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Cowles Foundation Paper 785
Estimating Long-Run Equilibria
Abstract
Our subject is estimation and inference concerning long-run economic equilibria in models with stochastic trends. An asymptotic
theory is provided to analyze a menu of currently existing estimators of cointegrated systems. We study in detail the single-equation
ECM (SEECM) approach of Hendry. Our theoretical results lead to prescriptions for empirical work, such as specifying SEECM's
nonlinearly and including lagged equilibrium relationships rather than lagged differences of the dependent variable as covariates.
Simulations support these prescriptions, and point to problems of overfitting not encountered in the semiparametric approach
of Phillips and Hansen (1990).
... Under our first approach, the methodology adopted is analogous to that of Mehra (1991) and Arize (1994), who employed an UECM in modeling money demand in the US. According to Phillips and Loretan (1991), a number of error correction formulations can be adopted in model specification. Banerjee et al. (1986) observe that the UECM approach allows for testing of cointegration of the variables in the model. ...
... In addition, the Granger representation theorem (Granger 1983) states that, if statistically significant error correction adjustment exists in a model, it implies cointegration of variables in that model. Moreover, according to Hall (1986), Phillips and Loretan (1991), Boswijk and Franses (1992) and Kremers, Ericson and Dolado (1992), the coefficient values of the lagged level dependent variable of an ECM can provide a robust check on the presence of a long-run cointegrating relationship. ...
The objective of this study is to empirically examine the status and sustainability of Australia, Hong Kong, Japan and Singapore as financial centers in the Asia-Pacific region. The sample period under investigation is from 1977 to 2002. This paper attempts to provide empirical evidence on significant factors such as taxes, economic activity, assets and liabilities of banks, regulation, socio-economic factors (education and quality of life) and the tax treatment of foreign institutions, that determine the status and sustainability of the above four financial centers. Although extensive research on financial centers has been conducted, there seems to be no empirical research focused on the above factors especially for Australia, Hong Kong, Japan and Singapore. This study uses three modeling approaches. Under the first approach: estimates of an error-correction model show the existence of a long-run relationship between the variables in the four financial centers. In the second approach: estimated pooled (panel) regression model indicates that majority of the variables under investigation are statistically significant when tested collectively for all four financial centers. Results of the third model show the importance of socio-economic and government intervention variables such as the education system, government economic policies, quality of life, the regulatory environment and the tax treatment of foreign corporations for the status and sustainability of financial centers. The main policy implication of this study is that business friendly government policies promoting economic growth and socio-economic development are important for healthy growth of financial centers.
... Moreover, as critics argue that the residuals of the first stage of the Engle-Granger two stage procedure are not well behaved and the standard t-statistic can not be used. Furthermore, according to Hall (1986), Phillips and Loretan (1991), and Boswijk and Fransers (1992), the coefficient values of the lagged level dependent variable of an ECM can provide a robust check of the existence of a long-run cointegrating relationship. Therefore, the use of UECM approach is justified. ...
The objective of this study is to carry out an empirical analysis of the relationship between trading volumes, returns and volatility on closed-end funds (CEFs) market in China using data for 1998-2003. In addition, the transmission of market volatility between Chinese stock market and CEF market is also examined. Further, empirical investigations are conducted on the relationship between premia of CEFs and their future net asset value returns, investor sentiment hypothesis and cointegration of fund share prices and net asset values. The lack of empirical studies on Chinese CEF and also the fast growth of funds in the last few years justify this research. The results of this study show that GARCH(1,1) model can capture the dynamic characteristic of CEF market in China and there is an asymmetric relationship between price change and trading volume. This study also provides evidence that the transmission of volatility occurs between stock market and closed-end fund market. Finally, the results suggest that investor sentiment hypothesis can explain the disparity between fund share prices and net asset values. But the rejection of cointegration between fund prices and net asset values indicates that excess returns cannot be obtained by investing in Chinese CEFs with lower discounts. The important policy implication from this research is that since daily price limits have a significant impact on the fluctuations of closed-end fund prices and the movement of discounts or premia of closed-end funds, policy makers should review the price limits
so as to improve market making activities.
Key Words: China, closed-end funds, GARCH model, error-correction model
JEL Classification: G23, G28, O16
... To ensure the reliability of our results, we employed two additional regression methods known as Fully-Modified Ordinary Least Squares (FMOLS) and Dynamic Ordinary Least Squares (DOLS), as proposed by (Phillips and Loretan, 1991;Pedroni, 2001). The results of these estimators, which are presented in Table 8, confirm that natural resource rents (NRR), rule of law (RL), digitalization (DIG), and economic growth (GDP) are significant factors in explaining CO 2 emissions in BRICS economies. ...
