Author: Sujan (page 2 of 3)

Finite Populations: How do we think about them?

Consider how a normal regression output on STATA looks.

Sample Regression Output


We find that along with the coefficients, we get other values like standard errors, p values, confidence intervals, etc. So what is the purpose of these stats?

The standard assumption in stat-econ literature is as follows: i)the observed sample is a random representative sample from the entire population, ii) we are interested in the true population parameters.

What does this mean? We assume that we pick a random representative sample from a population. After running a regression, we get a particular coefficient on all the x’s. We assume that in repeated sampling, we would get a distribution of coefficients for the x’s. In fact, one of the fundamental properties of a good estimator is unbiasedness or that the Expected Value of the coefficient from the sampling distribution is equal to the true value, i.e. the true coefficient is equal to the expected value of the coefficient in repeated sampling. Although we rarely do repeated sampling in practice, we do check for the significance of the coefficients with a null hypothesis that they are equal to zero. Thus, in a normal regression framework, the population has the true coefficients and is quite distinct from the samples which have a distribution of coefficients.

So what happens when we do have the entire population?

This is a tricky question, as we usually always assume that the population is infinite and we can never have the entire population. Thus, in cases of finite population, like the 28 states of India, it becomes a little bit tricky as to how one should interpret the regression output. I will attempt to summarise two popular views in the stat-econ literature in this regard.


One view says that if you have the entire population, the p values and t statistics are irrelevant.  The finite population is considered to be a fixed set of elements. The coefficients derived are the true relationship since you have the entire population and not a sample of the population. Thus, the concepts of hypothesis testing and significance become meaningless for an entire population. This is because the stats and tests are only relevant for a sample, and not the entire population. The caveat here is that the model has to be correctly specified.

Super Population / Underlying Process

This view states that the observations in the population are simply a sample from an infinite population. For example, if we’re looking at the 28 states in India, we can interpret the set of observations at one time period as a sample; and the set of observations across all time as the infinite super population.

This becomes important, especially if you want to make inferences not just about relationships today but also if you want the relationships to hold for similar groups in the future.

Another related but slightly different view would be that the observed outcomes in the population are the products of an underlying process. In that regard, what standard errors and other test stats capture become relevant. According to Abadie et al (2014) “there are for each unit missing potential outcomes for the treatment levels the unit was not exposed to.”

On a similar vein Wallis and Robers (1956) claim, “the totality of numbers that would result from indefinitely many repetitions of the same process of selecting objects, measuring or classifying them, and recording results.”

In these regard, test stats become important in understanding whether the coefficients generated are true or have been generated as a result of a chance outcome.



  1. Abadie A, Athey S, Imbens G, Wooldridge J (2014), Finite Population and Causal Standard Errors, NBER Working Paper Series.
    Available at:
  2. Asali M (2012), Can I make a regression model with the whole population? [Msg 1], ResearchGate.
    Message posted:
  3. Frick R (1998), Interpreting statistical testing: Process propensity, not population and random sampling, Behavioral Research Methods, Instruments, & Computers. Vol 30 (3), pp: 527-535
  4. Hartley H, Sielker Jr R (1975), A “Super Population-Viewpoint” for finite population sampling, Biometrics, Vol. 31 (2) , pp: 411-422
  5. Hidiroglou, Michael Arsene (1974), Estimation of regression parameters for finite populations , Iowa State University Digital Repository.
    Available at:
  6. January (2013), How to report data for an entire population? [Msg 1], CrossValidated.
    Message posted to:



Simple Guide to Getting Orthogonalized Impulse Response Functions

Vector Auto-Regressions or VARs are used in time series analyses when there may be inter-dependencies or relationships among multiple time series.  For example, we may want to understand the relationship between GDP, current account balance, and inflation rates. Running a normal OLS regression would be inappropriate as each variable affects the other variables; OLS estimates would have an endogeneity problem or the estimates would be biased. In such scenarios, we use VAR methods.

Recently, I was working on some time series data that had the issues of reverse causality. As a result, I had to use a VAR model to get orthogonalized impulse response functions (OIRFs) in order to understand the relationship between variables. In the attached presentation, I describe the theory behind this orthogonalization as well as the steps to generate OIRFs on STATA.

