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"""
Utility functions for difference-in-differences estimation.
"""
import
warnings
from
dataclasses
import
dataclass
,
field
from
typing
import
Any
,
Dict
,
List
,
Optional
,
Tuple
import
numpy
as
np
import
pandas
as
pd
from
scipy
import
stats
from
diff_diff
.
linalg
import
compute_robust_vcov
as
_compute_robust_vcov_linalg
from
diff_diff
.
linalg
import
solve_ols
as
_solve_ols_linalg
# Import Rust backend if available (from _backend to avoid circular imports)
from
diff_diff
.
_backend
import
(
HAS_RUST_BACKEND
,
_rust_project_simplex
,
_rust_sdid_unit_weights
,
_rust_compute_time_weights
,
_rust_compute_noise_level
,
_rust_sc_weight_fw
,
_rust_sc_weight_fw_with_convergence
,
_rust_sc_weight_fw_weighted
,
_rust_sc_weight_fw_weighted_with_convergence
,
)
# Numerical constants for optimization algorithms
_OPTIMIZATION_MAX_ITER
=
1000
# Maximum iterations for weight optimization
_OPTIMIZATION_TOL
=
1e-8
# Convergence tolerance for optimization
_NUMERICAL_EPS
=
1e-10
# Small constant to prevent division by zero
# Cache for critical values to avoid repeated scipy calls
_critical_value_cache
:
Dict
[
Tuple
[
float
,
Optional
[
int
]],
float
]
=
{}
def
_get_critical_value
(
alpha
:
float
,
df
:
Optional
[
int
]
=
None
)
->
float
:
"""Return cached critical value for (alpha, df) pair."""
key
=
(
alpha
,
df
)
if
key
not
in
_critical_value_cache
:
if
df
is
not
None
:
_critical_value_cache
[
key
]
=
float
(
stats
.
t
.
ppf
(
1
-
alpha
/
2
,
df
))
else
:
_critical_value_cache
[
key
]
=
float
(
stats
.
norm
.
ppf
(
1
-
alpha
/
2
))
return
_critical_value_cache
[
key
]
def
validate_binary
(
arr
:
np
.
ndarray
,
name
:
str
)
->
None
:
"""
Validate that an array contains only binary values (0 or 1).
Parameters
----------
arr : np.ndarray
Array to validate.
name : str
Name of the variable (for error messages).
Raises
------
ValueError
If array contains non-binary values.
"""
unique_values
=
np
.
unique
(
arr
[
~
np
.
isnan
(
arr
)])
if
not
np
.
all
(
np
.
isin
(
unique_values
, [
0
,
1
])):
raise
ValueError
(
f"
{
name
}
must be binary (0 or 1). "
f"Found values:
{
unique_values
}
"
)
def
warn_if_not_converged
(
converged
:
bool
,
method_name
:
str
,
max_iter
:
int
,
tol
:
Optional
[
float
]
=
None
,
stacklevel
:
int
=
3
,
)
->
None
:
"""Emit a UserWarning when an iterative solver exhausts max_iter without converging.
Shared helper for axis-B silent-failure fixes (iterative loops that otherwise
return the current iterate without signaling non-convergence).
"""
if
converged
:
return
tol_suffix
=
f" (tol=
{
tol
}
)"
if
tol
is
not
None
else
""
warnings
.
warn
(
f"
{
method_name
}
did not converge in
{
max_iter
}
iterations
{
tol_suffix
}
. "
"Results may be inaccurate."
,
UserWarning
,
stacklevel
=
stacklevel
,
)
def
compute_robust_se
(
X
:
np
.
ndarray
,
residuals
:
np
.
ndarray
,
cluster_ids
:
Optional
[
np
.
ndarray
]
=
None
)
->
np
.
ndarray
:
"""
Compute heteroskedasticity-robust (HC1) or cluster-robust standard errors.
This function is a thin wrapper around the optimized implementation in
diff_diff.linalg for backwards compatibility.
Parameters
----------
X : np.ndarray
Design matrix of shape (n, k).
residuals : np.ndarray
Residuals from regression of shape (n,).
cluster_ids : np.ndarray, optional
Cluster identifiers for cluster-robust SEs.
Returns
-------
np.ndarray
Variance-covariance matrix of shape (k, k).
"""
return
_compute_robust_vcov_linalg
(
X
,
residuals
,
cluster_ids
)
def
compute_confidence_interval
(
estimate
:
float
,
se
:
float
,
alpha
:
float
=
0.05
,
df
:
Optional
[
int
]
=
None
)
->
Tuple
[
float
,
float
]:
"""
Compute confidence interval for an estimate.
Parameters
----------
estimate : float
Point estimate.
se : float
Standard error.
alpha : float
Significance level (default 0.05 for 95% CI).
df : int, optional
Degrees of freedom. If None, uses normal distribution.
