Hello and welcome to this latest session where I can be talking about cryptocurrency with some guests who I'll introduce in a moment, but more specifically we're going to talk about seven metrics that support a bullish outlook for Ethereum and that's why, indeed, I've got the guys from the macro hive team on the call because it was from their very research that I wanted to get some more information about these seven reasons and very fortunate timing because it's the ninth of November. And overnight we've seen both Bitcoin and Ethereum hit fresh all time record highs, the actual crypto market now is hit $3 trillion US dollars for the very first time so really excited to have this conversation the most optimal timing where people of course are very interested in all cryptos but specifically the talk about Ethereum so just by way of introduction, I've got on the call Bilal Hafiz who's the CEO and editor of macro hive, and he was also the former head of global research like so Deutsche Bank and he's joined by his colleague Dalvir Mandara who's a quantitative researcher at macro hive as well so that further ado guys. The seven bullish reasons I'd love to get a breakdown and hear more about them. Great, thank you. Thank you very much. Thank you very much Anthony and yeah welcome everyone on to listen to this YouTube in this video. You know we are macro high. Traditionally, we tended to focus on more of what I guess now is called tradfire or traditional finance markets so you know bonds effects equities credit and so on. But in recent months we really have gone really deeply into the crypto market as well. One reason is it's obviously grown, you know exponentially in recent years, but also from a technology perspective, you know there's lots of elements of crypto that tells us that it's here to stay in one form or another. And from a finance perspective I think we're at an interesting juncture right now where the technology side is still there but lots of finance people are coming into the crypto space so this is in an interesting mix now of finance people kind of thinking about what crypto means. Now in terms of our work if you just go to, you know, the macro hive site, you know we have our normal, normal type of content but if you, if you click on here on crypto. We publish our pieces on crypto at the moment we're focusing primarily on Bitcoin and Ethereum. And I just wanted to show off a bit here hence going to this page here but back in a few weeks ago back in the summer, we said that Ethereum is likely to hit $5,000 in the coming weeks. And today on November the ninth. If I just pull up a blue boat screen here of Ethereum the ethers trading up close to $4,800. So we're almost at the $5,000 dollar mark. So we're, we're basically trading at close, close, at all time highs and close to our target of $5,000. This is Bitcoin, Bitcoin has also risen recently it had a bit of consolidation beforehand. And again, just to show off again, we published a piece a few weeks ago saying this is not the big Bitcoin correction where people were getting worried that this this consolidation here was the beginning to move down in Bitcoin we argued that that's not the case. Bitcoin is going to continue to rise. Now, what what gives us this level of confidence or conviction around this is that we built a framework to try to understand crypto. And what I find being a relative newcomer to the crypto world is that you tend to find that there's, you know, the research analysis side of crypto is almost like the the Wild West where people have outlandish targets and the real basis they look at charts or second analysis with breakouts and so on, which which has some value but it's not enough. And so what we try to do a metal hive is that we try to build some kind of framework on analytics around how to forecast crypto markets. So we use kind of flow positioning information but also a lot of on chain analytics, because one of the big advantages of crypto is that all the data is available to the public in one form or another because everything's on on the blockchain. And in this, in this video we're basically going to go through our framework for Ethereum, which is similar to our framework for Bitcoin as well. So the last piece we published on Ethereum, which kind of runs through the framework we published a week or so ago, where we talked about how we think Ethereum is going to outperform Bitcoin. And, you know, we provide some context here but if I just, you know, jump straight into the framework itself we essentially look at seven different factors that we think are most important for trying to understand the future direction of Ethereum and Bitcoin. I mean, before I go on, the one thing I just wanted to add is that I'm not really going to go into whether Ethereum has a future or not or whether Bitcoin has a future or not that's for a separate conversation, separate debate and we've had those debates before, said this is with the assumption that Ethereum's here to stay, given that, you know, how can we forecast Ethereum or indeed Bitcoin or other cryptocurrencies. So the first factor we like to look at is institutional demand and this probably has been perhaps the biggest story over the past year, year and a half since the advent of COVID where suddenly the mainstream finance community has gone into crypto. And it is really the technology guys or just people who had a particular interest in crypto and now suddenly mainstream institutions are investing in crypto as well. And the clearest manifestation of this is the rise of ETFs, ETF product exchange traded fund products which allows the average investor whether you're retail investor or whether you're an institutional investor to get exposure to Ethereum or to Bitcoin through a product that you're not allowed to buy. So many institutions are not allowed to hold Ethereum or Bitcoin directly on an exchange on the crypto exchange. Instead, they, they are allowed to hold an ETF, which has exposure to the underlying, which is Ethereum, or to Bitcoin. In the case of Ethereum, there's a whole range of ETFs that have been launched.  