Prior to the 2020 recession, the yield curve was only inverted for *** days, which was much shorter than the average *** days preceding the previous five U.S. recessions. For instance, the yield curve was inverted for *** days between the inversion in January 2006 and the start of the ********* recession. A yield curve inversion refers to the event where short-term Treasury bonds, such as *** or ***** month bonds, have higher yields than longer term bonds, such as ***** or **** year bonds. This is unusual, because long-term investments typically have higher yields than short-term ones in order to reward investors for taking on the extra risk of longer term investments. Monthly updates on the Treasury yield curve can be seen here.

As of July 22, 2025, the yield for a ten-year U.S. government bond was 4.38 percent, while the yield for a two-year bond was 3.88 percent. This represents an inverted yield curve, whereby bonds of longer maturities provide a lower yield, reflecting investors' expectations for a decline in long-term interest rates. Hence, making long-term debt holders open to more risk under the uncertainty around the condition of financial markets in the future. That markets are uncertain can be seen by considering both the short-term fluctuations, and the long-term downward trend, of the yields of U.S. government bonds from 2006 to 2021, before the treasury yield curve increased again significantly in the following years. What are government bonds? Government bonds, otherwise called ‘sovereign’ or ‘treasury’ bonds, are financial instruments used by governments to raise money for government spending. Investors give the government a certain amount of money (the ‘face value’), to be repaid at a specified time in the future (the ‘maturity date’). In addition, the government makes regular periodic interest payments (called ‘coupon payments’). Once initially issued, government bonds are tradable on financial markets, meaning their value can fluctuate over time (even though the underlying face value and coupon payments remain the same). Investors are attracted to government bonds as, provided the country in question has a stable economy and political system, they are a very safe investment. Accordingly, in periods of economic turmoil, investors may be willing to accept a negative overall return in order to have a safe haven for their money. For example, once the market value is compared to the total received from remaining interest payments and the face value, investors have been willing to accept a negative return on two-year German government bonds between 2014 and 2021. Conversely, if the underlying economy and political structures are weak, investors demand a higher return to compensate for the higher risk they take on. Consequently, the return on bonds in emerging markets like Brazil are consistently higher than that of the United States (and other developed economies). Inverted yield curves When investors are worried about the financial future, it can lead to what is called an ‘inverted yield curve’. An inverted yield curve is where investors pay more for short term bonds than long term, indicating they do not have confidence in long-term financial conditions. Historically, the yield curve has historically inverted before each of the last five U.S. recessions. The last U.S. yield curve inversion occurred at several brief points in 2019 – a trend which continued until the Federal Reserve cut interest rates several times over that year. However, the ultimate trigger for the next recession was the unpredicted, exogenous shock of the global coronavirus (COVID-19) pandemic, showing how such informal indicators may be grounded just as much in coincidence as causation.

The 2020 recession did not follow the trend of previous recessions in the United States because only six months elapsed between the yield curve inversion and the 2020 recession. Over the last five decades, 12 months, on average, has elapsed between the initial yield curve inversion and the beginning of a recession in the United States. For instance, the yield curve inverted initially in January 2006, which was 22 months before the start of the 2008 recession. A yield curve inversion refers to the event where short-term Treasury bonds, such as one or three month bonds, have higher yields than longer term bonds, such as three or five year bonds. This is unusual, because long-term investments typically have higher yields than short-term ones in order to reward investors for taking on the extra risk of longer term investments. Monthly updates on the Treasury yield curve can be seen here.

As of December 30, 2024, ** economies reported a negative value for their ten year minus two year government bond yield spread: Ukraine with a negative spread of ***** percent; Turkey, with a negative spread of 1332 percent; Nigeria with **** percent; and Russia with **** percent. At this time, almost all long-term debt for major economies was generating positive yields, with only the most stable European countries seeing smaller values. Why is an inverted yield curve important? Often called an inverted yield curve or negative yield curve, a situation where short term debt has a higher yield than long term debt is considered a main indicator of an impending recession. Essentially, this situation reflects an underlying belief among a majority of investors that short term interest rates are about to fall, with the lowering of interest rates being the orthodox fiscal response to a recession. Therefore, investors purchase safe government debt at today's higher interest rate, driving down the yield on long term debt. In the United States, an inverted yield curve for an extended period preceded (almost) all recent recessions. The exception to this is the economic downturn caused by the coronavirus (COVID-19) pandemic – however, the U.S. ten minus two year spread still came very close to negative territory in mid-2019. Bond yields and the coronavirus pandemic The onset of the coronavirus saw stock markets around the world crash in March 2020. This had an effect on bond markets, with the yield of both long term government debt and short term government debt falling dramatically at this time – reaching negative territory in many countries. With stock values collapsing, many investors placed their money in government debt – which guarantees both a regular interest payment and stable underlying value - in contrast to falling share prices. This led to many investors paying an amount for bonds on the market that was higher than the overall return for the duration of the bond (which is what is signified by a negative yield). However, the calculus is that the small loss taken on stable bonds is less that the losses likely to occur on the market. Moreover, if conditions continue to deteriorate, the bonds may be sold on at an even higher price, partly offsetting the losses from the negative yield.

