Chapter 14 Model Apps

Financial Crises and the Short-Run Model

Explore the models of Chapter 14 without any code. Every chart below is live: move its slider to change one part of the model and watch the curves respond, and hover over a line to read its values.

← Back to Chapter 14: Financial Crises and the Short-Run Model

See also: Chapter 14 Data Apps, the chapter’s data without code.

Financial frictions in the short-run model

Fig. 2: A housing bubble and a financial crisis

Move the slider to change the financial friction; in panel (b), watch where point D lands compared with B and C.

\[ R_t = R^{ff}_t + \bar{f} \]

\[ \tilde{Y}_t = \bar{a} - \bar{b}\bar{f} - \bar{b}\,(R^{ff}_t - \bar{r}) \]

where \(R_t\) is the rate firms and households pay, \(R^{ff}_t\) the fed funds rate, \(\bar{f}\) the risk premium and \(\bar{a} = -2\) the housing bust.

Takeaway. The Fed cuts its rate just enough to offset the housing bust, but firms borrow at that rate plus the premium, so each point of friction costs \(\bar{b}\) points of output, exactly like a fall in demand. With no friction the cut restores potential output and D sits on C; a friction of 2 points undoes the cut and puts D on B, and a larger one leaves the economy worse off than if the Fed had done nothing.

Source. Adapted from Fig. 14.2 in Jones (2024), Macroeconomics, 6th ed.

Fig. 3: The financial crisis in the AS/AD framework

Move the slider through the periods after the shock; watch the AS curve shift down and the economy slide along AD′ toward C.

\[ \tilde{Y}_t = \bar{a} - \bar{b}\bar{f} - \bar{b}\bar{m}\,(\pi_t - \bar{\pi}) \]

\[ \pi_t = \pi_{t-1} + \bar{\nu}\,\tilde{Y}_t \]

\[ \pi_C = \bar{\pi} + \frac{\bar{a} - \bar{b}\bar{f}}{\bar{b}\bar{m}} \]

where \(\bar{a} = -2\) is the housing bust, \(\bar{f} = 4\) the risk premium, \(\bar{m}\) the policy response, \(\bar{\nu}\) the slope of the Phillips curve and \(\pi_C\) long-run inflation.

Takeaway. The housing bust and the risk premium both shift the AD curve down, so in period 1 the economy jumps from A to B, with output and inflation both lower. Firms then expect last period’s lower inflation, the AS curve shifts down period after period, and the economy slides along AD′ toward C: output recovers to potential, but inflation keeps falling and ends below zero, in deflation.

Source. Adapted from Fig. 14.3 in Jones (2024), Macroeconomics, 6th ed.

Monetary policy, the output gap and money

Fig. 4: What the Taylor rule recommends and what the Fed did

Move the slider to change \(\bar{r}\) in the rule and watch its line shift; the title reads the rule minus the actual rate in 2002–2006.

\[ i_t = \bar{r} + \pi_t + 0.5\,(\pi_t - 2) + 0.5\,\tilde{Y}_t \]

where \(i_t\) is the fed funds rate the rule recommends, \(\pi_t\) core PCE inflation over the past year, \(\tilde{Y}_t\) short-run output and \(\bar{r}\) the long-run real interest rate.

Takeaway. The rule’s rate rises one for one with \(\bar{r}\), so the slider moves its whole line up or down by the same amount in every quarter, while the actual rate stays put. Whatever value you pick, the rule called for rates well above the actual ones in 2022, when inflation was high. The verdict on 2002–2006 depends on \(\bar{r}\): on average the rule sat above the actual rate then only for values of about 1 percent or more.

Sources. Data: Board of Governors of the Federal Reserve System, Federal Funds Effective Rate (FEDFUNDS), via FRED; U.S. Bureau of Economic Analysis, PCE price index excluding food and energy (PCEPILFE), via FRED; U.S. Bureau of Economic Analysis, Real Gross Domestic Product (GDPC1), via FRED; Congressional Budget Office, Real Potential Gross Domestic Product (GDPPOT), via FRED; recession dates: National Bureau of Economic Research, business cycle dates, as the indicator USREC, via FRED. The Taylor rule and short-run output, 100 × (GDPC1 / GDPPOT − 1), are our own calculations. Prepared files: data/ch14/fig14-4.csv, data/ch14/recessions.csv (see the data notes). Chart: inspired by Fig. 14.4 in Jones (2024), Macroeconomics, 6th ed.

The Great Depression in the short-run model

Fig. 12: The Great Depression in the IS/MP framework

Move the slider to add one shock at a time, from A to D; watch which curve shifts and read output in the title.

\[ \tilde{Y}_t = \bar{a} - \bar{b}\,(R_t - \bar{r}) \]

\[ R_t = i_t - \pi_t \]

where \(R_t\) is the real interest rate, \(i_t\) the nominal rate, which the Fed raises and then holds fixed, \(\pi_t\) inflation and \(\bar{a}\) the demand shock.

Takeaway. Each step pushes output further below potential: the Fed’s hike raises the real rate (A to B), and the stock market crash shifts the IS curve back (B to C). The slump then lowers inflation, and with the nominal rate held fixed the real rate rises again (C to D), which deepens the slump and lowers inflation once more: a deflationary spiral.

Source. Adapted from Fig. 14.12 in Jones (2024), Macroeconomics, 6th ed. The numbers follow the textbook’s worked exercise on the Great Depression.

Fig. 13: The Phillips curve and the Great Depression

Move the slider from A to D; each point’s height is how much inflation changes in a year, and the title reads it.

\[ \Delta\pi_t = \bar{\nu}\,\tilde{Y}_t \]

\[ \tilde{Y}_t = (1 + \bar{b}\bar{\nu})\,\tilde{Y}_{t-1} \]

where \(\Delta\pi_t\) is the change in inflation and \(\bar{\nu}\) the slope of the Phillips curve; the second line holds while the nominal rate stays fixed.

Takeaway. Inflation falls whenever output is below potential, and by more the deeper the slump, so the fall grows from B to C to D. Starting from zero inflation, that means deflation, and with the nominal rate fixed each point of deflation raises the real rate by a point, so the slump grows by the factor \(1 + \bar{b}\bar{\nu}\) each year.

Source. Adapted from Fig. 14.13 in Jones (2024), Macroeconomics, 6th ed.