Heteroskedasticity- and Autocorrelation-robust F and t Tests in Stata

2018 ◽  
Vol 18 (4) ◽  
pp. 951-980 ◽  
Author(s):  
Xiaoqing Ye ◽  
Yixiao Sun
Keyword(s):  
Method Of Moments ◽  
Instrumental Variable ◽  
Generalized Method Of Moments ◽  
Ordinary Least Squares ◽  
Type I ◽  
Variance Estimators ◽  
Normal Approximations ◽  
Chi Squared ◽  
Smoothing Parameters ◽  
Type Ii Errors

In this article, we consider time-series, ordinary least-squares, and instrumental-variable regressions and introduce a new pair of commands, har and hart, that implement more accurate heteroskedasticity- and autocorrelation-robust (HAR) F and t tests. These tests represent part of the recent progress on HAR inference. The F and t tests are based on the convenient F and t approximations and are more accurate than the conventional chi-squared and normal approximations. The underlying smoothing parameters are selected to target the type I and type II errors, which are the two fundamental objects in every hypothesis testing problem. The estimation command har and the postestimation test command hart allow for both kernel HAR variance estimators and orthonormal-series HAR variance estimators. In addition, we introduce another pair of new commands, gmmhar and gmmhart, that implement the recently developed F and t tests in a two-step generalized method of moments framework. For these commands, we opt for the orthonormal-series HAR variance estimator based on the Fourier bases because it allows us to develop convenient F and t approximations as in the first-step generalized method of moments framework. Finally, we present several examples to demonstrate these commands.

Shadow Economy, Corruption, and Economic Growth: An Empirical Analysis

2019 ◽  
Vol 47 (3) ◽  
pp. 276-294 ◽  
Author(s):  
Nedra Baklouti ◽  
Younes Boujelbene
Keyword(s):  
Economic Growth ◽  
Least Squares ◽  
Public Administration ◽  
Method Of Moments ◽  
Fixed Effects ◽  
Shadow Economy ◽  
Generalized Method Of Moments ◽  
Ordinary Least Squares ◽  
Negative Effects ◽  
Considerable Debate

There is considerable debate over the effects of both corruption and shadow economy on growth, but few studies have considered how the interaction between them might affect economic growth. We study how corruption levels in public administration affect economic growth and how this effect depends on the shadow economy. Using Ordinary Least Squares (OLS), fixed effects, and system generalized method of moments (GMM) on a dataset of 34 OECD countries over the period 1995-2014. The estimation results indicate that increased corruption and a larger shadow economy lead to decrease in economic growth. Results additionally indicate that the shadow economy magnifies the effect of corruption on economic growth. These results imply significant complementarities between corruption and the shadow economy, suggesting that the reduction of corruption will lead to a fall in the size of the shadow economy and will also reduce the negative effects of corruption on economic growth through the underground economy.

Intergenerational Income Elasticities, Instrumental Variable Estimation, and Bracketing Strategies

2020 ◽  
Vol 50 (1) ◽  
pp. 1-46
Author(s):  
Pablo A. Mitnik
Keyword(s):  
Instrumental Variable ◽  
Income Elasticity ◽  
Geometric Mean ◽  
Panel Study ◽  
Generalized Method Of Moments ◽  
Ordinary Least Squares ◽  
Point Estimate ◽  
Set Estimation ◽  
Iv Estimation ◽  
Short Run

The fact that the intergenerational income elasticity (IGE)—the workhorse measure of economic mobility—is defined in terms of the geometric mean of children’s income generates serious methodological problems. This has led to a call to replace it with the IGE of the expectation, which requires developing the methodological knowledge necessary to estimate the latter with short-run measures of income. This article contributes to this aim. The author advances a “bracketing strategy” for the set estimation of the IGE of the expectation that is equivalent to that used to set estimate (rather than point estimate) the conventional IGE with estimates obtained with the ordinary least squares and instrumental variable (IV) estimators. The proposed bracketing strategy couples estimates generated with the Poisson pseudo–maximum likelihood estimator and a generalized method of moments IV estimator of the Poisson or exponential regression model. The author develops a generalized error-in-variables model for the IV estimation of the IGE of the expectation and compares it with the corresponding model underlying the IV estimation of the conventional IGE. By considering both bracketing strategies from the perspective of the partial-identification approach to inference, the author specifies how to construct confidence intervals for the IGEs, in particular when the upper bound is estimated more than once with different sets of instruments. Finally, using data from the Panel Study of Income Dynamics, the author shows that the bracketing strategies work as expected and assesses the information they generate and how this information varies across instruments and short-run measures of parental income. Three computer programs made available as companions to the article make the set estimation of IGEs, and statistical inference, very simple endeavors.

