### Install xtdcce2 from GitHub

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

Use this command to install the latest stable version of xtdcce2 directly from its GitHub repository.

```stata
net install xtdcce2 , from("https://janditzen.github.io/xtdcce2/")
```

--------------------------------

### Install xtdcce2 Beta Versions from GitHub

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

This command allows installation of beta versions of xtdcce2, which may include experimental features or fixes.

```stata
net from https://janditzen.github.io/xtdcce2/
```

--------------------------------

### Install xtdcce2 Beta Versions (Pre v1.34)

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

Use this command to access and install beta versions of xtdcce2 released before version 1.34.

```stata
net from http://www.ditzen.net/Stata/xtdcce2_beta
```

--------------------------------

### Install xtdcce2 from SSC

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

This command installs the xtdcce2 package from the Statistical Software Components (SSC) archive, a common source for Stata user-written packages.

```stata
ssc install xtdcce2
```

--------------------------------

### Estimate CS-ARDL Model with ARDL(3,3,3) without Parentheses

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

This command estimates the same CS-ARDL model as the previous example but without using parentheses to group variables. It demonstrates an equivalent way to specify the long-run coefficients.

```stata
xtdcce2 d.y , lr(L(1/3).d.y L(0/3).dp L(0/3).d.gd) lr_options(ardl) cr(d.y dp d.gd) cr_lags(3) fullsample
```

--------------------------------

### Bootstrap Standard Errors with Fixed Seed

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

This command bootstraps standard errors with a fixed seed for reproducibility. It is a basic setup for bootstrapping in Stata.

```stata
estat bootstrap, seed(123)
```

--------------------------------

### Information Criteria for a Single Model (Single Option)

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

Get Information Criteria for a single, specified model of cross-section averages using the 'single' option. This is useful for comparing a specific model against all combinations.

```stata
estat ic, model(log_hc log_ck ) single
```

--------------------------------

### Information Criteria Calculation

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

Information Criteria (IC1, IC2, PC1, PC2) guide the selection of optimal cross-section averages. IC1 and IC2 are calculated automatically by xtdcce2. PC1 and PC2 can be calculated using `estat ic`. These criteria are only valid for static panel models.

```stata
xtdcce2
```

```stata
estat ic
```

--------------------------------

### Run Wild Bootstrap and Bootstrap Confidence Intervals

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

This command performs a wild bootstrap and calculates bootstrap confidence intervals. It includes options for 'wild' bootstrapping and 'percentile' confidence intervals, along with a fixed seed.

```stata
estat bootstrap, seed(123) wild percentile
```

--------------------------------

### xtdcce2 Syntax

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

Standard syntax for the xtdcce2 command, used for estimating heterogeneous coefficient models with common correlated effects in a dynamic panel.

```stata
xtdcce2 _depvar_ [_indepvars_] [_varlist2_ = _varlist_iv_] [ifin] ,
crosssectional(_varlist_[,cr_lags(_numlist_) rcce[(criterion(er/gr) scale npc(integer))] rcclassifier[(er gr replications(integer) standardize(integer) randomshrinkage noshrinkage)]]) 
[clustercrosssectional(_varlist_, clustercr(_varlist_) [cr_lags(_numlist_)]) 
globalcrosssectional(_varlist_[,cr_lags(_numlist_)]) pooled(_varlist_) cr_lags(_numlist_) 
NOCRosssectional ivreg2options(_string_) e_ivreg2_ ivslow noisily lr(_varlist_) lr_options(_string_) 
pooledconstant reportconstant pooledvce(_string_) noconstant trend 
pooledtrend jackknife recursive nocd exponent xtcse2options(_string_) 
showindividual fullsample fast fast2 blockdiaguse nodimcheck useqr useinvsym noomitted mgmissing]
```

