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Lecture 5: Firm-level misallocation: benchmark model and early results — Transcript

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0:00good morning good afternoon good evening
0:02to all of you on the call and to those
0:04joining I'm Doug Gan and one of the
0:07organizers of this course along with Joe
0:09kabosi and our speaker today Richard
0:11Rogerson and I want to welcome you all
0:14to today's um to today's lecture in the
0:19steg course on macro key Concepts in
0:23macroeconomic development as most of you
0:26know by now the
0:30this course is organized through steg
0:33which is a research program on
0:34structural transformation and economic
0:37growth the steg program is funded and
0:40supported by the foreign Commonwealth
0:42and Development Office of the United
0:44Kingdom as part of the UK Aid effort and
0:47we are delighted to have today I've lost
0:50track of what number lecture this is but
0:53today we have um the continuing lecture
0:56of the main lecture series from Richard
0:59Rogers who kicked us off with the very
1:01opening lecture of the series and
1:04Richard's going to talk today about
1:05misallocation at the level of firms and
1:09um we're really grateful to him again
1:10for making the time available and for
1:12putting the effort into preparing this
1:14talk just to give you a reminder of what
1:17the rules of the game are Richard will
1:20lecture I believe he's open to questions
1:24and interruptions from the small set of
1:26you who are in the virtual front row
1:29those of you who have your cameras and
1:31control your cameras and microphones
1:33should feel free to I think you have
1:36control of the rais hand um feature on
1:39zoom and if you're raising your hand and
1:42not getting any response you can you can
1:45try to blurt out a question you can just
1:47interrupt um please keep questions brief
1:51if possible for the rest of you if
1:54you're just on the call as a as an
1:57audience member you won't have access to
2:00raise hand or if you do it doesn't we
2:02can't respond to it but if you enter
2:05questions in the Q&A Joe and I will do
2:09our best to respond and anyone else who
2:11feels they want to weigh in as well
2:13we'll keep a conversation going there
2:15during the lecture and try to answer as
2:17many questions as we
2:18can so on that note I think Richard I'll
2:22turn it over to you and again with great
2:25thanks um you'll talk for about an hour
2:29and a quarter so and then save a little
2:31bit of time for Q&A at the end I believe
2:33is that right uh yeah that's the plan
2:35Doug so thanks for the introduction and
2:38yeah just to uh comment on some of what
2:41Doug said uh feel free those of you who
2:44are in the so-called front row uh feel
2:47free to interrupt with questions I think
2:50as a practical matter it's not
2:52necessarily that easy for me to see you
2:54raise your hand or anything so I mean I
2:57would just encourage you if you have a a
2:59question just kind of shout it interrupt
3:02and shout it out that's fine uh or as
3:06Doug said if you put something in chat
3:08then uh he or Joe uh may try to answer
3:12it so any I'm going to uh share my
3:20screen okay uh so there we are so this
3:25is the first of a couple of lectures in
3:28the regular series on misallocation and
3:32I'll start with a little bit of
3:34motivation uh so for those of you who've
3:37been tuning into the earlier lectures uh
3:42I mean I I talked a little bit about
3:44these issues my opening lecture but I
3:46know you also had a lecture uh multiple
3:49lectures on growth accounting exercises
3:52and while that remains an ongoing
3:54literature and there's issues still to
3:56be worked out I mean as as you know from
3:59those
4:00a common result in that literature is
4:02that aggregate differences in tfp are an
4:05important source of CrossCountry
4:07differences in living standards and and
4:11uh starting from that it raises the
4:13question of course is what are the
4:14forces that shape tfp differences and I
4:18guess if you are used to thinking about
4:20the solo model and using it to describe
4:23the evolution of a currently Advanced
4:26economy talking about the UK the United
4:29States or some other Western European
4:31economies or Japan you kind of are are
4:34taught that that uh tfp is is kind of a
4:38stand in for technological progress the
4:40Industrial Revolution was the beginning
4:43of these massive change uh technological
4:46innovations which had a huge impact on
4:48our ability to produce different types
4:51of goods and services and so you're kind
4:54of taught at an early stage to kind of
4:57identify the big a in front of the
4:59production fun
5:00with with technological change and so if
5:03I tell you that one country has a
5:06smaller big a than another country
5:08you're naturally led to think somehow
5:10technology has not diffused to that
5:13country and so uh certainly one key
5:15channel for thinking about differences
5:17in tfp is is the diffusion of
5:20Technologies or or more generally best
5:23practice methods uh I think it's
5:26important to keep in mind that that tfp
5:29uh we call it technology but lots of the
5:32things which which are in some ways part
5:34of Technology are not necessarily
5:37scientific advances in some technical
5:39sense think kind of the classic example
5:42I always tell students about is is Henry
5:44Ford in the assembly line there was no
5:47there's no patent there's no big uh
5:50innovation in the in the lab it's not a
5:52scientific it's a different way of
5:54organizing things so it's a it's a best
5:57practice method so that's certainly one
5:59one way to think about it but I want to
6:02uh the whole motivation for today's
6:04lecture is is that that may not be the
6:07whole story in terms of thinking about
6:09why tfp might be low in one country
6:12relative to another and if you just
6:14think a little bit deeper about what
6:17goes on in an economy you think about
6:19all the the different activities in an
6:22economy and the different people doing
6:24those different activities uh who's
6:26doing what then you could imagine in a
6:29an
6:30economy taking as given this this this
6:34the state of Technology that's present
6:36in that economy who does what how things
6:40are allocated that could have a big
6:42impact on how much output the economy
6:44produces what if you've got the wrong
6:46people making the important decisions uh
6:49then these seem like they could be uh
6:51first order things and so that's kind of
6:55what the misallocation literature is all
6:57about is this idea that even taking the
7:00state of overall technology and use of
7:03best practices as given there's a lot of
7:07I mean the resource allocation in a in a
7:10modern economy uh involves a lot of
7:12details in terms of where resources are
7:15allocated across different tasks and
7:18activities who's who's doing them and so
7:21the essence of the misallocation
7:22literatures is to think about the
7:25possibility that different economies are
7:28a are are differentially good at at
7:32handling that that problem and and kind
7:35of a key starting point to this is if
7:37you start thinking about that the first
7:40thing you realize is that models that
7:42start with an aggregate production
7:44function uh aren't going to be very
7:46helpful here that if you start with an
7:48aggregate production function you've
7:50kind of taken a reduced form approach
7:53and that big a in front of the aggregate
7:56production function would necessarily be
7:59a combination of both best practice
8:02methods and technology in use and how
8:05resources are being allocated and so the
8:08uh motivation for the misallocation
8:10literature is to kind of open up that
8:13aggregate production function think
8:16about all the diff the different types
8:19of decisions that get made in an economy
8:22and all the dimensions to Resource
8:24allocation and think about the
8:26possibility that differences in in in
8:28across economies and how effective they
8:31are at at at handling those resource
8:35allocation problems might in fact be an
8:37important contributor to tfp differences
8:40and so uh that's kind of the the
8:44starting point here's an outline for
8:46what I'm hoping to do today uh and I
8:49guess I want to emphasize in part this
8:52is uh the first of two lectures on
8:55misallocation and as the title for the
8:57lecture said this is really largely
9:00about Benchmark models of misallocation
9:03and then an application and showing some
9:06early results and so a lot of the
9:08lecture is actually going to focus on
9:10introducing you to the models that are
9:13common that you need to to have facility
9:16with if you want to work in the
9:17misallocation literature and so what I
9:20would say about uh this lecture this
9:23lecture is is not going to be a survey
9:26of results where I kind of tell you what
9:29the current state of understanding is
9:32about misallocation the object of
9:34today's literature T today's lecture is
9:37to kind of give you access to the tools
9:40so that you can actually uh contribute
9:42to the literature on misallocation so uh
9:45Pete kleo is going to give a lecture I
9:47know next week and he's going to talk a
9:50bit more about current results but today
9:52in some ways is kind of more about the
9:54the foundation if you want to work on
9:57misallocation these are kind of the
9:59tools you need to have some facility
10:01with and so the first thing we're going
10:03to do is introduce you to some Benchmark
10:06models of misallocation which is
10:08basically going to be uh the models we
10:11talk about today are going to be models
10:13that emphasize the fact that the total
10:16output in the economy is is what you get
10:18from adding up the output across
10:21individual firms and importantly those
10:23individual firms are going to be
10:25heterogeneous we're going to have a lot
10:28of production units that are
10:30heterogeneous and in a setting like that
10:32a key part of resource allocation is how
10:36resources get allocated to those
10:38heterogeneous units having done that
10:41we'll kind of have a clear sense of in
10:45the context of those sorts of models
10:48what are the effects uh that can lead to
10:51differences in Aggregate tfp and that'll
10:54help us highlight the role of
10:55misallocation per se and then I'm going
10:58to talk about two early papers in the
11:00literature that that have some results
11:03so one paper I have with Diego ruchia
11:06and then kind of the the seminal paper
11:09in the literature the 2009 QJ paper by
11:13Shen kleo I'll close with just a couple
11:16of issues so with that I'm going to jump
11:19in so to say at its uh core uh we need
11:24we want to think about models in which
11:27we think about aggregate out put in the
11:29economy being produced by a lot of
11:33heterogeneous producers and so uh
11:37there's three main models that you will
11:40come across uh for people who think
11:42about those Mo those uh want to think in
11:45that framework one of these is the hopen
11:48hind model a second one uh the meletz
11:51model and third the uh Lucas span of
11:54control model so I want to introduce you
11:57to all three of those models there's a
11:59sense in which uh the details differ but
12:03but there's a lot of common uh structure
12:06and common economics across those models
12:09but again if you want to work in this
12:10literature you kind of need to have a
12:12little bit of working knowledge of these
12:15models and so I'm going to the the first
12:18part of the lecture the goal is to kind
12:20of introduce you to these models I'm
12:23going to build them up in three steps so
12:27step one I'm going to talk about um
12:29static models in which there are
12:32multiple production units but actually
