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border-bottom:1px solid #aaaaaa">  </td></tr> <tr> <td height="40px" colspan="20" style="background:#C4D2DF; padding: 2px 2px 2px 2px; border-right:1px solid #aaaaaa; border-bottom:1px solid #aaaaaa"> <table align="right" border="0" cellpadding="2" cellspacing="0"> <tbody><tr> <td><div class="plainlinks plainlinksneverexpand" style="position:relative; width:17px; height:17px; overflow:hidden; text-decoration:none;"><div style="position:absolute; font-size:17px; overflow:hidden; line-height:17px; letter-spacing:17px;"><a rel="nofollow" class="external text" href="https://en.citizendium.org/wiki/index.php?title=Fiscal_policy/Tutorials&printable=yes"><span title="https://en.citizendium.org/wiki/index.php?title=Fiscal_policy/Tutorials&printable=yes" style="text-decoration:none;">   </span></a></div><a href="/wiki/File:Print_button.png" class="image" title="https://en.citizendium.org/wiki/index.php?title=Fiscal_policy/Tutorials&printable=yes"><img alt="https://en.citizendium.org/wiki/index.php?title=Fiscal_policy/Tutorials&printable=yes" src="/wiki/images/thumb/0/07/Print_button.png/17px-Print_button.png" decoding="async" width="17" height="17" srcset="/wiki/images/thumb/0/07/Print_button.png/26px-Print_button.png 1.5x, /wiki/images/thumb/0/07/Print_button.png/34px-Print_button.png 2x" data-file-width="45" data-file-height="45" /></a></div> </td></tr></tbody></table><i>Tutorials relating to the topic of <a href="/wiki/Fiscal_policy" title="Fiscal policy">Fiscal policy</a></i>. </td></tr></tbody></table></div> <div id="toc" class="toc" role="navigation" aria-labelledby="mw-toc-heading"><input type="checkbox" role="button" id="toctogglecheckbox" class="toctogglecheckbox" style="display:none" /><div class="toctitle" lang="en" dir="ltr"><h2 id="mw-toc-heading">Contents</h2><span class="toctogglespan"><label class="toctogglelabel" for="toctogglecheckbox"></label></span></div> <ul> <li class="toclevel-1 tocsection-1"><a href="#Fiscal_stability"><span class="tocnumber">1</span> <span class="toctext">Fiscal stability</span></a> <ul> <li class="toclevel-2 tocsection-2"><a href="#Overview"><span class="tocnumber">1.1</span> <span class="toctext">Overview</span></a></li> <li class="toclevel-2 tocsection-3"><a href="#Sustainability_and_stability"><span class="tocnumber">1.2</span> <span class="toctext">Sustainability and stability</span></a> <ul> <li class="toclevel-3 tocsection-4"><a href="#Sustainability"><span class="tocnumber">1.2.1</span> <span class="toctext">Sustainability</span></a></li> <li class="toclevel-3 tocsection-5"><a href="#"Structural"_deficits"><span class="tocnumber">1.2.2</span> <span class="toctext">"Structural" deficits</span></a></li> <li class="toclevel-3 tocsection-6"><a href="#Fiscal_instability"><span class="tocnumber">1.2.3</span> <span class="toctext">Fiscal instability</span></a></li> </ul> </li> </ul> </li> <li class="toclevel-1 tocsection-7"><a href="#The_fiscal_dilemma"><span class="tocnumber">2</span> <span class="toctext">The fiscal dilemma</span></a></li> <li class="toclevel-1 tocsection-8"><a href="#The_debt_trap_identity"><span class="tocnumber">3</span> <span class="toctext">The debt trap identity</span></a></li> <li class="toclevel-1 tocsection-9"><a href="#Notes_and_references"><span class="tocnumber">4</span> <span class="toctext">Notes and references</span></a></li> </ul> </div> <h2><span class="mw-headline" id="Fiscal_stability">Fiscal stability</span></h2> <h4><span class="mw-headline" id="Overview">Overview</span></h4> <p>The concept of <a href="/wiki/Fiscal_sustainability" title="Fiscal sustainability">fiscal sustainability</a> is often used in discussing <a href="/wiki/Fiscal_policy" title="Fiscal policy">fiscal policy</a> but it is absence is not directly observable. <a href="/wiki/Fiscal_instability" title="Fiscal instability">Fiscal instability</a>, on the other hand, can be observed from the conduct of the <a href="/wiki/CDS" title="CDS">CDS</a> and <a href="/wiki/Bond" class="mw-redirect" title="Bond">bond</a> markets. It is possible, moreover, that a fiscal stance which might otherwise be considered to be sustainable, may develop fiscal instability because of the development