xtbreak
estimating and testing for many known and unknown structural breaks in time series and panel data.
For an overview of xtbreak test see xtbreak test and for xtbreak estimate see xtbreak estimate.
Please cite as Ditzen, J., Karavias, Y. & Westerlund, J. (2021) Testing and Estimating Structural Breaks in Time Series and Panel Data in Stata. arXiv:2110.14550 [econ.EM]. A working paper describing xtbreak is available here.
Table of Contents
- Syntax
- Description
- Options
- Note on Panel Data
- Examples
- References
- How to install
- Citations
- Questions?
- About
- Changes
1. Syntax
Automatic estimation of number and location of break (sequential F-Test)
xtbreak depvar [indepvars] [if],
options1 options5
Testing for known structural breaks:
xtbreak test depvar [indepvars] [if],
breakpoints(numlist| datelist [,index| fmt(string)]) options1 options5
breakpoints() specifies the time period of the known structural break.
Testing for unknown structural breaks:
xtbreak test depvar [indepvars] [if],
hypothesis(1|2|3) breaks(#) options1 options2 options3 options4 options5
hypothesis(1\2\3) specifies which hypothesis to test, see hypothesises. breaks(#) sets the number of breaks.
Estimation of breakpoints
xtbreak estimate depvar [indepvars] [if], breaks(#) showindex options1 options2 options5
General Options
| options1 | Description |
|---|---|
| breakconstant | break in constant |
| noconstant | suppresses constant |
| nobreakvariables(varlist1) | variables with no structural break(s) |
| vce(type) | covariance matrix estimator, allowed: ssr, hac, np and nw |
Options for unknown breakdates
| options2 | Description |
|---|---|
| trimming(real) | minimal segment length |
Options for testing with unknown breakdates and hypothesis(2)
| options3 | Description |
|---|---|
| wdmax | Use weighted test statistic instead of unweighted |
| level(#) | set level for critical values |
Options for testing with unknown breakdates and hypothesis(3)
| options4 | Description |
|---|---|
| sequential | Sequential F-Test to obtain number of breaks |
Options for panel data
| options5 | Description |
|---|---|
| nofixedeffects | suppresses fixed effects (only for panel data sets) |
| breakfixedeffects | break in fixed effects |
| csd | add cross-section averages of variables with and without breaks. |
| csa(varlist) | Variables with breaks used to calculate cross-sectional averages |
| csanobreak(varlist) | Variables without breaks used to calculate cross-sectional averages |
| kfactors(varlist) | Known factors, which are constant across the cross-sectional dimension but are affected by structural breaks. Examples are seasonal dummies or other observed common factors such as asset returns and oil prices. |
| nbkfactors(varlist) | same as above but without breaks. |
Data has to be xtset before using xtbreak. depvars, indepvars and varlist1, varlist2 may contain time-series operators. Data has to be balanced.
2. Description
xtbreak test implements multiple tests for structural breaks in time series and panel data models. The number and period of occurence of structral breaks can be known and unknown. In the case of a known breakpoint xtbreak test can test if the break occurs at a specific point in time. For unknown breaks, xtbreak test implements three different hypothesises. The first is no break against the alterantive of s breaks, the second hypothesis is no breaks against a lower and upper limit of breaks. The last hypothesis tests the null of s breaks against the alterantive of one more break (s+1). For more details see xtbreak test.
xtbreak estimate estimates the break points, that is, it estimates T1, T2, ..., Ts. The underlying idea is that if the model with the true breakdates given a number of breaks has a smaller sum of squared residuals (SSR) than a model with incorrect breakdates. To find the breakdates, xtbreak estimate uses the alogorthim (dynamic program) from Bai and Perron (2003). All necessary SSRs are calculated and then the smalles one selected. For more details see xtbreak estimate.
xtbreak implements the tests for and estimation of structural breaks discussed in Bai & Perron (1998, 2003), Karavias, Narayan, Westerlund (2021) and Ditzen, Karavias, Westerlund (2021).
For the remainder we assume the following model:
y(i,t) = sigma0(1) + sigma1(1) z(i,t) + beta0(1,i) + beta1 x(i,t) + e(it) for t = 1,...,T1
y(i,t) = sigma0(2) + sigma1(2) z(i,t) + beta0(1,i) + beta1 x(i,t) + e(it) for t = T1+1,...,T2
...
y(i,t) = sigma0(s) + sigma1(s) z(i,t) + beta0(1,i) + beta1 x(i,t) + e(it) for t = Ts,...,T
where s is the number of the segment/breaks, z(i,t) is a NT1xq matrix containing the variables whose relationship with y breaks. A break in the constant is possible. x(i,t) is a NTxp matrix with variables without a break. sigma0(s), sigma1(s) are the coefficients with structural breaks and T1,...,Ts are the periods of the breakpoints.
