Hard versus Soft Intervention: Compliance Effects among Firms1

Thomas Lange

doi:10.2478/ntaxj-2025-0001

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Hard versus Soft Intervention: Compliance Effects among Firms1

Nordic Tax Journal

AHEAD OF PRINT

By: Thomas Lange

Open Access

|Feb 2026

Figures & Tables

Means of payroll tax and number of employees. Reference, audit, and letter groups.Notes: This figure plots point means and 95% confidence intervals from payroll tax remittance (in NOK), and the number of employees for years 2017 to 2020. The treatment, either audits or letters, takes place in year 2018, as visualized by the vertical, dotted line. The black line represents the annual mean of the audit group, the blue line represents the annual mean of the letter group, and the dotted line represents the mean of the reference group. The 95% confidence intervals are represented by the vertical error bars for each group.

Estimated audit and letter effects (base year 2017).Notes: This figure plots point DiD estimates from regressions of measures of logged payroll tax remittance and logged number of employees for the years 2017–2020, compared to the base year 2017, and compared to the reference group. (Difference between treatment and reference in years 2018, 2019, 2020, minus the difference between treatment and reference in 2017). The treatment, either audits or letters, take place in year 2018, visualized by the vertical line. The black line represents the estimated coefficients of the audit group, the grey line represents the estimated coefficients of the letter group, both estimations are compared to the reference group represented by the dotted line. The specification includes fixed effects on strata and firm ID. Standard errors are adjusted for 22 clusters in strata. Table A5 in the Appendix displays the coefficients and their standard errors.

Estimated annual letter effects (ATE) 2017–2020.Notes: This figure plots point estimates from annual letter regressions of measures of logged payroll tax remittance and logged number of employees for the years 2017–2020, compared to the reference group (x-line). The treatment takes place in the year 2018, visualized by the vertical line. The grey line represents the estimated coefficients of the letter group compared to the reference group, represented by the dotted line. Standard errors are adjusted for 22 clusters in strata. Table A6 in the Appendix displays the coefficients and their standard errors.

Estimated LATE of letter treatment (base year 2017).Notes: This figure plots annual point IV estimates from regressions of measures of logged payroll tax remittance and logged number of employees for the years 2017–2020, compared to the reference group (x-line). The treatment takes place in year 2018, visualized by the vertical line. The dark grey line represents the estimated coefficients of the 6,870 letter openers (LATE), and the light grey line represents the estimated coefficients of the 8,000 assigned to the letter group. Standard errors are adjusted for 22 clusters in strata. Table A7 in the Appendix displays the coefficients and their standard errors.

Estimated audit and letter (ATE) effects (base year 2017) on firm size 25 percentile

Treatment	(1)	(2)	(3)	(4)	(5)	(6)
Audit*2018	−0.161 (0.265)	−0.161 (0.201)	0.124 (0.079)	−0.011 (0.018)	−0.011 (0.015)	−0.011 (0.021)
Audit*2019	−0.058 (0.364)	−0.058 (0.235)	0.041 (0.101)	−0.002 (0.024)	−0.002 (0.020)	−0.002 (0.030)
Audit*2020	0.178 (0.344)	0.178 (0.242)	0.099 (0.108)	0.009 (0.025)	0.009 (0.024)	0.009 (0.029)
Letter*2018	−0.091 (0.136)	−0.091 (0.114)	0.018 (0.034)	−0.002 (0.007)	−0.002 (0.008)	−0.002 (0.007)
Letter*2019	−0.010 (0.157)	−0.010 (0.135)	0.110* (0.049)	0.001 (0.009)	0.001 (0.012)	0.001 (0.009)
Letter*2020	−0.187 (0.157)	−0.187 (0.143)	0.040 (0.043)	−0.007 (0.012)	−0.007 (0.014)	−0.007 (0.014)
Observations	30711	30711	123844	29439	29439	29439
R-squared	0.826	0.826	0.756	0.922	0.922	0.922

