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. . August 20, 2017 Email:kerrydu@sdu.edu.cn using Stata Econometric convergence test and club clustering . . Example Monte Carlo simulation The PSECTA package Econometric convergence test and club clustering Introduction . . . . 1 / 30 杜克锐 山东大学经济研究院

. . Example 5 . Monte Carlo simulation 4 . The PSECTA package 3 . . Econometric convergence test and club clustering 2 . Introduction . 1 . . Example Monte Carlo simulation The PSECTA package Econometric convergence test and club clustering Introduction . . . . 2 / 30 . Outline

. Convergence in economics refers to the hypothesis that all 2013), and corporate tax (Regis et al. 2015) (Camarero et al. 2013), house prices (Montanes and Olmos emissions (Panopoulou and Pantelidis 2009), eco-eciency e.g., cost of living (Phillips and Sul 2007), carbon dioxide Convergence analysis has also been applied in other topics, (1997); Luginbuhl and Koopman (2004) Durlauf (1995); Barro and Sala-i Martin (1997); Lee et al. Representative literature: Baumol (1986); Bernard and per-capita output economies would eventually converge in terms of 3 / 30 . . Example Monte Carlo simulation The PSECTA package Econometric convergence test and club clustering Introduction . . . . . Introduction

. Convergence in economics refers to the hypothesis that all 2013), and corporate tax (Regis et al. 2015) (Camarero et al. 2013), house prices (Montanes and Olmos emissions (Panopoulou and Pantelidis 2009), eco-eciency e.g., cost of living (Phillips and Sul 2007), carbon dioxide Convergence analysis has also been applied in other topics, (1997); Luginbuhl and Koopman (2004) Durlauf (1995); Barro and Sala-i Martin (1997); Lee et al. Representative literature: Baumol (1986); Bernard and per-capita output economies would eventually converge in terms of 3 / 30 . . Example Monte Carlo simulation The PSECTA package Econometric convergence test and club clustering Introduction . . . . . Introduction

. . being robust to the stationarity property of the series. trend stationarity or stochastic nonstationarity, thereby . . evolution in that behavior. . . (termed ‘log t’ regression test) . Phillips and Sul (2007) proposed a novel approach 4 / 30 . Example Monte Carlo simulation The PSECTA package Econometric convergence test and club clustering Introduction . . . . . Introduction 1 Accommodates heterogeneous agent behavior and 2 Does not impose any particular assumptions concerning

. . identify clusters of convergence subgroups. Phillips and Sul (2007) constructed a new algorithm to location, institution) subgroups based on some prior information (e.g., geographical Traditional studies typically divided all the individuals into clubs. convergence analysis is the possible existence of convergence Another commonly concerned issue involved in the . Example Monte Carlo simulation The PSECTA package Econometric convergence test and club clustering Introduction . . . . 5 / 30 . Introduction

. Monte Carlo simulation developed by Phillips and Sul (2007). perform the econometric convergence test and club clustering In this article, we introduce a new Stata module ‘psecta’ to . Example The PSECTA package . Econometric convergence test and club clustering Introduction . . . . 6 / 30 . Introduction

. Example common component. (2) u t (1) . . 7 / 30 Monte Carlo simulation . Econometric convergence test and club clustering Introduction . . . The PSECTA package . Time varying factor representation X it = g it + a it where g it represents systematic components such as permanent common components, and a it embodies transitory components. ( g it + a it ) X it = u t = δ it u t where δ it is a time varying idiosyncratic element and u t is a single

. X it N N loading coefficient relative to the panel average at time t . Eq. (3) h it is called the relative transition parameter which measures the (3) N . N 8 / 30 . Example . Monte Carlo simulation . . The PSECTA package . Econometric convergence test and club clustering Introduction . Time varying factor representation δ it h it = = 1 1 ∑ N ∑ N i =1 δ it i =1 X it indicates that the cross-sectional mean of h it is unity and the cross-sectional variance of h it satisfies the following condition: H it = 1 ( h it − 1) 2 → 0 if lim ∑ t →∞ δ it = δ, for all i . i =1

. Example (5) lim (4) X jt X it . . lim Monte Carlo simulation . . . The PSECTA package . Introduction Econometric convergence test and club clustering 9 / 30 . The log t regression test The convergence of X it requires the following condition: = 1 , for all i and j t →∞ t →∞ δ it = δ, for all i Assume the loading coefficient δ it as σ i δ it = δ i + σ it ξ it , σ it = L ( t ) t α , t ≥ 1 , σ i > 0 for all i

