"A man writes because he doubts, because he is tormented."

Tuesday, December 19, 2017

Tax Attractiveness Is Not Attractive: A Lesson from Asia-PacificCountries

During the last few months, many analysts were busy scrutinizing the tax cut plan proposed by Donald Trump and his cohorts at Republican Party. While the Wall Streets awaits in excitement, economists are generally wary.

The logic of tax incentive is simple yet deceptive. You as the government sacrifice some revenue from the foregone tax. You hope that the new investments will not only take over your duty (to boost the economy, to reduce the unemployment, etc.) but you will also reap rewards by taxing them in the future eventually.

The problem, however, is that this logic does not always hold in real life. Tax incentive induces aggressive tax planning, which can further distorts the economy and cause negative spillover to other countries (Oxfam, 2016).

Tax cuts also hinders the income redistribution efforts by government, which will widen the inequality. A study by Tax Policy Center, for instance, estimated that 82.8% of the benefit of the tax bill agreed to by House and Senate Republicans would go to the top 1% income. On the other hand, 53.4% of American households would see a tax increase. The costs of tax incentive may be too excessive. An estimation by Center on Budget and Policy Priorities projected that the same Republican tax bill would cost about $2.2 trillion over the first decade.

But what about the benefit? The benefit of tax break is often insignificant (see the latest and detailed study by Bartik 2017). A thorough analysis by Jason Furman and Lawrence Summers on Project Syndicates also highlights the many flaws of the alleged benefits of tax cuts. In one episode of Last Week Tonight, John Oliver even went as far to suggest – using Missouri-Kansas tax war as example – that it is more fiscally responsible to buy some people Ferraris and told them to ride around a bonfire made of burning money. Doing this inanity is 20 million dollar less costly than giving tax incentives, since the benefit of Missouri and Kansas tax break is essentially 0. (His rhetoric was extreme, but he was on point.)

Other studies such as Klemm and van Parys (2009), and Van Parys and James (2010) show that that there is no effect of tax incentives on total investment or economic growth. If there's any benefit, it appears to be modest and may not justify the forgone tax revenue (Chai and Goyal, 2008).

Even entrepreneurs only give tax incentive a lesser consideration, compared to other factors, when they are planning to invest/open a business. This is reinforced by the result of a study by UNIDO (2011). The UNIDO study shows that incentive ranks on the bottom of consideration factors. Incentive is also given lesser importance over time.

In fact, a lot of investors would still invest even if there is no tax incentive. The figures below show how many investors who'd still invest, according to studies in various countries compiled by Sebastian (2013).

Sebastian (2013) further argues that tax incentives do not create much jobs. Column (2) above gives the redundancy ratio, the percentage of investors who would have invested even without the tax incentives. Column (3) shows the percentage of jobs created by these marginal investors. Most of the numbers there above are negative, showing that tax incentives are often useless.

Measuring Tax Incentives Using Tax Attractiveness Index

Rather than measuring the effect of tax incentives to job creation (which requires a more "micro" data, whose collection is time consuming), I choose to go the "macro" way by analyzing the effect of tax incentives on FDI. Also, rather than using corporate tax rate, I use Tax Attractiveness Index (TAI) which is a rather comprehensive measure of tax incentives. I opt to use TAI because tax incentives can take many forms. Besides, many different forms of investment incentives is tax-related, but not generally included in the list of types of tax incentives, such as liberal safe harbors in transfer pricing rules, provisions that facilitate aggressive tax planning, and even tacit forms of lax tax enforcement (Zolt, 2015).

TAI covers various tax concessions beyond mere tax rate cut. Developed by Keller and Schanz (2013), TAI indexes anti-avoidance rules, CFC (Controlled Foreign Corporation) rules, corporate income tax rate, depreciation, membership in EU, group taxation regime, incentive for holding companies, loss carryback, loss carryforward, intellectual property/patent box regime, personal income tax rate, research and development incentives, taxation of capital gains, taxation of dividends received, thin capitalization rules, transfer pricing rules, tax treaty network, withholding tax rate of dividends, withholding tax rate of interest, and withholding tax rate of royalties.

Under the TAI framework, the less a country tax the income and regulate the taxes, the more attractive she is to attract FDI (Foreign Direct Investment), and vice versa. Tax havens have high TAI scores.

Since it can be argued that TAI is a more comprehensive measure of tax incentives than tax rates, I am interested in testing the assumption of “more incentive = more FDI” using TAI as the proxy. In this case, we can model TAI as the “cause” that leads to the increase of FDI inflow.

