- Should we use IV to estimate dynamic linear probability models with fixed effects? (link here)
I give a set of pros and cons of this procedure and conclude that this procedure should be treated with caution, especially in fixed-T settings. Even if we ignore the possibility that average marginal effects may not be point-identified, directly applying IV/GMM estimators to this dynamic LPM identifies incorrectly-weighted average marginal effects, which may differ from the true average marginal effect, under large-n, fixed-T or large-n, large-T asymptotics. I also show that there exist certain DGPs that can push the large-n, fixed-T limits of these IV estimators outside the identified set for the true average marginal effect. The only good news is that nonparametrically testing the point null of zero first-order state dependence is possible with default routines. Unfortunately, this nonparametric test can have low power. In relation to this, I demonstrate through an empirical example that the resulting IV/GMM estimates of the average treatment effect of fertility on female labor force participation are outside the nonparametric bounds under monotonicity.
- Simultaneous equations for discrete outcomes: Coherence and completeness using panel data (link here)
Modeling jointly determined discrete outcomes via simultaneous equations require the so-called coherency condition to guarantee the existence of a unique reduced form. These conditions effectively convert a model where the endogenous variables are jointly determined into a model that is triangular or recursive. In the spirit of a suggestion by Lewbel (2007), I propose using panel data to decide how the coherency condition will hold without restricting error supports or imposing triangularity for all observations.
- Estimation and inference in dynamic nonlinear fixed effects panel data models by projection (link here)
I develop a bias reduction method for the estimators of structural parameters of a panel data model (whether linear or nonlinear) using a projection argument. A corrected score is calculated by projecting the score vector for the structural parameters onto the orthogonal complement of a space characterized by incidental parameter fluctuations.
- The role of sparsity in panel data models (link here)
Sparsity of the fixed effects means that some fixed effects have absolute value of zero while others are bounded and other are large. The proposed estimator attempts to detect the large values of the fixed effects so that they can be removed in the second step. I tune the regularization parameter to encourage sparsity and allow for contemporaneously exogenous regressors. As a second step, I remove the large non-zero fixed effects so that pooled OLS may be applied.
- Large-n, large-T properties of an IV estimator based on the Ahn-Schmidt moment conditions (with Markus
Fritsch and Joachim Schnurbus, link here)
We propose an instrumental variables (IV) estimator based on nonlinear (in param- eters) moment conditions for estimating linear dynamic panel data models and derive the large sample properties of the estimator. We assume that the only explanatory variable in the model is one lag of the dependent variable and consider the setting where the absolute value of the true lag parameter is smaller or equal to one, the cross section dimension is large, and the time series dimension is either fixed or large. Estimation of the lag parameter involves solving a quadratic equation and we find that the lag parameter is point identified in the unit root case; otherwise, two distinct roots (solutions) result. We propose a selection rule that identifies the consistent root asymptotically in the latter case and derive the asymptotic distribution of the estimator for the unit root case and for the case when the absolute value of the lag parameter is smaller than one.
- Practical aspects of using quadratic moment conditions in linear AR(1) panel data models (with Markus
Fritsch and Joachim Schnurbus, link here)
We study the estimation of the lag parameter of linear dynamic panel data models with first order dynamics based on the quadratic Ahn and Schmidt (1995) moment conditions. Our contribution is twofold: First, we show that extending the standard assumptions by mean stationarity and time series homoscedasticity and employing these assumptions in estimation restores standard asymptotics and mitigates the non-standard distributions found in the literature. Second, we consider an IV estimator based on the quadratic moment conditions that consistently identifies the true population parameter under standard assumptions. Standard asymptotics hold for the estimator when the cross section dimension is large and the time series dimension is finite. We also suggest a data-driven approach to obtain standard errors and confidence intervals that preserves the time series dependence structure in the data.
- pdynmc: An R-package for estimating linear dynamic panel data models based on nonlinear moment conditions (with Markus Fritsch and Joachim Schnurbus, link here, forthcoming in The R Journal)
pdynmc is an R-package for GMM estimation of linear dynamic panel data models that are based on linear and nonlinear moment conditions as proposed by Anderson and Hsiao (1982), Holtz-Eakin, Newey, and Rosen (1988), Arellano and Bover (1995), and Ahn and Schmidt (1995). This paper describes the functionality of the package and the options regarding instrument type, estimation methodology, general configuration, specification testing and inference from the perspective of an applied statistician. The description of the functionality is based on replicating the results on a publicly available panel data set. Additionally, we link our implementation to other software and packages for GMM estimation of linear dynamic panel data models.
- Revisiting habits and heterogeneity in demands (with Markus Fritsch and Joachim Schnurbus, link here)
We conduct a narrow replication of Browning and Collado (Journal of Applied Econometrics 2007; 22(3): 625-640). They estimate a linear panel AR(1) version of an Engel curve for six consumption composites using iterated GMM. We find that the coefficient estimates and standard errors differ from the reported results when we use their instrument set; in particular, we find habit formation in non-durable services and no state dependence in small durables. Despite finding evidence for weak instruments, our results support most of the claims made in the original paper and are also unable to detect intertemporal dependence strong enough to resolve existing macro puzzles.
- A test of normality using an entropy-based transformation (with Shahzad Munir)
We propose a normality test that is valid in time series settings. We show that in a broad class of stationary processes, the proposed test statistic is asymptotically normal and does not require any kernel smoothing to consistently estimate the asymptotic variance of the proposed test. We also provide a Monte Carlo analysis to evaluate the finite-sample performance of the proposed test relative to existing moment-based tests in the time series literature. Our test performs better than Bai and Ng (2005) and other moment-based tests, but almost matches the performance of Lobato and Velasco (2004). The power of the test comes from deviations from a kurtosis equal to 3, and, as a result, has no power against asymmetric alternatives where kurtosis for these alternative match that of the normal distribution.
- Market Pricing of Fundamentals at the Shanghai Stock Exchange: Evidence from a Dividend Discount Model with Adaptive Expectations (with Mingyang Li and Linlin Niu, link here)
We document evidence of fundamental pricing at the Shanghai Stock Exchange using panel data of listed stocks from 1997 to 2018. We estimated key parameters, namely, the price elasticity of dividends and the expectation adjustment parameter, from a dividend discount model with adaptive expectations. The reduced form can be estimated using linear dynamic panel data methods which, given the size of the panel, requires us to apply methods that correct for incidental parameter bias and to use a subset of stocks that do not completely drive the aggregate dynamics of the exchange. The resulting price elasticity of dividends is about 0.37 based on annual data and about 0.51 based on quarterly data, both of which are sizable given high PD and PE ratios in the market. Our results imply that slow expectation adjustment contributes to ``bubble-like'' price patterns. We also show prices significantly react to macro information related to the discount rate, but these effects are very sensitive to the information set used.