^{1}

^{2}

It is generally believed that the signs of the estimated coefficient and its t value should be the same. This paper, however, shows that there may be an inconsistency in the signs of the estimated coefficient and its t value when we use the group mean dynamic OLS estimator developed by Pedroni (2001).

This paper shows the possibility of inconsistency in the signs of the group mean dynamic OLS estimator and its t value. According to basic econometrics and statistics, the t value is calculated by dividing the estimated coefficient by its standard error. Because the standard error is always positive, the sign of the t value becomes identical to the sign of the estimated coefficient [

Pedroni [

The remainder of this paper is as follows: Section 2 provides the model; Section 3 shows the simulation; Section 4 concludes.

We consider the estimation of the following model by using dynamic OLS.

where

group mean dynamic OLS estimator, we separately estimate this equation using every cross section. Then, we calculate the estimator with each estimated coefficient and

We show the possibility of inconsistency using a simulation. For simplicity, we assume that

The simulation strategy is as follows. First, we provide the values of

Case 1:

Case 2:

Case 3:

Second, we randomly generate the values of

estimator by using the generated data. This simulation is performed 10,000 times using STATA.

Case 1 and Case 2:

In this case, we expect that both cross sections take identical signs. Thus, we do not need to be concerned with the inconsistency. The result also shows consistency: every 10,000 samples take the same signs in the group mean dynamic OLS estimator and its t value.

Case 3:

In this case, the estimation of each cross section is expected to take opposite signs. Then it might be possible that inconsistency in the signs of the group mean dynamic OLS estimator and its t value occurs.

Coefficient | t Value | Sample Size | |
---|---|---|---|

Consistent | Positive | Positive | 2576 |

Negative | Negative | 2453 | |

inconsistent | Positive | Negative | 2488 |

Negative | Positive | 2483 |

In this paper, we show that there may be an inconsistency in the signs of the estimated coefficient and its t value when we use the group mean dynamic OLS estimator developed by Pedroni (2001).

We are grateful to three anonymous referees for their helpful comments and suggestions.