I estimate the result using panel data of 16 Asian-Pacific countries (Australia, Bangladesh, China, Hong Kong, India, Indonesia, Japan, South Korea, Malaysia, New Zealand, Pakistan, the Philippines, Singapore, Thailand, Taiwan, and Vietnam) from year 2007-2016. The choice of countries is conveniently made considering the availability of Tax Attractiveness Index data while still taking into account the possibility of agglomeration effect.

The data is taken from tax-index.org and Freedom House. Macroeconomic variables are taken from World Bank's World Data Indicator, except for Taiwan, which is taken from Asian Development Bank's Statistical Database System.

As usual, if you’re only interested in the results, proceed to "Results and Discussions".


I use the estimation based on Walsh and Yu (2010). The equation is:

Where where y denotes inward FDI as a share of GDP, X is the vector of macroeconomic and institutional variables, μ represents the time-invariant country-specific effects, ν is the error term. The macroeconomic factors included here are:

- openness (OPEN) which is export plus import scaled by GDP. The more active a country in international trade, the more it attracts investment
- real effective exchange rate (REER), to control the strength of domestic currency
- inflation (INFL), calculated as 3-year trailing average, to account for the reluctance to invest in high inlfation country
- GDP growth (GDPGROW) and logged GDP per capita (GDPPC)

The institutional factor included is Tax Attractiveness Index (TAI), which is our variable of interest. I also include Freedom House (FREE) to account for political stability.

All the variables involve can actually influence each others. For example, TAI may influence FDI, but FDI may influence tax policies which are reflected in TAI – the so called simultaneity. Simultaneity may cause ordinary least squares regression to be biased. To mitigate this bias, I employ Generalized Method of Moments (GMM). GMM is dynamic panel data technique proposed by Arellano and Bond (1991) that able to controls for simultaneity, unobserved country-specific effects, autocorrelation, as well as endogeneity. (Endogeneity means the variables are affected by other things outside the model.)

GMM transforms the equation above into first-differenced below

removes the time-invariant country-specific effects (μ), as it doesn’t change over time.

However, the original GMM (difference GMM) performs poorly if the dependent variable is close to random walk. Random walks happen when an apparent upward/downward trend is actually random. An oft-cited example of random walk phenomenon is stock price. I thus employ system-GMM developed by Blundell and Bond (1998) that is robust against random walk which may happen in FDI trend. The Stata module for system-GMM is provided by Roodman (2009).

There are other econometrics issues. First, my samples are too small*) to be able to handle lagged level of those variables and their difference as instruments. To reduce the instrument counts, I use Principle Component Analysis following, inter alia, Kapetanios and Marcellino (2010). To further account for the presence of heteroskedasticity and autocorrelation, the resulting standard error estimates are also made robust.

Results and Discussions

Tax Attractiveness Index is not statistically significant to FDI inflow (p-values = 0.438). Real exchange rate, openness, and freedom are statistically signifcant and positively correlated with FDI (all p-values < 0.05).

I repeat the calculation, this time using full instruments. The result remains similar: TAI is not statistically significant to FDI inflow (p-values = 0.513).


This study means that giving tax incentives, be it reducing tax rate and/or offering preferential tax regime, may not that significant in attracting FDI inflow. This finding may confirm that tax incentives are the of least concerns for the investors (at least within the context of this study).

This blogpost is just one of many studies that offer counter-narrative about the efficacy of tax incentives. So why does a country offer excessive tax incentives, or even going so far as to engage in tax competition with her neighbors? That is actually quite the puzzle. So whenever there's an argument for tax cut to attract investment, it must be taken with (lots of) grains of salt.


*) Kaiser-Meyer-Olkin score of sampling adequacy is 0.649, indicating mediocre samples but sufficient for factorability.


Arellano, M. and S. Bond. 1991. Some Tests of Specification for Panel Data: Monte Carlo Evidence and An Application to Employment Equations. The Review of Economic Studies 58: 277-97.

Bartik, T. J. 2017. A New Panel Database on Business Incentives for Economic Development Offered by State and Local Governments in the United States. Upjohn Research

Blundell, R., and S. Bond. 1998. Initial Conditions and Moment Restrictions in Dynamic Panel Data Models. Journal of Econometrics 87: 115-143

Chai, J. and R. Goyal. 2008. Tax Concessions and Foreign Direct Investment in the Eastern Caribbean Currency Union. International Monetary Fund Working Paper no. WP/08/257

Kapetanios, G., M. Marcellino. 2010. Factor-GMM Estimation with Large Sets of Possibly Weak Instruments. Computational Statistics & Data Analysis 54(11): 2655-2675

Keller, S. and D. Schanz. 2013. Measuring Tax Attractiveness across Countries. arqus - Working Paper No. 143.