I don't think we have one yet in the US, but I'm sure one is soon to come. We have the first Bitcoin futures ETF was launched a few weeks ago, which has helped the rally in Bitcoin. But nevertheless, there is ways for global investors to get exposure to Ethereum without having to hold Ethereum directly. So we track these ETF flows. Here shows you the ETF flows into Ethereum ETFs. And so what you can see is in recent weeks, there's been a surge of flows into Ethereum ETFs. And for us, this is a very bullish signal. So what you were seeing at the, at the end of the summer, or around October time, Ethereum prices started to go up. But there really wasn't much institutional flow supporting that, that, that price increase. But since, say the last, say three, four weeks, suddenly with this rise in either prices, you suddenly see institutional flow start to come in and it started to accelerate. So this metric for us is quite a bullish signal for Ethereum and either prices going forward. So this tells us that institutions are back in crypto, and they're buying Ethereum through these ETFs. And you'll see something similar on the Bitcoin side as well. So this is one metric. Is there any way for it's sorry about it. Is there any question on this for a regular person, let's say to access the type of outflow inflow data for this type of to obtain this metric, where would they go to do that. That's a good question. I mean, in terms of guessing this data. In theory, you could basically go to the ETF providers sites and I think they would each individual website would have the flow data that you can get. So you could kind of do it in a very manual basis. Otherwise, data providers, whether it's Bloomberg or Finnitive would have that data as well. I'm sure there's other cheaper lower cost data providers that may have this data as well. On top of that macro high what we're doing is we're publishing these charts on a weekly or bi-weekly basis so you could just come to the side and then you'll just see what the flows are so that's another way as well. So there are different ways, you know, some are more manual, you know, so there's kind of a range of ways you can get access to that data. Now the, so that's the first one, you know, trying to track institutional demand and for us the proxy the best way of cracking social demands ETFs. The second one is this whole idea of liquidity. And this is a bit more for the crypto geeks out there which is the idea that if people who hold the theorem so this is the people who actually hold the Ethereum coins directly so these are not people who use ETF so these are a bit more of the crypto native crowd. One measure of bullishness is how much liquidity to the people who hold a theorem what now so if you're very bullish, if I'm a hold up Ethereum and I'm very bullish on theorem. I probably don't care, I probably don't mind if I hold my theorem in a very illiquid form. So by illiquid form, what that means is that it's not easy for me to quickly buy and sell it. Now if I'm very worried about theorem, I'll want to hold it in a format which is very easy for me to quickly sell it. In the crypto world to simplify it, the liquid form would be to hold it and an exchange. So there's lots of exchanges, you know, whether it's Coinbase, Kraken and so on. There's a whole bunch of exchanges, which you can use to buy a theorem if you leave it at the exchange. It's very easy then to have a balance exchange, your theorem's held there. If you want to sell it, you can quickly just sell it because it's still on the exchange. So the balance is at the exchange. Alternatively, if I'm very bullish and I don't really want my theorem to be held by a third party, I can hold it in my private wallet. So I could have my special USB stick or version of it, which is a private wallet, and just hold it on there. And for me to kind of access that I need my really long code to be able to access access that that wallet. Or I could hold it in a custodian, a third party custodian, but in either way, it's held in a way which makes it harder for me to easily sell it. So if I'm holding in that form, that means I'm actually quite bullish, you know, so so I, you know, I'll go to an exchange to buy a theorem then I take it off the exchange and put it into a format that's illiquid which tells me which tells us the outsider is tracking these flows that actually this person's very bullish. What we do is we track flows onto and off exchanges. And the idea is that if this flows out of exchanges. That means that holders of theory are very bullish that they're basically taking off the exchange into a form that's illiquid. And so this is a chart which shows you exchange flows over the course of this year over 2021 and so you see in general. So basically in general people go into an exchange, they buy their theorem and then they take it off. So that means in general people who buy a theorem tend to be quite bullish. There are occasions though, where they push that if you're back onto the exchange and so you see here around Maytime this year you suddenly saw some spikes or flows back onto exchanges around this time and this was the time where Ethereum had a big rise and then fall. There's big correction here. And then over September or so when when the theorem was falling, you saw flows back onto the exchange. There's a level of bearishness. Now more recently there's only been outflows. It's been one way. So this tells you that the people who are buying Ethereum are basically taking it off exchange and they're comfortable having it in illiquid form which means that they're bullish on Ethereum. So that's the second measure we like to look at. So this is using exchange data, a bit more crypto native you could say. The third one is to look at the futures activity. So we know there's a whole bunch of futures have been launched that track Ethereum and also Bitcoin as well. And we basically like to look at the amount of open interest, the amount of contracts long and short together that are being used to trade Ethereum. So we don't care so much about positioning because in the end the positioning next to zero what we care about is just the size of that market.  