From 810753c3197956b82f19dcb6fb7039338d8c6cf5 Mon Sep 17 00:00:00 2001
From: Vahid Ahmadi <va.vahidahmadi@gmail.com>
Date: Tue, 5 Nov 2024 12:05:20 +0100
Subject: [PATCH 1/5] behavorial-response-post

---
 src/images/posts/behavorial-post.jpg          | Bin 0 -> 132206 bytes
 .../articles/behavioural-response-post.md     |  50 ++++++++++++++++++
 src/posts/posts.json                          |   9 ++++
 3 files changed, 59 insertions(+)
 create mode 100644 src/images/posts/behavorial-post.jpg
 create mode 100644 src/posts/articles/behavioural-response-post.md

diff --git a/src/images/posts/behavorial-post.jpg b/src/images/posts/behavorial-post.jpg
new file mode 100644
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diff --git a/src/posts/articles/behavioural-response-post.md b/src/posts/articles/behavioural-response-post.md
new file mode 100644
index 000000000..46099af67
--- /dev/null
+++ b/src/posts/articles/behavioural-response-post.md
@@ -0,0 +1,50 @@
+## Introduction
+
+Public policies change incentives and behaviours. When governments introduce or modify policies, individuals respond by adjusting their decisions. Workers may change their work hours,[^1] investors might shift when they realise gains,[^2] and businesses often adapt their practices in response.[^3] The static analysis fails to capture how individuals adjust their economic decisions when facing new incentives. This report presents how PolicyEngine currently models three key behavioural elasticities: income, substitution, and capital gains responses to policy changes to capture how individuals adjust their economic decisions in response to policy changes.
+
+Elasticities measure these behavioural responses to policy changes. An elasticity quantifies how much behaviour changes in response to a policy change \- higher elasticities indicate stronger behavioural responses, while lower ones suggest more limited adjustments. PolicyEngine currently incorporates three key behavioural responses in its analysis: income elasticity (work changes from overall income shifts), substitution elasticity (work changes from marginal reward shifts), and capital gains elasticity (investment timing responses to tax changes).
+
+## Labour supply
+
+PolicyEngine models how individuals respond to work incentives by changing their employment income using two standard elasticities- the income and substitution elasticities.
+
+### The income elasticity
+
+When people become richer, they might choose to work less. The income elasticity measures this behaviour \- how much work changes when total income changes. This matters for policies like broad tax changes or new benefits that affect how much money people have overall. Without considering this response, policy analysis might get work patterns wrong after income changes. Following the [Congressional Budget Office (CBO)](https://www.cbo.gov/sites/default/files/112th-congress-2011-2012/reports/43674-laborsupplyfiscalpolicy.pdf#page=4), PolicyEngine uses an income elasticity of \-0.05 for the UK as a default elasticity, meaning a 10% rise in income leads to a small 0.5% drop in work.
+
+### The substitution elasticity
+
+People work partly based on how much they keep from each extra hour of work. The substitution elasticity measures how work changes when this reward changes. For example, higher tax rates mean keeping less from each additional hour, which might lead to less overtime or part-time work. This response is key for analysing tax brackets or benefits that reduce earnings. Following the [Congressional Budget Office (CBO)](https://www.cbo.gov/sites/default/files/112th-congress-2011-2012/reports/43674-laborsupplyfiscalpolicy.pdf#page=4), PolicyEngine uses a substitution elasticity of 0.25 as a default elasticity, meaning people work about 2.5% less when they keep 10% less from each extra hour.
+
+## Capital gains elasticity
+
+When tax rates on investment gains change, people adjust when they sell their investments[^4]. Capital gains elasticity measures this effect. Unlike work hours, which are often fixed, people can usually choose when to sell investments. When capital gains tax rates go up, many wait to sell until rates are lower again. This response strongly affects how much money tax changes raise. PolicyEngine uses a capital gains elasticity of \-0.7 as a default elasticity, reflecting that investment timing is quite sensitive to tax rates.
+
+## How PolicyEngine models behavioural responses
+
+By default, PolicyEngine’s model assumes no behavioural responses. PolicyEngine's model adds behavioural responses to its tax-benefit calculations. For each simulated reform, the model first computes the effects of policy changes on income and tax rates. Then, it estimates three types of behavioural changes: how total income changes affect work, how marginal tax changes affect work hours, and how tax rates influence investment timing. By comparing scenarios with and without these behavioural responses, the model provides more accurate predictions of how policies affect people and government budgets.
+
+## Comparing static and dynamic analysis
+
+This section shows how incorporating behavioural responses affects policy analysis. By comparing estimates with and without behavioural responses, we illustrate the importance of accounting for how individuals and businesses adapt their economic decisions in response to policy changes.
+
+To demonstrate this comparison, we examine two tax reforms proposed by the UK government in October 2024: changes to Capital Gains Tax and employer National Insurance contributions. For a detailed analysis of these and other reforms proposed in the Autumn Budget, see [PolicyEngine's reform impact analysis](https://policyengine.org/uk/research/autumn-budget-2024-policy-choices). 
+
+In estimating the impacts of these reforms, we model how individuals with capital gains respond to changes in their marginal tax rate and how employers respond to changes in their tax liability by adjusting employee wages. The table below compares the five-year revenue impacts under both static and dynamic scenarios.
+
+| Reform | Static revenue impact	 | Dynamic revenue impact	 | Relative change |
+| :---- | :---- | :---- | :---- |
+| Levy employer pension NICs | 90.3 | 66.6 | \-26% |
+| Raise CGT to 24%	 | 21.5 | 10.1 | \-53% |
+
+## Conclusion
+
+In this report, we present how PolicyEngine models behavioural responses through income, substitution, and capital gains elasticities to capture how individuals adjust their economic decisions to policy changes. Using recent UK tax reforms as examples, we demonstrate how incorporating these behavioural responses changes government revenue compared to static analysis.
+
+[^1]:  Chetty, R., Guren, A., Manoli, D., & Weber, A. (2011). Are Micro and Macro Labor Supply Elasticities Consistent? A Review of Evidence on the Intensive and Extensive Margins. American Economic Review, 101(3), 471–475.
+
+[^2]:  Saez, E., Slemrod, J., & Giertz, S. H. (2012). The Elasticity of Taxable Income with Respect to Marginal Tax Rates: A Critical Review. Journal of Economic Literature, 50(1), 3-50.
+
+[^3]:  Feldstein, M., Behavioural Responses to Taxation: Lessons from the Tax Reform Act of 1986, American Economic Review, 1995\.
+
+[^4]:  Agersnap, Ole, and Owen Zidar (2021). "The Tax Elasticity of Capital Gains and Revenue-Maximizing Rates." American Economic Review: Insights, vol. 3, no. 4, pp. 399–416.
diff --git a/src/posts/posts.json b/src/posts/posts.json
index 79000f0af..faaeeba22 100644
--- a/src/posts/posts.json
+++ b/src/posts/posts.json
@@ -845,6 +845,15 @@
     "filename": "vat-school-comparison.md",
     "image": "vat-school-comparison-post.jpg"
   },
+  {
+    "title": "How PolicyEngine UK models behavioural responses",
+    "description": "PolicyEngine has enhanced its modelling with behavioural responses, including income, substitution and capital gains elasticities.",
+    "date": "2024-11-05 15:00:00",
+    "tags": ["uk", "policy", "elasticity", "featured"],
+    "authors": ["vahid-ahmadi"],
+    "filename": "behavioural-response-post.md",
+    "image": "behavorial-post.jpg"
+  },
   {
     "title": "Benefits uprating 2025/26",
     "description": "PolicyEngine projects Labour's 1.7% benefits uprating would cost £2.5 billion, mainly benefiting lower-income households.",