--------------------------------

### Predict xb vs xb2 calculation

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

Illustrates the difference in calculation between predict xb and xb2 options. xb calculates linear prediction on partialled out variables, while xb2 calculates on non-partialled out variables.

```stata
1. predict coeff, coeff
2. predict partial, partial
3. gen xb = coeff_x * partial_x
```

```stata
1. predict coeff, coeff
2. gen xb2 = coeff_x * x
```

--------------------------------

### xtdcce2fast Syntax

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

Optimized syntax for the xtdcce2fast command, designed for speed and large datasets in panel time series models with cross-sectional dependence.

```stata
xtdcce2fast _depvar_ [_indepvars_] [ifin] , crosssectional(_varlist_[,cr_lags(_numlist_) rcce[(criterion(er/gr) scale npc(integer))] rcclassifier[(er gr replications(integer) standardize(integer) randomshrinkage noshrinkage)]]) 
[clustercrosssectional(_varlist_, clustercr(_varlist_) [cr_lags(_numlist_)]) 
globalcrosssectional(_varlist_[,cr_lags(_numlist_)]) cr_lags(_string_) 
NOCRosssectional lr(_varlist_) lr_options(_string_) 
reportconstant noconstant cd fullsample notable cd postframe nopost ]
```

--------------------------------

### Estimate CS-ARDL Model with ARDL(3,3,3) using Parentheses

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

This command estimates a CS-ARDL model with an ARDL(3,3,3) specification, using parentheses to group variables that form the same long-run coefficient. This is an alternative to using _tsvarlist_ operators.

```stata
xtdcce2 d.y , lr((L(1/3).d.y) (L(0/3).dp) (L(0/3).d.gd) ) lr_options(ardl) cr(d.y dp d.gd) cr_lags(3) fullsample
```

--------------------------------

### Estimate Panel Model and Run CD Test

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

Estimates a panel version of the Solow model and then runs the standard CD test. Ensure data is tsset.

```stata
reg d.log_rgdpo log_hc log_ck log_ngd
xtcd2
```

--------------------------------

### Run CD Test with Kernel Density Plot

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

Runs the CD test and generates a kernel density plot of the cross-correlations using the 'kdensity' option. This helps visualize the distribution of cross-correlations.

```stata
xtcd2 res, kdensity
```

--------------------------------

### xtcd2 Command Syntax for Testing Cross-Sectional Dependence

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

The general syntax for the xtcd2 command, used to test for weak cross-sectional dependence in panel data models. It accepts a list of variables or residuals and various options for different test statistics.

```stata
xtcd2 [varlist] [if] [,pesaran cdw pea cdstar rho 
pca(integer) reps(integer) seed(integer)
kdensity name(string) heatplot[(absolute options_heatplot)] 
contour[(absolute options_contour) noadjust] ]
```

--------------------------------

### Predict command syntax

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

The general syntax for the predict command after running xtdcce2. Specify the new variable name and the desired output type.

```stata
predict [type] _newvar_ _ifin_ [ options ]
```

--------------------------------

### Estimate ECM/PMG Model with XTPMG Naming Convention

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

Estimates an ECM/PMG model using the 'xtpmgnames' option to match the naming convention of the 'xtpmg' command.

```stata
xtdcce2 d.c d.pi d.y if year >= 1962 , lr(L.c pi y) p(L.c pi y) nocross lr_options(xtpmgnames)
```

--------------------------------

### Run CD Test with Power Enhancement Approach

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

Applies the Power Enhancement Approach (PEA) using the 'pea' option to improve the power of the weighted CD test. Requires data to be tsset.

```stata
xtcd2 res, pea
```

--------------------------------

### Run Weighted CD Test with Multiple Repetitions

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

Performs the weighted CD test multiple times with different weights using the 'reps()' option to reduce dependence on specific weightings. Requires the 'cdw' option to be active.

```stata
xtcd2 res, cdw reps(20)
```

--------------------------------

### Bootstrap Confidence Intervals with estat

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

Use 'estat bootstrap' to calculate confidence intervals and standard errors. Supports wild and cross-section bootstraps. Default repetitions are 100.

```stata
estat bootstrap , [options]
```

