Estimation Of Impulse Response Function Research Articles

The causal relationship between female labor supply and fertility in the USA: updated evidence via a time series multi-horizon approach

The purpose of this paper is to investigate the causality between female labor supply and fertility in the presence of auxiliary variables such as education, female wages, and male relative cohort size. We employ annual time series data spanning the period 1948 to 2007 for both an aggregate and an age-specific group. Our econometric specification follows closely the concepts and procedures proposed by Dufour and Renault (Econometrica 66(5):1099–1125, 1998) and Dufour et al. (J Econom 132:337–362, 2006) in that we conduct multi-horizon causality tests that allow for direct and indirect effects to take place. The sign and economic importance of our results is assessed via the estimation of impulse response functions. Our results establish bidirectional indirect causality between female labor supply and fertility and suggest interesting causal chains among the system variables. Causality effects are stronger for the age-specific group.

Dynamic Effects of Fiscal Shocks Upon Diverse Macroeconomic Variables: A Structural VAR Analysis for Argentina

The paper studies the dynamic effects of fiscal policy shocks upon Argentine macroeconomic variables such as the gross domestic product, the inflation rate and the level of unemployment; a structural Vector Autoregression model is resorted to in order to estimate the impulse response functions; the econometric analysis is carried out for the period 1984-2005 (second quarter) and quarterly logarithmic real variables are used for the VAR´s specification. Point estimation of impulse response functions indicate both a relatively low statistical significance of fiscal shocks upon macroeconomic variables and a short-lived impact of innovations while at the same time cast doubts upon some traditionally accepted Keynesian macroeconomic policy prescriptions.

Prior Selection for Vector Autoregressions

Vector autoregressions (VARs) are flexible time series models that can capture complex dynamic interrelationships among macroeconomic variables. However, their dense parameterization leads to unstable inference and inaccurate out-of- sample forecasts, particularly for models with many variables. A potential solution to this problem is to use informative priors, in order to shrink the richly parameterized unrestricted model towards a parsimonious naive benchmark, and thus reduce estimation uncertainty. This paper studies the optimal choice of the informativeness of these priors, which we treat as additional parameters, in the spirit of hierarchical modeling. This approach is theoretically grounded, easy to implement, and greatly reduces the number and importance of subjective choices in the setting of the prior. Moreover, it performs very well both in terms of out-of-sample forecasting, and accuracy in the estimation of impulse response functions.

Limit Order Flow, Market Impact and Optimal Order Sizes: Evidence from NASDAQ TotalView-ITCH Data

In this paper, we provide new empirical evidence on order submission activity and price impacts of limit orders at NASDAQ. Employing NASDAQ TotalView-ITCH data, we find that market participants dominantly submit limit orders with sizes equal to a round lot. Most limit orders are canceled almost immediately after submission if not getting executed. Moreover, only very few market orders walk through the book, i.e., directly move the best ask or bid quote. Estimates of impulse-response functions on the basis of a cointegrated VAR model for quotes and market depth allow us to quantify the market impact of incoming limit orders. We propose a method to predict the optimal size of a limit order conditional on its position in the book and a given fixed level of expected market impact.

Is Economic Recovery a Myth? Robust Estimation of Impulse Responses

There is a lively debate on the persistence of the current banking crisis' impact on GDP. Impulse Response Functions (IRF) estimated by Cerra and Saxena (2008) suggest that the effects of earlier crises were long-lasting. We show that standard estimates of IRFs are highly sensitive to misspecification of the underlying data generation process. Direct estimation of IRFs by a methodology similar to Jorda's (2005) local projection method is robust to misspecifications of the data generation process but yields biased estimates when country fixed effects are added. We propose a simple method to deal with this bias, which we apply to panel data from 99 countries for the period 1974-2001. Our estimates suggest that an average banking crisis leads to an output loss of around 10 percent with little sign of recovery. GDP losses from banking crises are more severe for African countries and economies in transition.

Supply, Demand and Monetary Policy Shocks in a Multi-Country New Keynesian Model

This paper estimates and solves a multi-country version of the standard DSGE New Keynesian (NK) model. The country-specific models include a Phillips curve determining inflation, an IS curve determining output, a Taylor Rule determining interest rates, and a real effective exchange rate equation. The IS equation includes a real exchange rate variable and a countryspecific foreign output variable to capture direct inter-country linkages. In accord with the theory all variables are measured as deviations from their steady states, which are estimated as long-horizon forecasts from a reduced-form cointegrating global vector autoregression. The resulting rational expectations model is then estimated for 33 countries on data for 1980Q1-2006Q4, by inequality constrained IV, using lagged and contemporaneous foreign variables as instruments, subject to the restrictions implied by the NK theory. The multi-country DSGE NK model is then solved to provide estimates of identified supply, demand and monetary policy shocks. Following the literature, we assume that the within country supply, demand and monetary policy shocks are orthogonal, though shocks of the same type (e.g. supply shocks in different countries) can be correlated. We discuss estimation of impulse response functions and variance decompositions in such large systems, and present estimates allowing for both direct channels of international transmission through regression coefficients and indirect channels through error spillover effects. Bootstrapped error bands are also provided for the cross country responses of a shock to the US monetary policy. JEL Classification: C32, E17, F37, F42