To check the presentation, please click on this link

India’s Growth Slump: No Easy Answers

[This article was published by the Business Standard  on Tuesday, Oct 31, 2017. The article was written in collaboration with Anmol Agarwal, a classmate from LSE. To read the article on Business Standard, click here]


“We should be very careful lest fiscal actions undercut stability,” said Reserve Bank of (RBI) Governor, Urjit Patel, in response to a journalist’s query on fiscal stimulus packages during the monetary policy conference on October 2017. The Prime Minister’s Economic Advisory Council (PMEAC) has also recently expressed its reservations about a mid-term fiscal stimulus package by the government to revive India’s economic growth.


While critics of a fiscal stimulus cite stability — most notably upside risks — as a key reason against a fiscal stimulus, advocates routinely talk about the famed fiscal multiplier and how it would spur a much-needed economic revival.


Fiscal multipliers were first introduced to the world by John Maynard Keynes during the Great Depression of the 20th century. Keynes had argued that a recession could be curtailed by an increase in government expenditure, fuelling savings and capital formation. For instance, a rise in the government expenditure of $100 would raise the real GDP or gross domestic product of a country by more than $100 and bring it back on the path of economic growth.


Keynes and his policies began to be followed by policymakers all over the world until the advent of Milton Friedman, one of the most influential economic thinkers of the 20th century. Friedman challenged ‘naive Keynesianism’ (as he put it) and argued that a fiscal expansion is highly inflationary even as the neoclassical school argued that fiscal deficits brought about by an expansionary fiscal policy would result in rising interest rates, and a subsequent crowding out of private investment.


These ‘non-Keynesian’ effects of government spending were fist empirically documented in the 1990s in a series of researches published by the National Bureau of Economic Research (NBER), a leading economic research organisation in the US. The authors – Francesco Giavazzi of the NBER and Marco Pagano of the University of Naples Frederico II – studiedthe impact of fiscal contractions and expansions in Organisation for Economic Cooperation and Development (OECD) countries, and analysed their impact of private investment, consumption, and economic growth. The OECD is an intergovernmental economic organisation with 35 member countries, most of whom are high income and can be considered as being developed.


Interestingly, they found that spending cuts in Denmark (1983-86) and Ireland (1987-89) actually lead to an increase in aggregate demand and private consumption, stimulating economic growth. On the other hand, the Swedish fiscal expansion — where Swedish Government Debt to GDP jumped from 25 per cent in 1990 to 67.8 per cent by 1994 — counterproductively led to a fall in private consumption and investment. The authors called the events in Denmark and Ireland as ‘expansionary fiscal contractions’, while the events in Sweden as ‘contractionary budget expansions’.


Simply put, the impact of the fiscal multiplier in these cases was negative. These events were not anomalies as further studies have gone on to show several such outcomes from budgetary changes.


In India, there have always been divergent views about the effectiveness of a fiscal stimulus. An important Keynesian argument to illustrate the effectiveness of the multiplier is that a fiscal stimulus should increase income and eventually spur private savings and investment. Does this hold good for Indian? A look at the chart below suggests otherwise. India’s fiscal deficit as percentage of GDP declined continuously from 5.98 per cent in 2001-02 to 2.54  per cent in 2007-08. But, contradictory to the Keynesian view, domestic savings as a percentage of GDP show a continuous rise, peaking at around 38 per cent in 2007-08 when the deficit was the lowest.


Subsequently, there was a sharp decline in savings in 2008-09 due to the onset of the financial crisis in a situation economists commonly refer to as ‘savings paradox’ — where individuals desire to save more due to increasing uncertainty in the economy, but end up saving less due to a decline in their incomes as brought about by a crisis. Focusing on years after the crisis, fiscal deficit rose continuously from 2010-11 until 2014-15, but savings have been on a downward trajectory, clearly suggesting an absence of a Keynes style deficit–income-savings correlation in 


In the Study of State Finances report of 2016-17, the RBI expressed concerns about how increased market borrowings by the states could lead to higher bond yields and costs associated with borrowing. Even a significant part of the central government’s borrowing requirement is taken care of by market borrowings – based on budget estimates net market borrowings for the year 2017-18 stand at Rs 3.48 trillion, or about 64% of the gross fiscal deficit. Since an increased fiscal deficit is likely to be financed with market borrowings, it is likely that bond yields would rise. Theoretically, this can crowd out private investment and have a detrimental effect on the economy, especially at a time when banks are not willing to lend fearing rise in bad debts and many companies have been raising money from the corporate bond market. There have been several studies, which corroborate the relationship between a fiscal stimulus and higher cost of borrowing, including a 2004 study published by Economic & Political Weekly, where an RBI Economist Rajan Goyal, established the relationship for 