We use the yield curve to predict future GDP growth and recession probabilities. The spread between short- and long-term rates typically correlates with economic growth. Predications are calculated using a model developed by the Federal Reserve Bank of Cleveland. Released monthly.

As of December 2024, all United Kingdom government debt securities were returning positive yields, regardless of maturity. This places the yield of both UK short term bonds and long term bonds above that of major countries like Germany, France and Japan, but lower than the United States. What are government bonds? Government bonds are debt instruments where a certain amount of money is given to the issuer, in exchange for regular payments of interest over a fixed period. At the end of this period the issuer then returns the amount in full. Bonds differ from a regular loan through how they can be traded on financial markets once issued. This ability to trade bonds makes it more complex to measure the return investors receive from bonds, as the price they buy a bond for on the market may differ from the price the same bond was initially issued at. The yield is therefore calculated as what investors can expect to receive based on current market prices paid for the bond, not the value it was issued at. In total, UK government debt amounted to over 2.4 trillion British pounds in 2023 – with the majority being comprised of different types of UK government bonds. Why are inverted yield curves important? UK government bond yields over recent years have taken on a typical shape, with short term bonds having a lower yield than bonds with a maturity of 10 to 20 years. The higher yield of longer-term bonds compensates investors for the higher level of uncertainty in the future. However, if investors are sufficiently worried about both a short term economic decline, and low long term growth, they may prefer to purchase short term bonds in order to secure assets with regular interest payments in the here and now (as opposed to shares, which can lose a lot of value in a short time). This can lead to an inverted yield curve, where shorter term debt has a higher yield. Inverted yield curves are generally seen as a reliable indicator of a recession, with inverted yields occurring before most recent U.S. recessions. The major exception to this is the recession from the coronavirus pandemic – but even then, U.S. yield curves came perilously close to being inverted in mid-2019.

Graph and download economic data for 10-Year Treasury Constant Maturity Minus Federal Funds Rate (T10YFF) from 1962-01-02 to 2025-07-29 about yield curve, spread, 10-year, maturity, Treasury, federal, interest rate, interest, rate, and USA.

As of April 16, 2025, the UK bond market displayed a positive spread of **** basis points between 10-year and 2-year yields, indicating long-term rates slightly ***** short-term ones. The 5-year versus 2-year spread and the 2-year versus 1-year spread also showed a ******** value, at **** and **** basis points, respectively.

Synthetic and Real-World Surface Wave Dispersion Datasets

This dataset is designed for surface wave dispersion curve inversion, particularly suited for deep learning-based inversion studies. It provides both synthetic and real-world datasets, including global and local models, enabling the evaluation of various inversion methods such as zero-shot and few-shot strategies. Researchers can refer to the DispFormer framework for details on the model and the corresponding code used for inversion tasks. The related paper for DispFormer can be found here.

For further details on how to use the datasets and the associated neural network models, visit the GitHub repository: https://github.com/liufeng2317">https://github.com/liufeng2317

Datasets Overview

The LITHO1.0 global synthetic dataset is primarily used for pre-training the model. The Central and Western US Dataset (CWD) and Continental China Dataset (CCD) are used to validate the effectiveness of zero-shot and few-shot strategies. Finally, the datasets retrieved from the China Seismological Reference Model (CSRM) are used to test the model's performance on real-world data.

Data Files

• depth_vp_vs_rho.npz: Contains a 1-D velocity model, including depth, P-wave velocity, S-wave velocity, and density.
• depth_vs.npz: Contains a 1-D velocity model with depth and S-wave velocity (used for training the DispFormer).
• lon_lat.npz, lat_glat_lon.npz: Contain the station locations for the observed data.
• period_phase_group.npz: Contains synthetic and observed dispersion curves, including period, phase velocity, and group velocity.
• Folders train_data, valid_data, and test_data: Contain data directly used for training, validating, and testing the model

Example of Loading Data Using Python

Here is an example of how to load the data using Python:

import numpy as np
data_path = "" # Specify your data path
all_disp_loc = np.load(data_path)["data"] # Load data from the file

For more details on how to use the data, please refer to the DispFormer GitHub repository.