Klemm, A. and S. Van Parys. 2009. Empirical Evidence on the Effects of Tax Incentives. International Monetary Fund Working Paper no. WP/09/136

Oxfam. 2016. Tax Battles: The dangerous Global Race to the Bottom on Corporate Tax. Oxfam Policy Paper, 12 December 2016

Roodman, D. 2009. How to Do xtabond2: An Introduction to "Difference" and "System" GMM in Stata. Stata Journal 9(1): 86-136

Sebastian, J. 2014. Effectiveness of Tax and Non-Tax Incentives in Promoting Investments – Evidence and Policy Implications. Investment Climate Advisory Services Policy Paper, The World Bank Group, Washington, DC

UNIDO. 2011. Africa Investor Report: Towards Evidence-Based Investment Promotion Strategies. United Nations: United Nations Industrial Development Organizations

Van Parys, S. and S. James. 2010. "The Effectiveness of Tax Incentives in Attracting Investment: Panel Data Evidence from the CFA Franc Zone". International Tax and Public Finance 17(4)

Walsh, J. and J. Yu. 2010. Determinants of Foreign Direct Investment: A Sectoral and Institutional Approach. IMF Working Paper no. WP/10/187

Zolt, E. 2015. Tax Incentives: Protecting the Tax Base. United Nations, Paper for Workshop on Tax Incentives and Base Protection New York, 23-24 April 2015

Wednesday, November 22, 2017

Do ASEAN Countries Compete on Their Taxation Policies? A Nash Game Approach

Government often compete on their tax rates to attract investment. One of the issues in tax competition studies is how to measure the extent of such competition. Do countries only compete on their statutory tax rates (i.e. the tax rates based on the tax regulation)? At face value, this seems to be the case.

It turns out measuring tax competition based on statutory tax rates is misleading. Because the effective tax rates – the tax you actually pay divided by taxable income – most likely be lower than the statutory rates. If two companies get different tax incentives, they will have different effective tax rates. In a nutshell, statutory tax rates are too narrow to measure various tax concessions a government may offer.

Alternative measures were then developed. Put forward by Devereux and Griffith (1999), Effective Average Tax Rate (EATR) and Effective Marginal Tax Rate (EMTR) are two such measures that are widely used. However, as Altshuler and Goodspeed (2002) noted, EATR/EMTR are more likely only valid within firm-specific/project-specific scope. Altshuler and Goodspeed themselves use corporate tax revenue divided by GDP as their tax rates measure. This also has limitations that it is too wide, because it assumes that tax collection/tax enforcement efforts are ceteris paribus, and that the cyclical effect of economy is negligible.

Tax Attractiveness Index

Tax Attractiveness Index (TAI) was developed by Keller and Schanz (2013), and further updated by Dinkel, Keller, and Schanz (2016). TAI covered 20 different components of real-world tax systems. Those 20 components are: Anti-avoidance rules, CFC (Controlled Foreign Corporation) rules, corporate income tax rate, depreciation, membership in EU, group taxation regime, incentive for holding companies, loss carryback, loss carryforward, intellectual property/patent box regime, personal income tax rate, research and development incentives, taxation of capital gains, taxation of dividends received, thin capitalization rules, transfer pricing rules, tax treaty network, withholding tax rate of dividends, withholding tax rate of interest, and withholding tax rate of royalties.

TAI codes and calculates all of the above-mentioned features to yield an index of 0 to 1. Under the TAI framework, the less a country tax the income and regulate the taxes, the more attractive she is. So a country with 0% tax rate for any income – personal or corporate – and no taxation rules as specified above, will have TAI score of 1. On the other hand, a country which tax any income with 100% rate, and has strict taxation rules as specified above, will have TAI score of 0. Most tax havens have the score of 0,9.

TAI is not too narrow as statutory tax rate, and not too wide as tax revenue per GDP measure. (It still has limitations, see “Caveat” below*.) But to my knowledge, there hasn’t any study using TAI as a measure in the tax competition setting. So this will be first.

ASEAN countries included in this blogpost are Indonesia, Malaysia, Singapore, the Philippines, Thailand, and Vietnam. The period covered is 2007-2016, based on the availability of Tax Attractiveness Index in www.tax-index.org. Data for the control variables are taken from World Bank and Freedom House.

What follows is a wonkish preambule about the statistics. If you're interested in the results, proceeds to "Results" and "Conclusions."

Specifying the Nash Game

I use a spatial autoregressive model to estimate Nash game between jurisdiction, in this case ASEAN countries. This technique is widely used to estimate strategic interactions (Duncan and Gerrish 2014; Devereux et al. 2008; Brueckner 2003; Altshuler and Goodspeed 2002). Nash game here meaning country A influences country B and C’s taxation policies, but is also influenced by B and C’s taxation policies, simultaneously. The choice of neighbor is based on geographical distance (using CEPII data).