12:34no heterogeneity so that's just to kind
12:36of get us going so that's a small step
12:39away from an aggregate production
12:42function then step two we're going to
12:44introduce heterogenity into those static
12:47models and then step three is we're
12:49going to have uh Dynamic models with
12:52hogen so uh let me jump in I'm going to
12:57start with the uh the whole hind model
12:59and I guess as I said I'm I'm starting
13:02with kind of baby versions of all of
13:05these models so I'm going to talk about
13:08static models uh and right now with no
13:10heterogenity so so this is kind of the
13:13building block of a of a hopen hind
13:15model so uh in this version that I want
13:19to introduce you to we're going to have
13:20a single household so a representative
13:22household just like in the standard
13:24growth model this representative
13:27household is going to have one unit of
13:28time
13:30uh there's going to be a single good in
13:32this economy or you could say a single
13:34final good and this this representative
13:37household uh just cares about how much
13:39uh they consume of this single good so
13:41they've got uh a utility function U ofc
13:45okay so that's all on the household side
13:47just completely standard you could think
13:50of it as just a static snapshot of the
13:52one sector growth model household with a
13:55unit of time and they value consumption
13:57of the final good now on the production
14:00side that's where we deviate from the
14:04aggregate production function so the
14:06unit of production is going to be a
14:09plant and and a key part of this model
14:12is that there's a technology for
14:14creating plants and how do you create a
14:16plant you create a plant by using some
14:19labor and so in particular H bar units
14:23of Labor can create one plant what does
14:26it mean to create a plant when you
14:28create a plant you basically have access
14:31to a a production function for this
14:33plant and the production function for
14:35this plant is you give it some labor and
14:38it produces some of the output and it
14:40has a z in front of this function small
14:44F and a key feature of the uh hoenheim
14:47model is that this function f is
14:50decreasing returns to scale and that's
14:53uh not just a cosmetic assumption or a
14:56detail this is kind of at the Cor core
14:59of the economics of this model okay so
15:02that's the hopen hind model and as I say
15:05it's a model which deviates from an
15:08aggregate production function by saying
15:10that no production takes place in things
15:12called plants and we actually need to
15:15actually create these plants so it has a
15:17technology for creating a plant and then
15:19once you've created the plants that's
15:21gives you your ability to produce output
15:24so that's uh the hopen Hine model this
15:27simple building block of it
15:29the meletz
15:31model uh has uh say some elements in
15:35common I I say on the top here in some
15:38ways this is really Dixit diglets for
15:40those of you who are familiar with the
15:42literature and mallets in some ways is
15:45like a uh embedding Dixit the original
15:49Dixit diglets into a dynamic model with
15:52firm entry and exit and such uh but I'm
15:56just going to call it melet because of
15:58we headed into building up to the the
16:01full model so as in the hopen hind model
16:04uh we don't do anything on the household
16:06side it just looks like a static
16:08snapshot of the one sector growth model
16:11a single household a unit of time they
16:13value consumption so that's all standard
16:17then where we have something interesting
16:19is on the production side once again
16:23unit of production is a plant uh but now
16:26instead of plants producing
16:29uh units of the final good in this setup
16:32uh a plant produces what's called a
16:35particular variety so the plants all
16:38produce uh different things as in the
16:42hopen Hine model you create a plant by
16:44using some labor H bar units of Labor to
16:47create one plant once you create the
16:50plant uh it can then produce output of a
16:54particular variety and that plant uses
16:58labor a hi to produce output Yi a
17:01variety I there's this Z out in front
17:05and uh note that this production
17:08function I have as constant returns to
17:10scale in contrast to what we had in the
17:13hopen Hine model I could actually make
17:15this decreasing returns to scale but
17:18that's actually not uh required whereas
17:21in the hoenheim model that's kind of key
17:24um uh and in in most versions of this
17:28model you'll see that that constant
17:30returns to scale is used but then the
17:33extra detail here remember all of these
17:35plants in the melet model are producing
17:38different varieties now how do we
17:41aggregate those varieties into the final
17:43output and here's the production
17:46function that Aggregates the production
17:48of all the varieties into a final good
17:52which is what the household consumes and
17:55here you can see it's a CES aggregator
17:59and the assumption is that these things
18:00are are substitutes so that the row is
18:03between zero and one so so again looks a
18:08lot like the hope and hind model except
18:10now we have instead of all the plants
18:13producing the single final good here all
18:16the plants produce different varieties
18:19um they produce with constant returns to
18:21scale themselves but then we aggregate
18:24those uh into the final good and as as
18:27I'll show you in a couple couple slides
18:30in the hopen hind model the decreasing
18:32returns to scale and the production
18:34function here is a key source of
18:37curvature that's kind of the critical in
18:40this model in the mellet model or the
18:43Dixit stiglets model there's no Cur you
18:45do not need curvature here and it's
18:47because the curvature actually comes in
18:50here in terms of these things being uh
18:53substitutes but not perfect
18:55substitutes the third model as I said
18:58the Lucas span of control model once
19:01again on the household whoops on the
19:03household side this looks pretty much
19:07the same there's one little difference
19:09here is as previously I said there was a
19:13a representative household and in the
19:16Lucas manic control model we have to uh
19:19break that household apart and we have
19:21to talk about there being a unit mass of
19:24identical households each of these
19:26identical households has a unit of time
19:29preferences UFC so that's kind of the
19:32same as before on the production side
19:35unit of production is again a plant and
19:39and in the Lucas manic control model
19:42instead of saying that you have a
19:44technology for creating a plant in the
19:46Lucas Mana control model the setup is is
19:50that a plant requires a manager and some
19:53workers and so uh in some ways you could
19:57say all these potential plants exist so
20:00in that sense you don't have to create
20:02them but to operate them you have to
20:04allocate somebody to be a manager and
20:07then you give them some workers if a
20:09plant has a manager and you give it h
20:12workers it produces this amount here and
20:16just as in the hopen hind model this F
20:18is critically uh decreasing returns to
20:21scale and you might say this kind of
20:24looks like hopen Hine except there's no
20:27har bar member the hopen Hine model you
20:29needed H bar units of Labor to create
20:32the plant and here uh it doesn't look
20:35like you need any labor to create the
20:37plant but in fact Loosely speaking the
20:40fact that you have to allocate a manager
20:42in order to operate a plant is a little
20:45bit like uh playing the role of harar
20:48and so as you'll see in in a slide the
20:50Lucas model is a little bit uh like the
20:53hopen high model with h bar equal to one
20:56in a mathematical sense
20:59so those are three static models and I
21:04guess the just the key element of these
21:07models that we're using as our jumping
21:09off point are that these are models
21:12which by construction uh allow us to
21:15talk about uh there being multiple units
21:18that are producing the the aggregate
21:20output in the economy so I just want to
21:23spend a couple minutes talking about the
21:26the implications of these models in
21:29terms of of allocations so I'm going to
21:31talk about efficient allocations right
21:33now so the way I set up these simple
21:36models everything is symmetric so
21:40conditional upon any of these models
21:42however many plants are created because
21:44all the plants look the same uh all the
21:47plants are going to be treated
21:49identically uh by a social planner and
21:51so taking that into account if I said
21:54what are the social planner problems
21:56that tell us what efficient applications
21:59are in these economies the key decision
22:01in all of these economies for a social
22:03planner is how many plants to either
22:06create or operate I'm going to let that
22:09be n and conditional upon that that uses
22:13up a certain amount of Labor in the
22:15hopen Hine model if you want to create n
22:17plants you will have had to have
22:19allocated n times H bar units of Labor
22:22to creating plants in the melet model if
22:25you create n plants which then produce n
22:29varieties you will have used up n times
22:31H bar units of Labor creating those
22:34plants and and what's left over is one
22:36minus that and in the Lucas model if
22:39you're going to operate n plants then
22:41you must have allocated n units of Labor
22:44as managers and one minus n is what's
22:47left then you take what's left and you
22:50spread it evenly so in the Hop and hind
22:53model you take what's left 1 minus n
22:55overh Bar divide that evenly across all
22:58the plants this is how much each of them
23:00gets so each of them would produce F of
23:04that uh and then there's a n Out in uh
23:09front because you have end of those
23:10plants operating so this is what you
23:12would
23:13maximize uh I I should also have the the
23:17Z out in front there but of course uh Z
23:20Would is just scaling that up so that
23:22wouldn't play any role but that is a a
23:25typo there uh and then the mallet model
23:29you get the corresponding expression
23:31that then gets fed through the CES
23:33aggregator to get something that looks
23:35like this and then Lucas model you get
23:37that so that's what a social planner
23:40would do and the key problem for the
23:41social planner how many production units
23:45to have and as a result uh once you know
23:48how many production units you have you
23:50also know how big each of them will be
23:53so the social planner in these economies
23:55has to decide how many production units
23:58to have and how big they should be I
24:01won't go through the algebra but if we
24:04take the uh the production function f in
24:08the hopen Hine and Lucas uh models as as
24:12y to the alpha uh then these are the
24:15Expressions you get for the optimal
24:18number of plants and you can see in some
24:21ways these kind of all look the same I
24:23told you that Lucas is a little bit like
24:25hopen Hine with h bar equal to one and
24:28you you can see that the expression has
24:30exactly that feature I also emphasize
24:33that the hopen Hine model curvature is
24:36kind of a key feature of that model and
24:38curvature enters through the decreasing
24:40returns to scale of production function
24:43and you can see that Alpha is the
24:45measure of curvature and and that
24:47measure of curvature shows up in this
24:49expression for n and in the melet model
24:52we said there's no curvature in the
24:55individual production function but the
24:57curvature comes through the es
24:58aggregator and you can see that that's
25:00dictated by row and in fact row enters
25:03this expression just like Alpha up there
25:07what's the the economics Behind These
