VIII. Technological Change

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------=_NextPart_01C4D784.BAAFB9F0 Content-Location: file:///C:/26794655/PP15_files/pres.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C4D784.BAAFB9F0 Content-Location: file:///C:/26794655/PP15_files/slide0001.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" VIII. Technological Change

VIII. Technological Change<= /span>

Read:

Antle, J. and S. Capalbo, “An Introduction to Recent Developments in Production Theory and Productivity Measurement” Chapter 2 in Agricultural Productivity: Measurement and Explanation, S. Capalbo and J. Antle editors, Resources for the Future, Washington, D.C= ., 1988.

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Capalbo, S. Western Journal of Agricultural Economics

• Dorfman, J. and K. Foster, = Western Journal of <= /span>Agricultural Economics
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• Aoccdrni= g to rseearch at Cmabrigde Uinervtisy, it deosn't mttaer in waht oredr <= span style=3D'position:absolute;top:21.75%;left:12.17%;width:89.32%;height:7.5%= '>the ltteers in a wrod = are peclad, the olny iprmoetnt tihng is taht the frist and lsat = ltteer be in the rghit pclae.

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• The rse= t can be a total mses and you can sitll raed it wouthit porbelm.

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• Tihs is bcuseae the huamn mnid deos not raed ervey lteter by istlef, but the wrod as a wlohe. =

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•A. Types/Sources of Technological Change•
• = 1. Disembodied: changes in output per unit of input
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• 2. Embodied: changes in outp= ut due to changes in input quality
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•B. Primal = Rate of Technological Change

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• Start with a production func= tion, Q=3Df(x,t).

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Technological Change

• In a competitive equilibrium inputs are paid their VMP = and output price equals MC so:
•

•

note:    &= nbsp; =3D the elasticity of cost with respect to output

Equation (1) says that the primal rate of tech. change =3D = ;

the rate of change in output minus a scale-adjusted index <= /span>

of the rate of change of input use.

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Technological Change

•C. Dual (cost/profit function) Measure of = = Technical Change
• = ;

• Start with a cost function, C(Q,r,t).

•

•

•

• Using Shepard’s Lemma&= #13;

•

•

•

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text/html; charset="us-ascii" VIII. Technological Change

• The left-hand side is defined as the dual rate of technological change, and the right-hand side is interpreted as the index of the rat= e of change of factor prices plus a scale effect of technological change minus the = rate of change of total cost.
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• Now, totally differentiate the cost equation C=3DΣrixi= , in natur= al logarithm form.
•

•

•

• substitute (3) into (2) to g= et

•

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Technological Change

• multiplying both sides of (1) by       we = find that <= /span>
•

•

• so,

•

•
• Thus, we find that the dual = rate of tech. change equals the primal rate of tech. = change only when there is constant returns to scale (i.e.,        = ; ).
•

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fd+oPk3/o59IUid/JgBuI5gkX7laCMMZlLfQ3kJyCiNqeLjnHEZWpRt9VVx3sWO2ZyK/hbRIEiW/ lBpBBitZD2YVl8xY2rzZ0ELOgs3o7DxEs+UvjTKbFEXD6CcDpf+ERpl3NOZHV1F5Tlx5ChVTaVe3 YoXEq+qVSMQEZhM7ttg/tJquUmU7iZ1Zo3BNop2LqyrefvT2vtVVt5I4v0sJF/Y6TKSTNhgNu13c wfEhwkDcIqUsea1AEJbNbK48B4XozoBFcx44mnTAGi8KAAA7 ------=_NextPart_01C4D784.BAAFB9F0 Content-Location: file:///C:/26794655/PP15_files/slide0009.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" VIII. Technological Change

•D. Biased versus Neutral Tech. Change

•

• 1. Hicks = ;

•

• Examine the MRTS between capital and labor

• (e.g., MPK/MPL= ).

• = ;

• if it increas= es then the tech. change was

• labor saving/capital using
• if it is unchang= ed then the tech. change was neutral (not biased)
• if it decreas= es then the = tech change was

• capital saving/labor using

•

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•For Example,=

•

• Suppose that after the technical change = ;

•

•

•
• In order to move to the new optimal point from here we need to increase capital use and/or decrease labor use.= Therefore, the tech. change was capital using and labor saving as we said earlier.

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•Notes:

•
•a) Hick’s definition doesn’t specify where to = measure.&#= 13;
• - at some specified point?

• - at the cost minimizing or profit
• maximizing point?

• - anywhere along the expansion path?
• •   If production is homothetic= , then these are equi= valent.
•

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• = b) If production is non-homothetic then the expansion path is nonlinear
•
• - opt= imal input proportions change along the path. (neutral for path =3D neutral for= = MRTS at a point on t= he path)
•
• - not necessarily neutral with respect to = optimal factor proportions.
•

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•c) It is common to define the notion of Hicks neutrality= by saying the technological change is neutral if it is expansion path = preserving= .
•
• HNTC Þ Q=3DF(f(x),t) which says that t is weakly separable from x
•
• Extended HNTC Þ Q=3DA(t)f(x) which says they are strongly separable=

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•

•

•2. Primal Me= asure of Bias

•

•

•

•

• neutrality Þ B<= span style=3D'font-family:"Comic Sans MS";mso-ascii-font-family:"Comic Sans MS"; mso-bidi-font-family:"Times New Roman";font-size:58%;color:red;position:re= lative; top:.45em;mso-text-raise:-30%'>ij=3D0 for all i,j pairs.

•

•

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C1

C2

A

X1

X2

Q1

Q2

e(t<= span style=3D'font-family:"Comic Sans MS";font-size:50%;color:aqua;position:rel= ative; top:.37em;mso-text-raise:-25%'>2)

e(t<= span style=3D'font-family:"Comic Sans MS";font-size:50%;color:aqua;position:rel= ative; top:.37em;mso-text-raise:-25%'>1)

Bij measures slope change from C1<= span style=3D'mso-spacerun:yes'> to C2.

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Technological Change

•Notes:

•

• a) B<= span style=3D'font-family:"Comic Sans MS";font-size:58%;color:red;position:rela= tive; top:.37em;mso-text-raise:-25%'>ij is pairwise, and an n-input measure is

•

•

•

•

•

• Bi tells us if “on average” the marginal= product of x= i is increasing relative to all other inputs. Bi= >0 Þ techilogical change is xi usi= ng.

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• = b) Once we s= pecify a function and estimate we can test Bi= =3D0 which is neutral because B=3D0 for all= i and j implies Bi=3D0.
•

•
• c) The Bi’s are relative measures and do not = measure the absolute changes in marginal products. <= /div>
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• 3. Dual Meas= ure of Bias

•

•

•

• where xi =3D x= i(Q,r,t) is the compensated demand funct= ion derivable from the cost function via Shepard’s Lemma.

•

•

     Indirect Hick N= eutral Tech. Change is   <= /span>

     defined as: = ;

      Notice the weak separability of C(Q,r,t) r

     from t under neutrality.&= #13;

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Technological Change

• Conjecture/Definition:

•

•

•

•

• This measure is useful if the cost function is homotheti= c in output:

• C(Q,r,t)= =3Dg(Q,t)•f(r,t)

•

• So that the cost shares are independent of output, and consequently      is independent of the scale of output.

•

•
=
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• Non-homothetic Cost function implies non-linear expansion paths again and scale effects can = change the optimal factor ratio and the cost shares.

• Thus, there are two confound= ing effects of a technological change on the factor ratio. One is the p= ure bias effect and the other is a scale effect.      contains = both.