But Binance is the largest within the ones we show here in terms of the crypto native exchanges. But the overall open interest, the blue line here shows you that since around some October, we're tracking this on a shorter time period. There's a big increase in open interest, which is a bullish sign. Then if we look at CME, a traditional exchange which has a very large volumes in Ethereum and Bitcoin futures, you see something similar as well, where there's been a big increase in open interest as well. So this tells us that there's a lot of volumes or the amount of contracts on the exchanges are increasing. This kind of tells you that there's a lot of interest in the market from your institutions, as well as more crypto native investors. And again, this is a bullish signal for Ethereum. Now, the fourth one, and I'll talk about this before I hand off to Delve, we'll talk about the other remaining factors we look at is Hodler behavior. So Hodler is just kind of almost like a slang term to refer to crypto investors who tend to be buying hold of long-term investors. So it's basically another way of saying a long-term investors. So what we like to do is we like to track the behavior of Hodlers who have held Ethereum for different periods of time to get a sense of are people churning their portfolios a lot. Are they just buying and selling crypto a lot? Or are they just holding on to their Ethereum, which is more of a bullish signal? So the ones we care a lot about is we look a lot at the people who have held Ethereum for between six months and one year. So these are people who bought Ethereum six months ago, between six months ago to a year ago. So these would be people who are relatively new to crypto world. They've enjoyed some gains. And are they still holding on to their crypto? And are they making up a large portion of the crypto market? And what we find is that is indeed the case. Six months to one year, Hodlers are becoming a larger share of the overall Ethereum community. And that's a very bullish signal. We know that people who've held it for one year or five years or more are a fairly significant portion of the Ethereum markets. And the five-year plus people are holding around five, six per cent. The one-year plus community are holding around 15 to 20 per cent, the one to two-year mark. But what's interesting for us is the more recent entrants to Ethereum, are they still holding on? And they are. So our data shows they are holding on to Ethereum. And this for us is a bullish signal because what you don't want is you don't want just the long-term guys to be holding because they're the original kind of guys. If the newbies come into crypto or Ethereum and they're not holding on to Ethereum, then that's a bearish signal. In this case, it's a bullish signal which is which is constructive for Ethereum. So this is something we track. And this is based on chain analytics you can get hold of this data. I think what I'll do now is I'll hand it off now to Dalvier. Dalvier, do you want me to control the screen or do you want to control the screen? You can control the screen if you want. I'll go ahead and scroll down if that's easier. Okay, yeah, great. Let's do that. Okay, yeah. Thanks, Bill. So I'll go for the next three metrics we look at. And one of the first ones is that we look at the investor P&L that we're seeing in the crypto markets. So one of the benefits of the crypto markets is that we can track transactions much more easily than in traditional finance because everything is publicly available. So with that being said, we look at three different metrics and they vary between looking at unrealized profits and realized profits. So the first metric is called the percentage supply and profit. So if you scroll down a little bit, Bill. Yeah, so this is chart 11 here. So this is basically just showing you the percentage of all the circulating Ethereum supply that's in profit. And naturally, as the price rallies, you would expect this value to go up. And right now, it's touching almost 100% with the new all-time highs, which is something you kind of do expect. The next thing we look at is the size of these unrealized profits. So chart 12 shows you the unrealized profit as a percentage of market cap. And right now it's around 70% or this time as of when the article is published. So what that's telling us is that we've got 100% of the coins almost in circulating in profit. But the actual value of those unrealized profits are around 70% of market cap. Again, when the price rallies, naturally you would expect these ratios to increase. And then chart 13, this is a little bit more interesting. It's looking at a realized profit. So it's the realized value divided by the value at creation, or more simply, it's just a price sold divided by the price paid. So this is called the spent output profit ratio or SOPA for short. And a couple of interesting things about SOPA is that, you know, when the market is bullish and SOPA is increasing, it's telling us over the above one, it's telling us investors are realizing profits. If it's below one, it's telling us that they're realizing losses. Now naturally, if you look at the sort of the May bull run, when prices are registered to then all time highs, SOPA was increasing quite a lot with the price. That's telling you that investors are realizing profits at the new highs. If you look at the most recent bull run, so from October onwards, there's been spikes in SOPA, but it's bouncing between a lowerish level of about 1.04 and a highest level of 1.16. Which is relatively compared to the high scene in the May run of around 1.26. That's a much more muted increase. So what we're looking into that is that, well, this is a bullish signal in the sense that investors are not realizing profits at the new all time highs as much as they were before. So, you know, logically that suggests that investors are reluctant to realize profits at these highs because they feel that the price will increase further. So that's one thing about SOPA. The other thing is that historically looking at where this level crosses one in a bull market as it touches one or retest one. Historically, that's been a good time to buy and equally on the flip side in the bear market, as it retest one you kind of fade and it's been a good time to sell. So that's these these ratios naturally all three of them will increase as the Ethereum price increases. But you know, I think it gives a bit more of a context, you know, splitting out unrealized and realized in this way. So yeah, these three are giving very bullish signals at the moment. So onto that sort of different side of