From 37076c2720b01548d370e2447a6c5bb96f73a6e1 Mon Sep 17 00:00:00 2001
From: Vahid Ahmadi <va.vahidahmadi@gmail.com>
Date: Tue, 5 Nov 2024 12:10:30 +0100
Subject: [PATCH 2/5] fix-style

---
 .../articles/behavioural-response-post.md      | 18 +++++++++---------
 1 file changed, 9 insertions(+), 9 deletions(-)

diff --git a/src/posts/articles/behavioural-response-post.md b/src/posts/articles/behavioural-response-post.md
index 46099af67..79cba2bdc 100644
--- a/src/posts/articles/behavioural-response-post.md
+++ b/src/posts/articles/behavioural-response-post.md
@@ -28,23 +28,23 @@ By default, PolicyEngine’s model assumes no behavioural responses. PolicyEngin
 
 This section shows how incorporating behavioural responses affects policy analysis. By comparing estimates with and without behavioural responses, we illustrate the importance of accounting for how individuals and businesses adapt their economic decisions in response to policy changes.
 
-To demonstrate this comparison, we examine two tax reforms proposed by the UK government in October 2024: changes to Capital Gains Tax and employer National Insurance contributions. For a detailed analysis of these and other reforms proposed in the Autumn Budget, see [PolicyEngine's reform impact analysis](https://policyengine.org/uk/research/autumn-budget-2024-policy-choices). 
+To demonstrate this comparison, we examine two tax reforms proposed by the UK government in October 2024: changes to Capital Gains Tax and employer National Insurance contributions. For a detailed analysis of these and other reforms proposed in the Autumn Budget, see [PolicyEngine's reform impact analysis](https://policyengine.org/uk/research/autumn-budget-2024-policy-choices).
 
 In estimating the impacts of these reforms, we model how individuals with capital gains respond to changes in their marginal tax rate and how employers respond to changes in their tax liability by adjusting employee wages. The table below compares the five-year revenue impacts under both static and dynamic scenarios.
 
-| Reform | Static revenue impact	 | Dynamic revenue impact	 | Relative change |
-| :---- | :---- | :---- | :---- |
-| Levy employer pension NICs | 90.3 | 66.6 | \-26% |
-| Raise CGT to 24%	 | 21.5 | 10.1 | \-53% |
+| Reform                     | Static revenue impact | Dynamic revenue impact | Relative change |
+| :------------------------- | :-------------------- | :--------------------- | :-------------- |
+| Levy employer pension NICs | 90.3                  | 66.6                   | \-26%           |
+| Raise CGT to 24%           | 21.5                  | 10.1                   | \-53%           |
 
 ## Conclusion
 
 In this report, we present how PolicyEngine models behavioural responses through income, substitution, and capital gains elasticities to capture how individuals adjust their economic decisions to policy changes. Using recent UK tax reforms as examples, we demonstrate how incorporating these behavioural responses changes government revenue compared to static analysis.
 