Descriptive statistics by stratum_ Base year 2017

Strata	N	Payroll tax (μ)	Employees (μ)	SD	Audit (n)	SD	Letter (n)	SD
S1	199	479 174	429 103	11	8	22	51	41
S11	505	110 167	270 168	13	10	34	113	89
S12	1 904	328 739	509 941	14	16	148	472	415
S13	1 097	256 028	173 401	11	6	46	297	261
S15	3 288	255 995	241 945	10	10	67	877	757
S16	2 372	399 841	523 591	12	9	89	637	567
S17	3 065	447 220	637 986	10	12	76	861	746
S19	277	96 385	140 913	17	22	124	47	35
S20	753	147 690	182 643	14	18	53	177	159
S21	1 701	323 216	310 702	11	9	91	425	359
S23	875	342 038	321 279	10	8	91	246	214
S26	5 484	301 787	347 375	9	8	300	1 395	1 211
S27	368	257 976	248 780	25	14	92	79	73
S29	621	243 176	238 360	14	10	132	122	106
S3	1 809	104 121	120 253	10	9	32	505	399
S31	2 815	233 333	197 782	23	13	302	681	564
S33	775	222 703	258 052	8	7	91	203	173
S34	948	493 216	997 972	11	9	48	261	230
S37	146	500 468	669 059	13	10	20	34	34
S38	1 359	342 466	305 586	10	7	77	359	313
S5	151	453 951	607 734	11	10	20	39	36
S6	449	246 548	201 366	11	5	19	119	88

Estimated audit and letter (ATE) effects (base year 2017) on firm type self-employed

Treatment	(1)	(2)	(3)	(4)	(5)	(6)
Audit*2018	−0.183 (0.285)	−0.183 (0.213)	−0.183 (0.286)	−0.072+ (0.036)	−0.072+ (0.040)	−0.072* (0.035)
Audit*2019	0.025 (0.418)	0.025 (0.270)	0.025 (0.411)	−0.103* (0.048)	−0.103+ (0.054)	−0.103* (0.048)
Audit*2020	0.377 (0.344)	0.377 (0.281)	0.377 (0.338)	−0.058 (0.052)	−0.058 (0.060)	−0.058 (0.048)
Letter*2018	0.008 (0.128)	0.008 (0.120)	0.008 (0.114)	0.010 (0.024)	0.010 (0.020)	0.010 (0.019)
Letter*2019	−0.079 (0.182)	−0.079 (0.157)	−0.079 (0.134)	0.007 (0.037)	0.007 (0.029)	0.007 (0.033)
Letter*2020	−0.273 (0.214)	−0.273 (0.172)	−0.273* (0.116)	−0.018 (0.030)	−0.018 (0.033)	−0.018 (0.026)
Observations	22085	22085	22085	22085	22085	22085
R-squared	0.661	0.661	0.661	0.798	0.798	0.798

Stratum and NACE codes

Stratum	NACE 2	Description	N
S1	0	Missing NACE	31
S1	43	Specialized construction activities	144
S1	71	Architectural and engineering activities; technical testing and analysis	21
S1	90	Creative arts and entertainment activities	3
S11	3	Fishing and aquaculture	505
S12	77	Rental and leasing activities	102
S12	78	Employment activities	407
S12	79	Travel agency tour operator and other reservation service and related activities	231
S12	80	Security and investigation activities	104
S12	81	Services to buildings and landscape activities	480
S12	82	Office administrative office support and other business support activities	580
S13	96	Other personal service activities	1097
S15	86	Human health activities	2544
S15	87	Residential care activities	28
S15	88	Social work activities without accommodation	716
S16	10	Manufacture of food products	204
S16	13	Manufacture of textiles	59
S16	14	Manufacture of wearing apparel	33
S16	15	Manufacture of leather and related products	6
S16	16	Manufacture of wood and of products of wood and cork except furniture; manufacture of articles of straw and plaiting materials	228
S16	18	Printing and reproduction of recorded media	255
S16	20	Manufacture of chemicals and chemical products	2
S16	21	Manufacture of basic pharmaceutical products and pharmaceutical preparations	5
S16	22	Manufacture of rubber and plastic products	8
S16	23	Manufacture of other nonmetallic mineral products	60
S16	24	Manufacture of basic metals	29
S16	25	Manufacture of fabricated metal products, except machinery and equipment	591
S16	26	Manufacture of computer electronic and optical products	81
S16	27	Manufacture of electrical equipment	55
S16	28	Manufacture of machinery and equipment n.e.c.	152
S16	30	Manufacture of other transport equipment	27
S16	31	Manufacture of furniture	116
S16	32	Other manufacturing	195
S16	33	Repair and installation of machinery and equipment	266
S17	58	Publishing activities	640
S17	59	Motion picture video and television program production sound recording and music publishing activities	421
S17	60	Programming and broadcasting activities	29
S17	61	Telecommunications	87
S17	62	Computer programming consultancy and related activities	1665
S17	63	Information service activities	223
S19	1	Crop and animal production hunting and related service activities	277
S20	90	Creative arts and entertainment activities	480
S20	91	Libraries archives museums and other cultural activities	14
S20	93	Sports activities and amusement and recreation activities	259
S21	49	Land transport and transport via pipelines	1701
S23	43	Specialized construction activities	875
S26	41	Construction of buildings	5182
S26	42	Civil engineering	302
S27	55	Accommodation	368
S29	81	Services to buildings and landscape activities	621
S3	49	Land transport and transport via pipelines	1809
S31	56	Food and beverage service activities	2815
S33	43	Specialized construction activities	775
S34	50	Water transport	376
S34	51	Air transport	30
S34	52	Warehousing and support activities for transportation	404
S34	53	Postal and courier activities	138
S37	37	Sewerage	45
S37	38	Waste collection treatment and disposal activities; materials recovery	97
S37	39	Remediation activities and other waste management services	4
S38	45	Wholesale and retail trade and repair of motor vehicles and motorcycles	1359
S5	6	Extraction of crude petroleum and natural gas	19
S5	7	Mining of metal ores	2
S5	8	Other mining and quarrying	55
S5	9	Mining support service activities	75
S6	47	Retail trade, except for motor vehicles and motorcycles	449

