3.3.1 Econometric Model of Monetary Reaction Functions
Bearing in mind the potential problem of determinacy and identification in single equation estimation of the Taylor rule as postulated by Cochrane (2007), the baseline reduced form econometric specification of monetary reaction function has been taken from Henry, Levine & Pearlman, (2012). According to Cochrane (2009) and Cochrane (2011), the necessary condition for a system to exhibit saddle path stability is that the system is learnable and the rule is identifiable. It is important to note that without the second condition, i.e., if the rule is not identifiable, it will become observationally equivalent to an infinite number of other structurally equivalent rules on the saddle path equilibrium - or will be relevant only off the saddle path equilibrium. In their paper, Henry et al., (2012) argue that simplest form of the Taylor rule is not subject to Cochrane‟s criticism. According to them, if a rule is simple enough then it will satisfy the necessary conditions for local stability. If agents know the parameters and structure of the rest of the economy, then it turns out that a Taylor rule feeding back on both inflation and output is sufficient to be identified. To summarise their argument, a system of equations need to be considered, composed of a set of backward looking variables, forward looking variables and a policy variable. Further, it should be assume that a simple policy rule is in place which expresses the policy variable as a linear combination of backward and forward looking variables and meets the condition of saddle path stability. Such a system will be learnable and the rule will be identified given that the number of non-zero elements in the associated matrix of the target variables in the policy rule is less than or equal to the number of backward looking variables.
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Following the illustration of Henry, Levine & Pearlman, 2012; (HLP), let us consider a New Keynesian model with habit formation (denoted by the parameter „h‟) and a simple Taylor rule of inflation targeting.
…………... (1.HLP)
………... (2.HLP) ………... (3.HLP)
Substituting the policy variable in Equation of (1.HLP), a state space representation of the above system can be obtained which has exactly one stable root. This implies the jump variables can be expressed in terms of predetermined and as:
…………... (4.HLP) …………... (5.HLP)
It is shown that a stable saddle path specified above by (4.HLP) and (5.HLP) can produce a locally bounded equilibrium and be exploited to identify the inflation coefficient of the policy rule. Since, and both are correlated with , Ordinary Least Square regression of on will lead to inconsistent estimate of inflation stabilising coefficient. However, estimation by instrumenting the pre-determined variable like lagged output gap (i.e., ) which is uncorrelated to , can yield a consistent estimate of and it will be identified. This instance elucidates that the simplest form of inflation targeting Taylor rule can overcome Cochrane‟s critique. Following the spirit of their work, a simple and identifiable inflation targeting interest
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rate rule is specified in Equation (6) and considered as the Baseline Model for our analysis:
………. (6); where, ;
In Equation (6), „i‟ stands for country and „t‟ stands for time period. , , and are the nominal interest rate, inflation and the white noise error term of i-th country at period t. presents country specific effects in the behaviour of interest rate setting and measures the reaction of central banks over the cyclical variations of inflation. This model is estimated in the panel of developed and developing economies by the instrumental variable where lagged output gaps are chosen as the instruments following the arguments of Henry, Levine & Pearlman (2012).
After estimating the identifiable baseline Taylor type reaction function (6), the generalised version of interest rate reaction function that has been studied mostly in the literature, is taken into consideration. The generalised specification is given in equation (7).
……… (7); where,
Here, „ ‟, is the interest rate smoothing parameter of central bank, is the output gap in i-th country at period t and is the output gap stabilising coefficient. Note that is taken equal to zero in the baseline model of (6) and therefore, the baseline model can be considered as the inflation targeting specification of monetary reaction function.
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The generalised specification of (7) can be obtained by augmenting (6) with a one period lagged interest rate and relaxing the assumption of equals to zero. The motivation behind this is to incorporate the objectives of interest rate smoothing and output gap stabilisation of central banks in the reaction functions. In reality, it has been observed that there is a strong inertia in interest rate which essentially reveals the „gradualism‟ of monetary authority to respond to the macroeconomic outcomes. Therefore, this needs to be captured by interest rate smoothing factor. Parallel to this, keeping actual output near to its potential level for fostering economic growth is another important objective of central banks and thus, taken into model specification. The issue of identification raised by Cochrane (2007) may be tackled by providing a richer theoretical model; the model, in which such generalised version of the Taylor type reaction functions would be identified. Such an endeavour is beyond the scope of this chapter.
3.3.2 Specification of Research Hypothesis
At this point, it is imperative to put forward the main research hypotheses of the forthcoming empirical analysis. The investigation is now concerned to examine if the estimated value of „ ‟, is greater than one for advanced and developing countries. Thus, the necessary hypothesis testing can be constructed as:
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The presumption of this research hypothesis is to check whether the estimate of „ ‟ is greater than one for advanced economies but less than one for developing countries. If this presumption turns out to be statistically significant, then the conventional argument will be in place, i.e. active monetary policy in advanced countries has stabilised the inflation dynamics while it is absent in the developing economies. In other words, if the estimated value of „ ‟ is found to be less than one for developing economies, it can be argued that due to accommodative response of monetary policy, inflation has not been stabilised and therefore, it remains strongly volatile in the emerging countries. The research hypotheses mentioned above has been tested for both econometric models given in (6) and (7) to assess the role of monetary authority critically.
3.4 Data & Methodology