=
------=_NextPart_01C4D784.BAAFB9F0 Content-Location: file:///C:/26794655/PP15_files/slide0020_image053.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAAcAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAQABgAQ ABMAgwAAAAAAAAcGBwUEBAYFBQoICQsJCgMDAwgHBwsKCgkICAwKCwkHCAECAwECAwECAwRTEMhJ ZwhAjEtKBRh4jQFBhdIlGUeAWCeaqKlFp6iI3UYgfDhJ4XBIAHUjxRE5Ihg/tEVhMwDeALMWNGRg tJRbUkCZkwguA0FhUVtWym74Un6ERwAAOw== ------=_NextPart_01C4D784.BAAFB9F0 Content-Location: file:///C:/26794655/PP15_files/slide0021.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" VIII. Technological Change

xi

xj

Q1(t1)

Q1(t2)

The graph shows that we c= an get a change in the factor ratio even if the tech. change is not biased (i.e., expansion path preserving) when the expansion path is nonlinear (i.e., non-homothetic cost function). VIII. Technological Change

xi

xj

Q1(t1)

Q= 1(t2)

e(t1)
e(t= 2)
A

B

C

D

•

•

•

•

if non-neutral technical change is afoot, then     measures two = effects shown in the graph below. =
1). Scale effect due to movement along the expansion path from point A= to point B or point C to point D, and

2) Bias effect due to the shift in the expans= ion path: point A to point C= or point B to point D.

=
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------=_NextPart_01C4D784.BAAFB9F0 Content-Location: file:///C:/26794655/PP15_files/slide0022_image061.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhEwAXAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMABQAN ABAAgAAAAAAAAAIghI+hq3nhDJQRTFvteiixzoXdRY0miYLaVqqii8EtTBYAOx== ------=_NextPart_01C4D784.BAAFB9F0 Content-Location: file:///C:/26794655/PP15_files/slide0023.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" VIII. Technological Change

• Notes:

•
• 1. If the technology is homo= thetic so that the expansion paths are linear, then the = there is= no scale effect on the factor ration (xi/xj).
•
• 2. In general, the two effec= ts are confounded in     , and we need to adjust for the scale effect to get a measure of = the pure= bias effect.

------=_NextPart_01C4D784.BAAFB9F0 Content-Location: file:///C:/26794655/PP15_files/slide0023_image062.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhFwAbAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAQABwAN ABEAgwAAAAAAAAMDAwcGBwYFBQkICAsJCgcGBgwKCwoICQUEBAsKCgkHCAECAwECAwECAwRCcIgQ SAEY0M0JDh+FGURwaJmYgqCmAogqqqSZhVxg3G5+3ipEQmFb3RYv14gxaeE4DF4poDgUECie1qlN dXncLzcCADs= ------=_NextPart_01C4D784.BAAFB9F0 Content-Location: file:///C:/26794655/PP15_files/slide0024.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" VIII. Technological Change

• =

Define the scale adjusted measure as follows = ;

The last term can be interpreted as the scale effect of technological change due to = movement along the expansion path (i.e., the part of bias due to changing the scale of = output).

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        = ;      is a measure of the shift in the expansion= = path defined along the isocost line. Now, we = need to express      in cost function terms so that this is truly a dual measure.

Equation (5) is the total differential of C(Q,r,t) holding r and t fixed, i.e., the pure = scale effect.

<= ![endif]>
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The cost change due only to t is

If tech. change is neutral then the two must be offsetting and (5) and (6) are equal. Then,

and after rearranging:

RHS of 5

RHS of 6

This was in the last term of Bice

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Technological Change

Recall from earlier that

Substit= ute for dlnQ*/dt from previous

result = to get the scale adjusted dual

measure= of bias.

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Technological Change

• = The scale adjusted dual measure of bias is the sc= ale dependent measure minus the scale effect which depends = on 1) the elasticity of cost share with respect to output= , 2) the elasticity of scale, and 3)the dual rate of technological change. =

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• Note t= hat in the homothetic case the elasticity of the share with respect to output= is zero and .
•

•        Þ= ; biased= in favor of xi (i.e., xi using)

•

•        Þ= ; biased against xi (i.e., xi saving)

•

•        Þ= ; neutral technological change

•

= = =
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<= span style=3D'font-family:"Comic Sans MS";mso-ascii-font-family:"Comic Sans MS"; mso-bidi-font-family:"Times New Roman";font-size:64%;color:#3333CC;mso-col= or-index: 5'>E. Measurement of (Aggregate) Total Factor = Productivity

•Growth Accounting Approach to TFP Measurement
•
•Intuit= ion: “In the absence of technical change, the growth in total output can be explained by the growth in total in total input use.”
•
•The unexplained residual is attributed to techno= logical change.
•

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• = A very b= rief summary of some indexing = assumptions.

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Technological Change

•Using Index Numbers for TFP Measurement

•

• Example: Tornquist-Theil

• <= /span>TFP = =3D Q/X =3D aggregate output per unit of input.

•
• So, the rate of change of TFP is: =

•

•

•

Note: this is a continuous measure but we have discrete data.

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• = Tornqu= ist-Theil quantity indices to discretely approximate     and     are =

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Content-Location: file:///C:/26794655/PP15_files/slide0034.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" VIII. Technological Change

• Without specifying a functional form we would employ the following formula to = estimate= the discrete rate of change of TFP.

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Technological Change

• Implic= it assumptions underlying the growth = accounting approach.
•

• i) assumes a competitive ind= ustry

•

• ii) assumes CRTS =

• recall the primal rate of tech. change is= =

•

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Technological Change

• iii) assumes extended Hicks Neutrality

•
• iv) assumes input-output separability (i.e., <= /span> G(Q) =3D F(X)
•

------=_NextPart_01C4D784.BAAFB9F0 Content-Location: file:///C:/26794655/PP15_files/slide0037.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" VIII. Technological Change

3) Econometric Approaches to TFP Measurement<= /span>

• = Adv= antages

• - no assumptions about neutrality are necessary

•

• = - know the statistical properties of technical change estimates =

•

• = - no assumption about returns to scale

•

• = Dis= advantage

• = - must choose a functional form and = specification errors can be big

• <= /span>

------=_NextPart_01C4D784.BAAFB9F0 Content-Location: file:///C:/26794655/PP15_files/slide0038.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" VIII. Technological Change

• a) Du= al Approach (Capalbo’s paper)

•= recall equation (4) from earlier

•

•

•
• = but we also demonstrated in equation (1) that the primal rate of tech. change can be stated as
•

•

•

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Technological Change

• Substituting the second equation into the first yields:
•

•

•
• notice that the last term on the right hand side is the divisia form of     . Now, add and subtract       = to the right hand side.
•

=
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Technological Change

• Solving for the rate of TFP growth yields:= 3;

•

•

•

•
• Capalbo estimates a cost function and using those estimates she derives the pieces to the= above equation to compute . In her= case there are two outputs and two scale elasticities. Check = it out= .

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b) Primal Approaches (Dorfm= an and Foster)

• 1. Simple Technical Change

• =
• Comes directly from the defi= nition of the primal rate of tech. change.
•

•

•

•

•

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• recall that we derived in the first lecture on techno= logical change that
•

•

•

•

•
• An approximation of this base= d on an estimated production function is
•

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Technological Change

• 2. Flexible Technical Change

• =
• This approach is similar to = Simple Technical Change, but the estimates of come from the estima= tion of a production function with (potentially) time varying coefficients.