-[^1]:  Chetty, R., Guren, A., Manoli, D., & Weber, A. (2011). Are Micro and Macro Labor Supply Elasticities Consistent? A Review of Evidence on the Intensive and Extensive Margins. American Economic Review, 101(3), 471–475.
+[^1]: Chetty, R., Guren, A., Manoli, D., & Weber, A. (2011). Are Micro and Macro Labor Supply Elasticities Consistent? A Review of Evidence on the Intensive and Extensive Margins. American Economic Review, 101(3), 471–475.
 
-[^2]:  Saez, E., Slemrod, J., & Giertz, S. H. (2012). The Elasticity of Taxable Income with Respect to Marginal Tax Rates: A Critical Review. Journal of Economic Literature, 50(1), 3-50.
+[^2]: Saez, E., Slemrod, J., & Giertz, S. H. (2012). The Elasticity of Taxable Income with Respect to Marginal Tax Rates: A Critical Review. Journal of Economic Literature, 50(1), 3-50.
 
-[^3]:  Feldstein, M., Behavioural Responses to Taxation: Lessons from the Tax Reform Act of 1986, American Economic Review, 1995\.
+[^3]: Feldstein, M., Behavioural Responses to Taxation: Lessons from the Tax Reform Act of 1986, American Economic Review, 1995\.
 
-[^4]:  Agersnap, Ole, and Owen Zidar (2021). "The Tax Elasticity of Capital Gains and Revenue-Maximizing Rates." American Economic Review: Insights, vol. 3, no. 4, pp. 399–416.
+[^4]: Agersnap, Ole, and Owen Zidar (2021). "The Tax Elasticity of Capital Gains and Revenue-Maximizing Rates." American Economic Review: Insights, vol. 3, no. 4, pp. 399–416.

From c827ca9fb3c96abbe6fc77554524de1a71b7f2b5 Mon Sep 17 00:00:00 2001
From: Vahid Ahmadi <va.vahidahmadi@gmail.com>
Date: Mon, 11 Nov 2024 00:30:26 +0100
Subject: [PATCH 3/5] applying Max's comments

---
 .../articles/behavioural-response-post.md     | 78 ++++++++++++++-----
 src/posts/posts.json                          |  2 +-
 2 files changed, 58 insertions(+), 22 deletions(-)

diff --git a/src/posts/articles/behavioural-response-post.md b/src/posts/articles/behavioural-response-post.md
index 79cba2bdc..a06305f21 100644
--- a/src/posts/articles/behavioural-response-post.md
+++ b/src/posts/articles/behavioural-response-post.md
@@ -1,50 +1,86 @@
-## Introduction
+Public policies change incentives and behaviours. When governments introduce or modify policies, individuals respond by adjusting their decisions. Workers may change their work hours,[^1] investors might shift when they realise gains,[^2] and businesses often adapt their practices in response.[^3] The static analysis fails to capture how individuals adjust their economic decisions when facing new incentives.   
+This report presents how PolicyEngine currently models three key behavioural responses to policy changes :
 
-Public policies change incentives and behaviours. When governments introduce or modify policies, individuals respond by adjusting their decisions. Workers may change their work hours,[^1] investors might shift when they realise gains,[^2] and businesses often adapt their practices in response.[^3] The static analysis fails to capture how individuals adjust their economic decisions when facing new incentives. This report presents how PolicyEngine currently models three key behavioural elasticities: income, substitution, and capital gains responses to policy changes to capture how individuals adjust their economic decisions in response to policy changes.
+1. Income effects on labour supply  
+2. Substitution effects on labour supply  
+3. Capital gains tax responses
 
-Elasticities measure these behavioural responses to policy changes. An elasticity quantifies how much behaviour changes in response to a policy change \- higher elasticities indicate stronger behavioural responses, while lower ones suggest more limited adjustments. PolicyEngine currently incorporates three key behavioural responses in its analysis: income elasticity (work changes from overall income shifts), substitution elasticity (work changes from marginal reward shifts), and capital gains elasticity (investment timing responses to tax changes).
+To model these responses, we apply *elasticities,* which quantify the magnitude of the response: larger elasticities indicate stronger behavioural responses, while smaller ones suggest more limited adjustments. PolicyEngine empowers users to set their own elasticities, while we apply our best guesses in our reports. This review describes these responses and our selected elasticities. 
 
 ## Labour supply
 
-PolicyEngine models how individuals respond to work incentives by changing their employment income using two standard elasticities- the income and substitution elasticities.
+PolicyEngine models how individuals adjust their earnings through income and substitution effects. For example, one might work less if they have more income (they purchase leisure with income effects), or if they take home less for an additional hour of work (they substitute leisure over consumption at the margin).
 
 ### The income elasticity
 
-When people become richer, they might choose to work less. The income elasticity measures this behaviour \- how much work changes when total income changes. This matters for policies like broad tax changes or new benefits that affect how much money people have overall. Without considering this response, policy analysis might get work patterns wrong after income changes. Following the [Congressional Budget Office (CBO)](https://www.cbo.gov/sites/default/files/112th-congress-2011-2012/reports/43674-laborsupplyfiscalpolicy.pdf#page=4), PolicyEngine uses an income elasticity of \-0.05 for the UK as a default elasticity, meaning a 10% rise in income leads to a small 0.5% drop in work.
+When people become richer, they might choose to work less. The income elasticity measures this behaviour \- how much work changes when net income changes after taxes and transfers.
+
+By default, PolicyEngine applies the [Congressional Budget Office (CBO)](https://www.cbo.gov/sites/default/files/112th-congress-2011-2012/reports/43674-laborsupplyfiscalpolicy.pdf#page=4)’s central estimate of a **\-0.05** income elasticity, meaning a 10% rise in net income leads to a 0.5% drop in work. The [Office of Budget Responsibility](https://obr.uk/docs/dlm_uploads/NICS-Cut-Impact-on-Labour-Supply-Note.pdf#page=7) also applies a \-0.05 income elasticity for single mothers and men who are not single fathers, while applying elasticities between \-0.037 and \-0.185 for married or cohabitating women and lone parents, depending on the age of the youngest child.
 