References

1. Liu, F., Deng, B., Su, R., Bai, L. & Ouyang, W.. DispFormer: Pretrained Transformer for Flexible Dispersion Curve Inversion from Global Synthesis to Regional Applications[J]. arXiv preprint arXiv:2501.04366, 2025.
2. W. Shen, M. H. Ritzwoller, and V. Schulte‐Pelkum, “A 3‐D model of the crust and uppermost mantle beneath the Central and Western US by joint inversion of receiver functions and surface wave dispersion,” JGR Solid Earth, vol. 118, no. 1, pp. 262–276, Jan. 2013, doi: 10.1029/2012JB009602.
3. S. C. Griffiths, B. R. Cox, E. M. Rathje, and D. P. Teague, “Surface-wave dispersion approach for evaluating statistical models that account for shear-wave velocity uncertainty,” J. Geotech. Geoenviron. Eng., vol. 142, no. 11, p. 4016061, Nov. 2016, doi: 10.1061/(ASCE)GT.1943-5606.0001552.
4. M. E. Pasyanos, T. G. Masters, G. Laske, and Z. Ma, “LITHO1.0: An updated crust and lithospheric model of the Earth,” JGR Solid Earth, vol. 119, no. 3, pp. 2153–2173, Mar. 2014, doi: 10.1002/2013JB010626.
5. X. Xiao et al., “CSRM‐1.0: A China Seismological Reference Model,” JGR Solid Earth, vol. 129, no. 9, p. e2024JB029520, Sep. 2024, doi: 10.1029/2024JB029520.

Summary statistics for main variables.

At the end of 2024, the yield for a 30-year U.S. Treasury bond was **** percent, slightly higher than the yields for bonds with short-term maturities. Bonds of longer maturities generally have higher yields as a reward for the uncertainty about the condition of financial markets in the future.

Heterogeneous effects by region (FE estimation results).

MC3 Inversion Dip Distribution curve from Schlumberger. Measured in unitless.

This database is based on the statistical yearbook data of 30 provinces, municipalities and autonomous regions in China (excluding Hong Kong, Macao, Taiwan, and Tibet Autonomous Region) from 2000 to 2017, a total of 18 years of statistical yearbook data was used to conduct in-depth research on the reduction of CO2 emissions from the development of new energy in the region.

United States - 10-Year Treasury Constant Maturity Minus 3-Month Treasury Constant Maturity was -0.06% in July of 2025, according to the United States Federal Reserve. Historically, United States - 10-Year Treasury Constant Maturity Minus 3-Month Treasury Constant Maturity reached a record high of 5.18 in August of 1982 and a record low of -1.89 in May of 2023. Trading Economics provides the current actual value, an historical data chart and related indicators for United States - 10-Year Treasury Constant Maturity Minus 3-Month Treasury Constant Maturity - last updated from the United States Federal Reserve on July of 2025.

In June 2025, the yield on a 10-year U.S. Treasury note was **** percent, forecasted to decrease to reach **** percent by February 2026. Treasury securities are debt instruments used by the government to finance the national debt. Who owns treasury notes? Because the U.S. treasury notes are generally assumed to be a risk-free investment, they are often used by large financial institutions as collateral. Because of this, billions of dollars in treasury securities are traded daily. Other countries also hold U.S. treasury securities, as do U.S. households. Investors and institutions accept the relatively low interest rate because the U.S. Treasury guarantees the investment. Looking into the future Because these notes are so commonly traded, their interest rate also serves as a signal about the market’s expectations of future growth. When markets expect the economy to grow, forecasts for treasury notes will reflect that in a higher interest rate. In fact, one harbinger of recession is an inverted yield curve, when the return on 3-month treasury bills is higher than the ten-year rate. While this does not always lead to a recession, it certainly signals pessimism from financial markets.

Potential channel analysis (FE estimation results).

MC3 Inversion Dip with Maximum Number of Models curve from Schlumberger. Measured in unitless.

As of April 16, 2025, Germany's bond market displayed a positive spread of 77.2 basis points between 10-year and 2-year yields, indicating long-term rates above short-term ones. The 5-year versus 2-year spread was also positive, at **** basis points. On the other hand, the 2-year versus 1-year spread was negative, at **** basis points, suggesting a mildly inverted yield curve in shorter maturities. Negative spreads indicate a (partially) inverted yield curve. This often signals investor pessimism about short-term economic prospects, as investors seek the relative safety of long-term bonds, pushing those yields down relative to shorter-term bonds. An inverted yield curve is typically interpreted as a potential indicator of economic slowdown or recession, as it reflects expectations of lower interest rates in the future to stimulate the economy.

The yield on US 10 Year Note Bond Yield rose to 4.38% on July 30, 2025, marking a 0.05 percentage point increase from the previous session. Over the past month, the yield has edged up by 0.14 points and is 0.34 points higher than a year ago, according to over-the-counter interbank yield quotes for this government bond maturity. US 10 Year Treasury Bond Note Yield - values, historical data, forecasts and news - updated on July of 2025.