I employ instrumental variable – 2SLS (Two-Staged Least Squares**), with tax attractiveness index of the neighbors as the instrumented variable. The distance from neighbors is then used to compute the weighting matrix. The fitted values for the neighbor’s TAI are then used as instruments in the second-stage regression.

The equations are as follow:

where τ is the Tax Attractiveness Index (coded TAX), indexed by country and year, W is the weight matrix, and ρ is the coefficient of tax competition. The lower equation is the first-stage regression used to estimate the predicted weighted neighbor TAI. Here α is a vector of parameters on the instruments, γ is a vector of parameters on the exogenous regressors, and υit is the first stage error term. Wτ j≠i,t is the predicted weighted tax rates derived from the first stage regression.

The vector X is a standard set of controls used in the literature. I follow Duncan and Gerrish (2014) to use logged per capita GDP (GDP), inflation rate (INF), trade openness in constant prices (imports plus exports divided by GDP, coded as OPN), government expenditures as a percent of GDP (EXP), the Freedom House index of political freedom (FRE), the proportion of the population both over 65 (OLD) and under 15 (YOU), and the size of the rural population (RUR), μi and λt are country and year fixed effects, respectively. Neighbors’ variables will have the letter N- before the coding.

Kleibergen and Paap Lagrange multiplier test suggests that the instrumental variables are rightly identified***. Additionally, the Hansen J test of over-identifying restrictions does not reject the null hypothesis of a well-identified model. Therefore the instruments seem reasonably well suited for this purpose. Standard errors are made robust even in the presence of heteroscedasticity and autocorrelation.


NTAX (neighbors’ Tax Attractiveness Index) is statistically significant at 5%. Interestingly, the negative coefficient on NTAX suggests that an ASEAN country adopts stricter taxation policy when her neighbors adopt looser policy. And the opposite is also true. An ASEAN country adopts looser tax policy when her neighbors get stricter. Following Duncan and Gerrish (2014), while a priori expectation is a positive coefficient, it theoretically can take on any value between −1 and 1, which indicates strategic substitutes and complements, respectively. In this case, what happens is strategic substitutes.


The empirical findings in the tax literature seem to converge on values ∈ (0, 1], i.e. strategic complements, which is when countries compete to offer low tax rates or looser taxation policy as a response – the so-called race to the bottom. However, studies by Brueckner (2003), Altshuler and Goodspeed (2002) also find negative responses as what happens here.

What happens here? Either one of these: an ASEAN country opportunistically offering more taxation incentives to attract investment as her neighbors tighten their tax policies. Or, a country enacts stricter taxation rules to mitigate tax avoidance. This serves as a response to neighbors offering lax taxation rules. It's not a tax competition in the traditional, race to the bottom sense. This warrants further study.


* The limitation of TAI is that it assumes that a multinational corporation (MNC) exploits taxation rules holistically instead of partially. In reality, this is not the case. Let me give you an example. Country A offers R&D incentives, country B offers no withholding tax on interest income, and country C offers low corporate income tax rates. Suppose TAI of A is better than B and C. By TAI’s assumption, an MNC will prefer to locate in A. This is not what happens in real life. Most likely this will happen:
The manufacturing will be located in country C. The research division will be located in country A. The loan for making the factory in country C will be funneled by a special purpose vehicle in country B.

In other words, it is not accurate to assume that those 20 components of TAI should be given equal weights. Tax planning strategy of an MNC will utilize the tax rules of different countries, for different purposes. This is also what happens in "treaty shopping"/"treaty abuse" cases.

** The usage of 2SLS in small sample statistics is justified by Bollen (1996). Monte Carlo experiments also shows that 2SLS performs well in small sample, see Islam (1998). For similar usage of IV estimation in small sample, see Acemoglu, Johnson, and Robinson (2001)

*** The result of Kleibergen-Paap Lagrange Multiplier (LM) indicates a rather weak instrument (only significant at 10% instead of 5%).


Acemoglu, D., Johnson, S., and Robinson, J. A.. 2001. The Colonial Origins of Comparative Development: An Empirical Investigation. The American Economic Review, Vol. 91, No. 5 (Dec., 2001), pp. 1369-1401

Altshuler, R. and Goodspeed, T. J. 2002. Follow the Leader? Evidence on European and U.S. Tax Competition. Mimeo

Brueckner, J. K. 2003. Strategic Interaction among Governments: An Overview of Empirical Studies. International Regional Science Review 26 No. 2, pp. 175-188

Bollen, K. A. 1996. “An Alternative Two Stage Least Squares (2SLS) Estimator for Latent Variable Equations”. Psychometrika, March 1996, Volume 61, Issue 1, pp 109–121

