Tracking real-time data revisions in inflation persistence

Regarding the forecasting of real-time data, it is assumed that the third quarter release produces the best forecasts since it includes data from new and revised sources, which this paper finds is not necessarily the case. There seems to be a benchmark effect when estimating the local nonparametric regressions and the forecasts of real-time PCE and core PCE when examining the four benchmark periods beginning in 1996:Q1, 1999:Q4, 2003:Q4, and 2009:Q3. There is a benchmark effect with respect to the estimated local nonparametric slopes with the demarcation being at the 2003:Q4 benchmark, which is also the demarcation for the forecasting results. For the benchmark revisions periods of 1996:Q1 and 1999:Q4, the second quarter real-time data releases produce the smaller RMSE and for the benchmark revisions of 2003:Q4 and 2009:Q3, the third quarter real-time data releases produce forecasts with smaller RMSE approximately 58% and 60% of the time, respectively.

Abbreviations: PCE, Personal Consumption Expenditures; KWLS, Kernel Weighted Least Squares; "V_" as a prefix stand for vintage, i.e. V_2003:Q4 is vintage 2003:Q4, which means that the data sample ends in 2003: Q3; IRSC, integrated residual squares criterion; NPISH, Non-Profit Institutions Serving Households; SNA, System of Accounts; RMSE, Root Mean Square Error; MAE, Mean Absolute Error; NAICS, North American Industry Classification System; SIC, Standard Industrial Classification; ARSC, Average Residual Squares Criterion; I-O, Input – Output; EIA, Energy Information Administration; ATM, Automated Teller Machines; BEA, Bureau of Economic Analysis; SNA, System of Accounts     

Policy analysis in real time using IMF's monetary model

We investigate to what extent estimated relationships of the IMF's monetary model and their policy implications are sample dependent. We observe that estimates of the model's key parameters and model-based measures of macroeconomic disequilibria are highly dependent on the data vintage employed. Changes in parameter estimates solely due to data revisions are found to be much smaller than those owing to parameter instability, possibly reflecting model misspecification. Moreover, instability in parameter estimates contributes to more uncertainty in assessments of macroeconomic disequilibria than data revisions. Analyses based on a version of the model in difference form are also found to be quite sensitive to the data vintage employed, although to a lesser extent than those based on the standard version of the model with variables in levels.     

NONPARAMETRIC LIKELIHOOD: EFFICIENCY AND ROBUSTNESS*

Nonparametric likelihood is a natural generalization of parametric likelihood and it offers effective methods for analysing economic models with nonparametric components. This is of great interest, since econometric theory rarely suggests a parametric form of the probability law of data. Being a nonparametric method, nonparametric likelihood is robust to misspecification. At the same time, it often achieves good properties that are analogous to those of parametric likelihood. This paper explores various applications of nonparametric likelihood, with some emphasis on the analysis of biased samples and data combination problems.     

Nonparametric kernel estimation applied to forecasting: An evaluation based on the bootstrap

The results reported in this paper lend support to the nonparametric approach to estimating regression functions. This conclusion is based on a comparison of two sets of eight quarterly forecasts of U.S. hog supply generated by a well specified parametric dynamic model and by nonparametric kernel estimation. Despite the relatively small sample size, the nonparametric point forecasts are found to be as accurate as the parametric forecasts according to the mean square error and mean absolute error criteria. Bootstrap resampling is used to estimate the distributions of the forecast errors. The results of this exercise favour the nonparametric forecasts, which are found to have a tighter distribution.     

NONPARAMETRIC MODELS OF FINANCIAL LEVERAGE DECISIONS

This paper applies nonparametric decision tree models to the analysis of financial leverage decisions. This approach presents three appealing features: (i) the relationship between leverage and explanatory variables is not predetermined but is derived from information provided by the data, (ii) the models respect the fractional nature of leverage ratios, and (iii) each covariate is allowed to influence in different ways the financial leverage decisions of firms automatically assigned to different groups. Based on a data set of Portuguese firms, decision trees are used to tackle both classification (the decision to issue debt) and regression (the decision on the amount of debt to be issued, conditional on using debt) problems. It is found that: (i) two‐part models are the most appropriate specification for explaining the overall amount of debt used by firms, (ii) there are no drastic differences between the results produced by tree and parametric models, although some divergences may arise, and (iii) tree models suggest relationships between covariates and leverage that parametric models fail to capture, especially when the sample size is small.     