scholarly journals Measuring the optimal macroeconomic uncertainty index for Turkey

2016 ◽  
Vol 61 (210) ◽  
pp. 7-22 ◽  
Author(s):  
Havvanur Erdem ◽  
Rahmi Yamak
Keyword(s):  
Method Of Moments ◽  
Optimization Algorithm ◽  
Generalized Method Of Moments ◽  
Ordinary Least Squares ◽  
Macroeconomic Model ◽  
Parameter Estimations ◽  
Seemingly Unrelated Regressions ◽  
Macroeconomic Uncertainty ◽  
Turkish Economy ◽  
Uncertainty Index

The aim of this study is to calculate the optimal macroeconomic uncertainty index for the Turkish economy. The data used in the study are quarterly and cover the period 2002-2014. In this study the index is formed based on the small structural macroeconomic model. The study uses three important econometric processes. First, the model is estimated separately using generalized method of moments (GMM), seemingly unrelated regressions (SUR), and ordinary least squares (OLS). Secondly, the Broyden-Fletcher- Goldfarb-Shanno (BFGS) algorithm is applied as an optimization algorithm. The BFGS algorithm calibrates the model using GMM, SUR, and OLS parameter estimations of the benchmark parameters. Next, the index variables are weighted under the estimated optimal coefficients and, finally, are aggregated to produce the optimal macroeconomic uncertainty index.

scholarly journals Technology Import and China's Innovation Capability: Does Institutional Quality Matter?

2020 ◽  
pp. 93-104
Author(s):  
Haitao Wu ◽  
Siyu Ren ◽  
Guo Xie
Keyword(s):  
Linear Regression ◽  
Method Of Moments ◽  
Generalized Method Of Moments ◽  
Institutional Quality ◽  
Ordinary Least Squares ◽  
Three Dimensions ◽  
Quality Level ◽  
Innovation Capability ◽  
Regional Innovation ◽  
Technology Import

With the rapid growth of China's economy, technology import plays a crucial role in enhancing regional innovation capability. Based on inter-provincial panel data from 2007 to 2016, this paper uses three benchmark linear regression models of Ordinary Least Squares (OLS), Difference-Generalized Method of Moments (DIFF-GMM), and System-Generalized Method of Moments (SYS-GMM) to explore the improvement of China's regional innovation capability by technology import. Then, the regional institutional quality level is measured from the three dimensions of politics, economy, and law, and the two-step difference GMM threshold panel model is used to analyze the effect of technology import on regional innovation capability under different institutional quality conditions. The results show that: (1) In the benchmark linear regression model, technology import has a significant role in promoting regional innovation capability. (2) With the rise of regional corruption, the quality of political institution declines, and the promotion effect of technology import on regional innovation ability is weakened. (3) The improvement of the marketization level and intellectual property protection level strengthen the role of technology introduction in promoting regional innovation capability. On the contrary, in regions with low economic and legal institutional quality, technology import has no significant impact on regional innovation capability.

scholarly journals Modelling the Influences of Economic, Demographic, and Institutional Factors on Fiscal Pressure Using OLS, PCSE, and FD-GMM Approaches

2020 ◽  
Vol 12 (4) ◽  
pp. 1681
Author(s):  
Alina-Cristina Nuță ◽  
Florian-Marcel Nuță
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Method Of Moments ◽  
Generalized Method Of Moments ◽  
Ordinary Least Squares ◽  
Institutional Factors ◽  
Standard Errors ◽  
Panel Analysis ◽  
Fiscal Pressure ◽  
Robust Standard Errors

The purpose of our article is to assess the effect of diverse factors, such as economic, demographic, and institutional factors, on global and social fiscal pressure. The study is based on a panel analysis of 38 states during 2000–2017. We used ordinary least squares (OLS) as a base model for our estimations, and a linear regression with panel-corrected standard errors and a first difference generalized method of moments (GMM) with robust standard errors and orthogonal deviations. The results of our study indicate that the demographic and institutional factors involved in the analysis contribute to the identification of some variables that affect the global or social fiscal pressure.

scholarly journals A Comparison of Ordinary Least Squares and Least Absolute Error Estimation

1988 ◽  
Vol 4 (3) ◽  
pp. 517-527 ◽  
Author(s):  
Andrew A. Weiss
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Error Estimation ◽  
Method Of Moments ◽  
Linear Regression Model ◽  
Generalized Method Of Moments ◽  
Absolute Error ◽  
Ordinary Least Squares ◽  
Hausman Test ◽  
Heteroscedastic Errors

