Interest Rates and Business Cycles Fluctuations: a Focus on Higher Moments By Andrea Beccarini, University of L’Aquila, Italy.

Two Stylised Facts: - Non Linearity and Regimes in the Interest Rates process - Non Linearity and Regimes in the Business Cycles Variables Interest Rates and Business Cycles Fluctuations: a Focus on Higher Moments, by Andrea Beccarini

Use the C-Capm to explain the non linearity in the interest rates by expanding the expected marginal utility of future consumption for the F.O.C. Up to the fourth order: Interest Rates and Business Cycles Fluctuations: a Focus on Higher Moments, by Andrea Beccarini

This is consistent with: - Rationality assumption of the C-Capm: the representative agent is an optimiser; all information must be exploited for the agent to be rational. - Non linearity of the Business Cycles variables: the alternation of phases of recessions and expansions make non-normal the distribution of the total output. Interest Rates and Business Cycles Fluctuations: a Focus on Higher Moments, by Andrea Beccarini

The theoretical moment links interest rates with moments up to the fourth of the consumption (Business Cycles variable) Hence, non linearity in the interest rates may depend on the higher moments of Business Cycles i.e. asymmetry and kurtosis. Interest Rates and Business Cycles Fluctuations: a Focus on Higher Moments, by Andrea Beccarini

Furthermore, By testing the above model one may also verify: - Rationality of financial markets, implicit in the maximization problem and in the use of all available information. - Market risk aversion, represented by higher order utility function. - Precautionary Saving Hypothesis, represented by the significance of the second moment. Interest Rates and Business Cycles Fluctuations: a Focus on Higher Moments, by Andrea Beccarini

Asymmetry of the Business Cycles D 1 D 0 Strong Recession Rec.Expansion Strong Expansion DistributionExpected ValueVarianceThird Moment D0 E[x]=0Var[x] E[(x-E(x))^3]=0 D1 E[x]=0Var[x] E[(x-E(x))^3]>0 Risk aversion implies the preference of a positive third moment. Interest Rates and Business Cycles Fluctuations: a Focus on Higher Moments, by Andrea Beccarini

Statistical models for the Business Cycles variable: 1.Switching in Mean model (SM): 2.Switching in Mean, Autoregressive model (SWAR): Interest Rates and Business Cycles Fluctuations: a Focus on Higher Moments, by Andrea Beccarini

Moments of the Business Cycles variable as a function of the Switching in Mean model’s parameters: - First moment: - Second moment: - Third moment: Interest Rates and Business Cycles Fluctuations: a Focus on Higher Moments, by Andrea Beccarini

Estimation Strategy: Dependent variable: Euro area 3-months interest rates Technique: Linear model (OLS). Regime Switching model. Regressors: 1°, 2° and 3° moment of the Euro area GDP growth rate, (Business Cycles variable). Interest Rates and Business Cycles Fluctuations: a Focus on Higher Moments, by Andrea Beccarini

OLS regression’s results of real interest rates on Gdp moments (SM model). The first and third moments are significant and they have the expected sign.

Interest Rates and Business Cycles Fluctuations: a Focus on Higher Moments, by Andrea Beccarini OLS regression’s results of real interest rates on Gdp moments (SWAR(1) model). The first and third moments are significant and they have the expected sign.

Interest Rates and Business Cycles Fluctuations: a Focus on Higher Moments, by Andrea Beccarini R-S regression’s results of real interest rates on Gdp moments (SM model). The first, the second and third moments have the expected sign but they are only jointly significant.

Interest Rates and Business Cycles Fluctuations: a Focus on Higher Moments, by Andrea Beccarini R-S regression’s results of real interest rates on Gdp moments (SWAR(1) model). The first, the second and third moments have the expected sign but they are only jointly significant.

Main Results: - The positive relationship between the first moment of Gdp and the first difference of interest rates, consistently with basic C-Capm. - The negative relationship between the second moment of Gdp and the first difference of interest rates, hence Precautionary Saving motivations. - The positive relationship between the third moment of Gdp and the first difference of interest rates, consistently with the presence of relevant information in higher moments. Interest Rates and Business Cycles Fluctuations: a Focus on Higher Moments, by Andrea Beccarini

Other Results: - The importance of fitted moments of the Gdp rather than the row time series. - The evidence of the rational expectation formation rather than the adaptive formation. - The Precautionary Saving hypothesis rather than the Permanent Income Hypothesis. Interest Rates and Business Cycles Fluctuations: a Focus on Higher Moments, by Andrea Beccarini

The business cycles variable (Gdp) is not normal but shows signs of asymmetry; this is due to the alternation of recessions and expansions. The C-Capm implies the considerations of high moment of state variable (see the Taylor’s expansion up to the fourth order). All in all: - The theoretical model and the statistical evidence find a robust connection with interest rates and moments of the B.C up to the fourth order. - Rationality of Financial market, Risk Aversions, Precautionary Saving are sustained by theory and evidence. The interest rates are non-linear and embed a mixture of different stochastic processes.

Interest Rates and Business Cycles Fluctuations: a Focus on Higher Moments, by Andrea Beccarini Annex 1: Estimated parameters of the SM (switching in mean) model: The average rate of growth of the Gdp during expansions is 0.76; during recessions is The probability of remaining in the expansion phase is The probability of remaining in the recession phase is 0.71.

Interest Rates and Business Cycles Fluctuations: a Focus on Higher Moments, by Andrea Beccarini Annex 2: Estimated parameters of the SWAR(1) (switching in mean, autoregressive) model: The average rate of growth of the Gdp during expansions is 0.62; during recessions is The probability of remaining in the expansion phase is The probability of remaining in the recession phase is 0.43.

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Interest Rates and Business Cycles Fluctuations: a Focus on Higher Moments, by Andrea Beccarini