Friday, August 31, 2007
Thursday, August 30, 2007
Time to Do the Wrong Thing
In fact, since the history of the Greenspan era suggests that following an ex ante optimal policy for growth and inflation does create the impression that there is a Greenspan put, the Fed can expect that it will occasionally have to make a deliberate mistake. Something is wrong.
If the Fed doesn't cut the federal funds rate target in September -- barring a truly dramatic improvement in credit conditions or a series of economic reports that are either stronger or more inflationary than expected -- I will, as I said a few days ago, be puzzled, but perhaps not all that puzzled after all. By such inaction in the face of widening spreads and credit rationing, I argued then, the Fed would be "either making a mistake or acknowledging that they made a mistake earlier by not having raised the rate higher in the first place." But I hadn't considered the possibility of a deliberate mistake. Does one need to sacrifice a virgin on the altar of Moral Hazard Avoidance, not because it will in fact result in a better harvest, but because the people think so, and they won't bother planting unless you do?
Tuesday, August 28, 2007
Punch at Caesar's Funeral
At the end of the commentary, Mr. Gross does attempt to make an actual argument against interest rate cuts, but I fear he has confused metaphor with reality:
College students don't alleviate the after-effects of an evening spent at the punch bowl by returning to lap up the dregs. Just so, finance types should know that cheap money, credit on demand, and endless leverage aren't the cure for a hangover caused by too much cheap money, leverage, and credit on demand.Or perhaps he has merely forgotten some relevant history. Unlike me, Mr. Gross does have a degree in history, so perhaps he will be able to find historical examples to buttress his case. (There were none in this particular commentary.) But to my own sparsely tutored ear, his analogy bears an unpleasant resemblance to the type of argument that was often heard in policy circles during the period 1929-1932.
As a matter of macroeconomics, I would say that “cheap money, leverage, and credit on demand” are precisely the cure “for a hangover caused by too much cheap money, leverage, and credit on demand” – at least to the extent that said hangover carries a risk of recession or deflation. If only the Fed had provided cheap money and credit on demand in late 1929 and 1930 (or, for that matter, 1931 and 1932), history might have turned out quite differently (and, I dare say, better). Perhaps Mr. Gross can cite some recent history – the 1998 experience – as an example of what’s wrong with easing monetary policy in response to a mass deleveraging. I have to ask, though: If the choice is between risking another 1999 and risking another 1931, which one should we be more concerned about? I pause for reply....
Not that we really have to worry about a repeat of the 1930s. Ben Bernanke is an economic historian – and an expert on the Great Depression, at that. As soon as he gets a strong whiff of recession, he will do anything but repeat the mistakes of the early 1930s. But it’s also clear that Chairman Bernanke is bending over backward to avoid repeating 1998. The last three weeks have been a case study in how to loosen monetary policy without loosening monetary policy. And it’s worth noting that the US economy was a lot stronger going into 1998 than it was going into 2007.
The classic “punch bowl” metaphor adopted by Mr. Gross has (at least) one major limitation: unlike alcohol, money is pretty much essential to the functioning of a modern economy. Certainly the Fed should take away the ice cream before our waistlines start to inflate. But when our bulimic economy realizes it has eaten too much, there are healthier approaches than encouraging vomiting and fasting.
* I hesitate to use the word “conservative” in any substantive context, however. The fact that “conservatives” are calling for easy money is yet one more small contribution to the mounting evidence that such words have little left in the way of meaning.
Sunday, August 26, 2007
Long and Variable Lags
- The low financial literacy of US households;
- The financial innovation that has resulted in the massive securitisation of illiquid assets; and
- The low interest rate policy followed by Alan Greenspan’s Fed from 2001 to 2004,
So far I don’t particularly disagree, but Boeri and Guiso are then quick to paint Alan Greenspan, along with “the Keynesian sirens” whose song he chose to follow, as the villains in this matter. In my own view,
If there was a monetary policy mistake in 2002-2003, the mistake was a failure to anticipate the lag between policy action and results. When a monetary stimulus is transmitted through the housing market, the lags are apparently longer than the typical lags associated with monetary policy historically. Greenspan kept easing because he wasn’t seeing results from his earlier easing, and in retrospect, it appears that he just wasn’t waiting long enough for those results.From this passage, it may begin to become clear what I meant when I said, “The Fed should encourage the continuation of a housing boom (or something of that nature).” I realize that, at the peak of the boom, the stimulus was stronger than what the US economy needed, but the policy today seems to be one of keeping interest rates high enough to erase, ultimately, a large part of the boom, perhaps bringing the US economy back to where it was in mid-2004. (Even that is only if we assume no overshoot on the downside. And the current financial crisis is already laying the groundwork for just such an overshoot.).
