Important Econometric Problems Research Articles

Inferring causal impact using Bayesian structural time-series models

An important problem in econometrics and marketing is to infer the causal impact that a designed market intervention has exerted on an outcome metric over time. This paper proposes to infer causal impact on the basis of a diffusion-regression state-space model that predicts the counterfactual market response in a synthetic control that would have occurred had no intervention taken place. In contrast to classical difference-in-differences schemes, state-space models make it possible to (i) infer the temporal evolution of attributable impact, (ii) incorporate empirical priors on the parameters in a fully Bayesian treatment, and (iii) flexibly accommodate multiple sources of variation, including local trends, seasonality and the time-varying influence of contemporaneous covariates. Using a Markov chain Monte Carlo algorithm for posterior inference, we illustrate the statistical properties of our approach on simulated data. We then demonstrate its practical utility by estimating the causal effect of an online advertising campaign on search-related site visits. We discuss the strengths and limitations of state-space models in enabling causal attribution in those settings where a randomised experiment is unavailable. The CausalImpact R package provides an implementation of our approach.

Does Openness Matter for Financial Development in Africa?

This paper analyzes the links between financial and trade openness and financial development in Sub-Saharan African (SSA) countries. It is based on a panel dataset using methods that tackle slope heterogeneity, cross-sectional dependence and non-stationarity, important econometric problems that are often ignored in the literature. The results do not point to a general direct robust link between trade and capital account openness and financial development in SSA, once we control for other factors such as GDP per capita and inflation. But there is some indication that trade openness is more important for financial development in countries with better institutional quality. The findings might be due to a number of factors including distortions in domestic financial markets, relatively weak institutions and/or poor financial sector supervision. Thus, African policy makers should be cautious about expectations regarding immediate gains for financial development from greater international integration. Such gains are more likely to occur through indirect channels.

Subset Hypotheses Testing and Instrument Exclusion in the Linear IV Regression

This paper explores the sensitivity of plug-in based subset tests to instrument exclusion in linear IV regression. Recently, identification-robust statistics based on plug-in principle have been developed for testing hypotheses specified on subsets of the structural parameters. However, their robustness to instrument exclusion has not been investigated. Instrument exclusion is an important problem in econometrics and there are at least two reasons to be concerned. Firstly, it is difficult in practice to assess whether an instrument has been omitted. Secondly, in many instrumental variable (IV) applications, an infinite number of instruments are available for use in large sample estimation. This is particularly the case with most time series models. If a given variable, say X(t), is a legitimate instrument, so too are its lags X(t-1), X(t-2), ... Hence, instrument exclusion seems highly likely in most practical situations. In this paper, we stress that the usual high level assumption of the identification may be misleading when potential relevant instruments are omitted. We propose an analysis of the asymptotic distributions of the LIML estimator and the plug-in based statistics when potential instrument are omitted. Our results provides several new insights and extensions of earlier studies. We show that even when partial identification holds, the asymptotic distribution of the LIML estimator of the identified linear combination is no longer a Gaussian mixture, even though it is still consistent. This contrasts with the usual IV estimator of the identified linear combination, which is still asymptotically a Gaussian mixture despite the exclusion of relevant instruments. As a result, the asymptotic distributions of the plug-in based subset statistics that exploit the LIML estimator are modified in a way that could lead to size distortions. We provide an empirical illustration using a widely considered returns to education example, which clearly shows that the confidence sets of the returns to education resulting from the plug-in principle are highly sensitive to instrument exclusion.

Exploring the environmental Kuznets hypothesis: Theoretical and econometric problems

Focussing on the prime example of CO 2 emissions, we discuss several important theoretical and econometric problems that arise when studying environmental Kuznets curves (EKCs). An EKC refers to an inverse U-shaped relationship between a pollutant and economic activity. The dominant theoretical approach is given by integrated assessment modelling, which consists of economic models that are combined with environmental impact models. We critically evaluate the aggregation, model dynamics and calibration aspects and their implications for the validity of the results. We then turn to a discussion of several important econometric problems that go almost unnoticed in the literature. The most fundamental problems relate to nonlinear transformations of nonstationary regressors and, in a nonstationary panel context, to neglected cross-sectional dependence. We discuss the implications of these two major and some minor problems that arise in the econometric analysis of Kuznets curves. Our discussion shows that EKC modelling as performed to date is subject to major drawbacks at both the theoretical and the econometric level.

