A Monte Carlo study of growth regressions

Using Monte Carlo simulations, this paper evaluates the bias properties of estimators commonly used to estimate growth regressions derived from the Solow model. We explicitly allow for measurement error, country-specific fixed effects and regressor endogeneity. An OLS estimator applied to a single cross-section of variables averaged over time (the between estimator) performs best in terms of the extent of bias on each of the estimated coefficients. Fixed-effects and the Arellano–Bond GMM estimator overstate the speed of convergence under a wide variety of assumptions, while the between estimator understates it. Finally, fixed effects and Arellano–Bond bias towards zero the slope estimates on the human and physical capital accumulation variables, while the between estimator and the Blundell–Bond system GMM estimator bias these coefficients upwards.      

Structural stability in a cross-country neoclassical growth model

This paper tests for structural stability of the Solow growth model, as recently extended to human capital and applied to a large section of countries by Mankiw, Romer and Weil. The evidence is obtained by ranking each explanatory variable of the model in ascending order and then running recursive regressions and by then splitting the original sample according to cluster analysis before running separate regressions. The evidence shows that the model exhibits overall structural breaks; the convergence coefficient, however, is very stable; the coefficients of the production factors become unstable where the factors become very abundant or very scarce; the coefficient of labour growth is negative and significant, as required by the theory, only if a small group of countries with scarce labour is considered; the same coefficient is instead positive and significant for a group of countries with abundant labour and favourable initial income and investments; the coefficient of investment in human capital is not significant if abundant labour countries or, simply, if influential countries in the regression are not considered.     

A reflection principle for a random walk with implications for volatility estimation using extreme values of asset prices

In this paper, we derive a reflection principle for a random walk with the symmetric double exponential distribution. This allows us to come up with the closed form solution for the joint probability of the running maximum and the terminal value of the random walk. Based on this new theoretical result, we propose an extreme value estimator for the variance of the random walk that is not just approximately unbiased but exactly so. In simulations, we find that this estimator continues to be unbiased even when intraday mean reversion is present, as captured by the Binomial Markov Random Walk model. On the empirical side, we find that this estimator works well in a variety of global stock indices, including the S&P 500 Index, in the sense of being unbiased relative to the “usual” estimator, i.e., the sample variance of the daily returns.     

Estimation of Censored Regression Model: A Simulation Study

We investigate the finite sample performance of several estimators proposed for the panel data Tobit regression model with individual effects, including Honoré estimator, Hansen’s best two-step GMM estimator, the continuously updating GMM estimator, and the empirical likelihood estimator (ELE). The latter three estimators are based on more conditional moment restrictions than the Honoré estimator, and consequently are more efficient in large samples. Although the latter three estimators are asymptotically equivalent, the last two have better finite sample performance. However, our simulation reveals that the continuously updating GMM estimator performs no better, and in most cases is worse than Honoré estimator in small samples. The reason for this finding is that the latter three estimators are based on more moment restrictions that require discarding observations. In our designs, about seventy percent of observations are discarded. The insufficiently few number of observations leads to an imprecise weighted matrix estimate, which in turn leads to unreliable estimates. This study calls for an alternative estimation method that does not rely on trimming for finite sample panel data censored regression model.     

Evaluating Social Policy by Experimental and Nonexperimental Methods

Although it is important to establish causal relationships in social policy evaluation, the effects are difficult to observe due to sample selection. To evaluate the performance of estimators designed to handle sample selection bias, we analyse data from a Norwegian rehabilitation project with a randomised experimental design. The data permit us to compare the performance of different nonexperimental estimators with the experimental results. In our case study we find that nonexperimental evaluation based on sample selection estimators with selection terms that fail to meet conventional levels of statistical significance is highly unreliable. The difference in difference estimator and propensity score matching estimators perform better in our context.
JEL classification : C 51; J 24; H 43; I 12     

Reopening the convergence debate: A new look at cross-country growth empirics

There are two sources of inconsistency in existing cross-country empirical work on growth: correlated individual effects and endogenous explanatory variables. We estimate a variety of cross-country growth regressions using a generalized method of moments estimator that eliminates both problems. In one application, we find that per capita incomes converge to their steady-state levels at a rate of approximately 10 percent per year. This result stands in sharp contrast to the current consensus, which places the convergence rate at 2 percent. We discuss the theoretical implications of this finding. In another application, we perform a test of the Solow model. Again, contrary to prior reults, we reject both the standard and the augmented version of the model.     

Robust estimation of the simplified multivariate GARCH model

In this paper, robust M-estimation of multivariate GARCH models are considered. The simplified GARCH model is chosen that involves the estimation of only univariate GARCH models, and hence easy to estimate, and does not put additional constraints on the model. The results of Monte Carlo simulations showed that accurate estimates of conditional correlations can be obtained using these robust estimators when the errors are heavy-tailed. We also investigate the forecasting performance of the class of robust estimators in predicting value-at-risk using various evaluation measures and collect empirical evidences of the better predictive potential of estimators such as LAD and B-estimator over the widely-used quasi-maximum likelihood estimator for the estimation and prediction of multivariate GARCH models. Applications to real data sets are also presented.     