After a sharp fall at the onset of the 2008 financial crisis, India’s benchmark 10-year bond yield had an upward trend until 2014-15 (Source: Authors’ Calculations and Bloomberg)

Even those who advocate a fiscal stimulus acknowledge that fiscal multipliers only lead to economic growth when the increased government expenditure is spent productively. A study by the National Institute of Public Finance and Policy, a New Delhi-based economic policy think tank, in 2012 had found that a capital expenditure multiplier was 2.45, while other revenue expenditure multipliers were less than one. However, if one looks at India’s government capital expenditure, the trend is puzzling. In the years when the fiscal deficit was higher, there was a drop in the government’s capital expenditure. This clearly suggests that the quality of expenditure in a fiscal stimulus may not necessarily lead to an economic revival.


A fiscal stimulus will also have a bearing on India’s sovereign rating. It has been stuck at a low level, being upgraded only once in the past 25 years. On 2nd November 2016, the credit rating agency S&P Global Ratings kept the credit rating for unchanged at the lowest investment grade (BBB-), only 1 grade higher than a junk bond rating, with a stable outlook, citing India’s low per capita income and weak public finances as the major reasons. Moody’s and Fitch Ratings followed the suit, expressing scepticism regarding upgrading India’s rating in the near future.


The issue of consistently low ratings baffles Indian economists. India’s chief economic advisor Arvind Subramanian blamed the agencies for their ‘poor standards’, while India’s Economic Affairs Secretary, Shaktikanta Das, had said that rating agencies were out of touch with India’s reality. Even the OECD threw its weight behind India, suggesting that deserves a credit rating upgrade.


performance, growth prospects, debt position and the state of public finances are some of the key criteria used by rating agencies. With the growth rate sagging, India’s only hope of expecting a better rating in the future is for the government to be fiscally prudent. An untimely fiscal stimulus will lead the government missing the 3.2 per cent fiscal deficit target in fiscal year 2018, dent credibility of the government and ruin chances of upgradation in our sovereign rating. The investment climate continues to be weak – gross fixed capital formation as a percentage of GDP has steadily declined from 34.3 per cent in 2011-12 to 29.5 per cent in 2016-17. In such a scenario, missing the fiscal deficit target may dent the confidence of investors, which in turn, could end up threatening capital inflows.


When a patient is sick, the doctor will always suggest medicines but some of the medicines have side effects and taking too much of them may end up causing more harm than good to the patient. It’s time India’s policymakers prescribed the right remedy for the ills that have been plaguing the economy. Fiscal stimulus is not the panacea.

1. Francesco Giavazzi and Marco Pagano (1990), National Bureau of Economic Research, Can Severe Fiscal Contractions be Expansionary? Tales of Two Small European Countries (
2. Francesco Giavazzi and Marco Pagano (1995), National Bureau of Economic Research, Non Keynesian Effects of Fiscal Policy Changes: International Evidence (
3. Reserve Bank of (2017), State Finances: A Study of Budgets 2016-17 (
4. Rajan Goyal (2004), Economic and Political Weekly, Does Higher Fiscal Deficit Lead to Rise in Interest Rates


Clues for India: Looking at the puzzle of Total Factor Productivity and Capital Flows

[This article was published by the the London School of Economics South Asia Centre Blog (South Asia @ LSE)  on Monday, Oct 30, 2017. The article was written in collaboration with Aniruddha Ghosh, a classmate from LSE. To read the article on South Asia @ LSE, click here. The article was also posted by Oxford India Policy Blog, you can read it here]


While examining previous trends and research on capital flows and total factor productivity, Aniruddha Ghosh and Sujan Bandyopadhyay write that India must be careful to continue to maintain the positive correlation between growth and net foreign capital flows.

“Among all the means of power subordinate to the regulation of the State, the power of money is the most reliable, and thus the States find themselves driven to further the noble interest of peace, although not directly from motives of morality”— Immanuel Kant, “Perpetual Peace: A Philosophical Sketch”,1795

While the Kantian view on increasing economic integration was primarily driven by considerations of war and peace, international capital flows and their management have become pivotal to the macroeconomic growth and stability of modern economies. Over the course of the last two decades, India’s net capital flows have surged from little over the US $500 million in the first quarter of 1990-91 to the US $25.38 billion in the first quarter of 2017-18.