things. What we also like to look at what's unique about sort of cryptocurrency is that, you know, there's this concept of mining and hash rates and things like this, which is different to traditional finance and perhaps I'll provide a bit of context about what mining actually is before, you know, talking about each chart so Ethereum currently works on something called a proof of work consensus protocol. And it's instructive for me to say right now that it is going to transition to something called proof of stake going forward, but perhaps as a conversation for the time. But just to give a bit of idea of what proof of work means, the proof of work consensus protocol basically is a way of allowing the Ethereum network to come to a consensus about things like balance, transaction orders, you know, stops people from spending their coins twice, you know, offers resistance to attacks and makes the Ethereum network very maintainable. Now, proof of work, the idea of proof of work is it just sets the rules for the work that the underlying miners do now work in this context is just mining and mining is just a process of adding new blocks onto the blockchain. And without getting too into the technical details of it, you know, the more work that's done implies more mining that's done, which means more in the increases the length of the blockchain. And we can track this information so you one way to track mining activities to look at, you know, the compute power that's associated with the network so mining, you know, requires compute power and you know a lot of compute power to facilitate it. So what we look at is the hash rate on the network. So, the hash rate is basically just a measure of compute power of average compute power on the network. You know, as of the time the article is published it was around 736 terror hashes. The second, you know, currently latest numbers as of today, it's closer to around 786. So it's increasing. And more importantly, since bottoming out in, you know, late June after China crackdowns on crypto activity, it's had an upward trend ever since, and it's been consistently registering new all time highs. Now, from, from a perspective of markets, this means that the network has, you know, more security so it's lesser, you know, prone to attacks. It's prone to facilitate more transactions inherently because there's more compute power on the network. And we view this as a bullish sign. And in tandem with hash rates. We look at something called minor revenue. There's a bit of, just to give a bit of context about minor revenue. So what we look at is the comparison between Ethereum mining revenue and Bitcoin mining revenue. So we split it out. We consider it together, but there's two kind of types of revenues on a broader level. So there's fees that are minor in the network. So we look at, you know, how much money is going to be spent on the network. So what we look at is the comparison between Ethereum mining revenue and Bitcoin mining revenue. And we consider it together, but there's two kind of types of revenues on a broader level. So there's fees that are minors are paid for facilitating transactions, and then there's minted coins. So when a, when a minor adds a new block to the blockchain, they're rewarded with freshly minted coins. And these together form the total minor revenue. And what's, what's interesting about the comparison between Bitcoin and Ethereum is that, you know, ever since around August, you know, pretty, pretty largely outperforming Bitcoin in terms of minor revenue. And even in the latest sort of all runs that we've seen in both of them, Ethereum has seen a big jump. And whilst Bitcoin has been increasing, it's a much more muted level than what we're seeing in Ethereum. So we view this as a bullish sign for Ethereum. Again, so we'll have to scroll down a bit more. And then the last metric we look at, which is kind of specific to Ethereum in this context is the DeFi markets. DeFi stands for decentralized finance. And the key metric that we look at is, it's called total value locked. So the total value locked in DeFi is just the total sum of deposits of coins in decentralized finance protocols. So it could be in, you know, lending or other financial products, such as on, you know, decentralized exchanges and things of that nature. So what's important for us is that the DeFi space is, it's rapidly expanding. So, you know, here, the blue line is showing you the total value locked, which is across all protocols.  It's not just Ethereum. And as of the time of publishing the article, it was around $250 billion. The latest number as of today, you know, it's closer to $284 billion. And, you know, that shows you just how fast this, this market is, is increasing. So what we look at is, well, how much of this, you know, booming DeFi space is coming from Ethereum. Now, what you'll notice is that, you know, since the beginning of the year, the share of the DeFi space that's coming from Ethereum has been decreasing. And this is almost natural because of the fact that there's so many different protocols entering the space. But by, by and large, Ethereum is still the biggest player in this space. You know, right now it's currently at around, you know, 184 billion of the 284 billion is coming from Ethereum. So, you know, that puts it around a 66 to 67% dominance. And just to give you an idea of how far above the rest, that is the next biggest protocol in the space Binance contributes around $21 billion to that space, around a 6 or 7%.  