A VAR study finds that past values of central bank interest rates significantly improve predictions of future GDP growth, even after controlling for past GDP growth. This finding is best described as:
AProof that interest rates cause GDP growth via monetary transmission mechanisms
BEvidence that interest rates Granger-cause GDP growth — a statistical finding about predictive precedence, not structural causation
CEvidence that GDP growth Granger-causes interest rates, since the central bank responds to economic conditions
DA spurious correlation that requires an instrumental variable to interpret causally
Granger causality is a statistical test: does X's past predict Y beyond what Y's own past already predicts? Finding that it does establishes predictive precedence — not structural causation. It can still be confounded by omitted variables (e.g., a third factor that drives both interest rates and growth in sequence). Structural causation requires additional identification assumptions beyond what Granger testing provides.
Question 2 Multiple Choice
When computing impulse response functions from a VAR model, researchers must orthogonalize the shocks (e.g., via Cholesky decomposition). The ordering of variables matters because:
ADifferent orderings change the number of lag periods estimated in the model
BDifferent variable orderings produce different orthogonalized shocks and therefore different impulse responses, because the ordering encodes assumptions about which variables respond contemporaneously to which shocks
CCholesky decomposition is only numerically stable for specific variable orderings
DThe ordering determines which variables are treated as exogenous versus endogenous in the system
In a VAR, all variables are endogenous and shocks are correlated. To trace how a shock to one variable propagates, the shocks must be separated — but there is no unique way to do this without imposing structure. Cholesky decomposition achieves orthogonalization by recursively assigning shocks in order: the first variable's shock affects all others contemporaneously, but the second variable's shock does not affect the first contemporaneously, and so on. Different orderings produce different impulse responses, each encoding different causal assumptions. This is why ordering decisions require theoretical justification and why structural VAR extends the framework.
Question 3 True / False
A key advantage of VAR models over single-equation AR models is that VAR explicitly captures bidirectional and feedback relationships — where variable A influences variable B and variable B influences variable A over time.
TTrue
FFalse
Answer: True
This is the central motivation for VAR. A single-equation AR model for GDP growth uses only past GDP growth to predict future GDP growth, missing the role of unemployment, inflation, and interest rates in the dynamic system. VAR estimates a system of equations simultaneously, allowing GDP to affect unemployment and unemployment to affect GDP in subsequent periods — the feedback loops that characterize real economic dynamics. The 'vector' in VAR refers to the vector of variables evolving jointly.
Question 4 True / False
Granger causality, as tested in a VAR model, establishes that one variable produces structural changes in another — making it equivalent to evidence from a randomized experiment for observational time series.
TTrue
FFalse
Answer: False
Granger causality is a statistical criterion about predictive precedence: does X's past improve predictions of Y beyond Y's own past? This can be confounded by omitted variables — a third factor Z that drives X first and Y later would make X appear to Granger-cause Y even with no direct causal link. Randomized experiments establish structural causation by controlling assignment; Granger tests cannot replicate this because time series are observational. Structural VAR models attempt to recover causal identification by imposing theoretically motivated restrictions.
Question 5 Short Answer
Why does orthogonalizing VAR shocks via Cholesky decomposition require researchers to make causal assumptions about the ordering of variables, and what problem does this create for interpreting results?
Think about your answer, then reveal below.
Model answer: In a VAR, the error terms across equations are typically correlated — a surprise increase in GDP and a surprise drop in unemployment may occur together because both respond to some common contemporaneous factor. To isolate the effect of a shock to one variable, you must attribute the correlated variation to one equation first. Cholesky decomposition does this by assuming a recursive causal order: the first-ordered variable can affect all others contemporaneously, while the last-ordered variable only affects others with a lag. This ordering is a causal assumption, not a statistical one. The problem: different orderings produce different impulse responses, and there is often no consensus on the 'correct' ordering, making results sensitive to a researcher's untestable theoretical assumptions.
This is why the move from reduced-form VAR to structural VAR is necessary for causal interpretation. Structural VAR imposes restrictions grounded in economic theory (e.g., monetary policy cannot affect output within the same quarter) to identify orthogonal structural shocks. The Cholesky problem reveals a general truth: recovering causal dynamics from observational time series always requires imposing identifying assumptions — the question is whether those assumptions are explicit and theoretically justified.