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• = To cal= culate the flexible rate of technical change we use=
•

•

•

•
• Using Capalbo’s data Dorfman and Foster found   to be a more stable measure of tec= hnical change versus        and     &= nbsp; .
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= =
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file:///C:/26794655/PP15_files/script.js Content-Transfer-Encoding: quoted-printable Content-Type: application/javascript; charset="us-ascii" function LoadSld() { var sld=3DGetObj("SlideObj") if( !g_supportsPPTHTML ) { =09 sld.style.visibility=3D"visible" return } if( MakeNotesVis() ) return runAnimations =3D _InitAnimations(); =09 if( IsWin("PPTSld") ) parent.SldUpdated(GetSldId()) g_origSz=3DparseInt(SlideObj.style.fontSize) g_origH=3Dsld.style.posHeight g_origW=3Dsld.style.posWidth g_scaleHyperlinks=3D(document.all.tags("AREA").length>0) if( g_scaleHyperlinks ) InitHLinkArray() if( g_scaleInFrame||(IsWin("PPTSld") && parent.IsFullScrMode() ) ) document.body.scroll=3D"no" _RSW() if( IsWin("PPTSld") && parent.IsFullScrMode() ) FullScrInit(); =09 MakeSldVis(); ChkAutoAdv() if( runAnimations ) { if( document.all("NSPlay") ) document.all("NSPlay").autoStart =3D false; if( sld.filters && sld.filters.revealtrans ) setTimeout( "document.body.start()", sld.filters.revealtrans.duration * = 1000 ); else document.body.start(); } } function MakeSldVis()=20 { var fTrans=3Dg_showAnimation && SldHasTrans() if( fTrans )=09 { if( g_bgSound ) { idx=3Dg_bgSound.indexOf(","); pptSound.src=3Dg_bgSound.substr( 0, idx ); pptSound.loop=3D -(parseInt(g_bgSound.substr(idx+1))); } SlideObj.filters.revealtrans.Apply()=09 } SlideObj.style.visibility=3D"visible" if( fTrans ) SlideObj.filters.revealtrans.Play() } function MakeNotesVis()=20 { if( !IsNts() ) return false=20 SlideObj.style.display=3D"none" nObj =3D document.all.item("NotesObj") parent.SetHasNts(0) if( nObj ) {=20 nObj.style.display=3D"" parent.SetHasNts(1) } return 1 } function ChkAutoAdv() { if(SldHasTrans()) SlideObj.onfilterchange=3DAutoAdv else AutoAdv() } function AutoAdv() { if(!IsWin("PPTSld") || !gUseSldTimings )return var sld=3DGetCurSld() if( (sld.mAdvDelay>0) && !parent.IsFramesMode() ) setTimeout("parent.GoToNextSld()",sld.mAdvDelay) } function GetObj(id) { if(g_supportsPPTHTML) return document.all(id); else return document.getElementById(id); } function SldHasTrans() { return SlideObj.style.filter !=3D ""; } function GetSldId() { return sId=3Dlocation.href.substring(location.href.la= stIndexOf('/')+1) } function HideMenu() { if( frames["PPTSld"] && PPTSld.document.all.item("ctx= tmenu") && PPTSld.ctxtmenu.style.display!=3D"none" ) { PPTSld.ctxtmenu.styl= e.display=3D'none'; return true } return false } function IsWin( name ) { return window.name =3D=3D name } function IsNts() { return IsWin("PPTNts") } function IsSldOrNts() { return( IsWin("PPTSld")||IsWin("PPTNts") ) } function SupportsPPTAnimation() { return( navigator.platform =3D=3D "Win32"= && navigator.appVersion.indexOf("Windows")>0 ) } function SupportsPPTHTML() { var appVer=3Dnavigator.appVersion, msie=3DappVer.indexOf("MSIE "), ver=3D0 if( msie >=3D 0 ) ver=3DparseFloat( appVer.substring( msie+5, appVer.indexOf(";",msie) ) ) else ver=3DparseInt(appVer) return( ver >=3D 4 && msie >=3D 0 ) } function _RSW() { if( !g_supportsPPTHTML || IsNts() || ( !g_scaleInFrame && (!IsWin("PPTSld") || !parent.IsFullScrMode()) ) ) return var padding=3D0; if( IsWin("PPTSld") && parent.IsFramesMode() ) padding=3D6 cltWidth=3Ddocument.body.clientWidth-padding cltHeight=3Ddocument.body.clientHeight-padding factor=3D(1.0*cltWidth)/g_origW if( cltHeight < g_origH*factor ) factor=3D(1.0*cltHeight)/g_origH newSize =3D g_origSz * factor if( newSize < 1 ) newSize=3D1 s=3DSlideObj.style s.fontSize=3DnewSize+"px" s.posWidth=3Dg_origW*factor s.posHeight=3Dg_origH*factor s.posLeft=3D(cltWidth-s.posWidth+padding)/2 s.posTop=3D(cltHeight-s.posHeight+padding)/2 if( g_scaleHyperlinks ) ScaleHyperlinks( factor ) } function _InitAnimations() { animRuntimeInstalled =3D ''+document.body.localTime !=3D 'undefined'; isFullScreen =3D (window.name =3D=3D "PPTSld") && !parent.IsFramesMode(); g_animUseRuntime =3D g_showAnimation && animRuntimeInstalled && !(isFullSc= reen && parent.IsSldVisited()); if( g_animUseRuntime ) { collSeq =3D document.all.tags("seq"); if( collSeq !=3D null ) { for(ii=3D0;ii numSlds ) gSldJumpIdx =3D numSlds; if ( gSldJumpIdx >=3D 0 ) { if ( gSldJumpIdx =3D=3D 0 ) gSldJumpIdx =3D 1; var jumpTo =3D parseInt(gSldJumpIdx); gSldJump =3D 0; gSldJumpIdx =3D ""; win.GoToSld( parent.GetSldList().mList[jumpTo-1].mSldHref ) } } } function _KDH() { if( event.keyCode =3D=3D 8 ) { event.returnValue =3D 0; parent.GoToPrevSld(); } }function DocumentOnClick() { if( IsNts() || parent.HideMenu() ) return; if( ( g_allowAdvOnClick && (window.name=3D=3D"PPTSld") && !parent.IsFrames= Mode() ) || (event && event.keyCode=3D=3D32) ) { =09 if( g_animUseRuntime && g_animMainSequence && g_animMainSequence.cangonex= t ) return; parent.GoToNextSld(); } } var g_supportsPPTHTML =3D SupportsPPTHTML(), g_scaleInFrame =3D 1, gId=3D""= , g_bgSound=3D"", g_scaleHyperlinks =3D false, g_allowAdvOnClick =3D 1, g_showInBrowser = =3D 0, gLoopCont =3D 0, gUseSldTimings =3D 1; var g_showAnimation =3D g_supportsPPTHTML && SupportsPPTAnimation() && ( (w= indow.name=3D=3D"PPTSld" && !parent.IsFramesMode()) || g_showInBrowser );va= r g_animManager =3D null; var g_animUseRuntime =3D false; var g_animItemsToHide, g_animInteractiveItems, g_animSlideTime; var g_animMainSequence =3D null; var ENDSHOW_MESG=3D"End of slide show, click to exit.", SCREEN_MODE=3D"Fram= es", gIsEndShow=3D0, NUM_VIS_SLDS=3D46, SCRIPT_HREF=3D"script.js", FULLSCR_= HREF=3D"fullscreen.htm"; var gCurSld =3D gPrevSld =3D 1, g_offset =3D 0, gNtsOpen =3D gHasNts =3D gO= tlTxtExp =3D 0, gHasNarration =3D 0, gOtlOpen =3D true window.gPPTHTML=3DSupportsPPTHTML() var gMainDoc=3Dnew Array(new hrefList("slide0001.htm",1,-1,1),new hrefList(= "slide0046.htm",1,-1,1),new hrefList("slide0002.htm",1,-1,1),new hrefList("= slide0003.htm",1,-1,1),new hrefList("slide0004.htm",1,-1,1),new hrefList("s= lide0005.htm",1,-1,1),new hrefList("slide0006.htm",1,-1,1),new hrefList("sl= ide0007.htm",1,-1,1),new hrefList("slide0008.htm",1,-1,1),new hrefList("sli= de0009.htm",1,-1,1),new hrefList("slide0010.htm",1,-1,1),new hrefList("slid= e0011.htm",1,-1,1),new hrefList("slide0012.htm",1,-1,1),new hrefList("slide= 0013.htm",1,-1,1),new hrefList("slide0014.htm",1,-1,1),new hrefList("slide0= 015.htm",1,-1,1),new hrefList("slide0016.htm",1,-1,1),new hrefList("slide00= 17.htm",1,-1,1),new hrefList("slide0018.htm",1,-1,1),new hrefList("slide001= 9.htm",1,-1,1),new hrefList("slide0020.htm",1,-1,1),new hrefList("slide0021= .htm",1,-1,1),new hrefList("slide0022.htm",1,-1,1),new hrefList("slide0023.