25:10you can see so this as I say the social
25:13planner has to decide how many units to
25:16operate and and as a result of that how
25:19big each of these units is and what's
25:21the economics of the what's the
25:24fundamental economic trade-off here on
25:27the one hand creating units production
25:30units uses resources in the hopen Hine
25:33and meletz models you have to give up H
25:36bar units of Labor every time you want
25:38to create one of these production units
25:41so that seems kind of wasteful so why
25:43would you want to use up resources to
25:46create these production units well the
25:49reason that you do that is because of
25:51the curvature in these models in the
25:53hopen hind model you've got decreasing
25:56returns to scale here and so with
25:58production function the bigger a unit
26:00becomes the the lower its marginal
26:03productivity becomes so you could just
26:06create one unit and have a big unit but
26:08if you just had one big unit you've got
26:11all your labor there and the decreasing
26:13returns to scale are really kind of
26:15taking a bite out of your production if
26:18you actually said I'm gonna open up a
26:20second unit then by virtue of opening up
26:23a second unit you then go back to taking
26:27advantage of the fact that marginal
26:29product of labor is very high when a
26:31unit is small and by spreading labor
26:34over more units you're able to avoid
26:37some of the decreasing returns to scale
26:39and so the key tradeoff in these models
26:42is uh you avoid the the the decreasing
26:47returns to scale which in the meletz
26:49model comes from the curvature the
26:52substitutability across the varieties in
26:54the hopen Hine and Lucas models it just
26:56comes from this you're you're trading
26:59off resources used to create units uh
27:04versus uh uh facing the decreasing
27:07returns to
27:08scale okay uh that's what a social
27:11planner would do uh often we're
27:13interested in thinking about
27:15decentralized equilibria in these sorts
27:17of models I'll just mention that if you
27:21uh look at how these uh are done in the
27:24literature in the hopen hind model the
27:27standard equilibrium notion is
27:29competitive equilibrium you can do other
27:31things but that's kind of the standard
27:34uh you'll notice when people write down
27:36melet style models the standard
27:39equilibrium notion is not competitive
27:41equilibrium it's monopolistic
27:43competition in the market for the
27:46varieties uh with perfect competition
27:49elsewhere uh as I put on the slide here
27:52why in some ways they do that because
27:55they kind of have to and the reason for
27:57that is if you've got constant returns
28:00to scale at the Variety level uh and
28:04there's a fixed cost it turns out that a
28:06competitive equilibrium in that economy
28:09uh would never exist um so they actually
28:12have to deviate from competitive
28:14equilibrium in order to have a
28:16well-defined notion of a decentralized
28:20equilibrium uh and so monopolistic
28:22competition is standard and Lucas uh
28:26model once again there uh it's standard
28:29uh to just talk about a competitive
28:31equilibrium you can do other things uh
28:34but you don't have to do something
28:35different I guess is one way to think
28:37about it as I note at the bottom here uh
28:40in these models with an elastic labor
28:43all of these decentralized alloca
28:46equilibria uh generate efficient
28:48allocations so those social planners
28:50problems are what would
28:52happen so uh quick summary of what I've
28:55shown you so far so all three of these
28:58models endogenously determine what we
29:01can call the Intensive and extensive
29:03margins of production the numbers of
29:06producers and the size of each
29:08producer uh in these simple models kind
29:11of a uh unappealing feature is that the
29:15producer size distribution turns out to
29:17be
29:18degenerate that is all the producers in
29:21in the models I've introduced so far are
29:25going to be the same size so the size
29:27distribution is is degenerate um now
29:31critical to this was that in that
29:33analysis so far all plants had the same
29:36value of Z the plant level uh
29:39productivity parameter now in fact as a
29:42as an empirical matter there's massive
29:45literatures out
29:46there uh uh Chad cyers has a nice review
29:51paper in the Journal of economic
29:53literature you could look at but a
29:55robust empirical finding is when e
29:58economists look even within narrowly
30:00defined Industries uh in given economies
30:03they find large cross-sectional
30:05dispersion in z um and so the next step
30:10is for us to introduce that heterogen in
30:12Z that we actually see in the data into
30:15these models in order to uh have uh uh
30:20to produce models in which we get non
30:23degenerate size distributions and this
30:26is going to be critical as an input into
30:29thinking about the misallocation issue
30:31we talked about because the essence of
30:33misallocation has to do with the fact if
30:36you've got heterogeneous producers an a
30:40critical aspect of resource allocation
30:43is how to resources end up being
30:45allocated across those heterogeneous
30:48producers and so the next step is to add
30:51heterogenity into both of these
30:53Frameworks now when you start adding
30:56heterogenity there's kind of two
30:58different ways you could introduce it as
31:01I say here ex anti versus ex uh expost
31:05and the distinction has to do with is
31:08the zi observed if if each plant is
31:11going to have its own uh productivity
31:14parameter Z the question is do you
31:16observe this after the plant is created
31:19uh wh I said after and after in both
31:22cases that's a typo exante means you uh
31:26observe before the plant is created
31:27created xost means uh uh Z is observed
31:32after the plant is created so sorry
31:33about that uh typo as I say on the slide
31:37this is not a question of right or wrong
31:40uh there's good reason to think both of
31:43those are are
31:45plausible um but what I want to point
31:47out is is that the the choice matters in
31:50terms of the economics associated with
31:53it so so there's slightly different
31:55economics associated with each of those
31:58as I mentioned here in hopen hine and
32:01melet The Benchmark models typically
32:04have all the hogen being expost
32:08heterogen uh in the plants you use H bar
32:11units of Labor to produce a plant and
32:14then after you allocate that labor then
32:16the Z is a random draw so so you create
32:20the plant but you only find out how good
32:22the plant is after you've created it the
32:25lucasp control model in contrast
32:28traditionally assumes exanti
32:30heterogenity and they actually typically
32:33call it uh heterogeneous manager ability
32:37and so the high zi people become
32:40managers and the key issue in terms of
32:43xanti versus expost is if you know the
32:46zi before you create uh a plant uh then
32:51then there's actually selection issues
32:53in terms of which plants um you choose
32:56to create so let's uh embellish those
33:01models that we talked about with
33:03heterogen so I'm going to start with the
33:06adding xost heterogen into the hopen
33:08Hine
33:10model so in the hopen Hine model uh in
33:13this extension if we create a plant
33:16again it uses H bar units of labor but
33:20now we're going to get a draw Z from a
33:22distribution with a density um G so the
33:27all of these models I'm talking about uh
33:29assume that there's lots of plants it's
33:32like a uh technically there's a a
33:35measure of plants so we start with a lot
33:38of uh households we allocate a certain
33:41fraction of the
33:42labor and and because we're going to
33:44have a large number of plants and the
33:47draws are IID across plants this means
33:50we basically have a law of large numbers
33:53so in a from the perspective of a of a
33:55density the distribution of Z across
33:59plants that we create is just going to
34:02replicate the density from which these
34:04draws come from if you draw twice as
34:07many if you create twice as many plants
34:10then you'll just have twice as many
34:12plants of each Z so you just kind of
34:15scale this up so this is kind of key
34:18when I said
34:19the uh the heterogen is all exposed if
34:24you produce twice as many plants the
34:27average quality of the plant in terms of
34:29the average Z is unaffected you just get
34:32more of everything in this problem the
34:35social planner now has a slightly more
34:38interesting problem this social planner
34:40has to decide how many plants to create
34:43but because the plants that it creates
34:46will now have different Z's this social
34:49planner also has to decide how to
34:51allocate the remaining labor to those
34:54plants and so I'm gonna and so a plant
34:57of of productivity Z is going to get H
35:00of Z units of Labor and so the what's
35:03the social plannner problem the social
35:05planners problem this is going to be the
35:08total output that gets produced um uh as
35:13I said so so the distribution of plants
35:17is going to mimic the distribution that
35:19they draw from the G of Z if you give a
35:23plant of type z h of Z workers that
35:27plant will produce z h of Z to the alpha
35:30units of output we integrate across the
35:33density and then as I said the the more
35:36plants we create we just kind of uh
35:40proportionately increase this and here's
35:43the key constraint on labor which is the
35:46mass of plants you
35:48create uh h of Z times G of Z this is
35:52the labor allocated to a plant of type Z
35:56you integrate across the density so this
35:58is the total labor that's allocated
36:01across the plants scaled up by the
36:03number of plants and that has to be how
36:06much labor is left over after you've
36:08taken out the labor used to create the
36:11plants okay so this is a more
36:13interesting social planers problem
36:15because in this problem the social
36:18planner has to decide both how many
36:20plants to create and how to allocate
36:22labor across those plants uh the the
36:26rule the for order condition that the
36:28social that would come from the social
36:30planner's problem is that the social
36:32planner would equate the marginal
36:34product of labor across all the plants
36:37if that's not true then the social
36:39planner would reallocate and this is
36:41just the condition that says that that
36:43that's
36:44constant in terms of solving this model
36:48ask a question oh sure yeah so in the
36:52exante and the
36:53expost thing so do those Z represent
36:57things or are they really representation
37:00of the same true
37:02Z in the two kinds of
37:05models uh oh you could uh you can do
37:10that kind of uh in a general way they
37:14can be distinct you could have uh
37:17multiple dimensions of Z and one
37:20dimension could be uh differential have
37:24X antien and the other one could have X
37:27post heterogen so they they need not be
37:30you could have multiple dimensions of
37:33the plant level productivity and so in
37:35the end when we are going to answer some
37:37questions about the misallocation or the
37:39aggregate productivity those are bound
37:41to be different those results will have
37:43to be interpreted differently when we go
37:45through different models right uh that's
37:48true so uh you know the in terms of the
37:53model the details of the environment
37:57that you specify influence what
37:59efficient allocations look like and so
38:01those those details definitely matter
38:03and so at a general level you have to
38:06specify what those details are we'll see
38:11that it seems more like the managerial
38:13ability and how those are whether
38:15efficient people are setting up the
38:17plants and in expost case it more of
38:20looks like a Technology based thing that
38:23whether your production was efficient or