Estimated audit and letter (ATE) effects (base year 2017) on firm type private Ltd

Treatment	(1)	(2)	(3)	(4)	(5)	(6)
Audit*2018	0.191+ (0.093)	0.191** (0.069)	0.191* (0.092)	0.042+ (0.021)	0.042*** (0.011)	0.042* (0.020)
Audit*2019	0.070 (0.094)	0.070 (0.104)	0.070 (0.105)	0.078** (0.024)	0.078*** (0.019)	0.078** (0.025)
Audit*2020	0.077 (0.094)	0.077 (0.119)	0.077 (0.099)	0.045* (0.020)	0.045+ (0.025)	0.045+ (0.025)
Letter*2018	0.020 (0.031)	0.020 (0.043)	0.020 (0.033)	0.005 (0.005)	0.005 (0.007)	0.005 (0.005)
Letter*2019	0.130+ (0.064)	0.130* (0.058)	0.130* (0.055)	0.022+ (0.011)	0.022+ (0.012)	0.022+ (0.012)
Letter*2020	0.088 (0.070)	0.088 (0.066)	0.088 (0.058)	0.025+ (0.013)	0.025+ (0.014)	0.025+ (0.013)
Observations	131460	131460	131460	131460	131460	131460
R-squared	0.654	0.654	0.654	0.771	0.771	0.771

Estimated letter treatment effects vs_ no treatment

Year	Dep. Variable	Letter	SE
2017	Log Payroll Tax	0.109*	(0.039)
2018	Log Payroll Tax	0.127**	(0.041)
2019	Log Payroll Tax	0.219**	(0.075)
2020	Log Payroll Tax	0.150*	(0.069)
2017	Log Employees	0.035*	(0.011)
2018	Log Employees	0.039**	(0.011)
2019	Log Employees	0.055***	(0.013)
2020	Log Employees	0.053***	(0.011)

Estimated ITT vs LATE letter effects

Year	Dep. Variable	ITT	SE	LATE	SE
2017	Log Payroll tax	0.109*	(0.039)	0.127**	(0.045)
2018	Log Payroll tax	0.127**	(0.041)	0.148**	(0.050)
2019	Log Payroll tax	0.219**	(0.075)	0.255**	(0.088)
2020	Log Payroll tax	0.150*	(0.069)	0.174*	(0.082)
2017	Log Employees	0.035*	(0.011)	0.040	(0.015)
2018	Log Employees	0.039**	(0.011)	0.046***	(0.014)
2019	Log Employees	0.055***	(0.013)	0.064***	(0.015)
2020	Log Employees	0.053***	(0.011)	0.062***	(0.013)

