Chapter 9 Model Apps

An Introduction to the Short Run

Explore the models of Chapter 9 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 9: An Introduction to the Short Run

See also: Chapter 9 Data Apps, the chapter’s data without code.

Trend and cycle

Fig. 1: Economic fluctuations and short-run output

Move the slider to change the growth of potential output, and compare the two panels: watch which one changes and which stays put.

\[ \tilde{Y}_t \equiv \frac{Y_t - \bar{Y}_t}{\bar{Y}_t} \]

\[ Y_t = \bar{Y}_t\,(1 + \tilde{Y}_t) \]

where \(Y_t\) is actual output, \(\bar{Y}_t\) potential output, growing at the rate \(\bar{g}\), and \(\tilde{Y}_t\) short-run output, a wave between plus and minus 2 percent.

Takeaway. Short-run output is the percentage gap between actual and potential output, so the trend cancels out: changing the growth of potential output tilts both lines in panel (a) but leaves panel (b) exactly as it is. Faster trend growth hides the cycle in the level of output, which can keep rising right through the slump, while at zero growth the two panels show the same wave.

Source. Adapted from Fig. 9.1 in Jones (2024), Macroeconomics, 6th ed.

The Phillips curve

Fig. 6: The Phillips curve

Move the slider to change short-run output; the black dot slides along the line, and the title reads the change in inflation.

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

where \(\pi_t\) is inflation, \(\tilde{Y}_t\) short-run output in percent, and \(\bar{\nu} = 0.33\) the slope of the curve.

Takeaway. The Phillips curve turns short-run output into a change in inflation: when output is above potential, firms raise prices faster than everyone expected and inflation rises; when it is below, inflation falls. Only at potential, where the dot sits at the origin, does inflation hold steady, at whatever level it already has. The change is proportional to the gap, so a slump twice as deep lowers inflation twice as fast.

Source. Adapted from Fig. 9.6 in Jones (2024), Macroeconomics, 6th ed.

Fig. 7: The Phillips curve model against the U.S. data

Move the slider to change the model’s slope and watch the squared misses in the title; click a country in the legend to add it.

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

where \(\Delta\pi_t\) is the change in inflation from the year before, in points, \(\tilde{Y}_t\) short-run output and \(\bar{\nu}\) the slope.

Takeaway. The model predicts that inflation rises in years when output is above potential and falls when it is below, along a line through the origin whose slope the slider sets. The U.S. points do slope upward, and the squared misses are smallest for a slope of about one third, close to the best-fitting line. But many years lie far from any line, because shocks such as the oil crises of the 1970s and the surge of 2021–22 move inflation too.

Sources. Data: U.S. Bureau of Economic Analysis (BEA), Real Gross Domestic Product (GDPC1), via FRED; Congressional Budget Office (CBO), Real Potential Gross Domestic Product (GDPPOT), via FRED; U.S. Bureau of Labor Statistics (BLS), Consumer Price Index for All Urban Consumers (CPIAUCSL), via FRED; other countries: OECD, Economic Outlook No. 119, output gap (GAP), from the OECD Data Explorer (dataflow DSD_EO@DF_EO), and World Bank, World Development Indicators, Inflation, consumer prices (FP.CPI.TOTL.ZG), with gaps filled from the World Bank’s Global Inflation Database. Prepared files: data/ch09/fig9-7.csv and data/ch09/short_run_panel.csv (see the data notes). Chart: inspired by Fig. 9.7 in Jones (2024), Macroeconomics, 6th ed.

Okun’s law

Fig. 8: Okun’s law against the U.S. data

Move the slider to change the model’s slope and compare the squared misses in the title; click a country in the legend to add it.

\[ u_t - \bar{u} = -\tfrac{1}{2}\,\tilde{Y}_t \]

where \(u_t - \bar{u}\) is cyclical unemployment, in points, \(\tilde{Y}_t\) short-run output, and \(-\tfrac{1}{2}\) the textbook’s slope, which the slider changes.

Takeaway. Okun’s law predicts that unemployment rises above its natural rate when output falls below potential, along a line through the origin; a steeper slope means bigger swings in unemployment for the same output gap. The U.S. points form a tight, downward-sloping cloud, and the squared misses are smallest for a slope of about −0.6, a little steeper than the textbook’s rule of thumb of −1/2.

Sources. Data: U.S. Bureau of Economic Analysis (BEA), Real Gross Domestic Product (GDPC1), via FRED; Congressional Budget Office (CBO), Real Potential Gross Domestic Product (GDPPOT), via FRED; BLS, Unemployment Rate (UNRATE), via FRED; CBO, Noncyclical Rate of Unemployment, short-term (NROUST), via FRED; other countries: OECD, Economic Outlook No. 119, output gap (GAP), from the OECD Data Explorer (dataflow DSD_EO@DF_EO), and unemployment rate (UNR); the trend through each country’s unemployment rate is our own (Hodrick–Prescott). Prepared files: data/ch09/fig9-8.csv and data/ch09/short_run_panel.csv (see the data notes). Chart: inspired by Fig. 9.8 in Jones (2024), Macroeconomics, 6th ed.

Overstimulating the economy

Fig. 9: The Phillips curve and the booming economy

Move the slider to change the slope of the Phillips curve, and watch how fast inflation climbs in panel (b).

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

\[ \pi_t = \pi_0 + \bar{\nu}\,\tilde{Y}\,t \]

where output is held at \(\tilde{Y} = +3\) percent every year and inflation starts at \(\pi_0 = \bar{\pi} = 2\) percent.

Takeaway. Holding output above potential raises inflation not once but every year, by the same amount, so inflation climbs in a straight line without end. A steeper Phillips curve makes the climb faster and a flatter one slower, but no slope stops it: inflation stops rising only when output returns to potential.

Source. Adapted from Fig. 9.9 in Jones (2024), Macroeconomics, 6th ed., the textbook’s worked answer to Exercise 3 of Chapter 9 (“Overstimulating the economy”), which also inspired panel (b): the simulated inflation path is our own addition.