MODELING ADVERTISING CARRYOVER IN FLUID MILK: COMPARISON OF ALTERNATIVE LAG SPECIFICATIONS

The performance of restricted estimators such as Almon and Shiller in modeling advertising carryover is tested and compared to the unrestricted OLS estimator, using 1971-1988 monthly New York City fluid milk market data. Results indicate that in the absence of autocorrelation and multicollinearity among the lagged advertising variables, the unrestricted OLS estimator is still the preferred estimator, based on Mean Square Error and Root Mean Square Percent Error criteria. In this case, the Almon and Shiller estimators perform equally well, although next only to the OLS estimator. In the presence of autocorrelation or multicollinearity however, the restricted estimators may outperform the OLS estimator, in a MSE sense, with the flexible Shiller estimator (which subsumes the Almon) being more desirable.Marketing,

Regressions with Asymptotically Collinear Regressor

We investigate the asymptotic behavior of the OLS estimator for regressions with two slowly varying regressors. It is shown that the asymptotic distribution is normal one-dimensional and may belong to one of four types depending on the relative rates of growth of the regressors. The analysis establishes, in particular, a new link between slow variation and $L_p$-approximability. A revised version of this paper has been published in Econometrics Journal (2011), volume 14, pp. 304--320.Asymptotically collinear regressors; asymptotic distribution; Lp-approximability; OLS estimator

Cointegrating Polynomial Regressions

This paper develops a fully modified OLS estimator for cointegrating polynomial regressions, i.e. for regressions including deterministic variables, integrated processes and powers of integrated processes as explanatory variables and stationary errors. The errors are allowed to be serially correlated and the regressors are allowed to be endogenous. The paper thus extends the fully modified approach developed in Phillips and Hansen (1990). The FM-OLS estimator has a zero mean Gaussian mixture limiting distribution, which is the basis for standard asymptotic inference. In addition Wald and LM tests for specification as well as a KPSS-type test for cointegration are derived. The theoretical analysis is complemented by a simulation study which shows that the developed FM-OLS estimator and tests based upon it perform well in the sense that the performance advantages over OLS are by and large similar to the performance advantages of FM-OLS over OLS in cointegrating regressions.Cointegrating polynomial regression, fully modified OLS estimation, integrated process, testing

Asymptotic Properties of the Efficient Estimators for Cointegrating Regression Models with Serially Dependent Errors

In this paper, we analytically investigate three efficient estimators for cointegrating regression models: Phillips and Hansen's (1990) fully modified OLS estimator, Park's (1992) canonical cointegrating regression estimator, and Saikkonen's (1991) dynamic OLS estimator. First, by the Monte Carlo simulations, we demonstrate that these efficient methods do not work well when the regression errors are strongly serially correlated. In order to explain this result, we assume that the regression errors are generated from a nearly integrated autoregressive (AR) process with the AR coefficient approaching 1 at a rate of 1/T , where T is the sample size. We derive the limiting distributions of the three efficient estimators as well as the OLS estimator and show that they have the same limiting distribution under this assumption. This implies that the three efficient methods no longer work well when the regression errors are strongly serially correlated. Further, we consider the case where the AR coefficient in the regression errors approaches 1 at a rate slower than 1/T . In this case, the limiting distributions of the efficient estimators depend on the approaching rate. If the rate is slow enough, the efficiency is established for the three estimators; however, if the approaching rate is relatively fast, they have the same limiting distribution as the OLS estimator. This result explains why the effect of the efficient methods diminishes as the serial correlation in the regression errors gets stronger.Cointegration, second-order bias, fully modified regressions, canonical cointegrating regressions, dynamic ordinary least squares regressions

Asymptotic Distribution of the OLS Estimator for a Mixed Regressive, Spatial Autoregressive Model

We find the asymptotics of the OLS estimator of the parameters $\beta$ and $\rho$ in the spatial autoregressive model with exogenous regressors $Y_n = X_n\beta+\rho W_nY_n+V_n$. Only low-level conditions are imposed. Exogenous regressors may be bounded or growing, like polynomial trends. The assumption on the spatial matrix $W_n$ is appropriate for the situation when each economic agent is influenced by many others. The asymptotics contains both linear and quadratic forms in standard normal variables. The conditions and the format of the result are chosen in a way compatible with known results for the model without lags by Anderson (1971) and for the spatial model without exogenous regressors due to Mynbaev and Ullah (2006).mixed regressive spatial autoregressive model; OLS estimator; asymptotic distribution

Long horizon regressions with moderate deviations from a unit root

We consider long horizon regressions where the predictor with unknown degree of persistence follows a process of moderate deviations from a unit root. Some asymptotic properties of OLS estimator and of the t statistic are presented.

Local GMM Estimation of Time Series Models with Conditional Moment Restrictions

This paper investigates statistical properties of the local GMM (LGMM) estimator for some time series models defined by conditional moment restrictions. First, we consider Markov processes with possible conditional heteroskedasticity of unknown form and establish the consistency, asymptotic normality, and semi-parametric efficiency of the estimator. Second, inspired by simulation results showing that the LGMM estimator has a significantly smaller bias than the OLS estimator, we undertake a higher-order asymptotic expansion and analyze the bias properties of the LGMM estimator. The structure of the asymptotic expansion of the LGMM estimator reveals an interesting contrast with the OLS estimator that helps to explain the bias reduction in the LGMM estimator. The practical importance of these findings is evaluated in terms of a bond and option pricing exercise based on a diffusion model for spot interest rate.Conditional moment restrictions; Local GMM; Higher-order expansion; Conditional heteroskedasticity

Estimating the Intergenerational Correlation of Incomes : An Errors in Variables Framework

Because the permanent incomes of parents and children are typically unobservable, the estimation of the intergenerational correlation of incomes is usually carried out via averaging methods or instrumentation. In this paper we take the permanent income of the parent family to be unobserved, but we assume that a model for its determinants is known to the researcher. In turn, this leads us to propose two related estimators for the intergenerational correlation: a two-stage least squares procedure and a more efficient MIMIC estimator. The MIMIC framework also provides estimates for the determinants of permanent income and the variance parameters required to evaluate the bias of the OLS estimator. Using a US sample of parents and children we provide estimates for the intergenerational correlation ranging between 0.30 and 0.78. The bias of the OLS estimator is estimated to be in the order of 40%.intergenerational mobility; errors in variables