And we view this again as a bullish side for Ethereum. So as the total value locked increases and proportion of that coming from Ethereum is still dominating. We again view as a bullish sign for Ethereum. So, you know, thanks for the deal there. And, and just to sort of summarize the main points here so you know at the end we kind of summarizes that essentially we look at seven different factors, all of them currently are bullish for Ethereum institutional demand and the way we do that if we look at flows into ETFs. We're doing increasing flows, which is bullish. We look at liquidity demands are crypto investors willing to hold Ethereum in a illiquid form, for example in a private wallet and that is indeed the case people taking money off exchanges into their private shares is bullish for ETFs, bullish for Ethereum. Number three, we look at futures activity is open interest is there more activity on these exchanges, whether it was crypto exchanges or more traditional exchanges and that is indeed the case that's increasing. We look at hodler behavior back to number four and we're finding that the key cohort for six months to one year people who bought it more recently, the newbies are indeed holding crypto Ethereum, which is bullish. We look at the P and L of investors and we're finding that investors are have either realized or unrealized profits, which is quite constructive for them to continue to hold Ethereum, we look at mining activity and we find that revenues of Ethereum miners and the hash rate compute power dedicated to theorem is very high, which tells you that there's robustness to the overall system. And then finally we look at decentralized finance space and we find that there's a lot of Ethereum. That is being taken out of, of supply to be locked up to to underwrite the decentralized finance space the device space which means that there's less supply of Ethereum in full investors, which then naturally boosts up the Ethereum price.  And, and hopefully it provides a good framework and add some rigor to crypto markets in a way that you don't really find elsewhere and I mean researchers I kind of like to have some frameworks. And, and I think this is something that's quite useful as a way to kind of feel a bit more confident about your holdings or your investments in crypto space. So, thank you guys for the, for the rundown and what I'll do is, if we drop a comment below if you have any questions at all, I'm sure the three of us be more than willing to pick them up. So just just ask a question. If you have one, what I'll do as well is I'm just going to be loud has kindly said that because of this kind of one or video that we've done today that he's happy that if you go to the macro hive website and you just code, amplify 50 or one word at the checkout, and you'll get a 50% discount on your subscription for your prime plan so for one I for sure I mean I my job is tracking news that I don't have time to go to the granularity that these guys do, and I mean on them to do that. And so, you know, that's, they're the masters of that craft and I for one definitely use that resource for the purpose that they've just discussed so I'd highly highly recommend it but thank you for for watching. Thank you to you both for attending and I've got another episode coming out where I'm talking to a specialist in fintech about the metaverse, which will be coming out as well later on this week, which has a nice tie into some of the questions that we've had here as well so so stay tuned but Bilal, thank you very much. Great. Thanks for having us. Thank you.


One of the reasons that mathematicians are not satisfied with the I know it when I see it definition of continuity has to do with the useful property of continuous functions. This property is known as the intermediate value theorem. Continuous functions have the following property. Suppose a function is continuous over some interval between A and B, and let L be some value between F of A and F of B. Then there is some C in this interval for which F of C is equal to L. And this is quite a mouthful, but what it comes down to is the intermediate value theorem requires that a continuous function be equal to every value between F of A and F of B for some value in the interval between A and B. And to give you some idea of how fantastically useful this is, suppose F of X is continuous over the interval between 0 and 10. And suppose that besides being continuous, the only thing you know about F of X are its values at a couple of selected locations in that interval. Based on this information alone, we can tell how many solutions there are going to be to F of X equals 0 in this interval between 0 and 10. So since our function is continuous, we know we can apply the intermediate value theorem, so let's bring that in. Now one way of looking at the intermediate value theorem is through what you might call the Goldilocks principle. Suppose I'm trying to hit a certain function value. At some value of X, I might be too small. My function value might be less than what I want. And at some other value of X, my function value might be too big. It might be more than what I want. Then the intermediate value theorem guarantees that as long as the function is continuous between the two points, some place in between is going to be just right. So let's see if we can apply that. We want to find where F of X equals 0. So if I look at my function values, at X equals 0, my function value is 8, which is too big. At X equals 2, our function value is 1, which is too big. At X equals 4, our function value is minus 3, which is too small. And since my function is continuous, we can reason as follows. At X equals 2, we're too big. At X equals 4, we're too small. So some place in between will be just right. And so there is a solution to F of X equals 0, some place between 2 and 4. And by a similar argument, we see that there's at least one other place where we might have a solution. And so again, at X equals 6, we're too small, while at X equals 8, we're too big. So some place in between, we're just right. And so there's a solution between 6 and 8, and there's at least two solutions. One in the interval between 2 and 4, and one in the interval between 6 and 8. Now let's take a different tactic. We want to find an interval with the width of one unit in which we can find a solution to XQ plus 8X squared plus 50X plus 1621 equals 0. Now the first thing we want to establish is that the expression is a polynomial, which means that F of X is an algebraic function. And one of the things that's important to remember is that algebraic and transcendental functions are continuous everywhere they are defined. And that means we can apply the intermediate value theorem. So, since I have a target value of 0, if I can find a function value that is too large and a close by function value that is too small, then some place in between will be just right. So in order to do that, I might want to collect a couple of function values. So, for example, at X equals 0, our function value will be... And unless we're a politician, we can't tell anything from