--------------------------------

### Calculate Information Criteria with estat

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

Use 'estat ic' to calculate information criteria for selecting the optimal number of cross-section averages. Only valid for static panels.

```stata
estat ic , [options]
```

--------------------------------

### Econometric Model Equation (1)

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

Defines a dynamic panel data model with heterogeneous coefficients and unobserved common factors. This equation serves as the theoretical basis for the empirical models discussed.

```mathematica
y(i,t) = b0(i) + b1(i)*y(i,t-1) + x(i,t)*b2(i) + x(i,t-1)*b3(i) + u(i,t) u(i,t) = g(i)*f(t) + e(i,t)
```

--------------------------------

### Estimate Mean Group Growth Equation with Constant

Source: https://github.com/janditzen/xtdcce2/wiki/Home

Estimates a growth equation using the mean group approach, ensuring the constant is reported separately. Use the 'reportc' option to include the constant in the output.

```stata
xtdcce2 d.log_rgdpo L.log_rgdpo log_hc log_ck log_ngd , nocross reportc.
```

--------------------------------

### Predict residuals calculation

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

Demonstrates how to calculate residuals (e(i,t)) using the 'residuals' option. This represents the residuals of the regression with cross-sectional averages partialled out.

```stata
predict _newvar_ , residuals
```

--------------------------------

### Cross-Section Augmented Distributed Lag (CS-DL) Model Initial Equation

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

This equation represents the initial CS-DL model formulation for estimating the long run effect of x on y, including cross-sectional averages and differences of explanatory variables.

```mathematica
(8)  y(i,t) = w0(i) + x(i,t) * w2(i)  + delta(i) * (x(i,t) - x(i,t-1)) + sum [d(i)*z(i,s)] + e(i,t)
```

--------------------------------

### Predict Residuals and Run CD Test

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

Predicts residuals from a regression and then runs the CD test on these residuals. This is an alternative to running xtcd2 directly after regression.

```stata
reg d.log_rgdpo log_hc log_ck log_ngd
predict res, residuals
xtcd2 res
```

--------------------------------

### Estimate Static rCCE Model with Fixed Number of Eigenvectors

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

This command estimates a static rCCE model by hard-setting the number of regularized cross-section averages to three using the 'npc()' option. This bypasses the need to specify a selection criterion.

```stata
xtdcce2 log_rgdpo log_hc log_ck log_ngd , cr(log_rgdpo log_hc log_ck log_ngd, rcce(npc(3)))
```

--------------------------------

### Estimate Static rCCE Model

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

This command estimates a static Regularized CCE model for growth on human capital, physical capital, and population growth. It uses the default ER criterion for selecting eigenvectors.

```stata
xtdcce2 log_rgdpo log_hc log_ck log_ngd , cr(log_rgdpo log_hc log_ck log_ngd, rcce)
```

--------------------------------

### Information Criteria for Specific Model Combinations

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

Calculate Information Criteria for three different sets of cross-section averages, specified using the 'model()' option. The first model listed serves as the reference.

```stata
estat ic, model( (d.log_rgdpo log_hc log_ck log_ngd) (log_hc log_ck log_ngd) (log_hc log_ck ) )
```

--------------------------------

### Rank Condition Classifier with Default Settings

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

Calculate the rank condition classifier using the default settings for the CCE estimator. This is useful for ensuring consistent estimation in panel data models.

```stata
xtdcce2 d.log_rgdpo log_hc log_ck log_ngd , cr(_all, rccl) reportc
```

--------------------------------

### Information Criteria for a Single Model (Without Single Option)

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

Calculate Information Criteria for a single model of cross-section averages without the 'single' option. This will compare the specified model against all possible combinations.

```stata
estat ic, model(log_hc log_ck log_ngd)
```