In pure time series model breaks in the constant (or deterministics) are possible. In this case sigma0(s) is a constant with a structural break. Fixed effects in panel data models cannot have a break.
xtbreak will automatically determine whether a time series or panel dataset is used.
3. Options
Options
| Option | Description |
|---|---|
| breakpoints(numlist\datelist [,index\fmt(format)]) | specifies the known breakpoints. Known breakpoints can be set by either the number of observation or by the value of the time identifier. If a numlist is used, option index is required. For example breakpoints(10,index) specifies that the one break occurs at the 10th observation in time. datelist takes a list of dates. For example breakpoints(2010Q1) , fmt(tq) specifies a break in Quarter 1 in 2010. The option fmt() specifies the format and is required if a datelist is used. The format set in breakpoints() and the time identifier needs to be the same. |
| breaks(#) | specifies the number of unknwon breaks under the alternative. For hypothesis 2, breaks() can take two values, for example breaks(4 6) test for no breaks against 4-6 breaks. If only one value specfied, then the lower limit is set to 1. If h(3) and sequential is used, then breaks() defines the maximum number of breaks tested for. |
| showindex | show confidence intervals as index. |
| hypothesis(1\2\3) | specifies which hypothesis to test. h(1) test for no breaks vs. s breaks, h(2) for no break vs. s0 <= s <= s1 breaks and h(3) for s vs. s+1 breaks. Hypothesis 3 is the default. |
| sequential | sequential F-Test to determin number of breaks. The number of breaks is varied from s = 0 to breaks()-1 or floor(1/trimming). |
| breakconstant | break in constant. Default is no breaks in deterministics. |
| noconstant | suppresses constant. |
| nofixedeffects | suppresses individual fixed effects. |
| breakfixedeffects | break in fixed effects. |
| nobreakvariables(varlist1) | defines variables with no structural break(s). varlist1 can contain time series operators. |
| vce(type) | covariance matrix estimator, allowed: ssr, hac, hc and np. |
| trimming(real) | minimal segment length in percent. The minimal segment length is the minmal time periods between two breaks. The default is 15% (0.15). Critical values are available for %5, 10%, 15%, 20% and 25%. |
| error(real) | define error margin for partial break model. |
| wdmax | Use weighted test statistic instead of unweighted for the double maximum test (hypotheis 2). |
| level(#) | set level for critical values for weighted double maximum test. If a value is choosen for which no critical values exists, xtbreak test will choose the closest level. |
| csd | adds cross-section averages of variables with and without breaks. |
| csa(varlist) | specify the variables with and without breaks which are added as cross-sectional averages. xtbreak calculates internally the cross-sectional average. |
| csanobreak() | same as csa() but for variables without a break. |
| kfactors(varlist) | Known factors, which are constant across the cross-sectional dimension but are affected by structural breaks. Examples are seasonal dummies or other observed common factors such as asset returns and oil prices. |
| nbkfactors(varlist) | same as above but without breaks. |
4. Note on panel data
If a panel dataset is used, xtbreak differentiates between four models. The first model is a fixed effects model. A break in the fixed effects is not possible. The second and third models arewith a pooled constant (pooled OLS) with and without a break. The last model is a model with neither fixed effects nor a pooled constant.
The following table gives an overview:
| Model | Equation (xtbreak options) |
|---|---|
| Fixed Effects (nobreak) | y(i,t) = a(i) + b1 x(i,t) +s1(s) z(i,t,s) + e(it) |
| Fixed Effects(break) | y(i,t) = a(i,s) + b1 x(i,t) +s1(s) z(i,t,s) + e(it) (breakfixedeffects) |
| Pooled OLS (nobreak) | y(i,t) = b0 + b1 x(i,t) +s1(s) z(i,t,s) + e(it) (nofixedeffects) |
| Pooled OLS (break) | y(i,t) = b1 x(i,t) +s0(s) + s1(s) z(i,t,s) + e(it) (nofixedeffects breakconstant) |
| No FE or POLS | y(i,t) = b1 x(i,t) + s1(s) z(i,t,s) + e(it) (nofixedeffects noconstant) |
where b0 is the pooled constant without break, a(i) the fixed effects, b(1) a coefficient without break, s0(s) a pooled constant with break and s1(s) a coefficient with break.