Returns
-------
tuple
(lower_bound, upper_bound) of confidence interval.
"""
critical_value
=
_get_critical_value
(
alpha
,
df
)
lower
=
estimate
-
critical_value
*
se
upper
=
estimate
+
critical_value
*
se
return
(
lower
,
upper
)
def
compute_p_value
(
t_stat
:
float
,
df
:
Optional
[
int
]
=
None
,
two_sided
:
bool
=
True
)
->
float
:
"""
Compute p-value for a t-statistic.
Parameters
----------
t_stat : float
T-statistic.
df : int, optional
Degrees of freedom. If None, uses normal distribution.
two_sided : bool
Whether to compute two-sided p-value (default True).
Returns
-------
float
P-value.
"""
if
df
is
not
None
:
p_value
=
stats
.
t
.
sf
(
np
.
abs
(
t_stat
),
df
)
else
:
p_value
=
stats
.
norm
.
sf
(
np
.
abs
(
t_stat
))
if
two_sided
:
p_value
*=
2
return
float
(
p_value
)
def
safe_inference
(
effect
,
se
,
alpha
=
0.05
,
df
=
None
):
"""Compute t_stat, p_value, conf_int with NaN-safe gating.
When SE is non-finite, zero, or negative, ALL inference fields
are set to NaN to prevent misleading statistical output.
Accepts scalar inputs only (not numpy arrays). All existing inference
call sites operate on scalars within loops.
Parameters
----------
effect : float
Point estimate (treatment effect or coefficient).
se : float
Standard error of the estimate.
alpha : float, optional
Significance level for confidence interval (default 0.05).
df : int, optional
Degrees of freedom. If None, uses normal distribution.
Returns
-------
tuple
(t_stat, p_value, (ci_lower, ci_upper)). All NaN when SE is
non-finite, zero, or negative.
"""
if
not
(
np
.
isfinite
(
se
)
and
se
>
0
):
return
np
.
nan
,
np
.
nan
, (
np
.
nan
,
np
.
nan
)
if
df
is
not
None
and
df
<=
0
:
# Undefined degrees of freedom (e.g., rank-deficient replicate design)
return
np
.
nan
,
np
.
nan
, (
np
.
nan
,
np
.
nan
)
t_stat
=
effect
/
se
p_value
=
compute_p_value
(
t_stat
,
df
=
df
)
conf_int
=
compute_confidence_interval
(
effect
,
se
,
alpha
,
df
=
df
)
return
t_stat
,
p_value
,
conf_int
def
safe_inference_batch
(
effects
,
ses
,
alpha
=
0.05
,
df
=
None
):
"""Vectorized batch inference for arrays of effects and SEs.
Parameters
----------
effects : np.ndarray
Array of point estimates.
ses : np.ndarray
Array of standard errors.
alpha : float, optional
Significance level (default 0.05).
df : int, optional
Degrees of freedom. If None, uses normal distribution.
Returns
-------
t_stats : np.ndarray
p_values : np.ndarray
ci_lowers : np.ndarray
ci_uppers : np.ndarray
"""
effects
=
np
.
asarray
(
effects
,
dtype
=
float
)
ses
=
np
.
asarray
(
ses
,
dtype
=
float
)
n
=
len
(
effects
)
t_stats
=
np
.
full
(
n
,
np
.
nan
)
p_values
=
np
.
full
(
n
,
np
.
nan
)
ci_lowers
=
np
.
full
(
n
,
np
.
nan
)
ci_uppers
=
np
.
full
(
n
,
np
.
nan
)
# Undefined df (e.g., rank-deficient replicate design) → all NaN
if
df
is
not
None
and
df
<=
0
:
return
t_stats
,
p_values
,
ci_lowers
,
ci_uppers
valid
=
np
.
isfinite
(
ses
)
&
(
ses
>
0
)
if
not
np
.
any
(
valid
):
return
t_stats
,
p_values
,
ci_lowers
,
ci_uppers
t_stats
[
valid
]
=
effects
[
valid
]
/
ses
[
valid
]
if
df
is
not
None
:
p_values
[
valid
]
=
2.0
*
stats
.
t
.
sf
(
np
.
abs
(
t_stats
[
valid
]),
df
)
else
:
p_values
[
valid
]
=
2.0
*
stats
.
norm
.
sf
(
np
.
abs
(
t_stats
[
valid
]))
crit
=
_get_critical_value
(
alpha
,
df
)
ci_lowers
[
valid
]
=
effects
[
valid
]
-
crit
*
ses
[
valid
]
ci_uppers
[
valid
]
=
effects
[
valid
]
+
crit
*
ses
[
valid
]
return
t_stats
,
p_values
,
ci_lowers
,
ci_uppers
# =============================================================================
# Wild Cluster Bootstrap
# =============================================================================
@
dataclass
class
WildBootstrapResults
:
"""
Results from wild cluster bootstrap inference.
