Bruce Hansen

IV-PPML-HDFE. We are happy to introduce an instrumental-variable Poisson pseudo-maximum likelihood estimator with high-dimensional fixed effects. We also provide a robust and user-friendly ‘ivppmlhdfe’ package for Stata and Julia. More details here 👇 ideas.repec.org/p/drx/wpaper/2…

@jmwooldridge Ha ha!

I had a great time at the 20th NY Camp Econometrics, organized by Badi Baltagi. My only disappointment is that no one pointed out the intentional typo on the opening slide. 😬

Very excited for this Friday's Chamberlain Online Seminar, where we'll muse about "The Future of Econometrics." Check out this panelist lineup! Friday 3/27 at Noon ET. Come see!

@KhoaVuUmn Update the Econometrics tect?

Refund the tariffs!

@JesusFerna7026 @JohnHCochrane A simple calculation illustrates. Take 3 periods. Invest in period 1, rebalance in 2, and spend in 3. There is one risky asset and one riskless. It is a simple calculation to show that an optimal portfolio has the same risky share in each period. The glide path is suboptimal.

@JohnHCochrane I will check it out. I just finished the post for tomorrow. I will post it the morning, because it has more of an impact if I "sequence" the post right :)

I am always amazed that most people saving for retirement (or designing optimal Social Security systems) rarely take sequencing risk seriously. Simply put, sequencing risk is the risk associated with the order in which returns arrive over one’s lifetime. Sequencing risk hits you twice: while you are working and accumulating wealth, and again while you are retired and drawing it down. Today, I will focus on the first part. The retirement phase warrants its own discussion, and I will address it in a subsequent post. Let me walk you through an exercise I ran yesterday using actual historical U.S. stock market data from the past 80 years to illustrate how important sequencing risk is. I took the annual total returns of the S&P 500 (including reinvested dividends) from 1945 to 2024. The source is the dataset maintained by Aswath Damodaran at NYU Stern, a standard reference for long-run U.S. equity returns. I then deflated each year’s nominal return by the CPI-U inflation rate published by the Bureau of Labor Statistics to obtain real total returns, i.e., returns in constant purchasing power. Over this 80-year period, the S&P 500 delivered a geometric mean real total return of about 7.5% per year. That is an impressive number. But this average return masks a lot. Imagine a worker who starts investing at age 22 and retires at age 68. That gives them 46 years of contributions. In their first year, they contribute $1. Each subsequent year, they increase their contribution by 1% (roughly keeping pace with real wage growth). Every dollar is invested in the S&P 500. They never touch the money until retirement. No panic selling, no market timing, no strategy switching (and no management fees!). Textbook investing and waiting. I ran this exercise for every possible cohort for which the data allow. The first cohort starts investing in 1945 and retires in 1991. The second starts in 1946 and retires in 1992. And so on, all the way to the last cohort, which starts in 1978 and retires in 2024. This yields 34 cohorts, each investing for 46 years, making the same contributions and investing in the same index. The only difference among them is which 46-year slice of historical returns they happen to live through. The most fortunate cohort, the one that started investing in 1954 and retired in 2000, had $607 on the day of retirement (remember, all in real terms), with a real annual return of 8.82%. The unluckiest cohort, the one that started in 1963 and retired in 2009, accumulated $210, with a real annual return of 4.83%. Same contributions. Same index. Same strategy. Same investment horizon. Yet the luckiest retiree ended up with 2.9 times more wealth than the unluckiest. Why? The 1954 cohort had a spectacular final decade. The late 1990s delivered some of the best equity returns in American history, and those returns compounded on a large portfolio built over decades. They retired at the peak, at the end of 1999, before the dot-com crash. The 1963 cohort was not so fortunate. They spent their last working years running straight into the 2008 financial crisis. The S&P 500 lost over 36% in real terms in 2008 alone. That loss hit their portfolio when it was at its largest, right before retirement, with no time left to recover. Clearly, sequencing risk is not about the average return. Both the 1954 and 1963 cohorts experienced roughly similar average returns over their 46-year periods. The difference is when the good and bad years occurred. For the 1954 cohort, the bad years came early (when the portfolio was small) and the good years came late (when the portfolio was large). For the 1963 cohort, the opposite was true. In fact, sequencing risk is even worse because poor returns in the stock market are correlated with weak labor markets: you have a much higher probability of losing your job (or seeing your wage income fall) precisely when the market is doing poorly, preventing you from saving when prices are low and equities are most attractive. However, let me set that point aside today to simplify the exposition. The standard response of the financial planning industry to sequencing risk is the so-called glide path. The idea is simple: when you are young, you hold mostly