In the estimation of the breakpoints, cross-sectional averages are not taken into account.
5. Examples
Time Series
This example was presented in similar form at the Stata Conference 2021. We will try to estimate the breakpoints in the relationship between COVID infections in the US and excess from the virus in 2020 and 2021. Weekly data is available on GitHub. The variable deaths has the deaths from COVID and the variable cases contains the number of new covid cases. The idea is that initally more people died from COVID because it was a new virus. Then medical treatment advanced and vaccines became more available which should decrease deaths. On the other hand COVID cases have likely been underreported during the first wave. We assume that there is a lag between the a positive test and death of one week. The data is from the CDC.
First we load the data into Stata:
use https://github.com/JanDitzen/xtbreak/raw/main/data/US.dta
We start with no prior knowledge of i) the number of breaks and ii) the exact date of each break. Therefore before estimating the breakpoints we use the sequential F-Test based on hypothesis 2:
xtbreak deaths L1.cases
Sequential test for multiple breaks at unknown breakpoints
(Ditzen, Karavias & Westerlund. 2021)
----------------- Bai & Perron Critical Values -----------------
Test 1% Critical 5% Critical 10% Critical
Statistic Value Value Value
--------------------------------------------------------------------------------
F(1|0) 107.50 12.29 8.58 7.04
F(2|1) 31.25 13.89 10.13 8.51
F(3|2) 6.96 14.80 11.14 9.41
F(4|3) 1.18 15.28 11.83 10.04
F(5|4) 4.95 15.76 12.25 10.58
--------------------------------------------------------------------------------
Detected number of breaks: 2 2 2
--------------------------------------------------------------------------------
Number indicate highest number of breaks the null hypothesis is rejected.
Estimation of break points
T = 82
SSR = 226.85
--------------------------------------------------------------------------------
# Index Date [95% Conf. Interval]
--------------------------------------------------------------------------------
1 16 2020w20 2020w19 2020w21
2 59 2021w11 2021w9 2021w13
--------------------------------------------------------------------------------
We find two breaks, the first in week 20 in 2020 and the second in week 11 in 2021.
Next we test the hypothesis of no breaks against 2 breaks using hypothesis 1:
xtbreak test deaths L1.cases, hypothesis(1) breaks(2)
Test for multiple breaks at unknown breakdates
(Bai & Perron. 1998. Econometrica)
H0: no break(s) vs. H1: 2 break(s)
----------------- Bai & Perron Critical Values -----------------
Test 1% Critical 5% Critical 10% Critical
Statistic Value Value Value
--------------------------------------------------------------------------------
supW(tau) 134.70 9.36 7.22 6.28
--------------------------------------------------------------------------------
Estimated break points: 2020w20 2021w11
Trimming: 0.15
The test statistic is the same, however the critical values are smaller placing a lower bound on the rejection of the hypothesis.
Since we have an estimate of the breakpoints, we can test the two breakpoints as known breakpoints:
xtbreak test deaths L1.cases, breakpoints(2020w20 2021w8 , fmt(tw))
Test for multiple breaks at known breakdates
(Bai & Perron. 1998. Econometrica)
H0: no breaks vs. H1: 2 break(s)
W(tau) = 116.95
p-value (F) = 0.00
Since we are using a datelist, we need to specify the format of it. datelist also has to be the same format as the time identifier.
We have established that we have found 2 breaks. We can test the hypothesis 3, i.e. 2 breaks against the alternative of 3 breaks:
xtbreak test deaths L1.cases, hypothesis(3) breaks(3)
Test for multiple breaks at unknown breakpoints
(Bai & Perron. 1998. Econometrica)
H0: 2 vs. H1: 3 break(s)
----------------- Bai & Perron Critical Values -----------------
Test 1% Critical 5% Critical 10% Critical
Statistic Value Value Value
--------------------------------------------------------------------------------
F(s+1|s)* 6.96 14.80 11.14 9.41
--------------------------------------------------------------------------------
* s = 2
Trimming: 0.15
First, note that we have to define in breaks() the alternative, that is we use breaks(3). Secondly we cannot reject the hypothesis of 2 breaks.
So far we have assumed no break in the constant, only in the number of COVID cases. We can test for only a break in the constant and keep the coefficient of the cases fixed. To do so, the options nobreakvar(L.cases) and breakconstant are required.
xtbreak test deaths , breakconstant nobreakvar(L1.cases) breaks(3) h(1)
THIS IS AN ALPHA VERSION!