38:25not and whether people who used finally
38:28were
38:29efficient or not and in the exan case it
38:33is whether the efficient people started
38:35the business or not so these are
38:37actually measuring different kinds of
38:39things like there are different there
38:41completely two different dimensions of
38:43uh productivity that these are capturing
38:45yes just to connect them you could
38:48imagine uh take the Lucas span a control
38:51model and with the interpretation that
38:53the zi is the managerial quality I could
38:59uh extend that to say that yes managers
39:02differ people differ X an in their
39:04managerial quality but then even
39:07conditional upon choosing a manager with
39:10a high exante uh quality when I actually
39:14put them in a particular plant to manage
39:17there will still be a random draw on top
39:20of that and so both of those things will
39:22be present and the total productivity
39:25right could be either the summer the
39:27product of those two so so so as I say
39:30as I said there's no right or wrong that
39:33it's either or there's a sense in which
39:35in reality we could easily imagine both
39:37of those things are present yeah these
39:39are like superimposed upon each other
39:41these cannot be separated
39:44absolutely okay yeah thank you yeah uh
39:48okay so in terms of solving this simple
39:50model I have a few steps here and I see
39:53I'm I'm kind of not making that good a
39:56time in terms of G through the material
39:58I I was hoping to get uh but let me just
40:01say that in terms of solving this
40:03model uh you can kind of do it in three
40:06steps so you can solve for the maximal
40:09output conditional upon a unit of Labor
40:12being available and the distribution of
40:15plant productivities being equal to this
40:17which is what the distribution will
40:19necessarily look like call this uh y of
40:22one um then it turns out that uh the
40:27efficient allocation of Labor that Max
40:29that equates marginal products means
40:32that this condition is satisfied and the
40:34key Point here is if I gave you twice as
40:38much labor to allocate across a given
40:41distribution of firms um each h of Z
40:44scales with the total labor because
40:47nothing happens to the the total amount
40:49of Labor has no impact on the relative
40:52amount of Labor which means if there's
40:54twice as much labor to be allocated then
40:57everybody gets uh twice as much labor
41:00and so that means that total output uh
41:04just scales up uh H to the alpha times
41:07that y of one and then you can solve for
41:10the optimal number of plants to create
41:14by noting that total output looks like
41:16this and in some ways this says that
41:18this uh hopen hind model with the xost
41:22heterogen kind of looks a little bit
41:24like the uh H and hind model without
41:27heterogen where where Z is just equal to
41:31this y of one which takes into account
41:33the efficient amount of output you get
41:36from allocating labor across the
41:38unit
41:40um uh now I'm going to talk about adding
41:44an element of expost heterogenity into
41:47the hopen Hine this is just you know one
41:50way to do this but I want to do this to
41:53to illustrate a model where you've got
41:56Mo both margins um present and uh so one
42:01way to do that in the hopen hind model
42:03is I'm going to split that H into two
42:07parts uh one part called h e and the
42:10other part called har F and what I want
42:13to say is that creating a plant in the
42:15first place requires he bar units of
42:19Labor and it gives you a random draw
42:21from G of Z but then having created the
42:25plant if you actually want to operate it
42:28that's where this second component of
42:30the fixed cost comes in and you only
42:33have to pay this cost HF if you choose
42:38to operate the plant after creating it
42:40and this gives rise to a selection
42:42margin so so now this is a model that
42:45has uh both of those elements and I I
42:48have the social planners problem here
42:50but I think in the interest of time I'm
42:53not going to walk you through the the
42:55details there but the key point is now a
42:58social planner has to decide how many
43:02plants to create and then having created
43:05them it sees the productivities and now
43:08it has to decide which of these plants
43:10to operate and which not to operate and
43:13so in some ways there's an additional
43:15margin to the social planners problem
43:17which is uh which plants
43:20operate and and in the simple framework
43:24I have here the plants that operate you
43:27will equate marginal product of labor
43:29across those plants and there will
43:32actually be a simple threshold rule a
43:34selection rule for which plants operate
43:36you only operate plants above some um
43:40Zar so these are the multiple margins in
43:43the social planners problem so I've kind
43:46of introduced heterogen into the hopen
43:49Hine model just to make it concrete you
43:51can do this in the melet and Lucas model
43:54in just kind of a analogous way I'm not
43:56going to go through that um
44:00detail uh I just want to make one more
44:03comment about decentralizations in these
44:06environments with heterogeneous firms
44:08and and this is a distinction which is
44:10kind of important in terms of taking
44:13these models to the data um so if you do
44:17competitive equilibrium in hopen hine
44:20and Lucas um all the production units
44:22are producing the same good and so in a
44:25competitive equilibrium there's a single
44:28price for a single good and so the price
44:31of the output that's produced by all
44:33these units will be the same uh in the
44:37meletz model when there's no
44:40heterogenity uh then everybody charges
44:43the same price because everybody charges
44:46a markup over their
44:48their uh marginal cost but because
44:51there's no heterogenity in marginal cost
44:53there's no heterogenity in prices but
44:57when you introduce heterogen into the
44:59melet model and different production
45:01units have have different uh Z's so so
45:05different productivities that means that
45:08different units have different marginal
45:10costs if prices are a fixed markup over
45:13marginal cost you also get um heterogen
45:16in prices and so as I say that'll just
45:20be useful uh for us to kind of store in
45:22the back of our minds for some points
45:24I'm going to make a little bit later
45:28um so uh this is just kind of
45:32summarizing some of what I said about uh
45:35the dimensions of efficient allocations
45:38and as I kind of want to make the point
45:40here if you start with an aggregate
45:42production function and labor is the
45:44only uh factor of of production as in
45:47the models we've been talking about so
45:49far there's kind of just nothing to be
45:52said you just uh tell your workers to go
45:55to work and you get the output you yet
45:57there's kind of nothing interesting in
45:59terms of something that happens in the
46:02economy that that's going to influence
46:04how much output you get in the hopen
46:06Hine model without heterogen the first
46:09model we talked about there's a a
46:11non-trivial decision about how many
46:14plants to operate and how big the plants
46:16should be and different choices and and
46:19there's a the social planner there was a
46:22optimal number of plants to create and
46:24hence an optimal size of plant
46:27if you deviate from the optimal Choice
46:30you'll have a suboptimal level of output
46:32in that economy so there's already one
46:35interesting decision there how many
46:38plants to operate how big should they be
46:40when we went to the the hopen high model
46:43with expost
46:45heterogenity uh there's actually an
46:47additional dimension in addition to
46:49deciding how many plants to create after
46:52the fact the social planner also has to
46:54allocate labor across those PL
46:57and so you could also deviate from the
47:00efficient level of output by having the
47:03wrong allocation of Labor across those
47:05plants and then lastly when I the hopen
47:08hind model with both X anti and expost
47:12heterogen an additional Dimension is
47:15which plants are operating which plants
47:17are not operating so so in this uh hopen
47:21hind model with X anti and exost
47:23heterogenity you have this Rich set of
47:26decision which need to be made in the
47:28economy which are going to influence the
47:30total amount of output in the economy
47:33and this is true holding Tech the access
47:36to technology in a sense um fixed so uh
47:42in the interest of time I think I'm
47:44going to go a little bit quick here but
47:47I just want to uh so far I did
47:49everything static so I just want to talk
47:52about how to embed that into a dynamic
47:55framework because in some some settings
47:57the Dynamics uh will be particularly
48:01important so I'm just going to do this
48:03for the hopen hind model so I'm going to
48:05have a representative uh consumer so
48:08this will be like a version of the solo
48:12growth model but instead of having an
48:14aggregate production function we're
48:16going to build the production up from
48:18all these um individual units which get
48:21um created over time so as in the
48:24standard solo model nothing we don't
48:26change anything on the household side a
48:28representative consumer preferences that
48:31look like this uh endowed with one unit
48:35of
48:36time uh all the action is on the
48:39production side and you'll see this is
48:40going to look a lot like the uh basic
48:44building blocks we just talked about so
48:46the production unit is a plant a plant
48:50level production function looks like
48:52this so I've now extended to include
48:55capital and labor both as as inputs uh
48:59key is is that F has decreasing returns
49:02to scale and K and H we need some
49:05curvature here because kind of the
49:07essence of the hopen Hine model is is
49:10that it's wastes resources to create
49:12plant but the reason you're willing to
49:14waste those resources is because each
49:16plant has decreasing returns to scale so
49:19that's kind of a fundamental trade-off
49:21in these models so I now have this Z in
49:25front of a plant I'm now going to assume
49:27that this z uh evolves stochastically
49:30over time and I'm going to put a I'm
49:33just going to make it a finite Markoff
49:35chain you can uh make this a continuous
49:38uh process if you want notationally if I
49:41with a Markoff chain you can just
49:43describe it with a matrix so that's kind
49:45of nice and
49:46convenient um uh and then the Z for a
49:51particular plant is observed at the
49:52beginning of the period before they make
49:55any decisions uh so now in terms of the
49:59entry and exit which kind of gets to the
50:01things we talked about before uh there's
50:04a fixed cost hrf in units of Labor if a
50:08plant wants to remain in existence
50:10that's like that operating cost we
50:12talked about previously and then there's
50:14a fixed cost HR e in units of Labor to
50:18create a new plant and if you create a
50:21new plant you have to say where does the
50:23plant start from in terms of its Z and
50:26that's just like the models I talked
50:28about earlier that Z is going to be a
50:30random draw from some distribution with
50:33a density G on that finite set of of Z
50:38values those draws are IID across plants
50:41so I say this kind of just takes that
50:44static structure we talked about uh puts
50:47it into a dynamic setting in the context
50:49of the growth model a model that
50:51accumulates capital and the and then the
50:54one little twist I've added is to
50:57allow for the sorry about that the a
51:02plant is created it draws a z and then
51:05uh in a multi-period model we we allow
51:08for the possibility that that Z evolves
51:11stochastically over time so so that's