of <a href="/wiki/Debt_intolerance" title="Debt intolerance">debt intolerance</a> toward the government in question that had arisen from <a href="/wiki/Herding_(banking)" title="Herding (banking)">herding</a> behaviour in the bond market. Thus the avoidance of fiscal instability would appear to be the more pressing - and possibly more demanding - policy objective. </p> <h3><span class="mw-headline" id="Sustainability_and_stability">Sustainability and stability</span></h3> <h4><span class="mw-headline" id="Sustainability">Sustainability</span></h4> <p>If the annual interest payable on a government's debt rise faster than the national income, the point will eventually be reached at which they could would exceed the revenue that could be raised by taxation. The <a href="/wiki/Fiscal_policy/Tutorials#The_debt_trap_identity" title="Fiscal policy/Tutorials">debt trap identity</a> establishes that the budget surplus (or reduced deficit) needed to avoid an increase in the ratio of debt to GDP depends upon the level of that ratio and the difference between the interest rate payable on the debt and the growth rate of nominal GDP. </p> <h4><span id=".22Structural.22_deficits"></span><span class="mw-headline" id=""Structural"_deficits">"Structural" deficits</span></h4> <p>In discussions of the sustainability of the budget deficit during a <a href="/wiki/Recession" class="mw-redirect" title="Recession">recession</a>, an arbitrary distinction is often drawn between what are termed its "cyclical" and "structural" components. The cyclical component is defined for that purpose as that part of the budget deficit that is attributable to a temporary departure of national output from its trend, and which ceases when trend output growth resumes - and the structural component is defined as the remainder. The distinction has the merit of isolating that part of the budget deficit that is relevant to the question of sustainability. However, a reliable estimate of the size of a structural deficit is not possible until some time after the recession in question is over. It usually differs from the country's pre-crisis deficit as a result of loss of tax revenues from companies that fail during the crisis. Its isolation during a recession depends upon forecasts of unknowns, including the future trends of output and prices. Determination of the future trend of output depends, in turn upon estimates of the success of the investments corresponding to that part the deficit that complies with the <a href="/wiki/Golden_Rule_(finance)" title="Golden Rule (finance)">Golden Rule</a>. </p> <h4><span class="mw-headline" id="Fiscal_instability">Fiscal instability</span></h4> <p>An increase in the <a href="/wiki/Risk_premium" title="Risk premium">risk premium</a> that the bond market applies to a government's borrowing may increase the cost of its borrowing to an extent that increases the market's perception of its riskiness, in response to which the bond market may apply a further increase in its risk premium. (An expectation of a reduction in economic growth could also trigger such a response). Repetition of that sequence could eventually force the government to default by placing the cost of a roll-over of maturing debt beyond its capacity to raise the necessary funds. The market's awareness of that possibility may add to the destabilising effect of its actions. Unlike sustainability, fiscal instability is an observable phenomenon. </p> <h2><span class="mw-headline" id="The_fiscal_dilemma">The fiscal dilemma</span></h2> <p>Fiscal policy usually involves a choice between the objective of achieving economic growth and the need to avoid <a href="/wiki/Fiscal_instability" title="Fiscal instability">fiscal instability</a>. That choice arises, in particular, concerning the conduct of fiscal policy during a <a href="/wiki/Recession" class="mw-redirect" title="Recession">recession</a>. The operation of <a href="/wiki/Automatic_stabilisers" title="Automatic stabilisers">automatic stabilisers</a> during a <a href="/wiki/Recession" class="mw-redirect" title="Recession">recession</a> necessarily increases a country's budget deficit - sometimes to the extent of raising fears of fiscal instability. The choice