= htm",1,-1,1),new hrefList("slide0024.htm",1,-1,1),new hrefList("slide0025.h= tm",1,-1,1),new hrefList("slide0026.htm",1,-1,1),new hrefList("slide0027.ht= m",1,-1,1),new hrefList("slide0028.htm",1,-1,1),new hrefList("slide0029.htm= ",1,-1,1),new hrefList("slide0030.htm",1,-1,1),new hrefList("slide0031.htm"= ,1,-1,1),new hrefList("slide0032.htm",1,-1,1),new hrefList("slide0033.htm",= 1,-1,1),new hrefList("slide0034.htm",1,-1,1),new hrefList("slide0035.htm",1= ,-1,1),new hrefList("slide0036.htm",1,-1,1),new hrefList("slide0037.htm",1,= -1,1),new hrefList("slide0038.htm",1,-1,1),new hrefList("slide0039.htm",1,-= 1,1),new hrefList("slide0040.htm",1,-1,1),new hrefList("slide0041.htm",1,-1= ,1),new hrefList("slide0042.htm",1,-1,1),new hrefList("slide0043.htm",1,-1,= 1),new hrefList("slide0044.htm",1,-1,1),new hrefList("slide0045.htm",1,-1,1= )); /********************************************* Frameset functions These functions control slide navigation and state of the frameset. **********************************************/ function FullScrInit() { g_allowAdvOnClick =3D GetCurSld().mAdvOnClk document.body.style.backgroundColor=3D"black" document.oncontextmenu=3Dparent._CM; document.onkeydown =3D _KDH; document.ondragstart=3DCancel document.onselectstart=3DCancel self.focus() } function Redirect( frmId ) {=09 var str=3Ddocument.location.hash,idx=3Dstr.indexOf('#'), sId=3DGetSldId() if(idx>=3D0) str=3Dstr.substr(1); if( window.name !=3D frmId && ( sId !=3D str) ) { obj =3D GetObj("Main-File") window.location.href=3Dobj.href+"#"+sId return 1 } return 0 } var MHTMLPrefix =3D CalculateMHTMLPrefix();=20 function CalculateMHTMLPrefix() { if ( document.location.protocol =3D=3D 'mhtml:') {=20 href=3Dnew String(document.location.href)=20 Start=3Dhref.indexOf('!')+1=20 End=3Dhref.lastIndexOf('/')+1=20 if (End < Start)=20 return href.substring(0, Start)=20 else=20 return href.substring(0, End)=20 } return ''; } function GetTags(base,tag) { if(g_supportsPPTHTML) return base.all.tags(tag); else return base.getElementsByTagName(tag); } function UpdNtsPane(){ if(frames["PPTNts"]) PPTNts.location.replace( MHTMLP= refix+GetHrefObj( gCurSld ).mNtsHref ) } function UpdNavPane( sldIndex ){ if(gNavLoaded) PPTNav.UpdNav() } function UpdOtNavPane(){ if(gOtlNavLoaded) PPTOtlNav.UpdOtlNav() } function UpdOtlPane(){ if(gOtlLoaded) PPTOtl.UpdOtl() } function SetHasNts( fVal ) { if( gHasNts !=3D fVal ) { gHasNts=3DfVal UpdNavPane() } } function ToggleOtlText() { gOtlTxtExp=3D!gOtlTxtExp UpdOtlPane() } function ClearMedia() { // Clear any sounds playing before launching another browser window. Other= wise, // in fullscreen mode, you'll continue to hear the sound in the frames mod= e. if (PPTSld.pptSound) PPTSld.pptSound.loop =3D 0; } function FullScreen() {=20 if ( PPTSld.g_animUseRuntime ) PPTSld.document.body.pause(); ClearMedia(); var href =3D ( document.location.protocol =3D=3D 'mhtml:') ? FULLSCR_HREF = : FULLSCR_HREF+"#"+GetHrefObj(gCurSld).mSldHref; if(PPTNav.event.ctrlKey) { var w =3D (window.screen.availWidth * 1.0) / 2.0 var h =3D w * (PPTSld.g_origH * 1.0) / PPTSld.g_origW win =3D window.open( MHTMLPrefix+href,null,"toolbar=3D0,resizable=3D1,top= =3D0,left=3D0," + "width=3D"+ w + ",height=3D" + h ); if( win.document.body && PPTSld.g_animUseRuntime ) win.document.body.PPTSldFrameset=3Dwindow; } else { win =3D window.open( MHTMLPrefix+href,null,"fullscreen=3Dyes" ); if( win.document.body && PPTSld.g_animUseRuntime ) win.document.body.PPTSldFrameset=3Dwindow; } } function ToggleVNarration() { rObj=3DPPTSld.document.all("NSPlay") if( rObj && !PPTSld.g_animUseRuntime ) { if( (rObj.playState =3D=3D 1)||(rObj.playState =3D=3D 0) ) rObj.Play() else if( rObj.playState =3D=3D 2 ) rObj.Pause() else return; } else if( PPTSld.g_animUseRuntime ) { narObj =3D PPTSld.document.all("narrationID") if( narObj ) narObj.togglePause() } } function GetCurSldNum() { =20 obj=3DGetHrefObj(gCurSld) if( obj.mOrigVis =3D=3D 1 ) return obj.mSldIdx else =20 return gCurSld } function GetNumSlds() { =20 if( GetHrefObj(gCurSld).mOrigVis =3D=3D 1 ) return GetSldList().mNumVisSlds; else return GetSldList().mList.length } function GetSldNum( href ) { for(ii=3D0; ii 1 ) PopSldList(); else if( !IsFramesMode() ) { if( gLoopCont ) GoToFirst() else EndShow() } } function GoToPrevSld() { ii=3DgCurSld-1 if( ii > 0 ) { obj=3DGetHrefObj(ii) while ( obj && ( obj.mVis =3D=3D 0 ) && ( ii>0 ) ) obj=3DGetHrefObj(--ii) if( ii =3D=3D 0 ) ii=3D1 GoToSldNum(ii) } } function GoToFirst(){ GoToSld( GetHrefObj(1).mSldHref ) } function GoToLast() { ii=3DGetSldList().mList.length if( ii !=3D gCurSld ) GoToSld( GetHrefObj(ii).mSldHref ) } function GoToSldNum( num ) { if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue obj =3D GetHrefObj( num ) obj.mVis=3D1 gPrevSld=3DgCurSld gCurSld =3D num; PPTSld.location.replace(MHTMLPrefix+obj.mSldHref) if( IsFramesMode() ) { UpdNavPane(); UpdOtlPane(); UpdNtsPane() } } function GoToSld( href ) { if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue GetHrefObj( GetSldNum(href) ).mVis=3D1 PPTSld.location.replace(MHTMLPrefix+href) } function SldUpdated( id ) { if( id =3D=3D GetHrefObj(gCurSld).mSldHref ) return gPrevSld=3DgCurSld gCurSld=3DGetSldNum(id) if( IsFramesMode() ) { UpdNavPane(); UpdOtlPane(); UpdNtsPane() } } function PrevSldViewed(){ GoToSld( GetHrefObj(gPrevSld).mSldHref ) } function HasPrevSld() { return ( gIsEndShow || ( gCurSld !=3D 1 && GetHrefO= bj( gCurSld-1 ).mVis =3D=3D 1 )||( GetCurSldNum() > 1 ) ) } function HasNextSld() { return (GetCurSldNum() !=3D GetNumSlds()) } function CloseWindow() { if( HideMenu() ) return; =09 var event =3D PPTSld.event; if( !IsFramesMode() && event && (event.keyCode=3D=3D27 || event.keyCode=3D= =3D32 || event.type=3D=3D"click" ) ) window.close( self ); CatchNumKeys( self, event ); } function Unload() { gIsEndShow=3D0; } function SetupEndShow() { gIsEndShow=3D1; PPTSld.document.body.scroll=3D"no"; PPTSld.document.onkeypress=3DCloseWindow; PPTSld.document.onclick=3DCloseWindow; PPTSld.document.oncontextmenu=3D_CM; } function EndShow() { if( IsFramesMode() ) return if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue doc=3DPPTSld.document var dir =3D doc.body.dir if( dir !=3D "rtl" ) dir =3D "ltr"; doc.open() doc.writeln('