The (un)reliability of real-time output gap estimates with revised data

This paper investigates the differences between real-time and ex-post output gap estimates using a newly-constructed international real-time dataset over the period from 1973:Q1 to 2012:Q3. We extend the findings in Orphanides and van Norden (2002) for the United States that the use of ex-post information in calculating potential output, not the data revisions themselves, is the major cause of the difference between real-time and ex-post output gap estimates to nine additional OECD countries. The results are robust to the use of linear, quadratic, Hodrick–Prescott, Baxter–King, and Christiano–Fitzgerald detrending methods. By using quasi real-time methods, reliable real-time output gap estimates can be constructed with revised data.     

Estimation of hedonic price functions via additive nonparametric regression

We model a hedonic price function for housing as an additive nonparametric regression. Estimation is done via a backfitting procedure in combination with a local polynomial estimator. It avoids the pitfalls of an unrestricted nonparametric estimator, such as slow convergence rates and the curse of dimensionality. Bandwidths are chosen using a novel plug in method that minimizes the asymptotic mean average squared error (AMASE) of the regression. We compare our results to alternative parametric models and find evidence of the superiority of our nonparametric model. From an empirical perspective our study is interesting in that the effects on housing prices of a series of environmental characteristics are modeled in the regression. We find these characteristics to be important in the determination of housing prices.First version received: October 2002/Final version received: October 2003We thank B. Baltagi and two anonymous referees for their comments. The authors retain responsibility for any remaining errors.     

Nonparametric regression estimation with general parametric error covariance: a more efficient two-step estimator

Recently Martins-Filho and Yao (J Multivar Anal 100:309–333, 2009) have proposed a two-step estimator of nonparametric regression function with parametric error covariance and demonstrate that it is more efficient than the usual LLE. In the present paper we demonstrate that MY’s estimator can be further improved. First, we extend MY’s estimator to the multivariate case, and also establish the asymptotic theorem for the slope estimators; second, we propose a more efficient two-step estimator for nonparametric regression function with general parametric error covariance, and develop the corresponding asymptotic theorems. Monte Carlo study shows the relative efficiency loss of MY’s estimator in comparison with our estimator in nonparametric regression with either AR(2) errors or heteroskedastic errors. Finally, in an empirical study we apply the proposed estimator to estimate the public capital productivity to illustrate its performance in a real data setting.     

Inequality in democracies: Testing the classic democratic theory of redistribution

The classic democratic theory of redistribution claims that an increase in the mean-to-median (MM) income ratio causes a majority coalition in the electorate to collectively demand more redistribution. The functional dependence of redistribution on the MM income ratio is tested in parametric and nonparametric regression frameworks using an OECD panel dataset. While the parametric regression model is found to be misspecified rendering subsequent inference invalid, the robust nonparametric regression model fails to uncover evidence that the MM income ratio is relevant for predicting redistribution.     

基于多项式回归模型的货币供应与通货膨胀的实证分析

通货膨胀是当前中国国民经济发展中遇到的热点问题,从探讨与通货膨胀率关系最直接的变量货币供应量出发,首先定性的讨论它们之间的有关理论和关系,然后通过实际数据,采用R软件,用非参数LPE回归模型对货币供应与通货膨胀的因果关系进行实证分析,并将此结果与线性回归和多项式回归模型比较,得出多项式回归模型优良的结论,最后,通过实证结果分析,得出相应的结论。     

Modelling conditional heteroskedasticity: Application to the “IBEX-35” stock-return index