PLEASE CHECK FOR UPDATES PRIOR PUBLISHING ANY RESULTS OBTAINED WITH THIS VERSION!
Test for multiple breaks at unknown breakdates
(Bai & Perron. 1998. Econometrica)
H0: no break(s) vs. H1: 3 break(s)
----------------- Bai & Perron Critical Values -----------------
Test 1% Critical 5% Critical 10% Critical
Statistic Value Value Value
--------------------------------------------------------------------------------
supW(tau) 20.00 7.60 5.96 5.21
--------------------------------------------------------------------------------
Estimated break points: 2020w21 2020w46 2021w8
Trimming: 0.15
After testing for breaks thoroughly we can estimate the breaks and construct confidence intervals:
xtbreak estimate deaths L1.cases, breaks(2)
Estimation of break points
T = 82
SSR = 226.85
----------------------------------------------------------------------
# Index Date [95% Conf. Interval]
----------------------------------------------------------------------
1 16 2020w20 15 17
2 59 2021w11 57 61
----------------------------------------------------------------------
If we want to see the index of the confidence interval rather than the date, the option {cmd:showindex} can be used:
Estimation of break points
T = 82
SSR = 226.85
----------------------------------------------------------------------
# Index Date [95% Conf. Interval]
----------------------------------------------------------------------
1 16 2020w20 15 17
2 59 2021w11 57 61
----------------------------------------------------------------------
We can split the variable L1.cases into the different values for each regime using estat split. The variable list is saved in r(varlist) and we run a simple OLS regression on it:
. estat split
New variables created: L_cases1 L_cases2 L_cases3
. reg deaths `r(varlist)'
Source | SS df MS Number of obs = 82
-------------+---------------------------------- F(3, 78) = 338.24
Model | 2951.18975 3 983.729918 Prob > F = 0.0000
Residual | 226.851495 78 2.9083525 R-squared = 0.9286
-------------+---------------------------------- Adj R-squared = 0.9259
Total | 3178.04125 81 39.2350771 Root MSE = 1.7054
------------------------------------------------------------------------------
deaths | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
L_cases1 | .0589407 .0036153 16.30 0.000 .0517433 .0661381
L_cases2 | .0136155 .00045 30.26 0.000 .0127196 .0145114
L_cases3 | .0064061 .0009669 6.63 0.000 .0044812 .0083311
_cons | 1.304738 .3097613 4.21 0.000 .688051 1.921426
------------------------------------------------------------------------------
Finally, we can draw a scatter plot of the variables with a different colour for each segement. The command line is estat scatter varlist where varlist is the independent variable (X), the dependent variable is automatically added on the y-axis.
xtbreak estimate deaths L1.cases, breaks(2) showindex
estat scatter L.cases
With a bit more of codeing, see example.do, we can create a plot with confidence intervals:
Panel Exampels
We are using a dataset with the same variables as above, but on US State level. First we load the dataset:
use https://github.com/JanDitzen/xtbreak/raw/main/data/US_panel.dta
As before, we start with the sequential F-Test and the estimation of the break dates. We account for heteroskedasticity and autocorrelation by using an HAC robust variance estimator with the option vce(hac). Otherwise the syntax remains the same. xtbreak automatically detects if a panel or time series is used.
xtbreak deaths L.cases, vce(hac)
Sequential test for multiple breaks at unknown breakpoints
(Ditzen, Karavias & Westerlund. 2021)
----------------- Bai & Perron Critical Values -----------------
Test 1% Critical 5% Critical 10% Critical
Statistic Value Value Value
--------------------------------------------------------------------------------
F(1|0) 29.59 12.29 8.58 7.04
F(2|1) 37.75 13.89 10.13 8.51
F(3|2) 10.88 14.80 11.14 9.41
F(4|3) 21.38 15.28 11.83 10.04
F(5|4) 8.29 15.76 12.25 10.58
--------------------------------------------------------------------------------
Detected number of breaks: 4 4 4
--------------------------------------------------------------------------------
The detected number of breaks indicates the highest number of
breaks for which the null hypothesis is rejected.
