Network Regressions in Stata with unbalanced panel data and time varying network structures or spatial weight matrices.

Table of Contents

1. Syntax
2. Description
3. Options
4. Postestimation (Predict, Direct, indirect and total effects)
5. Saved Values
6. Examples
7. References
8. How to install
9. Questions?
10. About

nwxtregress depvar  indepvars [if], 
        ivarlag(W1[, sparse timesparse mata id(string)])
        [mcmcoptions absorb(varlist, keepsingeltons) transform(transfrom_varlist, transform_options)]

nwxtregress depvar  indepvars [if], 
        ivarlag(W1[, sparse timesparse mata id(string)])
        dvarlag(Ws:varlist[, sparse timesparse mata id(string)]
        [mcmcoptions absorb(varlist, keepsingeltons) transform(transfrom_varlist, transform_options)]

Data has to be xtset before use. W1 and Ws define the spatial weight matrix, default is Sp object. dvarlag() and ivarlag() define the spatial lag of the dependent and independent variables. ivarlag() is repeatable and multiple spatial weight matrices are supported.

nwxtregress requires Stata 14.2 or higher. python and frame can only be used with Stata 16 or higher.

nwxtregress , [update version]

nwxtregress, version displays the current version. nwxtregress, update updates nwxtregress from GitHub.

nwxtregress estimates Spatial Autoregressive (SAR) or Spatial Durbin (SDM) models. The spatial weight matrices are allowed to be time varying and the dataset can be unbalanced.

The SAR is:

y = rho W1 y + beta X + eps

The SDM is:

Y = rho W1 Y + beta X + gamma W2 X + eps

where W1 and W2 are spatial weight matrices, Y the dependent and X the independent variables.

nwxtregress can handle spatial weights in three formats: 1. square matrix, 2. sparse and 3. time sparse. Sparse matrices have the advantage that they save space and thus computational time and allow for time varying weights. The Sp environment only supports the square matrix format. nwxtregress can read square, sparse and time sparse formats if the data for the weights is in mata or saved in a frame.{p_end}

The spatial weights are a matrix with dimension N_g x N_g. It is time constant. An Example with a 5 x 5 matrix is:

    0    0.1  0.2  0
    0    0    0.1  0.2
    0.3  0.1  0    0
    0.2  0    0.2  0

The sparse matrix format is a v x 3 matrix, where v is the number of non-zero elements in the spatial weight matrix. The weight matrix is time constant. The first column indicates the destination, the second the origin of the flow. A sparse matrix of the matrix from above is:

       Destination  Origin    Flow
       1            2         0.1
       1            3         0.2
       2            3         0.1
       2            4         0.2
       3            1         0.3
       3            2         0.1
       4            1         0.2
       4            3         0.2

The time sparse format can handle time varying spatial weights. The first column indicates the time period, the remaining are the same as for the sparse matrix. For example, if there are two time periods and we have the matrix from above for the first and the square for the second period:

       Time    Destination    Origin    Flow
       1       1              2         0.1
       1       1              3         0.2
       1       2              3         0.1
       1       2              4         0.2
       1       3              1         0.3
       1       3              2         0.1
       1       4              1         0.2
       1       4              3         0.2
          (next time period)
       2       1              2         0.1
       2       1              3         0.4
       2       2              3         0.1
       2       2              4         0.4
       2       3              1         0.9
       2       3              2         0.1
       2       4              1         0.4
       2       4              3         0.4

Internally, nextregress will always use the time sparse format. This ensures that unbalanced panels do not pose a problem. nextregress comes with functions for creating sparse matrices, coplying a sparse matrix into a squared format, and functions for mathematical operations (transpose and multiplication).

nwxtregress can remove high dimensional fixed effects using reghdfe. The fixed effects are partialled out before spatial lags are cacluated. Constant is automatically removed when cmd:absorb() is used. The syntax is:

asorb(varlist, keepsingeltons)

nwxtregress can demean and standardize dependent and independent variables, before or after the calculation of the spatial lags. Spatial lags can be transformed as well. The syntax is:

transform([varlist] [, by(varname)) after nomean nosd wy wx])

Direct, indirect and total effects. can be calculated using estat impact. The syntax is

 estat impact [varlist] [, options]

varlist defines the variables for which the direct, indirect and total effects are displayed. If not specified, then estat impact will calculate the effects for all explanatory variables (indepvars).

estat impact saves the following in r():

predict can be used after nwxtregress. The syntax for predict is:

predict [type] varname [, options]

nwxtregress saves the following in e()

In addition to e() and r() nwxtregress saves informations about the estimation in a mata array. The contents are the weight matrix in time sparse format, residuals and results from the MCMC. Storing those saves time for estat impact and predict. The name default name of the array is _NWXTREG_OBJECT#, but can be set with the option asarray(). In general it is not recommended to change this setting.