a single example. So we'll try X equals 1 and see what we get. And there's not a whole lot of insight we can get at this point, so let's try X equals 2 and see what happens. X equals 3 gives us... And if we were infinitely patient, we could try X equals 4, X equals 5, X equals 6, but let's stop a moment and smell the roses. While we could try X equals 4, X equals 5, X equals 6, and so on, we might observe that the values that we're getting are increasing, and so maybe we're going the wrong way. So let's see what happens at X equals negative 1. Well, again, unless we're a politician, we can't generalize from a single example. So at X equals negative 2 or negative 3, and here at least it seems we're going in the right direction. And if we have infinite patients, then eventually we're going to find out that we have at X equals negative 13, a value of 166, and at X equals negative 14, a value of negative 255. And now I can apply the intermediate value theorem, or the Goldilocks principle. At negative 14, we're too small. At negative 13, we're too big. So some place in between, we're going to be just right. So that means f of c is going to be 0, where c is someplace between negative 14 and negative 13. While this works, it's worth remembering that all human progress comes from somebody asking, isn't there a better way of doing this? And so one way we might do this is we might start with larger steps. So instead of evaluating f of negative 1, negative 2, negative 3, and so on, maybe I evaluate f of negative 10 and f of negative 20. And so my Goldilocks principle says negative 10 is too big, negative 20 is too small, so I know that I'll hit 0 for something in between negative 20 and negative 10. And this is great, except our problem actually asks us to find an interval with the width of 1 unit, and the interval between minus 20 and minus 10 is 10 units wide. So this interval is too wide, so let's see if we can narrow it down. So I know there's a solution someplace between negative 10 and negative 20, so maybe I'll get lucky and it's right at negative 15. Well, if you don't play, you can't win. So let's evaluate our function at negative 15. And we don't win. However, our Goldilocks principle says that negative 10 is too big, negative 15 is too small, so there is a solution someplace between negative 15 and negative 10. But our interval is still too wide, so let's narrow it down some more. So I try something between negative 10 and negative 15. How about negative 13? And it doesn't work. But we can apply our Goldilocks principle again. Negative 15 is too small, negative 13 is too big, and so there must be a solution someplace between negative 15 and negative 13. So now we try X equals negative 14. And again, we see that negative 14 is too small, negative 13 is too big, so someplace in between negative 14 and negative 13 will have just right. And notice that we do have an interval with a width of 1 unit, which is what we wanted.


Model-implied instrument of variables on another technique for estimating latent variable models. This is not really a mainstream technique in management, but it received some attention recently and there are a couple of high-profile methodological papers that advocate this technique. The technique is also useful for diagnostics and it's useful if you want to understand what instrument of variables do. So let's take a look at what model-implied instrument of variables estimation technique for latent variable models does. When we have a latent variable model, the problem is that we're interested in the latent variables A and B, but we don't observe those variables directly. Rather, we observe indicators. We have A1, A2 and A3, B1, B2 and B3 and these indicators contain variance from the latent variable the As and Bs, but they also contain error. The E is unreliability and the specific variance the Q, W and R, ST and Y. The first technique that we learn when we start working with this kind of models is just to take some of the indicators and run a regression analysis. The problem with regression analysis of scale scores is that if those scale scores are contaminated measurement error which they pretty much always are, then the regression coefficients will be inconsistent and biased. The problem is really the measurement error of the independent variable. The reason why the measurement error of the dependent variable is not problematic, because the measurement error is assumed to be uncorrelated with the factors, so it just goes to the error to this regression analysis. There is no way for these measurement errors E's and Q, W and R to escape from the independent variable. We could fit a latent variable model with maximum likelihood estimation, but there are other techniques. The modeling plan instrumental variable technique has six steps or the analysis procedure that the Bollen, who is the leading advocate of this technique, recommends an analysis of six steps. The first two steps, the model specification and identification are the same with any other latent variable modeling approach. So the idea is that you first specify a model, then you ensure that the model is identified, so each latent variable must have a scale and must have sufficient number of indicators and so on. Then you have three steps that are unique to modeling plan instrumental variable estimation. The first thing, step number three, is that you do this latent to observed transformation. So basically you take some of these observed variables and use them as proxies for the latent variables. That produces inconsistent estimates in regression analysis, but you can do instrumental variable estimation. So you can use, if you use the A1 indicator as proxy for the factor A and B1 indicator as a proxy for the factor B, you can use the remaining indicators or substitute them as instrumental variables. Then you do instrumental variable estimation like two-stage least squares, which gives you the estimates and you can apply normal instrumental variable diagnostics, particularly for the exclusion criterion to just the model. Let's take a look at what this technique does. The first thing when we start analyzing this model with model implied instrumental variables, the first thing that we do is that we throw away indicators B2 and B3, so this is the base case. We could