In This Time is Different (2011), Carmen Reinhart and Kenneth Rogoff flag an important historical insight: Periods of high international capital mobility have repeatedly produced international banking crises, not only famously as they did in the 1990s, but historically.

Figure 1: Periods of high capital mobility have often been associated with higher incidence of banking crises Source: Bordo (2001), Caprio (2005), Kaminsky and Reinhart (1999), Obstfeld and Taylor (2004), Reinhart and Rogoff (2008) 

The traditional neoclassical technology models tell us that net financial capital flows should move from richer to poorer countries. That is, it should flow from countries that are capital-abundant, and thus lower returns, to those that are capital-scarce (higher returns) and have greater investment opportunities.

Robert Lucas Jr . has pointed out an empirical paradox using the 1988 data: If the traditional neoclassical model were true, the rate of return on a unit of capital investment in India would be nearly 58 times more than the return one would get in the US, yet the level of capital flows to India from the US were modest and nowhere near the levels the traditional theory predicted. Hence, the traditional neoclassical theory fails to imbibe the assumptions of cross-country differences in productivity and capital market imperfections. After accounting for cross-country differences in the fundamentals and capital market frictions, the risk-adjusted returns to investment should govern capital flows and therefore, should resolve the paradox. However, the paradox remains as relevant today given that the poorer countries of the world tend to run current-account surpluses (thus exporting capital) and the richer ones (most notably the US) tend to run current-account deficits (thus importing capital).

The paradox gets rather perverse when we move from absolute levels of income to income growth. In 2006,  “Foreign Capital and Economic Growth,” written by Eswar Prasad, Raghuram Rajan and Arvind Subramanian and published by the International Monetary Fund, took the question of capital flows one step forward. The paper presented evidence to support the intensification of the Lucas Paradox, while observing that within developing countries, growth and foreign capital inflows were, in fact, negatively correlated. This meant that poorer countries which had higher amounts of net foreign capital inflows had lower economic growth than those that didn’t. Additionally, within the group of poorer nations, capital flows out of countries that grow faster. Interestingly, this relationship breaks down for developed nations, i.e. developed nations have a positive correlation between growth and foreign flows.

The authors of the IMF paper argue that there could be a number of reasons why we see this anomaly between growth rates of developing countries and their foreign capital flows.

Firstly, successful developing countries may have a limited ability to absorb foreign capital flows due to structural impediments in their financial sector. Secondly, it is possible that developing nations actively make the choice to avoid excess foreign flows to prevent overvaluation of assets. And the final conclusion is that nations develop, structural impediments in their financial sectors reduce and their ability to absorb foreign flows increases – such that it can become a driver of growth, like industrialized nations, in the long run.

Figure 2: The composition of capital exporting countries has changed from higher to lower income countries and the Lucas Paradox seems to reinforce over time. Source:  Prasad, Rajan and Subramanian (2006)

Figure 3: Countries with higher growth have attracted less net foreign capital than medium- and low-growth groups. Particularly, China and India have been exporters of capital despite high economic growth. Source:  Prasad, Rajan and Subramanian (2006)  

To explain these rather perverse findings presented in the IMF paper , Francisco J.Buera and Yongseok Shin in their 2017 paper, “Productivity Growth and Capital Flows: The Dynamics of Reforms”, focus on the relationship between growth accelerations in total factor productivity (TFP) and capital flows. They attribute the observational findings to the disparate dynamics of aggregate savings and investment behavior. For the readers, TFP accounts for the growth in output not accounted for by the growth in inputs used for its production and is often synonymous with improvements in the technological state of an economy. A rising TFP is necessary for a higher economic growth rate and therefore, investment in R&D is essential for sustained economic growth.

Figure 4: Panels A and C show, respectively, the average of saving minus investment rates and TFP over the 33 episodes of sustained accelerations before 1980. The pre-1980’s negligible savings and investment gap confirms our understanding of limited capital flows.  Panels B and D show the average over 22 such episodes after 1980. Source: Francisco J. Buera and Yongseok Shin (2017)

Buera and Shin present the following observations using data for 22 sustained growth acceleration episodes post-1980. First, in contradiction to the predictions of standard neoclassical models, capital flows out of countries experiencing fast growth in output and TFP. Second, this pattern is a lot more prominent in the early stages of these growth accelerations, where many of these nations undergo economic reforms. These first generation reforms are primarily concerned with the removal of idiosyncratic distortions (tax-cuts) in their economies. Finally, capital outflows reflect a surge in aggregate savings and a delayed rise in aggregate investment at the onset of sustained growth accelerations. Interestingly, when the reform is a far-reaching one – it removes goods market distortions as well as improves the health of financial institutions (second generation reforms) – capital flows into the countries experiencing faster TFP growth.

