 Thank you very much. As stated, my name is John Landon Lane from Rutgers University. This is a joint project with a number of colleagues Ira Gang and Myung Soo Yoon. We have done many papers on this particular using these particular models for a number of different areas, income mobility and we've been talking quite a lot about looking at poverty and vulnerability and so this paper is our attempt, our first attempt to try and get a handle on measuring vulnerability in a developing economy. The last co-author, Senor Katsukova, is a young researcher who's intimately have intimate knowledge of the data that we're using so we've brought her onto the project which has been incredibly useful and working out what's going on here. So this paper is about trying to employ a rigorous empirical method to measuring vulnerability in the study of poverty dynamics. It's very related to the literature on mobility and mobility indices and so what we're going to use in this model is we're going to try and predict changes in income distribution over time, measure the size of the economy below the poverty line and predict its future size, measure the probability that any individual or household depending on how our data is formed will fall into poverty both in the short and the long run. So we can make predictions over next period's transition back into poverty or transition into poverty within 10 years, 20 years or whatever so we can we can we can break into short and medium and long run and I use the word endogenously here I should have quotes around it because this particular methodology we can actually sort of we can look at the results and see what is the vulnerable population and as we see from the results I'm going to report soon that changes depending on the circumstances as you would imagine so and I'll get to that when we apply it and talk about my results. Our methodology we're going to apply to data from Tajikistan there's a long history of why we are interested in Tajikistan but we have a panel data set for Tajikistan from 2007 to 2011 with three periods 2007 2009 2011 what's useful is the first period is a period of great stress in the economy the global financial crisis hit pretty hard the second period is a period of expansion and recovery and we're going to see quite different dynamics in terms of vulnerability and poverty in these two periods and that's quite illustrative so we're going to construct a formal measure of vulnerability that is consistent with some standard mobility axioms so that's nice it's a nice consistent interpretation and we're going to sort of we're going to show that the vulnerable set is not fixed it could be quite a large set of the population when times are bad but it could be very small when times are good as we're going to see so we're going to make that distinction so the next few slides I'm just going to briefly describe our model that we're going to use it's fairly a theoretical there's a number of heroic assumptions like all the economic models in underlying this model but we're trying to keep the number of heroic assumptions to as small as possible so we're going to use a discrete state first-order Markov model of income dynamics it's a model that's been used in modelling income dynamics for many many years it is I think a very natural way to think about changes in distribution the heroic assumption is the first-order assumption and that's this assumption hopefully I push the right button it's this assumption here if I can let pie be the cross-sectional probability distribution of income all this model says is that everything I need to know about today is captured in last the most recent periods information so any past information is not that is not needed that's the first-order assumption we're going to make that assumption although I do note that you don't have to make that assumption if you don't want to you can assume second third and fourth order models I can always reformulate the state space so that it becomes enough first-order model again so everything we do here is applicable to more complicated models we just haven't found many instances where you need to go past the first-order assumption so we don't so this the most important part of this model is the Markov transition probability matrix and it's a it's a matrix of probabilities of moving from one class income class into another okay I'm going to give an example soon and so we're going to and it's we're going to define income classes to suit our needs okay that's one of the nice things about it the the nice thing about this vulnerability index our vulnerability index is into I mean impervious to changes in the definition of the income classes so we don't it's not that important we're just going to make the definition suit our needs as I said there's a long history of using Markov models the model social and income mobilities going back to the 1953 of of Champanel Sharks did a lot of work in the 70s on income mobility and the famous paper on the Sharks mobility index Gweki Marshall and Zarkin did a lot of work in the 80s about how to estimate this model using Bayesian methods we're going to use Bayesian methods here for many reasons one is it makes life very very simple for us and then my favorite author and some other co-authors wrote a paper which started off our interest in these models and this paper we're going to show you a bit a little bit later on we decompose Sharks as measure into upward and downward movements and that's very important when we're talking about income mobility and poverty dynamics and as you're going to see so we're going to follow this mobility literature and we're going to define a vulnerability measure that's like a mobility measure that's going to be a function of these individual probabilities in the transition probability matrix what are our interesting functions of this probability matrix we're interested in the limit where is the income distribution going are we going to get a much higher proportion of people in the below the poverty line or is it going to go to zero that's an interesting important concept we're interested in this is a highly nonlinear function of the Markov probability matrix it's the left eigenvalue associated with the eigenvalue of one that's why we use Bayesian methods because we can get distributions for this nonlinear function and get confidence intervals very easy so that's why we use it we're going to look at some mobility measures and our measure of vulnerability let's go through a very simple example to sort of explain what we're doing suppose I broke the income distribution to only three categories very broad below the poverty line somewhere between the poverty line and in this case twice the poverty line which is some people use as the vulnerable population and those with incomes above the poverty line above the vulnerable line so more than twice income then the state of the world is represented by this vector these are probabilities that any individual household will be in below the poverty line in the vulnerable set or above the vulnerable set and we're going to track that and so our Markov probability matrix is just going to give you a three by three matrix this is the probability of being poor and staying poor this is the probability of being in the vulnerable set and staying vulnerable this is the probability of falling back into poverty this is the probability of falling back into poverty from the above the third income class and so our the most the two most important probabilities in this matrix in terms of our vulnerability measure is this first column set of probabilities and so we're going to find a weighted average our vulnerability measure is the weighted probability of a person or a household who's above the poverty line falling back into the poverty line in one period the nice thing about this is I could have 20 