Supply, Demand and Monetary Policy Shocks in a Multi-Country New Keynesian Model

This paper estimates and solves a multi-country version of the standard DSGE New Keynesian (NK) model. The country-specific models include a Phillips curve determining inflation, an IS curve determining output, a Taylor Rule determining interest rates, and a real effective exchange rate equation. The IS equation includes a real exchange rate variable and a countryspecific foreign output variable to capture direct inter-country linkages. In accord with the theory all variables are measured as deviations from their steady states, which are estimated as long-horizon forecasts from a reduced-form cointegrating global vector autoregression. The resulting rational expectations model is then estimated for 33 countries on data for 1980Q1-2006Q4, by inequality constrained IV, using lagged and contemporaneous foreign variables as instruments, subject to the restrictions implied by the NK theory. The multi-country DSGE NK model is then solved to provide estimates of identified supply, demand and monetary policy shocks. Following the literature, we assume that the within country supply, demand and monetary policy shocks are orthogonal, though shocks of the same type (e.g. supply shocks in different countries) can be correlated. We discuss estimation of impulse response functions and variance decompositions in such large systems, and present estimates allowing for both direct channels of international transmission through regression coefficients and indirect channels through error spillover effects. Bootstrapped error bands are also provided for the cross country responses of a shock to the US monetary policy.

TRANSMISSÃO INTER-REGIONAL DE PREÇOS NO MERCADO BRASILEIRO DE SOJA

Este estudo estima as elasticidades de transmissão entre pares de preços para a soja produzida no Mato Grosso e no Paraná; no Mato Grosso e no Rio Grande do Sul; e no Paraná e no Rio Grande do Sul, com o intuito de testar a validade da Lei do Preço Único entre esses mercados. Os dados empregados correspondem às médias mensais dos preços nesses estados, obtidos junto ao Centro de Estudos Avançados em Economia Aplicada (CEPEA), da ESALQ / USP, para o período de janeiro de 2001 a fevereiro de 2008. Para tal, utilizam-se testes de raiz unitária e de co-integração de Johansen, estimação da função impulso-resposta, decomposição da variância dos erros de previsão e estimação e análise do modelo vetorial de correção de erro (VEC). Os resultados indicam que as variações de preços de longo prazo, ocorridas no Rio Grande do Sul, são transmitidas quase que totalmente para os preços da soja no Paraná e no Mato Grosso. Dessa forma, esses mercados poderiam ser considerados perfeitamente integrados se a hipótese de perfeita integração entre mercados não tivesse sido rejeitada quando restrições foram impostas ao coeficiente de relacionamento de longo prazo. Portanto, a Lei do Preço Único não foi perfeitamente verificada nesses mercados de soja.

To difference or not to difference: a Monte Carlo investigation of inference in vector autoregression models

It is often unclear whether time series displaying substantial persistence should be modelled as a vector autoregression in levels (perhaps with a trend term) or in differences. The impact of this decision on inference is examined here using Monte Carlo simulation. In particular, the size and power of variable inclusion (Granger causality) tests and the coverage of impulse response function confidence intervals are examined for simulated vector autoregression models using a variety of estimation techniques. We conclude that testing should be done using differenced regressors, but that overdifferencing a model yields poor impulse response function confidence interval coverage; modelling in Hodrick-Prescott filtered levels yields poor results in any case. We find that the lag-augmented vector autoregression method suggested by Toda and Yamamoto (1995) – which models the level of the series but allows for variable inclusion testing on changes in the series – performs well for both Granger causality testing and impulse response function estimation.

VARs, common factors and the empirical validation of equilibrium business cycle models

Abstract Equilibrium business cycle models have typically less shocks than variables. As pointed out by Altug (1989) International Economic Review 30 (4) 889–920 and Sargent (1989) The Journal of Political Economy 97 (2) 251–287, if variables are measured with error, this characteristic implies that the model solution for measured variables has a factor structure. This paper compares estimation performance for the impulse response coefficients based on a VAR approximation to this class of models and an estimation method that explicitly takes into account the restrictions implied by the factor structure. Bias and mean-squared error for both factor- and VAR-based estimates of impulse response functions are quantified using, as data-generating process, a calibrated standard equilibrium business cycle model. We show that, at short horizons, VAR estimates of impulse response functions are less accurate than factor estimates while the two methods perform similarly at medium and long run horizons.