--------------------------------

### Standardize Variable for BKP Table 1 Reproduction

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

Use xtcse2 with the 'standardize' option to standardize a variable, as done in the BKP paper for reproducing Table 1. This is useful when working with data that requires specific preprocessing steps.

```Stata
xtcse2 gdp , standardize.
```

--------------------------------

### Estimate ARDL(3,3,3) without parenthesis

Source: https://github.com/janditzen/xtdcce2/wiki/Home

Provides an equivalent specification to the parenthesized version for ARDL(3,3,3) estimation without using parentheses for variable grouping. This relies on xtdcce2's default variable recognition.

```stata
xtdcce2133 d.y , lr(L(1/3).d.y L(0/3).dp L(0/3).d.gd) lr_options(ardl) cr(d.y dp d.gd) cr_lags(3) fullsample
```

--------------------------------

### Create Bar Plot with estat

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

Use 'estat bar' to generate a bar plot. Options like 'individual()' and 'combine()' can be used for customization.

```stata
estat bar _varlist_ {ifin} [,combine(_string_) individual(_string_) nomg cleargraph]
```

--------------------------------

### Sequential Information Criteria Calculation

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

Calculate Information Criteria for all possible combinations of cross-section averages and indicate the lowest ones. This sequential approach helps in identifying the optimal set of averages.

```stata
estat ic, seqential
```

--------------------------------

### Pooled Estimations Equations

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

These equations represent pooled estimations where parameters are constrained to be the same across units. The 'pooled(_varlist_)' option pools variables, and 'pooledconstant' pools the constant term.

```mathematica
(3-p) y(i,t) = b0 + b1*y(i,t-1) + x(i,t)*b2 + e(i,t),
(4-p) y(i,t) = b0 + x(i,t)*b2 + d(i)*z(i,t) + e(i,t),
(5-p) y(i,t) = b0 + b1*y(i,t-1) + x(i,t)*b2 + sum [d(i)*z(i,s)] + e(i,t).
```

--------------------------------

### Create Box Plot with estat

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

Use 'estat box' to generate a box plot. Ensure the graph type and any necessary options are specified.

```stata
estat box _varlist_ {ifin} [,combine(_string_) individual(_string_) nomg cleargraph]
```

--------------------------------

### Instrumental Variables Estimation

Source: https://github.com/janditzen/xtdcce2/wiki/Home

Uses 'endogenous_vars' and 'exogenous_vars' to specify instrumental variables. 'ivreg2options' can pass further options to ivreg2. 'fulliv' posts stored values from ivreg2.

```stata
xtdcce2 d.log_rgdpo L.log_rgdpo log_hc log_ck log_ngd (log_ck = L.log_ck), reportc
cr(d.log_rgdpo L.log_rgdpo log_hc log_ck log_ngd) cr_lags(3) ivreg2options(nocollin noid).
```

--------------------------------

### Estimate ARDL(3,3,3) with parenthesized variables

Source: https://github.com/janditzen/xtdcce2/wiki/Home

Estimates an ARDL(3,3,3) model with xtdcce2, using parentheses to group variables that form the same long-run coefficient. This is an alternative to using tsvarlist operators.

```stata
xtdcce2133 d.y , lr((L(1/3).d.y) (L(0/3).dp) (L(0/3).d.gd) ) lr_options(ardl) cr(d.y dp d.gd) cr_lags(3) fullsample
```

--------------------------------

### Pooled Estimations with Pooled Constant

Source: https://github.com/janditzen/xtdcce2/wiki/Home

Pools all coefficients and the constant using the 'pooled' and 'pooledconstant' options. Ensure variables are correctly specified in 'reportc' and 'cr'.

```stata
xtdcce2 d.log_rgdpo L.log_rgdpo log_hc log_ck log_ngd , reportc cr(d.log_rgdpo
L.log_rgdpo log_hc log_ck log_ngd) pooled(L.log_rgdpo log_hc log_ck log_ngd) cr_lags(3)
pooledconstant.
```