Figure 5: Net Capital Flows & Net Capital Flows as a percentage of GDP (RHS) for India since 1990. Note the peak of capital flows coincides with the Great Recession as ‘plata dulce’  moved around the world easily. Source: Authors’ Calculations and Bloomberg

Figure 6: Total Factor Productivity level growth in India, China, and the US. India has been on a rising TFP path. Source: Authors’ Calculations and The Conference Board

India has had a long and chequered history with foreign capital flows. The first few decades after independence were characterised by import substitution policies which placed severe restrictions on the flow of foreign goods and capital, and it is only in the last few decades that foreign flows to India have really picked up. In the last two decades, both net foreign capital flows and GDP have grown substantially indicating a positive correlation, though this positive correlation is not as strong as the traditional neoclassical models predict. In light of the fact that there have been rising TFP levels in recent years as well, India must be careful to continue to maintain this positive correlation between growth and net foreign capital flows. Rakesh Mohan, in a speech in 2008 in his capacity as the Deputy Governor of the Reserve Bank of India said, “A large surge in capital [in]flows over a short span of time in excess of domestic absorptive capacity of the economy can lead to upward pressure on the exchange rate, possible overheating of the economy and asset price bubbles. They can also pose the risk of an abrupt reversal, which may have potential negative real economic effects.” With far-reaching reforms in the goods and capital markets, it becomes imperative for the NDA government to keep these historical and policy insights in mind.

Nudging People the Right Way: A Couple of Personal Anecdotes

Richard Thaler, the 2017 winner of the Sveriges Riksbank Prize in Economic Sciences, lists out several fascinating insights into the human psyche in his book – Nudge : Improving Decisions about Health, Wealth and Happiness.

The two systems of thinkings is perhaps the most significant contribution that behavioral scientists like Thaler and Kanheman. The simple concept elegantly explains how the human mind thinks. We have an automatic system which is instinctive and quick, and a reflective system that is that is slow and self-conscious. I would encourage everyone to read Thaler’s Nudge and Kanheman’s Thinking Fast and Slow, to better understand this concept.

But moving back to Nudges. Thaler and his co-author Cass Sunstein advocate a philosophy of ‘libertarian paternalism’ throughout the book. To them, freedom of choice is sacrosanct and they don’t want to impede on the liberty of people under any circumstance. Yet, they believe that ‘choice architects’ can drive people’s actions in subtle smart ways, through nudges, to improve outcomes. The authors define a ‘nudge’ as an activity that would alter people’s behaviour in a predictable way, while ensuring that people have the option of not altering their behaviour at little or no cost, if they so desire. An example used in the book is that if moving the arrangement of food in a school cafetaria encourages students to eat healthier, that would count as a nudge. However, banning the sale of unhealthy food items would not count as one.

Nudges can be especially useful in less developed nations. With states not having resources to impose mandates or bans, altering peoples’ behaviour through nudges can be an efficient way of achieving optimal outcomes.

Mumbai’s suburban railways experimented with nudges to prevent fatalities on its network. Mumbai’s rail network sees several deaths every day as trains and rail facilities are packed to the brim during rush hour and infrastructure is not enough to deal with such heavy crowds. Yet despite providing over-bridges to cross tracks people often resort to crossing the tracks of foot to save time or due to laziness. Despite being considered an illegal activity that attracts fines and a possible prison sentence, crossing tracks is a widely prevalent phenomenon.

In 2010, the rail administration decided to try and use nudge theory to prevent deaths by crossing tracks. Along with a behavioural economics think tank, they designed a set of posters that showed a person being a mowed down by a train with an emphasis on the person’s facial expressions of fear and shock. These posters were placed at locations which were prone to crossing in the eye-line of people who may contemplate crossing the tracks. Previous campaigns had been restricted to announcements, or written signs that contained information about fined people had to pay in case they were caught crossing the tracks.

This was a unique effort where the state was actually trying to impose a ban via a nudge. While preliminary results did show that the efforts had reduced fatalities, there has been no comprehensive report on the effect of the campaign. Yet, this exercise does show that in cases where governments are unable to impose their mandates, nudge theory may help them along the way.