Robust Econometric Inference • ivx

Drawing statistical inference on the coefficients of a short- or long-horizon predictive regression with persistent regressors by using the IVX method of Magdalinos and Phillips (2009) and Kostakis, Magdalinos and Stamatogiannis (2015).

Installation

You can install the development version from GitHub with:

# Install release version from CRAN
install.packages("ivx")


# install.packages("devtools")
devtools::install_github("kvasilopoulos/ivx")

Usage

library(ivx)
library(magrittr)

This is a basic example, lets load the data first:

# Monthly data from Kostakis et al (2014)
kms %>%
  names()
#>  [1] "Date" "DE"   "LTY"  "DY"   "DP"   "TBL"  "EP"   "BM"   "INF"  "DFY" 
#> [11] "NTIS" "TMS"  "Ret"

Univariate

And then do the univariate estimation:

ivx(Ret ~ DP, data = kms) %>% 
  summary()
#> 
#> Call:
#> ivx(formula = Ret ~ DP, data = kms, horizon = 1)
#> 
#> Coefficients:
#>    Estimate Std. Error t value Wald Ind Pr(> chi)
#> DP 0.006489   0.004553   1.425    2.031     0.154
#> 
#> Joint Wald statistic:  2.031 on 1 DF, p-value 0.1541
#> Multiple R-squared:  0.002844,   Adjusted R-squared:  0.001877

ivx(Ret ~ DP, data = kms, horizon = 4) %>% 
  summary()
#> 
#> Call:
#> ivx(formula = Ret ~ DP, data = kms, horizon = 4)
#> 
#> Coefficients:
#>    Estimate Std. Error t value Wald Ind Pr(> chi)
#> DP 0.006931   0.004599   1.507    2.271     0.132
#> 
#> Joint Wald statistic:  2.271 on 1 DF, p-value 0.1318
#> Multiple R-squared:  0.01167,    Adjusted R-squared:  0.01358

Multivariate

And the multivariate estimation, for one or multiple horizons:

ivx(Ret ~ DP + TBL, data = kms) %>% 
  summary()
#> 
#> Call:
#> ivx(formula = Ret ~ DP + TBL, data = kms, horizon = 1)
#> 
#> Coefficients:
#>      Estimate Std. Error t value Wald Ind Pr(> chi)
#> DP   0.006145   0.004557   1.349    1.819     0.177
#> TBL -0.080717   0.057701  -1.399    1.957     0.162
#> 
#> Joint Wald statistic:  3.644 on 2 DF, p-value 0.1617
#> Multiple R-squared:  0.004968,   Adjusted R-squared:  0.003036

ivx(Ret ~ DP + TBL, data = kms, horizon = 4) %>% 
  summary()
#> 
#> Call:
#> ivx(formula = Ret ~ DP + TBL, data = kms, horizon = 4)
#> 
#> Coefficients:
#>      Estimate Std. Error t value Wald Ind Pr(> chi)
#> DP   0.006579   0.004601   1.430    2.045     0.153
#> TBL -0.073549   0.058238  -1.263    1.595     0.207
#> 
#> Joint Wald statistic:  3.527 on 2 DF, p-value 0.1715
#> Multiple R-squared:  0.018,  Adjusted R-squared:  0.01895

Robust inference (Demetrescu et al., 2023)

Eicker-White standard errors, the IVX tuning parameters and wild-bootstrap p-values (residual or fixed-regressor wild bootstrap):

ivx(Ret ~ DP + TBL, data = kms, robust = TRUE) %>%
  summary()
#> 
#> Call:
#> ivx(formula = Ret ~ DP + TBL, data = kms, robust = TRUE, horizon = 1)
#> 
#> Coefficients:
#>      Estimate Std. Error t value Wald Ind Pr(> chi)
#> DP   0.006145   0.004792   1.282    1.644     0.200
#> TBL -0.080717   0.057250  -1.410    1.988     0.159
#> (Eicker-White standard errors)
#> 
#> Joint Wald statistic:  2.893 on 2 DF, p-value 0.2354
#> Multiple R-squared:  0.004968,   Adjusted R-squared:  0.003036

mod <- ivx(Ret ~ DP + TBL, data = kms, beta = 0.9, cz = 5)
ivx_boot(mod, B = 999, type = "rwb", seed = 1)
#> 
#> Call:
#> ivx(formula = Ret ~ DP + TBL, data = kms, beta = 0.9, cz = 5, 
#>     horizon = 1)
#> 
#> Residual wild bootstrap, B = 999
#> 
#> Coefficients (bootstrap p-values):
#>     Estimate t value Wald Ind Pr(> chi) Pr(t < 0) Pr(t > 0)
#> DP   0.00502   0.925    0.855    0.5415   0.60761     0.392
#> TBL -0.12896  -1.581    2.498    0.1652   0.08308     0.917
#> 
#> Joint Wald statistic: 2.807, bootstrap p-value 0.4114

Yang et al. (2020) IVX-AR methodology

ivx_ar(hpi ~ cpi, data = ylpc) %>% 
  summary()
#> 
#> Call:
#> ivx_ar(formula = hpi ~ cpi, data = ylpc, horizon = 1)
#> 
#> Auto () with AR terms q = 4
#> 
#> Coefficients:
#>       Estimate Std. Error t value Wald Ind Pr(> chi)  
#> cpi -1.775e-04  8.532e-05  -2.080    4.326    0.0375 *
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Joint Wald statistic:  4.326 on 1 DF, p-value 0.03753
#> Multiple R-squared:  0.02721,    Adjusted R-squared:  0.02142
#> Wald AR statistic: 132.3 on 4 DF, p-value < 2.2e-16

Other IVX-based methods

function	method
`ivx_ra()`	residual-augmented IVX, short and long horizon (Demetrescu & Rodrigues 2022; Demetrescu, Rodrigues & Taylor 2023)
`ivx_qr()`, `ivx_qr_boot()`	IVX quantile regression (Lee 2016) and its block bootstrap (Fan & Lee 2019)
`ivx_sys()`	systems of predictive regressions (Kostakis et al. 2023)
`ivx_episodic()`	subsample tests for pockets of predictability (Demetrescu et al. 2022)
`ivx_iv()`	2SLS with sine / fractional / long-difference instruments (Breitung & Demetrescu 2015)
`ivx(..., lag_y = TRUE)`	lag-augmented IVX (Demetrescu 2014)

Non-IVX benchmarks

function	method
`cy_test()`	Bonferroni Q-test (Campbell & Yogo 2006; Cavanagh, Elliott & Stock 1995)
`arm()`	augmented regression method (Amihud, Hurvich & Wang 2009)
`elliott_cf()`	control-function regression with user-supplied covariates (Elliott 2011)
`hlt_test()`	hybrid switching t-test (Harvey, Leybourne & Taylor 2021)
`el_test()`	unified empirical likelihood test (Liu, Yang, Cai & Peng 2019)

The conditional likelihood test of Jansson & Moreira (2006) is not implemented: its critical values are conditional quantiles of a nonstandard joint distribution that must be obtained by numerical Fourier inversion (their Theorem 7), and the Q-test has higher finite-sample power in their own comparisons.

Please note that the ‘ivx’ project is released with a Contributor Code of Conduct. By contributing to this project, you agree to abide by its terms.

ivx: Robust Econometric Inference