--------------------------------

### Estimate Dynamic Growth Equation with Lags

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

Estimate a dynamic growth equation using xtdcce2, incorporating lags of cross-sectional averages. The number of lags is suggested to be around T^(1/3). After estimation, use xtcse2 with 'nocd' and 'residual' options to test for residual dependence and estimate alpha.

```Stata
xtdcce2 log_rgdpo L.log_rgdpo log_ck log_ngd log_hc , cr(log_rgdpo log_ck log_ngd log_hc) cr_lags(3) .
xtcse2 ,nocd residual lags(3) reps(200)
```

--------------------------------

### Estimate Static rCCE Model with GR Criterion

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

This command estimates a static rCCE model using the GR criterion instead of the default ER criterion for selecting eigenvectors. This allows for a different selection method for the regularized cross-section averages.

```stata
xtdcce2 log_rgdpo log_hc log_ck log_ngd , cr(log_rgdpo log_hc log_ck log_ngd, rcce(criterion(gr)))
```

--------------------------------

### Run Weighted CD Test with Rademacher Weights

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

Applies unit-specific rademacher weights using the 'cdw' option to prevent the CD test statistic from diverging, especially when many periodic specific parameters are used. Requires data to be tsset.

```stata
xtcd2 res, cdw
```

--------------------------------

### Information Criteria for Cross-Section Averages (Default)

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

Obtain Information Criteria (IC1 and IC2) for the current set of cross-section averages defined in the model. This is a standard step when using information criteria for model selection.

```stata
xtdcce2 d.log_rgdpo log_hc log_ck log_ngd , cr(_all) reportc
estat ic
```

--------------------------------

### Estimate Exponent of Cross-Sectional Dependence

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

Estimates the exponent of cross-sectional dependence using the xtcse2 command. Data must be xtset. Can predict residuals if varlist is empty.

```stata
xtcse2 [varlist] [if] [, pca(integer) standardize nocenter nocd 
RESsidual Reps(integer) size(real) tuning(real) lags(integer) ]
```

--------------------------------

### Estimate ARDL(1,1,1) with cross-sectional averages

Source: https://github.com/janditzen/xtdcce2/wiki/Home

Estimates an ARDL(1,1,1) model using xtdcce2, specifying long-run variables and lags of cross-sectional averages. Use this when variables are not enclosed in parentheses.

```stata
xtdcce2 d.y , lr(L.d.y dp L.dp d.gd L.d.gd) lr_options(ardl) cr(d.y dp d.gd) cr_lags(3) fullsample
```

--------------------------------

### Estimate ECM/PMG Model with Nodivide Option

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

Estimates an ECM/PMG model, recalculating long-run coefficients. The 'nodivide' option within 'lr_options()' is used to estimate equation (7) directly.

```stata
xtdcce2 d.c d.pi d.y if year >= 1962 , lr(L.c pi y) p(L.c pi y) nocross lr_options(nodivide)
```

--------------------------------

### Cross-Section Augmented Distributed Lag (CS-DL) - ARDL(1,3,3)

Source: https://github.com/janditzen/xtdcce2/wiki/Home

Estimates a CS-DL model for an ARDL(1,3,3) specification. Lags of first differences are included using 'L(0/2).'. 'cr_lags' specifies lag structures, and 'fullsample' is used for specific results.

```stata
xtdcce2 d.y dp d.gd L(0/2).d.(dp d.gd), cr(d.y dp d.gd) cr_lags(0 3 3) fullsample
```

--------------------------------

### Estimate CCE Model with Pooled Coefficients and Constant

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

Estimates a dynamic CCE model where specific coefficients and the constant term are pooled across units. This is achieved using the 'pooled' and 'pooledconstant' options.

```stata
xtdcce2 d.log_rgdpo L.log_rgdpo log_hc log_ck log_ngd , reportc cr(log_rgdpo  log_hc log_ck log_ngd) pooled(L.log_rgdpo  log_hc log_ck log_ngd) cr_lags(3) pooledconstant
```