If that was the mistake, then Bernanke may have made the same mistake in the other direction (and if so, he is apparently still making it). The housing bust that is taking place today is more or less a deliberate result of policy: the Fed wanted to slow down the economy, and the only way they could do it was to put the brakes on the housing market. Bernanke kept tightening in the first half of 2006 because he wasn’t seeing results from Greenspan’s earlier tightening (because the housing market was still booming, or it had just begun to slow down, and the macroeconomic effects weren’t yet apparent). Starting in the second half of 2006, Bernanke got what he was looking for: the monetary tightening from 2004 and 2005 finally was affecting economic growth.
If we look at the time lag from the beginning of the tightening (June 2004) to the point where the effect was first apparent (July 2006), it suggests that about half the impact of the tightening has yet to be felt. (Apply the same time lag to the end of the tightening, June 2006, and it suggests a peak effect starting in July 2008.) The hope, I suppose, is that we haven’t yet, even now, seen the full effect of Greenspan's original loosening outside the housing market, and that the residual effect of the loosening will counterbalance the effect of the tightening via the housing market. (For example, the dollar seems to have weakened very slowly, and we are beginning to see the effects on the trade balance.) When I think about it, that scenario seems pretty optimistic. It seems more likely that Bernanke has indeed repeated Greenspan’s mistake in reverse.
I guess some economists were perfectly happy with 2004, but I certainly wasn’t: the unemployment rate was 5.6% in June 2004; by a typical recent estimate, that’s almost a full percentage point above the natural rate. (The Philadelphia Fed’s most recent Survey of Professional Forecasters puts the median natural rate estimate at 4.65%. Anyone who has been following this blog since the beginning will know that I put the natural rate even lower.) So, while I don’t think the Fed should try to bring back the boom conditions of early 2006, I also don’t think it should deliberately “puncture” the “bubble.” Scrape off the froth, but don’t pour half the beverage down the drain.
Friday, August 24, 2007
Why No Liquidity Futures?
While the newborn derivatives may hedge individual, institutional and sector risk, they cannot hedge liquidity risk.That’s true. But why? Why aren’t there derivatives to hedge liquidity risk? Surely it’s possible to create a futures contract on a bid-ask spread (or maybe separate futures on the bid and the ask). Market-makers could even use the contracts to hedge against excessive liquidity. The contracts would require some kind of rule for dealing with situations when there is no observed bid, as is apparently the case with many mortgage-backed securities today, but presumably a rule can be worked out.
Wednesday, August 22, 2007
Did this in Housing seem an obvious bubble?
- It is still reasonable to believe that the housing boom was not a bubble; and
- Even if one believes that, one can still be ultra-bearish on housing today.
In this chart (an update of the earlier one), I plot an index of actual housing prices (the OFHEO Index, standardized to 1997Q2=100) and a crude estimate of the fundamental value of houses (CPI owner’s equivalent rent, capitalized at the 10-year TIPS yield plus a 2% risk premium, and expressed as an index standardized to 1997Q2=100).
My valuation method is crude, but it is not contrived. That is, I used what I considered the most obvious set of numbers, not some cherry-picked set designed to generate a certain result: I used the 10-year TIPS yield because it’s the most liquid market-determined long-term real interest rate for the US; I used 1997 as the base year because that is first year for which those yields are available; I added 2% because it’s an integer, and 1% was clearly too little, and 3% was clearly too much (at least prior to the last two weeks), and I used CPI-OER and OFHEO because those are first relevant indexes that I found for rents and house prices.
If you are willing to accept my crude approximation of the fundamental and my implicit (arbitrary but, I think, reasonable) assumption that prices in 1997Q2 were close to the fundamental, my results imply that there was no bubble this decade, but that housing prices now have to make a large downward adjustment due to a change in the fundamental. Actually, it is a conservative (that is, on the low side) estimate of how much adjustment prices have to make, because the relevant risk premium has clearly risen very recently, which would drive the fundamental values of houses down even further.
