##### Abstract

Norges Bank has been delegated the task of contributing to a steady growth of the Norwegian economy by keeping inflation low and stable. The goal is to keep the yearly growth in consumer prices at 2.5 percent in the medium run, balancing the inflation path with the overall capacity utilization whenever there is a conflict between the two, which corresponds to flexible inflation targeting. The main instrument for doing this is the sight deposit rate (foliorenten) on commercial banks' overnight deposits in Norges Bank, which affects money market rates through banks' marginal funding costs.

The policy rate decisions are based on analyses done with NEMO (the Norwegian Economy Model), as well as on general assessments about the state of the economy. NEMO is a large New Keynesian DSGE model representing the Norwegian mainland economy in a simplified and stylized manner. Uncertainty about the true structure of the economy is always an issue, and it is by no means certain that NEMO is the best possible description of it. A way to accommodate this uncertainty is to set the interest rate in a robust manner, meaning that monetary policy achieves a satisfactory level of macroeconomic stabilization also when the economy is highly different from the NEMO economy. Such policies that work well across a wide range of structural models are robust to model uncertainty.

However, robustness comes at the cost of optimality. Optimal policy is fine-tuned to the dynamics of a specific model, and does not perform well for completely different economies, as intuition suggests and many analyses show. A policy reaction function utilizing less model-specific information performs better on average across models, but naturally worse in each separate model, yet not substantially worse, as my results show. Such a restricted information rule is called a simple interest rate rule and is said to be robust if it performs well across a large variety of models.

Simple rules are commonly used by central banks in the conduct of monetary policy, of which there is thorough proof. Janet Yellen in the Board of Governors of the Federal Reserve System indicated that she uses "the Taylor rule" to provide her with " a rough sense of whether or not the funds rate is at a reasonable level". The popularity of simple interest rate rules is due to their applicability and the way they are intuitive and communicative to the general public, but most of all their robustness properties.

Norges Bank also uses simple rules to cross-check the policy derived from NEMO, among other the above-mentioned Taylor rule. The actual performance of these rules in the Norwegian economy has not been properly investigated, and little work has been done on robust simple rules is a good representation. A large share of the international literature has however found that the Taylor rule performs quite poorly, and in particular it appears not to be hard-hitting enough. This calls for a better robust rule for the Norwegian economy, which is the goal of my work to find. By analyzing the properties and performance of a number of different policy rules, I seek a rule tailored to the Norwegian economy that yields a satisfactory outcome in a variety of models.

I use five different models for the Norwegian economy, with NEMO as the benchmark model: two extensions of NEMO - "Credit NEMO" with a credit market incorporated, and a backward-looking version "Policy NEMO" - as well as a small open model economy, the "Leitemo-Gali-Monacelli" (LGM) model, and a slightly modified version of the macroeconometric model "Norwegian Aggregated Model" (NAM) by Bårdsen and Nymoen, which is a model in "the Norwegian tradition" similar to KVARTS used by the Statistics Norway and RIMINI previously used by Norges Bank. NAM differs substantially from the other four, and drives much of the results in this thesis, which gives sound justifications for including it in the set of models. All of the models prescribe highly divergent reaction functions for the nominal interest rate, and therefore constitute a good and wide-ranging base for robustness analyses.

I mostly base my work on the paper by Taylor and Wieland (2009) on robust simple interest rate rules. As they do, I first find the optimal coefficients in three specifications of a simple interest rate rule in each seperate model: one rule where the nominal interest rate responds only to inflation fluctuations and the output gap; one where the lagged interest rate is added in order to allow for more gradual adjustments, and one with the lagged output gap as well.

The optimization procedure is done in MatLab with the software Dynare and a search algorithm developed Junior Mai for internal use in Norges Bank.

My results show that since the optimized rules are fine-tuned to the dynamics of the rule-generating model, they yield remarkably less stability in the competing models. In particular miserable is the rule with only two variables from the LGM model applied in NAM, generating instability. There is also a strong conflict between the prescribed three variable rules in CN

and NAM.

In order to improve the achievement of the simple rules, I look at "Bayesian rules" where an average of the outcomes in the models is optimized in order to find the interest rate rule that best stabilizes this "model-mean". The Bayesian rules are more robust as they reduce the variability in each model compared to the first-best rule from another model. They also perform well in the models that they have not been optimized over, NEMO and Policy NEMO.

Robustness properties are evaluated using the relative increase in loss in a model stemming from the interchange of two policy rules translated into variability of inflation, a measure called Implied Inflation variability Premium (IIP). My results show a large dispersion of IIPs in the models, with the Bayesian rules naturally generating the lowest average IIP. In particular low IIPs are yielded by the rules where the relative importance of NAM in the optimization is tuned down. I find that rules that respond to last period's rate, inflation deviations from target and the current output gap is the most robust class of rules.

Another robustness tool used is fault tolerance (FT), where the relative increase in loss resulting from gradually varying the optimal value of a coefficient in a policy rule is displayed in a graph. FT is both used to measure to which extent a rule is robust towards small changes in the parameters, and how much a model is tolerant to different policies. The three-parameter interest rate rules is proved to be the most robust, and are hence the best to insure against model uncertainty with. NEMO and Policy NEMO are the most fault tolerant models, closely followed by CN, and NAM is the least tolerant.

At the end of the thesis I present what I refer to as "the Golden Interest Rule" (GIR), which is the rule that do best on average across the models. Through evaluating IIPs and FT of the different optimized rules, I found the properties of the best-performing rules, and tried several combinations of the parameter values that appeared to be optimal. GIR is as expected, a three-parameter rule that allows for a moderate degree of interest rate smoothing, yet not too much due to NAM. The long run responses to economic disturbances are substantially above the original Taylor rule, in particular three to inflation deviations from target and one and a half to GDP movements from trend. These strong reactions give sufficient stabilization of the real economy in all models considered.