Devereux, M. P. and Griffith, R. 1999. The Taxation of Discrete Investment Choices. The Institute for Fiscal Studies. Working Paper Series No. W98/16

Devereux, M. P., Lockwood, B. and Redoano, M. 2008. Do Countries Compete over Corporate Tax Rates? Journal of Public Economics 92, pp. 1210-1235

Dinkel, A., Keller, S., and Schanz, D.. 2016. Tax Attractiveness and the Location of German-controlled Subsidiaries. Review of Managerial Science, pp 1-47

Duncan, D., and Gerrish, E. 2014. Personal Income Tax Mimicry: Evidence from International Panel Data. Int Tax Public Finance (2014) 21, pp. 119–152

Islam, N. 1998. Small Sample Performance of Dynamic Panel Data Estimators: A Monte Carlo Study on the Basis of Growth Data. Emory University Department of Economics Working Paper

Keller, S. and Schanz, D.. 2013. Measuring Tax Attractiveness across Countries. arqus-Working Paper No. 143.


Wednesday, September 27, 2017

On 26

"Lord of my love, to whom in vassalage
Thy merit hath my duty strongly knit,
To thee I send this written embassage,
To witness duty, not to show my wit:
Duty so great, which wit so poor as mine
May make seem bare, in wanting words to show it..."
(William Shakespeare - Sonnet XXVI)

Reading Shakespeare's 26th sonnet feels like a kindred spirit to me. He, as I do, felt an agony, that having a "wit so poor" makes his poetry seem bare, for his lord of his love is so great that there are no adequate "words to show it."

Verbiage and profundity are of no use. So, let me speak about your 26th year in a parlance that I am familiar with. For, as Pablo Neruda also said in his 26th sonnet, "...in every pure landscape, the earth has imitated you."

You may think 26 as a mundane number, unwarranted for further peroration. But behind its unremarkable facade, lies interesting things.

I can speak of 26 as the atomic number of iron. Seems trite, indeed, as iron is the most common element of the earth. But lest you forget, iron is the backbone of mankind and its civilization – in our machines, in our houses, in our weapons. It is also there as the core of the earth, and it is also there in blood that runs in our veins.

26 is also the number of letters of Latin alphabets, without which there will be very little ideas to communicate.

26 is, quite simply, what moves our world. And so when you think that this year is just another year, you may miss its importance to your life.

In fact, 26 in itself is not just a boring number. It is the only solution for Fermat's sandwich theorem. Named after the great mathematician, Pierre Fermat, who was the first to prove that 26 is the only number between a perfect square number (25, which is 5^2) and a cube (27, which is 3^3).

You can count from 1 to infinity, and you would find that 26 – and only 26 – is uniquely sandwiched between a square and a cube. And so is this year may not like any other in your life.

You know, N, things are actually getting a bit more interesting if you mix numbers with the words of God. YHWH – the name of biblical God – for instance, turns into 26 when you assign it using gematria. (Yod is 10, Waw is 6, and He is 5 each. So together 10 + 5 + 6 + 5 makes 26.)

But I like this one better: if you search at Greek Strong's Concordance, the 26th entry is ἀγάπη – agape, which means love.

So may your 26th birthday be full of Godly blessing, and be full of love.

Happy birthday, N.

With love, A.

Wednesday, August 16, 2017

How to Reduce Inequality in Indonesia

This piece is a more technical appendix of what I’ve wrote in Birokreasi about inequality. You can read the article here http://birokreasi.com/2017/08/rusak/.

In that article, I mentioned the research of Martinez-Vazquez, et al. (2014) concerning what fiscal policies (i.e., taxation and expenditure policies) that can reduce inequality.

The aforementioned study measures inequality by using Gini ratio, in which the closer it is to zero, the more equal society is. Martinez-Vazquez and co. found that progressive taxes such as corporate and personal income tax can reduce Gini ratio. Therefore, the better a country collects income taxes, the better she is in reducing inequality. It is also understandable as progressive taxation levies higher rate for entity with higher income.

On the other hand, Martinez-Vazquez, et al. found that regressive taxation (such as Value Added Tax) will increase inequality. It is understandable because in regressive taxation, the tax burden is similar across the population, regardless of their levels of income. Meaning that a billionaire and a farmer will pay the same amount of taxes when they purchase similar goods/services.

With regards to expenditure policy, generally it is found that the more a government dedicate their revenue to fund social expenditure, housing, education, and healthcare, the better she is in reducing inequality. As middle and lower income households are provided better access towards such needs by the government, not only they have better living standards, but they will also have more disposable income.

I am not interested in testing whether their findings are similar in the case of Indonesia. (My friend, Mikhail Nugroho Adi Setiawan, replicated Martinez-Vazquez, et al.’s study in his junior thesis. He found that their conclusions also hold for ASEAN countries.)