Some people have pointed out that, historically, interest rates do not explain most of the changes in aggregate housing prices, and that, in fact, if you model housing prices empirically using interest rates as one of the predictors, the results show that prices in late 2005 (where my two lines cross) were already far above the predicted value. People interpret this empirical finding to mean that housing prices must have been in a bubble. I see several problems with this argument:
- This is one of those situations in economics where theory matters. If you want to argue that prices have moved far above the fundamental, you need a theory of what the fundamental value is; you can’t simply fit a bunch of possibly relevant variables empirically in a linear model and assume that the fitted value is the fundamental value. For example, if housing markets have become more efficient over time, then housing prices could have been deviating from the fundamental in all those past years and only now following the fundamental. And even if prices in the past did follow the fundamental, you would need to choose the exact right set of variables in order to get the correct fit, and you would need to choose the right functional form; otherwise, the coefficients on your variables will be biased, and, in particular, you may be underestimating the importance of interest rates.
- If real interest rates are the most important variable, how do you represent them prior to 1997? There is no available series: you have to start with nominal rates and make some assumption about what expected inflation rate is applicable.
- In an empirical fit, how do you account for the price adjustment process? Everyone knows that housing prices adjust slowly, so to make a meaningful empirical fit, you need a theory (explicit or implicit) about the adjustment process. If you ignore the adjustment process, you’re implicitly assuming that adjustment is instantaneous, which is obviously wrong. In particular, you will run into problems when there are dramatic changes in the fundamental, as for example, with the very low real interest rates in the late 1970s followed by the very high real interest rates in the early 1980s.
Tuesday, August 21, 2007
I come to bury the Housing Boom, not to praise it.
- The housing boom was a good thing; therefore
- Far from worrying about moral hazard, the Fed should be deliberately rewarding those who participated; and
- (At least according to my reading of the macroeconomy) The Fed should encourage the continuation of a housing boom (or something of that nature).
My basic argument is quite simple: without the housing boom, there would have been no economic recovery, and…recovery is good.
It’s not very controversial that the housing boom was the main reason for the economic recovery, so let’s do a thought experiment in which we re-run the years since 2001 without a housing boom. Would something else have happened instead to produce a recovery? Let’s line up the candidates.
First, fiscal policy. We did have a war, two large tax cuts, and a large new entitlement benefiting the age group with the highest marginal propensity to spend. The consensus is that all these were not enough. Perhaps they would have prevented the recession from getting worse, but without the direct and indirect effects of the housing boom, any recovery would have been meager at best. OK, how about a big public works program? Not a bad idea, if you ask me, but this is where we have to begin distinguishing between thought experiment and fantasy. If your conception has a public works program that dwarfs the New Deal being passed by a Republican Congress and signed by George W. Bush, I recommend you get in touch with George Lucas about the special effects.
What about an export boom (and/or substitution of domestic products for imports) supported by a weak dollar? That is, after all, the traditional mechanism by which monetary policy is supposed to operate in an open economy with a flexible exchange rate. The first problem that arises is that the US exchange rate against many countries isn’t (and, most emphatically, wasn’t) flexible, and even when it is nominally flexible, the competing products are often effectively priced in dollars. One could imagine a mildly successful beggar-thy-neighbor policy against Europe (supposing that, in the absence of a housing boom, the dollar would have crashed against the Euro in 2002 instead of falling gradually over 5 years). At best, that gives us a mild (and somewhat stagflationary) recovery in the US and a severe recession in Europe (which, as you may recall, had its own problems in the early years of this decade). All in all, the possibilities created by a falling dollar (in place of the housing boom) are not impressive.
So what’s left? An investment boom supported by low interest rates? If it didn’t happen when the federal funds rate was at 1%, would it have happened if the rate had fallen to 0%? I tend to doubt it. An investment boom supported by “quantitative easing”? Possibly, but it took Japan years even to hit on that possibility, and the jury is still out on whether quantitative easing was the real reason for Japan’s recovery. The premise that such a policy would have been tried successfully in the US during this decade is speculative at best. Other ideas? Money dropping from the sky? Maybe, but remember, “Helicopter Ben” didn’t take over the Fed until 2006. And so on….Rather than going from the bizarre to the more bizarre, I’m just going to reassert my premise and suggest that the burden of proof is now on anyone who disagrees: Without the housing boom, there would have been no economic recovery.
