Christopher Sims, VAR Model And Impulse-Response Analysis

2011 Nobel Economics Prize winner Christopher Sims (who passed away yesterday) revolutionised macroeconomics by developing the Vector Auto Regression (VAR) model and impulse-response analysis.

Till the 1970s, macroeconomic analysis involved taking a large system of equations built around a Keynesian macroeconomic model and statistically estimating them. The estimated system was then used to:

1. Interpret time series

2. Make economic forecasts

3. Conduct policy experiments

These large models were successful in explaining the historical data. But in the 1970s, Western countries had high inflation along with low growth and high unemployment. During this period of 'stagflation', the large models started showing instabilities - which created problems.

In 1980, Christopher Sims wrote a paper titled "Macroeconomics And Reality" (Econometrica, 22k+ citations) to solve this problem. He developed a new methodology using a new model called Vector Auto Regression (VAR). VAR is basically a system of N equations of N variables in which each variable is a function of:

1. Its own past values

2. Past values of the other variables

3. Some exogenous shocks.

His methodology has 3 steps:

1. Estimate the VAR model and forecast the macroeconomic variables - by separating unexpected movements in the variables from expected movements.

2. Identification - ie, break down these unexpected movements into structural shocks (ie, shocks that are the fundamental causes of macroeconomic fluctuations).

3. Impulse-response analysis - ie, trace out the dynamic impact of these shocks on subsequent movements in all the variables.

Sims' new methodology revolutionised macroeconomics. Today, VAR model and impulse-response analysis have become the basic tools of macroeconomic analysis. They are used to answer questions like:

1. What causes economic cycles?

2. What are the effects of fiscal policy?

3. What are the effects of monetary policy?

The pic is from Sims' paper. It shows the impulse-response analysis of America's GDP - ie, it shows how GDP is affected by 6 variables: money supply, GDP itself, unemployment, wages, prices and import prices (top to bottom). As you can see, the graphs do not show the confidence intervals. In the 1970s/80s, computers were not very powerful - so it was difficult to calculate the confidence intervals. In recent times, of course, every impulse-response graph shows the confidence intervals . . .

Info-source: Nobel Prize Org

Budget 2026-27 Analysis

BUDGET 2026-27 ANALYSIS

# Fiscal deficit is decreasing from 4.4% of GDP (2025-26) to 4.3% (2026-27) - a decrease of 0.1% points. This is good.

# Nominal GDP is estimated to grow/increase in 2026-27 by 10%.

The 4 Budget components are changing from 2025-26 to 2026-27 like this:

1. Revenue Receipts (good income - ie, taxes)

This is increasing by 7.2% - which is less than the GDP growth rate (10%). This is bad.

2. Capital Receipts (bad income - ie, loans)

This is increasing by 8.8% - which is less than the GDP growth rate. This is good.

3. Revenue Expenditure (bad spending - salaries, schemes, subsidies)

This is increasing by 2% - which is less than the GDP growth rate. This is good.

4. Capital Expenditure (good spending - ie, infrastructure)

This is increasing by 22.1% - which is more than the GDP growth rate. This is good.

The low increase in Revenue Receipts is due to the recent GST tax cuts. But overall this is both a pro-growth and fiscally disciplined Budget . . .

Best Movies Of 2025

Best Movies Of 2025

1. Kantara: Chapter 1

2. Dhurandhar

3. Phule

4. 120 Bahadur

5. Haq

6. Tanvi The Great

7. F1

8. Complete Unknown

9. Avatar: Fire And Ash

10. Mission Impossible: Final Reckoning

'Dhurandhar' Movie Review

MOVIE REVIEW

How do you kill a pack of wolves? You send a tiger disguised as a wolf into the wolves' den - and kill them one by one. 'Dhurandhar' is the story of an Indian spy who infiltrates Pakistan's network of mafia gangs, intelligence agencies and terrorist groups - and gives them a dose of their own medicine.

An excellent action-thriller. A grand epic that must be seen on the big screen. A must-watch for every Indian.

Written and directed by Aditya Dhar. Starring Ranveer Singh, Sanjay Dutt, Akshaye Khanna, Arjun Rampal and R Madhavan . . .