Attributes
----------
se : float
Bootstrap standard error of the coefficient.
p_value : float
Bootstrap p-value (two-sided).
t_stat_original : float
Original t-statistic from the data.
ci_lower : float
Lower bound of the confidence interval.
ci_upper : float
Upper bound of the confidence interval.
n_clusters : int
Number of clusters in the data.
n_bootstrap : int
Number of bootstrap replications.
weight_type : str
Type of bootstrap weights used ("rademacher", "webb", or "mammen").
alpha : float
Significance level used for confidence interval.
bootstrap_distribution : np.ndarray, optional
Full bootstrap distribution of coefficients (if requested).
References
----------
Cameron, A. C., Gelbach, J. B., & Miller, D. L. (2008).
Bootstrap-Based Improvements for Inference with Clustered Errors.
The Review of Economics and Statistics, 90(3), 414-427.
"""
se
:
float
p_value
:
float
t_stat_original
:
float
ci_lower
:
float
ci_upper
:
float
n_clusters
:
int
n_bootstrap
:
int
weight_type
:
str
alpha
:
float
=
0.05
bootstrap_distribution
:
Optional
[
np
.
ndarray
]
=
field
(
default
=
None
,
repr
=
False
)
def
summary
(
self
)
->
str
:
"""Generate formatted summary of bootstrap results."""
lines
=
[
"Wild Cluster Bootstrap Results"
,
"="
*
40
,
f"Bootstrap SE:
{
self
.
se
:.6f
}
"
,
f"Bootstrap p-value:
{
self
.
p_value
:.4f
}
"
,
f"Original t-stat:
{
self
.
t_stat_original
:.4f
}
"
,
f"CI (
{
int
((
1
-
self
.
alpha
)
*
100
)
}
%): [
{
self
.
ci_lower
:.6f
}
,
{
self
.
ci_upper
:.6f
}
]"
,
f"Number of clusters:
{
self
.
n_clusters
}
"
,
f"Bootstrap reps:
{
self
.
n_bootstrap
}
"
,
f"Weight type:
{
self
.
weight_type
}
"
,
]
return
"
\n
"
.
join
(
lines
)
def
print_summary
(
self
)
->
None
:
"""Print formatted summary to stdout."""
print
(
self
.
summary
())
def
_generate_rademacher_weights
(
n_clusters
:
int
,
rng
:
np
.
random
.
Generator
)
->
np
.
ndarray
:
"""
Generate Rademacher weights: +1 or -1 with probability 0.5.
Parameters
----------
n_clusters : int
Number of clusters.
rng : np.random.Generator
Random number generator.
Returns
-------
np.ndarray
Array of Rademacher weights.
"""
return
np
.
asarray
(
rng
.
choice
([
-
1.0
,
1.0
],
size
=
n_clusters
))
def
_generate_webb_weights
(
n_clusters
:
int
,
rng
:
np
.
random
.
Generator
)
->
np
.
ndarray
:
"""
Generate Webb's 6-point distribution weights.
Values: {-sqrt(3/2), -sqrt(2/2), -sqrt(1/2), sqrt(1/2), sqrt(2/2), sqrt(3/2)}
with equal probabilities (1/6 each), giving E[w]=0 and Var(w)=1.0.
This distribution is recommended for very few clusters (G < 10) as it
provides better finite-sample properties than Rademacher weights.
Parameters
----------
n_clusters : int
Number of clusters.
rng : np.random.Generator
Random number generator.
Returns
-------
np.ndarray
Array of Webb weights.
References
----------
Webb, M. D. (2014). Reworking wild bootstrap based inference for
clustered errors. Queen's Economics Department Working Paper No. 1315.
Note: Uses equal probabilities (1/6 each) matching R's `did` package,
which gives unit variance for consistency with other weight distributions.
"""
values
=
np
.
array
(
[
-
np
.
sqrt
(
3
/
2
),
-
np
.
sqrt
(
2
/
2
),
-
np
.
sqrt
(
1
/
2
),
np
.
sqrt
(
1
/
2
),
np
.
sqrt
(
2
/
2
),
np
.
sqrt
(
3
/
2
),
]
)
# Equal probabilities (1/6 each) matching R's did package, giving Var(w) = 1.0
return
np
.
asarray
(
rng
.
choice
(
values
,
size
=
n_clusters
))
def
_generate_mammen_weights
(
n_clusters
:
int
,
rng
:
np
.
random
.
Generator
)
->
np
.
ndarray
:
"""
Generate Mammen's two-point distribution weights.
Values: {-(sqrt(5)-1)/2, (sqrt(5)+1)/2}
with probabilities {(sqrt(5)+1)/(2*sqrt(5)), (sqrt(5)-1)/(2*sqrt(5))}.