The local Solow growth model

This paper generalizes the empirical analysis of the Solow growth model to account for country-specific heterogeneity. This generalization relaxes the assumption made in bulk of empirical growth studies that all countries possess identical aggregate production functions. Our empirical results indicate that there is substantial country-specific heterogeneity in the Solow parameters-heterogeneity that is associated with differences in initial income. We therefore conclude that the explanatory value of the Solow growth model is substantially enhanced by allowing for country-specific, i.e. local, production functions.     

The asymptotic efficiency of semiparametric estimators for censored linear regression models

This paper presents numerical comparisons of the asymptotic mean square estimation errors of semiparametric generalized least squares (SGLS), quantite, symmetrically censored least squares (SCLS), and tobit maximum likelihood estimators of the slope parameters of censored linear regression models with one explanatory variable. The results indicate that the SCLS estimator is less efficient than the other two semiparametric estimators. The SGLS estimator is more efficient than quantile estimators when the tails of the distribution of the random component of the model are not too thick and the probability of censoring is not too large. The most efficient semiparametric estimators usually have smaller mean square estimation errors than does the tobit estimator when the random component of the model is not normally distributed and the sample size is 500–1,000 or more.     

Small Sample Properties Of Existing And New Estimators Of The Autocorrelation Coefficient And Regression Coefficients In The Context Of Ar(1) Errors

This study systematically and comprehensively investigates the small sample properties of the existing and some new estimators of the autocorrelation coefficient and of the regression coefficients in a linear regression model when errors follow an autoregressive process of order one. The new estimators of autocorrelation coefficient proposed here are based on the jackknife procedure. The jackknife procedure is applied in two alternative ways: first to the regression itself, and second to the residuals of the regression model. Next, the performance of the existing and new estimators of autocorrelation coefficient (thirty-three in total) is investigated in terms of bias and the root mean squared errors. Finally, we have systematically compared all of the estimators of the regression coefficients (again thirty-three) in terms of efficiency and their performance in hypothesis testing. We observe that the performance of the autocorrelation coefficient estimators is dependent upon the degree of autocorrelation and whether the autocorrelation is positive or negative. We do not observe a direct link between the bias and efficiency of an estimator. The performance of the estimators of the regression coefficients also depends upon the degree of autocorrelation. If the efficiency of regression estimator is of concern, then the iterative Prais-Winsten estimator should be used since it is most efficient for the widest range of independent variables and values of the autocorrelation coefficient. If testing of the hypothesis is of concern, then the estimators based on jackknife technique are certainly superior and are highly recommended. However, for negative values of the autocorrelation coefficient, the estimators based on Quenouille procedure and iterative Prais-Winsten estimator are comparable. But, for computational ease iterative Prais-Winsten estimator is recommended.

     

Robust Volatility Estimation with and Without the Drift Parameter

We find the closed form solution for the joint probability of the running maximum and the drawdown of the Brownian motion with a non-zero drift parameter at a random time that is exponentially distributed and independent of the Brownian motion. This characterization leads us to come up with a robust method of estimating volatility using open, high, low and closing prices. We rigorously show the independence of robust volatility estimators based on extreme values of asset prices relative to the standard robust volatility estimator based on closing price alone. We further prove that the proposed robust volatility ratio is unbiased with no drift parameter. Moreover, we find that the robust volatility ratio with a non-zero drift parameter has only a second order effect. We have shown that our proposed extreme value robust volatility estimator is 2–3 times relatively more efficient when compared to the classical robust volatility estimator based on Monte Carlo simulation experiment. On the empirical side, we test the proposed robust volatility ratio based on high and low prices on different asset classes like stock indices, exchange rate and precious metals.

     

Persistence of Shocks to Output in Austria and Theories of Economic Growth

The paper analyzes the degree of output persistence in GDP in order toempirically discriminate between the Solow growth model, the perfect competition endogenous growth model and the imperfect competition endogenous growth model for the case of Austria. Wefind that a shock in the growth rate of output induces a permanent and larger effect on the level of GDP. This leads us to refute the Solow growth model and the perfect competition model of endogenous growth.We may not reject the imperfect competition growth model.     

Hierarchically spatial autoregressive and moving average error model

This paper considers a hierarchically spatial autoregressive and moving average error (HSEARMA) model. This model captures the spatially autoregressive and moving average error correlation, the county-level random effects, and the district-level random effects nested within each county. We propose optimal generalized method of moments (GMM) estimators for the spatial error correlation coefficient and the error components' variances terms, as well as a feasible generalized least squares (FGLS) estimator for the regression parameter vector. Further, we prove consistency of the GMM estimator and establish the asymptotic distribution of the FGLS estimator. A finite-scale Monte Carlo simulation is conducted to demonstrate the good finite sample performances of our GMM-FGLS estimators.     

