OLSHODRICK—Least squares with Hodrick standard errors

[TomDoan]

@OLSHODRICK computes a least squares regression with the covariance matrix proposed by Hodrick(1992) "Dividend Yields and Expected Stock Returns: Alternative Procedures for Inference and Measurement", Review of Financial Studies, vol 5, no 3, 357-386.

Note that the calculation is specific to multiple step predictability regressions. It uses the residuals from a one-step regression to compute the covariance matrix for a k-step regression.

OLSHodrick.src

Detailed description

aluminum.xls

Data file for example

(12.36 KiB) Downloaded 1133 times

[ziucqea]

Hi all. I'm doing data analysis for my thesis. For some reason, when running regression involving one regressor, del_l_n, RATS gives stadard error of 0 to all regressors, which definitely doesn't look right. I've attached my source and an example is:

@OLSHodrick(steps=1,onestep=z41) z41
# constant del_bdi_lag del_crb del_l_n

Linear Regression - Estimation by Least Squares with Hodrick standard errors
Dependent Variable Z41
Monthly Data From 1986:04 To 2017:04
Usable Observations 369
Degrees of Freedom 365
Skipped/Missing (from 373) 4
Mean of Dependent Variable 0.0021704629
Std Error of Dependent Variable 0.0134891456
Standard Error of Estimate 0.0131667459
Sum of Squared Residuals 0.0632775673
Durbin-Watson Statistic 1.8905

Variable Coeff Std Error T-Stat Signif
************************************************************************************
1. Constant 0.0020714824 0.0000000000 0.00000 0.00000000
2. DEL_BDI_LAG 0.0000036880 0.0000000000 0.00000 0.00000000
3. DEL_CRB 0.0735049493 0.0000000000 0.00000 0.00000000
4. DEL_L_N 0.0071249449 0.0000000000 0.00000 0.00000000


Can anyone suggest why this is the case? I've also tried the same spec using Newey-West standard errors and they definitely shouldn't be 0.

Thank you,
Keith

[TomDoan]

Hodrick standard errors don't apply to one-step forecasts.

[ziucqea]

Hodrick standard errors don't apply to one-step forecasts.

Hi. Do you you mean this function doesn't support 1-step ahaead forecasts? Because Hodrick (1992) should be applicable, see, for example, Predictability of currency carry trade and asset pricing implications, Journal of Financial Economics, Bakshi and panayotov (2013).

Also, del_l_n is the only variable that gives this error; the other regressors (del_crb, del_ted, etc) give correct errors.

[TomDoan]

Because del_l_n is missing 4 data points in the middle. The Hodrick standard errors formula doesn't allow for missing values in the middle. Note that "Hodrick" standard errors with steps=1 are just Eicker-White errors and LINREG(ROBUSTERRORS) is perfectly happy with missing values. The whole point of Hodrick's paper is to deal with multi-step predictability where there's an issue with serially correlated residuals.

[ziucqea]

Because del_l_n is missing 4 data points in the middle. The Hodrick standard errors formula doesn't allow for missing values in the middle. Note that "Hodrick" standard errors with steps=1 are just Eicker-White errors and LINREG(ROBUSTERRORS) is perfectly happy with missing values. The whole point of Hodrick's paper is to deal with multi-step predictability where there's an issue with serially correlated residuals.

Many thanks Tom.