Estimation of break points
N = 60
T = 82
SSR = 37.78
Trimming = 0.15
--------------------------------------------------------------------------------
# Index Date [95% Conf. Interval]
--------------------------------------------------------------------------------
1 15 2020w19 2020w18 2020w20
2 34 2020w38 2020w37 2020w39
3 47 2020w51 2020w50 2020w52
4 59 2021w11 2021w10 2021w12
--------------------------------------------------------------------------------
We find evidence for 2 and 4 breaks. As this is a panel data set, we account for cross-section dependence as well using csa(L.cases) and we set the minimal length to 10% with minlength(0.1):
. xtbreak deaths L.cases, vce(hac) csa(L.cases) trimming(0.1)
Sequential test for multiple breaks at unknown breakpoints
(Ditzen, Karavias & Westerlund. 2021)
----------------- Bai & Perron Critical Values -----------------
Test 1% Critical 5% Critical 10% Critical
Statistic Value Value Value
--------------------------------------------------------------------------------
F(1|0) 10.80 13.00 9.10 7.42
F(2|1) 8.10 14.51 10.55 9.05
F(3|2) 12.77 15.44 11.36 9.97
F(4|3) 4.47 15.73 12.35 10.49
F(5|4) 9.27 16.39 12.97 10.91
F(6|5) 5.22 16.60 13.45 11.29
F(7|6) 5.05 16.78 13.88 11.86
F(8|7) 5.61 16.90 14.12 12.26
F(9|8) 4.89 16.99 14.45 12.57
--------------------------------------------------------------------------------
Detected number of breaks: . 3 3
--------------------------------------------------------------------------------
The detected number of breaks indicates the highest number of
breaks for which the null hypothesis is rejected.
Estimation of break points
N = 60
T = 82
SSR = 25.99
Trimming = 0.10
--------------------------------------------------------------------------------
# Index Date [95% Conf. Interval]
--------------------------------------------------------------------------------
1 15 2020w19 2020w18 2020w20
2 47 2020w51 2020w50 2020w52
3 57 2021w9 2021w8 2021w10
--------------------------------------------------------------------------------
Cross-section averages:
with breaks: L.cases
Using this we observe that the values of the test stastic across all F-Statistics are relatively low. We are never able to reject the hypothesis of no break at a level of 1%. Using a level of 5%, we are able to reject F(1|0) and F(3|2), which implies either no break or 2 breaks. We will investigate this next.
We test the null of no breaks against up to 5 breaks and abbreviate hypothesis with h:
xtbreak test deaths L.cases, h(2) breaks(5) trim(0.1) vce(hac) csa(L.cases)
T
Test for multiple breaks at unknown breakdates
(Ditzen, Karavias & Westerlund. 2021)
H0: no break(s) vs. H1: 1 <= s <= 5 break(s)
----------------- Bai & Perron Critical Values -----------------
Test 1% Critical 5% Critical 10% Critical
Statistic Value Value Value
--------------------------------------------------------------------------------
UDmax(tau) 12.20 13.07 9.52 8.05
--------------------------------------------------------------------------------
* evaluated at a level of 0.95.
Trimming: 0.10
Cross-section averages:
with breaks: L.cases
We find evidence for breaks, thus we are going to test the alternatives of one and three breaks:
xtbreak test deaths L.cases, h(1) breaks(1) trim(0.1) vce(hac) csa(L.cases)
Test for multiple breaks at known breakdates
(Karavias, Narayan & Westerlund. 2021)
H0: no break(s) vs. H1: 1 break(s)
----------------- Bai & Perron Critical Values -----------------
Test 1% Critical 5% Critical 10% Critical
Statistic Value Value Value
--------------------------------------------------------------------------------
supW(tau) 10.80 13.00 9.10 7.42
--------------------------------------------------------------------------------
Estimated break points: 2020w19
Trimming: 0.10
Cross-section averages:
with breaks: L.cases
and
xtbreak test deaths L.cases, h(1) breaks(3) trim(0.1) vce(hac) csa(L.cases)
Test for multiple breaks at unknown breakdates
(Ditzen, Karavias & Westerlund. 2021)
H0: no break(s) vs. H1: 3 break(s)
----------------- Bai & Perron Critical Values -----------------
Test 1% Critical 5% Critical 10% Critical
Statistic Value Value Value
--------------------------------------------------------------------------------
supW(tau) 12.20 8.42 6.84 6.09
--------------------------------------------------------------------------------