What I am interested to find out is how those policies play out during the periods after they were implemented. One of the tools for this is Vector Autoregression (VAR).

VAR models the how a variable (for instance, inequality) changes over time by the influence of its own lagged value (inequality in the previous year) and the past value of the variable that influences it (say, last year’s education expenditure). VAR modeling is also useful because it does not require as much a priori assumption about how the forces influencing a variable. Therefore, we can set aside econometric issues such as simultaneity and endogeneity. What is needed is a list of variables which can be hypothesized to affect each other within certain period of time.

The data used in this post is collected from IMF Government Financial Statistics, Laporan Keuangan Pemerintah Pusat and Anggaran Pendapatan dan Belanja Negara of various years, also Badan Pusat Statistik. The data I used in VAR modeling is from fiscal year 1990-2014.

To implement VAR, we must test how much lags are needed for the independent variable to affect dependent variable. For instance, increasing education expenditure for the current year may not directly reduce inequality for that year. The effect may be felt 2 or 3 years after the policy was implemented.

To obtain the best lags, we can subject the variables to a battery of tests. We can then select which one is the best based on several criteria. The usual criteria for lag selection test are, inter alia, final prediction error (FPE), Akaike’s information criterion (AIC), Schwarz’s Bayesian information criterion (SBIC), and the Hannan and Quinn information criterion (HQIC). Luckily, the command “varsoc” in statistical software STATA can do a comprehensive job.

After obtaining the appropriate lags, I subject all variables into VAR equations. However, reading VAR statistical output can be tedious.

To ease how we picture the relationship between fiscal policies and Gini ratio, I transform the VAR results into Impulse Response Function (IRF). In this case, fiscal policies such as corporate income tax (CIT), personal income tax (PIT), indirect taxes (INDIRECT), social expenditure (SOCIAL), housing expenditure (HOUSE), education expenditure (EDU), and healthcare expenditure (HEALTH) can be seen as the “impulse”. That is, they trigger a response in Gini ratio in the form of ups (worsening inequality) and downs (reducing inequality) in the periods that follow. To better illustrate how IRF works, imagine you throw a stone into a pond. The stone is the impulse, and the waves that show on the surface are the responses.

So, in terms of taxation policy, the IRF results are as follow:

In general, we can expect personal income tax to reduce Gini ratio in the next year after policy implementation. On the contrary, increasing VAT in the current year will lead to an increase in Gini ratio in the next year.

Interestingly, I found that an increase in corporate income tax may even worsen the inequality. There may be several causes. First, following the finding of Martinez-Vazquez, et al., the more open the economy, the higher share of the CIT that would fall on labor income, making this corporate income tax less progressive (Martinez-Vazquez, et al., 2014:110). Secondly, as in the case of Indonesia, our corporate income tax is not progressive to begin with. Currently, our corporate income tax rate is flat at 25%. (It started to be a flat tax since fiscal 2009, with the issuance of Law Number 36 Year 2008 concerning Income Tax, in which the corporate tax rate changed from progressive into single 28% rate). This may be the case to redesign our corporate income tax rate to be progressive again.

On the public spending side, the results are as follows:

An increased spending in healthcare and social expenditure will lead to a decrease in Gini ratio at least two years after implementation. An increase in education expenditure, however, increases Gini ratio one year after implementation, yet reduces it afterward in year two. Similarly, an increase in housing expenditure will increase Gini ratio in the first year.

It can be theorized that housing expenditure (at least in Indonesia) generally benefits middle-to-higher class instead of the poorest part of the population. In other words, it only enables middle to high class – who already have a steady stream of income – to accumulate more wealth. But this conjecture may be wrong. Thus, a further study is needed.

Conclusion: to reduce inequality, we need to better redistribute income via personal income tax. We also want to increase healthcare and social spending. A more progressive corporate income tax and a better-targeted housing policy are also needed if we want to reduce inequality.

(H/T to Mikhail for providing the necessary dataset.)


Martínez-Vazquez, Jorge, Violeta Vulovic, and Blanca Moreno Dodson. 2014. “The Impact of Tax and Expenditure Policies on Income Distribution: Evidence from a Large Panel of Countries.” Hacienda Pública Española 200 (2012): October, 6th. 2014

Wednesday, September 28, 2016

Many Happy Birthday, N

‘Tis the time of the year when I hate to write. Not because it is a tedious task, but because this day is the day the siren of our old age rings again. I hate birthday because I don’t want to grow old. I don’t want you either to grow old. I hope you won’t get old. I want you to be forever young. You know, I always imagine you as a sempiternal doe, running around in the steppes. You are fascinatingly beautiful. So free and blissful, even death dares not conquer. That, my love, is my first and foremost prayer.