On Calculation of the Extended Gini Coefficient

The conventional formula for estimating the extended Gini coefficient is a covariance formula provided by Lerman and Yitzhaki (1989). We suggest an alternative estimator, obtained by approximating the Lorenz curve by a series of linear segments. In a Monte Carlo experiment designed to assess the relative bias and efficiency of the two estimators, we find that, when using grouped data with 20 or fewer groups, our new estimator has less bias and lower mean squared error than the covariance estimator. When individual observations are used, or the number of groups is 30 or more, there is little or no difference in the performance of the two estimators.     

Conditional convergence and the dynamics of the capital-output ratio

Output per worker can be expressed as a function of technological efficiency and of the capital-output ratio. Because technology is exogenous in the Solow model, all of the endogenous convergence dynamics take place through the adjustment of the capital-output ratio. This paper uses the empirical behavior of the capital-output ratio to estimate the speed of conditional convergence of economies towards their steady-state paths. We find that the conditional convergence speed is about seven percent per year. This is somewhat faster than predicted by the Solow model and is significantly higher than reported in most previous studies based on output per worker regressions. We show that, once there are stochastic shocks to technology, standard panel econometric techniques produce downward-biased estimates of convergence speeds, while our approach does not. The views expressed in this paper are our own, and do not necessarily reflect the views of the Central Bank and Financial Services Authority of Ireland or the ESCB.     

Estimating the gravity model when zero trade flows are frequent and economically determined

ABSTRACT

Since the 1950s, we have known that the presence of zero-valued dependent variables can seriously bias econometric estimates whether the zeros are included or excluded. Yet the widely-used gravity model is frequently estimated on samples that include large fractions of zeros. An influential paper by Santos Silva and Tenreyro – based on simulations that include no economically-determined zeros – concludes that the bias problems resulting from zeros and those resulting from heteroscedasticity and nonlinearity can be solved using the Poisson Pseudo-Maximum-Likelihood (PPML) model including the zero values. This paper begins by adapting the Santos Silva and Tenreyro experimental design to include economically-determined zeros to see whether this conclusion continues to hold. With this design, it finds that alternative estimators have lower bias than PPML. Changing to a Monte Carlo design that replicates the much-higher real-world frequency of predicted values near zero restores the finding of lower bias with the PPML estimator. The results highlight the need for very careful design of Monte Carlo experiments when evaluating alternative estimators of the gravity model.     

Path-dependent economic growth with technological trajectory

This paper develops an integrated model of neoclassical and endogenous growth, which accounts for both income inequalities across countries and the convergence hypothesis, while all the growth stylized facts are satisfied. The model in this paper assumes that an economy industrializes in two stages. In the first stage, the economy starts industrialization through factor accumulation (the Solow stage); and after sufficient factor accumulation, it switches to the second stage of endogenous growth through innovation (the AK stage). Therefore, it becomes crucial to determine when switching from the Solow to the AK stages is implemented. We model this switching problem as a two-stage optimal control and show that the growth rate declines during the Solow stage, while in the AK stage it becomes constant. In addition, we draw several policy implications.     

Estimating average economic growth in time series data with persistency

This paper studies estimation of average economic growth in time series models with persistency. In particular, a joint estimation of the trend coefficient and the autoregressive parameter is considered. An analysis on the proposed estimator is provided. Our analysis is also extended to the case with general disturbance distributions. A nonlinear M estimator and a class of partially adaptive M estimators which adapt themselves with respect to a measure of the tailthickness are considered. The joint estimator and its partially adapted version are compared with several conventional estimators. Monte Carlo experiments indicate that the proposed estimators have good finite sample performance. We use the proposed estimation procedure to estimate the growth rates for real GNP and consumer price index in 40 countries.     

A spatial merger estimator with an application to school district consolidation

This paper develops a spatial merger estimator to explain political integration generally and then applies this method to a wave of school district mergers in the state of Iowa during the 1990s. Our estimator is rooted in the economics of matching and thus accounts for three important features of typical merger protocol: two-sided decision making, multiple potential partners, and spatial interdependence. Rather than simply explaining when a particular region is likely to experience a wave of political integration, our method allows us to explore the factors driving which specific subregional mergers take place. This allows us to explore how those districts that merge choose with which of their neighbors to do so. Our results highlight the importance of state financial incentives for consolidation, economies of scale, diseconomies of scale, and a variety of heterogeneity measures in this particular application. We also demonstrate the power of our estimator, relative to existing estimators, to detect a statistically significant role for heterogeneity factors. While our application is limited to school district consolidation, our method can be adapted to include the salient features of many spatial integration problems.     

Dynamic Seemingly Unrelated Cointegrating Regressions

We propose the parametric Dynamic Seemingly Unrelated Regression (DSUR) estimator for simultaneous estimation of multiple cointegrating regressions. DSUR is efficient when the equilibrium errors are correlated across equations and is applicable for panel cointegration estimation in environments where the cross section is small relative to the available time series. We study the asymptotic and small sample properties of the DSUR estimator for both heterogeneous and homogeneous cointegrating vectors. We then apply the method to analyse two long-standing problems in international economics. Our first application revisits the estimation of long-run correlations between national investment and national saving. Our second application revisits the question of whether the forward exchange rate is an unbiased predictor of the future spot rate.