OLS design fixed effects model results

	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
Arm	2017	2018	2019	2020	2017	2018	2019	2020
Audit	0.198+ (0.114)	0.386* (0.185)	0.337+ (0.168)	0.399* (0.179)	0.000 (0.022)	0.034 (0.031)	0.079* (0.037)	0.082* (0.038)
Letter	0.095* (0.039)	0.114* (0.041)	0.206* (0.075)	0.136+ (0.069)	0.038** (0.011)	0.043** (0.011)	0.058*** (0.013)	0.055*** (0.011)
Observations	30961	30961	30961	30961	30961	30961	30961	30961
R-squared	0.045	0.030	0.026	0.026	0.112	0.089	0.058	0.042

Reported remittance of payroll tax (NOK) and number of employees (2017–2020)

		Payroll Tax			Employees

	Year	N	Mean	SD	N	Mean	SD
Population	2017	30 869	300 651	416 841	30961	11.95	11.41
	2018	30 813	311 326	550 902	30961	11.99	14.25
	2019	30 807	318 893	702 543	30961	11.46	17.6
	2020	30 667	285 473	733 289	30961	10.22	15.6

Reference	2017	20 919	300 638	423 045	20987	11.72	11.07
	2018	20 893	310 461	586 372	20987	11.71	13.68
	2019	20 884	319 539	776 792	20987	11.15	16.84
	2020	20 786	287 767	815 942	20987	9.99	16.06

Audit Arm	2017	1 970	284 822	342 069	1974	14.05	14.42
	2018	1 964	299 351	388 336	1974	14.21	14.92
	2019	1 966	299 264	434 835	1974	13.49	15.67
	2020	1 964	253 812	417 955	1974	11.82	14.24

Letter Arm	2017	7 980	304 594	417 213	8000	12.04	11.42
	2018	7 956	316 552	485 016	8000	12.18	15.47
	2019	7 957	322 046	529 603	8000	11.78	19.82
	2020	7 917	287 302	539 802	8000	10.41	14.63

Cost-benefit analysis

	Audit (A)	Letter (L)	Reference (R)	A-R	L-R
Marginal cost (MC)	12 740	0	0	12 740	0
β (%) 2018	0.1320	0.0192	0	0.1320	0.0192
Δ (NOK) 2017–2018	14 529	11 958	9 823	4 706	2 135
β*Δ = Marginal revenue (MR)	1 918	230	0	1 918	230
MR-MC	−10 822	230	0	−10 822	230

Two sample T-statistics payroll tax and employees in the base year 2017

Arm	Payroll Tax	t	P> \|t\|	Employees	t	P> \|t\|
Audit	284821.6 (342068.8)			14.07107 (14.42238)
Letter	304594 (417212.9)			12.05564 (11.42717)
Combined	300679.2 (403508.8)	1.9480	0.0514	12.45467 (12.10517)	−6.6322	0.0

Correlation matrix dependent variables

	Log Payroll Tax	Log Revenue	Log Employees	Log Salary
Log Payroll tax	1.000
Log Revenue	0.613	1.000
Log Employees	0.495	0.395	1.000
Log Salary	0.909	0.644	0.530	1.000

Population selection criteria

Criteria
1. Total revenue in 2017 > NOK 100,000
2. If not 1, then total revenue in 2016 ≥ NOK 200,000.
3. Mean active work relations per month is ≤ 20
4. Mean active employees per month is ≥ 5
5. If not 4, then registered > NOK 100,000 on subcontracts and/or foreign services in 2016
6. Private limited companies (AS) self-employed (ENK) and Norwegian foreign-registered enterprises (NUF)
7. No termination date registered
8. Sectors in public service, defense and public social security are excluded

Estimated audit and letter (ATE) effects (base year 2017)