' + ENDSHOW_MESG + '
') doc.close() } function SetSldVisited(){ GetSldList().mList[gCurSld-1].mVisited=3Dtrue } function IsSldVisited(){ return GetSldList().mList[gCurSld-1].mVisited } function hrefList( sldHref, visible, advDelay, advClk ) { this.mSldHref=3D this.mNtsHref =3D sldHref this.mOrigVis=3D this.mVis =3D visible this.mVisited=3D false this.mAdvDelay=3D advDelay this.mAdvOnClk=3D advClk } function SldList(arr,curSld,fEnd) { this.mCurSld =3D curSld; this.mList =3D new Array(); var idx =3D 1; for(ii=3D0;ii 0) { PushSldList(sldList,fEnd); gCurSld =3D 1; } else if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue } function PushSldList(arr,fEnd) { var ii =3D gSldStack.length; gSldStack[ii] =3D new SldList(arr,gCurSld,fEnd); GoToSld( gSldStack[ii].mList[0].mSldHref ); } function PopSldList() { if (gSldStack[gSldStack.length-1].fEndShow) EndShow() else { gCurSld =3D gSldStack[gSldStack.length-1].mCurSld; gSldStack[gSldStack.length-1] =3D null; gSldStack.length--; var sldList =3D gSldStack[gSldStack.length-1]; GoToSld( sldList.mList[gCurSld - 1].mSldHref ); } } var custShowList=3Dnew Array(); /********************************************* Navigation button implementation There are 2 types of buttons: ImgBtn, TxtBtn implemented as function objects. They share a similiar interface so the event handlers can call SetActive, for example, on a button=20 object without needing to know exactly=20 what type of button it is. **********************************************/ //---------------------------------- function ImgBtn( oId,bId,w,action ) //---------------------------------- { var t=3Dthis t.Perform =3D _IBP t.SetActive =3D _IBSetA t.SetInactive=3D _IBSetI t.SetPressed =3D _IBSetP t.SetDisabled=3D _IBSetD t.Enabled =3D _IBSetE t.ChangeIcon =3D null t.UserAction =3D action t.ChgState =3D _IBUI t.mObjId =3D oId t.mBorderId=3D bId t.mWidth =3D w t.mIsOn =3D t.mCurState =3D 0 } function _IBSetA() { if( this.mIsOn ) { obj=3Dthis.ChgState( gHiliteClr,gShadowClr,2 ) obj.style.posTop=3D0 } } function _IBSetI() { if( this.mIsOn ) { obj=3Dthis.ChgState( gFaceClr,gFaceClr,1 ) obj.style.posTop=3D0=20 } } function _IBSetP() { if( this.mIsOn ) { obj=3Dthis.ChgState( gShadowClr,gHiliteClr,2 ) obj.style.posLeft+=3D1; obj.style.posTop+=3D1 } } function _IBSetD() { =20 obj=3Dthis.ChgState( gFaceClr,gFaceClr,0 ) obj.style.posTop=3D0=20 } function _IBSetE( state ) { var t=3Dthis GetObj( t.mBorderId ).style.visibility=3D"visible" if( state !=3D t.mIsOn ) { t.mIsOn=3Dstate if( state ) t.SetInactive() else t.SetDisabled() } } function _IBP() { var t=3Dthis if( t.mIsOn ) { if( t.UserAction !=3D null ) t.UserAction() if( t.ChangeIcon ) { obj=3DGetObj(t.mObjId) if( t.ChangeIcon() ) obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-4)*t.mWidth else obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-0)*t.mWidth } t.SetActive() } =20 } function _IBUI( clr1,clr2,nextState ) { var t=3Dthis SetBorder( GetObj( t.mBorderId ),clr1,clr2 ) obj=3DGetObj( t.mObjId ) obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-nextState)*t.mWidth-obj= .style.posTop t.mCurState=3DnextState return obj } //----------------------------------------- function TxtBtn( oId,oeId,action,chkState ) //----------------------------------------- { var t=3Dthis t.Perform =3D _TBP t.SetActive =3D _TBSetA t.SetInactive=3D _TBSetI t.SetPressed =3D _TBSetP t.SetDisabled=3D _TBSetD t.SetEnabled =3D _TBSetE t.GetState =3D chkState t.UserAction =3D action t.ChgState =3D _TBUI t.mObjId =3D oId t.m_elementsId=3D oeId t.mIsOn =3D 1 } function _TBSetA() { var t=3Dthis if( t.mIsOn && !t.GetState() ) t.ChgState( gHiliteClr,gShadowClr,0,0 ) } function _TBSetI() { var t=3Dthis if( t.mIsOn && !t.GetState() ) t.ChgState( gFaceClr,gFaceClr,0,0 ) } function _TBSetP() { if( this.mIsOn ) this.ChgState( gShadowClr,gHiliteClr,1,1 ) } function _TBSetD() { =20 this.ChgState( gFaceClr,gFaceClr,0,0 ) this.mIsOn =3D 0 } function _TBSetE() { var t=3Dthis if( !t.GetState() ) t.ChgState( gFaceClr,gFaceClr,0,0 ) else t.ChgState( gShadowClr,gHiliteClr,1,1 ) t.mIsOn =3D 1 } function _TBP() { var t=3Dthis if( t.mIsOn ) {=20 if( t.UserAction !=3D null ) t.UserAction() if( !t.GetState ) return if( t.GetState() ) t.SetPressed() else t.SetActive() } =20 } function _TBUI( clr1,clr2,lOffset,tOffset ) { SetBorder( GetObj( this.mObjId ),clr1,clr2 ) Offset( GetObj( this.m_elementsId ),lOffset,tOffset ) } function Offset( obj, top, left ){ obj.style.top=3Dtop; obj.style.left=3Dle= ft } function SetBorder( obj, upperLeft, lowerRight ) { s=3Dobj.style; s.borderStyle =3D "solid" s.borderWidth =3D 1=20 s.borderLeftColor =3D s.borderTopColor =3D upperLeft s.borderBottomColor=3D s.borderRightColor =3D lowerRight } function GetBtnObj(){ return gBtnArr[window.event.srcElement.id] } function BtnOnOver(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetActive() } function BtnOnDown(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetPressed() } function BtnOnOut(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetInactive() } function BtnOnUp() { b=3DGetBtnObj() if( b !=3D null ) b.Perform() else Upd() } function GetNtsState(){ return parent.gNtsOpen } function GetOtlState(){ return parent.gOtlOpen } function GetOtlTxtState(){ return parent.gOtlTxtExp } function NtsBtnSetFlag( fVal ) { s=3Ddocument.all.item( this.m_flagId ).style s.display=3D"none" if( fVal ) s.display=3D"" else s.display=3D"none" } function _BSetA_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S= etActive() } function _BSetI_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S= etInactive() } function _BSetP_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S= etPressed() } function _BSetA_BorderImg() {=20 b =3D gBtnArr[this.mBorderId]=20 if( b !