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  • "A Bayesian Analysis of Linear Regression Models with Highly Collinear Regressors", by M. Hashem Pesaran and Ron P. Smith, forthcoming in Econometrics and Statistics, October 2018

    Abstract: Exact collinearity between regressors makes their individual coefficients not identified. But, given an informative prior, their Bayesian posterior means are well defined. Just as exact collinearity causes non-identification of the parameters, high collinearity can be viewed as weak identification of the parameters, which is represented, in line with the weak instrument literature, by the correlation matrix being of full rank for a finite sample size T, but converging to a rank deficient matrix as T goes to infinity. The asymptotic behaviour of the posterior mean and precision of the parameters of a linear regression model are examined in the cases of exactly and highly collinear regressors. In both cases the posterior mean remains sensitive to the choice of prior means even if the sample size is sufficiently large, and that the precision rises at a slower rate than the sample size. In the highly collinear case, the posterior means converge to normally distributed random variables whose mean and variance depend on the prior means and prior precisions. The distribution degenerates to fixed points for either exact collinearity or strong identification. The analysis also suggests a diagnostic statistic for the highly collinear case. Monte Carlo simulations and an empirical example are used to illustrate the main …findings.
    JEL Classifications: C11, C18
    Key Words: Bayesian identi…cation, multicollinear regressions, weakly identi…ed regression coefficients, highly collinear regressors.
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    Note: A previous version of the paper was distributed as CESifo Working Paper 6785 under the title of "Posterior Means and Precisions of the Coefficients in Linear Models with Highly Collinear Regressors"

  • "Double-question Survey Measures for the Analysis of Financial Bubbles and Crashes", by M. Hashem Pesarann and Ida Johnsson, forthcoming in Journal of Business and Economic Statistics, August 2018

    Abstract: This paper proposes a new double-question survey whereby an individual is presented with two sets of questions; one on beliefs about current asset values and another on price expectations. A theoretical asset pricing model with heterogeneous agents is advanced and the existence of a negative relationship between price expectations and asset valuations is established, and is then tested using survey results on equity, gold and house prices. Leading indicators of bubbles and crashes are proposed and their potential value is illustrated in the context of a dynamic panel regression of realized house price changes across key Metropolitan Statistical Areas (MSAs) in the US. In an out-of-sample forecasting exercise it is also shown that forecasts of house price changes (pooled across MSAs) that make use of bubble and crash indicators perform signi…ficantly better than a benchmark model that only uses lagged and expected house price changes.
    JEL Classifications: C83, D84, G12, G14.
    Key Words: Price expectations, bubbles and crashes, house prices, belief valuations.
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  • "Half-Panel Jackknife Fixed Effects Estimation of Linear Panels with Weakly Exogenous Regressors", by Alexander Chudik, M. Hashem Pesarann and Jui-Chung Yang, SSRN Working Paper No. 281, forthcoming in Journal of Applied Econometrics, January 2018

    Abstract: This paper considers estimation and inference in fixed effects (FE) linear panel regression models with lagged dependent variables and/or other weakly exogenous (or predetermined) regressors when N (the cross section dimension) is large relative to T (the time series dimension). The paper first derives a general formula for the bias of the FE estimator which is a generalization of the Nickell type bias derived in the literature for the pure dynamic panel data models. It shows that in the presence of weakly exogenous regressors, inference based on the FE estimator will result in size distortions unless N/T is suffciently small. To deal with the bias and size distortion of FE estimator when N is large relative to T, the use of half-panel Jackknife FE estimator is proposed and its asymptotic distribution is derived. It is shown that the bias of the proposed estimator is of order [code], and for valid inference it is only required that N/T[code], as N, T [code] jointly. Extensions to panel data models with time effects (TE), for balanced as well as unbalanced panels, are also provided. The theoretical results are illustrated with Monte Carlo evidence. It is shown that the FE estimator can suffer from large size distortions when N > T, with the proposed estimator showing little size distortions. The use of half-panel jackknife FE-TE estimator is illustrated with two empirical applications from the literature.
    JEL Classifications: C32, E17, E32, F44, F47, O51, Q43.
    Key Words: Panel Data Models, Weakly Exogenous Regressors, Lagged Dependent Variable, Fixed Effects, Time Effects, Unbalanced Panels, Half-Panel Jackknife, Bias Correction
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  • "Tests of Policy Interventions in DSGE Models", by M. Hashem Pesaran and Ron P. Smith, forthcoming in Oxford Bulletin of Economics and Statistics, October 2017.

    Abstract: This paper considers tests of the effectiveness of a policy intervention, de…ned as a change in the parameters of a policy rule, in the context of a macroeconometric dynamic stochastic general equilibrium (DSGE) model. We consider two types of intervention, fi…rst the standard case of a parameter change that does not alter the steady state, and second one that does alter the steady state, e.g. the target rate of infl‡ation. We consider two types of test, one a multi-horizon test, where the post-intervention policy horizon, H, is small and fi…xed, and a mean policy effect test where H is allowed to increase without bounds. The multi-horizon test requires Gaussian errors, but the mean policy effect test does not. It is shown that neither of these two tests are consistent, in the sense that the the power of the tests does not tend to unity as H, unless the intervention alters the steady state. This follows directly from the fact that DSGE variables are measured as deviations from the steady state, and the effects of policy change on target variables decay exponentially fast. We investigate the size and power of the proposed mean effect test by simulating a standard three equation New Keynesian DSGE model. The simulation results are in line with our theoretical fi…ndings and show that in all applications the tests have the correct size; but unless the intervention alters the steady state, their power does not go to unity with H.
    JEL Classifications: C18, C54, E65.
    Key Words: Counterfactuals, policy analysis, policy ineffectiveness test, macroeconomics.
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