My second prayer is for you to be able to forgive me. I, for lack of better word, am nothing but thorns in your wilderness. I give you nothing but wounds. Yet you always give me grace and compassion. I took you – took us – for granted. I stopped listening to small things. I was clumsy and forgetful as ever. I harangued you even when you want me to just shut up. Yet you were always patient. Yet I did those mistakes again and again.

You offered me salvation. I put you on the cross instead.

I have nothing to give you as a birthday present but an apology for all these clashes I caused during this year.

Speaking of our little fights, here’s an equation I remember:
They say this is the key for lasting relationship. But what does it mean? It means that it would be better for a couple to argue on small problem and fix it as soon as possible than to keep the resentment build up. Of course, a relationship without a fight is more desirable. But it is impossible. After all, maybe it is true what Publius Terentius Afer once wrote in his comedic play: “Amantium irae amoris integratio est.” Fights are what bring lovers together.

So my next prayer is that I wish we can still argue about kittens and puppies and today’s millenials for years ahead, rather than become strangers again. Because I love you, and won’t cease to do so even when time and space divide us. I won’t cease, unless you wish for it.

Oh, and I hope we can travel somewhere. Of course you’ll be paying. Last year I wish you’d be richer than I am, and now you are. I’ll promise this time I won’t prefer staying on bed.

Live long. Live happily. And be prosper.

Amatus es. Ego semper amabo te.

Your kitten,


PS: Just this afternoon I saw a culinary travelogue on AFC. There's this bakpao vendor in Malaysia whose mom is still working in the kitchen, making the dough. She's 83. She's been working on the shop since 70 years ago. Yet she chooses to work there simply because she doesn't want to stay idle. I always imagine that how you'd be like 70 years from now.

Monday, September 19, 2016

A Game Theory of Essay Grading

So, it's been awhile since my last post.

What intrigued me to write in here again was my lecturer. My taxation seminar lecturer, Mr. Riko Riandoko, has a very interesting grading method. (He's an awesome guy.) Basically, Mr. Riko gave us task to each write an essay every week. However, the grading system was like this (with some adjustments to make the assumption simpler):

- Everyone submits the essays to one designated student.

- That student removes the writers' names from every essay, leaving only the title. The essays then are put online on a cloud drive.

- Everyone then read and ranks the essays from the best to the worst EXCEPT for her own essay. (Thus A ranked B, C, D's essays; B ranked A, C, and D's, and so forth.)

- To make it simple, the ranking used scoring system, with the best essay given highest score, 2nd best given the 2nd highest score, and so forth. So if there are 10 essays, one would give the best essay 9, the 2nd best 8, and so forth. One must give her own essay a 0 score, due to the above rule. The winner is the one with most total score.

This system makes me think of some questions.

a) Assuming full honesty (no coalition in which the members give the highest score to members of that coalition, and no one give her own essay score > 0) what is the probability of one winning?

b) Is such coalition possible?


The first ones is not so easy to calculate. First, the possible combination of scoring (or the probability space) from a student's perspective with regard to her own essay is (n-1)^(n-1), with n as the total students in the class. This configuration got large the more the students are. For instance, if there are 3 students, there are 2^2 or 4 possible scores from A's perspective (2, 3, 3, and 4):

2 if both B and C give A each 1 score;
3 if either B gives 1 and C gives 2, or the reverse;
4 if both B and C give A score of 2.

If there are 4 students, the possible configuration of scores becomes 27. If there are 5 students, 64. 6 students? 125.*)

This makes calculation of exact probability get increasingly difficult in scale. Remember that it is basically similar to the probability of getting k in n-run. Even for binary outcomes (coin flip, "success"/"failure"), the equation is ugly, moreover the calculation. The equation is:

And that is only for two kinds of outcome. But Mr. Riko's essay grading have (n-1) possible outcomes. I'd rather pass this one over.

However! one can calculate the average expected score of her own essay. Since these scores are independent and identically distributed random variables, we can calculate the expected score E(s) using mid range method. This estimation is robust, as the n of students got large enough the expected mean will follow the central limit theorem.

The highest possible score for A is (n-1)^2, that is if everyone else votes A's essay with highest score. The lowest possible score for A is (n-1), in which everyone else thinks A's essay is the worst. Using midrange, it is easy to see that the expected score for A is:

Interestingly, this is also the score where there is no winner! Recall that the expression n(n-1)/2 is formula for 1+2+3+...+(n-1). This score is what everyone gets when there is Condorcet voting paradox. Condorcet voting paradox happens when the situation is as follows:

A voted B > C > D
B voted C > D > A
C voted D > A > B
D voted A > B > C

So everyone basically gets voted highest exactly once, 2nd highest exactly once, and so forth until she also gets the lowest score exactly once. Therefore, for the example above, A gets 1, 2, and 3, with the total score of 6. But so do B, C, D! They all get 6. In which no one wins (or everyone wins, if you're that "glass half full" guy.) What a bummer.