 ### The substitution elasticity
 
-People work partly based on how much they keep from each extra hour of work. The substitution elasticity measures how work changes when this reward changes. For example, higher tax rates mean keeping less from each additional hour, which might lead to less overtime or part-time work. This response is key for analysing tax brackets or benefits that reduce earnings. Following the [Congressional Budget Office (CBO)](https://www.cbo.gov/sites/default/files/112th-congress-2011-2012/reports/43674-laborsupplyfiscalpolicy.pdf#page=4), PolicyEngine uses a substitution elasticity of 0.25 as a default elasticity, meaning people work about 2.5% less when they keep 10% less from each extra hour.
+People work partly based on how much they keep from each extra hour of work. The substitution elasticity measures how work changes when this reward changes. For example, higher tax rates or steeper benefit phase-outs mean keeping less from each additional hour, which might lead to less overtime or part-time work. By default, PolicyEngine applies the [Congressional Budget Office (CBO)](https://www.cbo.gov/sites/default/files/112th-congress-2011-2012/reports/43674-laborsupplyfiscalpolicy.pdf#page=4)’s central elasticity averaged over primary earners, which is **0.25**, meaning people work 2.5% less when they keep 10% less from each extra hour after taxes and transfers.  
+Unlike the [OBR](https://obr.uk/docs/dlm_uploads/NICS-Cut-Impact-on-Labour-Supply-Note.pdf), which separately models extensive margins (participation) and intensive margins (hours worked), PolicyEngine follows CBO in using single elasticities that combine both responses. The OBR's intensive margin elasticities vary by demographic group, ranging from 0.094 to 0.439. PolicyEngine plans to add separate extensive margin responses in future versions, which will require estimating potential wages for individuals currently out of the labour force.
+
+### An illustrative example
+
+To understand how these elasticities work, consider a worker earning £30,000 per year. This worker currently faces a marginal tax rate of [28%](https://policyengine.org/uk/household?focus=householdOutput.netIncome&household=49381) (combining income tax and National Insurance) and takes home [£24,961](https://policyengine.org/uk/household?focus=householdOutput.netIncome&household=49381) after taxes and transfers. At the current tax rates, this worker's net-of-tax wage rate is 72% of her gross wage. Now imagine a new policy that increases basic income tax by 1p (from 20% to 21%). In this case, PolicyEngine calculates that this new policy decreases her net income by [£175](https://policyengine.org/uk/household?focus=householdOutput.netIncome&reform=53461&region=uk&timePeriod=2025&baseline=1&household=49381).
+
+For this worker earning £14.42 per hour (£30,000/2,080 hours), the take-home pay per extra hour drops from £10.38 to £10.21 under the new policy – a 1.6% decrease. Using PolicyEngine's central estimates, we calculate two effects:
+
+1. Substitution effect: Workers reduce hours by 0.25% for each 1% decrease in wages. A 1.6% wage decrease leads to a 0.4% reduction in hours (1.6% × 0.25).  
+2. Income effect: Workers increase hours by 0.05% for each 1% drop in income. The £175 decrease represents a 0.7% drop in take-home pay (£175/£24,961), leading to a 0.035% increase in hours (0.7% × \-0.05).
+
+The net effect combines these responses: 0.4% decrease minus 0.035% increase equals a 0.365% decrease. Given the baseline of £30,000 earnings and 2,080 hours, this translates to a predicted 7 fewer work hours and £109 less earnings per year.
 
 ## Capital gains elasticity
 
-When tax rates on investment gains change, people adjust when they sell their investments[^4]. Capital gains elasticity measures this effect. Unlike work hours, which are often fixed, people can usually choose when to sell investments. When capital gains tax rates go up, many wait to sell until rates are lower again. This response strongly affects how much money tax changes raise. PolicyEngine uses a capital gains elasticity of \-0.7 as a default elasticity, reflecting that investment timing is quite sensitive to tax rates.
+When tax rates on investment gains change, people adjust when they sell their investments,[^4] how much they invest, and how they structure their investments. The capital gains elasticity measures this effect. While conceptually similar to the substitution effect for labour supply (measured with respect to the net-of-tax marginal wage), economists generally represent the capital gains elasticity as the percent change in capital gains with respect to a 1p change in the capital gains tax rate. It therefore has the opposite sign of substitution elasticity.
+
+We have not identified any UK-specific studies on capital gains elasticities, so PolicyEngine relies on US research evidence. US studies distinguish between permanent elasticities (long-term responses to sustained tax changes) and transitory elasticities (temporary responses as people time their sales around tax changes). Dowd and McClelland (2019)[^5] found an overall elasticity of \-0.79 examining US federal and state tax returns from 1999-2008. Earlier work by Auten and Clotfelter (1982)[^6] found a permanent elasticity of \-0.37 and a higher transitory elasticity of \-1.05.  
+PolicyEngine uses an elasticity of **\-0.7** as a default amount for the UK context, reflecting our belief that UK capital gains respond less to policy change than US capital gains do. Several factors drive this difference: the US has more tax-advantaged investment vehicles, more generous real estate tax treatment,[^7] a more active trading culture,[^8][^9] and the ability to relocate investments across state tax jurisdictions to minimise combined state and federal liabilities.[^10] The UK's unified tax system and fewer tax-advantaged accounts suggest a smaller response to tax changes. Users can adjust this default elasticity in their analysis.
 