--------------------------------

### Create Range Plot with estat

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

Use 'estat rcap' to generate a range plot. Options 'individual()' and 'combine()' are available for customization.

```stata
estat rcap _varlist_ {ifin} [,combine(_string_) individual(_string_) nomg cleargraph]
```

--------------------------------

### Estimate CCE Model with Instrumental Variables

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

Estimates a dynamic CCE model using instrumental variables, specifying endogenous and exogenous variables. Additional 'ivreg2' options like 'nocollin' and 'noid' can be passed through.

```stata
xtdcce2 d.log_rgdpo L.log_rgdpo log_hc log_ck log_ngd  (log_ck = L.log_ck), reportc cr(log_rgdpo  log_hc log_ck log_ngd) cr_lags(3) ivreg2options(nocollin noid)
```

--------------------------------

### Estimate Mean Group Growth Equation without Explicit Constant Reporting

Source: https://github.com/janditzen/xtdcce2/wiki/Home

Estimates a growth equation using the mean group approach without explicitly reporting the constant. The constant is partialled out and included in the overall estimation.

```stata
xtdcce2 d.log_rgdpo L.log_rgdpo log_hc log_ck log_ngd , nocross.
```

--------------------------------

### Error Correction Model (Pooled Mean Group Estimator) - Basic

Source: https://github.com/janditzen/xtdcce2/wiki/Home

Estimates an Error Correction Model using the pooled mean group estimator. Variables for the long-run cointegration vector are defined in 'lr()'. Ensure homogeneity by including corresponding variables in 'p()'.

```stata
xtdcce2 d.c d.pi d.y if year >= 1962 , lr(L.c pi y) p(L.c pi y) cr(_all) cr_lags(2)
```

--------------------------------

### Cross-Section Augmented Distributed Lag (CS-DL) - ARDL(1,1,1)

Source: https://github.com/janditzen/xtdcce2/wiki/Home

Estimates a CS-DL model for an ARDL(1,1,1) specification. 'cr_lags' uses a numlist to define lag structures for different variables. 'fullsample' is used to reproduce specific results.

```stata
xtdcce2 d.y dp d.gd d.(dp d.gd), cr(d.y dp d.gd) cr_lags(0 3 3) fullsample
```

--------------------------------

### Cross-Section Augmented Distributed Lag (CS-DL) Model Equation

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

This equation represents a general ARDL(py,px) model estimated using the CS-DL approach. It directly estimates long-run effects and includes cross-sectional averages and differences of explanatory variables.

```mathematica
(8)  y(i,t) = w0(i) + x(i,t) * w2(i)  + sum(l=1,px) delta(i,l) * (x(i,t-l) - x(i,t-l-1))  + sum [d(i)*z(i,s)] + e(i,t)
```

--------------------------------

### General Factor Model Specification

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

This code block illustrates the general factor model used in panel data analysis, where a variable depends on unobserved common factors and a cross-sectionally independent error term. It assumes both the time dimension (T) and the number of cross-sectional units (N) increase to infinity.

```mathematica
x(i,t) = sum(j=1,m) b(j,i) f(j,t) + u(i,t)
i = 1,...,N and t = 1,...,T
```

--------------------------------

### CS-ARDL Long Run Coefficients Formula

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

Formulas for calculating long-run coefficients in a CS-ARDL model. These are derived after estimating short-run coefficients.

```mathematica
(9) y(i,t) = b0(i) + sum(l=1,py) b1(i,l) y(i,t-l) + sum(l=0,px) b2(i,l) x(i,t-l) +  sum [d(i)*z(i,s)] + e(i,t),
```

```mathematica
(10) w2(i) = sum(l=0,px) b2(i,l) / ( 1 - sum(l=1,py) b1(i,l))
```

```mathematica
(11) w1(i) = 1 - sum(l=1,py) b1(i,l).
```

