Modelling Category Inflation with Multiple Inflation Processes: Estimation,Specification and Testing1

Zero-inflated ordered probit (ZIOP) and middle-inflated ordered probit (MIOP) models are finding increasing favour in the discrete choice literature. We propose generalizations to these models – which collapse to their ZIOP/MIOP counterparts under a set of simple parameter restrictions – with respect to the inflation process. These generalizations form the basis of a new specification test of the inflation process in ZIOP and MIOP models. Support for our generalization framework is principally demonstrated by revisiting a key ZIOP application from the economics literature, and reinforced by the reassessment of an important MIOP application from political science. Our specification test supports the generalized models over the original ZIOP/MIOP ones, suggesting an important role for it in modelling zero- and middle-inflation processes.     

Robustness of Logit Analysis: Unobserved Heterogeneity and Mis‐specified Disturbances*

In probit and logit models, the β coefficients vary inversely with the variance of the disturbances. The omission of a relevant orthogonal regressor leads to increased unobserved heterogeneity, and this depresses the β coefficients of the remaining regressors towards zero. For the probit model, Wooldridge (Econometric Analysis of Cross Section and Panel Data, MIT Press, Cambridge, MA, 2002) has shown that this bias does not carry over to the effect of these regressors on the outcome. We find by simulations that this also holds for the logit model, even when omitting a variable leads to severe mis‐specification of the disturbance. More simulations show that logit analysis is quite insensitive to pure mis‐specification of the disturbance as such.     

WHICH AGGLOMERATION EXTERNALITIES MATTER MOST AND WHY?

This paper revisits the ongoing discussion on the importance of agglomeration externalities – specifically specialization, diversity and competition effects – that may contribute to innovation, productivity and urban employment growth. Previous meta‐analyses suggested that the evidence on agglomeration externalities is strongly context‐specific. Expanding an earlier analysis of 31 articles, we seek to draw in this paper more robust conclusions by means of the statistical evidence for agglomeration externalities presented in 73 scientific articles, all building on the seminal work of Glaeser et al. (1992). Our results confirm that the heterogeneity among studies is huge and can only be partially accounted for by means of an ordered probit analysis. Additionally, some evidence of publication bias is found. We conclude that the conventional lines of inquiry in this literature may now have reached strongly diminishing returns. New lines of inquiry, using rich micro‐level data on firms and workers, dynamic general equilibrium models at the macro level, more attention for spatial and temporal variation in the impacts of agglomeration, and further investigations into the spatial scope of externalities are promising avenues for further research that can enhance our understanding of how agglomeration externalities continue to fuel our increasingly urbanized world.     

Modelling Inflation Volatility

This paper discusses estimation of US inflation volatility using time‐varying parameter models, in particular whether it should be modelled as a stationary or random walk stochastic process. Specifying inflation volatility as an unbounded process, as implied by the random walk, conflicts with priors beliefs, yet a stationary process cannot capture the low‐frequency behaviour commonly observed in estimates of volatility. We therefore propose an alternative model with a change‐point process in the volatility that allows for switches between stationary models to capture changes in the level and dynamics over the past 40 years. To accommodate the stationarity restriction, we develop a new representation that is equivalent to our model but is computationally more efficient. All models produce effectively identical estimates of volatility, but the change‐point model provides more information on the level and persistence of volatility and the probabilities of changes. For example, we find a few well‐defined switches in the volatility process and, interestingly, these switches line up well with economic slowdowns or changes of the Federal Reserve Chair. Moreover, a decomposition of inflation shocks into permanent and transitory components shows that a spike in volatility in the late 2000s was entirely on the transitory side and characterized by a rise above its long‐run mean level during a period of higher persistence. Copyright © 2015 John Wiley & Sons, Ltd.     