The implication of having no economic recovery is that we would have slack resources the whole time – the sort of event that used to be called a depression before the term fell victim to political correctness. Thus, comparing my counterfactual world to the actual world, all the extra production that we got out of the US economy was done with resources that would otherwise have been wasted. From a macroeconomic point of view, all those extra houses and such were free – a free lunch, if you will. (I won’t abide any more TANSTAAFL: in Keynesian economics there has always been a free lunch; that was the main point of the General Theory.) So those who say that the housing boom was a bad thing are saying that we should have turned down that free lunch when it was offered.
And what of those who participated in the boom? To my mind, they are in the same category as the Iraqi Shiite rebels in 1991. They helped US policymakers accomplish their laudable goals. (I won’t apologize for being a supporter of both Desert Storm and this decade’s economic recovery.) Sir Alan even flew a mission over their region to drop leaflets touting the virtues of ARMs. And now should we leave them to be massacred? I’m not saying we should invade the mortgage derivatives market and set up a democratic regime by force. But at the very least, don’t we have a humanitarian moral duty to declare a no fly zone?
This post is already too long, and I have to get back to my real job. I haven’t even finished arguing my second point, and the third point is clearly going to be the hardest to defend. For now I’m going to have to abort, hoping to continue tomorrow. Have patience, gentle friends….
But Dean Baker says the Housing Boom was an obvious bubble:
And Dean Baker is an honorable man;
So are they all, all honorable men*…
* Yeah, OK, some of them are honorable women, I guess. Sorry, but the ART is doing Julius Caesar this season, and Shakespeare's lines already glide silently but pervasively through the New England air.
Monday, August 20, 2007
A September Cut would Make Sense
The Fed’s mandate is to pursue price stability and maximum employment. It pursues these objectives by influencing macroeconomic conditions in the real economy, but it influences those conditions using only financial instruments. In particular, it tries to hold the federal funds rate at a level that will produce the best macroeconomic results.
However, the federal funds rate has no direct influence on the real economy. It has indirect influence through a number of channels, and it also acts as an indicator of other indirect influences that Fed policy has on the real economy. I won’t attempt an exhaustive list of these channels and influences, but among them are: corporate bond yields, which help determine capital spending choices by corporations; commercial loan rates, which also help determine capital spending by businesses; commercial paper rates, which help determine the cost of holding inventories; consumer interest rates, which help determine spending by consumers; mortgage interest rates, which help determine housing demand and consumers’ ability to draw on home equity; housing values, which help determine consumer spending through a so-called wealth effect; and the availability of credit, which influences all these things by determining consumers’ and businesses’ ability to take advantage of whatever rates are offered.
One thing all the mechanisms I listed, and undoubtedly some others that I didn’t list, have in common is that they have all deteriorated recently even as the federal funds rate target has remained constant. As far as financial influences on the real economy are concerned, the Fed is effectively (if unintentionally) following a tighter policy today than it was a few months ago. So if the Fed believed a month ago that a 5.25% federal funds rate would produce the optimal set of consequences for the real economy, it would not make much sense to believe today that 5.25% will still produce optimal consequences, unless, of course, the Fed thought that the condition of the real economy had strengthened.
But from the recent inter-meeting policy statement, it is readily apparent that the Fed does not believe the condition of the real economy has strengthened. If anything, it has gotten worse. Therefore, it seems to me, if the Fed governors choose to leave the federal funds rate target at 5.25% in the September meeting (again, barring dramatic improvements between now and then), they are either making a mistake or acknowledging that they made a mistake earlier by not having raised the rate higher in the first place.
* Just for the record, I do think that the Fed should ease, but that’s not the topic of this post.
Sunday, August 19, 2007
Guess I’ll keep reading Barron’s and the Journal, Murdoch notwithstanding....
So what did they have to say? Basically nothing. I grabbed the business section first, assuming there would be a relevant article on the front page. Instead I found an article about the personal jet service business, an advice piece on how to negotiate with liars, and an article about a corrupt building contractor. Inside the business section? Still nothing. OK, how about the front section? Nothing. Umm…the real estate section? Nothing. Finally, in desperation, I picked up the “Ideas” section and found a commentary by Robert Kuttner on the roots of the mortgage crisis. Interesting, but only tangentially topical.
