stochastic and deterministic components in the time series. The results reveal a complex picture. While the series clearly exhibit trending behavior, the tests provide ambiguous evidence as to whether this trend should be treated as deterministic or stochastic. The analysis considers both trend-stationary and difference-stationary representations for the series, concluding that a stochastic trend (difference-stationary) representation is more appropriate for the subsequent analysis, given the data and the theoretical implications. This choice is justified by the argument that assuming a deterministic trend might be overly restrictive, particularly given the unusual nature of the sample period.

Following the time-series analysis, the study proceeds to investigate potential long-run relationships (cointegration) between the macroeconomic variables using Johansen's (1995) cointegration methodology within the framework of a vector error correction model (VECM). The choice of difference-stationary representation from the previous step directly impacts the interpretation of the cointegrating characteristics. The analysis explores several alternative model specifications to determine the most appropriate representation of the data. This involves examining the properties of different income variables—the standard monthly index of economic activity (LIMAE) and a modified index excluding agriculture and copper mining (LIMAEX)—and employing both logarithmic and semi-log specifications for the nominal policy interest rate. The choice of these specifications directly impacts the results of the cointegration tests. Further specification issues are explored including the role of real financial wealth, alternative interest rate measures (deposit rates), and the impact of inflation volatility on money demand. The paper's methodology includes extensive testing to determine the most efficient model based on the observed data and statistical properties. Results from trace statistics are used to determine the most appropriate model specification regarding deterministic components.

A significant portion of the analysis focuses on the role of real financial wealth in the money demand model. The authors acknowledge that relatively few studies include wealth as a regressor due to data limitations. However, where reliable data exist, studies have demonstrated a considerable impact of net wealth on money demand. The research draws parallels with studies in the UK which identified wealth effects in money demand functions, noting that the wealth effect captures two offsetting processes: a classical income effect (assuming money is a normal good) and a portfolio diversification effect. The net effect of rising wealth on money demand is therefore ambiguous, though empirical evidence from the UK and other studies suggests a positive but often small effect. The Chilean study aims to contribute to this literature by investigating whether, and to what extent, real financial wealth affects money demand in the Chilean context, given the availability of relevant data for the 1986-2000 period. This is crucial for refining the accuracy and overall explanatory power of the model.

The research explores alternative specifications for the opportunity cost of holding money. The baseline model uses the short-run nominal policy interest rate (TEP), but the authors investigate whether adding other interest rate measures or decomposing the nominal interest rate improves the model's fit. Three main variations are considered. First, the impact of including the interest rate on deposits is examined. Second, the nominal interest rate is decomposed into its inflation and real interest rate components, to determine if there is a differential response to each component. Finally, the potential for currency substitution is explored by including the ex-post rate of depreciation of the nominal exchange rate. The findings suggest that a model defined solely in terms of the short-run nominal policy rate of interest provides the most efficient specification for the transactions demand for money over the study period. Neither adding additional interest rates, nor decomposing the nominal rate, nor including exchange rate effects significantly improves the model's statistical power. This reinforces the importance and sufficiency of the nominal policy rate as a key driver of money demand in the Chilean economy during the study period.

The paper concludes that a simplified model utilizing only the short-run nominal policy interest rate is most efficient for representing the transactions demand for money during the period under study. This conclusion is reached after an extensive evaluation of alternative model specifications, each designed to enhance the accuracy and explanatory power of the money demand model. The authors demonstrate the process of model selection by systematically testing various specifications and justifying their choice based on the statistical properties of the different models. This includes assessing the statistical significance of estimated coefficients, the overall fit of the models, and the out-of-sample predictive power. The emphasis is on finding the most parsimonious model that adequately captures the key relationships and provides robust forecasts. The justification for model selection prioritizes both statistical efficiency and economic plausibility of the estimated parameters, aligning with the goals of constructing a reliable and practically useful model for predicting money demand in Chile. The selection of a simpler model, despite the availability of more complex options, highlights the importance of parsimony and robustness in econometric modeling.

This section details the estimation of a dynamic error-correction model (ECM) for the transactions demand for money in Chile. The ECM incorporates both short-run dynamics and the long-run equilibrium relationship identified through the cointegration analysis. The model's specification includes the error-correction term, representing deviations from the long-run equilibrium, and lagged values of the relevant variables (income, interest rates, and potentially wealth). The significance of the error-correction coefficient is crucial; a negative and significant coefficient supports the assumption of difference-stationarity (as opposed to trend-stationarity) for the underlying variables. This means that the model accurately captures the adjustment process towards long-run equilibrium. The study further investigates the impact of inflation volatility on money demand by including a measure of inflation volatility (the change in the 12-month moving standard deviation of monthly inflation) as a regressor. The inclusion of this variable is supported by the observation that the private sector tends to hold lower money balances when inflation is volatile. The estimated model provides insights into the short-run and long-run elasticities of money demand with respect to income and interest rates, providing crucial information about the dynamic response of money demand to economic shocks.

A key aspect of the analysis involves evaluating the model's out-of-sample forecasting performance. The model's ability to accurately predict money demand during the 1998-99 recession, a period of significant economic disruption in Chile, is of particular interest. The initial out-of-sample forecasts, using the error-correction model estimated up to 1998, exhibit significant shortcomings. The model systematically overpredicts money demand during the recovery phase of 1999 and into 2000. This poor performance is analyzed, considering two possibilities: model overfitting or a structural break due to the negative shock to money demand following the regional stabilization crisis of 1998. To address the issue, the model is adjusted by adding an 'intercept-correction' to account for the observed shift in the velocity of circulation around late 1998. This adjustment significantly improves the out-of-sample forecast accuracy, emphasizing the importance of capturing structural changes in the long-run equilibrium of the money demand function. The study concludes that the inclusion of an intercept correction removes the systematic bias observed in the previous out-of-sample forecasts, showing the importance of accommodating structural breaks in econometric models.

The study concludes that a relatively simple, yet robust, single-equation error-correction model effectively captures the transactions demand for money in Chile from 1986 to 2000. This model outperforms the partial adjustment model used by the Central Bank of Chile in terms of within-sample forecast accuracy. This superiority is attributed to the error-correction model's inherent ability to handle cointegration and the inclusion of inflation volatility as a regressor. Crucially, after accounting for a structural shift in the velocity of circulation around late 1998, the model demonstrates good out-of-sample predictive power, effectively eliminating the systematic forecast errors observed in the previous model. The model's success in forecasting during periods of both economic growth and the 1998-99 recession highlights its robustness and reliability for policy analysis. The strong performance of the error correction model, particularly compared to the Central Bank's existing model, strengthens the case for utilizing improved econometric techniques for monetary policy analysis.

Despite its success, the study identifies limitations and suggests avenues for future research. First, the improved out-of-sample forecasting performance relies on an 'intercept-correction' to the long-run money demand function, introduced to accommodate the velocity shift in late 1998. Further research is needed to determine the persistence of this shift and whether it reflects a temporary or permanent change in money demand behavior. This necessitates the incorporation of additional data beyond the available 1986-2000 sample period to provide a clearer understanding of long-run equilibrium. Second, the study acknowledges that the measure of wealth used is rather rudimentary, overlooking non-financial assets like housing and other financial assets such as pensions. A more comprehensive measure of private sector real wealth is required to improve the accuracy of the model and to better capture the complexities of wealth effects on money demand. Finally, expanding the scope of the analysis to include the demand for interest-bearing financial assets is suggested, as this would allow for a more thorough investigation of financial innovation and wealth effects—factors which are increasingly important in modern economies.