=3D null && this.mIsOn && !b.GetState() ) { obj=3Dthis.ChgState( gHiliteClr,gShadowClr,2 ) obj.style.posTop=3D0 } } function _BSetI_BorderImg() {=20 b =3D gBtnArr[this.mBorderId] if( b !=3D null && this.mIsOn && !b.GetState() ) { obj=3Dthis.ChgState( gFaceClr,gFaceClr,1 ) obj.style.posTop=3D0 } } var gHiliteClr=3D"THREEDHIGHLIGHT",gShadowClr=3D"THREEDSHADOW",gFaceClr=3D"= THREEDFACE" var gBtnArr =3D new Array() gBtnArr["nb_otl"] =3D new TxtBtn( "nb_otl","nb_otlElem",parent.ToggleOtlPan= e,GetOtlState ) gBtnArr["nb_otlElem"] =3D new TxtBtn( "nb_otl","nb_otlElem",parent.ToggleOt= lPane,GetOtlState ) gBtnArr["nb_nts"] =3D new ImgBtn( "nb_nts","nb_ntsBorder",10,parent.ToggleN= tsPane ) gBtnArr["nb_nts"].SetActive =3D _BSetA_BorderImg; gBtnArr["nb_nts"].SetInactive =3D _BSetI_BorderImg; gBtnArr["nb_ntsBorder"] =3D new TxtBtn( "nb_ntsBorder","nb_ntsElem",parent.= ToggleNtsPane,GetNtsState ) gBtnArr["nb_ntsElem"] =3D new TxtBtn( "nb_ntsBorder","nb_ntsElem",parent.To= ggleNtsPane,GetNtsState ) gBtnArr["nb_prevBorder"] =3D gBtnArr["nb_prev"]=3D new ImgBtn( "nb_prev","n= b_prevBorder",30,parent.GoToPrevSld ) gBtnArr["nb_nextBorder"] =3D gBtnArr["nb_next"]=3D new ImgBtn( "nb_next","n= b_nextBorder",30,parent.GoToNextSld ) gBtnArr["nb_sldshw"]=3D new ImgBtn( "nb_sldshw","nb_sldshwBorder",18,parent= .FullScreen ) gBtnArr["nb_sldshwBorder"] =3D new TxtBtn( "nb_sldshw","nb_sldshwBorder",pa= rent.FullScreen,null ) gBtnArr["nb_sldshwBorder"].SetActive =3D _BSetA_Border; gBtnArr["nb_sldshwBorder"].SetInactive =3D _BSetI_Border; gBtnArr["nb_sldshwText"] =3D new TxtBtn( "nb_sldshw","nb_sldshwText",parent= .FullScreen,null ) gBtnArr["nb_sldshwText"].SetActive =3D _BSetA_Border; gBtnArr["nb_sldshwText"].SetInactive =3D _BSetI_Border; gBtnArr["nb_voice"] =3D gBtnArr["nb_voiceBorder"] =3D new ImgBtn( "nb_voice= ","nb_voiceBorder",18,parent.ToggleVNarration ) gBtnArr["nb_otlTxtBorder"] =3D gBtnArr["nb_otlTxt"]=3D new ImgBtn( "nb_otlT= xt","nb_otlTxtBorder",23,parent.ToggleOtlText ) gBtnArr["nb_ntsBorder"].m_flagId=3D "nb_nts" gBtnArr["nb_ntsBorder"].SetFlag =3D NtsBtnSetFlag gBtnArr["nb_otlTxt"].ChangeIcon=3D GetOtlTxtState /********************************************* Context menu implementation _CM() is the function that's hooked up to the oncontextmenu event. Once we're asked to show the menu, we first build it by creating DIVs on-the-fly. Then we position it=20 within the screen area so it doesn't get clipped. Creating the DIVs using createElement() means we don't have to write out any extra HTML into the slide HTML files. **********************************************/ var sNext=3D"Next",sPrev=3D"Previous",sEnd=3D"End Show",sFont=3D"Arial",sAr= row=3D"Arrow",sFreeform=3D"Freeform",sRect=3D"Rectangle",sOval=3D"Oval" function ShowMenu() { BuildMenu(); var doc=3DPPTSld.document.body,x=3DPPTSld.event.clientX+doc.scrollLeft,y= =3DPPTSld.event.clientY+doc.scrollTop m =3D PPTSld.document.all.item("ctxtmenu") m.style.pixelLeft=3Dx if( (x+m.scrollWidth > doc.clientWidth)&&(x-m.scrollWidth > 0) ) m.style.pixelLeft=3Dx-m.scrollWidth m.style.pixelTop=3Dy if( (y+m.scrollHeight > doc.clientHeight)&&(y-m.scrollHeight > 0) ) m.style.pixelTop=3Dy-m.scrollHeight m.style.display=3D"" } function _CM() { if( !parent.IsFullScrMode() ) return; if(!PPTSld.event.ctrlKey) { ShowMenu() return false } else HideMenu() } function BuildMenu() { if( PPTSld.document.all.item("ctxtmenu") ) return var mObj=3DCreateItem( PPTSld.document.body ) mObj.id=3D"ctxtmenu" mObj.style.visibility=3D"hidden" var s=3DmObj.style s.position=3D"absolute" s.cursor=3D"default" s.width=3D"120px" SetCMBorder(mObj,"menu","black") var iObj=3DCreateItem( mObj ) SetCMBorder( iObj, "threedhighlight","threedshadow" ) iObj.style.padding=3D2 CreateMenuItem( iObj,sNext,M_GoNextSld,M_True ) CreateMenuItem( iObj,sPrev,M_GoPrevSld,M_HasPrevSld ) =09 CreateSeparator( iObj ) CreateMenuItem( iObj,sEnd,M_End,M_True ) mObj.style.visibility=3D"visible" } function Cancel() { window.event.cancelBubble=3Dtrue; window.event.returnVa= lue=3Dfalse } function Highlight() { ChangeClr("activecaption","threedhighlight") } function Deselect() { ChangeClr("threedface","menutext") } function Perform() { e=3DPPTSld.event.srcElement if( e.type=3D=3D"menuitem" && e.IsActive() ) e.Action() else PPTSld.event.cancelBubble=3Dtrue } function ChangeClr( bg,clr ) { e=3DPPTSld.event.srcElement if( e.type=3D=3D"menuitem" && e.IsActive() ) { e.style.backgroundColor=3Dbg e.style.color=3Dclr } } function M_HasPrevSld() { return( parent.HasPrevSld() ) } function M_GoNextSld() { if( gIsEndShow ) M_End(); else GoToNextSld() } function M_GoPrevSld() { if( gIsEndShow ) { gIsEndShow=3D0; history.back();= PPTSld.event.cancelBubble=3Dtrue; } else GoToPrevSld() } function M_True() { return true } function M_End() { window.close( self ) } function CreateMenuItem( node,text,action,eval ) { var e=3DCreateItem( node ) e.type=3D"menuitem" e.Action=3Daction e.IsActive=3Deval e.innerHTML=3Dtext if( !e.IsActive() ) e.style.color=3D"threedshadow" e.onclick=3DPerform e.onmouseover=3DHighlight e.onmouseout=3DDeselect s=3De.style; 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charset="us-ascii" VIII. Technological Change ------=_NextPart_01C4D784.BAAFB9F0 Content-Location: file:///C:/26794655/PP15_files/outline.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii"

