We consider the popular 'bounds test' for the existence of a level relationship in conditional equilibrium correction models. By estimating response surface models based on about 95 billion simulated F-statistics and 57 billion t-statistics, we improve upon and substantially extend the set of available critical values, covering the full range of possible sample sizes and lag orders, and allowing for any number of long-run forcing variables. By computing approximate P-values, we find that the bounds test can be easily oversized by more than 5 percentage points in small samples when using asymptotic critical values. 1 McNown et al. (2018) propose a bootstrap procedure for the Pesaran et al. (2001) test that allows for conclusive inference when the test statistic falls within the two bounds. 2 Previously tabulated CVs for a small set of sample sizes can be found in Fuller (1976) and Dickey (1976) for the univariable and Banerjee, Dolado and Mestre (1998) for the multivariable setting. 3 Cook (2001) compares the response surfaces from Cheung and Lai (1995a) with those from MacKinnon (1991) and concludes that adjusting for the lag order leads to a gain in power. RS estimates for finite-sample CVs of other unit-root tests are provided by Cheung

In this article, I describe the xtdpdqml command for the quasimaximum likelihood estimation of linear dynamic panel-data models when the time horizon is short and the number of cross-sectional units is large. Based on the theoretical groundwork by Bhargava and Sargan (1983, Econometrica 51: 1635-1659 and Hsiao, Pesaran, and Tahmiscioglu (2002, Journal of Econometrics 109: 107-150), the marginal distribution of the initial observations is modeled as a function of the observed variables to circumvent a short-T dynamic panel-data bias. Both random-effects and fixed-effects versions are available.Keywords: st0463, xtdpdqml, dynamic panel data, random effects, fixed effects, short-T bias, quasi-maximum likelihood estimation, initial observations, unbalanced panel data 1. In Stata, these least-squares estimators for the random-effects and fixed-effects models are implemented in the command xtreg.c 2016 StataCorp LP st0463 2. Note the missing q in the command name xtdpdml compared with the xtdpdqml command discussed in this article. The names are constructed by combining Stata's xt prefix for panel-data commands, dpd as an abbreviation for dynamic panel data, and ml or qml for the full-information maximumlikelihood or the QML method, respectively. 3. While in principal the QML estimators can be extended to include higher-order lags of the dependent variable, this requires additional modeling effort and is not implemented in xtdpdqml.

We present a sequential approach to estimating a dynamic Hausman-Taylor model. We first estimate the coefficients of the time-varying regressors and subsequently regress the first-stage residuals on the time-invariant regressors. In comparison to estimating all coefficients simultaneously, this two-stage procedure is more robust against model misspecification, allows for a flexible choice of the first-stage estimator, and enables simple testing of the overidentifying restrictions. For correct inference, we derive analytical standard error adjustments. We evaluate the finite-sample properties with Monte Carlo simulations and apply the approach to a dynamic gravity equation for US outward foreign direct investment. 1 Schooling itself is a time-invariant regressor in his data set. Yet it is hard to argue that its coefficient is identified because Andini uses only the first differences of time-varying regressors as instruments. These instruments are generally assumed to be uncorrelated with any time-invariant variable. 526 2 Plümper and Troeger (2007) proposed a three-stage approach for the static model that they label "fixed effects vector decomposition." In a symposium on this method, Breusch, Ward, Nguyen, and Kompas (2011) and Greene (2011) show that the first two stages can be characterized by an instrumental variables estimation with a particular choice of instruments, and that the third stage is essentially meaningless. 3 Hoeffler (2002) argues similarly. 4 As Binder, Hsiao, and Pesaran (2005) and Bun and Windmeijer (2010) emphasize, GMM estimators might suffer from a weak instruments problem when the autoregressive parameter approaches unity or when the variance of the unobserved unit-specific effects is large. Moreover, the number of instruments can rapidly become large relative to the sample size. The consequences of instrument proliferation, summarized by Roodman (2009), range from biased coefficient and standard error estimates to weakened specification tests. 5 Our two-stage procedure fits into the framework of sequential estimators discussed by Newey (1984). While our paper is only concerned with linear panel data models, Honoré and Kesina (2017) recently suggested related two-stage approaches for some nonlinear models. They use a bootstrap procedure to obtain valid standard errors in contrast to our analytical standard error correction.

In models with endogenous regressors, a standard regression approach is to exploit just-identifying or overidentifying orthogonality conditions by using instrumental variables. In just-identified models, the identifying orthogonality assumptions cannot be tested without the imposition of other nontestable assumptions. While formal testing of overidentifying restrictions is possible, its interpretation still hinges on the validity of an initial set of untestable just-identifying orthogonality conditions. We present the kinkyreg command for kinky least-squares inference, which adopts an alternative approach to identification. By exploiting nonorthogonality conditions in the form of bounds on the admissible degree of endogeneity, feasible test procedures can be constructed that do not require instrumental variables. The kinky least-squares confidence bands can be more informative than confidence intervals obtained from instrumental-variables estimation, especially when the instruments are weak. Moreover, the approach facilitates a sensitivity analysis for standard instrumental-variables inference. In particular, it allows the user to assess the validity of previously untestable just-identifying exclusion restrictions. Further instrument-free tests include linear hypotheses, functional form, heteroskedasticity, and serial correlation tests.

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