Determinants of United Kingdom General Insurance Company Performance

ABSTRACTDynamic financial analysis has become one of the important tools that actuaries use to model the underwriting and investment operations of insurance companies. The first step in carrying out the analysis is to investigate the most important factors affecting company performance. This paper identifies the determinants of the performance of United Kingdom general insurance companies using a panel data set consisting of economic data and Financial Services Authority/Department of Trade and Industry returns over the period 1986 to 1999. Three performance measures are used to capture different aspects of insurance operations. These measures are related to a number of economic and firm specific variables, chosen on the basis of relevant theory and literature. An ordinary least squares regression model and two panel data models are estimated for each of three performance measures. This paper also addresses several important econometric problems that are usually ignored in applied work in the context of panel data analysis. Based on the empirical results, this study finds that liquidity, unexpected inflation, interest rate level and underwriting profits are statistically significant determinants of the performance of U.K. general insurers.

Hypothesis testing in the presence of nuisance parameters

How to deal with nuisance parameters is an important problem in econometrics because of the non-experimental nature of economic data. This paper suggests a new approach to dealing with such parameters in the context of hypothesis testing. It involves calculating p-values conditional on values for key nuisance parameters and then taking a weighted average of these values with the weights reflecting the likelihood or posterior probabilities of these values being true. Two specific applications are discussed. These are testing linear regression coefficients in the presence of first-order autoregressive (AR(1)) disturbances and testing for AR(1) disturbances in the dynamic linear regression model. For the former testing problem, a Monte Carlo experiment demonstrates that the new procedure typically provides more accurate inferences than the accepted conventional tests.

Bootstrap Bartlett Adjustment in Seemingly Unrelated Regression

Abstract Seemingly unrelated regression (SUR) is a method introduced by Zellner (1962) for estimating several regression equations simultaneously, a common and important problem in econometrics. This article considers hypothesis testing in SUR using the log-likelihood ratio (LLR) test. Although the asymptotic distribution of this statistic is well known, substantial departures occur in samples of the size commonly employed by economists. Significance levels given by the use of this asymptotic distribution are too low, sometimes by an order of magnitude, leading to the rejection of too many true null hypotheses. A common approach to this problem is to use a Bartlett (1937) adjustment to the LLR statistic, in which the test statistic is multiplied by a factor derived from second-order asymptotics before it is referred to the asymptotic χ2(q) distribution. This article proposes that the Bartlett adjustment factor be computed using Efron's bootstrap (1979, 1982). In the cases examined, this leads to more accu...

A note on the importance of cost structures for the behavior of Political Action Committees

In sum, the cost environment in which PACs operate will directly influence both their behavior and their ability to ‘buy’ political benefits. Recognition of these effects implies that the conclusions of earlier studies that different PACs follow inherently different strategies, or that PACs are not rational in their contributory allocations are premature, and indeed, insupportable in the absence of cost analysis. Attention to costs also suggests that some important econometric problems may attend the investigation of PAC behavior.

Selection of Regressors

Selection of regressors is an old and important problem in econometrics as well as in any other field that uses regression analysis. Many criteria of selection have been proposed in the econometric and other literature, but I have not found a good unified treatment of the subject. This paper is such an attempt. Selection of regressors should be based on economic-theoretic considerations as well as on statistical evidence. Economic theory can ofteni indicate what regressors should be included in any equation, and sometimes, but less often, a class of functional forms that should be considered. In addition, it canl often tell the researcher the likely sign of a coefficient and sometimes even a shorter range within which the coefficient is likely to lie. These types of a priori information should be utilized either formally by means of the Bayesian method or informally by means of the classical method. Hence, mechanical reliance on goodness of fit should be avoided as much as possible. However, other things being equal, it would be convenient to be able to choose a regression equation on the basis of a single statistic such as the sum of squared residuals or its monotonic transformation, R2. However, R2 has an obvious weakness; i.e. it can be maximized by maximizing the number of regressors. Therefore, some kind of correction that accounts for the degrees of freedom is necessary. In the econometric literature, Theil [1961, p. 213] was the first to propose such a correction, and since then his R2 has become an important index with which an econometrician judges the merit of a regression equation. However, a theoretical weakness of Theil's R2 is that it is not based on an explicit consideration of a loss fuLnction. For a criticism of K2 on an empirical ground, see Mayer [1975]. In this paper I reiterate my suggestion (Amemiya [1966] and [1972]) to develop a selection criterion based on minimizing the unconditional mean square prediction error (UMSPE) as the risk functioni, which results in a modification of R2 that corrects for the degrees of freedom to a greater extent than Theil's R2. I call this Prediction Criterion (PC) and show that it can be used as a selection criterion in the nonlinear regression model and/or in the case where the error term has a general variancecovariance matrix. Thus it has a wide applicability.