No= tes

Slide Show

Outline

1

VIII. Technologi= cal Change

Read:

Antle, J. and S. Capalbo, “An Introduction to Recent Developme= nts in Production Theory and Productivity Measurement” Chapter 2 i= n Agricultural Productivity: Measurement and Explanation, S. Capalbo and J. Antle editors, Resources for the Future, Washington, D.C., 1988.

Capalbo, S. Western Journal of Agricultural Economics

Dorfman, J. and K. Foster, Western Journal of Agricultural Economics=

2

"Aoccdrnig = to rseearch at Cmabrigde..."

Aoccdrnig to rseearch at Cmabrigde Uinervtisy, it deosn't mttaer in waht oredr the ltteers in a wrod are peclad, the olny iprmoetnt tihn= g is taht the frist and lsat ltteer be in the rghit pclae.

The rset can be a total mses and you can sitll raed it wouthit porb= elm.

Tihs is bcuseae the huamn mnid deos not raed ervey lteter by istlef, but the wrod as a wlohe.

3

"A"

A. Types/Sources of Technological Change

1. Disembodied: changes in output per unit of input

2. Embodied: changes in output due to changes in input quality

4

"B"

B. Primal Rate of Technological Change

Start with a production function, Q=3Df(x,t).

5

"In a compe= titive equilibrium inputs..."

In a competitive equilibrium inputs are paid their VMP and output p= rice equals MC so:

6

"C"

C. Dual (cost/profit function) Measure of Technical Change

Start with a cost function, C(Q,r,t).

Using Shepard’s Lemma

7

"The left-h= and side is defined..."

The left-hand side is defined as the dual rate of technological cha= nge, and the right-hand side is interpreted as the index of the rate of change of factor prices plus a scale effect of technological change minus the rate of change of total cost.

8

"Now"<= /a>

Now, totally differentiate the cost equation C=3DΣr_{ix_i,
in natural logarithm form.}

substitute (3) into (2) to get

9

"multiplyin= g both sides of (..."

multiplying both sides of (1) by       we find that

so,

Thus, we find that the dual rate of tech. change equals the primal = rate of tech. change only when there is constant returns to scale (i.e.,<= span style=3D'mso-spacerun:yes'>       = ;   ).

10

"D"

D. Biased versus Neutral Tech. Change

1. Hicks

Examine the MRTS between capital and labor

(e.g., MP_K/MP_L).

if it increases then the tech. change was

labor saving/capital using

if it is unchanged then the tech. change was neutral (not biased)<= /li>
if it decreases then the tech change was

capital saving/labor using

11

"For Examp= le"

For Example,

Suppose that after the technical change

In order to move to the new optimal point from here we need to incr= ease capital use and/or decrease labor use. Therefore, the tech. change= was capital using and labor saving as we said earlier.

12

"Notes&quo= t;

Notes:

a) Hick’s definition doesn’t specify where to measure.
- at some specified point?

- at the cost minimizing or profit

maximizing point?
- anywhere along the expansion path?

   If production is homothetic, then these are equivalent.

13

"b"

b) If production is non-homothetic then the expansion path is nonli= near

- optimal input propo= rtions change along the path. (neutral for path =3D neutral for MRTS at a point on the path= )

- not necessarily neutral with respect to optimal factor proportions.

14

"c"

c) It is common to define the notion of Hicks neutrality by saying t= he technological change is neutral if it is expansion path preserving.<= /li>

HNTC Þ Q=3DF(f(x),t) which sa= ys that t is weakly separable from x

Extended HNTC Þ Q=3DA(t)f(x) which say= s they are strongly separable

15

"2"

2. Primal Measure of Bias

neutrality Þ B_ij=3D0 for= all i,j pairs.

16

17

"Notes&quo= t;

Notes:

a) B_ij is pairwise, and an n-input measure is

B_itells us if “on average” the marginal pro= duct of x_i is increasing relative to all other inputs. B_i>0 Þ techilogic= al change is x_i using.

18

"b"

b) Once we specify a function and estimate we can test B_{i =3D0
which is neutral because B_ij=3D0 for all i and j implies =
B_i=3D0.}

c) The B_i’s are relative measures and do not measu= re the absolute changes in marginal products.

19

"3"

3. Dual Measure of Bias

where x_i=3D x_i(Q,r,t) is the compensated dem= and function derivable from the cost function via Shepard’s Lemma.=

20

"Conjectur= e/Definition"

Conjecture/Definition:

This measure is useful if the cost function is homothetic in output= :

C(Q,r,t)=3Dg(Q,t)•f(r,t)

So that the cost shares are independent of output, and consequently      is independent of the scale of output.

21

"Non-homot= hetic Cost function implies non-linear..."

Non-homothetic Cost function implies non-linear expansion paths aga= in and scale effects can change the optimal factor ratio and the cost shares.

22

23

24

"Notes&quo= t;

Notes:

1. If the technology is homothetic so that the expansion paths are linear, then the there is no scale effect on the factor ration (xi/x_j).

2. In general, the two effects are confounded in     , and we = need to adjust for the scale effect to get a measure of the pure bias eff= ect.

25

26

27

28

29

"The scale adjusted dual measure..."

The scale adjusted dual measure of bias is the scale dependent meas= ure minus the scale effect which depends on 1) the elasticity of cost sh= are with respect to output, 2) the elasticity of scale, and 3)the dual r= ate of technological change.

30

"Note that= in the homothetic..."

Note that in the homothetic case the elasticity of the share with respect to output is zero and .

     &nbs= p; Þ

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E. Measurement = of (Aggregate) Total Factor Productivity

Growth Accounting Approach to TFP Measurement

Intuition: “In the absence of technical change, the growth in total output can be explained by the growth in total in total input use.”

The unexplained residual is attributed to technological change.

32

"A very br= ief summary of..."

A very brief summary of some indexing assumptions.

33

"Using Ind= ex Numbers for TFP..."

Using Index Numbers for TFP Measurement

Example: Tornquist-Th= eil

TFP =3D Q/X =3D aggregate output per unit of input.

So, the rate of change of TFP is:

34

"Tornquist= -Theil quantity indices to discretely..."

Tornquist-Theil quantity indices to discretely approximate     and     are

35

"Without specifying a functional form..."

Without specifying a functional form we would employ the following formula to estimate the discrete rate of change of TFP.

36

"Implicit assumptions underlying the growth"

Implicit assumptions underlying the growth accounting approach.

i) assumes a competitive industry

ii) assumes CRTS

recall the primal rate of tech. change is

37

"iii"=

iii) assumes extended Hicks Neutrality

iv) assumes input-output separability (i.e., G(Q) =3D F(X)

38

3) Econometric Approaches to TFP Measurement

Advantages

- no assumptions about neutrality are necessary

- know the statistical properties of technical change estimates

- no assumption about returns to scale

Disadvantage

- must choose a functional form and specification errors can be bi= g

39

"a"

a) Dual Approach (Capalbo’s paper)

recall equation (4) from earlier

but we also demonstrated in equation (1) that the primal rate of te= ch. change can be stated as

40

"Substitut= ing the second equation into..."

Substituting the second equation into the first yields:

notice that the last term on the right hand side is the divisia form of     .= Now, add and subtract       to the right hand side.

41

"Solving f= or the rate of..."

Solving for the rate of TFP growth yields:

Capalbo estimates a cost function and using those estimates she der= ives the pieces to the above equation to compute . In her case there are two o= utputs and two scale elasticities. Check it out.

42

b) Primal Appro= aches (Dorfman and Foster)

1. Simple Technical Change

Comes directly from the definition of the primal rate of tech. chan= ge.

43

"recall th= at we derived in..."

recall that we derived in the first lecture on technological change that

An approximation of this based on an estimated production function = is

44

"2"

2. Flexible Technical Change

This approach is similar to Simple Technical Change, but the estima= tes of come from the estim= ation of a production function with (potentially) time varying coefficient= s.

45

"To calcul= ate the flexible rate..."

To calculate the flexible rate of technical change we use

Using Capalbo’s data Dorfman and Foster found   to be a more stable measure of technical change versus        and       .

46

"HAPPY&quo= t;

HAPPY HOLIDAYS!!