equities. As you age, you gradually shift toward bonds. By the time you are near retirement, most of your portfolio is in bonds. A common implementation is a linear rule: start with 90% in stocks at age 22 and reduce the equity share steadily until you reach 20% in stocks at age 68. This is roughly what target-date retirement funds do. The logic is sound in principle. You reduce your exposure to equities precisely when a crash would hurt you most. If 2008 happens when you are 65 and 80% of your portfolio is in bonds, the equity crash barely affects you. I applied this glide path strategy to the same 34 cohorts, using historical real returns on the S&P 500 for the equity portion and real returns on 10-year U.S. Treasury bonds (from Damodaran) for the bond portion. Each year, the portfolio is rebalanced to the glide path weights. The glide path does what it is intended to do: it reduces dispersion. The gap between the best and worst cohorts narrows from 2.9x under pure equities ($607 vs. $210) to 1.6x under the glide path ($292 vs. $178), but so does the upside. The best equity cohort (1954–2000) earned a geometric mean real return of 8.82% per year. The best glide path cohort (1975–2021) earned 6.59%. That is a 2.2 percentage point gap. Over 46 years of compounding, a 2.2 percentage-point annual yield yields an enormous difference in terminal wealth: the best glide-path outcome ($292) is less than half the best equity outcome ($607). In other words, the cost of this insurance is substantial. In fact, the median cohort ends up meaningfully poorer under the glide path than under 100% equities. You are not trimming a bit of upside. You are forgoing a substantial share of your expected wealth at retirement. This should not be surprising. Over the long run, equities have outperformed bonds by a wide margin. The equity risk premium is one of the most robust facts in finance. Every year you shift a dollar from stocks to bonds, you accept a lower expected return. Do this for 25 years of your career (roughly the back half, when the glide path has you increasingly in bonds), and the cumulative cost from foregone compounding is very large. But the part that makes me most uncomfortable with the standard glide path advice is that bonds are not safe. People hear “bonds” and think “safe.” They are not. Bonds carry two risks that are easy to forget when inflation is low and interest rates are stable. The first is inflation risk. A conventional bond pays you a fixed nominal coupon (yes, there are TIPS and similar instruments, but they have their own problems, so let me skip them for today). If inflation rises above the market’s expectations when the bond was issued, the real value of those payments declines. The cohorts that retired through the 1970s learned this the hard way. In the data, the real return on 10-year Treasuries was negative in multiple years during the 1970s. The second is interest rate risk. When interest rates rise, the market value of existing bonds declines. The longer the maturity of your bond, the larger the hit. In 2022, the Bloomberg U.S. Aggregate Bond Index declined by approximately 19% in real terms. If you were 65 and had just shifted most of your portfolio into bonds following the standard glide path advice, you would have lost nearly a fifth of your “safe” allocation in a single year. And here is the real sting of 2022: equities fell, too. The S&P 500 lost about 24.5% in real terms that year. The glide path assumes bonds will be there to cushion you when stocks fall. In 2022, both fell together. The cushion was not there. This is not some once-in-a-century event. Stocks and bonds have moved in the same direction before: the 1940s, the 1970s, and in 2022. The negative correlation between stocks and bonds that many investors take for granted is a feature of the disinflationary period from roughly 1982 to 2020. It is not a law of nature. Let me be clear: I am not saying the glide path is wrong. For many people, it is the right choice. If a 30% equity crash near retirement would force you to sell assets at the worst possible time to cover living expenses, the insurance is worth paying for. However, you should know what you are paying. The glide path (or variations of it that I am skipping in the interest of space) is not free. It entails substantial costs in expected returns. Worse, the insurance itself can fail. Bonds can lose money in real terms for extended periods. Bonds can fall at the same time as equities. The glide path reduces sequencing risk. It does not eliminate it. It also introduces risks of its own. The deeper lesson from this exercise is that a substantial part of your retirement outcome depends on when you are born. You can do everything right (save diligently from your first paycheck, invest consistently, stay the course through every crash, never panic sell) and still end up with vastly different results than someone who did the same thing a decade earlier or later. The 1963 cohort did nothing wrong. They just had the misfortune of turning 68 in 2009. No allocation strategy eliminates this. Even under the glide path, the best cohort ends up with substantially more than the worst. Sequencing risk is, to a significant extent, a matter of luck. Next time: what happens when sequencing risk hits you in retirement, when you are drawing down instead of building up. The math there is, if anything, even more unforgiving.