of course simply take a sum of B2, B3 and B1 and use that as a proxy. But we need to have one variable that is the proxy for the dependent variable B and one variable that is the proxy for the independent variable A. And the recommended approach is to take the scaling indicator. So we take the scaling indicator A1, we take the scaling indicator B1, we proxy the latent variables with these indicators. Now we know that in this recursion analysis, as I explained, if we simply regress B1 and A1, the estimates will be inconsistent and biased because of the estimation of the measurement error in A1. So how do we deal with this problem? Well econometricians have figured out that you can actually use instrumental variables to deal with this problem too. The way that we normally learn about instrumental variables is that we learn that they can be applied for omitive variable bias, they can be applied to correct for simultaneous bias, but instrumental variables, importantly, can also be used to deal with measurement error. And it's sometimes referred to as a multiple indicator solution in econometrics because we are using multiple indicators and for one variable, one of them is the proxy and the others serve as instruments. So how does it work? Well it works that we have, we want to estimate the regression between B and A and we know that using A1 and B1 is going to cause the estimates to be biased and inconsistent. We can replace B with B1, no problems because the measurement error of B1 is going to go to the error term because it's uncorrelated. But now the problem here is that if we replace A with A1, we can have, we can present it in two different ways, we will have and the measurement error of A1, if that goes to the error term, we will have an endogeneity problem because the indicator A1 will correlate with its own measurement error. So that leads to an endogeneity problem. However, if we take a closer look at this model, we can see that the measurement error of A1, the E and Q, they are uncorrelated with the indicators A2 and A3. So A2 and A3 are correlated with A1 but only because they share the variance from the latent variable not because of the error term. So we actually have A2 and A3 that are relevant, they are correlated with A1 and they are also excluded because they don't correlate with the error term of A1 and they can be used as instrumental variables. What will then happen is that when we regress A1 and A2 and A3 in the first stage of a two-stage discretization analysis, the errors can't be predicted from these scores, they go to the error term and the fitted value of A1 can be used here in the regression analysis to explain B1 and we will get a consistent estimate of beta. So this is the model implied instrumental variables approach. We find the instrumental variables, we need to find out instrumental variables that are uncorrelated with the measurement errors, typically they will be either from other variables that are correlated or from the same latent variable. Then we apply two-stage least squares GMM or we can use any other instrumental variable estimation technique. Then we do model testing using Sargon test or any other standard tests that we apply after instrumental variable estimation. Here is a recent example of this technique in action, an article by Benjamin Ture and his co-authors and they explained that they used instrumental variables, they said Bollins work, they said Woolwich's work that talks about this as a multiple indicator solution and they mentioned endogeneity, which is misleading because this is not really an endogeneity correction technique, but this is more about an estimating of a model that we assume to be correct that doesn't have endogeneity. So the endogeneity only occurs because we have measurement error in the indicators and that's the only kind of endogeneity that this technique can deal with. Then they show the equations and what's interesting here is that the equation here is actually exponential because this is Poisson regression model and this modeling plot instrument available at least Bollins work and Woolwich's discussion on the multiple indicator solution they only concern the linear case so they don't talk about nonlinear model but I did some simulations after conducting the authors and it seems that this approach actually works with nonlinear models as well although I can't really explain why that's the case but if I were to use this technique in nonlinear models I would probably dig a bit deeper in the literature to find a proof that says that it actually works in that case too. So why would someone use this technique? So there's a bit of selling here the point is probably not it's a bit misleading but there are a couple of genuine advantages in this estimation technique. One is that it is more robust to measurement error with some caveats. This is from Bollins article and they generate data from this kind of model so they have latent variables measured with two indicators each and they have L1 and L2 regression coefficient 0.2 L2 and L3 regression coefficient 0.2 and they have L1 and L3 regression coefficient 0.8 and they leave out this regression path so it's a full mediation model I mean and then they mis-specify the model as full medias then they estimate it with normal maximum likelihood and model implied instrument of values. What we can see here is that in the mis-specified model the factor loading estimates that they get don't vary between the mis-specified model and when the correct model is estimated. So this mis-specification in the latent variable model does not affect factor loading estimates but it does affect the maximum likelihood estimates and this tells us something important when you have a maximum likelihood estimate or any other full information estimate where you estimate everything together you use all information from the sample to estimate the parameters and the mis-specification in one part of the model the omitted one path can cause all the other estimates in the model to be unbiased but if you estimate it piece by piece like you do with this model implied instrument of variable approach you would for example estimate this L2 to R to Z4 path separately then that bias would not happen So the effects of mis-specification are local so this is the key selling point