Inflation expectations in India: Learning from household tendency surveys

We use a large household survey that is being conducted by the Reserve Bank of India since 2005 to estimate the dynamics of aggregate inflation expectations over a volatile inflation regime. A simple average of the quantitative responses produces biased estimates of the official inflation data. We therefore estimate expectations by quantifying the reported directional responses. We perform quantification by using the hierarchical ordered probit model, in addition to the balance statistic. We find that the quantified expectations from qualitative forecasts track the actual inflation rate better than the averages of the quantitative forecasts, highlighting the filtering role of qualitative tendency surveys. We also report estimates of the disagreement among households. The proposed approach is particularly suitable in emerging economies, where inflation tends to be high and volatile.     

Diagnostic Tests of Cross‐section Independence for Limited Dependent Variable Panel Data Models*

This article considers the problem of testing for cross‐section independence in limited dependent variable panel data models. It derives a Lagrangian multiplier (LM) test and shows that in terms of generalized residuals of Gourieroux et al. (1987) it reduces to the LM test of Breusch and Pagan (1980) . Because of the tendency of the LM test to over‐reject in panels with large N (cross‐section dimension), we also consider the application of the cross‐section dependence test (CD) proposed by Pesaran (2004) . In Monte Carlo experiments it emerges that for most combinations of N and T the CD test is correctly sized, whereas the validity of the LM test requires T (time series dimension) to be quite large relative to N. We illustrate the cross‐sectional independence tests with an application to a probit panel data model of roll‐call votes in the US Congress and find that the votes display a significant degree of cross‐section dependence.     

The Analysis of Seasonal Long Memory: The Case of Spanish Inflation*

This paper describes semiparametric techniques recently proposed for the analysis of seasonal or cyclical long memory and applies them to a monthly Spanish inflation series. One of the conclusions is that this series has long memory not only at the origin but also at some but not all seasonal frequencies, suggesting that the fractional difference operator (1−L¹²)^d should be avoided. Moreover, different persistent cycles are observed before and after the first oil crisis. Whereas the cycles seem stationary in the former period, we find evidence of a unit root after 1973, which implies that a shock has a permanent effect. Finally, it is shown how to compute the exact impulse responses and the coefficients in the autoregressive expansion of parametric seasonal long memory models. These two quantities are important to assess the impact of aleatory shocks such as those produced by a change of economic policy and for forecasting purposes, respectively.     

Leading Indicators for Euro‐area Inflation and GDP Growth*

In this paper, we evaluate the role of a set of variables as leading indicators for Euro‐area inflation and GDP growth. Our leading indicators are taken from the variables in the European Central Bank's (ECB) Euro‐area‐wide model database, plus a set of similar variables for the US. We compare the forecasting performance of each indicator ex post with that of purely autoregressive models. We also analyse three different approaches to combining the information from several indicators. First, ex post, we discuss the use as indicators of the estimated factors from a dynamic factor model for all the indicators. Secondly, within an ex ante framework, an automated model selection procedure is applied to models with a large set of indicators. No future information is used, future values of the regressors are forecast, and the choice of the indicators is based on their past forecasting records. Finally, we consider the forecasting performance of groups of indicators and factors and methods of pooling the ex ante single‐indicator or factor‐based forecasts. Some sensitivity analyses are also undertaken for different forecasting horizons and weighting schemes of forecasts to assess the robustness of the results.     

The Political Economy of Low Inflation

What are the politics of inflation? This question is usually raised solely when inflation rates are high. All levels of inflation, however, high and low, are the outcome of political conflicts. But no current approach to the study of inflation — sociological, neoclassical, modern political economy — adequately captures the full range of political issues at stake, and this leads to problems for both theory and policy. This paper critiques the existing perspectives on inflation and then focuses on three theoretical issues raised by those critiques: the economic costs of inflation; the concept of monetary neutrality from economic and political perspectives; and the importance of disaggregating economic growth statistics. Finally, the paper introduces and explores a contending approach to the analysis of the political economy of inflation: a ‘micro‐politics’ perspective. This approach is the only one to address the politics of low inflation, which is of great significance for contemporary political economy.     