Treatment	(1)	(2)	(3)	(4)	(5)	(6)
Audit*2018	0.124 (0.081)	0.124+ (0.068)	0.124 (0.079)	0.019 (0.023)	0.019+ (0.012)	0.019 (0.022)
Audit*2019	0.041 (0.093)	0.041 (0.098)	0.041 (0.101)	0.045 (0.026)	0.045* (0.018)	0.045 (0.027)
Audit*2020	0.099 (0.097)	0.099 (0.109)	0.099 (0.108)	0.025 (0.022)	0.025 (0.023)	0.025 (0.025)
Letter*2018	0.018 (0.028)	0.018 (0.040)	0.018 (0.034)	0.005 (0.006)	0.005 (0.007)	0.005 (0.006)
Letter*2019	0.110+ (0.056)	0.110* (0.054)	0.110* (0.049)	0.021+ (0.010)	0.021+ (0.011)	0.021+ (0.011)
Letter*2020	0.040 (0.054)	0.040 (0.062)	0.040 (0.043)	0.019 (0.012)	0.019 (0.013)	0.019 (0.012)
Observations	123844	123844	123844	123844	123844	123844
R-squared	0.756	0.756	0.756	0.835	0.835	0.835

Estimated audit and letter (ATE) effects (base year 2017) on firm type Norwegian registered foreign company

Treatment	(1)	(2)	(3)	(4)	(5)	(6)
Audit*2018	0.009 (1.179)	0.009 (1.361)	0.009 (1.285)	−0.478 (0.283)	−0.478 (0.323)	−0.478 (0.316)
Audit*2019	−1.474 (1.292)	−1.474 (1.719)	−1.474 (1.454)	−0.339 (0.248)	−0.339 (0.308)	−0.339 (0.289)
Audit*2020	−1.457 (1.462)	−1.457 (1.589)	−1.457 (1.556)	−0.262 (0.266)	−0.262 (0.345)	−0.262 (0.291)
Letter*2018	0.003 (0.588)	0.003 (0.580)	0.003 (0.600)	−0.051 (0.055)	−0.051 (0.062)	−0.051 (0.054)
Letter*2019	1.345 (0.832)	1.345 (0.815)	1.345* (0.573)	0.062 (0.132)	0.062 (0.113)	0.062 (0.136)
Letter*2020	0.589 (1.086)	0.589 (0.932)	0.589 (0.799)	0.011 (0.174)	0.011 (0.153)	0.011 (0.182)
Observations	1260	1260	1260	1260	1260	1260
R-squared	0.685	0.685	0.685	0.768	0.768	0.768

T-statistics payroll tax and employees in the base year 2017

Arm	Payroll Tax	t	P > \|t\|	Employees	t	P > \|t\|
Audit	3658.342 (6721.756)	0.54	0.592	0.297 (0.321)	0.92	0.366
Letter	5317.589 (3322.063)	1.60	0.124	0.116 (0.190)	0.61	0.548

Observations	30869			30961
R-squared Audit	0.055			0.124
R-squared Letter	0.000			0.000

References

Authors

Metrics

Articles in this issue

DOI: https://doi.org/10.2478/ntaxj-2025-0001 | Journal eISSN: 2246-1809

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Language: English

Submitted on: Mar 19, 2023

Accepted on: Dec 5, 2024

Published on: Feb 11, 2026

Published by: DJØF Publishing, Nordic Tax Research Council

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

behavioral economics,

treatment effect Models,

instrumental variables

Related subjects:

Business and economics,

Business management,

Business law,

Political economics,

Public finance and fiscal theory,

Law,

History, philosophy and sociology of law,

Public law,

Tax and accounting law

© 2026 Thomas Lange, published by DJØF Publishing, Nordic Tax Research Council
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

AHEAD OF PRINT

Hard versus Soft Intervention: Compliance Effects among Firms1

Figures & Tables

Figure 1:

Figure 2:

Figure 3:

Figure 4:

Figure AF1:

Estimated audit and letter (ATE) effects (base year 2017) on firm size 25 percentile

Descriptive statistics by stratum_ Base year 2017

Estimated audit and letter (ATE) effects (base year 2017) on firm type self-employed

Stratum and NACE codes

Estimated audit and letter (ATE) effects (base year 2017) on firm type private Ltd

Estimated letter treatment effects vs_ no treatment

Estimated ITT vs LATE letter effects

OLS design fixed effects model results

Reported remittance of payroll tax (NOK) and number of employees (2017–2020)

Cost-benefit analysis

Two sample T-statistics payroll tax and employees in the base year 2017

Correlation matrix dependent variables

Population selection criteria

Estimated audit and letter (ATE) effects (base year 2017)

Estimated audit and letter (ATE) effects (base year 2017) on firm type Norwegian registered foreign company

T-statistics payroll tax and employees in the base year 2017

Paradigm

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