 ## How PolicyEngine models behavioural responses
 
-By default, PolicyEngine’s model assumes no behavioural responses. PolicyEngine's model adds behavioural responses to its tax-benefit calculations. For each simulated reform, the model first computes the effects of policy changes on income and tax rates. Then, it estimates three types of behavioural changes: how total income changes affect work, how marginal tax changes affect work hours, and how tax rates influence investment timing. By comparing scenarios with and without these behavioural responses, the model provides more accurate predictions of how policies affect people and government budgets.
+By default, the PolicyEngine web app assumes no behavioural responses. When users specify nonzero elasticities, it adds behavioural responses to its tax-benefit calculations. For each simulated reform, the model first computes the effects of policy changes on income and tax rates. Then, it estimates three behavioural changes: how total income changes affect work, how marginal tax changes affect work hours, and how tax rates influence investment timing. Because each person’s earnings can affect household net income differently, we calculate marginal tax rates with respect to each of the top three earners, and apply each of their labour supply responses, separately. Finally, we recalculate taxes and benefits following the earnings and capital gains change.
 
 ## Comparing static and dynamic analysis
 
-This section shows how incorporating behavioural responses affects policy analysis. By comparing estimates with and without behavioural responses, we illustrate the importance of accounting for how individuals and businesses adapt their economic decisions in response to policy changes.
+Here we demonstrate how incorporating behavioural responses affects policy analysis by examining a tax reform proposed by the UK government in October 2024: change to Capital Gains Tax. For a detailed analysis of this and other reforms proposed in the Autumn Budget, see [PolicyEngine's reform impact analysis](https://policyengine.org/uk/research/autumn-budget-2024-policy-choices). 
 
-To demonstrate this comparison, we examine two tax reforms proposed by the UK government in October 2024: changes to Capital Gains Tax and employer National Insurance contributions. For a detailed analysis of these and other reforms proposed in the Autumn Budget, see [PolicyEngine's reform impact analysis](https://policyengine.org/uk/research/autumn-budget-2024-policy-choices).
+In estimating the impacts of this reform, we model how individuals with capital gains respond to changes in their marginal tax rate. The table below compares the five-year revenue impacts under both static and dynamic scenarios.
 
-In estimating the impacts of these reforms, we model how individuals with capital gains respond to changes in their marginal tax rate and how employers respond to changes in their tax liability by adjusting employee wages. The table below compares the five-year revenue impacts under both static and dynamic scenarios.
-
-| Reform                     | Static revenue impact | Dynamic revenue impact | Relative change |
-| :------------------------- | :-------------------- | :--------------------- | :-------------- |
-| Levy employer pension NICs | 90.3                  | 66.6                   | \-26%           |
-| Raise CGT to 24%           | 21.5                  | 10.1                   | \-53%           |
+| Reform | Static revenue impact	 | Dynamic revenue impact	 | Relative change |
+| :---- | :---- | :---- | :---- |
+| Basic rate to 18% Higher/additional rate to 24%	 | 21.5 | 10.1 | \-53% |
 
 ## Conclusion
 
-In this report, we present how PolicyEngine models behavioural responses through income, substitution, and capital gains elasticities to capture how individuals adjust their economic decisions to policy changes. Using recent UK tax reforms as examples, we demonstrate how incorporating these behavioural responses changes government revenue compared to static analysis.
+In this report, we present how PolicyEngine models three behavioural responses:
+
+1. **Income effect for labour supply: \-0.05 elasticity** (a 10% increase to net income reduces work hours by 0.5%)  
+2. **Substitution effect for labour supply: 0.25 elasticity** (a 10% increase to the net marginal wage increases work hours by 2.5%)  
+3. **Capital gains response: \-0.7 elasticity** (a 10% increase in the marginal tax rate with respect to capital gains reduces capital gains by 7%)
+
+While this report focuses on these three core elasticities, PolicyEngine is expanding its behavioural modelling capabilities. For instance, we developed responses to [employer National Insurance contributions](https://policyengine.org/uk/research/autumn-budget-24-employer-ni), indicating the extent to which employers pass on the burden to lower wages. Using the CGT reform as an example demonstrates the importance of these behavioural responses. PolicyEngine's flexibility allows users to adjust behavioural response assumptions such as labour elasticities and capital gains elasticity to analyse the impact of public policies.  
+
+
+[^1]:  Chetty, R., Guren, A., Manoli, D., & Weber, A. (2011). Are Micro and Macro Labor Supply Elasticities Consistent? A Review of Evidence on the Intensive and Extensive Margins. American Economic Review, 101(3), 471–475.
+
+[^2]:  Saez, E., Slemrod, J., & Giertz, S. H. (2012). The Elasticity of Taxable Income with Respect to Marginal Tax Rates: A Critical Review. Journal of Economic Literature, 50(1), 3-50.
+
+[^3]:  Feldstein, M., Behavioural Responses to Taxation: Lessons from the Tax Reform Act of 1986, American Economic Review, 1995\.
+
+[^4]:  Burman, Leonard E., and William C. Randolph. "Measuring permanent responses to capital-gains tax changes in panel data." The American Economic Review (1994): 794-809.
+
+[^5]:  Dowd, Tim, and Robert McClelland. 2019\. "The Bunching of Capital Gains Realizations." National Tax Journal 72(2): 323-358.
+
+[^6]:  Auten, Gerald, and Charles Clotfelter. 1982\. "Permanent versus Transitory Tax Effects and the Realization of Capital Gains." Quarterly Journal of Economics 97(4): 613-632.
 