Poverty, Job Creation, Growth, Exports & Government Policy

1. Which is the most important problem in economics? Poverty.

2. What is the solution for poverty? Job creation.

3. What leads to job creation? Economic growth.

4. What else leads to job creation? Exports.

5. What more leads to job creation? Government policy.

Now:

a) Poverty is studied by Development Economics.

b) Job creation is studied by Labour Economics.

c) Growth is studied by Macroeconomics.

d) Exports is studied by Trade Economics.

e) Government policy is studied by Public Economics.

But the most interesting thing in economics is the inter-connections among all these different economic forces/phenomena . . .

Nobel Economics Prize 2025: Creative Destruction

How does economic growth happen due to creative destruction? Must the government subsidise the R&D (research & development) of private companies? This year's (2025) Nobel Economics Prize winners Philippe Aghion and Peter Howitt answered these questions in their 1992 Econometrica paper 'A Model Of Growth Through Creative Destruction' (17k+ citations). They derived the equations for the Equilibrium Rate of Creative Destruction (ERCD) for two scenarios:

A. Free market situation (pic: top equation)

B. Social optimal solution (pic: bottom equation)

z* = ERCD = Probability of a firm making a product of better quality (0<z*<1)

('SP' in bottom equation = Social Planner)

α = Marginal cost = Units of intermediate product used to make one unit of final product (0<α<1)

β = Discount factor = Weightage people give to future consumption (0<β<1)

γ = Innovation step size = Increase in product quality (γ>1)

ψ = R&D productivity (ψ>0)

L = Total amount of labour

The two equations are different - so the free market ERCD and the social optimal ERCD are NOT the same. There are 3 differences:

1. Top equation: Numerator's first term has γ. Bottom equation: Numerator's first term has (γ−1) - which is <γ. So bottom equation's z* < top equation's z*. So social optimal ERCD < free market ERCD. Why? Consider an old firm selling a product of a certain quality and making profit P1. Then a new firm innovates and makes a product of better quality. Now this new product will completely replace the old product in the market. Thus the old firm now makes zero profit and the new firm makes profit P2 (P2>P1). So the new firm's incentive to innovate is the entire amount P2. But the gain to society is just the difference in quality between the two products - given by P2-P1 (<P2). Thus firms innovate at a faster rate than is socially optimal. That is, free market ERCD > social optimal ERCD.

2. Top equation: Denominator has an extra +β. So top equation's z* < bottom equation's z*. So free market ERCD < social optimal ERCD. Why? Because the free market ERCD is decided only by the firms trying to maximise their own profits. But society gives weightage to the future, and hence to innovation - thus increasing the social optimal ERCD. And the more this weightage, the more important is innovation - and the higher is the social optimal ERCD.

3. Bottom equation: Numerator's first term has α^[-1/(1-α)]. Since α<1, this term is >1. So bottom equation's z* > top equation's z*. So social optimal ERCD > free market ERCD. This is because monopolistic firms charge too high prices and hence under-use the intermediate products.

Thus #1 makes free market ERCD > social optimal ERCD. And #2 and #3 make free market ERCD < social optimal ERCD. The relationship is decided by the values of the parameters α, β, γ, ψ and L. If free market ERCD < social optimal ERCD, then government must subsidise R&D - in order to increase the ERCD from the free market level to the social optimal level . . .

'Phule' Movie Review

'PHULE' MOVIE REVIEW

An excellent movie about Jyotirao Phule and Savitribai Phule - the great social reformers who uplifted lower-castes and rehabilitated widows in the 1800s. They started schools for lower-caste children (especially girls) and opened shelters for widows. They ignited a revolution in Poona that spread to the whole country. Maharaja Sayaji Rao Gaekwad of Baroda rightly conferred upon Jyotirao Phule the title of 'Mahatma'. Later social reformers like Gandhiji and Ambedkar would draw inspiration from them. 'Phule' is a moving and inspiring story of courage, sacrifice and service. Written/directed by Anant Mahadevan and starring Pratik Gandhi and Patralekha Paul. Pranaam, Jyotirao and Savitribai . . .