This distribution satisfies E[v]=0, E[v^2]=1, E[v^3]=1, which provides
asymptotic refinement for skewed error distributions.
Parameters
----------
n_clusters : int
Number of clusters.
rng : np.random.Generator
Random number generator.
Returns
-------
np.ndarray
Array of Mammen weights.
References
----------
Mammen, E. (1993). Bootstrap and Wild Bootstrap for High Dimensional
Linear Models. The Annals of Statistics, 21(1), 255-285.
"""
sqrt5
=
np
.
sqrt
(
5
)
# Values from Mammen (1993)
val1
=
-
(
sqrt5
-
1
)
/
2
# approximately -0.618
val2
=
(
sqrt5
+
1
)
/
2
# approximately 1.618 (golden ratio)
# Probability of val1
p1
=
(
sqrt5
+
1
)
/
(
2
*
sqrt5
)
# approximately 0.724
return
np
.
asarray
(
rng
.
choice
([
val1
,
val2
],
size
=
n_clusters
,
p
=
[
p1
,
1
-
p1
]))
def
wild_bootstrap_se
(
X
:
np
.
ndarray
,
y
:
np
.
ndarray
,
residuals
:
np
.
ndarray
,
cluster_ids
:
np
.
ndarray
,
coefficient_index
:
int
,
n_bootstrap
:
int
=
999
,
weight_type
:
str
=
"rademacher"
,
null_hypothesis
:
float
=
0.0
,
alpha
:
float
=
0.05
,
seed
:
Optional
[
int
]
=
None
,
return_distribution
:
bool
=
False
,
)
->
WildBootstrapResults
:
"""
Compute wild cluster bootstrap standard errors and p-values.
Implements the Wild Cluster Residual (WCR) bootstrap procedure from
Cameron, Gelbach, and Miller (2008). Uses the restricted residuals
approach (imposing H0: coefficient = null_hypothesis) for more accurate
p-value computation.
Parameters
----------
X : np.ndarray
Design matrix of shape (n, k).
y : np.ndarray
Outcome vector of shape (n,).
residuals : np.ndarray
OLS residuals from unrestricted regression, shape (n,).
cluster_ids : np.ndarray
Cluster identifiers of shape (n,).
coefficient_index : int
Index of the coefficient for which to compute bootstrap inference.
For DiD, this is typically 3 (the treatment*post interaction term).
n_bootstrap : int, default=999
Number of bootstrap replications. Odd numbers are recommended for
exact p-value computation.
weight_type : str, default="rademacher"
Type of bootstrap weights:
- "rademacher": +1 or -1 with equal probability (standard choice)
- "webb": 6-point distribution (recommended for <10 clusters)
- "mammen": Two-point distribution with skewness correction
null_hypothesis : float, default=0.0
Value of the null hypothesis for p-value computation.
alpha : float, default=0.05
Significance level for confidence interval.
seed : int, optional
Random seed for reproducibility. If None (default), results
will vary between runs.
return_distribution : bool, default=False
If True, include full bootstrap distribution in results.
Returns
-------
WildBootstrapResults
Dataclass containing bootstrap SE, p-value, confidence interval,
and other inference results.
Raises
------
ValueError
If weight_type is not recognized or if there are fewer than 2 clusters.
Warns
-----
UserWarning
If the number of clusters is less than 5, as bootstrap inference
may be unreliable.
Examples
--------
>>> from diff_diff.utils import wild_bootstrap_se
>>> results = wild_bootstrap_se(
... X, y, residuals, cluster_ids,
... coefficient_index=3, # ATT coefficient
... n_bootstrap=999,
... weight_type="rademacher",
... seed=42
... )
>>> print(f"Bootstrap SE: {results.se:.4f}")
>>> print(f"Bootstrap p-value: {results.p_value:.4f}")
References
----------
Cameron, A. C., Gelbach, J. B., & Miller, D. L. (2008).
Bootstrap-Based Improvements for Inference with Clustered Errors.
The Review of Economics and Statistics, 90(3), 414-427.
MacKinnon, J. G., & Webb, M. D. (2018). The wild bootstrap for
few (treated) clusters. The Econometrics Journal, 21(2), 114-135.
"""
# Validate inputs
valid_weight_types
=
[
"rademacher"
,
"webb"
,
"mammen"
]
if
weight_type
not
in
valid_weight_types
:
raise
ValueError
(
f"weight_type must be one of
{
valid_weight_types
}
, got '
{
weight_type
}
'"
)
unique_clusters
=
np
.
unique
(
cluster_ids
)
n_clusters
=
len
(
unique_clusters
)
if
n_clusters
<
2
:
raise
ValueError
(
f"Wild cluster bootstrap requires at least 2 clusters, got
{
n_clusters
}
"
)
if
n_clusters
<
5
:
warnings
.
warn
(
f"Only
{
n_clusters
}
clusters detected. Wild bootstrap inference may be "
"unreliable with fewer than 5 clusters. Consider using Webb weights "
"(weight_type='webb') for improved finite-sample properties."