-[^1]: Chetty, R., Guren, A., Manoli, D., & Weber, A. (2011). Are Micro and Macro Labor Supply Elasticities Consistent? A Review of Evidence on the Intensive and Extensive Margins. American Economic Review, 101(3), 471–475.
+[^7]:  U.S. Congress, House Committee on Financial Services, *The Future of Housing in America: A Comparison of the United Kingdom and United States Models of Affordable Housing*, hearing, 114th Congress, 2nd session, May 12, 2016\.
 
-[^2]: Saez, E., Slemrod, J., & Giertz, S. H. (2012). The Elasticity of Taxable Income with Respect to Marginal Tax Rates: A Critical Review. Journal of Economic Literature, 50(1), 3-50.
+[^8]:  Odean, T. (1999). Do investors trade too much? *American Economic Review*, 89(5), 1279-1298.
 
-[^3]: Feldstein, M., Behavioural Responses to Taxation: Lessons from the Tax Reform Act of 1986, American Economic Review, 1995\.
+[^9]:  Financial Expert. (n.d.). [A summary of the differences between UK and US investors](https://www.financial-expert.co.uk/differences-between-uk-and-us-investors/).
 
-[^4]: Agersnap, Ole, and Owen Zidar (2021). "The Tax Elasticity of Capital Gains and Revenue-Maximizing Rates." American Economic Review: Insights, vol. 3, no. 4, pp. 399–416.
+[^10]:  [Tax Policy Center (2023)](https://taxpolicycenter.org/briefing-book/how-do-us-taxes-compare-internationally)
diff --git a/src/posts/posts.json b/src/posts/posts.json
index faaeeba22..005084ed1 100644
--- a/src/posts/posts.json
+++ b/src/posts/posts.json
@@ -848,7 +848,7 @@
   {
     "title": "How PolicyEngine UK models behavioural responses",
     "description": "PolicyEngine has enhanced its modelling with behavioural responses, including income, substitution and capital gains elasticities.",
-    "date": "2024-11-05 15:00:00",
+    "date": "2024-11-12 15:00:00",
     "tags": ["uk", "policy", "elasticity", "featured"],
     "authors": ["vahid-ahmadi"],
     "filename": "behavioural-response-post.md",

From 79c0915ff2b9f167c0a1cdc00091e8692359f684 Mon Sep 17 00:00:00 2001
From: Vahid Ahmadi <va.vahidahmadi@gmail.com>
Date: Mon, 11 Nov 2024 00:33:23 +0100
Subject: [PATCH 4/5] style fixed

---
 .../articles/behavioural-response-post.md     | 45 +++++++++----------
 src/posts/posts.json                          |  2 +-
 2 files changed, 23 insertions(+), 24 deletions(-)

diff --git a/src/posts/articles/behavioural-response-post.md b/src/posts/articles/behavioural-response-post.md
index a06305f21..1a9c551b0 100644
--- a/src/posts/articles/behavioural-response-post.md
+++ b/src/posts/articles/behavioural-response-post.md
@@ -1,11 +1,11 @@
-Public policies change incentives and behaviours. When governments introduce or modify policies, individuals respond by adjusting their decisions. Workers may change their work hours,[^1] investors might shift when they realise gains,[^2] and businesses often adapt their practices in response.[^3] The static analysis fails to capture how individuals adjust their economic decisions when facing new incentives.   
+Public policies change incentives and behaviours. When governments introduce or modify policies, individuals respond by adjusting their decisions. Workers may change their work hours,[^1] investors might shift when they realise gains,[^2] and businesses often adapt their practices in response.[^3] The static analysis fails to capture how individuals adjust their economic decisions when facing new incentives.  
 This report presents how PolicyEngine currently models three key behavioural responses to policy changes :
 
-1. Income effects on labour supply  
-2. Substitution effects on labour supply  
+1. Income effects on labour supply
+2. Substitution effects on labour supply
 3. Capital gains tax responses
 
-To model these responses, we apply *elasticities,* which quantify the magnitude of the response: larger elasticities indicate stronger behavioural responses, while smaller ones suggest more limited adjustments. PolicyEngine empowers users to set their own elasticities, while we apply our best guesses in our reports. This review describes these responses and our selected elasticities. 
+To model these responses, we apply _elasticities,_ which quantify the magnitude of the response: larger elasticities indicate stronger behavioural responses, while smaller ones suggest more limited adjustments. PolicyEngine empowers users to set their own elasticities, while we apply our best guesses in our reports. This review describes these responses and our selected elasticities.
 