income classes I could break this distribution to 20 income classes I get the same number so it doesn't matter how I break this up that's the important thing we can also talk about multiple period vulnerability so the nice thing about the Markov model is this is the statement of the model if I wanted to ask what's going to happen to the cross-sectional distribution in five periods or ten periods it just I just am multiplying the current state vector by the kth power of this transition probability matrix and let those elements let p11 soup k be the element of that matrix pk so our k period vulnerability mobility index or k period vulnerability index sorry is just this weighted average of those elements of the matrix and we can estimate that we can get standard errors for that we can get confidence intervals for that without any problem so how do we do this in this paper the details are in the paper I'm not going to go through the gory details but not as gory as some other estimation procedures are we're going to use Bayesian methods why do we use Bayesian methods it's actually very simple in this case the posterior distribution of the parameters of interest are known and I can make iid draws from the posterior distribution without having to use Markov chain Monte Carlo so this is the one example where you can just do iid sampling from the posterior distribution so we do that we're going to use priors here are going priors are very useful in this context because there are times when you might if you break the income distribution into very small categories you might have a small data problem priors are going to smooth out some of the problems you get and and if you use maximum likelihood you run in some some numerical problems the priors are going to help us get round some of these nasty numerical problems but they're going to be the priors are designed to elicit what our beliefs are but they're not going to be driving the results here we can also add covariates so I can get marginal effects of individual characteristics on this vulnerability index okay it's not done in this paper yet it was done in a earlier paper for another conference about three weeks ago and it just hasn't made its way into this paper but it can be done it's actually pretty simple and I think it's going to make a a nice contribution to the rest of this paper okay so we're going to apply this to Tajikistan we have a balance panel for the three years as I said it's a very nice time to be looking at this data because of the fact that there is a crisis in the middle of it we have a period of a recession and a period of expansion Tajikistan is a very poor country and there's a lot of remittances and a lot of mobility of people moving out to work outside of Tajikistan and send money back there are some very big differences in terms of the composition of households so we get a lot of variability here it's actually quite a nice data set to look at we're only scratching the surface so far the head count ratio is the proportion of the population below the poverty line is 46.7 so there's a large amount of poverty here in our study we're going to use the household level LS, MS data set so we're going to use income and expenditure accounts total income is total income it's including auto consumption it includes remittances net transfers labor income and the poverty line we're going to use is given by the World Bank it's based on a calorie based poverty line 139 Sonomi per person we're going to divide we're going to convert our household measured income into relative to this poverty line per person and here's we break we break our data up into 11 bins this is the people below the poverty line you see that we've broken up the category from equal to the poverty line to twice the poverty line into a finer grid that's for a little bit later on we're going to try and see where the vulnerable set really is and then two to three, three to four so these are everything's in real terms so we can compare across time the blue line is the income distribution in 1907 the reddish line is what the limiting distribution would look like under the transition that we estimate so it looks like things are getting worse in that first transition in the second transition things are getting much better all right we start off with a lot of people in in poor or invulnerable and it's all moving to the right so that's what we see there so first of all let's look at some mobility measures the first column is the shawarix measure which is overall mobility you can see that the mobility between the two periods is pretty similar a little bit higher in the second period this is our contribution from an earlier paper we decompose this into upward and downward movements you can see the income ability is all down or two thirds down one third up in the second period it's completely reversed okay so very similar shawarix measures quite different in terms of its upward and downward components we look at our vulnerability measures the overall vulnerability measures are one period vulnerability two period vulnerability and five period vulnerability are point three point three four and about point three five okay so it's a 35 an average probability of falling into poverty in that first period which is very high in the second period the probability of falling into poverty from outside of the poverty line is much lower of order of two percent okay so there's a big difference between the two so the first attempt of putting covariates into the model but this is not these are not marginal facts but you can look at the difference there's a big difference between rural and urban rural households are more likely this is just looking at the first period rural households are more likely to be more vulnerable households with no remittances are more vulnerable households with lower education are more vulnerable these are you know these are i'm kicking in an open door here we also look at informal versus known formal in people with informal sector activity in their households so we have another paper where we use income and expenditure accounts to identify households that we think are in the informal sector so we use that methodology here we find that being in the informal sector is a is is like a little safety net in periods of um we have some other papers showing that when we're in a recession the informal sector activity increases those households that are moved into informal sector are certainly less vulnerable how can we use this to determine the vulnerable set here are the individual probabilities of falling back into poverty we can see that around about three times the poverty line there seems to be a quite a significant step down and probability this is around about point two these ones are about point three five so if we were rather informally trying to work out what is the vulnerable class here it's maybe three times the poverty line this is a very coarse approximation we could do a much more finer attempt in the second period what's the vulnerable set if i was using point three nobody right if you're using five percent it might be this is a bit weird i'm not sure what's going on here we have to look in the data a bit more but everything's very small here so in summary hopefully i've met my other brother hasn't gone off yet uh this is a methodology we think is going to be very useful it's simple to implement as i said we can now add covariance to get marginal effects on this vulnerability measure so you can actually start asking questions about what particular characteristics make a household vulnerable and we applied this method to as you can start i'm quite happy with the results we're getting sensible results i don't think any of these results are going to startle anybody but we think this is a useful approach going forward so thank you very much for your time thank you