,
UserWarning
,
)
# Initialize RNG
rng
=
np
.
random
.
default_rng
(
seed
)
# Select weight generator
weight_generators
=
{
"rademacher"
:
_generate_rademacher_weights
,
"webb"
:
_generate_webb_weights
,
"mammen"
:
_generate_mammen_weights
,
}
generate_weights
=
weight_generators
[
weight_type
]
n
=
X
.
shape
[
0
]
# Step 1: Compute original coefficient and cluster-robust SE
beta_hat
,
_
,
vcov_original
=
_solve_ols_linalg
(
X
,
y
,
cluster_ids
=
cluster_ids
,
return_vcov
=
True
)
original_coef
=
beta_hat
[
coefficient_index
]
assert
vcov_original
is
not
None
se_original
=
np
.
sqrt
(
vcov_original
[
coefficient_index
,
coefficient_index
])
t_stat_original
=
(
original_coef
-
null_hypothesis
)
/
se_original
# Step 2: Impose null hypothesis (restricted estimation)
# Create restricted y: y_restricted = y - X[:, coef_index] * null_hypothesis
# This imposes the null that the coefficient equals null_hypothesis
y_restricted
=
y
-
X
[:,
coefficient_index
]
*
null_hypothesis
# Fit restricted model (but we need to drop the column for the restricted coef)
# Actually, for WCR bootstrap we keep all columns but impose the null via residuals
# Re-estimate with the restricted dependent variable
beta_restricted
,
residuals_restricted
,
_
=
_solve_ols_linalg
(
X
,
y_restricted
,
return_vcov
=
False
)
# Create cluster-to-observation mapping for efficiency
cluster_map
=
{
c
:
np
.
where
(
cluster_ids
==
c
)[
0
]
for
c
in
unique_clusters
}
cluster_indices
=
[
cluster_map
[
c
]
for
c
in
unique_clusters
]
# Step 3: Bootstrap loop
bootstrap_t_stats
=
np
.
zeros
(
n_bootstrap
)
bootstrap_coefs
=
np
.
zeros
(
n_bootstrap
)
for
b
in
range
(
n_bootstrap
):
# Generate cluster-level weights
cluster_weights
=
generate_weights
(
n_clusters
,
rng
)
# Map cluster weights to observations
obs_weights
=
np
.
zeros
(
n
)
for
g
,
indices
in
enumerate
(
cluster_indices
):
obs_weights
[
indices
]
=
cluster_weights
[
g
]
# Construct bootstrap sample: y* = X @ beta_restricted + e_restricted * weights
y_star
=
np
.
dot
(
X
,
beta_restricted
)
+
residuals_restricted
*
obs_weights
# Estimate bootstrap coefficients with cluster-robust SE
beta_star
,
residuals_star
,
vcov_star
=
_solve_ols_linalg
(
X
,
y_star
,
cluster_ids
=
cluster_ids
,
return_vcov
=
True
)
bootstrap_coefs
[
b
]
=
beta_star
[
coefficient_index
]
assert
vcov_star
is
not
None
se_star
=
np
.
sqrt
(
vcov_star
[
coefficient_index
,
coefficient_index
])
# Compute bootstrap t-statistic (under null hypothesis)
if
se_star
>
0
:
bootstrap_t_stats
[
b
]
=
(
beta_star
[
coefficient_index
]
-
null_hypothesis
)
/
se_star
else
:
bootstrap_t_stats
[
b
]
=
0.0
# Step 4: Compute bootstrap p-value
# P-value is proportion of |t*| >= |t_original|
p_value
=
np
.
mean
(
np
.
abs
(
bootstrap_t_stats
)
>=
np
.
abs
(
t_stat_original
))
# Ensure p-value is at least 1/(n_bootstrap+1) to avoid exact zero
p_value
=
float
(
max
(
float
(
p_value
),
1
/
(
n_bootstrap
+
1
)))
# Step 5: Compute bootstrap SE and confidence interval
# SE from standard deviation of bootstrap coefficient distribution
se_bootstrap
=
float
(
np
.
std
(
bootstrap_coefs
,
ddof
=
1
))
# Percentile confidence interval from bootstrap distribution
lower_percentile
=
alpha
/
2
*
100
upper_percentile
=
(
1
-
alpha
/
2
)
*
100
ci_lower
=
float
(
np
.
percentile
(
bootstrap_coefs
,
lower_percentile
))
ci_upper
=
float
(
np
.
percentile
(
bootstrap_coefs
,
upper_percentile
))
return
WildBootstrapResults
(
se
=
se_bootstrap
,
p_value
=
p_value
,
t_stat_original
=
t_stat_original
,
ci_lower
=
ci_lower
,
ci_upper
=
ci_upper
,
n_clusters
=
n_clusters
,
n_bootstrap
=
n_bootstrap
,
weight_type
=
weight_type
,
alpha
=
alpha
,
bootstrap_distribution
=
bootstrap_coefs
if
return_distribution
else
None
,
)
def
check_parallel_trends
(
data
:
pd
.