--------------------------------

### Estimate Growth Equation with Cross-Sectional Dependence

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

Estimate a growth equation using xtdcce2, including cross-sectional averages (cr) of specified variables. After estimation, use xtcse2 with the 'res' option to check for residual cross-sectional dependence.

```Stata
xtdcce2 log_rgdpo L.log_rgdpo log_ck log_ngd log_hc , cr(log_rgdpo log_ck log_ngd log_hc) .
xtcse2, res
```

--------------------------------

### Common Correlated Effects (xtdcce2 default)

Source: https://github.com/janditzen/xtdcce2/wiki/Home

Estimates the Common Correlated Effects model by default, including cross-sectional averages. Use when unobserved common factors between units need to be accounted for.

```Stata
xtdcce2, crosssectional(depvar indepvars) cr_lags(0)
```

--------------------------------

### Predict Partialled Out Variables from CCE Model

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

Predicts the partialled out variables from a CCE model estimation using the 'partial' option. Regressing on these variables should yield similar results to the original estimation.

```stata
predict partial, partial
```

--------------------------------

### Error Correction Model (ECM/PMG) ARDL Transformation

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

This equation shows the transformation of an ARDL model for ECM/PMG estimation, differentiating between homogenous long run and heterogeneous short run effects. It is presented without cross-sectional averages for readability.

```mathematica
(6)y(i,t) = phi(i)*(y(i,t-1) - w0(i) - x(i,t)*w2(i)) + g1(i)*[y(i,t)-y(i,t-1)] + [x(i,t) - x(i,t-1)] * g2(i) + e(i,t),
```

--------------------------------

### Estimate Static Common Correlated Effects Model with Specified Cross-Sectional Variables

Source: https://github.com/janditzen/xtdcce2/wiki/Home

Estimates a static common correlated effects model by explicitly defining the variables to be used as cross-sectional averages. This is equivalent to using 'cr(_all)' when all variables are specified.

```stata
xtdcce2 d.log_rgdpo log_hc log_ck log_ngd , reportc cr(d.log_rgdpo log_hc log_ck
log_ngd).
```

--------------------------------

### Exponent Estimation in Residuals

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

This formula estimates the exponent alpha in residuals using significant pair-wise correlations, as proposed by BKP (2019). It requires a vector of ones and a matrix of significant pair-wise correlations.

```mathematica
alpha = ln(tau' delta tau) / [2 ln(N)]
```

--------------------------------

### Predict Partialled Out Values

Source: https://github.com/janditzen/xtdcce2/wiki/Home

Creates new variables containing the partialled out values.

```stata
predict partial_var, partial
```

--------------------------------

### Variance of Mean Group Coefficient b1(mg)

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

Formula for estimating the variance of the mean group coefficient b1(mg) in a dynamic panel data model. This is used in the Mean Group Estimator.

```mathematica
var(b(mg)) = 1/N sum(i=1,N) (b1(i) - b1(mg))^2
```

--------------------------------

### Predict Coefficients from CCE Model

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

Predicts the unit-specific coefficients from a CCE model estimation using the 'coefficients' option. The mean of these coefficients should match the mean group estimate.

```stata
predict coeff, coefficients
```

```stata
sum coeff_log_hc.
```

--------------------------------

### Predict cfresiduals calculation

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

Shows how to calculate residuals including common factors (u(i,t)) using the 'cfresiduals' option. Note that if a constant is used in xtdcce2, it will be included in u(i,t) unless reported using the 'reportconstant' option.

```stata
predict _newvar_ , cfresiduals
```

--------------------------------

### Estimate Static Common Correlated Effects Model with Zero Cross-Sectional Lags

Source: https://github.com/janditzen/xtdcce2/wiki/Home

Estimates a static common correlated effects model with explicitly set zero cross-sectional lags, meaning only contemporaneous cross-sectional averages are used. This is equivalent to the default behavior.

```stata
xtdcce2 d.log_rgdpo log_hc log_ck log_ngd , reportc cr(d.log_rgdpo log_hc log_ck
log_ngd) cr_lags(0).
```