@StephenM That's how my grandparents came! Immigration has been a wonderful blessing for the United States, economically and culturally.

In America, for generations now, the policy has been that anyone who would economically benefit from moving to the US can do so, exercise the franchise in the US and their children, the moment they are born, will be full American citizens with all the rights and benefits therein.

Plenty of countries in history have experimented with importing a foreign labor class. The West is the first and only civilization to import a foreign labor class that is granted full political rights, including welfare & the right to vote. All visas are a bridge to citizenship.

@GovPressOffice @Noahpinion Fire Stephen Miller

Stephen Miller 3 days ago: Alex Pretti is a domestic terrorist. Stephen Miller today: Fire Kristi Noem. She went rogue!!!

@Noahpinion Can Miller be impeached? How could Congress remove him from power?

Remember, Noem is a nobody. An expendable attack dog. Everything is coming from Miller.

Thinking about pursuing a MA in Quantitative Economics? Consider our new STEM-designated program at the University of Wisconsin linkedin.com/posts/jean-fra…

The Pretti family’s heartbreaking request to all of us: get the truth out about our son. Alex was an ICU nurse at the Minneapolis VA whose last act was to protect the woman next to him. We will not let this Administration spread lies.

BREAKING: A witness who was just 5 feet from Alex Pretti filed an affidavit depicting what she saw. She says he didn’t touch any of the officers and didn’t appear to be resisting. He was merely helping a woman who had been pepper-sprayed. She’s is terrified that ICE is looking for her, saying they are lying and she doesn’t know what they will do to her if they find her.

@ben_golub It was -18F, not including wind chill, all morning. I think the students can live without discussion sections one week.

certain schools in the area are made of stronger stuff

The latest #StataNow update added more VCE options for linear models: ▪️HAC & Driscoll–Kraay SEs ▪️HC2/HC3 SEs with clustering ▪️Hansen (2025) inference adjustment ▪️Multiple nonnested clusters for IV Learn more: stata.com/statanow/vce-o… #Stata #StataTip #StataCommunity

@brandnewaldhelm If you are interested in prob and statistics, I highly recommend my book "Probability and Statistics for Economists", available from Amazon

@BruceEHansen Wow, this is way too complicated for me. I might need your help. I'm very interested in statistics and probability theory and would love to discuss it with you

Upgrade to StataNow 19.5! It includes cluster robust jackknife standard errors, adjusted p-values, and confidence intervals, similar to those described in my recent papers. The commend is "reg y x1 x2, vce(hc3 clustervar, dfadjust hansen)".

@5_utr My R package for the same use is posted on my webpage.

It replaces "reg y x1 x2, cluster(clustervar)"

Newly published translation.

Having RFK Jr. as HHS secretary is one of the ~2-3 worst things about Trump 2.0 so far, great job by Susan Collins et. al. noahpinion.blog/p/did-rfk-just…