Does the Globe live in a completely different world than I do? I mean…Hello? The Fed cut the discount rate this week (!!) – the first explicit easing of Fed policy this business cycle, and an unprecedented mode of easing (cutting the discount rate spread over the federal funds target, increasing the maturity of discount window loans, and verbally encouraging banks to borrow from the discount window). To a macro geek like me, the very fact of a first easing makes it the biggest news story of the year. Considering the unprecedented methods, it should be the biggest story of the decade. (Although…OK…I do recall something about a big war in one of those “Ira” countries in the middle east…that might be important, too…and something about a huge hurricane a couple years back…had something to do with jazz musicians, I think…or was it a tidal wave??)
Granted, I don’t expect the Globe to cater to the interests of macro geeks, but…you’d think the business section at least would take some interest in gargantuan pieces of news from the financial markets. After all, Boston is home to one of the world’s largest mutual fund companies, among other important financial services businesses, and it sits a few short hours’ train ride away from the world’s financial center. Surely many of the Globe’s readers care about these things. Don’t they?
Saturday, August 18, 2007
Business Contractions by Month-of-Decade
I went through the last 15 decades (actually starting in 1855, when the NBER dating starts, and ending in 2004 to give an integer number of total decades) and calculated the frequencies of business cycle contractions (using the NBER dates) for each month of the decade. For example, January of the “zero” year is the first month, February of the “zero” year is the second month,…,January of the “one” year is the 13th month,…,January of the “two” year is the 25th month, and so on. (You can click on the picture to see a larger version.) These results are purely empirical and may not mean anything, and I’m not sure how to do statistical tests on them, because I find it hard to make a rigorous distinction about what is a sensible hypothesis to test.
But there is at least one thing that seems hard to attribute to chance: the highest frequency of contractions is just after the beginning of the decade, and the lowest frequency of contractions is just before the end of the decade. Since 1855, there has been only one contraction that included the second quarter of a "nine" year (1949). Whereas in 10 out of 15 of the "zero" years, at least November has been a recession month. And at least 3 of the remaining 5 are not very impressive: November 1940 wasn’t a contraction, but the nation was still recovering from the Great Depression, so it wasn’t exactly business as usual either; November 1980 technically wasn’t a contraction, but it was part of a very short expansion sandwiched between two contractions; November 2000 wasn’t a contraction just yet, but as I recall, the winds of recession were in the air. (Maybe somebody who knows the history better than I do will have stories about 1880 and 1950.)
If we take this chart seriously as a prediction for the future, it has an interesting implication for the present time. There is a peak late in the “seven” year, after which the chance of contraction drops rapidly. That suggests that right now is a critical time to avoid recession, and if we can get through the next few quarters without one, we can expect smooth sailing for the remainder of the decade.
The chart may also be depressing for Democrats and heartening for Republicans. During the first few months of President Obama’s term, it will look like he inherited a strong economy. Then once the unimpeded Democratic initiatives are implemented, it will appear that they are destroying the economy. The trick, though, for a Democratic president, will be to reduce initial expectations and have people expect a longer-run payoff. That seemed to work for Reagan, anyhow. Alternatively, one could hope that the recession will be as shallow as possible and the recovery as strong as possible, which worked for Nixon. My advice to the next president is to figure out now a way to blame 2010 on Bush and then save your real economic ammunition for 2011 and 2012. With any luck, it could be the second Clinton boom. (As per tradition, Clinton will be facing a Republican congress.)
Friday, August 17, 2007
To Put or Not To Put
Let me be more precise. There was, and is (and ever more shall be, if the Fed does its job well), a put on the general price level. So if you’re speculating directly on the general price level, you can expect some degree of protection from the Fed. For example, if you buy TIPS and short nominal Treasury notes, and if you maintain enough capital to meet a reasonable range of margin calls, Ben Bernanke will make sure you don’t go broke. (He will also try his damnedest to make sure you don’t make any money out of the deal either, but that’s another story.) If you are following this strategy, consider yourself protected. If your enemies are following this strategy, and it pisses you off that they are being protected by the Fed, go ahead and send hate mail to Ben Bernanke. He welcomes your hatred. (Not that I have inside information on this point; it’s just that any reasonable central banker should welcome the hatred of those who think deflation is acceptable.)