--------------------------------

### CD Test Statistic Formula (Balanced Panel)

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

This formula represents the CD test statistic for a balanced panel, summing pairwise correlation coefficients.

```text
CD = [2*T / (N*(N-1))]^(1/2) * sum(i=1,N-1) sum(j=i+1,N) rho(ij),
```

--------------------------------

### Empirical Model Equation (2)

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

The empirical model derived from equation (1), excluding the lag of variable x and including cross-sectional means. This is a general form supported by `xtdcce2`.

```mathematica
y(i,t) = b0(i) + b1(i)*y(i,t-1) + x(i,t)*b2(i) + sum[d(i)*z(i,s)] + e(i,t)
```

--------------------------------

### Error Correction Model (ECM/PMG) Equation

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

This equation represents a version of the ECM/PMG model estimated by xtdcce2 using OLS. It includes long-run variables specified with 'lr(_varlist_)' and 'pooled(_varlist_)', and first differences as independent variables.

```mathematica
(7)	y(i,t) = o0(i) + phi(i)*y(i,t-1) + x(i,t)*o2(i) + g1(i)*[y(i,t)-y(i,t-1)] + [x(i,t) - x(i,t-1)] * g2(i) + e(i,t),
```

--------------------------------

### Predict Residuals from CCE Model

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

Predicts the residuals (e(i,t)) from a CCE model estimation using the 'residuals' option. These residuals do not include the partialled out factors.

```stata
predict residuals, residuals
```

--------------------------------

### Asymptotic Distribution of CD Test Statistic

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

Under the null hypothesis, the CD test statistic is asymptotically normally distributed with a mean of 0 and a variance of 1.

```text
CD ~ N(0,1)
```

--------------------------------

### Estimate ECM/PMG Model with Long-Run Variables

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

Estimates an Error Correction Model (ECM) or Panel Mean Group (PMG) model by defining long-run cointegration vector variables. Ensures homogeneity of long-run effects by including variables in the 'pooled' option.

```stata
xtdcce2 d.c d.pi d.y if year >= 1962 , lr(L.c pi y) p(L.c pi y) nocross
```

--------------------------------

### Variance of Mean Group Coefficients pi(mg)

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

Formula for estimating the variance of the mean group coefficients pi(mg), which includes intercept and slope coefficients. This is used in the Mean Group Estimator.

```mathematica
var(pi(mg)) = 1/N sum(i=1,N) (pi(i) - pi(mg))(p(i)-pi(mg))'
```

--------------------------------

### Predict Coefficients

Source: https://github.com/janditzen/xtdcce2/wiki/Home

Creates a variable containing the estimated cross-section specific values for all coefficients. The name of the new variable is newvar_varname.

```stata
predict newvar_varname, coefficients
```

--------------------------------

### Predict Residuals with Common Factors

Source: https://github.com/janditzen/xtdcce2/wiki/Home

Use this option to calculate residuals that include common factors, approximated by cross-sectional averages. This is equivalent to calculating u(i,t) = g(i)*f(g) + e(i,t).

```stata
predict newvar , residuals
```

--------------------------------

### Estimate Cross-Sectional Dependence Exponent

Source: https://github.com/janditzen/xtdcce2/blob/master/README.md

Use xtcse2 to estimate the exponent of cross-sectional dependence for regression variables. This is typically run before the main xtdcce2 estimation.

```Stata
xtcse2 d.log_rgdpo L.log_rgdpo log_hc log_ck log_ngd.
```

--------------------------------

### Estimate Static Common Correlated Effects Model

Source: https://github.com/janditzen/xtdcce2/wiki/Home

Estimates a static common correlated effects model using all cross-sectional averages. The 'cr(_all)' option includes all independent and dependent variables as cross-sectional averages.

```stata
xtdcce2 d.log_rgdpo log_hc log_ck log_ngd , cr(_all) reportc.
```