51:14the the model and as I say this uh model
51:19is like the one sector growth model
51:23except it has this richness on the
51:25production side where instead of me just
51:27plopping down some aggregate production
51:29function I now build up the total output
51:34uh total uh output produced in this
51:37economy by talking about the output
51:39produced by a whole bunch of individual
51:41plants at any point in time these plants
51:44are heterogeneous in their
51:46productivities on top of that they also
51:49evolve stochastically over time so if
51:52you follow plants over time you'll see
51:54that some plants grow some plants shrink
51:57some go out of business new plants are
52:00created so it's a model which has the
52:04beauty at an aggregate level of
52:06something that looks like the one sector
52:07growth model but it also has this
52:10richness in terms of of of what goes on
52:13on the production side and just as the
52:15static models we talked about have this
52:18Rich set of of dimensions for what it
52:21means to have an efficient allocation
52:23this model will inherit those those
52:25features as as
52:27well uh so in the slides I guess the
52:31slides will be available to all of you I
52:33kind of go through the some of the
52:35formalism of describing the uh recurs
52:41the recursive competitive equilibrium
52:43for this kind of uh uh elaborate uh
52:47version of the one sector growth model
52:49with this richness on the technology
52:51side so I think you know the slides are
52:55available and I'm going to let you kind
52:57of uh go through peruse those uh
53:02later um let me just say that the to
53:06kind of extend some of our earlier
53:09discussion I'm going to talk right now
53:10about a steady state um so in a steady
53:13state there'll be some wage rate and
53:15some rental rate of capital there'll be
53:18some aggregate labor there'll aggregate
53:21Capital stock there'll be some aggregate
53:22labor that's used but then kind of the
53:26interesting element of this model is is
53:28kind of the rich set of uh heterogen on
53:32the production side so in a state state
53:35there'll be this invariant distribution
53:38of plant level
53:40productivities there'll be a massive
53:43entry each period there'll be some
53:45plants that exit so there'll be an exit
53:47rule for plants and then in terms of the
53:51total capital and total labor there'll
53:53be an allocation of that across plants
53:57which differ in their values of Z so
53:59that's kind of the the core of this
54:02model I'm going to skip the the
54:05definition I also have some slides on
54:08how you how easy it is to solve for the
54:12steady state which I'm actually also
54:14going to um skip over in the interest of
54:17time uh and this is kind of key in terms
54:21of setting the stage for the
54:23misallocation literature or more
54:25generally uh using these models to think
54:28about differences in aggregate
54:32tfp because in this
54:34model uh we can now think about all the
54:38things which might differ across two
54:40economies that might give
54:43rise to differences in Aggregate tfp and
54:47so the first thing to note I said that
54:49mear of of
54:51z uh is the distribution of
54:54productivities across plants in an
54:57economy and those uh when plants are
55:01created they draw from G so one thing
55:04you could say is suppose two economies
55:07uh have different G's that they draw
55:09from and you might say well this maybe
55:11is one way to capture that some uh
55:15economies are kind of away from the
55:17techn tech uh technological Frontier
55:21they're not using best practices so that
55:24the the new plants that are created are
55:27kind of in some uh productivity Sense on
55:30in a stochastic sense worse than the
55:32plants that get created elsewhere so
55:34this is like just saying embedding it
55:37directly into yes plants are kind of
55:41plant by plant plants that get created
55:44in one country are worse than in another
55:46plant in terms of productivity that's
55:48going to ultimately feed into the
55:51equilibrium distribution of plants
55:53across
55:54Z uh there could be something about the
55:57stochastic evolution of productivity
55:59that that maybe you start a plant and
56:02then if a plant is accessing modern
56:05technology and best practices there's a
56:07sense in which it gets on a particular
56:09trajectory and maybe that differs across
56:12countries so this is like kind of
56:14hardwiring things through
56:17technology but then the the core of the
56:20misallocation literature is to say in
56:22this sort of model that's not the whole
56:24story there's actually these kind of uh
56:27really important other decisions or
56:29potentially important other decisions
56:31how do you allocate even taking the
56:33distribution of disease as given how do
56:37you allocate labor across the differenes
56:39how do you allocate Capital across the
56:41differenes how do you decide which
56:43plants to close down so these are all
56:46decisions that will influence how much
56:49total output you produce even taking the
56:52distribution of the Z's as given and so
56:56uh as I say down here distortions that
56:59affect the ability or incentive of firms
57:02to adopt Frontier Technologies or use
57:04them those kind of show up in one and
57:07two uh but distortions that prevent
57:10resources from being directed to their
57:12most productive uses kind of show up
57:14here and so this is a a model which kind
57:17of lets you look inside the the black
57:20box of the aggregate production function
57:22into the different things which might
57:24give rise to to measured differences in
57:27aggregate um
57:29tfp and so um that's kind of the jumping
57:33off point in a sense for the
57:35misallocation uh literature as I say
57:39here uh you know just summarizing from
57:41the previous SL in an economy with
57:44producers that are heterogeneous in
57:46productivity the allocation of inputs
57:48across producers will influence
57:51emphasize measured aggregate tfp so the
57:54idea is you could have two economies
57:57that plant by plant look identical in
58:00terms of the productivities but if in
58:02one of these economies they do something
58:06uh bad in terms of how they allocate
58:08resources across those plants one of
58:10these economies will produce less output
58:13than the other economy even though they
58:15have the same amount of capital and the
58:17same amount of Labor so that will show
58:19up as a difference in in uh in measured
58:23Aggregate tfp and so so the second point
58:26I mentioned here which is you know even
58:30before one does anything to try and put
58:33numbers on anything just as you're
58:35thinking could this be plausible as they
58:38say hey there's countless examples of
58:40the things that governments do that kind
58:43of are associated with what we might
58:45think of misallocating inputs across
58:48producers and I I mention here kind of
58:51corruption or crony capitalism that in
58:54uh many that this happens in all
58:57economies but I think you know if you
58:59just kind of read press reports and
59:02stuff uh less developed economies uh
59:05where institutions are not so strong uh
59:08corruption is is uh more uh present uh
59:13SL crony capitalism you've got people
59:16running firms who shouldn't be running
59:18them but they're well connected so
59:20they're getting access to either
59:22government contracts low interest loans
59:24from the government tax exemption so
59:26there you so it's easy to think about
59:29all these things which go on in less
59:31developed economies which probably show
59:34up as misallocation and which then feed
59:37into differences in tfp and so the idea
59:41is uh to say something about how
59:44important um that might be and so having
59:47kind of laid the groundwork there I want
59:49to talk about uh two papers which have
59:53tried to put some numbers on this uh so
59:55the first one is a paper by myself and
59:58Diego ruia uh read 2008 and I'll go a
1:00:02little bit quickly here just because
1:00:05we're uh time is is uh quickly passing
1:00:10so what uh ruchu and I did was was
1:00:14the following we took one of these kind
1:00:16of actually little bit of a simple hope
1:00:18and hind style model and we actually uh
1:00:22just said the following without trying
1:00:24to connect to reality you write down one
1:00:27of these models and you can see
1:00:29conceptually uh these models have the
1:00:32potential to create differences in
1:00:34aggregate tfp due to kind of messing
1:00:37around with how you allocate labor
1:00:39across heterogeneous production units
1:00:42and so uh what we did was I say very
1:00:46simple-minded we kind of said let's just
1:00:48kind of take one of these models and
1:00:50just explore whether how easy it is to
1:00:54get big differences in TF p uh from
1:00:57messing around with things that way uh
1:01:00do you end up with big differences or
1:01:01small differences just as a way to kind
1:01:03of uh get a sense of are we in the
1:01:06ballpark for thinking about things so we
1:01:09took a uh as I say a little bit of a
1:01:12simple version of The Hop andhim model
1:01:15relative to what I just told you we took
1:01:18in elastic labor Supply uh this was the
1:01:22F the plant level production function uh
1:01:25that we
1:01:27postulated we kind of got rid of the
1:01:30action on the exit um margin by just
1:01:35saying that there's uh one of the Z's is
1:01:38actually equal to zero and that's an
1:01:40absorbing State uh so that's the sense
1:01:43in which we have exit but we had the the
1:01:45fixed operating cost we actually set to
1:01:48zero and then uh exit kind of happens
1:01:52because there's a probability Lambda
1:01:54that you go to this absorbing state so
1:01:57it's uh basically a very I I have a
1:02:00fundamental question so yeah so when you
1:02:04said that uh suppose uh two countries
1:02:06have similar distribution of
1:02:07productivity across plants but just due
1:02:10to different allocation of inputs one is
1:02:13able to produce more and another is not
1:02:14able to but that is static view of the
1:02:18economy it might be that the government
1:02:20and the market disciplined in another
1:02:22economy and so the allocation was a bit
1:02:24distorted but down the line say 5 years
1:02:28from now that it is better for that
1:02:30economy so are we taking into account
1:02:33the this Dynamic effect of the market
1:02:35disciplining or the government actions
1:02:38or is it just onetime view of the
1:02:40allocation we are
1:02:42interest so I mean at a general level
1:02:46the framework I've laid out can handle
1:02:50the the broad Dynamic uh question you're
1:02:53talking about so it's a so you can have
1:02:56some
1:02:58policies you you have to so you will
1:03:00aggregate the output across ears and
1:03:02then save out some aggregate output is
1:03:04it so well I would say it differently
1:03:07that you know one of the reasons we like
1:03:09if you're thinking about policies where
1:03:11there are Dynamic effects then a dynamic
1:03:15model allows you to talk about you know
1:03:18the policy happens today and we can
1:03:20trace out the effects over time so we
1:03:23don't have to literally add them up we
1:03:26can actually Trace out those those
1:03:28effects and then we can uh you know do
1:03:32we can compute the effects period by
1:03:34period and and Trace out the
1:03:37Dynamics I was just uh what I focused on
1:03:41in my uh words was just we could take
1:03:45two economies in steady state both of
1:03:48them can be in steady state and by
1:03:51virtue of being in steady state the
1:03:53Aggregates are not changing over time
1:03:56and then we could compare the tfp those
1:03:59steady state tfp levels but that's just
1:04:02one particular context in which you can
1:04:04make that comparison if you have