The impression that there is a put on certain other assets arises from the fact that various assets are correlated with the general price level in complicated ways. So if you bought stock during 1998, when the general price level in the US was fairly stable and there were deflationary forces afoot in the world, you could be confident that Greenspan would bale you out. You have to recognize, though, that when he bails you out, it doesn’t mean he likes you. It just means he dislikes deflation. On the other hand, if you bought stock during early 2000, when the inflation rate was showing signs of acceleration, you couldn’t count on Greenspan to protect you. Those who did somehow found themselves unable to exercise that protective put that they thought they owned.
In retrospect, it seems clear that the Fed reacted too quickly and too aggressively in 1998, and not quickly enough in 2000-2001. Ben Bernanke has the benefit of hindsight on both of those episodes, and he will presumably try to steer and intermediate path. A lot of people (more than in 1998, one might imagine) will end up bankrupt, and certain pundits will watch them and curse the Fed for risking a meltdown. A lot of people (more than in 2001-2002, one might hope) will find that their perhaps ill-advised investments recover enough to avoid bankruptcy, and certain pundits will watch them and curse the Fed for encouraging inappropriate risk-taking. And those who make their living by writing straddles on general price indexes (if there are any such people) will, in all likelihood, keep on happily collecting premiums as if nothing were happening.
Wednesday, August 08, 2007
The New York Times on Exchange Rates
I grant you the editorial does not appear to have been written by someone who had just finished getting an A in a course in open economy macroeconomics, but I think the editorial has a point, which Greg and Dean are missing. There are two reasons that the dollar can weaken. First, it can weaken because US interest rates fall (relative to foreign rates), making dollars less attractive. That is a “movement along” the demand curve for dollars. Second, it can weaken because people demand fewer dollars at any given interest rate. That is a “shift” in the demand curve for dollars*. What the Times is saying is that the right way to weaken the dollar is by inducing a movement along the demand curve, whereas Bush administration policies are instead causing the curve to shift.
While it’s debatable just how much influence public policy has on the position of the demand curve, it certainly has some influence. Surely Dean Baker, who perpetually complains about the Clinton-Rubin strong dollar policy, will not deny this. I’m personally skeptical about Dean’s maintained hypothesis that Clinton-Rubin policies had much impact on dollar demand, but I think there is a good case to be made that the Bush policies identified by the Times do have considerable impact. When a nation continues to run budget deficits in the face of a negative personal savings rate, there is a tendency for investors to lose confidence in that nation’s currency and to demand less of it at any given interest rate.
The difference in effect between a shift in the demand curve and a movement along the curve is important, though I don’t think the Times identifies that difference quite correctly, or at least the Times doesn’t make the true difference clear. The editorial implies that a shift in the currency demand curve is more inflationary than a movement along that curve. That may be true in the long run, but it's not obvious that it’s true in the short run. The true difference (assuming monetary policy is working well) is that, with a shift in the demand curve, the stimulus from the improved trade balance is offset by reduced domestic investment, whereas, with a movement along the curve (assuming that movement results from increased domestic savings), the stimulus is offset by reduced consumption. I think Greg and Dean will agree that the latter is preferable.
In the long run, less investment leads to a lower growth rate of productive capacity, which slows the rate of labor productivity growth, and much contemporary opinion holds that slowing productivity growth brings about an unfavorable shift in the Phillips curve, causing inflation to accelerate more rapidly (or decelerate less rapidly) at any given level of employment. Thus, in a sense the Times is right to argue that the “shift” strategy is inflationary (because it reduces investment). Perhaps the anticipation of such future inflationary conditions is what reduces the Fed’s “room to maneuver” in the face of a weakening currency. The Times doesn’t spell out this argument, but it makes some sense to me if that’s what they had in mind.
* In the model I have in mind, the quantity of dollars demanded depends on relative interest rates, and then the foreign exchange value of the dollar depends on the quantity demanded (as if the supply of dollars in the foreign exchange market were perfectly inelastic). The demand curve to which I refer represents the first relationship, and the value of the dollar is then determined by the second relationship. Obviously this is a simplification, since the bond markets and the foreign exchange market have to come into equilibrium simultaneously, and there really is not a perfectly inelastic supply of dollars. For purposes of the present analysis, however, I don’t think this simplification distorts the point I’m trying to make.