of this technique there are also other important advantages of this technique the second is that it always provides estimates so sometimes maximum likelihood estimation will fail and you don't know why it fails either your software will not converge or it will give you nonsense values or missing standard or something like that it might be difficult to travel through but this will always give some kind of result and because you are estimating one equation at a time in the system it's easy to see where problems are located so it's good for diagnostics it's also easy to understand if you understand instrument of variable estimation and two stage least squares you can simply run this model compared to maximum likelihood estimation if you really want to understand why and how it works you need to understand a bit of the theory behind maximum likelihood or how do you calculate the likelihood a bit of matrices because the models are calculated the matrix form, something about numerical optimization and so on so you need to understand quite a lot to be able to really explain what your software does in this approach you only need to understand what qualifies an instrument of variable and you need to understand two stage least squares both of which are pretty simple to do okay but there are also some disadvantages of this technique I point them out in this email to SCM net email list and the disadvantages are that the robustness against mispecification is is kind of like not it has a caveat so the thing is that model implied instrument of variables are robust for mispecification as long as that mispecification does not make any of your instruments to be invalid so if you have a mispecification that makes any of the variables that you use as instrument of variables invalid then that mispecification will make the model implied instrument of variable estimates very bad but maximum likelihood estimates are affected to a much lesser degree and I use this metaphor of a stake so if you put too much salt in a stake then in maximum likelihood estimation the salt is spread all over the stake so all estimates are biased to some extent but the stake is still edible it's just a bit too salty with model implied instrument of variables you put all the salt in one place and as long as you don't bite that one place then things are going to be fine but if you bite that one place it's completely inedible so you're basically getting robustness but what you trade is the severity of the problem if it hits you so if there is one part of the model that is mispecified most of the time you are okay with model implied instrument of variables but when you are not okay then the results are really bad the second problem with model implied instrument of variables is that it is less efficient so originally in the basic case three indicators of the dependent variable we just throw two away and throwing away information is generally not a good principle but it's useful for diagnostics so this is one tool in the toolbox and it probably should not be your only tool maximum likelihood estimation probably shouldn't be your only tool either but you need to have a toolbox from which you pick what is the right tool for a task some places where this is useful is as I said for diagnostics so this is from Stata's user manual and they explain that one potential cause of problems in SCM estimation is that your starting values can be bad and to understand why starting values could be bad it's useful to understand where the starting values come from well the starting values of Stata and many other SCM software are calculated using instrument of variable techniques very similar to the model implied instrument of variable estimation technique that I just presented so if you see a weird starting value then now you know where it comes from like many other techniques this technique also has a couple of misconceptions and I mentioned already in the two paper researchers seem to think that this technique has some capability to deal with endogeneity it does not so this is a very explicit example this model implied instrument of variable technique is used for testing for omitted variable bias it just can't do that there is no evidence that it would be able to do that and there is no reason that it could but nevertheless these researchers say claim that it could without any evidence the site balance work which is the relevant work to site when you use this technique the balance makes no such claims and well if you take a look at this recent article in journal of management for how to deal with endogeneity they also mention model implied instrument of variable techniques as one potentially useful technique it's not useful technique for dealing with endogeneity it is useful technique for estimating latent variable models but if that latent variable model if there is endogeneity between the latent variables then this technique doesn't do anything finally how do you apply the technique the technique is basically an application of two sets of squares which is fairly basic thing to do the hard part is to identify the instruments fortunately there are two good software packages for finding the instruments Baldry has programmed a mere search or a mere find package for data where you input your model and then it gives you the instrument of variables then you put them into the two-stage list or whatever and then Fisher has written a package for R that does the instrument search and also estimates of model implied instrument of variable estimates and I actually programmed the instrument search algorithm for this software package because the original algorithm was pretty slow and they did it for a paper that created it faster so model implied instrument of variables is certainly worth learning about because it's useful for diagnostics if your model doesn't converge then running it one equation at a time with this model that this approach that always give you results can give you useful information for travel suiting but should this model or this estimation approach completely replace maximum likelihood estimates for most research or most use cases probably not it's another way of the estimating that has different advantages than maximum likelihood estimates but I will still go for ML estimates as a default alternative