1:04:06economies that are not in steady state
1:04:08then uh you might also be interested in
1:04:11in not just the points in time but the
1:04:13Dynamics and these these Frameworks
1:04:16allow you to do that but you'll see the
1:04:18the two examples I'm going to talk about
1:04:20today from the literature uh were're
1:04:23were're both uh just kind of looking at
1:04:26point in time but as to your question
1:04:30you shouldn't think that the logic of
1:04:33these uh of misallocation and these
1:04:36Frameworks can only be used to talk
1:04:38about those static
1:04:40things okay okay thank you
1:04:45uh okay so that's the uh setup so then
1:04:49we uh calibrate this model I'll say a
1:04:53standard calibration I'm not going to go
1:04:54through the detail but again the object
1:04:57here was to say let's take a plausibly
1:05:00calibrated version that kind of mimics
1:05:03the aggregate facts because the H and
1:05:05hind type model at an aggregate level
1:05:08looks like the one sector growth model
1:05:09so we want parameters so that at that
1:05:12level it looks standard and then the the
1:05:16novel feature relative to the one sector
1:05:18growth model is what happens at the firm
1:05:20side so then the idea is to parameterize
1:05:24things so that so that you get something
1:05:26that looks like a reasonable firm siiz
1:05:28distribution and and firm Dynamics so so
1:05:31we did that and then as I said the idea
1:05:35is get some sense as to how big of
1:05:38effects you could get on tfp by uh
1:05:42distorting uh allocations across firms
1:05:47and and uh the way we did this um
1:05:53uh was was as a kind of a stand in we
1:05:57said one way to think about distorting
1:06:01allocations across individual producers
1:06:03and this kind of is motivated a little
1:06:05bit if you're thinking crony capitalism
1:06:07or corruption that some producers are
1:06:10getting favored treatment uh this is
1:06:13like having individual taxes or
1:06:16subsidies on producers and so uh that's
1:06:20that's how we're going to achieve this
1:06:22uh these this Distortion or this
1:06:26misallocation and so we did this in a
1:06:29very uh highly parameterized uh way
1:06:33where we said that uh we're going to
1:06:35have one group of producers that gets a
1:06:38subsidy another uh set of producers that
1:06:40gets a tax and we're gonna that's going
1:06:43to distort the allocations across these
1:06:46producers and then does that uh produce
1:06:50big effects or or small effects and so
1:06:53we actually considered two different
1:06:56specifications uh which we called
1:06:59uncorrelated and correlated distortions
1:07:02and the idea is the uncorrelated case
1:07:04was was that the TOA is independent of Z
1:07:08so there could be you know Loosely
1:07:10speaking some people are connected with
1:07:13the government and some people are not
1:07:16um but whether you're how connected you
1:07:18are with the government is kind of
1:07:21independent of how uh productive you are
1:07:25and and so whether you get taxed or
1:07:27subsidized has no correlation with the Z
1:07:30and the second case is where ta was
1:07:33correlated with with
1:07:35z and again I'm not using my time very
1:07:39well so I'm GNA race ahead a little bit
1:07:43um here's kind of um the key numbers and
1:07:46I guess uh I'm going to have you focus
1:07:49on just the second row here so this is
1:07:51the case of the uncorrelated distortions
1:07:55and this this is uh uh the tax rate
1:07:59that's on the the people who are being
1:08:01penalized and the the corresponding tax
1:08:06rate uh for the those being subsidized
1:08:09is chosen so that the steady state
1:08:11capital stock stays unchanged anyways
1:08:14this relative tfp uh basically says that
1:08:18you can uh there's a sense in which
1:08:20going to 04 is kind of maxing out the
1:08:24Distortion because at that point you've
1:08:26kind of reallocated all the resources
1:08:29and the point here is is you can get a
1:08:31tfp difference of about
1:08:338% there and the message we kind of took
1:08:36away from that is is that if you mess
1:08:39around with things but even if you do it
1:08:42in a crazy way but it's kind of
1:08:44completely random uh although you can
1:08:47get some effects that 8% when you're
1:08:50talking about the level of living
1:08:53standards between richest and poorest
1:08:54countries is actually not that uh
1:08:57powerful um the next exercise is do this
1:09:02where we're now taxing the productive
1:09:06and subsidizing the unproductive uh and
1:09:09now you can see when you max that out
1:09:11you start to get tfp differences on the
1:09:14order of 30% again that's not going to
1:09:16get you all the way to the productivity
1:09:19differences uh we see across rich and
1:09:22poor countries but that gives you kind
1:09:23of a big chunk so that actually seemed
1:09:25kind of um promising so the the
1:09:30punchline from from this was that if the
1:09:33nature of of misallocation is is that
1:09:36you're shifting resources from high
1:09:40productivity uh to low productivity
1:09:42establishments um then there's um scope
1:09:45for that to be pretty powerful in terms
1:09:47of aggregate
1:09:49tfp and I do want to emphasize in these
1:09:52models with heterogeneous production
1:09:54units
1:09:55uh there's a tendency to think oh if
1:09:57you're moving resources from high
1:09:59productive to low productive that must
1:10:01be bad uh and it suggests oh maybe it
1:10:04would be good if we moved resources from
1:10:06less productive to more productive but I
1:10:09want to emphasize in in these models uh
1:10:12with decreasing returns to scale there's
1:10:14an efficient allocation across units and
1:10:18it's not that you want to move all the
1:10:19resources to the high Z units because
1:10:23decreasing returns to scale kick in
1:10:26and so it's also true starting from an
1:10:28efficient allocation if you just said
1:10:31let's subsidize the high productivity
1:10:33people and tax the low productivity
1:10:35people that would also be bad for
1:10:38aggregate tfp it turns out that won't
1:10:41have very big effects in part because
1:10:44there's not that much scope for
1:10:46misallocation uh relative to an
1:10:48efficient allocation there because most
1:10:51of the labor is already in the high
1:10:53productivity units so
1:10:56um I in the time remaining I'm going to
1:11:00uh go for another 7 minutes or so uh so
1:11:04this was all saying it looks like
1:11:06there's scope for for this to
1:11:08potentially um matter but now the
1:11:11question is you know let's try to say
1:11:13something about does it really matter uh
1:11:16in the real world and so critical for
1:11:18that is me getting some senses to how
1:11:21much
1:11:22misallocation uh exists in the world so
1:11:25those previous exercises I talked about
1:11:28were just inventing misallocation and
1:11:30saying if we had misallocation could we
1:11:32get big effects the key question is is
1:11:35there a lot of
1:11:37misallocation in the real world so how
1:11:39are we going to make Headway on that I
1:11:42want to talk about two different
1:11:43approaches a direct versus an indirect
1:11:47uh the direct approach which is kind of
1:11:50a a natural one to follow is pick a
1:11:55source of something which you think
1:11:57creates misallocation try and go out in
1:11:59the world and measure it and feed it
1:12:02into the models uh one uh large
1:12:06literature that has done that is is a
1:12:08literature on on imperfections in
1:12:11capital markets to try and measure uh
1:12:14those differences across countries that
1:12:17limits the uh efficient allocation of
1:12:20capital across units and and get a sense
1:12:23of how big those are alternative
1:12:26approach uh which I call the indirect
1:12:28approach is to say uh let's not worry
1:12:31about what the source of misallocation
1:12:33is let's just try and measure the amount
1:12:36of misallocation without identifying the
1:12:39underlying source so what's the uh the
1:12:44the pros and cons here is is that uh you
1:12:47might like the direct approach because
1:12:49you actually have taken a stand on on
1:12:52what is causing the misallocation and so
1:12:55you can trace it to the underlying
1:12:57Source the disadvantage of the direct
1:13:00approaches is if you think that a lot of
1:13:03the
1:13:04misallocation is coming from uh things
1:13:07that we might Loosely call corruption or
1:13:09crony capitalism or from a whole diffuse
1:13:13set of uh institutional features then
1:13:17there may not be one easily measured
1:13:20single factor which causes it and so the
1:13:23benefit of the indirect approach
1:13:25uh is is is that it allows you to cast a
1:13:29wider net uh rather than focusing on one
1:13:32particular thing that you might be able
1:13:35to measure so I want to uh the indirect
1:13:38approaches is what uh Shay and clean now
1:13:41used and so I want to talk briefly about
1:13:43that before I talk about their results
1:13:46and so the indirect approach as I say
1:13:49rather than trying to take a stand on
1:13:51where misallocation comes from it says
1:13:54let's just try and measure how much
1:13:56misallocation there is and the key idea
1:14:00in this is as I've mentioned a couple
1:14:02times in a uh these models I've written
1:14:07down efficient
1:14:09allocations uh you know the the simple
1:14:12hopen hind model I talked about earlier
1:14:14efficiency required that a marginal
1:14:17product of labor was equalized across
1:14:20those units which is a condition that
1:14:21looks like this and then it means if
1:14:24this condition does not hold then we
1:14:26have misallocation so we basically could
1:14:29just look for violations of that
1:14:33condition uh and the bigger the
1:14:35violation the more the misallocation now
1:14:38how do you identify those those
1:14:41violations well if you take a stand on
1:14:44functional form on the functional form
1:14:46for the production function and in
1:14:48particular the Y to the alpha that I had
1:14:51talked about before it turns out that
1:14:54equating marginal products also means
1:14:57that you equate average products of
1:15:00Labor so if you actually have data on
1:15:03output at the at the uh prod at plant
1:15:06level and labor at the plant level then
1:15:09you can actually check for violations of
1:15:11this and you can actually uh just assess
1:15:15how much misallocation there is and in
1:15:18fact just to make that
1:15:20concrete suppose I posit this production
1:15:24function at the plant level Yi is equal
1:15:27to Z hi to the alpha and so now this is
1:15:30like a snapshot in time and you take a
1:15:33stand on what Alpha is suppose I give
1:15:36you data at the plant level on output
1:15:40and and labor then total output in the
1:15:44data is equal to this total labor is
1:15:47equal to that and tfp in that data uh in
1:15:52a with a one sector one factor
1:15:55interpretation is y over
1:15:59H and so if we could solve for the Z we
1:16:03could then solve for the level of output
1:16:05that would result if we allocated labor
1:16:08efficiently call that Yar and then the
1:16:11point is if you've got data on Y and H
1:16:15and you take a stand on the production
1:16:17function you can actually back out the
1:16:19zis so you can just solve for zi that
1:16:22way once you know the zis you can in a
1:16:26sense solve the social planners problem
1:16:28and say given you've got this much labor
1:16:30what's the most output you could
1:16:32generate and you can solve for y over y
1:16:37star and that's the effect of
1:16:38misallocation on tfp and implicitly y
1:16:43star will be bigger than y as long as Yi
1:16:46over hi is not constant uh that is
1:16:50marginal products are not
1:16:52equated so one uh
1:16:57uh issue that we have to talk about in
