We show how to easily implement a Roy-Zellner test for poolability in STATA and we offer an application to the Grunfeld dataset.poolability, Roy-Zellner test, Grunfeld dataset

Andrea Vaona

English

Research Papers in Economics

 
 
 
 
 
 
 
 
 
 
Andrea Vaona 
 
STATA tip : a quick trick to perform 
a Roy-Zellner test for poolability in 
STATA 
 
 
 
 
 
Quaderno N. 08-04 
 
 
 
 
 
 
 
 
 
 
 
 
Decanato della Facoltà di Scienze economiche 
Via G. Buffi, 13  CH-6900 Lugano STATA tip: A quick trick to perform a Roy-Zellner test for 
poolability in Stata 
 
 
Andrea Vaona
1 
University of Lugano, CH, and Kiel Institute for the World Economy, DE 
andrea.vaona@lu.unisi.ch 
 
 
Vaona (2008) and Schiavo and Vaona (2008) showed two empirical applications of the Roy-Zellner 
test for poolability that have attracted considerable interest. This note shows a quick trick to implement 
this test in Stata, once applying it to the slope coefficients of a linear model. 
In a given panel sample ()
d
it it x y
+ ∈
1 , R , let yit and xit respectively be the observations of the dependent 
and of the d independent variables for individual i at time t. Suppose to have the following model: 
it it i it x y ε β α + + =        ( 1 )  
where  it ε  is a stochastic error and α and βi are coefficients. The null hypothesis of the Roy-Zellner test 
applied to the slope coefficients is that  
β β = i                  (2) 
under the assumption that  it i it u + =η ε , where ηi∼N(0,
2
η σ ) and uit∼N(0,
2
u σ ). The difference with a 
Chow test is that the latter one tests (2) under the hypothesis that εit∼N(0,
2
ε σ ). Baltagi (2001) 
recommends to rely on a Roy-Zellner test for poolability unless being sure that the underlying 
assumption of the Chow test is correct.  
We discuss here how to easily implement a Roy-Zellner test in Stata. The procedure is in three steps. 
First, we interact the regressors with a set of individual dummies to obtain the unpooled data. Second, 
we run a random effect regression on the unpooled data. Finally, we test for the equality of the 
individual coefficients.  
As in Baltagi (2001) we illustrate this procedure using the Grunfled dataset, which concerns 10 large 
manufacturing firms (whose indexes are contained in the variable firm) from 1935 to 1954 (a time 
index is contained in the variable year). We would like to explain real gross investment (I) as a function 
of outstanding shares (F) and the real value of the capital stock (C). 
First tsset the dataset: 
 
. tsset firm year 
 
Then generate a set of individual dummy variables 
 
. xi, prefix(F) i.firm 
 
. gen Ffirm_1=1 if firm==1 
 
. replace Ffirm_1=0 if firm!=1 
 
                                                 
1 The author would like to thank Finn Martensen for an helpful comment. The usual disclaimer applies. Interact these dummies with the regressors, F and C: 
 
. foreach var of varlist C F{ 
. foreach num of numlist 1(1)10{ 
.               gen `var'_`num'=`var'*Ffirm_`num' 
.        } 
.} 
 
Run a random effect regression for the unpooled data: 
 
. quietly xtreg  I F_* C_*, re 
 
Test for the equality of the coefficients of the unpooled data: 
 
. test (F_1 = F_2 = F_3 = F_4 = F_5 = F_6 = F_7 = F_8 = F_9 = F_10) (C_1 = C_2 = C_3 = C_4 = 
C_5 = C_6 = C_7 = C_8 = C_9 = C_10) 
 
Stata uses a Wald test distributed as a χ
2 with 18 degrees of freedom, which returns a value of 739.84, 
rejecting the null of poolability consistently with the results contained in Baltagi (2001). 
 
References  
Baltagi, Badi (2001), Econometric Analysis of Panel Data, Wiley: Chichester, UK. 
Schiavo, Stefano and Vaona, Andrea (2008), “Poolability and the Finance – Growth Nexus: a 
Cautionary Note”, Economics Letters, 98, 2, pp. 144-147. DOI: 
http://dx.doi.org/10.1016/j.econlet.2007.04.015 
Vaona, Andrea (2008), “Regional Evidence on Financial Development, Finance Term Structure and 
Growth”, Empirical Economics, 34, 1, pp. 185-201. DOI: http://dx.doi.org/10.1007/s00181-007-0153-
2.  
 
 
QUADERNI DELLA FACOLTÀ 
 
 
 
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via G. Buffi 13  CH 6900 Lugano 
e-mail: biblioteca@lu.unisi.ch 
 
The  working  papers  (printed  version)  may  be  obtained  by  contacting  the  Biblioteca universitaria  di 
Lugano 
via G. Buffi 13  CH 6900 Lugano 
e-mail: biblioteca@lu.unisi.ch 
 
 
 
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A. Vaona, STATA tip : a quick trick to perform a Roy-Zellner test for poolability in 
STATA 
 
 
 

Econometric Analysis of Panel Data,

The working papers (printed version) may be obtained by contacting the Biblioteca universitaria di Lugano via G. Buffi 13 CH 6900 Lugano e-mail: biblioteca@lu.unisi.ch Quaderno n.

STATA tip: A quick trick to perform a Roy-Zellner test for poolability in Stata

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STATA tip: A quick trick to perform a Roy-Zellner test for poolability in Stata

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