Sequential numerical integration in nonlinear state space models for microeconometric panel data

This paper discusses the estimation of a class of nonlinear state space models including nonlinear panel data models with autoregressive error components. A health economics example illustrates the usefulness of such models. For the approximation of the likelihood function, nonlinear filtering algorithms developed in the time‐series literature are considered. Because of the relatively simple structure of these models, a straightforward algorithm based on sequential Gaussian quadrature is suggested. It performs very well both in the empirical application and a Monte Carlo study for ordered logit and binary probit models with an AR(1) error component. Copyright © 2008 John Wiley & Sons, Ltd.     

Exact permutation tests for non-nested non-linear regression models

This paper proposes exact distribution-free permutation tests for the specification of a non-linear regression model against one or more possibly non-nested alternatives. The new tests may be validly applied to a wide class of models, including models with endogenous regressors and lag structures. These tests build on the well-known J test developed by Davidson and MacKinnon [1981. Several tests for model specification in the presence of alternative hypotheses. Econometrica 49, 781–793] and their exactness holds under broader assumptions than those underlying the conventional J test. The J-type test statistics are used with a randomization or Monte Carlo resampling technique which yields an exact and computationally inexpensive inference procedure. A simulation experiment confirms the theoretical results and also shows the performance of the new procedure under violations of the maintained assumptions. The test procedure developed is illustrated by an application to inflation dynamics.     

A zero-inflated ordered probit model,with an application to modelling tobacco consumption

Data for discrete ordered dependent variables are often characterised by “excessive” zero observations which may relate to two distinct data generating processes. Traditional ordered probit models have limited capacity in explaining this preponderance of zero observations. We propose a zero-inflated ordered probit model using a double-hurdle combination of a split probit model and an ordered probit model. Monte Carlo results show favourable performance in finite samples. The model is applied to a consumer choice problem of tobacco consumption indicating that policy recommendations could be misleading if the splitting process is ignored.     

Estimation in a generalization of bivariate probit models with dummy endogenous regressors

The purpose of this paper is to provide guidelines for empirical researchers who use a class of bivariate threshold crossing models with dummy endogenous variables. A common practice employed by the researchers is the specification of the joint distribution of unobservables as a bivariate normal distribution, which results in a bivariate probit model. To address the problem of misspecification in this practice, we propose an easy‐to‐implement semiparametric estimation framework with parametric copula and nonparametric marginal distributions. We establish asymptotic theory, including root‐n normality, for the sieve maximum likelihood estimators that can be used to conduct inference on the individual structural parameters and the average treatment effect (ATE). In order to show the practical relevance of the proposed framework, we conduct a sensitivity analysis via extensive Monte Carlo simulation exercises. The results suggest that estimates of the parameters, especially the ATE, are sensitive to parametric specification, while semiparametric estimation exhibits robustness to underlying data‐generating processes. We then provide an empirical illustration where we estimate the effect of health insurance on doctor visits. In this paper, we also show that the absence of excluded instruments may result in identification failure, in contrast to what some practitioners believe.     

STATE DEPENDENCE AND HETEROGENEITY IN HEALTH USING A BIAS‐CORRECTED FIXED‐EFFECTS ESTIMATOR

This paper estimates a dynamic ordered probit model of self‐assessed health with two fixed effects: one in the linear index equation and one in the cut‐points. This robustly controls for heterogeneity in unobserved health status and in reporting behavior, although we cannot separate both sources of heterogeneity. We find important state dependence effects, and small but significant effects of income and other socioeconomic variables. Having dynamics and flexibly accounting for unobserved heterogeneity matters for those estimates. We also contribute to the bias correction literature in nonlinear panel models by comparing and applying two of the existing proposals to our model. Copyright © 2012 John Wiley & Sons, Ltd.     