1:16:59the context of this is is the following
1:17:03that at the heart of this method is the
1:17:06fact that an efficient allocation has
1:17:09this property if this doesn't hold then
1:17:12we conclude there's misallocation
1:17:14another way to spin this is that we have
1:17:18a model which implies this we go to the
1:17:22data and then you find that that doesn't
1:17:24hold
1:17:25and then the question is does that mean
1:17:28your model's not good or does it mean
1:17:30that there's um some misallocation and
1:17:33that's a little bit of a deep question
1:17:35for this uh so-called indirect approach
1:17:39in that it identifies
1:17:42misallocation as departures from some of
1:17:45the conditions uh that the model implies
1:17:48would hold if there were not any
1:17:50misallocation and again uh it could be
1:17:53that the model is not not specified
1:17:56properly uh as opposed to their actually
1:17:59being misallocation so that's a a
1:18:03danger
1:18:05uh how should I do this given I've not
1:18:08used my time very well um I think I'm
1:18:13gonna uh say the following so so that's
1:18:16kind of the essence of things I
1:18:19mentioned earlier that uh Richard if you
1:18:23have if you if you take five more
1:18:25minutes and if you if you can stay for
1:18:27five more minutes to questions we can go
1:18:29five minutes late does that work out
1:18:31does that help you uh that helps me so
1:18:34let's do that I'll take a few more
1:18:36minutes then and and we'll have the
1:18:37questions after the the
1:18:41time
1:18:44uh okay so as I mentioned before uh in
1:18:49hopen hine or Lucas model where you
1:18:51assume that there's just a single good
1:18:53then there's a single
1:18:55price uh and and an issue in terms of
1:18:59taking these models to the data is that
1:19:02when I did that previous description I
1:19:04said suppose I give you data on Yi and
1:19:07hi but in fact you never really have
1:19:11data on yi yi is the physical output
1:19:14produced Micro Data what it usually
1:19:17gives you is pi times Yi so the price
1:19:21times you basically get a measure of
1:19:23sales so so or Revenue so that's what
1:19:26you get there if you kind of go to the
1:19:29data with the hopen hind model and
1:19:32assume that that the P's are all the
1:19:34same then knowing if the P's are all the
1:19:37same then you can infer relative outputs
1:19:41because the P's cancel uh and it turns
1:19:44out that's all fine but kind of a key
1:19:46question is if you think when you go to
1:19:49the data that there's actually heterogen
1:19:51in PS then the hopen hind model is
1:19:55actually not very good for connecting to
1:19:58the data because it it kind of uh embeds
1:20:02a kind of a serious specification eror
1:20:04and so uh to the extent that people
1:20:07think that that different plants are
1:20:10producing slightly diff either different
1:20:13uh varieties or you might think
1:20:15different qualities of a particular
1:20:17good it suggests that we need to think
1:20:20about price heterogen and for that
1:20:22reason in many applications including
1:20:25the Shay clean out that I'm going to uh
1:20:26still get to today um the melet
1:20:29framework is kind of the dominant
1:20:31framework for connecting to the data so
1:20:33in some ways the underlying economics
1:20:35are kind of um almost the same but
1:20:39there's this extra detail which turns
1:20:41out to be relevant when connecting to
1:20:43the data that we need to be mindful of
1:20:46the fact that that prices might differ
1:20:49and so it turns out you can also do all
1:20:51of what I did in a melet style model
1:20:54this is the basic melet model that I
1:20:57talked about and the key thing here is
1:21:01is that in a melet style model if we
1:21:05said what what holds in an efficient
1:21:08allocation it turns out that an
1:21:10efficient
1:21:11allocation uh the average revenue
1:21:14product of labor will be equated across
1:21:18producers so in the hophey model that I
1:21:21talked about we had no pi and P J that
1:21:25was those PS are the same so they cancel
1:21:27so he said that Yi over hi I is equal to
1:21:30YJ over HJ and we said going to the data
1:21:35with that is kind of a little bit
1:21:37misguided if we think there's heterogen
1:21:39adum PS in the when we extend to the
1:21:42melet model uh the implication of that
1:21:45model is is that an efficient allocation
1:21:48will have the property that Pi Yi over
1:21:52hi is equal to PJ y j over HJ because
1:21:56the data we see Pi * Yi and we see hi we
1:22:01can actually evaluate this in the data
1:22:04without being worried that we've imposed
1:22:08uh something highly counterfactual in
1:22:10terms of uh not allowing for prices to
1:22:12diver so this gives us an alternative
1:22:15simple condition for identifying
1:22:18misallocation now this can be
1:22:21generalized uh to a uh setting where
1:22:24there's both labor and capital and in
1:22:27that setting it turns out the
1:22:28implication is that you can uh an
1:22:32efficient allocation is going to equate
1:22:35average revenue product of labor across
1:22:37plants and average revenue product of
1:22:40capital across plants uh on the slides I
1:22:43talk about how it is that by you can uh
1:22:47just with data on Revenue capital and
1:22:52labor you can actually
1:22:55also back out the Z's uh at the plant
1:22:58level uh using the demand system that
1:23:01corresponds to the CES and you can do
1:23:05this calculation once you've computed
1:23:07the actual Z's you can compute what a
1:23:09social planner would do in terms of
1:23:11total
1:23:13output uh so I got that in the slides so
1:23:17I won't talk about that what I want to
1:23:19do next is is talk about the the sheay
1:23:22and kleo um
1:23:24paper which is in the Gen saying so the
1:23:28Shane clean up paper as I say is the
1:23:31kind of the single most important paper
1:23:34in the misallocation literature and this
1:23:36paper did two things first of all it it
1:23:39basically developed the methodology that
1:23:42I've worked through where it said you
1:23:44give me data on uh Revenue uh at the
1:23:49plant level labor at the plant level and
1:23:52capital at the plant level and and I
1:23:54will actually uh tell you how much
1:23:57misallocation there is so it's basically
1:24:00you give me that data they created this
1:24:02framework for how to take that data
1:24:05uncover the zis implicitly uncover the
1:24:10distortions and uh also calculate how
1:24:13much extra output we could get from
1:24:16allocating things uh uh efficiently and
1:24:20having developed that methodology they
1:24:22then said let's take this methodology
1:24:25and we're going to look at the
1:24:26manufacturing sectors in China India and
1:24:29the us and we're going to evaluate the
1:24:32extent of misallocation in these three
1:24:35economies and the key finding the reason
1:24:37this paper is so important uh is the key
1:24:41finding was that misallocation is big
1:24:45and in particular it's much bigger in
1:24:47China and India than in the US so just
1:24:50to kind of go back to where we started
1:24:53today's lecture the key Insight is is
1:24:56that misallocation does seem to be an
1:24:59important component of differences in
1:25:02aggregate or in this case aggregate
1:25:05manufacturing uh tfp across countries
1:25:09and I'll just show you a couple I'll
1:25:13just show you here's kind of uh the key
1:25:16well I'll show you this is a picture
1:25:18this is the distribution of
1:25:21tfp um R across uh these these three
1:25:24countries is say an efficient allocation
1:25:27um there would be no spread in any of
1:25:30these and the key Point here even in the
1:25:32United States this thing is is far from
1:25:35degenerate but you can see in India and
1:25:38China there's actually much more
1:25:40dispersion the more dispersion there is
1:25:42in this measure this like average
1:25:44revenue product uh this means there's
1:25:47there's more misallocation and then
1:25:49here's the the numbers that you attach
1:25:52to this and so this is you the uh tfp
1:25:56gains from equalizing tfpr within
1:25:59Industries so this is getting rid of all
1:26:02the misallocation how much extra TF
1:26:05aggregate tfp could you get uh and you
1:26:08can see for China we're talking about uh
1:26:11kind of on average doubling things for
1:26:14India roughly doubling things and for
1:26:16the United States getting an extra uh 30
1:26:19to
1:26:2140% so that's their key finding
1:26:25the the last thing I want to talk about
1:26:27is just some of these issues and some of
1:26:29these I suspect Pete will make some
1:26:32additional reference to so kind of the
1:26:36as I say the shake cleanout paper is
1:26:37particularly important because it
1:26:39actually um put some numbers on
1:26:41misallocation and set it at uh you know
1:26:45a rigorous exercise to say this is
1:26:47actually a big deal but as I said there
1:26:50are some uh questions in the background
1:26:53and in particular particular because
1:26:55they've used this indirect approach uh
1:26:58the question is are these wedges these
1:27:01these misallocation that they measure is
1:27:04it evidence of model misspecification or
1:27:06is it really um distortions away from
1:27:10efficient allocations and I mentioned
1:27:13two possibilities here so example one uh
1:27:18uh in their model K overh should not
1:27:21vary across producers in an efficient
1:27:23allocation
1:27:25but the question is if we observe K
1:27:28varying across producers in reality is
1:27:30this misallocation or is it evidence
1:27:33that different producers are using uh
1:27:36heterogeneous
1:27:37Technologies Technologies which have
1:27:39different Capital intensity and if they
1:27:42are using at a given point in time
1:27:44Technologies with different Capital
1:27:46intensities then you an efficient
1:27:48allocation would in fact still have
1:27:50variation there second example uh uh in
1:27:56the data there's meas there's always
1:27:58measurement error and so how do we
1:27:59detect the difference between
1:28:01measurement error and a true Distortion
1:28:03so these are issues the literature has
1:28:07uh uh has the follow-up literature has
1:28:11addressed uh but in terms of the kind of
1:28:15some question marks uh when you follow
1:28:18the indirect approach and get these
1:28:19numbers uh kind of the general question
1:28:22is how do we know we've identified true
1:28:26distortions versus uh either model
1:28:29misspecification or measurement error in
1:28:31the data as I said if you follow the
1:28:35direct approach then you have a bit
1:28:38more uh confidence that that the what's
1:28:42coming from the measured differences in
1:28:44policies is actually reflecting uh
1:28:48misallocation so I've talked too long
1:28:51I'm actually going to stop there
1:28:53hopefully I've uh set the stage for Pete
1:28:56next week to kind of get you more up to
1:28:59date and I will now uh take questions
1:29:02for a
1:29:04while fantastic thanks Richard you've
1:29:07got some people to call on in the um
1:29:10directly from the front row I see a
1:29:12question from rul and a question from
1:29:15Andre Okay and one from
1:29:18Fatu okay why don't we take the three
1:29:20questions in in sequence and then you
1:29:22can answer the three so rul Andre and
1:29:26then Fatu and then we'll take another
1:29:31round um hello so my impression from
1:29:35this literature is that when you read um
1:29:37especially those papers of work um about
1:29:39the frictions in the capital markets is
1:29:41that depending on the model you use even
1:29:44if you abstract from all of the
1:29:45measurement errors you can get like
1:29:47super different results so how can we
1:29:50actually assess uh the fit of this to
1:29:54the actual differences in
1:29:58tfp
1:30:00well I'm not I guess I would ask you to
