Title: Essays on Large Panel Data Analysis
Description: A growing number of studies in macroeconomics and finance have attempted to utilize large panel data sets. Large panel data sets contain rich information on the dynamics of many cross-sectional units over long time periods. These data sets often consist of numerous series in different categories that reflect the multifaceted aspects of an economy. In other circumstances, data sets are constructed from a large number of series at a highly disaggregated level within the same category so that they can reveal dynamics in greater detail. Numerous studies have proven the usefulness of large panel data sets in improving forecast performance, distinguishing common shocks from idiosyncratic shocks, and uncovering the discrepancies in dynamics between aggregate series and disaggregated series. To gain the most from large panel data sets, econometric models should allow all the key characteristics of these rich data sets without distortion. Among the pervasive and important characteristics of large panels are dynamics, heterogeneity, and cross-sectional dependence.

While there has been a great deal of research on each of these three features, the consequences of jointly incorporating them into a single model have not been extensively studied in the existing literature. Chapter 1 of this dissertation considers dynamic heterogeneous panels with cross-sectional dependence (DHP+CSD) that allow for all three key characteristics at the same time. Cross-sectional dependence is modeled through the use of a common factor structure in the error terms. We propose an estimator for the DHP+CSD model and develop an asymptotic theory under a large N and large T setup. The estimator relies on an iterative principal component method to cope with the challenges in estimation arising from the greater generality of the DHP+CSD model. The proposed estimator is shown to be consistent under non-stringent conditions and performs well in finite samples. Furthermore, the overall performance of the estimator is satisfactory even if no factor structure is present. Consequently, the DHP+CSD approach facilitates prudent estimation without requiring an additional procedure of pre-testing cross-sectional dependence.

The econometric tool developed in Chapter 1 can be particularly useful in analyzing possible discrepancies in persistence between an aggregate series and its underlying disaggregated series. It is well-known that an aggregate series can exhibit drastically different dynamics from its underlying processes. Early literature focuses on the role of heterogeneity in the dynamics of disaggregated series, whereas recent studies note that the dynamics of common factors also play an important role. Therefore, it is essential to use a model that incorporates dynamics, heterogeneity, and cross-sectional dependence (that arises from common factors) for analyzing the dynamics of disaggregated series. We apply the DHP+CSD estimator to investigate the dynamics of disaggregated data sets in two important empirical contexts: the purchasing power parity (PPP) hypothesis and the intrinsic persistence of inflation. Most studies have relied on models that utilized dynamics and heterogeneity without considering common factors.

Given the important role of common factor dynamics, revisiting the issue of aggregation with the DHP+CSD model in these empirical contexts can meaningfully extend the existing studies. Chapter 2 of this dissertation investigates the dynamics of sectoral real exchange rates in the context of the PPP hypothesis. It is widely known that aggregate exchange rates exhibit a considerable degree of persistence, serving as evidence against the PPP hypothesis. Recent studies, however, report that persistence estimates are markedly lower if exchange rate dynamics are examined at the disaggregated level. Given the focus on the dynamics of disaggregated series, a persistence analysis of sectoral exchange rates perfectly fits into the DHP+CSD framework. Consistent with recent studies, our estimation results show that the persistence of sectoral exchange rates is indeed lower than that of aggregate exchange rates. In addition, the persistence estimates from the DHP+CSD model are substantially lower than the estimates from those models that ignored the dynamics of common factors.

This suggests that the estimates of the latter models might be vulnerable to distortions caused by ignoring some key features of the given large panel data set. We also document the difference in responses with respect to common shocks and idiosyncratic shocks. This analysis is possible primarily because the DHP+CSD model can distinguish the two types of shocks. On average, common shocks appear to have approximately 50% more persistent effects on the economy than idiosyncratic shocks. Chapter 3 aims to assess the persistence of inflation at the disaggregated level. Persistence is widely accepted as one of the key characteristics of inflation. Similar to the recent PPP literature, however, numerous studies have also found considerably lower persistence at the disaggregated level. Since many empirical studies often disregard the possible dynamics of common factors, there is room for refining the existing analysis by adopting the DHP+CSD model. Given the estimated dynamics of sectoral inflation, we also attempt to measure the degree of intrinsic persistence at the disaggregated level.

Intrinsic persistence is a useful concept for identifying the structural sources of inflation persistence; a low intrinsic persistence implies that most of the inflation persistence is inherited from the real marginal costs. Because low intrinsic persistence also implies less inertia, it is associated with forward-looking behavior in price-setting. In contrast to the substantial degrees of estimated intrinsic persistence in the literature, we find that price-setting is markedly forward-looking at the disaggregated level; in approximately half of all sectors in the U.S. economy, price-setting is close to purely forward-looking. In measuring intrinsic persistence through the DHP+CSD model, we establish a relationship between the DHP+CSD model and the sectoral New Keynesian Phillips Curves. Recovering the structural parameters of intrinsic persistence from the reduced-form DHP+CSD estimates serves as an alternative framework of structural analysis for inflation dynamics. In conclusion, this dissertation develops a useful econometric method for analyzing large panel data sets and illustrates its practical value by applying it to two important empirical contexts: the PPP hypothesis and the intrinsic persistence of inflation.

With the DHP+CSD model, we can analyze the dynamics of disaggregated series more precisely and shed new light on the discrepancies in persistence between an aggregate series and its underlying disaggregated series. We also illustrate that the developed model has potential as a reduced-form representation of structural models for further structural analysis. All things considered, it is hoped that this dissertation provides a useful econometric framework for large panel data analysis.