In this video tutorial, we demonstrate to find, install and run multipurt and pescadf which are commonly known as Second Generation Unit Root Tests using Stata. The tests are established in Pesaran (2007) and Pesaran, Smith, and Yamagata (2009). The tests are commonly known as second generation unit root tests because of their model specification modified the conventional approaches to unit root tests. Other panel unit root tests include Levin and Lin (1992) pooled ADF test (levinlin), Im, Pesaran, and Shin (1997) averaged unit root test for heterogeneous panels (IPS) (ipshin), Maddala andWu (1999) Fisher combination test (MW) (xtfisher), Breitung (2000), Hadri (2000), Harris & Tzavalis (1999) (xtunitroot with options breitung, hadri, ht, respectively, in addition to the above tests). These are also known is first generation or conventional panel unit root tests.
Following Stata helpfile for -multipurt-, The Maddala and Wu (1999) test assumes/allows for heterogeneity in the autoregressive coefficient of the Dickey-Fuller regression and ignores cross-section dependence in the data. Building on the Fisher-principle it constructs a chi-squared statistic, whereby the p-values of country-specific (A)DF tests are transformed into logs and summed across panel members. Multiplied by -2 this sum is then distributed chi-squared with 2N degrees of freedom under the null of nonstationarity in all panel members/series. The Pesaran (2007) CIPS test allows for assumes/allows for heterogeneity in the autoregressive coefficient of the Dickey-Fuller regression and allows for the presence of a single unobserved common factor with heterogeneous factor loadings in the data. The statistic is constructed from the results of panel-member-specific (A)DF regressions where cross-section averages of the dependent and independent variables (including the lagged differences to account for serial correlation) are included in the model (referred to as CADF regressions). The averaging of the group-specific results follows the procedure in the Im, Pesaran and Shin (2003) test. Under the null of nonstationarity the test statistic has a non-standard distribution.
Stata helpfile for -pescadf mention that: pescadf runs the t-test for unit roots in heterogenous panels with cross-section dependence, proposed by Pesaran (2003). Parallel to Im, Pesaran and Shin (IPS, 2003) test, it is based on the mean of individual DF (or ADF) t-statistics of each unit in the panel. Null hypothesis assumes that all series are non-stationary. To eliminate the cross dependence, the standard DF (or ADF) regressions are augmented with the cross section averages of lagged levels and first-differences of the individual series (CADF statistics). Considered is also a truncated version of the CADF statistics which has finite first and second order moments. It allows to avoid size distortions, especially in the case of models with residual serial correlations and linear trends (Pesaran, 2003).
References for the given two second generation unit root tests are given below:
Pesaran, M. H. (2007). A simple panel unit root test in the presence of cross-section dependence. Journal of Applied Econometrics, 22(2), 265-312.
Pesaran, M. H., Smith, V., & Yamagata, T. (2009). Panel unit root tests in the presence of a multifactor error structure. (Cambridge University, unpublished working paper, September)
More Stata codes: https://sites.google.com/site/medevecon/code#TOC-xtcipsm
Data for -multipurt- can be downloaded from here: http://sites.google.com/site/medevecon/publications-and-working-papers/agri_stata9.zip
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