DataFrame
,
outcome
:
str
,
time
:
str
,
treatment_group
:
str
,
pre_periods
:
Optional
[
List
[
Any
]]
=
None
,
)
->
Dict
[
str
,
Any
]:
"""
Perform a simple check for parallel trends assumption.
This computes the trend (slope) in the outcome variable for both
treatment and control groups during pre-treatment periods.
Parameters
----------
data : pd.DataFrame
Panel data.
outcome : str
Name of outcome variable column.
time : str
Name of time period column.
treatment_group : str
Name of treatment group indicator column.
pre_periods : list, optional
List of pre-treatment time periods. If None, infers from data.
Returns
-------
dict
Dictionary with trend statistics and test results.
"""
if
pre_periods
is
None
:
# Assume treatment happens at median time period
all_periods
=
sorted
(
data
[
time
].
unique
())
mid_point
=
len
(
all_periods
)
//
2
pre_periods
=
all_periods
[:
mid_point
]
pre_data
=
data
[
data
[
time
].
isin
(
pre_periods
)]
# Compute trends for each group
treated_data
=
pre_data
[
pre_data
[
treatment_group
]
==
1
]
control_data
=
pre_data
[
pre_data
[
treatment_group
]
==
0
]
# Simple linear regression for trends
def
compute_trend
(
group_data
:
pd
.
DataFrame
)
->
Tuple
[
float
,
float
]:
time_values
=
group_data
[
time
].
values
outcome_values
=
group_data
[
outcome
].
values
# Normalize time to start at 0
time_norm
=
time_values
-
time_values
.
min
()
# Compute slope using least squares
n
=
len
(
time_norm
)
if
n
<
2
:
return
np
.
nan
,
np
.
nan
mean_t
=
np
.
mean
(
time_norm
)
mean_y
=
np
.
mean
(
outcome_values
)
# Check for zero variance in time (all same time period)
time_var
=
np
.
sum
((
time_norm
-
mean_t
)
**
2
)
if
time_var
==
0
:
return
np
.
nan
,
np
.
nan
slope
=
np
.
sum
((
time_norm
-
mean_t
)
*
(
outcome_values
-
mean_y
))
/
time_var
# Compute standard error of slope
y_hat
=
mean_y
+
slope
*
(
time_norm
-
mean_t
)
residuals
=
outcome_values
-
y_hat
mse
=
np
.
sum
(
residuals
**
2
)
/
(
n
-
2
)
se_slope
=
np
.
sqrt
(
mse
/
time_var
)
return
slope
,
se_slope
treated_slope
,
treated_se
=
compute_trend
(
treated_data
)
control_slope
,
control_se
=
compute_trend
(
control_data
)
# Test for difference in trends
slope_diff
=
treated_slope
-
control_slope
se_diff
=
np
.
sqrt
(
treated_se
**
2
+
control_se
**
2
)
t_stat
,
p_value
,
_
=
safe_inference
(
slope_diff
,
se_diff
)
return
{
"treated_trend"
:
treated_slope
,
"treated_trend_se"
:
treated_se
,
"control_trend"
:
control_slope
,
"control_trend_se"
:
control_se
,
"trend_difference"
:
slope_diff
,
"trend_difference_se"
:
se_diff
,
"t_statistic"
:
t_stat
,
"p_value"
:
p_value
,
"parallel_trends_plausible"
:
p_value
>
0.05
if
not
np
.
isnan
(
p_value
)
else
None
,
}
def
check_parallel_trends_robust
(
data
:
pd
.
DataFrame
,
outcome
:
str
,
time
:
str
,
treatment_group
:
str
,
unit
:
Optional
[
str
]
=
None
,
pre_periods
:
Optional
[
List
[
Any
]]
=
None
,
n_permutations
:
int
=
1000
,
seed
:
Optional
[
int
]
=
None
,
wasserstein_threshold
:
float
=
0.2
,
)
->
Dict
[
str
,
Any
]:
"""
Perform robust parallel trends testing using distributional comparisons.
Uses the Wasserstein (Earth Mover's) distance to compare the full
distribution of outcome changes between treated and control groups,
with permutation-based inference.