Now, the second question. Is it possible to form a coalition with some friends so that at least one of the members wins, or at least guaranteed above average score? It is interesting to answer that in game theory perspective.

My theorem is that, yes, such coalition is possible. Such coalition has to adhere to some rules, however. 

1) Members of coalition must vote cyclically among themselves. If a coalition exists between A, B, and C, A must vote B > C; B must vote C > A; and C must vote A > B.

2) There must exist at least someone who is outside the coalition, a.k.a. that forever alone guy who doesn't have friend.

My theorem: there exists coalition c with members of (k+1) so that E(c) > E(s). In other words, maximizing the possibility of getting the most score. Such coalition must have k that satisfies the equation:

The left side is derived from the total score from Condorcet voting amongst its members, plus the additional expected scores from non-members.

There exist finitely many solutions for this, except where k = 0 (no coalition) and k = n-1 (i.e. everyone is in the coalition, which is basically going back to the Condorcet voting paradox above). However I can't prove the generality of this theorem. In other words, I don't know if this always applies in general. My math is rusty.

If, however, this is the case, then the best strategy for a rational agent is indeed to form a coalition. A student will have better chance of winning if she makes a deal with her friends.

I don't know if anyone has put some thoughts to this type of game theory. If I recall correctly, most of social choice literature dealt with voters that are clearly distinct from the candidates. For example, election, in which Marquis de Condorcet, Kenneth Arrow, Allan Gibbard, and Amartya Sen extensively concerned themselves with. Or maybe Keynesian beauty contest-like situation.

In Mr. Riko's grading case, all voters are also all the candidates, except that they can't vote for themselves – creating the incentive to cooperate with opponents. Another difference from election is that a vote does not necessarily correspond to a score of 1, but ∈ of {1, 2, 3, ..., n-1}.

All in all, this got me spending much time in warkop, looking at its walls like a dumb ass.


Post script:

*) The all possible ordering, class-wide, is even nastier as the n of students gets increasingly large. It is the (n-1) permutation of (n-1) elements, to the power of n. In other words, it is.

Even for 3 students, the possible class score ordering is large. Take a look:

0, 1, 2   0, 2, 1
1, 0, 2   1, 0, 2
1, 2, 0   1, 2, 0

0, 1, 2   0, 2, 1
2, 0, 1   2, 0, 1
1, 2, 0   1, 2, 0

0, 1, 2   0, 2, 1
1, 0, 2   1, 0, 2
2, 1, 0   2, 1, 0

0, 1, 2   0, 2, 1
2, 0, 1   2, 0, 1
2, 1, 0   2, 1, 0

For a class with 4 students? It's 6^4 possible ordering, or exactly 1296. I'd rather not imagine how big it is for a class with 39 students like mine.

Wednesday, October 7, 2015

Tentang Cinta yang Menua

Kita masih muda, sayang. Kita hanya merasa dikejar usia, dikejar cita-cita. Terlalu sering berlari, tanpa ada waktu untuk berpikir, tanpa ada waktu untuk menangis. Lantas cermin-cermin seakan selalu memantulkan betapa tuanya kita. Mempertontonkan kekalahan kita.

Tak ada yang perlu dikhawatirkan, sayang, biar matahari hari-hari ini sedang dingin dan senja selalu gelap. Kita hanya perlu mencinta. Entah seberapa besar. Entah sampai kapan. Rasanya tidak perlu ditanyakan. Bagiku itu cukup, dan semoga cukup juga bagimu.

Semoga telingaku juga cukup bagimu untuk mendengarkanmu saat kau sedang lelah dan marah pada dunia. Semoga pelukanku cukup bagimu untuk menghangatkanmu saat kau sedang menggigil. Karena aku tak punya apa-apa dan tak tahu apa-apa tentang jalan nasib dan sisa waktu kita. Semoga aku, dalam bagian umurmu, menjadi salah satu di antara penanda-penanda bahagiamu.

Tak ada lilin dan kue malam ini. Doa-doa sudah terucap seperti biasa. Kini saatnya berlayar lagi. Temukanlah bintang selatanmu. Menjelajahlah. Janganlah lupa untuk sesekali menikmati samudera, serta berbuat baik kepada semesta. Kelak jika perahumu sudah penuh, atau sauhmu terasa lebih berat dari biasa, aku akan ada sebagai tempatmu pulang. Kujanjikan akan selalu ada cinta di rumah yang menyambutmu pulang.

Selamat ulang tahun.

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