##### Abstract

In this thesis I estimate different versions of the New Keynesian

Phillips curve as a part of a standard small open economy DSGE

model. The estimation method I use is Bayesian Maximum Likelihood,

and the data are Norwegian quarterly data for the period

1989Q1--2007Q4. One advantage of estimating the model as a system,

is that one takes into account the cross-restrictions between the

equations of the model, as opposed to single equation methods which

focus on one relationship at the time. The system method therefore

forces the expectations in the model to be formed in a model

consistent way. Of course, this is an advantage only as long as the

model is not mis-specified. The Bayesian approach also allows us to

take advantage of prior information from other empirical studies, as

well as from theory, in a formal way.

The supply side of the model is represented by two types of firms,

importers and producers. I assume that the law of one price is

violated in the short-run. This implies that exchange rate movements

will not immediately be passed through to consumer prices of

imported goods. In the baseline specification I follow Rotemberg

(1982) and Hunt and Rebucci (2005) and assume quadratic price

adjustment costs. In addition, I consider an alternative

specification following Gal\'{\i} and Gertler (1999). They assume

that only a fraction of producers get to change their price each

period and that some of them follow a rule of thumb in their price

setting. The demand side consists of a continuum of equal consumers

who maximize discounted expected utility, where utility in each

period depends on consumption and leisure. The consumers are assumed

to have habit persistence in their consumption preferences. The

government collects lump-sum taxes and spends them on domestic

goods, and the central bank is assumed to follow a simple Taylor

rule in interest rate setting. The rest of the world is regarded as

one big economy, and it is approximated by autoregressive processes.

The benchmark DSGE model includes flexible hybrid Phillips curves

based on Rotemberg pricing behavior. I compare this specification to

alternative specifications of the New Keynesian Phillips curve,

including a purely forward looking version. To compare model fit I

use the posterior odds ratio.

My main findings are that expected future inflation is dominant in

the New Keynesian Phillips curve. This result applies to both

domestic and imported inflation. When comparing the models, the more

flexible the Phillips curves are towards putting weight on expected

future inflation, the better the model fits the data. A model with a

hybrid New Keynesian Phillips curve with a restriction of

fifty-fifty on the coefficients on expected future inflation and

lagged inflation gives the poorest data fit. A classic purely

forward looking New Keynesian Phillips curve gives better data fit

than a flexible hybrid curve. This, however, may be a result of the

fact that the purely forward looking curve contains fewer estimated

parameters than the hybrid, flexible curve and that it has better

priors by construction. I also estimate two models with slightly

more ad hoc versions of the price-setting rules. One version is a

homogeneous hybrid Phillips curve in which the coefficients on both

expected future inflation and lagged inflation are allowed to vary

between zero and one. The other is similar, but where the

homogeneity restriction is relaxed. The results are the same as for

the benchmark model, the expected future inflation term is dominant.

For the non-homogeneous model, the sum of the coefficient estimates

on the inflation terms in the domestic price curve is not that far

away from unity, but more so for the import price curve. However,

the relative data fit between these two models indicates that

homogeneity is not a too strong assumption.