VARs, Common Factors and the Empirical Validation of Equilibrium Business Cycle Models

Equilibrium business cycle models have typically less shocks than variables. As pointed out by Altug, 1989, and Sargent, 1989, if variables are measured with error, this characteristic implies that the model solution for measured variables has a factor structure. This Paper compares estimation performance for the impulse response coefficients based on a VAR approximation to this class of models and an estimation method that explicitly takes into account the restrictions implied by the factor structure. Bias and mean squared error for both factor based and VAR based estimates of impulse response functions are quantified using, as a data generating process, a calibrated standard equilibrium business cycle model. We show that, at short horizons, VAR estimates of impulse response functions are less accurate than factor estimates while the two methods perform similarly at medium and long run horizons.

Measurement of the coolant flow rate using correlation of temperature fluctuations

The transit time of the coolant, and thus its velocity, has been measured using the temperature fluctuation at the outlet of a reactor core. An impulse response function estimation is introduced, which substitutes the widely used cross-correlation measurement technique. It is shown in theory and practice that the time delay estimation is improved when using the impulse response function instead of the cross-correlation function in parameter estimation. Extremely low velocities (down to 2 cm/sec) have been measured in a natural circulation regime in a research reactor.

Recursive estimation of impulse response function using covariance information in linear continuous stochastic systems

This paper proposes a new recursive least-squares (RLS) estimation algorithm for an impulse response function in linear continuous-time wide-sense stationary stochastic systems. It is assumed that the input signal to the unknown impulse response function is contaminated by additive white Gaussian observation noise. The output signal from the system related with the impulse response function is observed with additive white Gaussian noise. The impulse response function is estimated recursively in terms of the variance of the white Gaussian observation noise included in the input signal, the autocovariance function of the process before the observation noise is added to the input signal, the crosscovariance function between the output observed value and the input observed value, concerning the system based on the unknown impulse response function.

Detection versus Estimation in Event-Related fMRI: Choosing the Optimal Stimulus Timing

With the advent of event-related paradigms in functional MRI, there has been interest in finding the optimal stimulus timing, especially when the interstimulus interval is varied during the imaging run. Previous works have proposed stimulus timings to optimize either the estimation of the impulse response function (IRF) or the detection of signal changes. The purpose of this paper is to clarify that estimation and detection are fundamentally different goals and to determine the optimal stimulus timing and distribution with respect to both the accuracy of estimating the IRF and the power of detection assuming a particular hemodynamic model. Simulated stimulus distributions are varied systematically, from traditional blocked designs to rapidly varying event related designs. These simulations indicate that estimation of the hemodynamic impulse response function is optimized when stimuli are frequently alternated between task and control states, with shorter interstimulus intervals and stimulus durations, whereas the detection of activated areas is optimized by blocked designs. The stimulus timing for a given experiment should therefore be generated with the required detectability and estimation accuracy.

Scaling in economics: a reader's guide

This paper discusses examples of scaling laws in economics and finance. It argues that these regularities in data are useful for disciplining theory formation. Estimation of the conditional predictive distribution and estimation of impulse response functions is a main goal of econometric work. Scaling type regularities give useful information on the underlying data generating process. The ability of scaling laws to suggest lines of potentially fruitful research was illustrated by the suggestion of several speculative research projects in this paper. Most importantly, the paper stresses the challenges that face empirical and theoretical researchers who wish to make use of scaling law type regularities to improve econometric identification of the underlying causal data generating mechanism. Copyright 1999 by Oxford University Press.

Two updated methods for impulse response function estimation

The impulse response function (IRF) is a complete description of the dynamic behaviour of a linear structure. The study of effectively identifying this function is still far from complete. The conventional method, i.e., the inverse discrete Fourier transform (IDFT) of the frequency response function (FRF) has been proved to be inaccurate. After investigation of some features of the FRF, two revised approaches for IRF estimation are advocated. One is called the imaginary part transform and the other compensatory amendment. The former exploits the energy concentration property of the imaginary part of the FRF and the feasibility of obtaining the IRF from it. The latter is a simple revision of the conventional method by taking the frequency truncation into consideration. A numerical example is provided to demonstrate that the two revised methods given in this paper produce much more accurate IRF estimations than the conventional solution.