 ## Labour supply
 
@@ -28,7 +28,7 @@ To understand how these elasticities work, consider a worker earning £30,000 pe
 
 For this worker earning £14.42 per hour (£30,000/2,080 hours), the take-home pay per extra hour drops from £10.38 to £10.21 under the new policy – a 1.6% decrease. Using PolicyEngine's central estimates, we calculate two effects:
 
-1. Substitution effect: Workers reduce hours by 0.25% for each 1% decrease in wages. A 1.6% wage decrease leads to a 0.4% reduction in hours (1.6% × 0.25).  
+1. Substitution effect: Workers reduce hours by 0.25% for each 1% decrease in wages. A 1.6% wage decrease leads to a 0.4% reduction in hours (1.6% × 0.25).
 2. Income effect: Workers increase hours by 0.05% for each 1% drop in income. The £175 decrease represents a 0.7% drop in take-home pay (£175/£24,961), leading to a 0.035% increase in hours (0.7% × \-0.05).
 
 The net effect combines these responses: 0.4% decrease minus 0.035% increase equals a 0.365% decrease. Given the baseline of £30,000 earnings and 2,080 hours, this translates to a predicted 7 fewer work hours and £109 less earnings per year.
@@ -46,41 +46,40 @@ By default, the PolicyEngine web app assumes no behavioural responses. When user
 
 ## Comparing static and dynamic analysis
 
-Here we demonstrate how incorporating behavioural responses affects policy analysis by examining a tax reform proposed by the UK government in October 2024: change to Capital Gains Tax. For a detailed analysis of this and other reforms proposed in the Autumn Budget, see [PolicyEngine's reform impact analysis](https://policyengine.org/uk/research/autumn-budget-2024-policy-choices). 
+Here we demonstrate how incorporating behavioural responses affects policy analysis by examining a tax reform proposed by the UK government in October 2024: change to Capital Gains Tax. For a detailed analysis of this and other reforms proposed in the Autumn Budget, see [PolicyEngine's reform impact analysis](https://policyengine.org/uk/research/autumn-budget-2024-policy-choices).
 
 In estimating the impacts of this reform, we model how individuals with capital gains respond to changes in their marginal tax rate. The table below compares the five-year revenue impacts under both static and dynamic scenarios.
 
-| Reform | Static revenue impact	 | Dynamic revenue impact	 | Relative change |
-| :---- | :---- | :---- | :---- |
-| Basic rate to 18% Higher/additional rate to 24%	 | 21.5 | 10.1 | \-53% |
+| Reform                                          | Static revenue impact | Dynamic revenue impact | Relative change |
+| :---------------------------------------------- | :-------------------- | :--------------------- | :-------------- |
+| Basic rate to 18% Higher/additional rate to 24% | 21.5                  | 10.1                   | \-53%           |
 
 ## Conclusion
 
 In this report, we present how PolicyEngine models three behavioural responses:
 
-1. **Income effect for labour supply: \-0.05 elasticity** (a 10% increase to net income reduces work hours by 0.5%)  
-2. **Substitution effect for labour supply: 0.25 elasticity** (a 10% increase to the net marginal wage increases work hours by 2.5%)  
+1. **Income effect for labour supply: \-0.05 elasticity** (a 10% increase to net income reduces work hours by 0.5%)
+2. **Substitution effect for labour supply: 0.25 elasticity** (a 10% increase to the net marginal wage increases work hours by 2.5%)
 3. **Capital gains response: \-0.7 elasticity** (a 10% increase in the marginal tax rate with respect to capital gains reduces capital gains by 7%)
 
-While this report focuses on these three core elasticities, PolicyEngine is expanding its behavioural modelling capabilities. For instance, we developed responses to [employer National Insurance contributions](https://policyengine.org/uk/research/autumn-budget-24-employer-ni), indicating the extent to which employers pass on the burden to lower wages. Using the CGT reform as an example demonstrates the importance of these behavioural responses. PolicyEngine's flexibility allows users to adjust behavioural response assumptions such as labour elasticities and capital gains elasticity to analyse the impact of public policies.  
+While this report focuses on these three core elasticities, PolicyEngine is expanding its behavioural modelling capabilities. For instance, we developed responses to [employer National Insurance contributions](https://policyengine.org/uk/research/autumn-budget-24-employer-ni), indicating the extent to which employers pass on the burden to lower wages. Using the CGT reform as an example demonstrates the importance of these behavioural responses. PolicyEngine's flexibility allows users to adjust behavioural response assumptions such as labour elasticities and capital gains elasticity to analyse the impact of public policies.
 
+[^1]: Chetty, R., Guren, A., Manoli, D., & Weber, A. (2011). Are Micro and Macro Labor Supply Elasticities Consistent? A Review of Evidence on the Intensive and Extensive Margins. American Economic Review, 101(3), 471–475.
 
-[^1]:  Chetty, R., Guren, A., Manoli, D., & Weber, A. (2011). Are Micro and Macro Labor Supply Elasticities Consistent? A Review of Evidence on the Intensive and Extensive Margins. American Economic Review, 101(3), 471–475.
+[^2]: Saez, E., Slemrod, J., & Giertz, S. H. (2012). The Elasticity of Taxable Income with Respect to Marginal Tax Rates: A Critical Review. Journal of Economic Literature, 50(1), 3-50.
 
-[^2]:  Saez, E., Slemrod, J., & Giertz, S. H. (2012). The Elasticity of Taxable Income with Respect to Marginal Tax Rates: A Critical Review. Journal of Economic Literature, 50(1), 3-50.
+[^3]: Feldstein, M., Behavioural Responses to Taxation: Lessons from the Tax Reform Act of 1986, American Economic Review, 1995\.
 
