##### Abstract

In this thesis I estimate hazard functions of price observations using observed retail prices for Norway in the period 1975--2004. The hazard function gives the probability that we observe a price change in month t, given that the price has been constant for t-1 months.

Time-dependent and state-dependent models of price setting behavior are two common theories in macroeconomics used to explain nominal price rigidities. Time-dependent price setting models are characterized by exogenous timing of price readjustments, and two widely used time-dependent models are given in Calvo [1983] and Taylor [1980]. If price setters are homogenous the resulting hazard function in the Calvo model will be constant for all duration lengths. If prices are set as in the Taylor model, the hazard function should have a spike of value one at the contract renewal and be zero for all other duration lengths. Further, several contracts with different lengths in the economy result in several spikes in the hazard function, and aggregation of heterogeneous price setters in the Calvo model results in a downward sloping hazard function (Álvarez, Burriel, and Hernando [2005]). In state-dependent models of price setting, the timing of price readjustments is endogenous. One theory of state-dependent pricing is the existence of a cost attached to the action it takes to change the price. The timing of price changes under state-dependent models depends on economic conditions like inflation. Nakamura and Steinsson [2008] shows that menu cost models can give rise to a multitude of different shapes of the hazard function.

In order to find evidence on state-dependent and time-dependent models, I estimate hazard functions based on a data set of monthly retail price observations in Norwegian firms in the period 1975--2004, using an estimator called the Kaplan-Meier hazard rate. The Kaplan-Meier hazard rate is a nonparametric method and is estimated from the number of price changes observed for each duration lengths divided by number of price spells ``at risk''.

One problem with applying the Kaplan-Meier hazard rate is that it assumes that the sample is homogeneous. I find, however, clear evidence of heterogeneity across different outlets. E.g. Energy items are characterized by frequent price changes (as much as 68 per cent of the price spells have duration equal to one month in this sector), while Services are characterized by infrequent price changes (only 35 per cent of the price spells have duration equal to one month). In order to take account of this heterogeneity I have constructed one hazard rate for each item, and then aggregated by taking the mean. This implies that each item is weighted equally instead of each price spell. Another problem with survival analysis is the problem of censored price spells. Censoring occurs when the start or end of a price spell is not observed, and therefore implies that we do not know the exact duration of a price spell that is censored. However, I find that adjusting for left-censored price spells do not alter the hazard rate very much.

I find that the aggregate hazard rate shows evidence on a negative duration dependence, and with spikes every 12th month. This means that overall the probability of observing a price change is lower the longer the price have been constant, but that the probability of observing a price change is high the 12th, 24th and 36th month with constant price. Álvarez, Burriel, and Hernando [2005] shows that aggregation of several Calvo and Taylor models results in a hazard function with a negative duration dependence, and this can therefore be one possible explanation of why the aggregated hazard rate has negative duration dependence. I also investigate how the hazard function changes from a period with high and volatile inflation (1974--1989) to a period of low and stable inflation (1990--2004). I find that the hazard function from the period with high and volatile inflation is higher than the hazard function from the period of low and stable inflation. One implication of this is that the period with high and volatile inflation is characterized with more frequent price changes than the period with low and stable inflation.

I also find large differences in estimated hazard rates for different product categories. E.g. the hazard rate for the HICP product type Energy is high and volatile, while the hazard rate for the HICP product type Service is low and with regular spikes every 12th month.

All calculations are done in STATA and the thesis is written in LaTeX.