This paper compares alternative time-varying volatility models for daily stock-returns using data from Spanish equity index IBEX-35. Specifically, we estimate a parametric family of models of generalized autoregressive heteroskedasticity (which nests the most popular symmetric and asymmetric GARCH models), a semiparametric GARCH model, the generalized quadratic ARCH model, the stochastic volatility model, the Poisson Jump Diffusion model and, finally, a nonparametric model. Those models which use conditional standard deviation (specifically, TGARCH and AGARCH models) produce better fits than all other GARCH models. We also compare the within sample predictive power of all models using a standard efficiency test. Our results show that the asymmetric behaviour of responses is a statistically significant characteristic of these data. Moreover, we observe that specifications with a distribution which allows for fatter tails than a normal distribution do not necessarily outperform specifications with a normal distribution.     

Recent approaches to estimating Engel curves

Classical approaches of estimating cross-section Engel curves are based on parametric models. However, misspecification of a parametric model implies that information of structural nature might be masked. An alternative avoiding problems related to predetermined functional relations is the nonparametric approach. This paper surveys recent advances of nonparametric statistics in their relevance to estimating cross-section Engel curves.     

Nonlinear interest rate reaction functions for the UK

We empirically analyze Taylor-type equations for short-term interest rates in the United Kingdom using quarterly data from 1970Q1 to 2006Q2. Starting from strong evidence against a simple linear Taylor rule, we model nonlinearities using logistic smooth transition regression (LSTR) models. The LSTR models with time-varying parameters consistently track actual interest rate movements better than a linear model with constant parameters. Our preferred LSTR model uses lagged interest rates as a transition variable and suggests that in times of recessions the Bank of England puts more weight on the output gap and less so on inflation. A reverse pattern is observed in non-recession periods. Parameters of the model change less frequently after 1992, when an inflation target range was announced. We conclude that for the analysis of historical monetary policy, the LSTR approach is a viable alternative to linear reaction functions.     

Alcohol availability and crime: a robust approach

The relationship between alcohol availability and crime is investigated in this study. It first considers common parametric specifications that have been used in the literature. After applying a powerful consistent conditional moment test for correct specification, it is found that these common parametric specifications are rejected by the data. The study then proceeds with a robust nonparametric method that can have a rate of convergence close to that for a correctly specified parametric model when the underlying relationship is somewhat linear. The application of nonparametric methods reveals structure present in the data that would remain undetected when applying common parametric specifications, but more importantly reveals that the impact of alcohol availability is considerably higher than one might believe on the basis of the misspecified parametric model. It is also found that the marginal effect of alcohol availability on crime changes with the level of alcohol availability.     

An in-sample and out-of-sample empirical investigation of the nonlinearity in house prices of South Africa

This paper tests whether housing prices in the five segments of the South African housing market, namely large-middle, medium-middle, small-middle, luxury and affordable, exhibit non-linearity based on smooth transition autoregressive (STAR) models estimated using quarterly data from 1970:Q2 to 2009:Q3. Findings point to an overwhelming evidence of non-linearity in these five segments based on in-sample evaluation of the linear and non-linear models. We next provide further support for non-linearity by comparing one- to four-quarters-ahead out-of-sample forecasts of the non-linear time series model with those of the classical and Bayesian versions of the linear autoregressive (AR) models for each of these segments, for the out-of-sample horizon 2001:Q1 to 2009:Q3, using the in-sample period 1970:Q2 to 2000:Q4. Our results indicate that barring the one-, two and four-step(s)-ahead forecasts of the small segment, the non-linear model always outperforms the linear models. In addition, given the existence of strong causal relationship amongst the house prices of the five segments, the multivariate versions of the linear (classical and Bayesian) and STAR (MSTAR) models were also estimated. The MSTAR always outperformed the best performing univariate and multivariate linear models. Thus, our results highlight the importance of accounting for non-linearity, as well as the possible interrelationship amongst the variables under consideration, especially for forecasting.     