has to be made between increasing the deficit further in order to mitigate the severity of the recession, and reducing it in order to maintain investor confidence. That choice is complicated by the fact that, in the absence of effective action to counter the recession, its increasing severity might in any case raise the budget deficit to an extent that would cause a loss of confidence. The consensus policy choice before 2008 had been to refrain from fiscal expansion and to counter the recession solely by an expansionary <a href="/wiki/Monetary_policy" title="Monetary policy">monetary policy</a>. But in face of the threat posed by the international <a href="/wiki/Crash_of_2008" title="Crash of 2008">crash of 2008</a>, most of the <a href="/wiki/Group_of_Twenty" title="Group of Twenty">G20 governments</a> considered it necessary to use discretionary fiscal policy to augment the diminishing effects of monetary expansion. The recession came to an end in 2009, but in view of the perceived fragility of the recovery, the dilemma remained: whether to implement immediate tax increases or public expenditure cuts, or to postpone such action pending signs of a sufficiently robust recovery (without which the economy's <a href="/wiki/Automatic_stabilisers" title="Automatic stabilisers">automatic stabilisers</a> could ensure a continuing increase in the <a href="/wiki/Budget_deficit" title="Budget deficit">budget deficit</a>. </p><p>A fiscal dilemma also arises at times of economic stability. A <a href="/wiki/Structural_deficit" title="Structural deficit">structural deficit</a> that is devoted entirely to <a href="/wiki/Self-financing_government_investment" title="Self-financing government investment">self-financing government investment</a> is, by definition, sustainable. The use for that purpose of voluntary borrowing rather than compulsory taxation must be presumed to increase growth in view of the <a href="/wiki/Taxation#Aggregate_effects" title="Taxation">growth-reducing effects of taxation</a>. The dilemma is whether - and how far - to sacrifice some growth prospects by limiting deficit-financed investment in order to maintain sufficient unused capacity to borrow in order to mitigate the effects of a <a href="/wiki/Recession" class="mw-redirect" title="Recession">recession</a> or other emergencies. Perceptions of the prospects and severity of such emergencies may be expected to influence the judgement that is made, and an upward revision of those perceptions may be expected to follow a severe recession. </p><p><br /> </p> <h2><span class="mw-headline" id="The_debt_trap_identity">The debt trap identity</span></h2> <p>According to the debt trap identity (proved below), the increase, Δd, in <a href="/wiki/National_debt" class="mw-redirect" title="National debt">national debt</a> in any given year, as a percentage of <a href="/wiki/Gross_Domestic_Product" title="Gross Domestic Product">GDP</a> is given by: </p> <dl><dd><dl><dd><dl><dd><dl><dd><dl><dd><dl><dd>Δd = f + d(r - g)</dd></dl></dd></dl></dd></dl></dd></dl></dd></dl></dd></dl> <p>where d is the amount of the accumulated debt as a percentage of GDP at the beginning of the year, <br /> and f is the <a href="/wiki/Primary_budget_balance" title="Primary budget balance">primary budget deficit (or surplus)</a> for the year (shown with a negative negative sign if a surplus) as a percentage of GDP,<br /> r is the interest rate payable on the debt, <br /> and g is the then current nominal GDP growth rate. </p><p>So that if Δd = 0 </p> <dl><dd><dl><dd><dl><dd><dl><dd><dl><dd><dl><dd><dl><dd>f = -d(r - g)</dd></dl></dd></dl></dd></dl></dd></dl></dd></dl></dd></dl></dd></dl> <p>- which is to say that to avoid an increase in public debt in the course of any year, the budget deficit during that year must not be greater than the opening level of debt multiplied by the difference between the interest rate on the debt and the GDP growth rate in that year (and that means a budget surplus if the interest rate is greater than the growth rate). </p><p>If, for example, r were 5% and g were 2% then a debt of 50% of gdp would require a surplus of 1.5% of GDP, a debt of 100% of GDP would require a surplus of 3% of gdp, and so