NEW! DSGE model with Government and Spillovers a la Arrow!

Taxes in DSGE Models

DSGE Model with Government: How Taxes Shape the Economy

When economists talk about Dynamic Stochastic General Equilibrium (DSGE) models, they’re really talking about a powerful lens for understanding how economies work. At their core, these models bring together households, firms, and governments, and show how their decisions interact over time in the face of uncertainty.

In this article, I want to share a version of the model where the government plays a role — not by building roads or consuming goods, but simply by taxing and redistributing income. This small change has big consequences.

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The package includes:

Matlab .mod files for my two models! Taxes and Learning by doing a la Arrow!
PDF with step by step solution and explanations. (Recursive method)
Matlab files to produce the scenario analysis graphs for IRFS and simulated variables.

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Why Add Government?

In the classic Real Business Cycle (RBC) model, households decide how much to work, consume, and save, while firms hire labor and use capital to produce goods. The story is elegant but limited: it leaves out something crucial — the government.

When we add the government, two new elements come in:

It taxes labor and capital income, so workers take home less and savers earn a lower return on investment.
It rebates all of that money back to households in the form of lump-sum transfers.

At first glance, this might look like a wash — the government takes money and gives it back. But the way it does this changes the economy’s behavior.

Taxes Change Incentives

Taxes are not neutral. Even though families eventually get transfers back, the fact that their wage and return on savings are taxed makes them behave differently. Workers see less reward for each hour worked, so they work a little less. Savers earn less on their capital, so they invest less.

The transfers, on the other hand, are neutral in the sense that they don’t affect these marginal choices. They just shift income around. This means they boost disposable income but don’t change the decision at the margin to work or save.

This is why in the mathematical solution, transfers seem to “disappear.” They don’t vanish from the system — they just don’t show up in the first-order decisions. What really matters for behavior are the after-tax returns.

Simulating the Model

To see the difference government makes, I simulated two versions of the model using Dynare.

In the no-tax economy, households keep all their labor and capital income. Output, consumption, and investment grow at healthier levels. The economy reacts strongly to productivity shocks, with quick rebounds and higher long-run growth.
In the taxed economy, the government collects a share of labor and capital income and gives it back as transfers. Disposable income shifts, but private activity contracts. Households consume less, work less, and invest less. Over time, this means lower capital accumulation, higher interest rates, and weaker growth.

Both economies face the same sequence of productivity shocks, but the paths they follow look very different.

IRFS are diminished by taxation

The IRFs illustrate the dynamic effects of a productivity shock under taxation versus no taxation. With taxes, households consume and invest less, supply less labor, and output falls more sharply. Distortions persist over time, showing how fiscal wedges amplify downturns and dampen long-run recovery.

Taxes distort firms and households' incentives

The simulated time series compare steady dynamics in taxed and untaxed economies. Without taxes, output, consumption, investment, and capital accumulate at higher levels. Under taxation, transfers rise, but disposable income, labor supply, and private investment remain lower, generating systematically weaker growth paths despite identical sequences of productivity shocks.

Why This Matters

This exercise might sound theoretical, but it teaches something important about policy. Even if a government returns all of its revenue back to families, the way it collects that revenue matters. Taxes on labor and capital are distortionary: they affect choices and reduce efficiency.

In reality, governments do spend on goods and services, and they may borrow to finance deficits. But even in this simple setup — where the government does nothing but tax and rebate — we see how fiscal policy can shape economic dynamics in powerful ways.

Final Thoughts

The DSGE model with government is a small extension of the RBC framework, but it captures one of the most important insights of modern macroeconomics: policy changes incentives, and incentives shape outcomes.

By simulating this model, we can see how economies evolve differently depending on whether taxes are present. Transfers don’t change decisions at the margin, but taxes do — and that difference is what drives the long-run gap between the taxed and untaxed economies.

This kind of modeling is why DSGE remains central to economic research and policy analysis. It shows us not just what happens when shocks hit, but also how the rules of the game — taxes, transfers, policies — shape the way households and firms respond.