Parameters
----------
data : pd.DataFrame
Panel data with repeated observations over time.
outcome : str
Name of outcome variable column.
time : str
Name of time period column.
treatment_group : str
Name of treatment group indicator column (0/1).
unit : str, optional
Name of unit identifier column. If provided, computes unit-level
changes. Otherwise uses observation-level data.
pre_periods : list, optional
List of pre-treatment time periods. If None, uses first half of periods.
n_permutations : int, default=1000
Number of permutations for computing p-value.
seed : int, optional
Random seed for reproducibility.
wasserstein_threshold : float, default=0.2
Threshold for normalized Wasserstein distance. Values below this
threshold (combined with p > 0.05) suggest parallel trends are plausible.
Returns
-------
dict
Dictionary containing:
- wasserstein_distance: Wasserstein distance between group distributions
- wasserstein_p_value: Permutation-based p-value
- ks_statistic: Kolmogorov-Smirnov test statistic
- ks_p_value: KS test p-value
- mean_difference: Difference in mean changes
- variance_ratio: Ratio of variances in changes
- treated_changes: Array of outcome changes for treated
- control_changes: Array of outcome changes for control
- parallel_trends_plausible: Boolean assessment
Examples
--------
>>> results = check_parallel_trends_robust(
... data, outcome='sales', time='year',
... treatment_group='treated', unit='firm_id'
... )
>>> print(f"Wasserstein distance: {results['wasserstein_distance']:.4f}")
>>> print(f"P-value: {results['wasserstein_p_value']:.4f}")
Notes
-----
The Wasserstein distance (Earth Mover's Distance) measures the minimum
"cost" of transforming one distribution into another. Unlike simple
mean comparisons, it captures differences in the entire distribution
shape, making it more robust to non-normal data and heterogeneous effects.
A small Wasserstein distance and high p-value suggest the distributions
of pre-treatment changes are similar, supporting the parallel trends
assumption.
"""
# Use local RNG to avoid affecting global random state
rng
=
np
.
random
.
default_rng
(
seed
)
# Identify pre-treatment periods
if
pre_periods
is
None
:
all_periods
=
sorted
(
data
[
time
].
unique
())
mid_point
=
len
(
all_periods
)
//
2
pre_periods
=
all_periods
[:
mid_point
]
pre_data
=
data
[
data
[
time
].
isin
(
pre_periods
)].
copy
()
# Compute outcome changes
treated_changes
,
control_changes
=
_compute_outcome_changes
(
pre_data
,
outcome
,
time
,
treatment_group
,
unit
,
caller_label
=
"check_parallel_trends_robust"
,
)
if
len
(
treated_changes
)
<
2
or
len
(
control_changes
)
<
2
:
return
{
"wasserstein_distance"
:
np
.
nan
,
"wasserstein_p_value"
:
np
.
nan
,
"ks_statistic"
:
np
.
nan
,
"ks_p_value"
:
np
.
nan
,
"mean_difference"
:
np
.
nan
,
"variance_ratio"
:
np
.
nan
,
"treated_changes"
:
treated_changes
,
"control_changes"
:
control_changes
,
"parallel_trends_plausible"
:
None
,
"error"
:
"Insufficient data for comparison"
,
}
# Compute Wasserstein distance
wasserstein_dist
=
stats
.
wasserstein_distance
(
treated_changes
,
control_changes
)
# Permutation test for Wasserstein distance
all_changes
=
np
.
concatenate
([
treated_changes
,
control_changes
])
n_treated
=
len
(
treated_changes
)
n_total
=
len
(
all_changes
)
permuted_distances
=
np
.
zeros
(
n_permutations
)
for
i
in
range
(
n_permutations
):
perm_idx
=
rng
.
permutation
(
n_total
)
perm_treated
=
all_changes
[
perm_idx
[:
n_treated
]]
perm_control
=
all_changes
[
perm_idx
[
n_treated
:]]
permuted_distances
[
i
]
=
stats
.
wasserstein_distance
(
perm_treated
,
perm_control
)
# P-value: proportion of permuted distances >= observed
wasserstein_p
=
np
.
mean
(
permuted_distances
>=
wasserstein_dist
)
# Kolmogorov-Smirnov test
ks_stat
,
ks_p
=
stats
.
ks_2samp
(
treated_changes
,
control_changes
)
# Additional summary statistics
mean_diff
=
np
.
mean
(
treated_changes
)
-
np
.
mean
(
control_changes
)
var_treated
=
np
.
var
(
treated_changes
,
ddof
=
1
)
var_control
=
np
.
var
(
control_changes
,
ddof
=
1
)
var_ratio
=
var_treated
/
var_control
if
var_control
>
0
else
np
.
nan
# Normalized Wasserstein (relative to pooled std)
pooled_std
=
np
.
std
(
all_changes
,
ddof
=
1
)
wasserstein_normalized
=
wasserstein_dist
/
pooled_std
if
pooled_std
>
0
else
np
.