In a linear-regression model with heteroscedastic errors, we consider two tests: a Hausman test comparing the ordinary least squares (OLS) and least absolute error (LAE) estimators and a test based on the signs of the errors from OLS. It turns out that these are related by the well-known equivalence between Hausman and the generalized method of moments tests. Particular cases, including homoscedasticity and asymmetry in the errors, are discussed.

scholarly journals Applications of Generalized Method of Moments Estimation

2001 ◽  
Vol 15 (4) ◽  
pp. 87-100 ◽  
Author(s):  
Jeffrey M Wooldridge
Keyword(s):  
Time Series ◽  
Panel Data ◽  
Least Squares ◽  
Cross Section ◽  
Method Of Moments ◽  
Generalized Method Of Moments ◽  
Ordinary Least Squares ◽  
Estimation Problems ◽  
Method Of Moments Estimation ◽  
Moments Estimators

I describe how the method of moments approach to estimation, including the more recent generalized method of moments (GMM) theory, can be applied to problems using cross section, time series, and panel data. Method of moments estimators can be attractive because in many circumstances they are robust to failures of auxiliary distributional assumptions that are not needed to identify key parameters. I conclude that while sophisticated GMM estimators are indispensable for complicated estimation problems, it seems unlikely that GMM will provide convincing improvements over ordinary least squares and two-stage least squares--by far the most common method of moments estimators used in econometrics--in settings faced most often by empirical researchers.

scholarly journals Determinants of Growth in Indonesia

2019 ◽  
Vol 3 (2) ◽  
pp. 255-277
Author(s):  
Raymond Rayendra Elven
Keyword(s):  
Human Capital ◽  
Least Squares ◽  
Method Of Moments ◽  
Fixed Effects ◽  
Generalized Method Of Moments ◽  
Physical Capital ◽  
Ordinary Least Squares ◽  
Fixed Effects Model ◽  
Income Per Capita ◽  
Per Capita

Paper ini bertujuan untuk mengidentifikasi faktor-faktor penentu pertumbuhan ekonomi di Indonesia. Untuk itu, dilakukan analisis terhadap data panel dari 33 provinsi di Indonesia mulai tahun 2006 sampai 2015. Analisis empiris pada paper ini melibatkan dua metode estimasi: 1) Ordinary Least Squares (OLS) dengan Fixed Effects Model, dan 2) Generalized Method of Moments (GMM). Hasil penelitian menunjukkan bahwa rasio investasi sebagai akumulasi persediaan physical capital, tingkat pendidikan sebagai akumulasi persediaan human capital, pertumbuhan penduduk, desentralisasi, dan perdagangan memiliki dampak positif yang signifikan terhadap pendapatan per kapita. Selanjutnya, pengeluaran pemerintah dan proporsi penganut agama Islam memiliki pengaruh negatif yang signifikan terhadap pendapatan per kapita. Disisi lain, proporsi penganut agama Kristen Protestan dan Kristen Katolik tidak memiliki pengaruh terhadap pendapatan per kapita.This paper identifies the determinants of economic growth in Indonesia. To accomplish this, panel data for 33 provinces in Indonesia, for the years of 2006 through 2015, were analyzed. The empirical analysis involved two estimation methods: 1) Ordinary Least Squares (OLS) with a Fixed Effects Model, and 2) Generalized Method of Moments (GMM). The results reveal that investment ratio as the stock of physical capital, education level as the stock of human capital; population growth, decentralization, and trade across the provinces have a significant positive impact on the income per capita. Government expenditures and the proportion of adherents to the Islam religion have a significant negative influence on the income per capita. However, the proportion of adherents to the Protestant and the Catholic religions do not affect the income per capita.

Inference for Iterated GMM Under Misspecification

Econometrica ◽  
2021 ◽  
Vol 89 (3) ◽  
pp. 1419-1447
Author(s):  
Bruce E. Hansen ◽  
Seojeong Lee
Keyword(s):  
Asymptotic Distribution ◽  
Method Of Moments ◽  
Asymptotic Variance ◽  
Generalized Method Of Moments ◽  
Gmm Estimator ◽  
Variance Matrix ◽  
Variance Estimators ◽  
Asymptotic Distribution Theory ◽  
Simulation Results ◽  
Inference Methods

This paper develops inference methods for the iterated overidentified Generalized Method of Moments (GMM) estimator. We provide conditions for the existence of the iterated estimator and an asymptotic distribution theory, which allows for mild misspecification. Moment misspecification causes bias in conventional GMM variance estimators, which can lead to severely oversized hypothesis tests. We show how to consistently estimate the correct asymptotic variance matrix. Our simulation results show that our methods are properly sized under both correct specification and mild to moderate misspecification. We illustrate the method with an application to the model of Acemoglu, Johnson, Robinson, and Yared (2008).

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