## Date of Award

May 2015

## Degree Type

Dissertation

## Degree Name

Doctor of Philosophy

## Department

Economics

## First Advisor

Ehsan Soofi

## Second Advisor

Kundan Kishor

## Committee Members

Ehsan Soofi, Kundan Kishor, Mohsen Bahmani-Oskooee, Niloy Bose, Suyong Song

## Keywords

Bayesian Hierarchical Model, Entropy, Financial Intermediaries, Kullback- Leibler Divergence, Mutual Information, Survey of Professional Forecasters

## Abstract

This dissertation consists of three essays in the broad area of Information Theory, Bayesian econometrics and financial economics. The first essay (Chapter 1) is about measuring uncertainty and disagreement of economic forecasters within the context of the survey based method.

Uncertainty is an intangible concept and its value is not observable, so in order to deal with the causes and consequences of economic uncertainty we need to have a proper measurement method. Survey based methodology is one of the prominent approaches in the literature. Survey of professional forecasters (SPF) is one of the important surveys that economists use to measure the uncertainty. Each quarter Central Banks survey panels of experts on the current and future states of the US economy. Each expert provides a probability distribution for the pre-assigned categories of an economic variable such as GDP and consumer price index. Recently, Shannon entropy has been used for measuring the uncertainty of the economic variable based on the forecasters' distributions. We develop this line of research by utilizing the full power of the information theoretic and Bayesian machineries. The Kullback-Leibler divergence provides a strong measure of disagreement among the forecasters as well as the expected information provided by the forecasters about the economic variable in a random environment. This measure

formalizes the idea of forecasters retain portions of the information that the environment

provides for predicting the economic variable, along the lines of \citet{Sims2003, Sims2006, Sims2010} theory of rational inattention. In this context, the environment plays the role of the noisy channel of the communication theory.

The maximum entropy probability vectors derived based on the moments of the forecasters distributions provide upper bounds for the uncertainty. Bayesian models combine the uncertainty about the unknown probability distribution of the economic variable and the forecasters uncertainties. The uncertainty about each economic forecaster's uncertainty measure is taken into account in two ways, Bayesian hierarchical models for the uncertainty measure, and Dirichlet prior for the vector of probabilities of the categories. We apply Bayesian hierarchical models to the SPF data to explore the time patterns of aggregate uncertainty measures about the US inflation rate during 1992-2012 and use Dirichlet models to study the uncertainty of a panel of forecasters about the inflation rate.

The second essay (Chapter 2) extends the idea of measuring uncertainty and disagreement, that we have developed in the previous section, into the model based framework. Various models of uncertainty have been studies in the literature. Time series models of hetroskedasticity such as Autoregressive Conditional Hetroskedasticity (ARCH) model of Engle (1982) and its extension in which conditional variance surrounding the prediction is time varying are some of the models have been studied in the literature. Recently the unpredictability of economic conditions is described as the decision makers' uncertainty about the economy (Ludvigson and Ng (2013)). Since the correct model is unknown, ignoring the other potential models could result in underestimating or overestimating the measure of uncertainty. In this essay, we consider the model uncertainty by taking into account a set of plausible models instead of relying on a single model. We focus on the diffusion index model and set up the model space as the set of linear models constructed by different combination of principle components. We view each model as an economic forecaster, and the posterior predictive distribution of each model is assumed as an individual probability distribution about the the economic variable. Defining the aggregate measure of uncertainty and disagreement among different models' predictive distribution and explore the relationship between in the direction I will be chasing in the second paper.

The final essay (Chapter 3) is on the predictability of asset return using the information contained in balance sheet activities of market based financial intermediaries.

The interconnection between the balance sheet activities of financial intermediaries, asset prices and macroeconomic activities have been studied in the literature. Adrian and Shin(2010) examine the predictability of the excess asset return and show that the leverage growth of security broker dealers as well as the asset growth of shadow banking system could forecast the excess return of an extensive list of financial portfolios. Some other authors points the effect of the balance sheet activities of financial intermediaries on economic activities. In this chapter we investigate whether the balance sheet variables of financial intermediaries could provide new information beyond what is concealed in the macroeconomic variables in predicting asset returns as well as economic activities. Using a large panel of data set of macroeconomic variables as well as the balance sheet variables of financial intermediaries in the context of dynamic factor model, we estimate the latent factors that explain the variation of economic as well as financial variables. Implementing the estimated latent factors together with the leverage growth of security broker dealers and the asset growth of shadow banking system, we observe that leverage growth of security broker dealers and the asset growth of shadow banking system have predicting power beyond the macroeconomic as well as the balance sheet variables of financial intermediaries in sample and out of sample forecast.

## Recommended Citation

Shoja, Mehdi, "Essays on Survey and Model Based Econoomic Forecasts" (2015). *Theses and Dissertations*. 927.

https://dc.uwm.edu/etd/927