Industrialization is fueled by economic development, which raises the value of obtained natural resources. However, exploitation and excessive usage of natural resources in various sectors can have a negative impact on the environment. This paper examined the impact of Carbon dioxide emissions (CO 2), natural resource rents, rule of law, digitalization, and economic growth (GDP) in (Brazil, Russia, India, China, and South Africa) BRICS between 1990 and 2021. The empirical findings based on the Method of Moment Quantile Regression (MMQREG) confirm that GDP and natural resources have a negative association with CO 2 emissions, indicating that these two variables adversely affect carbon emissions in BRICS countries. Interestingly, the outcomes also reveal that digitalization and effective rule of law tackle the issue of CO 2 emissions effectively throughout all quantiles. Moreover, the robustness checks of Fully-Modified Ordinary Least Square (FMOLS), and Dynamic Ordinary Least Square (DOLS) confirm and support the outcomes of MMQREG. Based on the study findings, we propose that the current environmental policies of BRICS member countries do not efficiently tackle CO 2 emissions. To cope with carbon emissions and resource exploitation, the selected nations should restructure their natural resources-related policies for a sustainable environment by prioritizing the efficient utilization of natural resources and adopting clean and green energy for sustainable economic growth.
Ekonomik büyümeyi artıran nedenlerin başında beşeri sermaye stoğuna yapılan yatırımlar gelmektedir. Bu yatırımlardan biri de sağlık harcamalarıdır. Bir ülkedeki sağlık harcamalarının artması, eğitimin etkisiyle bilinçli toplumun sağlık hizmetlerinden daha verimli yararlanmasına ve dolayısıyla o toplumun gelişmesine ve refah seviyesinin artmasına pozitif katkı sağlayacaktır. Çalışmada Türkiye’de 2000-2018 dönemlerine ait ekonomik büyüme ve sağlık harcamaları değişkenleri arasındaki uzun dönem ilişki Auto Regressive Distributed Lag, (ARDL, Gecikmesi Dağıtılmış Otoregresif Model) testi ile incelenmiştir. Yapılan analizler sonucunda ekonomik büyüme ile sağlık harcamaları arasında pozitif ve anlamlı uzun dönemli bir ilişki olduğu gözlemlenmiştir.
This study analyzed the effect of government financing on agriculture value added in Nigeria between 2003 and 2022 using annual time series data sourced from Central Bank of Nigeria Statistical Bulletin and World Bank Development. Agricultural value added was used as the dependent variable while government financing on agriculture was used as the independent variable. Auto Regressive Distributed Lag (ARDL) Model was used to analyze data. The results of ARDL Model revealed that government financing on agricultural sector had a significant negative relationship with agricultural value added in Nigeria. The researcher therefore recommended that there should be increase in the amount of funds which the Central bank of Nigeria injects into the agricultural sector through the agricultural credit guarantee and also monitor and ensure compliance that these funds are used for the purpose they were meant for and not diverted.
Tomando una muestra de 24 países OCDE, mediante un panel cointegrado se proporciona evidencia empírica a nivel grupal e individual del efecto positivo del gasto en investigación, desarrollo e innovación sobre el crecimiento económico durante el periodo 2000-2019. Partiendo de que las patentes fungen como proxy de la innovación y utilizando el estimador de mínimos cuadrados ordinarios dinámicos para panel, se corrobora la existencia de una relación de equilibrio de largo plazo para la cual, y en términos per cápita, un aumento del 1,0% en el stock de patentes genera un incremento en el PIB de 0,52%. Asimismo, un aumento del 1,0% en el gasto en I+D deriva en un crecimiento de 1,27% en el PIB. De manera complementaria, implementando una prueba de causalidad tipo Granger para panel, se encuentra una relación positiva y significativa entre el gasto en I+D y el stock de patentes, el stock de patentes y el crecimiento, y el gasto en I+D y el crecimiento.
This collection of published papers records the development of an approach to econometric modelling that has reached a highly successful stage. The methodology of modelling ‘observational data’, as opposed to experimental data, which can be replicated, is analysed to highlight the fundamental flaws in various approaches, and the possibilities of others. Criteria for model adequacy are formulated (congruence and encompassing), and alternative approaches to building empirical models are compared on their ability to deliver such models. A typology of models elucidates their properties, and a taxonomy of information sources clarifies testing. Estimation is summarized by an estimator generating equation. The value of exploring the development path is to reveal by attempted applications why many widely used approaches are inadequate. The outcome is to demonstrate the viability of a general‐to‐specific approach that commences from a specification deemed more than adequate to characterize the evidence, and simplifies to a parsimonious representation that captures the main factors. By artificial Monte Carlo simulations on experiments designed by others, the success of that approach is established, leading to automatic model selection by software that can outperform practitioners.
This paper develops a forecasting procedure based on a Bayesian method for estimating vector autoregressions. The procedure is applied t o 10 macroeconomic variables and is shown to improve out-of-sample forecasts relative to univariate equations. Although cross-variable responses are damped by the prior, considerable interaction among the variables is shown to be captured by the estimates We provide unconditional forecasts as of 1982:12 and 1983:3. We also describe how a model such as this can be used to make conditional projections and to analyze policy alternatives. As an example, we analyze a Congressional Budget Office forecast made in 1982: 12 Although no automatic causal interpretations arise from models like ours, they provide a detailed characterization of the dynamic statistical interdependence of a set of economic variables, information that may help in evaluating causal hypotheses without containing any such hypotheses.