-[^3]:  Feldstein, M., Behavioural Responses to Taxation: Lessons from the Tax Reform Act of 1986, American Economic Review, 1995\.
+[^4]: Burman, Leonard E., and William C. Randolph. "Measuring permanent responses to capital-gains tax changes in panel data." The American Economic Review (1994): 794-809.
 
-[^4]:  Burman, Leonard E., and William C. Randolph. "Measuring permanent responses to capital-gains tax changes in panel data." The American Economic Review (1994): 794-809.
+[^5]: Dowd, Tim, and Robert McClelland. 2019\. "The Bunching of Capital Gains Realizations." National Tax Journal 72(2): 323-358.
 
-[^5]:  Dowd, Tim, and Robert McClelland. 2019\. "The Bunching of Capital Gains Realizations." National Tax Journal 72(2): 323-358.
+[^6]: Auten, Gerald, and Charles Clotfelter. 1982\. "Permanent versus Transitory Tax Effects and the Realization of Capital Gains." Quarterly Journal of Economics 97(4): 613-632.
 
-[^6]:  Auten, Gerald, and Charles Clotfelter. 1982\. "Permanent versus Transitory Tax Effects and the Realization of Capital Gains." Quarterly Journal of Economics 97(4): 613-632.
+[^7]: U.S. Congress, House Committee on Financial Services, _The Future of Housing in America: A Comparison of the United Kingdom and United States Models of Affordable Housing_, hearing, 114th Congress, 2nd session, May 12, 2016\.
 
-[^7]:  U.S. Congress, House Committee on Financial Services, *The Future of Housing in America: A Comparison of the United Kingdom and United States Models of Affordable Housing*, hearing, 114th Congress, 2nd session, May 12, 2016\.
+[^8]: Odean, T. (1999). Do investors trade too much? _American Economic Review_, 89(5), 1279-1298.
 
-[^8]:  Odean, T. (1999). Do investors trade too much? *American Economic Review*, 89(5), 1279-1298.
+[^9]: Financial Expert. (n.d.). [A summary of the differences between UK and US investors](https://www.financial-expert.co.uk/differences-between-uk-and-us-investors/).
 
-[^9]:  Financial Expert. (n.d.). [A summary of the differences between UK and US investors](https://www.financial-expert.co.uk/differences-between-uk-and-us-investors/).
-
-[^10]:  [Tax Policy Center (2023)](https://taxpolicycenter.org/briefing-book/how-do-us-taxes-compare-internationally)
+[^10]: [Tax Policy Center (2023)](https://taxpolicycenter.org/briefing-book/how-do-us-taxes-compare-internationally)
diff --git a/src/posts/posts.json b/src/posts/posts.json
index 005084ed1..ae5bf80e6 100644
--- a/src/posts/posts.json
+++ b/src/posts/posts.json
@@ -849,7 +849,7 @@
     "title": "How PolicyEngine UK models behavioural responses",
     "description": "PolicyEngine has enhanced its modelling with behavioural responses, including income, substitution and capital gains elasticities.",
     "date": "2024-11-12 15:00:00",
-    "tags": ["uk", "policy", "elasticity", "featured"],
+    "tags": ["uk", "policy", "behavioural-responses", "featured"],
     "authors": ["vahid-ahmadi"],
     "filename": "behavioural-response-post.md",
     "image": "behavorial-post.jpg"

From 401f2f8c254d9717da2f66730c928dd73a34c12d Mon Sep 17 00:00:00 2001
From: Vahid Ahmadi <va.vahidahmadi@gmail.com>
Date: Mon, 11 Nov 2024 10:34:52 +0100
Subject: [PATCH 5/5] rename files

---
 ...ehavorial-post.jpg => behavioural-responses.jpg} | Bin
 ...al-response-post.md => behavioural-responses.md} |   0
 src/posts/posts.json                                |   4 ++--
 3 files changed, 2 insertions(+), 2 deletions(-)
 rename src/images/posts/{behavorial-post.jpg => behavioural-responses.jpg} (100%)
 rename src/posts/articles/{behavioural-response-post.md => behavioural-responses.md} (100%)

diff --git a/src/images/posts/behavorial-post.jpg b/src/images/posts/behavioural-responses.jpg
similarity index 100%
rename from src/images/posts/behavorial-post.jpg
rename to src/images/posts/behavioural-responses.jpg
diff --git a/src/posts/articles/behavioural-response-post.md b/src/posts/articles/behavioural-responses.md
similarity index 100%
rename from src/posts/articles/behavioural-response-post.md
rename to src/posts/articles/behavioural-responses.md
diff --git a/src/posts/posts.json b/src/posts/posts.json
index ae5bf80e6..f3fb59271 100644
--- a/src/posts/posts.json
+++ b/src/posts/posts.json
@@ -851,8 +851,8 @@
     "date": "2024-11-12 15:00:00",
     "tags": ["uk", "policy", "behavioural-responses", "featured"],
     "authors": ["vahid-ahmadi"],
-    "filename": "behavioural-response-post.md",
-    "image": "behavorial-post.jpg"
+    "filename": "behavioural-responses.md",
+    "image": "behavioural-responses.jpg"
   },
   {
     "title": "Benefits uprating 2025/26",