Nonparametric quantile regression analysis of R&D-sales relationship for Korean firms

This paper applies the nonparametric quantile regression estimation procedure to the analysis of the innovation-firm size relationship using Korean manufacturing firms data. Due to the high asymmetric distribution of R&D expenditure, the mean regression does not capture properly the stylized facts of R&D behavior; hence it underestimates the sales elasticity. Comparing the parametric estimates and nonparametric estimates allows us to see that there exists a nonlinear relationship in innovative activity and sales. Dividing the data into three groups according to the sales volume, the elasticity in the medium-sized firms is the biggest for scientific firms. This result conforms that the findings of Scherer (1965) coincide with findings from Korean manufacturing firms data in the sense that R&D expenditure tends to increase faster than firm size with size up to a point and then more slowly among larger firms. For the non-scientific firms, it steadily increases showing increasing returns to scale in innovative activity in large firms.     

Measuring the output gap in Switzerland with linear opinion pools

We use the recently proposed linear opinion pool methodology of Garratt et al. (2014) to construct real-time output gap estimates for Switzerland over the out-of-sample period from 2003:Q1 to 2015:Q4. The model space consists of a large number of bivariate VAR specifications for the output gap and inflation, with each VAR specification using a different estimate of the output gap, lag order, and structural break information. We find that the linear opinion pool performs rather poorly. Real-time estimates of the output gap are no more accurate than those from some simple benchmark models, no more robust to ex post revisions than the real-time estimates of the individual univariate output gaps, and do not produce more accurate forecasts of inflation. The key driver of ‘good’ forecast performance is structural break information. Once the same structural break information is conditioned upon in all prediction models, the gain from averaging over many different pools of models that utilize various output gap estimates or lag structures in the VAR specification is of negligible magnitude.     

The relationship between childhood obesity and food insecurity: a nonparametric analysis

Childhood obesity and food insecurity are major public health concerns in the United States and other developed countries. Research on the relationship between the two has provided mixed results across a variety of data sets and empirical methods. Common throughout this research, however, is the use of parametric frameworks for empirical analyses. This study moves beyond parametric methods by examining the relationship between childhood obesity and food insecurity among low-income children with nonparametric regression techniques. We examine data from the Child Development Supplement (CDS) of the Panel Study of Income Dynamics (PSID), a nationally representative data set from the US. Consistent with recent work, our parametric analyses indicate that there is no statistically significant relationship between childhood obesity and food insecurity. In contrast, our nonparametric results indicate that the probability of being obese varies markedly with the level of food insecurity being experienced by the child. Moreover, this relationship differs across relevant subgroups including those defined by gender, race/ethnicity and income. Fully understanding the relationship between childhood obesity and food insecurity has significant policy implications.     

Forecasting with real-time macroeconomic data: The ragged-edge problem and revisions

Real-time macroeconomic data are typically incomplete for today and the immediate past (‘ragged edge’) and subject to revision. To enable more timely forecasts the recent missing data have to be imputed. The paper presents a state-space model that can deal with publication lags and data revisions. The framework is applied to the US leading index. We conclude that including even a simple model of data revisions improves the accuracy of the imputations and that the univariate imputation method in levels adopted by The Conference Board can be improved upon.     

Semi-parametric models for satisfaction with income

An overview is presented of some parametric and semi-parametric models, estimators, and specification tests that can be used to analyze ordered response variables. In particular, limited dependent variable models that generalize ordered probit are compared to regression models that generalize the linear model. These techniques are then applied to analyze how self-reported satisfaction with household income relates to household income, family composition, and other background variables. Data are drawn from the 1998 wave of the German Socio-Economic Panel. The results are used to estimate equivalence scales and the cost of children. We find that the standard ordered probit model is rejected, while some semi-parametric specifications survive specification tests against nonparametric alternatives. The estimated equivalence scales, however, are often similar for the parametric and semi-parametric specifications.JEL Classification: C14, C35, D12Correspondence to: Charles BellemareWe are grateful to an anonymous referee and to participants of a CeMMAP/ESG workshop at University College London and seminars at CentER (Tilburg University) and Humboldt University Berlin for useful comments.