# Estimating the Competitive Storage Model: A Simulated Likelihood Approach

## TL;DR

This paper introduces a particle filter maximum likelihood estimator for the competitive storage model, improving inference accuracy in commodity markets with dependent shocks and limited data, outperforming existing methods.

## Contribution

The paper presents a novel particle filter estimator tailored for the competitive storage model, enhancing bias and precision over previous quasi-maximum likelihood approaches.

## Key findings

- Estimator outperforms composite quasi-maximum likelihood in bias and precision.
- Precision improves faster with more data compared to existing methods.
- Model fits natural gas prices better than traditional time-series models.

## Abstract

This paper develops a particle filter maximum likelihood estimator for the competitive storage model. The estimator is suitable for inference problems in commodity markets where only reliable price data is available for estimation, and shocks are temporally dependent. The estimator efficiently utilizes the information present in the conditional distribution of prices when shocks are not iid. Compared to Deaton and Laroque's composite quasi-maximum likelihood estimator, simulation experiments and real-data estimation show substantial improvements in both bias and precision. Simulation experiments also show that the precision of the particle filter estimator improves faster than for composite quasi-maximum likelihood with more price data. To demonstrate the estimator and its relevance to actual data, we fit the storage model to data set of monthly natural gas prices. It is shown that the storage model estimated with the particle filter estimator beats, in terms of log-likelihood, commonly used reduced form time-series models such as the linear AR(1), AR(1)-GARCH(1,1) and Markov Switching AR(1) models for this data set.