Fitting IVX Models — ivx • ivx

ivx fits predictive regression models. The method allows standard chi-square testing for regressors with different degrees of persistence, from stationary to mildly explosive, and can be used for both short- and long-horizon predictive regressions.

Usage

ivx(
  formula,
  data,
  horizon,
  na.action,
  weights,
  contrasts = NULL,
  offset,
  model = TRUE,
  x = FALSE,
  y = FALSE,
  beta = 0.95,
  cz = 1,
  bandwidth = NULL,
  robust = FALSE,
  lag_y = FALSE,
  ...
)

# S3 method for class 'ivx'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

Arguments

formula: an object of class "formula" (or one that can be coerced to that class): a symbolic description of the model to be fitted.
data: n optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which lm is called.
horizon: is the horizon (default horizon = 1 corresponds to a short-horizon regression). For horizon > 1 the estimator and modified Wald statistic are those of Kostakis et al. (2023), eqs (15) and (23): K-period sums of the response and of the lagged predictors, a single-lag instrument in the signal matrix and the K-period sum of the instrument in the covariance.
na.action: a function which indicates what should happen when the data contain NAs. The default is set by the na.action setting of options, and is na.fail if that is unset. The ‘factory-fresh’ default is na.omit. Another possible value is NULL, no action. Value na.exclude can be useful.
weights: an optional vector of weights to be used in the fitting process. Should be NULL or a numeric vector. If non-NULL, weighted least squares is used with weights weights (that is, minimizing sum(w*e^2)); otherwise ordinary least squares is used.
contrasts: an optional list. See the contrasts.arg of model.matrix.default.
offset: this can be used to specify an a priori known component to be included in the linear predictor during fitting. This should be NULL or a numeric vector or matrix of extents matching those of the response. One or more offset terms can be included in the formula instead or as well, and if more than one are specified their sum is used. See model.offset
model: logical. If TRUE the model.frame of the fit is returned.
x: an object of class "ivx", usually, a result of a call to ivx.
y: logical. If TRUE the response of the fit is returned.
beta, cz: tuning parameters of the IVX instrument \(z_t = \sum_{j=0}^{t-1} (1 - c_z/n^\beta)^j \Delta x_{t-j}\). Defaults (beta = 0.95, cz = 1) follow Kostakis et al. (2015).
bandwidth: Newey-West bandwidth for the long-run covariance estimate. The default NULL uses \(n^{1/3}\) as in Kostakis et al. (2015).
robust: logical. If TRUE the Eicker-White (heteroskedasticity-robust) form of the IVX covariance matrix is used (Demetrescu et al., 2023). Only available for horizon = 1.
lag_y: logical. If TRUE the regression is augmented with the lagged dependent variable (column y_lag), instrumented by itself, as in Demetrescu (2014): this can raise the local power of the IVX test when the predictors are highly persistent and endogenous, at no cost otherwise. The joint Wald statistic still tests only the predictors. Only for horizon = 1.
...: additional arguments to be passed to the low level regression fitting functions (see lm).
digits: the number of significant digits to use when printing.

Value

an object of class "ivx".

References

Magdalinos, T., & Phillips, P. (2009). Limit Theory for Cointegrated Systems with Moderately Integrated and Moderately Explosive Regressors. Econometric Theory, 25(2), 482-526.

Kostakis, A., Magdalinos, T., & Stamatogiannis, M. P. (2015). Robust econometric inference for stock return predictability. The Review of Financial Studies, 28(5), 1506-1553.

Demetrescu, M., Georgiev, I., Rodrigues, P. M. M., & Taylor, A. M. R. (2023). Extensions to IVX methods of inference for return predictability. Journal of Econometrics, 237(2), 105271.

Kostakis, A., Magdalinos, T., & Stamatogiannis, M. P. (2023). Taking stock of long-horizon predictability tests: Are factor returns predictable? Journal of Econometrics, 237(2), 105380.

Demetrescu, M. (2014). Enhancing the local power of IVX-based tests in predictive regressions. Economics Letters, 124(2), 269-273.

Examples


# Univariate
ivx(Ret ~ LTY, data = kms)
#> 
#> Call:
#> ivx(formula = Ret ~ LTY, data = kms, horizon = 1)
#> 
#> Coefficients:
#>      LTY  
#> -0.06649  
#> 

# Multivariate
ivx(Ret ~ LTY + TBL, data = kms)
#> 
#> Call:
#> ivx(formula = Ret ~ LTY + TBL, data = kms, horizon = 1)
#> 
#> Coefficients:
#>      LTY       TBL  
#>  0.07624  -0.13497  
#> 

# Longer horizon
ivx(Ret ~ LTY + TBL, data = kms, horizon = 4)
#> 
#> Call:
#> ivx(formula = Ret ~ LTY + TBL, data = kms, horizon = 4)
#> 
#> Coefficients:
#>      LTY       TBL  
#>  0.09322  -0.14164  
#> 

wt <- runif(nrow(kms))
ivx(Ret ~ LTY, data = kms, weights = wt)
#> 
#> Call:
#> ivx(formula = Ret ~ LTY, data = kms, weights = wt, horizon = 1)
#> 
#> Coefficients:
#>     LTY  
#> -0.0705  
#> 

# lag-augmented IVX (Demetrescu, 2014)
ivx(Ret ~ DP, data = kms, lag_y = TRUE)
#> 
#> Call:
#> ivx(formula = Ret ~ DP, data = kms, lag_y = TRUE, horizon = 1)
#> 
#> Coefficients:
#>       DP     y_lag  
#> 0.007587  0.094223  
#>