nan
# Assessment: parallel trends plausible if p-value > 0.05
# and normalized Wasserstein is small (below threshold)
plausible
=
bool
(
wasserstein_p
>
0.05
and
(
wasserstein_normalized
<
wasserstein_threshold
if
not
np
.
isnan
(
wasserstein_normalized
)
else
True
)
)
return
{
"wasserstein_distance"
:
wasserstein_dist
,
"wasserstein_normalized"
:
wasserstein_normalized
,
"wasserstein_p_value"
:
wasserstein_p
,
"ks_statistic"
:
ks_stat
,
"ks_p_value"
:
ks_p
,
"mean_difference"
:
mean_diff
,
"variance_ratio"
:
var_ratio
,
"n_treated"
:
len
(
treated_changes
),
"n_control"
:
len
(
control_changes
),
"treated_changes"
:
treated_changes
,
"control_changes"
:
control_changes
,
"parallel_trends_plausible"
:
plausible
,
}
def
_compute_outcome_changes
(
data
:
pd
.
DataFrame
,
outcome
:
str
,
time
:
str
,
treatment_group
:
str
,
unit
:
Optional
[
str
]
=
None
,
caller_label
:
str
=
"parallel-trend diagnostic"
,
)
->
Tuple
[
np
.
ndarray
,
np
.
ndarray
]:
"""
Compute period-to-period outcome changes for treated and control groups.
Parameters
----------
data : pd.DataFrame
Panel data.
outcome : str
Outcome variable column.
time : str
Time period column.
treatment_group : str
Treatment group indicator column.
unit : str, optional
Unit identifier column.
Returns
-------
tuple
(treated_changes, control_changes) as numpy arrays.
"""
if
unit
is
not
None
:
# Unit-level changes: compute change for each unit across periods
data_sorted
=
data
.
sort_values
([
unit
,
time
])
data_sorted
[
"_outcome_change"
]
=
data_sorted
.
groupby
(
unit
)[
outcome
].
diff
()
# Remove NaN from first period of each unit. The first period per unit
# has no prior observation to diff against, so n_units drops are
# expected. Anything beyond that is a silent side-effect of gaps or
# NaN outcomes — surface the excess via warning (axis-E drop counter).
n_units_observed
=
int
(
data_sorted
[
unit
].
nunique
())
n_dropped
=
int
(
data_sorted
[
"_outcome_change"
].
isna
().
sum
())
n_unexpected_drops
=
max
(
0
,
n_dropped
-
n_units_observed
)
if
n_unexpected_drops
>
0
:
warnings
.
warn
(
f"
{
caller_label
}
: dropped
{
n_dropped
}
row(s) with NaN "
f"first-differences;
{
n_units_observed
}
are the expected "
f"first-period-per-unit drops, and
{
n_unexpected_drops
}
are "
f"additional NaN first-differences (e.g. NaN outcomes or "
f"unit-period gaps upstream). Parallel-trend statistics are "
f"computed on the remaining rows."
,
UserWarning
,
stacklevel
=
3
,
)
changes_data
=
data_sorted
.
dropna
(
subset
=
[
"_outcome_change"
])
treated_changes
=
changes_data
[
changes_data
[
treatment_group
]
==
1
][
"_outcome_change"
].
values
control_changes
=
changes_data
[
changes_data
[
treatment_group
]
==
0
][
"_outcome_change"
].
values
else
:
# Aggregate changes: compute mean change per period per group
treated_data
=
data
[
data
[
treatment_group
]
==
1
]
control_data
=
data
[
data
[
treatment_group
]
==
0
]
# Compute period means
treated_means
=
treated_data
.
groupby
(
time
)[
outcome
].
mean
()
control_means
=
control_data
.
groupby
(
time
)[
outcome
].
mean
()
# Compute changes between consecutive periods
treated_changes
=
np
.
diff
(
treated_means
.
values
)
control_changes
=
np
.
diff
(
control_means
.
values
)
return
treated_changes
.
astype
(
float
),
control_changes
.
astype
(
float
)
def
equivalence_test_trends
(
data
:
pd
.
DataFrame
,
outcome
:
str
,
time
:
str
,
treatment_group
:
str
,
unit
:
Optional
[
str
]
=
None
,
pre_periods
:
Optional
[
List
[
Any
]]
=
None
,
equivalence_margin
:
Optional
[
float
]
=
None
,
)
->
Dict
[
str
,
Any
]:
"""
Perform equivalence testing (TOST) for parallel trends.
Tests whether the difference in trends is practically equivalent to zero
using Two One-Sided Tests (TOST) procedure.
Parameters
----------
data : pd.DataFrame
Panel data.
outcome : str
Name of outcome variable column.
time : str
Name of time period column.
treatment_group : str
Name of treatment group indicator column.
unit : str, optional
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