Testing for Misspecification in Binary Response Models with Competing Distributions*

In empirical studies, the probit and logit models are often used without checks for their competing distributional specifications. It is also rare for econometric tests to be focused on this issue. Santos Silva [Journal of Applied Econometrics (2001 ), Vol. 16, pp. 577–597] is an important recent exception. By using the conditional moment test principle, we discuss a wide class of non‐nested tests that can easily be applied to detect the competing distributions for the binary response models. This class of tests includes the test of Santos Silva (2001 ) for the same task as a particular example and provides other useful alternatives. We also compare the performance of these tests by a Monte Carlo simulation.     

Contrasting Models of the Effect of Inflation on Growth

Abstract.  The paper formulates a nesting model for studying the theoretical literature on inflation and endogenous growth. It analyses different classes of endogenous growth models, with different usage of physical and human capital, with different exchange technologies. First, the paper shows that a broad array of models can all generate significant negative effects of inflation on growth. Second, it shows that these models can be differentiated primarily by the fact whether there is a Tobin-type effect of inflation and also whether the inflation–growth effect becomes weaker as the inflation rate rises, a non-linearity, or stays essentially constant over the range of inflation rates. The paper compares these features of the models to empirical evidence as a way to summarize the efficacy of the models.     

New Methods for Forecasting Inflation,Applied to the US*

Models for the 12‐month‐ahead US rate of inflation, measured by the chain‐weighted consumer expenditure deflator, are estimated for 1974–98 and subsequent pseudo out‐of‐sample forecasting performance is examined. Alternative forecasting approaches for different information sets are compared with benchmark univariate autoregressive models, and substantial out‐performance is demonstrated including against Stock and Watson's unobserved components‐stochastic volatility model. Three key ingredients to the out‐performance are: including equilibrium correction component terms in relative prices; introducing nonlinearities to proxy state‐dependence in the inflation process and replacing the information criterion, commonly used in VARs to select lag length, with a ‘parsimonious longer lags’ parameterization. Forecast pooling or averaging also improves forecast performance.     

Unemployment and liquidity constraints

We present a dynamic framework for the interaction between borrowing (liquidity) constraints and deviations of actual hours from desired hours, both measured by discrete‐valued indicators, and estimate it as a system of dynamic binary and ordered probit models with panel data from the Panel Study of Income Dynamics. We analyze a household's propensity to be liquidity constrained by means of a dynamic binary probit model. We analyze qualitative aspects of the conditions of employment, namely whether the household head is involuntarily overemployed, voluntarily employed, or involuntarily underemployed or unemployed, by means of a dynamic ordered probit model. We focus on the possible interaction between the two types of constraints. We estimate these models jointly using maximum simulated likelihood, where we allow for individual random effects along with an autoregressive process for the general error term in each equation. A novel feature of our method is that it allows for the random effects to be correlated with regressors in a time‐invariant fashion. Our results provide strong support for the basic theory of constrained behavior and the interaction between liquidity constraints and exogenous constraints on labor supply. Copyright © 2007 John Wiley & Sons, Ltd.     

Weak Identification of Forward‐looking Models in Monetary Economics*

Recently, single‐equation estimation by the generalized method of moments (GMM) has become popular in the monetary economics literature, for estimating forward‐looking models with rational expectations. We discuss a method for analysing the empirical identification of such models that exploits their dynamic structure and the assumption of rational expectations. This allows us to judge the reliability of the resulting GMM estimation and inference and reveals the potential sources of weak identification. With reference to the New Keynesian Phillips curve of Galí and Gertler [Journal of Monetary Economics (1999) Vol. 44, 195] and the forward‐looking Taylor rules of Clarida, Galí and Gertler [Quarterly Journal of Economics (2000) Vol. 115, 147], we demonstrate that the usual ‘weak instruments’ problem can arise naturally, when the predictable variation in inflation is small relative to unpredictable future shocks (news). Hence, we conclude that those models are less reliably estimated over periods when inflation has been under effective policy control.