. . (6) H t log the following ‘log t’ regression model: Specifically, the hypothesis test can be implemented through null hypothesis of convergence . Phillips and Sul (2007) developed a regression t test for the Example Monte Carlo simulation The PSECTA package Econometric convergence test and club clustering Introduction . . . . 10 / 30 . The log t regression test H 0 : δ i = δ and α ≥ 0 ( H 1 ) − 2 log ( log ( t )) = a + blog ( t ) + ε t for t = [ rT ] , [ rT ] + 1 , ..., T with r > 0

. The PSECTA package s b implies a one-sided t test. . Example Monte Carlo simulation . Econometric convergence test and club clustering Introduction . . . . 11 / 30 . The log t regression test Phillips and Sul (2007) further showed that b = 2 α and H 0 is conveniently tested through the weak inequality null α ≥ 0 . It ˆ b − b t b = ⇒ N (0 , 1)

. . . . . . . . . . . 12 / 30 . Example Monte Carlo simulation The PSECTA package Econometric convergence test and club clustering Introduction . . . . . Club convergence test and clustering 1 Cross-section sorting 2 Core group Formation 3 Sieve individuals for club membership 4 Recursion and stopping rule 5 Club merging

. standard errors. routines; by default, user-written mata functions are used. nomata implements the regression mainly through the Stata discarded before regression; default is 0.3. kq(#) specifies the first kq proportion of the data to be Options kq( # ) nomata , in if logtreg varname . Syntax with heteroskedasticity- and autocorrelation-consistent logtreg performs the log t test using linear regression . . . . Introduction Econometric convergence test and club clustering The PSECTA package Monte Carlo simulation Example . 13 / 30 . The logtreg command [ ] [ ] [ ]

. . fails to sieve individuals for clusters; default is 0.05. incr(#) specifies the increment of cr when the initial cr value 0. cr(#) specifies the critical value for club clustering; default is discarded before regression; default is 0.3. kq(#) specifies the first kq proportion of the data to be Options noprtlogtreg cr( # ) incr( # ) maxcr( # ) adust fr( # ) nomata name( varname ) kq( # ) gen( newvarname ) psecta varname , Syntax (2007) analysis using the algorithm proposed by Phillips and Sul psecta implements club convergence and clustering . Example Monte Carlo simulation The PSECTA package Econometric convergence test and club clustering Introduction . . . . 14 / 30 . The psecta command [ ]

. . the last fr proportion periods; The default is fr(0). fr(#) specifies sorting individuals by the time series average of Schnurbus et al. (2016) . adjust specifies using the adjusted method proposed by maxcr(#) specifies the maximum of cr value; default is 50. Options noprtlogtreg cr( # ) incr( # ) maxcr( # ) adust fr( # ) nomata name( varname ) kq( # ) gen( newvarname ) psecta varname , Syntax (2007) analysis using the algorithm proposed by Phillips and Sul psecta implements club convergence and clustering . Example Monte Carlo simulation The PSECTA package Econometric convergence test and club clustering Introduction . . . . 15 / 30 . The psecta command [ ]

. . classications. gen(newvarname) creates a new variable to store club routines; by default, user-written mata functions are used. nomata implements the regression mainly through the Stata maxcr(#) specifies the maximum of cr value; default is 50. Options noprtlogtreg cr( # ) incr( # ) maxcr( # ) adust fr( # ) nomata name( varname ) kq( # ) gen( newvarname ) psecta varname , Syntax (2007) analysis using the algorithm proposed by Phillips and Sul psecta implements club convergence and clustering . Example Monte Carlo simulation The PSECTA package Econometric convergence test and club clustering Introduction . . . . 16 / 30 . The psecta command [ ]

. . noprtlogtreg suppresses the estimation results of the logtreg. xtset is used. the clustering results; by default, the panel variable specied by name(varname) specifies a panel variable to be displayed for Options noprtlogtreg cr( # ) incr( # ) maxcr( # ) adust fr( # ) nomata name( varname ) kq( # ) gen( newvarname ) psecta varname , Syntax (2007) analysis using the algorithm proposed by Phillips and Sul psecta implements club convergence and clustering . Example Monte Carlo simulation The PSECTA package Econometric convergence test and club clustering Introduction . . . . 17 / 30 . The psecta command [ ]