The Theory And Empirical Research Of Nonlinear Monetary Policy Rules

The central bank can implement discretionary or monetary policy rule to controlmacroeconomy. Discretionary monetary policy means the central bank take the discretionarymeasures in accordance with the judgment of the economic situation, to achieve the establishedobjectives of monetary policy. However, Friedman (1969) pointed out that in the context ofdiscretionary monetary policy, the central bank will just conduct monetary policy for the currentstate of the economy, because they assume that proxies’ expectations are given. So the centralbank’s discretionary monetary policy can’t stabilize proxies’ expectations, and impact on itscredibility, also discretionary monetary policy will impact systematic adjustment of the interestrate, and fluctuations in interest rates will increase. All these will have a negative impact on theeconomy. Compared to the discretionary monetary policy, monetary policy rule means thecentral bank adjust instrument variables (nominal interest rate or monetary supply) based oneconomic status (output gap or inflation gap and so on). The central bank will set commitmentmechanism in the context of monetary policy rules, and it will impact proxies’ expectationssystemically, so the central bank implement monetary policy not only for the current economicstatus but also for the expectations, and the central bank will insist on the implementation of therules of monetary policy until the economy is in a steady state. Monetary policy rules canenhance the central bank’s credibility, and stabilize economy by slightly systematic adjustmentsof monetary policy instrument variables.Through studying on the monetary policy rules, we can comprehend monetary policyoperations of the central banks, and establish reasonable expectations. So it can enhance thetransparency of the monetary policy operations, thereby improve the effect of monetary policy,including reducing the volatility of inflation and output, and promoting a fast, stable andsustained economic growth.In this paper, we firstly study on the formation mechanism of monetary policy rules. Wederivate the linear Taylor rule, by minimizing loss function of the central bank, under theconditions that the central bank’s loss function is quadratic and the aggregate supply curve islinear function. On this basis, we derivate the nonlinear monetary policy rules, by introducingasymmetric preferences of the central bank as well as the convex aggregate supply curve. The results show that the optimal monetary policy rules will exhibit nonlinear characteristics whenthe central bank’s loss function is not quadratic or the aggregate supply curve is nonlinear form.However, the nonlinear function form is complex among nominal interest rate, inflation gap andoutput gap. In order to facilitate the empirical test, we construct time-varying parameters Taylorrule and time-varying parameters smooth transition regression models to test the above complexnonlinear relation of monetary policy rules when the central bank’s loss function is not quadraticor the aggregate supply curve is nonlinear form, and we test the nonlinearity of monetary policyrules using the data of7-day inter-bank offered rate, inflation gap and output gap.On the basis of the analysis of the nonlinear mechanism of monetary policy rules, we alsoanalysis the causes of the nonlinearity of monetary policy rules, nonlinear forms of the monetarypolicy rules and the intrinsic associated mechanism between monetary policy rules andinflation/business cycles. First, we test the asymmetric preferences of the central bank, as wellas the nonlinearity of the Phillips curve. In this paper, we represent the central bank’spreferences, by increasing exponential parameters of the output gap and inflation gap in thelinear exponential loss function, the new loss function can capture the central bank’s asymmetricand “zone-like” preference. We combine this with conventional linear models of aggregate supplyand aggregate demand to derive a flexible nonlinear model of optimal monetary policy that allowsfor both zone-like and asymmetric behavior. We estimate the parameters of the monetary policyreaction function by the generalized moment method. Through constraint corresponding parameters,we test asymmetric and “zone-like” preferences of the central bank, and we find that the preferencesof central bank is asymmetric, and the loss function of the central bank is not affected when theinflation gap and output gap is in “zone-like” area. Because dynamic adjustment of the inflationmay be instable and nonlinear, so we improve the linear Phillips curve and construct a smoothtransition regression model of Phillips curve. We can judge whether the Phillips curve is convexby test the linearity relationship between output gap and inflation in the nonlinear smoothtransition regression models.To test for nonlinearity of monetary policy rules in china, we construct a time-varyingparameters model on base of the linear Taylor rule. Time-varying parameters Taylor rule not onlycapture the declining trend of the nominal equilibrium interest rate, the time-varyingcharacteristics of the interest rate reaction to output gap and inflation gap, but also it can capturethe time-varying characteristics of interest rate smoothing adjustment. We estimate thetime-varying parameters of the Taylor rule by Gibbs-sampling method, to overcome theshortcoming of classical method which is the combination of Kalman filter and maximumlikelihood estimation method. Secondly, we construct the time-varying parameters smoothtransition regression models on base of time-varying parameters model of Taylor rule, and introduce the method of linearity test and choosing method of transition function. In comparisonwith the linear Taylor rule, the time-varying parameters smooth transition regression models ofTaylor rule can capture the nonlinear adjustment feature of monetary policy instrument variables,as well as structural changes characteristic of monetary policy rules. Through testing the linearityof time-varying parameters smooth transition regression models, we find that China’s monetarypolicy rules is obvious nonlinear, and the mode of monetary policy rules changes in1999.China’s monetary policy operations showed strong discretionary before1999, but the monetarypolicy operations is rule after1999.After testing the nonlinearity of monetary policy in China, we also test the nonlinearassociated mechanism between monetary policy rules and inflation/business cycles. Firstly, weidentificate the different regimes where Taylor rule obeys or does not obey Taylor principle byconstruct Taylor rule with the Markov regime switching model. Through unit root tests ofinflation rate series in different regimes, we can test whether Inflation rate series is stationary inthe regime where Taylor rule obeys Taylor principle, and Inflation rate series is not stationary inthe regime where Taylor rule does not obey Taylor principle. Secondly, we test the thresholdeffect of Taylor rule when the threshold variable is cumulative year-on-year growth rate of GDP,analysis the adjustment mode of monetary policy in different stages of business cycles(recession regimes and expansion regimes). We construct the markov-switching rationalexpectations models of monetary policy on the base of the Taylor rule models with the threshold.Through calculate the impulse response function of markov-switching rational expectationsmodels of monetary policy, we measure asymmetric reaction of real output, inflation andnominal interest rates to aggregate supply shocks, aggregate demand shocks and monetarypolicy shocks, so we examines the intrinsic correlation mechanism of monetary policy rules andthe business cycle.