Estimated break points: 2020w19 2020w51 2021w9
Trimming: 0.10
Cross-section averages:
with breaks: L.cases
Given that we are just about to reject the null hypothesis in the case of 1 break, we will assume 3 breaks. Next we are going to estimate the break points and run a fixed effects regression:
. xtbreak estimate deaths L.cases, breaks(3) trim(0.1) vce(hac) csa(L.cases)
Estimation of break points
N = 60
T = 82
SSR = 25.99
Trimming = 0.10
--------------------------------------------------------------------------------
# Index Date [95% Conf. Interval]
--------------------------------------------------------------------------------
1 15 2020w19 2020w18 2020w20
2 47 2020w51 2020w50 2020w52
3 57 2021w9 2021w8 2021w10
--------------------------------------------------------------------------------
Cross-section averages:
with breaks: L.cases
estat split L.cases
New variables created: L_cases1 L_cases2 L_cases3 L_cases4
xtreg deaths `r(varlist)', fe
Fixed-effects (within) regression Number of obs = 4,920
Group variable: ID Number of groups = 60
R-squared: Obs per group:
Within = 0.8144 min = 82
Between = 0.9721 avg = 82.0
Overall = 0.8565 max = 82
F(4,4856) = 5325.62
corr(u_i, Xb) = 0.3305 Prob > F = 0.0000
------------------------------------------------------------------------------
deaths | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
L_cases1 | .0745328 .0008793 84.76 0.000 .072809 .0762566
L_cases2 | .0123852 .0001553 79.77 0.000 .0120808 .0126895
L_cases3 | .0157277 .000136 115.67 0.000 .0154611 .0159942
L_cases4 | .0077951 .0002327 33.50 0.000 .0073389 .0082512
_cons | .0172031 .0018211 9.45 0.000 .0136328 .0207734
-------------+----------------------------------------------------------------
sigma_u | .03534295
sigma_e | .10880368
rho | .09544505 (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(59, 4856) = 7.29 Prob > F = 0.0000
6. References
Andrews, D. W. K. (1993). Tests for Parameter Instability and Structural Change With Unknown Change Point. Econometrica, 61(4), 821–856. link.
Bai, B. Y. J., & Perron, P. (1998). Estimating and Testing Linear Models with Multiple Structural Changes. Econometrica, 66(1), 47–78. link.
Bai, J., & Perron, P. (2003). Computation and analysis of multiple structural change models. Journal of Applied Econometrics, 18(1), 1–22. link.
Ditzen, J., Karavias, Y. & Westerlund, J. (2021) Testing for Multiple Structural Breaks in Panel Data. Available upon request.
Ditzen, J., Karavias, Y. & Westerlund, J. (2021) Testing and Estimating Structural Breaks in Time Series and Panel Data in Stata. arXiv:2110.14550 [econ.EM]. link.
Karavias, Y, Narayan P. & Westerlund, J. (2021) Structural breaks in Interactive Effects Panels and the Stock Market Reaction to COVID–19. Available upon request.
Slides
- Slides 2020 Swiss Stata User Group Meeting
- Slides 2021 German Stata User Group Meeting
- Slides 2021 US Stata Conference
7. How to install
The latest version of the xtbreak package can be obtained by typing in Stata:
net from https://janditzen.github.io/xtbreak/
xtbreak requires Stata 15 or newer.
8. Citations
xtbreak has been used in:
-
Regulator, E., Fallon, J., Cunningham, M. and da Silva Rosa, R., 2021. Methodological issues in estimating the equity beta for Australian network energy businesses. Link
-
Gabriel Chodorow-Reich, Adam M. Guren, and Timothy J. McQuade, 2021. "The 2000s Housing Cycle With 2020 Hindsight: A Neo-Kindlebergerian View". NBER Working Paper No. 29140. Link
9. Questions?
Questions? Feel free to write us an email, open an issue or start a discussion.
10. Authors
Jan Ditzen (Free University of Bozen-Bolzano)
Email: [email protected]
Web: www.jan.ditzen.net
Yiannis Karavias (University of Birmingham)
Email: [email protected]
Web: https://sites.google.com/site/yianniskaravias/
Joakim Westerlund (Lund University)
Email: [email protected]
Web: https://sites.google.com/site/perjoakimwesterlund/
Please cite as follows:
Ditzen, J., Karavias, Y. & Westerlund, J. (2021) Testing and Estimating Structural Breaks in Time Series and Panel Data in Stata. arXiv:2110.14550 [econ.EM].
11. Changes
This version 1.0 - 23.10.2021
Changes 0.02 to 1.0:
- fixed error in wdmax test. Used wrong critical values.
- added sequential F-Test and general xtbreak y x syntax.
- bug fixes in var/cov estimators.
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