forth. </p><p>(Proof:- <small> Let D and Y be the levels of public debt and GDP at the beginning of a year; and,<br /> let F be the primary, or discretionary budget deficit (the total deficit excluding interest payments) and,<br /> let r be the annual rate of interest payable on the public debt; <br />and assume that  F, r, and g are all mutually independent. </small></p><p><small>- then the public debt at the end of the year is  D<sub>1</sub> = D + F +Dr; the GDP at the end of the year is   Y<sub>1</sub> = Y(1 + g); <br />and the ratio of public debt to GDP has risen from  D/Y to  (D + F + Dr)/{Y(1 + g); </small></p><p><small>- thus the increase in the ratio of public debt to GDP in the course of a year is: </small></p><small><dl><dd><dl><dd><dl><dd>Δ(D/Y) = (D + F + Dr)/{Y(1 + g)} - D/Y</dd></dl></dd></dl></dd></dl></small><small><p>Let 1/{Y(1;+ g)} = A  andso that AY = 1/(1 + g) ,and  1/AY = 1 + g  <br /> - then:<br /> </p></small><small><dl><dd><dl><dd><dl><dd>Δ(D/Y) = A(D + F + Dr) - D/Y <dl><dd>=  A( D + F + Dr  - D/AY)</dd></dl></dd></dl></dd></dl></dd></dl></small><small><p>- and substituting 1 + g for 1/AY: </p></small><small><dl><dd><dl><dd><dl><dd><dl><dd>=  A( D + F + Dr - D - Dg)</dd></dl></dd></dl></dd></dl></dd></dl></small><small><p>substituting for A: </p></small><small><dl><dd><dl><dd><dl><dd>Δ(D/Y) = {F + D(r - g)}/{Y(1 + g)}</dd></dl></dd></dl></dd></dl></small><small><p>or, approximately:- </p></small><small><dl><dd><dl><dd><dl><dd>Δ(D/Y) = {F + D(r - g)}/Y <dl><dd>= F/Y + (r - g)D/Y</dd></dl></dd></dl></dd></dl></dd></dl></small><small><p>Let  f = F/Y ,and d = D/Y<br /> </p><p>- then                 Δd  =  f + d(r - g) </p><p>where f is the primary budget deficit as a percentage of GDP, and d is public debt as a percentage of GDP) </p></small><p><small></small> </p> <h2><span class="mw-headline" id="Notes_and_references">Notes and references</span></h2> <span style="font-size: 85%;"><div class="reflist" style="list-style-type: decimal;"> </div></span>  </div> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://citizendium.org/wiki/index.php?title=Fiscal_policy/Tutorials&oldid=700560">https://citizendium.org/wiki/index.php?title=Fiscal_policy/Tutorials&oldid=700560</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Special:Categories" title="Special:Categories">Categories</a>: <ul><li><a href="/wiki/Category:Tutorials" title="Category:Tutorials">Tutorials</a></li><li><a href="/wiki/Category:Economics_Tutorials" title="Category:Economics Tutorials">Economics Tutorials</a></li><li><a href="/wiki/Category:Politics_Tutorials" title="Category:Politics Tutorials">Politics Tutorials</a></li><li><a href="/wiki/Category:Subpages" title="Category:Subpages">Subpages</a></li><li><a href="/wiki/Category:Economics_Extra_Subpages" title="Category:Economics Extra Subpages">Economics Extra Subpages</a></li><li><a href="/wiki/Category:Politics_Extra_Subpages" title="Category:Politics Extra Subpages">Politics Extra Subpages</a></li><li><a href="/wiki/Category:All_Content" title="Category:All Content">All Content</a></li><li><a href="/wiki/Category:Economics_Content" title="Category:Economics Content">Economics Content</a></li><li><a href="/wiki/Category:Politics_Content" title="Category:Politics Content">Politics Content</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden categories: <ul><li><a href="/wiki/Category:Economics_tag" title="Category:Economics tag">Economics tag</a></li><li><a href="/wiki/Category:Politics_tag" title="Category:Politics tag">Politics tag</a></li></ul></div></div> </div> </div> <div id="mw-navigation"> <h2>Navigation menu</h2> <div id="mw-head"> <nav id="p-personal" class="vector-menu mw-portlet mw-portlet-personal vector-user-menu-legacy" aria-labelledby="p-personal-label" role="navigation" > <h3 id="p-personal-label" class="vector-menu-heading " > <span class="vector-menu-heading-label">Personal tools</span> </h3> <div class="vector-menu-content"> <ul class="vector-menu-content-list"><li id="pt-login" class="mw-list-item"><a href="/wiki/index.php?title=Special:UserLogin&returnto=Fiscal+policy%2FTutorials" title="To edit pages, [[Special:RequestAccount|get a contributor account]]. 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