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
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1	VIII. Technologi= cal Change Read: Antle, J. and S. Capalbo, “An Introduction to Recent Developme= nts in Production Theory and Productivity Measurement” Chapter 2 i= n Agricultural Productivity: Measurement and Explanation, S. Capalbo and J. Antle editors, Resources for the Future, Washington, D.C., 1988. Capalbo, S. Western Journal of Agricultural Economics Dorfman, J. and K. Foster, Western Journal of Agricultural Economics=
2	"Aoccdrnig = to rseearch at Cmabrigde..." Aoccdrnig to rseearch at Cmabrigde Uinervtisy, it deosn't mttaer in waht oredr the ltteers in a wrod are peclad, the olny iprmoetnt tihn= g is taht the frist and lsat ltteer be in the rghit pclae. The rset can be a total mses and you can sitll raed it wouthit porb= elm. Tihs is bcuseae the huamn mnid deos not raed ervey lteter by istlef, but the wrod as a wlohe.
3	"A" A. Types/Sources of Technological Change 1. Disembodied: changes in output per unit of input 2. Embodied: changes in output due to changes in input quality
4	"B" B. Primal Rate of Technological Change Start with a production function, Q=3Df(x,t).
5	"In a compe= titive equilibrium inputs..." In a competitive equilibrium inputs are paid their VMP and output p= rice equals MC so:
6	"C" C. Dual (cost/profit function) Measure of Technical Change Start with a cost function, C(Q,r,t). Using Shepard’s Lemma
7	"The left-h= and side is defined..." The left-hand side is defined as the dual rate of technological cha= nge, and the right-hand side is interpreted as the index of the rate of change of factor prices plus a scale effect of technological change minus the rate of change of total cost.
8	"Now"<= /a> Now, totally differentiate the cost equation C=3DΣr_{ix_i, in natural logarithm form.} substitute (3) into (2) to get
9	"multiplyin= g both sides of (..." multiplying both sides of (1) by we find that so, Thus, we find that the dual rate of tech. change equals the primal = rate of tech. change only when there is constant returns to scale (i.e.,<= span style=3D'mso-spacerun:yes'> = ; ).
10	"D" D. Biased versus Neutral Tech. Change 1. Hicks Examine the MRTS between capital and labor (e.g., MP_K/MP_L). if it increases then the tech. change was labor saving/capital using if it is unchanged then the tech. change was neutral (not biased)<= /li> if it decreases then the tech change was capital saving/labor using
11	"For Examp= le" For Example, Suppose that after the technical change In order to move to the new optimal point from here we need to incr= ease capital use and/or decrease labor use. Therefore, the tech. change= was capital using and labor saving as we said earlier.
12	"Notes&quo= t; Notes: a) Hick’s definition doesn’t specify where to measure. - at some specified point? - at the cost minimizing or profit maximizing point? - anywhere along the expansion path? If production is homothetic, then these are equivalent.
13	"b" b) If production is non-homothetic then the expansion path is nonli= near - optimal input propo= rtions change along the path. (neutral for path =3D neutral for MRTS at a point on the path= ) - not necessarily neutral with respect to optimal factor proportions.
14	"c" c) It is common to define the notion of Hicks neutrality by saying t= he technological change is neutral if it is expansion path preserving.<= /li> HNTC Þ Q=3DF(f(x),t) which sa= ys that t is weakly separable from x Extended HNTC Þ Q=3DA(t)f(x) which say= s they are strongly separable
15	"2" 2. Primal Measure of Bias neutrality Þ B_ij=3D0 for= all i,j pairs.
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17	"Notes&quo= t; Notes: a) B_ij is pairwise, and an n-input measure is B_itells us if “on average” the marginal pro= duct of x_i is increasing relative to all other inputs. B_i>0 Þ techilogic= al change is x_i using.
18	"b" b) Once we specify a function and estimate we can test B_{i =3D0 which is neutral because B_ij=3D0 for all i and j implies = B_i=3D0.} c) The B_i’s are relative measures and do not measu= re the absolute changes in marginal products.
19	"3" 3. Dual Measure of Bias where x_i=3D x_i(Q,r,t) is the compensated dem= and function derivable from the cost function via Shepard’s Lemma.=
20	"Conjectur= e/Definition" Conjecture/Definition: This measure is useful if the cost function is homothetic in output= : C(Q,r,t)=3Dg(Q,t)•f(r,t) So that the cost shares are independent of output, and consequently is independent of the scale of output.
21	"Non-homot= hetic Cost function implies non-linear..." Non-homothetic Cost function implies non-linear expansion paths aga= in and scale effects can change the optimal factor ratio and the cost shares.
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24	"Notes&quo= t; Notes: 1. If the technology is homothetic so that the expansion paths are linear, then the there is no scale effect on the factor ration (xi/x_j). 2. In general, the two effects are confounded in , and we = need to adjust for the scale effect to get a measure of the pure bias eff= ect.
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29	"The scale adjusted dual measure..." The scale adjusted dual measure of bias is the scale dependent meas= ure minus the scale effect which depends on 1) the elasticity of cost sh= are with respect to output, 2) the elasticity of scale, and 3)the dual r= ate of technological change.
30	"Note that= in the homothetic..." Note that in the homothetic case the elasticity of the share with respect to output is zero and . &nbs= p; Þ	31	E. Measurement = of (Aggregate) Total Factor Productivity Growth Accounting Approach to TFP Measurement Intuition: “In the absence of technical change, the growth in total output can be explained by the growth in total in total input use.” The unexplained residual is attributed to technological change.
32	"A very br= ief summary of..." A very brief summary of some indexing assumptions.
33	"Using Ind= ex Numbers for TFP..." Using Index Numbers for TFP Measurement Example: Tornquist-Th= eil TFP =3D Q/X =3D aggregate output per unit of input. So, the rate of change of TFP is:
34	"Tornquist= -Theil quantity indices to discretely..." Tornquist-Theil quantity indices to discretely approximate and are
35	"Without specifying a functional form..." Without specifying a functional form we would employ the following formula to estimate the discrete rate of change of TFP.
36	"Implicit assumptions underlying the growth" Implicit assumptions underlying the growth accounting approach. i) assumes a competitive industry ii) assumes CRTS recall the primal rate of tech. change is
37	"iii"= iii) assumes extended Hicks Neutrality iv) assumes input-output separability (i.e., G(Q) =3D F(X)
38	3) Econometric Approaches to TFP Measurement Advantages - no assumptions about neutrality are necessary - know the statistical properties of technical change estimates - no assumption about returns to scale Disadvantage - must choose a functional form and specification errors can be bi= g
39	"a" a) Dual Approach (Capalbo’s paper) recall equation (4) from earlier but we also demonstrated in equation (1) that the primal rate of te= ch. change can be stated as
40	"Substitut= ing the second equation into..." Substituting the second equation into the first yields: notice that the last term on the right hand side is the divisia form of .= Now, add and subtract to the right hand side.
41	"Solving f= or the rate of..." Solving for the rate of TFP growth yields: Capalbo estimates a cost function and using those estimates she der= ives the pieces to the above equation to compute . In her case there are two o= utputs and two scale elasticities. Check it out.
42	b) Primal Appro= aches (Dorfman and Foster) 1. Simple Technical Change Comes directly from the definition of the primal rate of tech. chan= ge.
43	"recall th= at we derived in..." recall that we derived in the first lecture on technological change that An approximation of this based on an estimated production function = is
44	"2" 2. Flexible Technical Change This approach is similar to Simple Technical Change, but the estima= tes of come from the estim= ation of a production function with (potentially) time varying coefficient= s.
45	"To calcul= ate the flexible rate..." To calculate the flexible rate of technical change we use Using Capalbo’s data Dorfman and Foster found to be a more stable measure of technical change versus and .
46	"HAPPY&quo= t; HAPPY HOLIDAYS!!