This paper studies the asymptotic properties of instrumental variable (IV) estimates of multivariate cointegrating regressions
and allows for deterministic and stochastic regressors as well as quite general deterministic processes in the data-generating
mechanism. It is found that IV regressions are consistent even when the instruments are stochastically independent of the
regressors. This phenomenon, which contrasts with traditional theory for stationary time series, is a beneficial artifact
of spurious regression theory whereby stochastic trends in the instruments ensure their relevance asymptotically. Problems
of inference are also addressed and some promising new theoretical results are reported. These involve a class of Wald tests
which are modified by semiparametric corrections for serial correlation and for endogeneity. The resulting test statistics
which we term fully-modified Wald tests have limiting X2 distributions, thereby removing the obstacles to inference in cointegrated systems that were presented by the nuisance parameter
dependencies in earlier work.
Some simulation results are reported which seek to explore the sampling behaviour of our suggested procedures. These simulations
compare our fully modified (semiparametric) methods with the parametric error-correction methodology that has been extensively
used in recent empirical research and with conventional least squares regression. Both the fully-modified and errorcorrection
methods work well in finite samples and the sampling performance of each procedure confirms the relevance of asymptotic distribution
theory, as distinct from super-consistency results, in discriminating between statistical methods.
Available information is considered as partitioned into the sets: past, present, and future observations, other data of competing models and theory knowledge. In each case, specific concepts are relevant to empirical model formulation (e.g. innovations for past data, exogeneity for present, encompassing for contending models, etc.) and various properties of such concepts are established (viz. encompassing is transitive and asymmetric). Relationships between concepts are developed (e.g. encompassing entails variance-dominance in linear models), and related to the notion of a progressive research strategy. An empirical model illustrates the various criteria. Model selection by dynamic simulation tracking performance is critically evaluated.
We consider a nonstationary vector autoregressive process which is integrated of order 1, and generated by i.i.d. Gaussian errors. We then derive the maximum likelihood estimator of the space of cointegration vectors and the likelihood ratio test of the hypothesis that it has a given number of dimensions. Further we test linear hypotheses about the cointegration vectors.The asymptotic distribution of these test statistics are found and the first is described by a natural multivariate version of the usual test for unit root in an autoregressive process, and the other is a χ2 test.
This paper gives a survey of some recent results on problems of identifiability (or, more general, of the relation between the observations and certain system characteristics) for linear dynamic errors-in-variables models. For a large part of the paper the noise components are assumed to be mutually uncorrelated. After the general problem statement, a rather complete analysis of the single-input–single-output case is given. Also the case of three variables and the case where the number of inputs is equal to the number of outputs are discussed in detail. Finally, the use of higher-order cummulant spectra for identifiability is investigated.
This paper introduces a general procedure for decomposition of non-stationary time series into a permanent and transitory component allowing both components to be stochastic. The permanent component is shown to be a random walk with drift and the transitory or cyclical component is a stationary process with mean zero. The decomposition methodology, which depends only on past data and therefore is computable in ‘real time’, is applied to the problem of measuring and dating business ‘cycles’ in the portwar U.S. economy. We find that measured expansions and contractions are of roughly equivalent duration and that our dating of cyclical episodes tends to lead the traditional NBER dating and, to a lesser extent, the ‘growth cycle’ chronology of Zarnowitz and Boschan (1977).
We consider an autoregressive linear process $\{x_t\}$, a one-sided moving average, with summable coefficients, of independent identically distributed variables $\{e_t\}$ with zero mean and fourth moment, such that $\{e_t\}$ is expressible in terms of past values of $\{x_t\}$. The spectral density of $\{x_t\}$ is assumed bounded and bounded away from zero. Using data $x_1,\cdots, x_n$ from the process, we fit an autoregression of order $k$, where $k^3/n \rightarrow 0$ as $n \rightarrow \infty$. Assuming the order $k$ is asymptotically sufficient to overcome bias, the autoregression yields a consistent estimator of the spectral density of $\{x_t\}$. Furthermore, assuming $k$ goes to infinity so that the bias from using a finite autoregression vanishes at a sufficient rate, the autoregressive spectral estimates are asymptotically normal, uncorrelated at different fixed frequencies. The asymptotic variance is the same as for spectral estimates based on a truncated periodogram.
Tests for unit roots in autoregressive models (tests for stationarity) are popular in the macroeconomics literature. Monte Carlo experiments in Schwert (1987) show that unit root tests derived for pure autoregressive processes have different sampling distributions when the true process is a mixed autoregressive-integrated moving average (ARIMA) process. Tests suggested by and , Phillips (1987), Phillips and Perron (1986), and and are applied to a variety of monthly and quarterly macroeconomic time series to illustrate the effects of ARIMA model specification on inferences about stationarity.