An example dataset with USE/MAKE table data from the BEA’s website and links between industries is available GitHub. The dataset IO.dta contains the linkages (spatial weights) and the dataset VA.dta the firm data. We want to estimate capital consumption by using compensation and net surplus as explanatory variables.

First we load the data from the W dataset and convert into a SP object for the year 1998.

use https://janditzen.github.io/nwxtregress/examples/IO.dta
keep if Year == 1998
replace sam = 0 if sam < 0
replace sam = 0 if ID1==ID2
keep ID1 ID2 sam
reshape wide sam, i(ID1) j(ID2)
spset ID1
spmatrix fromdata WSpmat = sam* , replace

Next, we load the dataset with the firm data and estimate a SAR with a time constant spatial weight matrix. We also obtain the total, direct and indirect effects using estat impact. For reproducibility we set a seed.

use https://janditzen.github.io/nwxtregress/examples/VA.dta
nwxtregress cap_cons compensation net_surplus , dvarlag(WSpmat) seed(1234)
estat impact

The disadvantage is that the spatial weight are constant across time and we had to get rid of all negative numbers. To allow for time varying spatial weights, we load the W dataset again and but load it into the frame IO:

frame create IO
frame IO: use https://janditzen.github.io/nwxtregress/examples/IO.dta

Using the VA dataset again, we can estimate the SAR model with time varying spatial weights. To do so we use the options frame(name), where name indicates the frame and the weight matrix name corresponds to the variable names. The data is in timesparse format so we need to use the option timesparse. Finally it is nessary to define the year identifier and the origin and destination of the flows using the id() option:

nwxtregress cap_cons compensation net_surplus ,
dvarlag(sam, frame(IO) id(Year ID1 ID2)  timesparse) 
seed(1234) 

Alternatively we can load the spatial weight matrix into mata:

frame IO: putmata Wt = (Year ID1 ID2 sam), replace
nwxtregress cap_cons compensation net_surplus , 
dvarlag(Wt, mata timesparse) seed(1234)

If we want to estimate an SDM by adding the option ivarlag():

nwxtregress cap_cons compensation net_surplus , 
dvarlag(Wt,mata timesparse) ivarlag(Wt: compensation,mata timesparse )  
seed(1234)

Use Python (requires Stata 16 or later) to improve speed of calculating the LUD:

nwxtregress cap_cons compensation net_surplus , dvarlag(Wt,mata timesparse) ivarlag(Wt: compensation,mata timesparse )  seed(1234) python

Transform data by demeaning and standardising it:

nwxtregress cap_cons compensation net_surplus , dvarlag(Wt,mata timesparse) ivarlag(Wt: compensation,mata timesparse )  seed(1234) transform(_all, by(ID)

or

nwxtregress cap_cons compensation net_surplus , dvarlag(Wt,mata timesparse) ivarlag(Wt: compensation,mata timesparse )  seed(1234) standardize

Partial out firm and year fixed effects (requires reghdfe):

nwxtregress cap_cons compensation net_surplus , dvarlag(Wt,mata timesparse) ivarlag(Wt: compensation,mata timesparse )  seed(1234) absorb(ID Year)

We can also define two different spatial weight matrices:

mata: Wt2 = Wt[selectindex(Wt[.,4]:>2601.996),.]
nwxtregress cap_cons compensation net_surplus , 
dvarlag(Wt, mata timesparse) 
ivarlag(Wt: net_surplus, mata timesparse) 
ivarlag(Wt2: compensation, mata timesparse) seed(1234)

Total, direct and indirect effects can be calculated using estat impact:

estat impact

To predict fitted values and residuals predict can be used:

predict xb
predict residuals, residual

Please cite as:

Ditzen, Grieser, Zekhnini. (2023). nwxtregress - network regression in Stata.

The latest version of the nwxtregress package can be obtained by typing in Stata:

net from https://janditzen.github.io/nwxtregress/

or

net install nwxtregress , from(https://janditzen.github.io/nwxtregress/)

Questions? Feel free to write us an email, open an issue or start a discussion.

Email: [email protected]

Web: www.jan.ditzen.net

Email: [email protected]

Web: https://www.williamgrieser.com/

Email: [email protected]

Web: https://sites.google.com/view/moradzekhnini/home

This version 0.3 as of 13.11.2023

Version 0.3

• support for reghdfe v. 6.12

Version 0.2

• bug when absorb() option used fixed
• bug when non sparse matrix used with estat fixed

Version 0.132

• bug when absorb() used fixed, sometimes variables were not updated correctly.

Version 0.131

• moved python code to nwxtregress.py
• added option impact

Version 0.13

• added options absorb() and transform()
• bugfixes when using fixed effects
• Python support for BarryPace trick

Version 0.12

• Support for Python to calculated LUD

Version 0.03 (alpha)

• Bugs in sparse matrix multiplication and return if non sparse matrix is used fixed.