Macroeconomic shocks do not affect everyone in the same way. The response of a household, firm or region may depend on the state it is in before the shock occurs. Put differently, an economic condition – such as a family’s wealth, a company’s financial health or a part of the country’s exposure to a particular risk – will shape the reactions to changes in the wider economy. Understanding these differences matters because the overall effect on the economy depends on who responds, and by how much.
Economists often combine state-dependent local projections with measures of macroeconomic shocks to study these differences. But even when the shock measure is external (or ‘exogenous’), the estimated relationship need not reveal how the causal response varies with the state.
In my research with Joel David (Federal Reserve Bank of Chicago), Xiyu Jiao (University of Gothenburg) and Weining Wang (University of Bristol), we show when it does – and why the standard approach can still give a misleading picture (David et al, 2026).
When do these estimates have a causal meaning?
Our first result identifies a condition under which local projections reveal causal state-dependent responses. At each point after the shock, the outcome must depend on the shock in a proportional way, although the size of the effect may vary flexibly with the state. The way in which the shock propagates over time must also remain stable.
This condition is built into many modern macroeconomic models with heterogeneous households or firms, including heterogeneous agent New Keynesian (HANK) models. State-dependent local projections can then reveal causal responses without requiring researchers to specify the full model.
The condition can fail when shocks alter the propagation mechanism – for example, by making borrowing constraints bind, triggering a regime change or producing different effects for positive and negative shocks.
Why a straight line can be misleading
Even when state-dependent local projections have a causal interpretation, the standard specification may still fail to reveal what researchers care about.
The usual approach assumes that the response changes in a straight line with the state. This produces a single coefficient that appears to show whether responses rise or fall as the state changes.
But that coefficient is only an average summary. A positive estimate does not necessarily mean that groups with higher values of the state respond more strongly. A small coefficient may likewise conceal large but offsetting differences.
With this in mind, our study develops a more flexible method that allows the shape of the response to emerge from the data. Instead of reducing the relationship to a single slope, it estimates how the response changes across the full range of the state. It also provides confidence bands showing how precisely that relationship is estimated.
What happens when we apply the method to firms?
We apply the method to US firms’ investment following unexpected changes in monetary policy. We measure firms’ state using ‘distance to default’. A higher distance to default means that a firm is financially safer.
The standard linear model suggests that safer firms respond more strongly to an interest rate cut. Our flexible estimates instead show a hump-shaped pattern: firms near the middle of the distribution of financial health respond most, while both the riskiest and safest firms respond less.
The difference is large. Four years after the shock, the linear model predicts that the investment response of a typical firm is less than five percentage points larger than that of a firm near the risky end of the distribution. Our flexible model puts the difference above 20 percentage points.
When comparing very safe firms with typical firms, the two approaches even produce opposite conclusions.
Why does this matter for the wider economy?
The linear model also understates the aggregate importance of financial differences. It implies that they add about 0.09 percentage points to the response of aggregate investment, compared with about one percentage point under our flexible model – roughly ten times as much.
The broader lesson is that learning who responds most requires discipline in two directions: enough economic structure to justify a causal interpretation, but enough flexibility to let the response take its true shape.