1:30:04kind of fill in a little bit more when
1:30:06you're saying you get results all over
1:30:09the place uh could you just say a bit
1:30:11more about what you're referring to
1:30:14there no for example I I'm really
1:30:17interested in this literature and one of
1:30:18the things I I I find um starking is
1:30:22that for example if you read some paper
1:30:24about um um for example starting the
1:30:28role of collateral constraints as in I
1:30:30don't know mid andu for example and but
1:30:34if you read some other papers speaking
1:30:36about some other kind of frictions you
1:30:37actually find like super different
1:30:39results so it's it's hard for me to make
1:30:42some kind of um assessment
1:30:45on where we are actually how how we do
1:30:48we know these things Richard can I just
1:30:50propose that we that we collect the set
1:30:52of questions and then you
1:30:54answer use your time and allocate it
1:30:57efficiently okay sounds good okay so
1:31:00that's one from R let's have Andre and
1:31:03then Fatu and then
1:31:07Jeremy yes thank you Richard um so I had
1:31:11I had two questions but um most
1:31:14important one would be you sure how
1:31:17sensitive this was to some stuff how
1:31:19sensitive is this to the entry and exit
1:31:22conditions like uh
1:31:24you think
1:31:26there's that altering that could
1:31:29represent significant differences and my
1:31:32other question more in general is how
1:31:34perfect are we assuming these markets
1:31:36[Music]
1:31:38are that's it
1:31:42two um Hello thank you so much for the
1:31:45lecture um I just had one question and I
1:31:47was just wondering whether it's possible
1:31:49to extend the or to generalize this mod
1:31:53these models not only to include Capital
1:31:56but also intermediate
1:31:58inputs intermediate inputs yeah yeah
1:32:02thanks um
1:32:05Jeremy I'll stick to one
1:32:08question we can get a some kind of a
1:32:10dispersion in the marginal revenue
1:32:12products but then from there we want to
1:32:16get some number of if we got rid of this
1:32:18dispersion what would the increase in
1:32:20output be and my understanding is that
1:32:22that kind of relies
1:32:25on whatever the number is we have for
1:32:28the decreasing returns to scale I'm
1:32:30wondering how do how have we estimated
1:32:33that decreasing returns to
1:32:37scale great um Richard you want to take
1:32:40a stab at those sure all excellent
1:32:45questions
1:32:46uh I won't answer them in order I'll
1:32:49just say a couple specific things so
1:32:51first of all intermediate input
1:32:54can easily be added and in fact
1:32:57there's uh recent work I'll say one of
1:33:00my colleagues at Princeton Ezra
1:33:02oberfield uh and a co-author are looking
1:33:06at the extent to which uh institutional
1:33:10differences across countries feed into
1:33:14uh how Supply chains are created and
1:33:17depending upon how you do Supply chains
1:33:20that has an impact on whether you Source
1:33:22intermediate in puts from elsewhere or
1:33:25you actually produce them internally and
1:33:27so this is another uh potentially
1:33:30important margin so so I've kind of
1:33:33shown you the tip of the iceberg here in
1:33:35a model where there's just capital and
1:33:39labor and that's kind of where all the
1:33:41action is but you can imagine extending
1:33:44this to think about all the different
1:33:47margins that are involved in in
1:33:49production I'll just say another paper
1:33:52which I don't know if Pete will talk
1:33:53about it next
1:33:54week uh all this has been about just how
1:33:57much capital and how much labor goes to
1:34:00different producers another key question
1:34:03is which labor goes where and so there's
1:34:06a Pete has a paper with three other
1:34:08co-authors which I'm a big fan of
1:34:11talking about the misallocation of
1:34:13talent arguing that you know uh factors
1:34:17like discrimination in uh some uh
1:34:21settings in some countries either on
1:34:24gender or race uh religion can influence
1:34:29which people go to which occupations
1:34:31because they could be barriers there uh
1:34:33that would be another important source
1:34:35of misallocation so in some ways these
1:34:38models I've talked about today are kind
1:34:39of the where the literature started and
1:34:42it's kind of the tip of the iceberg but
1:34:43you can think about all the rich set of
1:34:47decisions in a modern economy uh that in
1:34:51that involve how you allocate which
1:34:53resources to which activities at which
1:34:55producers and all of those things are
1:34:58are potentially up for grabs in terms of
1:35:01things that could be distorted that that
1:35:03might have an impact on
1:35:05tfp so uh in terms of you there's a
1:35:10question about the curvature parameter
1:35:12and they say you know in the Hop and
1:35:14Hine it's the decrease and returns at
1:35:16the plant level I'm going to say that's
1:35:18a a parameter which comes up in lots of
1:35:21those models and I think it's fair to
1:35:23say the there are different people
1:35:26who've estimated it but I would say it's
1:35:28I don't think it's all that tightly
1:35:30pinned down so there is a an empirical
1:35:33issue there if you do the melet version
1:35:37the curvature parameter is the
1:35:39elasticity of substitution in the
1:35:42production function and there's actually
1:35:44a whole bunch of people who who have
1:35:46produced estimates of that parameter so
1:35:49in that formulation there's actually a
1:35:52large body of empirical work which kind
1:35:54of paints a picture that they think they
1:35:56know what that parameter is uh so you
1:36:00know things are a little bit blurred
1:36:02across the two specifications but if you
1:36:06follow the
1:36:07melet's uh view approach uh there's
1:36:11actually quite a bit of evidence to draw
1:36:13on there not to say it's definitive
1:36:16because there's still many issues there
1:36:18but I'd say there's a fair bit of
1:36:20evidence and the early question that
1:36:23said
1:36:24you know different people are finding
1:36:26different results I'm going to say you
1:36:29know in a certain sense this is uh the
1:36:31nature of research in economics this is
1:36:34a young literature even old literatures
1:36:37in economics continue to argue about
1:36:41what the quantitative impact is but the
1:36:43way we make
1:36:44progress is by being rigorous in writing
1:36:48things down trying to take them to the
1:36:51data trying to assess uh what the
1:36:54quantitative impacts are that's a pro a
1:36:57process which will will go on in time
1:37:00and and it's by building models and
1:37:04understanding which things in those
1:37:06models matter and and how to connect
1:37:09those things with the data that we uh
1:37:12presumably are going to make Headway so
1:37:14so I don't think of it as a problem that
1:37:17at current there are different people
1:37:19who've made different assumptions and
1:37:21gotten different answers this is kind of
1:37:23the part of the progress in terms of
1:37:25economic research is to get those things
1:37:27out there and and then to try and follow
1:37:30up to understand what's going
1:37:33on Richard I have another question for
1:37:36you from Federico coachen who says is
1:37:39there any empirical evidence on how
1:37:41these wedges might evolve over time so
1:37:46for example for the same firm do they
1:37:48change as time passes do we have
1:37:50anything that tries to trace these
1:37:52things through
1:37:54um in a dynamic
1:37:55sense uh yes and actually you know this
1:37:59uh we could talk about that for quite a
1:38:01while so there's a a paper by uh three
1:38:06or four co-authors I know one of I'm
1:38:08blanking on all the the names right now
1:38:11yand deler is one of them it's in the
1:38:14jpe but it basically uh argued was was a
1:38:20one paper which argues that the Shay
1:38:22clean now has a lot of
1:38:25misspecification and the nature of the
1:38:26misspecification they emphasized is they
1:38:28said let's assume that there's some
1:38:30adjustment costs on Capital and we all
1:38:33know in a model with adjustment costs
1:38:36you wouldn't uh an efficient allocation
1:38:38wouldn't equate the instantaneous uh
1:38:41marginal product of capital across firms
1:38:43because you need to take into account
1:38:45the adjustment costs and in a world
1:38:47where there's
1:38:49idiosyncratic uh temp transitory shocks
1:38:52and adjustment costs uh you're not going
1:38:55to always move all the capital to equate
1:38:58marginal products because you understand
1:39:00you're going to have to undo some of
1:39:02that in the future if the shocks are
1:39:04transitory uh and so that's a a setting
1:39:09in which you don't equate things now if
1:39:11you said how important are those forces
1:39:16that kind of gets to the question of you
1:39:18would like to see the dynamic properties
1:39:20of the wedges because if it's Transit
1:39:23shocks and adjustment costs that's
1:39:26creating the dispersion in in average
1:39:29revenue products there should be a
1:39:31definite uh time series uh pattern that
1:39:34you see in terms of of how those shocks
1:39:37behave over time and I would say uh
1:39:41there's scope for more work on this uh
1:39:46uh you basically would need panel high
1:39:48quality panel data at the firm level to
1:39:50do this and and there's a
1:39:53limited access I guess to those sorts of
1:39:56data sets so I think it's a key area for
1:39:59additional research but some of the
1:40:01research that I have seen on that shows
1:40:04that the wedges are actually quite
1:40:06persistent uh suggesting that the
1:40:09adjustment cost story is kind of not
1:40:11really a particularly good
1:40:13rationalization for the patterns we see
1:40:15in the
1:40:16data uh and the other thing I would say
1:40:19is on a more substantive note perhaps is
1:40:23that uh in the context of China where we
1:40:26know that uh me sh and kleo do talk
1:40:29about this they actually find that
1:40:31state-owned enterprises are getting too
1:40:34many resources relative to an efficient
1:40:36allocation which I think is a result
1:40:38that many people find plausible and
1:40:41intuitive in some ways lend support to
1:40:44the results they're getting but then you
1:40:47can look as China is kind of lessening
1:40:50some of those distortions over time do
1:40:52you actually see the the wedges changing
1:40:55over time and Shaye and kleo actually
1:40:57find some evidence for those things
1:40:59decreasing over time on the flip side
1:41:02India has also uh made lots of reforms
1:41:06and the literature to kind of Trace out
1:41:08the Dynamics of the wedges in India has
1:41:12I'd say has found a little bit less
1:41:14supportive evidence for changes that we
1:41:17think are reducing misallocation that it
1:41:20actually shows up in the wedges but I
1:41:22would say that's a huge area for future
1:41:25research is to think about these in a
1:41:27dynamic setting and get access to the
1:41:30data that allows you to think about it
1:41:32to analyze it systematically thank you
1:41:34so much Richard I think we should
1:41:36probably wrap up given that we've gone a
1:41:39bit over time I want to thank and
1:41:41congratulate the hardcore of um 125 or
1:41:46so participants who stuck with us to The
1:41:48Bitter End thank you so much again
1:41:50Richard for the clarity of the
1:41:52exposition
1:41:53and thanks as always to Mandy Chan and
1:41:57Christy mcneel and Lauren wearing from
1:41:59CPR who do the backend stuff that makes
1:42:03these things possible um and again
1:42:05thanks for thanks Richard for um
1:42:08stepping up and giving us a second
1:42:10lecture here so we'll look forward to
1:42:13hearing from Pete CLE now next week and
1:42:16thanks again everyone we look forward to
1:42:18seeing you back

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